A national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

National Renewable Energy Laboratory 

Innovation for Our Energy Future 

Integrated Wind Energy/ 

Desalination System 

October 11, 2004 — July 29, 2005 

GE Global Research

Niskayuna, New York 

Subcontract Report 

NREL/SR-500-39485 

October 2006 

NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 
Integrated Wind Energy/ 

Desalination System 

October 11, 2004 — July 29, 2005 

GE Global Research

Niskayuna, New York 

NREL Technical Monitor: Scott Schreck 

Prepared under Subcontract No. YAM-4-33200-09 

Subcontract Report 

NREL/SR-500-39485 

October 2006 

National Renewable Energy Laboratory

1617 Cole Boulevard, Golden, Colorado 80401-3393 

303-275-3000 • www.nrel.gov 

Operated for the U.S. Department of Energy 

Office of Energy Efficiency and Renewable Energy 

by Midwest Research Institute • Battelle 

Contract No. DE-AC36-99-GO10337
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Contents 

Acronyms and Abbreviations..................................................................................................... x 

1 Executive Summary ............................................................................................................ 1 

2 Introduction......................................................................................................................... 3 

2.1 Motivation for Wind Desalination ............................................................................... 5 

2.2 Scope of Program......................................................................................................... 8 

3 Model Description............................................................................................................. 10 

3.1 Overview of Required Models................................................................................... 10 

3.2 Component Model Description.................................................................................. 10 

3.2.1 Wind Model........................................................................................................ 10 

3.2.2 Wind Turbine Model (wind input to power output) ........................................... 13 

3.2.3 Variable Speed Drive and Motor Model............................................................. 21 

3.2.4 Reverse Osmosis Membrane Module................................................................. 22 

3.2.5 Reverse Osmosis Vessels and Banks.................................................................. 26 

3.2.6 Energy Recovery ................................................................................................ 27 

3.2.7 Water Pumps....................................................................................................... 28 

3.2.8 Energy Storage ................................................................................................... 29 

3.2.9 Valves ................................................................................................................. 29 

3.2.10 Flow Junction ..................................................................................................... 29 

3.2.11 Flow Network..................................................................................................... 30 

4 Cost of Water Calculation................................................................................................. 31 

4.1 Steady-State Cost Model............................................................................................ 31 

4.1.1 Capital Costs....................................................................................................... 31 

4.1.2 Operating Costs .................................................................................................. 33 

4.1.3 Total Cost ........................................................................................................... 35 

4.1.4 Example Calculations ......................................................................................... 35 

4.1.5 Results ................................................................................................................ 41 

4.2 Cost of Water and Wind Statistical Representation................................................... 43 

4.3 Grid Power Prices ...................................................................................................... 45 

5 Wind Desalination Configurations.................................................................................... 47 

5.1 Overall System Requirements.................................................................................... 47 

5.1.1 Design Goals and Design Process Overview...................................................... 47 

5.1.2 Constraint Description........................................................................................ 50 

5.2 Seawater..................................................................................................................... 50 

5.2.1 SW-WE-a1 System Design................................................................................. 52 

iii 
5.2.2 Cost of Water Analysis .......................................................................................60 

5.2.3 Design Space Analysis........................................................................................61 

5.2.4 SWWE-a3 Nominal Design ................................................................................77 

5.2.5 Cost of Water Analysis .......................................................................................80 

5.2.6 Design Space Analysis........................................................................................81 

5.3 Brackish Water...........................................................................................................92 

5.3.1 BW-WE-a1 Nominal Design ..............................................................................93 

5.3.2 Cost of Water Analysis .......................................................................................98 

5.3.3 Design Space Analysis........................................................................................99 

6 Wind Desalination Design Optimization.........................................................................114 

6.1 Overview of Wind Desalination Topologies............................................................114 

6.1.1 Grid-Isolated and Design Choices/Optimization Opportunities .......................114 

6.1.2 Grid-Connected and Design Choices/Optimization Opportunities ...................115 

6.2 Grid-Isolated Results................................................................................................115 

6.2.1 Plant Sizing Analysis with Regard to Cost-of-WaterCOW ..............................115 

6.2.2 Sizing Energy Storage.......................................................................................124 

6.2.3 Plant Operation Concepts..................................................................................125 

6.3 Grid-Connected Results............................................................................................126 

6.3.1 Wind-Reverse Osmosis Viability Analysis.......................................................126 

6.3.2 Cost of WaterCOW Results ..............................................................................127 

6.3.3 Plant Operation Concepts..................................................................................130 

7 Conclusions .....................................................................................................................131 

8 Future Work.....................................................................................................................133 

9 Toray Membrane America Design Guidelines ................................................................134 

10 References .......................................................................................................................135

Appendix A: Toray Reverse Osmosis, Brackish Water, and Seawater Elements...................138 

iv 
Figures

Figure 2-1. Process steps and components of RO desalination systems ..........................................4 

Figure 2-2. Cost categories for an RO-based desalination system...................................................6 

Figure 2-3. RES resource availability correlated to potential impaired water sources and potential

beneficiaries ..............................................................................................................................7 

Figure 3-1. Wind PSD....................................................................................................................13 

Figure 3-2. Wind speed profile generated with the Kaimal PSD model ........................................13 

Figure 3-3. WTG model structure ..................................................................................................14 

Figure 3-4. Wind turbine model block diagram .............................................................................15 

Figure 3-5. Two mass rotor model .................................................................................................15 

Figure 3-6. Wind power Cp curves ................................................................................................16 

Figure 3-7. Diagram of DFIG and converters ................................................................................17 

Figure 3-8. DFIG equivalent circuit ...............................................................................................17 

Figure 3-9. Diagram of PM synchronous generator.......................................................................18 

Figure 3-10. Control block diagram of PM generator model.........................................................19 

Figure 3-11. Model validation result ..............................................................................................20 

Figure 3-12. Typical variable speed motor drive and induction motor ..........................................21 

Figure 3-13. Simplified variable speed motor drive and motor model...........................................22 

Figure 3-14. RO spiral-wound membrane arrangement.................................................................22 

Figure 3-15. RO unit, membrane element contained in a high-pressure vessel .............................22 

Figure 3-16. Banks of RO vessels in a seawater desalination plant ...............................................26 

Figure 3-17. Work exchanger ERD................................................................................................28 

Figure 3-18. Flow network.............................................................................................................30 

Figure 5-1. Schematic diagram of two-stage RO membrane system .............................................48 

Figure 5-2. Schematic diagram of a single-stage RO membrane system.......................................48 

Figure 5-3. Flow chart for determining RO configuration inputs ..................................................50 

Figure 5-4. SW-WE-a1 configuration with interstage boost..........................................................52 

Figure 5-5. SW-WE-a1 configuration with DWEER feed boost ...................................................53 

Figure 5-6. Algorithm for solving first stage of filtration model equation.....................................54 

Figure 5-7. Power calculations for SW-WE-a1 design with interstage boost ................................57 

Figure 5-8. Power calculations for SW-WE-a1 design with DWEER boost .................................57 

Figure 5-9. SW-WE-a1 interstage boost flow diagram ..................................................................58 

Figure 5-10. SW-WE-a1 DWEER boost flow diagram .................................................................59 

Figure 5-11. Summary costs for the steady-state SW-WE-a1 configuration .................................61 

Figure 5-12. RO system configuration SWWE-a1.........................................................................62 

Figure 5-13. Percentage distance from constraint at N2 = 3,000 rpm,...........................................67 

v 
Figure 5-14. Percentage distance from constraint at N2 = 3,000 rpm, .......................................... 67 

Figure 5-15. Percentage distance from constraints at N2 = 3,000 rpm,......................................... 67 

Figure 5-16. Permeate flow for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 15........................... 68 

Figure 5-17. Permeate flow for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 39........................... 68 

Figure 5-18. Permeate flow for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 55........................... 68 

Figure 5-19. Total power for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 15............................... 69 

Figure 5-20. Total power for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 39............................... 69 

Figure 5-21. Total power for N2 = 3000 rpm, N3 = 3000 rpm, and S2 = 55................................. 69 

Figure 5-22. Specific power for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 15.......................... 70 

Figure 5-23. Specific power for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 39.......................... 70 

Figure 5-24. Specific power for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 55.......................... 70 

Figure 5-25: Recovery ratio for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 15 .......................... 71 

Figure 5-26. Recovery ratio for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 39 .......................... 71 

Figure 5-27. Recovery ratio for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 55 .......................... 71 

Figure 5-28. Distance from constraint comparison for changes in ................................................ 72 

Figure 5-29. Permeate flow comparison for changes in N2 for fixed N3 and S2.......................... 72 

Figure 5-30. Total power consumption comparison for variation in N2 for.................................. 73 

Figure 5-31. Specific power consumption comparison for variation in N2 for ............................. 73 

Figure 5-32: Recovery ratio comparison for variation in N2 for fixed N3 and S2........................ 73 

Figure 5-33. Distance from constraint comparison for changes in N3 for..................................... 74 

Figure 5-34. Permeate flow comparison for changes in N3 for fixed N2 and S2.......................... 74 

Figure 5-35. Total power consumption comparison for variation in N3 for.................................. 75 

Figure 5-36. Specific power consumption comparison for variation in N3 for ............................. 75 

Figure 5-37. Recovery ratio comparison for variation in N3 for fixed N2 and S2 ........................ 76 

Figure 5-38. SW-WE-a3 configuration with DWEER feed boost................................................. 77 

Figure 5-39. Power calculations for SW-WE-a3 design with DWEER boost ............................... 78 

Figure 5-40. SW-WE-a3 DWEER boost flow diagram................................................................. 79 

Figure 5-41 Summary costs for the steady-state SW-WE-a3 configuration.................................. 81 

Figure 5-42. RO system configuration SWWE-a3 ........................................................................ 82 

Figure 5-43. Percentage distance from constraint for N2 = 3,000 rpm, recycle valve at 0% and 

20% opening ........................................................................................................................... 85 

Figure 5-44. Percentage distance from constraint for N2 = 3,540 rpm, recycle valve at 0% and 

20% opening ........................................................................................................................... 86 

Figure 5-45. Percentage distance from constraint for N2 = 3,900 rpm, recycle valve at 0% and 

20% opening ........................................................................................................................... 86 

Figure 5-46. Permeate flow for N2 = 3,000 rpm, recycle valve .................................................... 86 

Figure 5-47. Permeate flow for N2 = 3,540 rpm, recycle valve at 0% and 20% opening ............. 87 

vi 
Figure 5-48. Permeate flow for N2 = 3,900 rpm, recycle valve at 0% and 20% opening..............87 

Figure 5-49. Total power for N2 = 3,000 rpm and recycle valve position.....................................87 

Figure 5-50. Total power for N2 = 3,540 rpm and recycle valve position at 0% and 20% 

opening....................................................................................................................................88 

Figure 5-51. Total power for N2 = 3,900 rpm and recycle valve position.....................................88 

Figure 5-52. Specific energy consumption for N2 = 3,000 rpm and recycle valve position at 0% 

and 20% opening.....................................................................................................................88 

Figure 5-53. Specific energy consumption for N2 = 3,540 rpm and recycle valve position at 0% 

and 20% opening.....................................................................................................................89 

Figure 5-54. Specific energy consumption for N2 = 3,900 rpm and recycle valve position at 0% 

and 20% opening.....................................................................................................................89 

Figure 5-55. System recovery ratio for N2 = 3,000 rpm and recycle valve position at 0% and 20%

opening....................................................................................................................................90 

Figure 5-56. System recovery ratio for N2 = 3,540 rpm and recycle valve position at 0% and 20%

opening....................................................................................................................................90 

Figure 5-57. System recovery ratio for N2 = 3,900 rpm and recycle valve position at 0% and 20%

opening....................................................................................................................................91 

Figure 5-58. BW-WE-a1 configuration with DWEER boost.........................................................94 

Figure 5-59. Power calculations for BW-WE-a1 design with DWEER boost...............................96 

Figure 5-60. BW-WE-a1 DWEER boost flow diagram.................................................................97 

Figure 5-61. Summary costs for the steady-state BW-WE-a1 configuration.................................99 

Figure 5-62. RO system configuration BWWE-a1 ......................................................................100 

Figure 5-63. Percentage distance from constraint at N2 = 3,000 rpm,.........................................104 

Figure 5-64. Percentage distance from constraint at N2 = 3,000 rpm,.........................................104 

Figure 5-65. Percentage distance from constraint at N2 = 3,000 rpm,.........................................105 

Figure 5-66. Permeate flow for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 20 .........................105 

Figure 5-67. Permeate flow for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 40 .........................105 

Figure 5-68. Permeate flow for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 60 .........................106 

Figure 5-69. Total power consumed at N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 20..............106 

Figure 5-70. Total power consumed at N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 40..............106 

Figure 5-71. Total power consumed at N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 60..............107 

Figure 5-72: Specific power consumption at N2 = 3,000 rpm, ....................................................107 

Figure 5-73. Specific power consumption at N2 = 3,000 rpm, ....................................................107 

Figure 5-74. Specific power consumption at N2 = 3,000 rpm, ....................................................108 

Figure 5-75. System recovery ratio for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 20 .............108 

Figure 5-76. System recovery ratio for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 40 .............108 

Figure 5-77. System recovery ratio for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 60 .............109 

Figure 5-78: Distance from constraint comparison for changes in N2 for fixed N3 and S2........109 

vii 
Figure 5-79. Permeate flow comparison for changes in N2 for fixed N3 and S2........................ 109 

Figure 5-80. Total power consumption comparison for variation in N2 for fixed N3 and S2..... 110 

Figure 5-81. Specific power consumption comparison for variation in N2 for fixed N3 and S2 110 

Figure 5-82. Recovery ratio comparison for variation in N2 for fixed N3 and S2 ...................... 111 

Figure 5-83. Distance from constraint comparison for changes in N3 for fixed N2 and S2........ 111 

Figure 5-84. Permeate flow comparison for changes in N3 for fixed N2 and S2........................ 112 

Figure 5-85. Total power consumption comparison for variation in N3 for fixed N2 and S2..... 112 

Figure 5-86. Specific power consumption comparison for variation in N3 for fixed N2 and S2 113 

Figure 5-87. Recovery ratio comparison for variation in N3 for fixed N2 and S2 ...................... 113 

Figure 6-1. Maximum permeate flow as a function of available power for plant SWWE-a3 ..... 116 

Figure 6-2. Optimal operating parameters as a function of available power, plant SWWE-a3; 

dotted lines represent the available parameter variation ranges ........................................... 117 

Figure 6-3. Recovery of a function of available power for optimal results ................................. 117 

Figure 6-4. Permeate flux for optimal results on configuration SWWE-a3................................. 118 

Figure 6-5. Constrained variables for optimal results on configuration SWWE-a3 .................... 118 

Figure 6-6. Concentration polarization for optimal results on RO configuration SWWE-a3...... 119 

Figure 6-7. RO pressure drop and specific energy consumption for optimal results on 

configuration SWWE-a3 ...................................................................................................... 119 

Figure 6-8. Probability of mean wind speeds at turbine hub height, A = 10.43, k = 2 ................ 121 

Figure 6-9. Generated power as a function of wind speed........................................................... 122 

Figure 6-10. Annual average COW for plant SWWE-a3, operated as grid isolated, as a function of 

the number of RO vessels installed ...................................................................................... 123 

Figure 6-11. Contribution to the COW for an optimal grid-isolated RO plant powered by a wind 

turbine................................................................................................................................... 124 

Figure 6-12. Comparison of the SCOW for a grid-connected wind-powered desalination plant and 

its grid-powered counterpart................................................................................................. 127 

Figure 6-13. COW structure for the 158-vessel grid-connected wind-RO desalination plant, 

assuming $0.08/kWh grid energy cost.................................................................................. 128 

Figure 6-14. COW structure for the 158-vessel desalination plant, powered only with grid energy,

assuming a $0.08/kWh energy cost ...................................................................................... 129 

viii 
Tables 

Table 3-1. Operational Limits for a Seawater Membrane Element.......................................... 25 

Table 3-2. Operational Limits for a Brackish Water Membrane Element ............................... 25 

Table 3-3. RO System Constraints ........................................................................................... 27 

Table 4-1. Major Cost Components of a Wind Turbine System .............................................. 32 

Table 4-2. Direct Capital Costs as a Percentage of Delivered Equipment Total (DET) Cost.. 33 

Table 4-3. Capital Costs for Seawater SW-WE-a1 Configuration........................................... 36 

Table 4-4. Manufacturing Costs for Seawater SW-WE-a1 Configuration............................... 37 

Table 4-5. Capital Costs for Seawater SW-WE-a3 Configuration........................................... 38 

Table 4-6. Manufacturing Costs for Seawater SW-WE-a3 Configuration............................... 39 

Table 4-7. Capital Costs for Brackish Water BW-WE-a1 Configuration ................................ 40 

Table 4-8. Manufacturing Costs for Brackish Water BW-WE-a1 Configuration .................... 41 

Table 4-9. Cost Comparisons for Seawater Desalination......................................................... 42 

Table 4-10. Cost Comparisons for Brackish Water Desalination............................................. 42 

Table 4-11. Optimization Data Output Format for RO Plant ................................................... 44 

Table 5-1. Model Seawater Feed Composition ........................................................................ 51 

Table 5-2. Membrane Design Parameters ................................................................................ 53

Table 5-3: Input Parameters for the Configuration SWWE-a1. ............................................... 62 

Table 5-4: Input Space Parameter Ranges for Configuration SWWE-a1. ............................... 64 

Table 5-5: Constraint Definition for Configuration SWWE-a1. .............................................. 64 

Table 5-6: Input Parameters for the Configuration SWWE-a3. ............................................... 82 

Table 5-7: Input Space Parameter Ranges for Configuration SWWE-a3. ............................... 83 

Table 5-8: Constraint Definition for Configuration SWWE-a3. .............................................. 83 

Table 5-9 Model Brackish Water Feed Composition............................................................... 92 

Table 5-10 Membrane Design Parameters ............................................................................... 94 

Table 5-11: Input Parameters for the Configuration BWWE-a1............................................ 100 

Table 5-12: Input Space Parameter Ranges for Configuration BWWE-a1............................ 101 

Table 5-13: Constraint Definition for Configuration BWWE-a1........................................... 101 

Table 6-1. Optimal Operating Parameters for Plant SWWE-a3 ............................................ 120 

Table 6-2. Performance of Optimal Wind-RO Plant ............................................................. 123 

Table 6-3. Performance of a Grid-Connected Wind-RO Plant............................................... 128 

Table 6-4. Performance of an RO Plant Using Only Grid Power. ......................................... 129 

Table 6-5. Receding Horizon Approach for Wind-RO Operating Strategies......................... 130 

ix 
Acronyms and Abbreviations 

cmh.........................................cubic meters per hour 

COE........................................cost of energy

COW ......................................cost of water 

DET........................................delivered equipment total

DFIG ......................................doubly fed induction generator 

DOE .......................................U.S. Department of Energy

ED ..........................................electrodialysis 

ERD........................................energy recovery device

GE ..........................................General Electric Company

GEGR.....................................GE Global Research 

gfd ..........................................gallons per square foot per day

gpm ........................................gallons per minute 

lmh .........................................liter per square meter per hour 

MED.......................................multi-effect distillation 

MSF........................................multistage flash 

MW ........................................megawatt 

O&M......................................operation and maintenance 

PM..........................................permanent magnet 

ppm ........................................parts per million 

PSD ........................................power spectral density

psi...........................................pounds per square inch 

PV ..........................................photovoltaic 

REC........................................rural energy cooperative 

RES ........................................renewable energy source

RO..........................................reverse osmosis 

SCOW....................................specific cost of water 

TDS........................................total dissolved solids 

WHO......................................World Health Organization 

WTG ......................................wind turbine generator 

x 
1 Executive Summary

Water needs have been increasing rapidly worldwide, even in nations like the United States, 

where abundant freshwater has been available at a relatively low cost. Population growth, 

increased industrial use, and pollution may limit the nation’s capability to satisfy freshwater 

demands over the next few decades. Hence, in the United States, developing new water 

resources by purifying impaired resources is critical for meeting future water needs. 

Desalination techniques are characterized by large energy expenditures to generate potable 

water. The associated cost of energy (COE) is a dominant factor in the water desalination 

economy. In this scenario, reverse osmosis (RO), a major approach to desalination, is gaining 

increased acceptance as a viable technique, mainly because of its low energy consumption 

and design flexibility. 

Because of recent and projected technological advances, reverse osmosis will most likely 

continue to be the lowest cost technology associated with potable water production. However, 

for many projected water-starved regions of the United States and remote, inland areas where 

grid connectivity is limited, the energy cost associated with reverse osmosis based 

desalination may render the desalination solution economically infeasible. Hence, alternative 

solutions are required to produce potable water. 

A likely candidate for replacing traditional RO desalination systems is a hybrid approach in 

which renewable energy sources (RES) such as wind energy are coupled with an RO 

desalination system. The broad acceptance of RES-RO systems is limited by: 

• Operability over a large power envelope 

• Robustness to feedwater variation 

• Management of multiple, often conflicting, requirements 

• In-situ monitoring of membrane degradation and compensation via operations and 

chemicals 

• Reduction in cost of water (COW) for commercialization. 

An approach to interfacing RES and RO systems must address the issues of operability, 

robustness, and management of membrane constraints with regard to power fluctuations. At 

the same time, a highly flexible RO system must be developed in conjunction with energy 

management and operational strategies. An RES-RO system with advanced operations can be 

developed, but its effectiveness must be measured in terms of its energy consumption and 

ultimately COW. Hence, the overall goal of this particular study is to investigate multiple 

concepts for integrating wind turbines and RO desalination systems for feasibility and 

efficiency. This effort is unique in that it addresses the constraints of variable power input on 

desalination system operation to arrive at a process that can accommodate a maximum level 

of wind turbine power variation and remain economically viable. A principal motivation for 

this project is the simplicity and low cost with which water can be delivered where energy, a 

major component of RO-based desalination system cost, is reduced. 

1 
The program focuses on the following fundamental activities to address its objectives: 

• Develop component models, including wind turbine system, RO system, energy 

recovery devices, and energy storage, for the major components of an RES-RO system 

and their integration into a system-level concept. Develop an integrated energy and 

water cost model that can be used to evaluate and trade off various RES-RO 

configurations. 

• Develop and analyze various RES-RO configurations as to their robustness to power 

fluctuations and ability to meet water quality requirements with the lowest COW. 

• Develop a methodology to size, evaluate, and operate an RES-RO system in 

operational modes such as grid connected, grid connected with direct coupling, and 

grid isolated with energy storage. 

2 
2 Introduction 

Water needs have been increasing rapidly worldwide because of population and industrial 

growth. In the past, water was seen as mainly a Middle Eastern or African issue; however, 

with the growth in Asia and North America, this viewpoint may no longer hold. In contrast to 

many areas of the world, the United States has enjoyed an abundant supply of freshwater at 

relatively low cost. Over the next few decades, however, population growth, increased 

industrial use, and pollution may strain the nation’s ability to supply the necessary quantities 

of safe freshwater. A case in point is the recent and projected growth in the southeastern and 

southwestern regions of the country where safe freshwater shortages occur routinely in 

drought years. The potential inability to meet the growing needs for freshwater can adversely 

affect public health and various economic sectors such as agriculture. A combination of water 

conservation, reuse, recycling, and development of new water sources is critical to ensure an 

adequate supply of safe freshwater at a reasonable cost. Since conventional water resources 

are limited, the development of new ones will most likely come from impaired resources such 

as brackish water and seawater in addition to water generated during energy production (oil, 

natural gas, and coal bed methane production)1. 

Developing new water resources by purifying impaired resources is seen as critical for 

meeting future water needs. For desalination, impaired resources may be grouped into various 

categories by their saline content, which is referred to as total dissolved salts (TDS). 

Typically, freshwater contains less than 1,000 milligrams of salt per liter of water, or 1000 

parts per million (ppm). Brackish water, on the other hand, is associated with TDS content of 

1,000−10,000 ppm. Finally, seawater typically has at least 10,000 ppm of TDS. The goal of 

desalination is to purify the water stream of these impaired resources so the TDS content in 

the resultant stream is 500 ppm or lower. 

At present, there are two major approaches to desalination: thermal-based and membranebased solution. Thermal-based desalination is predicated on the use of phase change or 

distillation techniques to reduce the TDS content of an impaired water resource. Mature 

thermal-based technologies such as multistage flash (MSF) or multi-effect distillation (MED) 

use simple processes. Simply put, thermal-based solutions use energy input in the form of 

heat to evaporate the impaired water and then condense the resulting vapor stream to produce 

potable water. Because a large amount of heat input is required, thermal desalination systems 

are typically colocated with power plants for electrical generation where steam is readily 

available. Consequently, the economics of thermal desalination require large centralized water 

and power production and low cost of energy (COE) for steam production. These factors are 

easily achieved in some regions such as the Middle East, so thermal desalination is a costeffective technology for producing potable water in these areas

2

. 

In many regions, thermal-based solutions are not cost effective because of the high COE 

associated with steam production. Consequently, in these regions, membrane-based 

desalination is a viable solution. Membrane-based solutions use either electrical potential or 

pressure as the driving force to separate substances via diffusion across a semipermeable 

membrane. In the case of electrical potential, the technology is often referred to as 

electrodialysis (ED). In ED, positive (cation) and negative (anion) ions are transported 

through a semipermeable membrane by applying a voltage across a pair of electrodes. 

3 
Alternate configurations of cation- and anion-permeable membranes are placed between each 

pair of electrodes. As the ions are driven to the electrode with the opposite charge, dissolved 

salt is separated and concentrated in a separate channel and results in a potable water stream3. 

ED has favorable economics for brackish water and small-scale systems compared to other 

desalination methods. However, for TDS concentrations higher than 10,000 ppm, the COE 

associated with the ED is higher than with other desalination technologies. In addition, for 

large-scale plants, the economies of scale are more favorable for other membrane 

technologies such as reverse osmosis (RO)3. 

RO is a pressure-driven membrane separation process in which the water from a pressurized 

saline solution is separated from the solutes via diffusion across a semipermeable membrane. 

The pressure required to drive the separation process depends on the resistance of the 

membrane and on the saline concentration of the water. RO systems consist of additional 

process steps beyond pressurization and separation for producing potable water. An overview 

of the RO system and its major components is shown in Figure 2-1. 

Chemical Addition

- p H A djustments

- Flocculants

- Anti-Scalants

- Chlorine Energy Recovery De Chlorination

Brine Concentrate

Feed Water

Potable Water (Permeate) z

Media Cartridge High Media Cartridge High dia Cartridge High RO System

Filter Filter Pressure Filter Filter Pressure lter Filter Pressure

Pretreatment Pump

Figure 2-1. Process steps and components of RO desalination systems 

The initial process step of an RO system is pretreatment, which is critical to ensure membrane 

surfaces remain clean to maintain performance and reduce fouling or degradation. Therefore, 

suspended solids are removed via sand filtration or filtration through other media. 

Pretreatment consists of fine filtration. and addition of acid or other chemicals to inhibit salt 

precipitation and microbial growth. Finally, chemicals are added to ensure pH and alkalinity 

levels are within a specified range that corresponds to the membrane manufacturer’s 

requirements. 

The second process step in an RO system consists of increasing the pressure of the feedwater 

and pumping the feedwater through closed vessels. An RO system consists of multiple closed 

vessels that are connected in parallel; each closed vessel consists of multiple elements in 

series. Since the feedwater input at each closed vessel is approximately equivalent with regard 

to pressure and flowrate, the performance of the overall system can be ascertained by the 

performance of a single vessel. In a closed vessel, each element separates the dissolved salts 

from the water, which results in a potable water flux across the membrane. The flux declines 

axially along the length of the membrane because of the increase in salinity of the water, 

which is caused by the separation process and the pressure loss along the length of the 

4 
membrane. In each closed vessel, the potable water, often termed permeate, is collected as is 

the concentrate or brine solution. The brine solution is of higher TDS than the inlet stream 

because of the salt separation. 

The third and fourth process steps are applied to the permeate and the brine concentrate, 

respectively. The permeate is post-treated to stabilize the water for distribution; gases such as 

hydrogen sulfide may be removed and pH may be adjusted. Since the pressure drop in an RO 

system is slight, the brine concentrate has significant pressure energy, which if recovered can 

improve overall system efficiency and cost. Hence, in the fourth process step, pressure energy 

in the brine is recovered through an energy recovery device (ERD) and then disposed. 

The widespread use of desalination techniques, whether thermal or membrane based, is 

predicated on the economics associated with the process. In both approaches, capital and 

energy costs dominate. One method to compare the economics associated with thermal 

processes and membrane processes, specifically RO, is to look at energy used per cubic meter 

of potable water for seawater desalination. For seawater, thermal systems consume 3.5–4.5 

kWh/m3 versus 3.0–4.5 kWh/m3 for RO systems. Thermal and RO systems have similar 

energy use; RO has a slightly lower energy use. In contrast to thermal techniques, which are 

mature and have little technology development, RO-based systems have continued to improve 

their energy efficiency through technology development. In fact, with the current focus on 

improving ERDs, development of low-pressure membranes, and pH-robust membranes, RO is 

expected to continue to provide the lowest energy use and hence, lowest cost associated with 

potable water production. Finally, because significant heat must be input in the form of steam 

for thermal systems, the ability to site a thermal desalination facility in noncentralized 

distribution systems is limited. RO-based solutions, on the other hand, do not face this issue 

because the main energy input is electrical, which is readily available from the electrical grid. 

For grid-isolated cases, RO systems can be integrated with power generation devices such as 

diesel engines or renewable energy sources such as wind or photovoltaic (PV) power. Thus, 

RO-based desalination is gaining momentum and increased acceptance as a viable 

desalination technique. 

2.1 Motivation for Wind Desalination 

The development of potable water from underused resources such as brackish water and 

seawater is predicated on the use of desalination techniques. Desalination has the potential to 

address current and future water needs, but it has been plagued by high cost, which makes it 

noncompetitive with natural resources used today. Of the available desalination techniques 

(RO, multistage flash (MSF), multi-effect distillation (MED), electrodialysis (ED), and vapor 

compression (VC), RO consistently has the highest demonstrated energy efficiency, typically 

3–4.5 kWh/m3. Even with its higher efficiency, energy cost still accounts for roughly 45% of 

the cost of water (COW) in RO-based systems (Figure 2-2)1

. For many projected waterstarved regions of the United States and remote, inland areas where grid connectivity is 

limited, the retail COE is $0.08–$0.12/kWh. Even though the cost of generating energy has 

dropped to approximately $0.04/kWh for remote areas, the costs associated with transmission 

and distribution make up a large percentage of the retail energy cost. Hence, alternative 

solutions are required to produce potable water. 

5 
Figure 2-2. Cost categories for an RO-based desalination system 

A likely candidate for replacing traditional RO desalination systems is a hybrid approach 

where renewable energy sources (RES) such as wind energy and photovoltaics (PV) are 

coupled with an RO desalination system. To understand the advantages of RES-RO systems, 

we considered the cost structure associated with traditional desalination systems (Figure 2-2). 

Energy, capital, and operation and maintenance (O&M) costs are major factors. The 

advantages of RES-RO systems address these factors. 

• The COE associated with transmission and distribution is avoided by coupling energy 

generation directly to RO systems with RES. Hence, the COE of desalination systems 

can be significantly reduced. Energy generation costs associated with photovoltaic 

systems (PV) are still high, but wind energy cost is projected to reach $0.04/kWh, 

which will make wind desalination cost competitive. 

• The predominant cost of RES systems is capital expenditures. For wind energy, 

roughly 89% of the COE is associated with capital expenditures; the remaining 11% is 

O&M. The shift in RES systems from fuel cost to capital cost significantly alters the 

cost structure for RES-based desalination systems. The shift from COE to capital 

expenditures is a favorable proposition, since capital cost can be amortized over a 

longer horizon. In addition, the shift to capital expenditures reduces the sensitivity to 

fluctuations in fuel cost. For RES some of the COE shown in Figure 2-2 would also 

shift to O&M. The resulting cost structure of RES-RO systems, in conjunction with 

the high energy efficiency of RO, provides a cost-competitive approach for addressing 

the nation’s water needs. 

• The availability of RES throughout the nation correlates to potential impaired water 

resources that can be used to develop new, safe freshwater (Figure 2-3). Specifically, 

the plains states have significant saline aquifers that can be cultivated to yield 

freshwater for the agricultural economy. Wind and photovoltaic energy sources are 

prevalent in these areas and can be used for desalination. In the Southwest, specifically 

New Mexico, Texas, and Colorado, significant population growth is projected. 

Additional challenges to meeting the ever-increasing water demand include 

restrictions of water rights on the use of available freshwater sources. If the saline 

aquifers can be processed through RES-RO systems, the water shortages might be 

alleviated in this area. 

6 
• A final example is associated with rural energy cooperatives (RECs). Approximately 

55% of RECs are located in the same region as the saline aquifers. Renewable sources 

are available and government grants have been offered for their development, so RECs 

represent a large customer base for the proposed technology (Figure 2-3). 

Figure 2-3. RES resource availability correlated to potential impaired water sources 

and potential beneficiaries 

The challenge with RES-RO systems, however, is how to interface these two technologies. 

RES systems are characterized by transient operation that leads to electrical energy variation. 

Desalination systems, especially RO systems, are designed for continuous steady-state 

operation. Conventional approaches for addressing the operability mismatch between RES 

and RO use electrical energy storage systems such as batteries or alternative energy sources 

such as diesel engines to yield a stable power source. This approach, however, greatly 

increases the capital cost of the hybrid system and, in some cases, the system’s COE. The end 

result is an increase in COW. 

Novel RES-desalination systems have been proposed in the literature, and some have been 

demonstrated4−10. For example, Thomson et al. consider the use of a Clark pump in 

conjunction with advanced control strategies to reduce the specific energy consumption in a 

laboratory-scale demonstration4. Carta et al. describe a wind desalination system in the 

Canarian Archipelago where various desalination approaches have been tested in conjunction 

with wind5

. This work highlights that RO is the most appropriate technique for stand-alone 

power generation situations. The operational strategy brings the flywheel, pumps, and RO 

segments online as power is available and removes sections of the RO system as power is 

reduced. Finally, Miranda et al. employ a control strategy that attempts to maximize energy 

extracted and water throughput despite power fluctuations6

. These recent results address the 

fundamental issue of RES-RO systems—the design of a system and the selection of an 

operational strategy that accommodates the maximum power variation without compromising 

7 
water quality or COW. These results show promise, but issues of economic feasibility, 

performance, and commercialization still remain. The technical limitations that prevent the 

broad acceptance of RES-RO systems can be broken down into the following areas: 

• Operability over a large power envelope 

• Robustness to feedwater variation (TDS, temperature, etc.) 

• Management of multiple, often conflicting, requirements (load balancing, membrane 

operability, water quality, permeate flux) 

• In-situ monitoring of membrane degradation and compensation via operations and 

chemicals 

• Reduction in cost of water (COW) for commercialization. 

2.2 Scope of Program 

An approach to interfacing RES and RO systems addresses the issues of operability, 

robustness, and management of membrane constraints with regard to power fluctuations, and 

must develop a highly flexible RO system in conjunction with energy management and 

operational strategies. An RES-RO system with advanced operations can be developed, but its 

effectiveness must be measured in terms of its energy consumption and ultimately COW. 

Hence, the overall goal of this study is to investigate multiple concepts for integrating wind 

turbines and RO desalination systems for feasibility and efficiency. This effort is unique in 

that it addresses the constraints of variable power input on desalination system operation to 

arrive at a process that can accommodate a maximum level of wind turbine power variation 

and remain economically viable. A principal motivation of this project is the simplicity and 

low cost with which water can be delivered where a major component of RO-based 

desalination system cost―energy―is reduced. 

The program focuses on the following fundamental activities to address its objectives: 

• Develop component models for the major components, including wind turbine system, 

RO system, energy recovery devices (ERDs), and energy storage of the RES-RO 

system and their integration into a system-level concept. 

• The component models include wind turbine system, RO system, energy recovery 

devices, and energy storage. 

• Develop an integrated energy and water cost model that can be used to evaluate and 

trade off various RES-RO configurations. 

• Develop and analyze various RES-RO configurations as to their robustness to power 

fluctuations and ability to meet water quality requirements with the lowest COW. 

• Develop a methodology to size, evaluate, and operate an RES-RO system in 

operational modes such as grid connected, grid connected with direct coupling, and 

grid isolated with energy storage. 

These activities and the corresponding results are described in the following sections. Section 

3 provides a description of the component models that are used to analyze the RES-RO 

system. Section 4 provides details about the integrated energy and water cost model. Section 4 

8 
highlights the assumptions in the cost analysis for the energy and water portions of the RESRO system. Section 5 describes the RES-RO configurations that have been investigated for 

this concept study. The nominal operating points associated with each configuration and the 

operational design space are described. Section 5 considers seawater and brackish water 

conditions. For developing a methodology to size a RES-RO system and its operating 

strategy, the most cost-effective seawater RES-RO configuration is chosen. The design 

optimization associated with the selected configuration is described in Section 6. In Section 6, 

design optimization and cost analysis for grid-connected, grid-connected with direct coupling, 

and grid-isolated operational scenarios are described. Section 7 summarizes the conclusions 

of the concept study and Section 8 highlights potential avenues for future work. 

9 
3 Model Description 

3.1 Overview of Required Models 

In this section, we present a brief description of the models used in later sections to: 

1. Develop a methodology to design and analyze hybrid wind-RO systems that handle all 

the physical constraints and the process economy simultaneously. 

2. Define the operating space of a flexible RO system and explore it to achieve 

maximum performance.

3. Develop a realistic wind-RO COW that accounts for fluctuations in available power 

and product water flow rate and quality. 

4. Develop operating strategies for minimizing COW. 

The complexity of the models has been adjusted to give accurate physical representation for 

these objectives, without incurring unnecessary computational effort. More precisely, the 

performance of the RO process may be insensitive to fast transients in the power electronics 

that may achieve their steady-state operation in a few milliseconds. In these cases, standard 

model reduction techniques were applied to eliminate dynamic behaviors that would render 

simulations impractical without improving modeling accuracy. The main focus has been to 

capture cause-and-effect behavior of wind power variations on membrane performance and 

RO economy. Thus, models of dynamics with time scales of 0.1 s or shorter; for example, fast 

transients in the electrical systems, have been greatly simplified. 

3.2 Component Model Description 

3.2.1 Wind Model 

Wind speed is highly variable, both geographically and temporally, and varies over a 

multitude of temporal and spatial time scales. In terms of using a wind turbine to generate 

power, this variation is amplified by the fact that the available energy in the wind varies as the 

cube of the wind speed. Consequently, the location of a wind farm or any other plant that 

relies on the exploitation of the wind resource for power generation must be considered to 

ensure superior economic performance. 

Wind is driven by differences in the temperature of the Earth’s surface. Geographic variations 

in wind speed thus originate in differences in solar exposure between geographic regions. 

Surface heating by the sun is stronger during the daytime, close to the equator, and on land 

masses. Warm air rises and circulates in the atmosphere before it sinks back to cooler regions. 

This results in various wind characteristics such as: 

• A daily peak in wind speed caused by the Earth’s rotation 

• Characteristic wind directions in various that are caused by the air flow between the 

poles and the equator 

• Local wind effects such as characteristic diurnal wind speeds near coasts or in 

mountains that are caused by the nonuniformity of the Earth’s surface 

10 
• Surface roughness and the nature of the terrain in specific locations such as mountains 

or forests also affect the variation of the wind speed. 

From a temporal point of view, wind speeds vary over several time scales

7

. Of particular 

interest are the annual variations in wind speed, which are used in the next sections to 

estimate the average annual power generation by a wind turbine, and, further, to find an 

annual average COW produced with a wind-powered water desalination plant. Also of interest 

are short-term (turbulent) variations in the wind speed, as their models represent the basis for 

generating time-dependent wind speed profiles that are used to obtain the dynamic simulation 

results presented in the sections to follow. 

• In some locations, a very slow long-term (year-to-year) variation of the wind can 

occur. Such effects are not easy to estimate or predict, given the limited historical data. 

Long-term changes in wind speed are induced by climate change (global warming) 

and global climate phenomena like el nino. Long-term variations in wind speed are not 

accounted for in the present calculations. 

• Annual and Seasonal Variations: Although year-to-year variations in the annual 

mean wind speeds are hard to predict, wind speed variations during one year can be 

well characterized statistically. The Weibull distribution gives a good representation of 

the distribution of mean wind speeds over a year (the mean wind speed is the wind 

speed averaged over a short period of time, typically 10 min). The Weibull probability 

density function in Eq. 3-1 

f (V ) = k V

A

k

k 

−1 

exp⎜

⎜

⎛

−

⎝

⎜

⎜

⎛V

A ⎠

⎟

⎟

⎞

k 

⎟

⎟

⎞

Eq. 3-1 

⎝ ⎠

can be used to determine that the average yearly wind speed for a specific location 

(site) in Eq. 3-2, 

∞

V = ∫Vf (V )dV Eq. 3-2 

0 

and the probability of the mean wind speed at a site be within a certain wind speed 

range [V1 ,V2 ] in Eq. 3-3. 

V2 

P1,2 = ∫ f (V )dV Eq. 3-3 

V1 

The scale parameter A and the shape parameter k are determined experimentally from wind 

speed measurements and are site specific. If k is exactly 2, the distribution is known as a 

Rayleigh distribution, and is in fact typical to many locations. 

• Synoptic and Diurnal Variations: Over intervals shorter than one year, wind speed 

changes are more random and, evidently, less predictable. Considering a spectral 

approach to the analysis of wind speeds at a certain site, a peak in the frequency 

spectrum of wind is often seen around four days. This peak corresponds to relatively 

11 
short-term variations in the wind speed, called synoptic variations, which are 

associated with large-scale weather changes such as the appearance or disappearance 

of areas with high or low atmospheric pressure and weather fronts moving across the 

Earth’s surface. Many locations also show large diurnal peaks that are driven by local 

thermal effects. Because there is no generally valid model, and because synoptic and 

diurnal variations in wind speed depend on location, they are not considered in this 

work. 

• Changes over seconds and minutes occur as well. These wind speed fluctuations are 

called turbulence. Over short time intervals (a few seconds to about 10 minutes), 

wind speed can be described as the sum of the mean wind speed V (taken as a 10-min 

average) and the turbulent variation of the wind speed, 

V (t) =V +V0 (t). 

In this expression, turbulent variations of the wind have a zero mean when averaged 

over 10 minutes. 

The principal causes of turbulence are the friction between moving air masses and the Earth’s 

surface and the thermal effects that cause air masses to move vertically as a result of 

temperature and density gradients between the atmospheric layers. These effects are often 

interconnected. 

Turbulence is a complex stochastic phenomenon that cannot be characterized in terms of 

deterministic equations; therefore, statistical methods are used. Turbulence is well described 

mathematically by its intensity and by power spectral density (PSD). 

Turbulence intensity is a measure of the overall level of turbulence. It is defined in Eq. 3-4 as: 

σ I = Eq. 3-4 V 

where σ is the standard deviation of wind speed variations about the mean wind speed V , 

usually defined as a 10-min average. 

Turbulence intensity depends on the roughness of the ground surface, on the height above the 

surface, and on topographical features such as hills or mountains and local features, including 

trees and buildings. 

The turbulence intensity contains no temporal information; i.e., data regarding the frequency 

of wind speed change. This information is given by the turbulence power spectral density 

function (PSD), S(f). A power spectral density model is also needed to generate wind speed 

time series that depend on different mean wind speeds V and turbulence intensities I. 

One commonly used power spectral density model is the one proposed by Kaimal. The 

Kaimal PSD is given in Eq. 3-5 by: 

S( f ) = σ2 

(1+ 6

4L

fL 

1

1

/

/ 

V

V )

5 / 3 Eq. 3-5 

where 

12 
S = the longitudinal velocity spectrum 

σ = is the standard deviation of wind speed 

V = the mean wind speed 

f = the frequency (in Hz) 

Another commonly accepted PSD model is the one proposed by von Karman, which is 

given in Eq. 3-6 by: 

S( f ) = σ2 4L2 /V 

2 5 / 6 Eq. 3-6 (1+ 70.8( fL2 /V ) ) 

For this study, the values of the length scales in the PSD models above were considered to be 

L1 =170m and L2 = 72.992m . 

3.2.1.1 WIND PROFILE GENERATION 

WindSim, a software package developed at GE Energy, was used to generate wind speed 

profiles to test the transient operation of the wind-powered desalination plant. The profiles 

were generated with mean wind speeds of 1−27 m/s, considering a turbulence intensity of 0.1. 

Figures 3-1 and 3-2 present a 50-min wind profile for a mean speed of 5 m/s, along with the 

power spectrum of the wind and, for comparison purposes, the Kaimal PSD computed with 

the same mean wind speed and standard deviation. 

Power Spectral Density S(f) 4

10 6.5 

-4 10 4

-6 10 3.5 10-3 10-2 10-1 100 101 0 500 1000 1500 2000 2500 3000 3500 

log(Frequency), Hz time, s 

Figure 3-1. Wind PSD Figure 3-2. Wind speed profile

generated with the Kaimal PSD model

The spectrum of the generated wind closely follows the Kaimal model for frequencies greater 

than 0.004 Hz, that is, for time scales of 5 min or shorter. 

3.2.2 Wind Turbine Model (wind input to power output) 

The GE 1.5-megawatt (MW) wind turbine has been used as a base to model the wind turbine 

for this wind desalination study. A doubly fed induction generator (DFIG), like the one used 

in the GE 1.5-MW wind turbine generator (WTG) is modeled for grid-connected study based 

on extensive GE knowledge and experience with the machine model. However, technical 

constraints that are associated with DFIG prevent it from being applied to the grid-isolated 

2 

Wind Data 

Kaimal PSD 6 10

5.5 

Wind speed, m/s 

0

10

m2/s2 Hz-1 

5 

-2 10

4.5 

13 
case. To model the grid-isolated wind desalination system, a permanent magnet (PM) 

synchronous generator is modeled. The PM machine model is simulated based on literature 

and engineering experiences with similar turbine and generator parameters such as speed, 

voltage rating, and inertia, used by the GE 1.5-MW DFIG model to be comparable. 

DFIG has AC excitation supplied by a back-to-back converter that is directly connected at the 

rotor winding. The PM synchronous generator has no external electric excitation system, and 

a back-to-back converter that is connected to its stator is used to interface it with the grid. The 

models provided have been simplified to reduce the computation time, so only the sections of 

the model with time constants that are significant to the rest of the system are left. 

Specifically, the very fast dynamics associated with the control of the generators and 

converters (current and voltage regulators) have been modeled as algebraic approximations of 

their response. Representation of the turbine mechanical controls has been simplified as well. 

The simplified model has a compound time constant of approximately 0.5 s. The models are 

valid only for balanced three-phase system time domain simulations. Although simplified, 

these models still allow the accurate representation of the effect of wind speed fluctuation on 

the electrical output of the WTG. 

The WTG model has two major components: 

• The wind turbine and turbine control model include simplified mechanical controls, 

rotor inertia, rotor speed, and wind power as a function of wind speed (power curve). 

• The generator and converter model uses an algebraic model to approximate the long 

time constant dynamics (> 0.5 s) and steady-state performance of the generator, backto-back converters, their interface with downstream system (desalination system and 

grid), and several hardware-related constraints. For the PM generator, simple dump 

load and battery characteristics are also included. 

Figure 3-3 shows an overview block diagram of the model structure. 

Figure 3-3. WTG model structure 

3.2.2.1 WIND TURBINE AND TURBINE CONTROL MODEL 

The wind turbine model provides a simplified representation of a complex electromechanical 

system. The block diagram is shown in Figure 3-4. In simple terms, the function of the wind 

14 
turbine is to extract as much power from the available wind as possible within its designed 

capability (current, voltage, and power). The wind turbine model represents the relevant 

controls and mechanical dynamics of the wind turbine. 

Figure 3-4. Wind turbine model block diagram 

Rotor Model 

The rotor model includes the rotor inertia for the WTG rotor, which uses the mechanical 

power and the electrical power to compute the rotor speed. A two-mass rotor model has been 

used with separate masses for the turbine and generator (Figure 3-5) to allow the possible 

mechanical oscillations in the WTG shaft to be simulated. 

Figure 3-5. Two mass rotor model 

Wind Power Module 

The wind power module of the model computes the wind turbine mechanical power from the 

energy contained in the wind with the formula in Eq 3-7: 

15 
Eq. 3-7 

Where 

P = the mechanical power extracted from the wind 

ρ = the air density in kg/m3 

Ar = the area swept by the rotor blade in m2 

VW = the wind speed in m/s 

Cp = the power coefficient, which is a function of λ and θ

λ = the ratio of the rotor blade tip speed and the wind speed 

θ = the blade pitch angle in degree 

Cp is a characteristic of the wind turbine and is usually provided as a set of curves that relate 

Cp to λ with θ as a parameter. An example of a set of Cp curves is shown in Figure 3-6. 

Curves were fitted on a representative GE wind turbine Cp curve to find the best 

mathematical representation of the Cp curves used in the model. 

Power Coefficient (

Cp) 

Tip Speed Ratio ( λ ) 

Figure 3-6. Wind power Cp curves 

3.2.2.2 GENERATOR AND CONVERTER MODEL 

Grid-Connected WTG Model 

The generator is model based on GE 1.5-MW WTG, which is a DFIG. Its detailed electrical 

and control diagram is shown in Figure 3-7. 

The generator model combines the behavior of the induction generator and the field 

converters, and ignores the fast transient such as the pulse width-modulated switching of the 

converters. This simplified model takes as inputs the mechanical power, electrical speed from 

the gearbox, and grid references such as voltage and frequency, and output the currents as 

well as the electrical power. Therefore, no mechanical state variables are modeled in this 

generator model. They are included in the turbine model as addressed in previous section. 

As with conventional generator models, a set of equivalent circuits in d-q frame is used to 

represent the DFIG (Figure 3-8). 

16 
}

{

VGLine_Fbk 

IGLine_Fbk

{

VGRotor_Fbk 

IGRotor_Fbk 

{ {{ ILine_Fbk 

VLine_Fbk 

{

nRotor_Fbk 

VDC_Fbk 

Gate Driver 

Current 

Regulator 

Current 

Command 

VDC_Fbk } IGRotor_Fbk 

VGRotor_Fbk 

VGLine_Fbk 

IGLine_Fbk 

nRotor_Fbk 

Gate Driver 

Current 

Regulator 

VDC VDC_Fbk 

{VLine_Fbk

ILine_Fbk 

515V 

33kV 

iq_Rot_Cmd id_Rot_Cmd iq_Grid_Cmd 

Doubly-fed 

Induction 

Generator 

Regulator id_Rot_Cmd_Spill= generation id_Grid_Cmd 

Torque_Cmd PF_Cmd VDC_Cmd Generator

Figure 3-7. Diagram of DFIG and converters 

R s

L m

Lσs

+ 

U2d

1d i 2d i

R r

+ 

ωλ 2q

+ 

U1d

d iμ

ωλ1q Lσr

+ 

Rs ωλ1d Lσs Lσr ωλ 2d Rr

+ 

+ 

U2q

1q i 2q i

L m

+ 

+ 

U1q

q iμ

Figure 3-8. DFIG equivalent circuit 

In the figure, λ is the flux linkage, U and i are the voltage and current, R and L represent the 

resistance and inductance. The related state equations for current, voltage, and flux linkage 

are derived from these equivalent circuits. 

17 
Several assumptions were made based on the characteristics of the DFIG and the needs of 

wind desalination studies: 

• The system is grid connected, which is required by current DFIG technology. 

• Fast transient of converters are ignored. The system represents the WTG response to 

wind speed variation at long time constant dynamics (> 0.5 s) and steady state. 

• The system is represented in d-q frame and is referenced to the stator side. 

Grid-Isolated WTG Model 

The DFIG WTG, as presently implemented, cannot be operated as grid isolated. A PM 

generator and converter system was modeled to study a stand-alone wind desalination system. 

The detailed electrical and control diagram of the system is shown in Figure 3-9. 

Because specific PM WTG design and manufacturing experience is limited, a simplified 

model was developed based on textbook theory

8

 and engineering experience on related 

systems. The model applies Kirchoff’s law and DC link voltage stability control theory to 

represent a typical PM generator and its converter interface with loads. DC link current 

and voltage between the back-to-back grid converters were used as the main system 

stability and control measures. The modeled system control block diagram is shown in 

Figure 3-10. 

{

VGLine_Fbk 

IGLine_Fbk

{

VGRotor_Fbk 

IGRotor_Fbk 

{ {{ ILine_Fbk 

VLine_Fbk 

{

nRotor_Fbk 

VDC_Fbk 

Gate Driver 

Current 

Regulator 

VDC Regulator 

VDC_Fbk } IGRotor_Fbk 

VGRotor_Fbk 

VGLine_Fbk 

IGLine_Fbk 

nRotor_Fbk 

{

Gate Driver 

VSec 

Regulator 

VDC 

Regulator VDC_Fbk 

{VLine_Fbk

ILine_Fbk 

iq_Rot_Cmd id_Rot_Cmd iq_Grid_Cmd 

PM 

Machine 

VDC_Cmd PF_Cmd 

Figure 3-9. Diagram of PM synchronous generator 

Due to limited design and manufacturing experience specifically on PM wind turbine 

generator, a simplified model was developed based on textbook theory 

9

 and engineering 

experience on related systems. The model applies Kirchoff’s law and DC link voltage 

stability control theory to provide a representation of a typical PM generator and its 

converter interface with loads. DC link current and voltage between the back-to-back grid 

converters were used as main system stability and control measures. The modeled system 

control block diagram is shown in Figure 3-10. 

18 
The required sampling time of the simulated system forced a reduction in the order of the 

machine and inverter simulation. The only state variables considered are the DC link 

capacitor and the machine shaft mechanical inertia. The machine side inverter current 

control is represented only through its active current regulator (q-axis) that generates the 

current charging or discharging the DC link capacitor as well as the torque generated by 

the machine. The typical bandwidth for the actual current regulator is on the order of a 

thousand radian/s and can be replaced by a unity gain. The command for this current 

comes from a DC link voltage controller of much lower bandwidth that was included in 

the model. 

 The block diagram shows the computation of the DC link voltage. The integrator 

representing the mechanical shaft receives as inputs the torque from wind power, and the 

generator loading. The mechanical speed together with the inverter current is used to 

calculate the power fed from the machine into the DC bus circuit. The active power 

requested by the load through the grid side inverter is subtracted from this generator 

power and then divided by the DC link voltage. The result represents the actual current 

flowing from the machine and grid side inverter. The other contributors to charge or 

discharge of the capacitor are the current coming in and out of the battery, and the current 

to a dump whenever a predetermine over-voltage is reached. This can be reduced to Eq. 

3-8. A simplified supervisory control was represented by a power flow limiter that 

controls the amount of active power sent to the desalination plant. 

I DCLink = I generator − Iload + I battery − I dumpload 

Eq. 3-8 

VDC_Fbk VDC 

VDC_Cmd -

Pwind 

RDump 

IBattery 

-

+ 

IC 

-

IC 

PMot 

N 

D 

n 

Friction 

IInvGen C s

1 

pu 

J s

1 

pu 

IMot~Te 

D 

N 

Controller 

N 

D 

-

0 

IMax 

0 

-

PLoad 

n~VMot PLim 

-

IC 

Tfilt 

s 

1 

0 

PLim PLimFilt 

0 

PMax 

PLimit 

To Pump 

current 

regulator 

-PMax 

Figure 3-10. Control block diagram of PM generator model 

The required sampling time of the simulated system forced a reduction in the order of the 

machine and inverter simulation. The only state variables considered are the DC link 

capacitor and the machine shaft mechanical inertia. The machine side inverter current control 

is represented only through its active current regulator (q-axis), which generates the current 

that charges or discharges the DC link capacitor as well as the torque generated by the 

machine. The typical bandwidth for the current regulator is about 1000 radian/s and can be 

19 
replaced by a unity gain. The command for this current comes from a DC link voltage 

controller of much lower bandwidth that was included in the model. 

The block diagram shows the computation of the DC link voltage. The integrator that 

represents the mechanical shaft receives as inputs the torque from wind power and the 

generator loading. The mechanical speed and the inverter current are used to calculate the 

power fed from the machine into the DC bus circuit. The active power requested by the load 

through the grid side inverter is subtracted from this generator power and then divided by the 

DC link voltage. The result represents the current that flows from the machine and grid side 

inverter. The other contributors to charge or discharge of the capacitor are the current coming 

in and out of the battery, and the current to a dump whenever a predetermined overvoltage is 

reached. This can be reduced to Eq. 3-8. A simplified supervisory control was represented by 

a power flow limiter that controls the amount of active power sent to the desalination plant. 

Several assumptions are made about the grid-isolated WTG model for the wind desalination 

analysis: 

• The same parameters from the grid-connected WTG model are applied for this gridisolated model to be comparable. 

• Fast transients of the control are ignored; only the major states such as voltage

regulation and turbine inertia are represented. 

• The system represents the WTG response to wind speed variation at steady state (> 0.5 

sec.). 

STEADY-STATE MODEL VALIDATION 

The grid-connected DFIG model was validated against the power curve of GE 1.5-MW WTG. 

The comparison result is shown in Figure 3-11. Given that the model is greatly simplified, the 

slight error is acceptable for this study. 

0 

200 

400 

600 

800 

1000 

1200 

1400 

1600 

1800 

Po

wer (kW) 

0 5 10 15 20 25 30 35 

Wind Speed (m/s) 

Pow er Curve of GE1.5MW WTG Pow er Curve of DFIG Model 

Figure 3-11. Model validation result 

The similar power curve was also used for the grid-isolated system model, assuming that the 

PM WTG gives similar performance. 

20 
SUMMARY 

This WTG system model includes the major components of a typical wind turbine: DFIG for 

grid-connected operation and PM generator for stand-alone operation. The DFIG is modeled 

with parameters that are based on extensive design information and from test data extracted 

from GE products. The PM generator and the inverter models were developed based on a 

reduced model that accounts only for the relatively slow electrical transients. They appear to 

give a realistic approximation of WTG behavior at a sampling time that is suitable for this 

wind desalination analysis. 

3.2.3 Variable Speed Drive and Motor Model 

The variable speed drives are major components in the electrical system and are used as prime 

movers for the desalination water pumps. They are controlled and constrained by the 

desalination system operation requirements and the WTG power and stability requirements. 

A typical AC motor drive includes a rectifier, a large DC link capacitor, and a variable 

frequency inverter, which regulates the speed (frequency) and torque (current) of the motor. 

An illustration of this type of variable speed motor drive that uses an induction motor is 

shown in Figure 3-12. 

Mechanical 

Torque 

current & f 

Regulation 

Mechanical

Torque

current & f 

Regulation

Figure 3-12. Typical variable speed motor drive and induction motor 

Since the power electronic controls have very high bandwidth and given the desalination 

system has a relatively large time constant, fast transients such as the pulse width-modulated 

switching of the power electronics were simplified to capture only the speed (frequency) and 

torque (current) control behaviors of the machine. The simplified model is shown in Figure 

3-13. The performance indicator control block regulates the speed by measuring the speed 

feedback from the motor. As already mentioned, the fast-acting current regulator was replaced 

by a gain with a variable torque limiter, whose value was provided by the WTG. This ensures 

the motor always operates within the available power supplied by the WTG. The output of the 

torque regulator is then subtracted from the load torque and the result fed to the integrator that 

represents the machine and pump inertia. One of the major improvements of this model is that 

it can consider variable power (current) from the WTG and regulate the current, and in turn 

control the torque and speed of the motor. 

21 
Veriable Speed Drive Motor 

Current 

Limiter 

1

Speed_ref PI gain J pus

- - Speed

Regulation Motor 

0 Current Inertia 

Regulation 

Speed_fbk T_load 

Figure 3-13. Simplified variable speed motor drive and motor model 

3.2.4 Reverse Osmosis Membrane Module 

The RO membrane module is a spiral-wound arrangement of a polyamide membrane (Figure 

3-14), contained in a high-pressure cylindrical vessel (Figure 3-15). In this arrangement, highsalinity water is pressurized to overcome the osmotic pressure against the membrane surface. 

By means of the RO principle, low-salinity water permeates through the membrane and is 

collected in the central perforated pipe. For given feedwater state (pressure, concentration, 

and temperature), the membrane physical characteristics dictate the permeate flow and 

concentration. 

Figure 3-14. RO spiral-wound membrane arrangement 

Feedwater 

Concentrate flow 

Permeate flow 

Spiral-wound element 

High-pressure vessel 

Figure 3-15. RO unit, membrane element contained in a high-pressure vessel 

22 
The RO elements are designed for continuous operation, receive a constant stream of 

feedwater, and generate constant streams of permeate and brine (or concentrate). Standard RO 

plants use constant operating pressures and flows, and may consider long-term adjustments to 

accommodate changes in the feedwater properties and changes in the filtration process caused 

by membrane degradation. 

The model developed for the RO element predicts the concentrate pressure flowrates of 

permeate and concentrate streams and their corresponding concentrations given the feed state 

(flow rate, concentration, pressure, and temperature) and the permeate pressure. The 

functional relationship is given in Eq. 3-9 by 

[Pc, Qp, Qc, Cp Cc] = RO_element(Qf, Cf, Pf, Pp, T) Eq. 3-9 

where 

Pc = Concentrate pressure, Pa 

Qp = Permeate flow rate, m3

/s 

Qc = Concentrate flow rate, m3

/s 

Cp = Permeate pressure, Pa 

Cc = Concentrate concentration, kg/m3 

Qf = Feed flow rate, m3

/s 

Cf = Feed concentration, kg/m3 

Pf = Feed pressure, Pa 

Pp = Permeate pressure, Pa 

T = Feed temperature, °C 

The membrane filtration behavior was predicted by the so called “solution-diffusion” model 

(see, for example, Meares 197610, Odendaal et al. 199611, Schwinge et al. 200412). This model 

takes into account the effect of membrane polarization; that is, the increment of concentration 

near the membrane interface in the brine channel caused by the salt released by the permeate 

flow. Our model solves the following solution-diffusion equations (Eq. 3-10) to calculate 

membrane behavior. 

J = { f − p − [ ( ) m π ( ) w A p p π c − cp ]}

Js = Jwc p = B(cm − cp ) Eq. 3-10 

w c = (c − c ⋅ psg) eJ / k + psg c m 

23 
where 

J = Water volumetric flux through the membrane, cm3

/cm2/s w 

Js = Salt mass flux through the membrane, g/cm2

/s 

A = Water permeability, cm/s/atm 

B = Salt permeability, cm/s 

k = Mass transfer coefficient, cm/s 

c = Concentration, g/l 

p = Pressure, atm 

c = (c f + cc )/ 2 

π ( ) c = Osmotic pressure corresponding to concentration c , atm 

psg = c p / cm , Salt passage 

Subindex f = Feed 

Subindex p = Permeate 

Subindex m = Membrane interface 

Subindex c = Concentrate 

The solution diffusion model depends critically on the membrane parameters k , A , and B . 

The mass transfer coefficient k depends on the water properties and the geometric dimensions 

of spiral-wound design. The permeabilities can be corrected by temperature and pressure. 

Details on these calculations can be found in Taniguchi et al. 200013 and Da Costa et al. 

199414 and references therein. The model developed under this program incorporates 

correction of permeabilities by temperature effects. 

The model for pressure drop in the brine channel, DP , is described by Eq. 3-11, where K is a 

constant. 

DP = K⎜

⎜

⎛

⎝

Qf 

2 

+ Qc ⎟

⎟

⎞

⎠

1.5 

Eq. 3-11 

There are several manufacturers of spiral-wound RO modules with similar performance 

characteristics. The RO models we developed are based on the commercial membrane 

elements TM820-370 for seawater and TM720-370 for brackish water, both by Toray 

Membrane America, Inc. 

The spiral-wound elements need to satisfy a set of operational constraints to achieve 

expected performance in terms of product quality, energy efficiency, maintenance costs, 

and membrane life. Typical operational limits are available from the manufacturers (see, 

for example, Toray design guidelines in Section 9. Table 3-1 summarizes the set of RO 

element constraints for seawater application, and Table 3-2 summarize the set of RO 

24 
element constraints associated with brackish water that are used for the calculations in this 

report. 

Table 3-1. Operational Limits for a Seawater Membrane Element 

Parameter Limit Meaning 

c c m / < 1.2 Polarization 

Pf < 1200 psi Feed pressure 

Qc > 15 gpm Concentrate flow 

w J < 20.6 gfd Permeate flux through membrane 

DP < 10 psi Pressure drop in the brine channel 

Table 3-2. Operational Limits for a Brackish Water Membrane Element 

Parameter Limit MEANING 

c c m / < 1.2 Polarization 

Pf < 600 psi Feed pressure 

Qc > 15 gpm Concentrate flow 

w J < 28.3 gfd Permeate flux through membrane 

DP < 10 psi Pressure drop in the brine channel 

The following simplifying assumptions have been used for the RO models: 

• The input/output behavior of one spiral-wound module can be predicted in its whole 

operating range by using the solution-diffusion equations with average water state 

along the element. 

• The flow within the RO element develops instantaneously for changes in the 

membrane pressure. 

• The time response of concentration c to changes in the model inputs can be modeled 

as in Eq. 3-12, where css is the steady-state value for concentration given by the 

solution-diffusion equations, s is the frequency variable for the Laplace transformation, 

and T is the time constant in seconds. 

1 

c = css Eq. 3-12 T s +1 

• The permeabilities A and B were assumed to be independent of the membrane

pressure. Typical pressure corrections can be found in Taniguchi et al. 2001.15

• Membrane degradation effects are not considered. 

25 
The RO element model can be used to represent the behavior of membrane elements, since 

the transport parameters are calculated based on geometric data and nominal permeability 

values, which are typically available from membrane manufacturers. The current model has 

been adjusted to represent seawater membranes that are commercialized by GE Water. The 

predicted input-output behavior was within 2% of the values of pressures, concentrations, and 

flows given by comparable models used by GE Water at the tested operational points. 

3.2.5 Reverse Osmosis Vessels and Banks 

Under typical operating conditions, a single RO element produces a permeate flow that is 

around 7% of the feed flow, that is, the element operates at a 7% recovery. To achieve higher 

recoveries in a single stage and reduce the impact of pretreatment costs (and to reduce the 

vessel capital costs), arrangements of several RO elements connected in series are commonly 

used within the same vessel. 

The physical model for a vessel with multiple RO elements is obtained by concatenation of 

several models of RO elements, and connects the concentrate channel of a given element to 

the feed channel of the following one. More precisely, a model of an n-element vessel is 

simply obtained by repeated use of the element model in Eq. 3-9, as follows in Eq. 3-13. 

[Pck, Qpk, Qck, Cpk, Cck] = RO_element(Qfk, Cfk, Pfk, 

Ppk, T) Eq. 3-13 

with Qfk =Qck-1, Cfk =Cck-1, Pfk =Pck-1 

The inputs to this vessel model are Qf1, Cf1, Pf1, Pp1 and T, and the outputs, Pcn, Qpn, Qcn, 

Cpn, Ccn. 

The maximum flow a vessel can handle is limited by the maximum diameter of the associated 

membrane element. Most spiral-wound manufacturers produce modules up to 8 in. diameter. 

For higher flows, several vessels are connected in parallel to achieve the desired flow (see 

Figure 3-16). 

Figure 3-16. Banks of RO vessels in a seawater desalination plant 

26 
Models of an entire bank of RO vessels connected in parallel are obtained from the vessel 

model in Eq. 3-13. Under the assumption that all the vessels in the same bank have identical 

input/output behavior, the model for the bank is obtained by multiplying the feed, permeate, 

and concentrate flows by the number of vessels in the bank. 

A seven-element vessel with membranes TM820-370 was developed and tested against 

the results of Toray software to determine the accuracy of the model in Eq. 3-1316. The 

pressures, concentrations, and flows for the individual elements were all within a 10% 

discrepancy with the Toray models. 

The constraints in Table 3-3 are observed for the RO system (in addition of those in Table 3-1 

and Table 3-2): 

Table 3-3. RO System Constraints 

Parameter LIMIT RATIONALE FOR CONSTRAINT 

dt 

dPf 

< 7.25 psi/s Feed pressure rate of change at the first element in an 

RO bank 

DP < 58 psi Pressure drop across an RO vessel 

3.2.6 Energy Recovery 

The RO desalination process is characterized by relatively small pressure drops across the 

vessel brine channel. That is, the concentrate flow conserves a large proportion of the energy 

available in the feedwater flow. Numerous ERDs have been designed to recover the energy in 

the concentrate stream and transfer it back to the feed flow stream to reduce the energy 

expended in feedwater pressurization (and hence, to improve the energy efficiency of RO 

desalination). These devices are commercially available in a wide range of technologies (see, 

for example, MacHarg 200117 and Liberman 200418 for ERD classifications and typical 

performances). 

The most efficient ERDs use positive displacement technology and achieve efficiencies of 

92%−96%. In this study, we model a work exchanger, which is a representative member of 

the positive displacement ERD class manufactured by Calder AG. 

The work exchanger transfers energy from the concentrate flow to the feedwater flow via a set 

of cylindrical vessels and low-friction pistons that travel along the vessel by the pressure 

difference. Typically, while one vessel is pressurizing the feedwater in work stroke, the other 

is discarding the concentrate at a low pressure in flush stroke. The work exchanger uses a set 

of valves and a control system to reverse the piston movements at the end of each stroke to 

achieve nearly continuous operation (see Figure 3-17). 

27 
Piston in 

Qc in, Cc in 

Qc out, Cc out 

Qf out, Cf out 

Qf in, Cf in 

High pressure work stroke High pressure 

feedwater concentrate 

Low pressure Piston in Low pressure 

feedwater concentrate flush stroke 

Figure 3-17. Work exchanger ERD 

The ERD model calculates the feedwater input and output flows Qfin and Qfout, and feedwater 

outputs concentration Cfout, and pressure Pfout as a function of the input concentrations Cfin, 

Ccin and the pressures Pcin, Pfin, Pcout. The functional relationship of this model is given in Eq. 

3-14 by 

[Qcin, Qfout, Cfout, Pfout] = WEER (Ccin, Cfin, Pcin, Pfin, Pcout) Eq. 3-14 

The ERD model accounts for leakage flow in the valves, mixing between concentrate and 

feedwater within the vessel, and overall pressure/flow characteristics, as given by the 

product specifications19. 

The model in Eq. 3-14 is static, and is assumed that the flow within the ERD develops 

instantaneously with changes in the input and output pressures. 

3.2.7 Water Pumps 

Models for the water pumps are necessary to represent the pressure heads obtained by the 

high-pressure, booster, and interstage pumps at design and off-design conditions, for any 

given rotational speed and flow. The pump models have the functional representation shown 

in Eq. 3-15: 

[H, η , P, T] = PMP_HP(Q,N) Eq. 3-15 

where 

H = Pressure head across the pump, psi 

η = Pump efficiency 

P = Power consumed, W 

T = Torque, lb ft 

The pump model developed for this program uses a parametric implementation of pump 

characteristics that is easily adapted for different commercial products and uses standard 

corrections for speed and flow at off-design conditions (see Veres 199420 and Karassik et al. 

197621). For the RO configurations presented in the following sections, pump models were 

developed according to the pump characteristics provided by the pump manufacturer FEDCO. 

28 
3.2.8 Energy Storage 

A simple battery model was developed to study the impact of energy storage in the operating 

strategies for grid-connected and grid-isolated wind turbine configuration. 

The battery model has only one state, the battery charge xc and is given by Eq. 3-16: 

x&b = Bp 

B p ≤ B p Eq. 3-16 max 

xb min ≤ xb < xb max 

where 

Bp 

= Power drawn from the battery, W 

B = Maximum charging and discharging rate for the battery, W p max 

xb min 

= Maximum charge, Joul 

xbmax = Maximum charge, Joul 

The battery model does not account for the effects of temperature, capacity, and efficiency 

degradation, which affect the performance of the cells. 

3.2.9 Valves 

The valve model calculates the flow Q as a function of the valve opening y, inlet and outlet 

pressures P1 and P2, according to Eq. 3-1722 

Q = y Cv 

( )

ρ

P 1 −P2 Eq. 3-17 

where 

C v = Valve flow coefficient 

ρ = Density, kg/m3 

Q = Volumetric flow, m3

/s 

3.2.10 Flow Junction 

Flow junction models are used to predict the concentration and flow of two or more water 

streams converging to a single stream by mass balance of water and salt. The functional form 

is shown in Eq. 3-18: 

[Qout, Cout] = FJn(Q1, C1, ..., Qn, Cn) Eq. 3-18 

where 

29 
C1 ... Cn = Concentration of input streams 1 to n, kg/m3 

Q1 ... Qn = Flow of input streams 1 to n, m3

/s 

Cout = Concentration of output stream, kg/m3 

Qout = Flow of output stream, m3

/s 

All the converging streams are assumed to be at the same pressure and temperature. 

3.2.11 Flow Network 

The flow network model is used to calculate pressures, flows, and concentrations throughout 

an RO plant under nominal and off-design conditions. The RO plant consists of a set of RO 

banks, pumps, valves, and flow junctions that are interconnected through pipes. The operating 

point of the system is dictated by the environmental variables (pressures, temperatures, and 

concentrations at the system interface) and by the set points of the available control knobs. 

Referring to Figure 3-18, for example, the external pressures are feed pressure P0, permeate 

pressure P15, and brine discharge pressure P16; the control variables are pump speeds N1 and 

N2, valve opening V1, and the number of active vessels S1. 

P0 

C0 

T0 

Q0 

DWEER 

RO > 

>

PMP_BS 

PMP_HP 

0 

1 

2 

3 

4 5 

6 

7 

8 

9 

11 12

N1 

N2 

V1 14 

S1 

P15 

P16 

16 

FJ3 

VA 

FJ2 

FJ2 

RO1 

Good permeate 

Bad permeate 

10 

13 

1-V1 

VA 

Figure 3-18. Flow network 

The network model uses the Newton-Raphson method to solve a set of algebraic equations 

(the pressure/flow characteristics and the energy and mass balances of every component)

22. 

The water temperature is assumed to remain constant throughout the RO system, and the 

friction losses are assumed to be small enough to neglect temperature changes in the water. 

The RO network’s limits of operation are given by the maximum and minimum speeds of the 

electrical motors and pumps, maximum and minimum flows in the ERD, water quality 

requirements, membrane limitations, and maximum number of vessels. 

30 
4 Cost of Water Calculation 

4.1 Steady-State Cost Model 

The cost model for the wind-powered desalination system consists of two major parts, the 

capital costs associated with purchased equipment and installed facilities required, and the 

operating costs incurred to produce freshwater permeate. The basis for all capital and 

operating costs is in year-end 2004 U.S. dollars/m3 product water. In cases where reference 

costs were found in previous years’ costs, the costs were recalculated in year-end 2004 dollars 

by applying the Marshall and Swift Index

23. The cost for a past year is multiplied by the ratio 

of the Marshall and Swift for 2004 over the Marshall and Swift index for that given year. 

Each specific cost model is based on the model analysis of the combined wind-RO system 

configuration. The wind power is used to drive a 1.5-MW electrical turbine that has a 36% 

capacity factor, which means that 540 kW of power are generated on average over the course 

of a year for a standard wind profile. Since each configuration is based on a 1.5-MW wind 

turbine system with 36% capacity factor, the steady-state analysis of the configuration gives 

the maximum output of water for that configuration and is the lower bound on the cost per 

unit water produced. 

4.1.1 Capital Costs 

4.1.1.1 Reverse osmosis system 

The capital cost model for each configuration includes three major sections: the purchased 

equipment costs, the direct capital costs, and the indirect capital costs. When combined, 

these form the total capital investment. This is a standard method for capital cost 

estimation24. Purchased equipment sizes are determined from the requirements of each 

configuration and the associated costs are from several sources. The chemical storage 

tanks, permeate product tank, and cartridge filter costs come from the Matches Web site 

(www.matche.com)

25, which is known in the chemical process industry as a source for upto-date estimates of equipment costs based on size and materials of construction. Pump 

costs are determined from correlation curves24 and software calculations26. RO 

membranes and housing costs were determined directly from recent RO system 

analyses27,28, and the ERD costs were determined from vendor information29. 

Once the capital costs for the RO, freight, and taxes (2% of purchased equipment costs) 

and miscellaneous charges (5% of purchased equipment costs) are added24, the delivered 

equipment total costs are obtained for the RO system. 

4.1.1.2 Energy system 

The wind turbine costs were based on the 1.5-MW turbine models and were determined by 

internal GE cost models for this equipment. The main components of the WTG system are 

shown in Table 4-1. The battery systems for extra power in low wind conditions were 

determined from power calculations and costs from internal GE resources. The wind turbine 

capital costs encompass the cost of electricity produced by the turbine and are amortized over 

the assumed 20-year lifetime of the turbine system. In this way, no operating costs are 

31 
associated with wind-generated electricity, only with grid-connected electricity. Since these 

energy capital costs include delivery, taxes, installation, and financing, they are added to the 

direct and indirect capital costs of the RO system. In this way the capital costs for the energy 

system are separated from those of the RO system. 

Table 4-1. Major Cost Components of a Wind Turbine System 

Wind turbine cost components 

Blades 

Aerodynamic control system 

Rotor hub 

Miscellaneous costs (labor for factory assembly) 

Low-speed shaft, bearings, and couplings 

Gearbox 

Generator 

Mechanical braking system 

Mainframe (chassis) 

Yaw system, including drives, dampers, brakes, and bearings 

Nacelle cover 

Work platform 

Tower 

Control and electrical systems 

4.1.1.3 Direct capital costs 

Next, the direct capital costs are calculated24 based on correlations for the chemical process 

industry, using the delivered equipment total costs as the basis. These costs include 

installation, instrumentation, controls, wiring, piping, valves, and facilities. The feed well 

development costs are also calculated here based on the flow requirement of feedwater and a 

500 m3

/d flow for each well of depth 50 m30. Combining the delivered equipment total costs 

and the direct capital costs gives the total direct capital costs associated with the 

configuration. Table 4-2 shows the calculations for these costs as a percentage of the 

delivered equipment total (DET)24. 

4.1.1.4 Indirect capital costs 

Indirect capital costs include engineering time, supervision, and contractor construction costs. 

These are estimated from the total direct capital costs

24. Engineering, supervision, and 

contractor construction costs are each 30% of the total direct costs, respectively. 

32 
4.1.1.5 Total capital investment 

The total of the direct and indirect capital costs, including the wind energy capital costs, is the 

total direct and indirect capital costs. The total fixed capital investment is found by adding a 

contingency factor to account for design issues, pricing changes, etc. (10% of the total direct 

and indirect capital costs). The working capital required for the project is the cash on hand for 

ongoing expenses incurred during construction and startup. It is 10% of the total fixed capital 

investment24, and is added to the total fixed capital investment to yield the total capital 

investment. This total capital investment represents the sum of all these costs, and is the 

capital required to design, buy, install, and construct the wind-powered desalination 

configuration. 

Table 4-2 Direct Capital Costs as a Percentage of DET Cost 

Direct Capital Expenditure % of DET 

Installation 40 

Instruments and Controls 20 

Piping and Valves (installed) 30 

Electrical 20 

Buildings 10 

Yard Improvements 20 

Service Facilities 5 

4.1.2 Operating Costs 

The other portion of water costs for desalination is the operating costs incurred during plant 

operation. The first major component of operating costs is total fixed costs related to interest, 

taxes, insurance, depreciation, labor, and maintenance. The other major variable is operating 

cost, which includes raw materials, utilities, and waste disposal costs. 

4.1.2.1 Interest on capital 

Interest payments for capital are based on the total capital investment and the interest rate 

using an amortization factor, a, shown in Eq. 4-130. The interest rate i, is taken as 8%, which 

is average for this type of cost estimation, and the plant lifetime n is taken as 20 years. 

i(1+ i)

n Eq. 4-1 a =

(1+ i)

n −1

4.1.2.2 Labor and maintenance costs 

Labor costs were determined from desalination industry standards/m3 of water30. Supplies and 

general maintenance are taken as 20% and 4%, respectively, of labor costs. Replacement costs 

for a membrane system, a battery system, and the wind turbine system are accounted for in 

annual operating costs based on the lifetime of the equipment. The membranes are assumed to 

last three years, the battery system 10 years, and the wind turbine 20 years. The total cost for 

33 
replacement is then divided by the lifetime in years and expensed annually. Routine 

maintenance on the wind turbine is broken out separately and based on GE average costs for a 

1.5-MW turbine system. 

4.1.2.3 Taxes, insurance, and depreciation 

Taxes and insurance are accounted for as 2% of total capital investment and depreciation is 

10% of total capital investment24. 

4.1.2.4 Total fixed costs 

Summing all interest, labor, maintenance, replacement, insurance, taxes, and depreciations 

costs yield the total fixed cost for annual operation. Since these costs are incurred 

independently of the RO system’s production level, they are referred to as fixed costs. 

4.1.2.5 Variable costs 

Costs that depend on the level of plant production are referred to as variable costs. These 

include the costs of raw materials, waste disposal, and utilities. The total permeate production 

is calculated by the number of operating hours in a year and the hourly permeate flowrate 

determined by the model configuration. This amount of water is the steady-state production 

basis for the cost model. 

The raw materials costs are based on chemical use for pre- and post-treatment of the water. In 

this model, the costs for a variety of chemicals have been included to meet any specific water 

treatment option. Sources for chemical costs are given in the references section28,31−32. For the 

configurations presented here, the two pretreatment chemicals used are sulfuric acid for pH 

adjustment and scale inhibitor to prevent fouling of the membrane system. Configuration 

model software from Toray Membrane America, Inc. determined the acid use, based on 

incoming feed and desired product pH of water33. Scale inhibitor use was taken as an average 

value of 0.05g/m3

 of permeate30. 

Waste disposal costs vary from site to site. In some sites, discharge of brine may be feasible 

(surface or well); in others waste disposal may be required. The model builds in a cost that 

can vary based on disposal amount and cost. For this model, an average of $0.018/m3

 is used 

to estimate these costs based on the volume of brine34. Chemical cleaning is sometimes 

periodically needed, although not desired, as the plant must be shut down. Any waste 

chemical solutions must be disposed at a cost. This model assumes that at most 0.1% of the 

volume product water will be used for chemical cleaning purposes. These waste disposal costs 

are small, even if the volume is 1% of the total product, and represents fractions of a penny 

per cubic meter of product. 

Wind-generated electricity costs are rolled into the wind turbine capital costs. Battery power 

is also accounted for in the capital costs. The only utility that is used is any grid electricity if 

the unit is connected to the grid and circumstances dictate that grid power should be used. In 

this case, the average COE is based on U.S. government statistics

35. 

34 
4.1.3 Total Cost 

By adding the total fixed costs to the total variable costs (annual operating costs) per cubic 

meter of permeate water product, the total cost of manufacturing is obtained in U.S.$/m3

 (or 

alternatively per 1,000 U.S. gallons of water produced). This number is also compared to the 

costs obtained from several references over the last six years

27,30,34,36,37. Costs from references 

are updated to end of year 2004 U.S. dollars by using the Marshal and Swift Index 

calculation. 

4.1.4 Example Calculations 

Tables 4-3−4-8 show example capital and manufacturing cost calculations for seawater and 

brackish water design configurations. The configurations will be described in more detail in 

section 5. The results shown here are the costs for the steady-state model configurations using 

a 1.5-MW turbine system as the source of power. 

35 
Table 4-3. Capital Costs for Seawater SW-WE-a1 Configuration 

36
Table 4-4. Manufacturing Costs for Seawater SW-WE-a1 Configuration 

37
Table 4-5. Capital Costs for Seawater SW-WE-a3 Configuration 

38
Table 4-6. Manufacturing Costs for Seawater SW-WE-a3 Configuration 

39
Table 4-7. Capital Costs for Brackish Water BW-WE-a1 Configuration 

40
Table 4-8. Manufacturing Costs for Brackish Water BW-WE-a1 Configuration 

4.1.5 Results 

The overall costs for seawater and brackish water, respectively, are summarized in Table 4-9 

and Table 4-10, along with the specific energy, which is defined as the ratio of the annual 

energy required to operate the plant to the total amount of permeate water produced. 

Comparisons to other calculations found in the references are also given. The reference 

calculations have been updated to year end 2004 U.S. dollars.23 

The data show that the total manufacturing costs for a 1.5-MW wind-powered seawater 

desalination system are about $1.22/m3

 of product on the scale of 5200−5700 m3/d of 

permeate product water, and using a specific energy of 2.3−2.5 kWh/m3

 of product water. 

This cost is about $0.20−0.80/m3

 lower than the references cited for nonwind-powered 

systems

27,30,34 and wind-powered systems36. The scale for the wind-powered system is 

somewhat larger than some of the references, and would thus have a somewhat lower cost. 

Also, specific factors such as energy costs and site development and waste factors can account 

41 
for the deviations from the wind-powered numbers. The specific energy consumption is on 

par with the references27,30,36,38,39. 

For brackish water, Table 4-10 gives a total manufacturing cost of about $0.59/m3

, and using 

a specific energy consumption of 0.74 kWh/m3

 of product water. This is in line with estimates 

for nonwind-powered systems costs27,37 and specific energy consumption37, although there are 

few data points for comparison. 

Table 4-9. Cost Comparisons for Seawater Desalination 

Design or Reference COW ($/m3

) Specific Energy 

(kWh/m3

) 

SW-WE-a1 1.20 2.27 

SW-WE-a3 1.24 2.48 

Dietrich and Robert [27] 

(1-10 MM gal/d permeate scale, 2005) 

1.51 2−3 

Hafez and El Manharawy [34] 

(4800 m3

/d permeate scale, 2002) 1.42 

Ettouney et al. [30] 

(4000 m3

/d permeate scale, 1992) 2.68 

5 

Ettouney et al. [30] 

(4546 m3

/d permeate scale, 1999) 1.48 

5 

Garcia-Rodriguez et al. [36] 

(3000 m3

/d permeate scale, Wind RO system, 2001) 2.01 

4 

Manth et al. [Error! Bookmark not defined.] (2003) 2−4 

MacHarg [Error! Bookmark not defined.] 2.5−3.5 

Table 4-10. Cost Comparisons for Brackish Water Desalination 

Design or Reference COW 

($/m3

) 

Specific Energy 

(kWh/m3

) 

BW-WE-a1 0.59 0.74 

Dietrich and Robert [27] Min Cost 0.11 

Dietrich and Robert [27] Max Cost 1.00 

Afonso et al. [37] (93,150 m3/d - large scale, 2004) 0.31 0.83 

42 
4.2 Cost of Water and Wind Statistical Representation 

Because of the stochastic nature and variability of the wind resource (and consequently the 

variability of the amount of power generated by a wind turbine) the RO water desalination 

plant is designed to operate at different levels of available power. In particular, for gridisolated plants, the amount of permeate (freshwater obtained from desalination) will vary with 

the power available for running the plant, and, evidently, with the speed of the wind available 

for generating that power. Specifically, at higher wind speeds, when more power is available, 

a feed stream of higher flowrate can be processed and more permeate can be obtained, and 

vice-versa. Consequently, the COW produced by the RO desalination plant is to be expected 

to vary over time, and computing an average/levelized COW over one year of operation is 

essential to realistically evaluate the economic performance of wind-powered RO 

desalination. 

In light of these facts, the objective of finding an optimal (from a COW point of view) windpowered RO desalination plant configuration was addressed in two steps: 

1. The optimal operating parameters of the RO desalination plant were computed, such 

that the maximum permeate flow is obtained for a given available power level. 

2. The optimization results from step 1 and the cost models presented earlier, along with 

statistical wind speed data, were used to size the RO plant so the average yearly COW 

is minimized. 

In step 1, the deterministic part of the system (the RO desalination plant) was analyzed, and 

the optimal operating parameters of the plant were computed, such that the maximum 

permeate flow is obtained for a given available power level. The input parameters available to 

control the plant operation are the speeds N (in rpm) of the pumps, the number S of RO 

vessels used in the RO banks, and the valve opening V of the permeate recycle streams. While 

we determined the optimal set points for these parameters at each power setting, we took care 

to satisfy all the economic and physical constraints imposed on the operation of the plant (see 

below for details particular to each configuration). Thus, the optimization problem in Eq. 4-1 

max Permeate Flowrate 

N ,S ,V 

subject to : Eq. 4-1 

Power = Available Power 

Operating Constraints 

was solved considering that the available power ranges of 70−1500 kW, and resulted in a 

table of optimal (from a maximum permeate flow rate point of view) input parameters as a 

function of the power available for operating the RO plant: Table 4-11 shows the prototype 

results. 

In Table 4-11, index j refers to the equipment or stream number; for example, if several 

pumps are installed in the plant, each will have its optimal setting: pump 2 at available power 

P1 would have the optimal rpm N2,1. 

43 
Table 4-11. Optimization Data Output Format for RO Plant 

Available 

Power, kW 

Optimal 

Nj rpm 

Optimal 

Sj (vessels) 

Optimal recycle 

Vj 

Maximum permeate flow, 

Qp, gpm 

P1 Nj,1 Sj,1 Vj,1 Qp,1 

M M M M M

Pn Nj,n Sj,n Vj,n Qp,n 

In step 2, the statistical description of the wind resource was used to obtain an average/ 

levelized SCOW for a plant where Sk RO vessels are installed (Eq. 4-2): 

SCOWk =

C0 (Sk ) + ∑n

j 1 

Cp (ROPower,Vj ,$e ) ⋅ wj 

+ ∑n Cc (ROPower,Vj ) ⋅ wj Eq. 4-2 =

Qk 

j=1 

where 

Co (Sk ) = the annual charges for a plant with Sk vessels, computed 

as the sum of the yearly fixed charges, capital 

depreciation, insurance premiums, and maintenance and 

warranty charges of the plant 

C (ROPower,Vj ) = the cost (per cubic meter of permeate) of chemicals, c 

consumables, and labor for a plant operated at a 

(possibly wind-speed dependent) power consumption 

ROPower 

Cp (ROPower,Vj ,$e ) = yearly cost of purchasing energy and the gains from 

selling energy, when the plant is operated at 

consumption ROPower, with the wind turbine 

producing the amount of power corresponding to the 

mean wind speed Vj , and the grid energy prices given 

by $. e

Qk = ∑n

j Qj (ROPower,Vj ) ⋅ wj is the average yearly or expected value of the permeate =1 

flow rate, computed under the same operating assumptions as above. 

Co (Sk ), Cc (ROPower,Vj ) , and Cp (ROPower,Vj ,$e ) are functional representations of the 

specific COW calculation algorithm presented in earlier in this section. 

A total number of n mean wind speeds Vj are considered, with their respective Weibull 

probabilities wj (Vj ) = f (Vj ) *

, so that ∑n 

= wj (Vj ) =1. 40 Hence, the average COW is 

j 1 

* wj (Vj ) = f (Vj ) effectively denotes the probability of the mean wind speed taking values in an 

infinitesimal interval around Vj . 

44 
obtained as the sum of the annual plant charges, the expected values of chemical costs, energy 

costs, divided by the expected value of yearly permeate flow rate. 

To determine the specific cost of water (SCOW), the power Pj generated by the wind turbine, 

for a given (Weibull-distributed) mean wind speed Vj , is computed from the turbine power 

curve. The Weibull probability density function describes the distribution of mean wind 

speeds at a standard height (10 m); wind speeds are therefore scaled to obtain the 

corresponding mean speeds at the height of the turbine hub: 

α

Vj,hub = Vj 

⎛

⎜

⎜

10m ⎞

⎟

⎟ Eq. 4-3

⎝ hhub ⎠

where 

α = 0.143 = the vertical shear exponent 

The power made available to and consumed by the RO plant, ROPower, and the power 

generated by the wind turbine, Pj, are equal only if a grid-isolated case with no energy storage 

is considered. For grid-connected configurations, the power consumption of the plant may at 

times exceed or be surpassed by the amount of power generated. When there is a mismatch 

between power production and consumption, the difference can be covered by purchasing 

energy from or selling energy to the grid. Also, energy can be drawn from or spent on 

charging a battery system. Energy purchases and sales have an impact on the SCOW, 

depending on the energy purchase and sale prices, $ , and are duly accounted for in the e

SCOW function. No cost is associated with disposing of the excess energy generated by the 

turbine; in case that energy cannot be sold to the grid. 

The calculation of the SCOW also takes into account that the plant cost and the SCOW 

increase as the number of RO vessels installed in the plant, Sk, increases. In the cost 

calculations, the operation of the plant is assumed to be flexible with respect to the number of 

RO vessels used. That is, when Sk vessels are in the plant, any number 1<Sactual<Sk of vessels 

may be used to achieve the maximum permeate flow rate for ROPower, the power available. 

When no grid connection is available, the plant will idle when the wind turbine does not 

generate power and no energy is stored, as the permeate flow rate is reduced to zero. The time 

intervals when the wind speed is too low for power generation (when the mean wind speed is 

below the generator cut-in speed) are also accounted for in computing the average SCOW. In 

such cases, SCOW is reduced to the specific fixed cost of the plant. 

4.3 Grid Power Prices 

The grid-connected configuration gives the system the flexibility to buy electricity when the 

wind speed is low, and sell the extra power when the wind speed is high. However, selling 

power depends on the contractual agreement between the power seller and the utility. The 

utility usually purchases the excess electricity at the wholesale or “avoided cost” price, which 

is much lower than the retail price. Some states have legislatures that require at least some 

utilities to offer net metering, which means that a customer who produces excess electricity 

can deliver it to the local utility, spinning the utility meter backward and gaining a credit, 

45 
which can be used later when power is needed from the grid. This provides the customer with 

full retail value for all the electricity produced. So far most net metering applies only to small 

wind turbine, PV or other generation sources.41 This study assumed no net metering and that 

the extra power will be sold back to the grid at a negotiated price, which is assumed to be a 

small percentage of the buying price. 

46 
5 Wind Desalination Configurations 

5.1 Overall System Requirements 

Wind desalination may be a viable alternative for increasing the availability of potable water 

in inland and coastal regions. As such, different desalination topologies must be evaluated for 

these two cases. In the inland application, wind desalination will primarily be dedicated to the 

purification of brackish water, which is is typically defined to be less than 10,000 ppm of 

TDS. A potential complicating factor for inland and coastal areas is grid connectivity. Hence, 

understanding the operational impact on the desalination system under various scenarios is 

important. One configuration described in this section will be analyzed further with regard to 

the following grid connectivity scenarios: 

• Wind turbine and desalination plant grid connected 

• Wind turbine and desalination plant coupled with the capability to purchase energy 

from the grid 

• Grid independence with energy storage. 

To effectively examine these system variants, a set of topologies for seawater and brackish 

water conditions is investigated in this work. For the seawater case, a single-stage and a twostage system are investigated. For brackish water, a two-stage system is investigated. Based 

on the design analysis, a single configuration is selected for further design with respect to 

plant sizing and operations. The methodology that is developed for the selected configuration 

is applicable to other configurations and presents a general framework for defining a wind 

desalination facility. 

5.1.1 Design Goals and Design Process Overview 

The main criteria for each wind-RO design are that it provides reasonable RO system 

parameters, is flexible to model inputs, and matches the power outputs of the wind turbine to 

the power requirements of the RO system. The design begins with the wind power available 

to accomplish these tasks. In this case a 1.5-MW wind turbine was chosen as the base-case 

power source because it is a standard GE model that is deployed in field applications and it 

allows for easy scale-up by employing a series of these turbines to produce the desired power. 

The output power of these turbine systems varies depending on the wind profile. For this case, 

a class II wind profile is assumed, which gives a turbine capacity factor of 36%. This means 

that the 1.5-MW turbine will provide on average 540 kW of power for the RO system. 

Standard single- and two-stage systems were considered for the RO model. The single-stage 

system takes a saline feed and provides product permeate to meet specifications in a single 

pass; the two-stage system takes brine output from the first stage and further removes water 

from it to increase product output. Pumps are used at each stage to achieve proper pressures 

for RO. In addition, an ERD (dual work exchanger energy recovery [DWEER] or turbine 

type) is used to recover the output energy of the waste brine and pressurize feed into the 

membranes. Schematic designs of the two systems are shown in Figure 5-1 and Figure 5-2. 

47 
Acid tank 

Filter Pump 

Seawater 

Feed - Well 

Filter 

Filter 

Feed 

Filter 

Solids 

RO Feed 

Pump 1 

High-P 

Main 

RO Feed 

RO-1 

Permeate 1 

Concentrate 1 

RO-2 

Permeate 2 

Concentrate 2 

DWEER 

Low-P Brine Out 

Low-P 

Feed Bypass 

Low-P 

Feed 

HP 

RO Make-up 

Feed 

Product Water 

Acid Pump 

Acid 

Feed 

RO-2 

Feed 

Inter-Bank 

Booster Pump 

High-P 

Combined 

RO Feed 

RO Feed 

Pump 2 

Feed 

Booster 

Pump 

Figure 5-1. Schematic diagram of two-stage RO membrane system 

Acid tank 

Filter Pump 

Seawater 

Feed - Well 

Filter 

Filter 

Feed 

Filter 

Solids 

RO Feed 

Pump 

High-P 

Feed 

RO-1 

Permeate Product 

Concentrate 

DWEER 

Low-P Brine Out 

Low-P 

Feed Bypass 

Low-P 

Feed

 Make-up 

Feed 

Acid Pump 

Acid 

Feed 

Booster 

Pump 

High-P 

Make-Up 

Feed 

High-P 

RO Feed 

Figure 5-2. Schematic diagram of a single-stage RO membrane system 

Power calculations on the pumps determine the amount of power required to pump a given 

flow through the RO system. The flow rates and pressures are set to nominal values that are in 

the ranges necessary for the RO to operate, with typical membrane recoveries of 35%−45% 

for seawater and 75%−85% for brackish water. This power is then compared to the available 

power from the wind turbine. The system flow is then adjusted and the power recalculated. 

This iteration is continued until the power requirements of the pumps in the RO system match 

the wind turbine output. The overall pump power calculation is given in Eq. 5-1. 

48 
P = H Q Eq. 5-1

ε

where 

P = the power 

H = the head pressure difference between the inlet and outlet streams 

Q = the stream flow-rate 

ε = the overall pump efficiency 

The schematic energy iteration calculation is given in Figure 5-3. Once the nominal values are 

obtained from this power calculation, they are applied to specific steady-state design 

configurations and optimized with RO system calculation software

33 to arrive at a specific RO 

design that meets the design parameters for water quality and power requirements. When the 

design is optimized to meet these criteria, a capital and operating cost model is applied (see 

Section 4 of this report) to obtain an overall COW for this steady-state configuration. 

With this baseline design and cost complete, the configuration is then simulated with the 

combined wind-RO system model to develop a transient configuration model that accounts 

for variations in wind, water output, and optimization strategies. A cost for each strategy is 

then developed. 

49 
Inputs 

Q, H, ε, RO % Recovery, 

Wind Class, tolerance 

Calculate Wind Power 

Available PA 

Calculate Pump 

Power Requirements 

PR 

PR ≈PA 

within tolerance 

Update Q & H values 

No 

Yes 

Output become

Steady State

Model Inputs

H, Q, ε, % Recovery

Figure 5-3. Flow chart for determining RO configuration inputs 

5.1.2 Constraint Description 

The analysis that follows explicitly accounts for the physical and operational constraints in the 

wind desalination system, including the power generation constraints in the wind turbine 

(Section 3.2.2), RO constraints (Table 3-1, Table 3-2, and Table 3-3), and speed limitations 

for the electrical drives and pumps. Some design parameters like maximum number of RO 

vessels were left unlimited, because the purpose of this section is to obtain entitlement 

analysis; sizing of these parameters is handled in Section 6. 

5.2 Seawater 

The seawater RO design objective is to obtain a viable commercial wind/RO system 

configuration that can provide purified product water at a cost that is competitive with 

traditionally powered RO systems. Because there is a plentiful supply of seawater in many 

50 
areas of the world where there is no power infrastructure, or where energy costs are high, 

designing a wind-powered RO system that can produce competitively priced water is 

desirable. The challenges are that seawater dissolved solids can vary greatly. Other solid 

contaminants also pose an issue, as they must be removed by settling or filtration before RO 

treatment. Also, the corrosiveness of seawater requires attention to materials of construction 

in system design. For the seawater systems to be considered, the TDS of the feed seawater is 

taken as ~35,100 ppm. Table 5-1 shows the breakdown of cations and anions in the model 

seawater considered, which is taken as typical seawater from the Toray RO model program33. 

Table 5-1. Model Seawater Feed Composition 

Component Concentration 

(ppm) 

CATIONS 

Calcium 408 

Magnesium 1,298 

Sodium 10,768 

Potassium 388 

ANIONS 

Bicarbonate 143 

Chlorine 19,380 

Sulfate 2,702 

Boron 1.1 

Phosphate 0.5 

Carbonate 2.29 

NON-VALENT 

Silicon Dioxide 15 

Carbon Dioxide 2.4 

TDS 35,106 

pH 7.8 

Taking this input and the methodology outlined in section 5.1.1, steady-state models for the 

single-stage and two-stage RO systems were developed. The design goals were to provide the 

maximum amount of water for the given power input (product yield) and the water quality to 

meet World Health Organization (WHO) standards42 (product quality). Because product yield 

and quality typically are at odds with one another, some different RO system sizes and 

pressure and pumping schemes were considered for the given power requirements. 

51 
5.2.1 SW-WE-a1 System Design 

The first design considered was a two-stage RO system, with energy recovery and the option 

of interstage pumping to boost pressure in the second stage. This model is designated SWWE-a1. The SW refers to seawater, the WE is for work exchanger (energy recovery) and the 

a1 design is a two-stage system (Figure 5-1). In performing the power calculations outlined in 

section 5.1.1, two design options concerned the interstage boost and the DWEER described in 

section 3.2.6. The first option was to provide a pump to boost the brine outlet pressure from 

the first stage before entering the second stage. The second was to provide a booster pump to 

the feed, which has already recovered energy from the DWEER, but is still at a lower pressure 

than the main feed system to the RO unit. Based on a power and pressure study of each of 

these possible configurations, there were only two viable alternatives: (1) to provide an 

interstage booster pump (Figure 5-4), which precludes the necessity of a post-DWEER 

booster pump, since the brine pressure out of the second stage is high enough to power the 

DWEER so the DWEER feed pressure is equal to that of the main feed pressure; and (2) to 

use no interstage boost, and therefore, a booster pump is needed after the DWEER to provide 

the necessary makeup feed pressure (Figure 5-5). Acid tank 

Filter Pump 

Seawater 

Feed - Well 

Filter 

Filter 

Feed 

Filter 

Solids 

RO Feed 

Pump 1 

High-P 

Main 

RO Feed 

RO-1 

Permeate 1 

Concentrate 1 

RO-2 

Permeate 2 

Concentrate 2 

DWEER 

Low-P Brine Out 

Low-P 

Feed Bypass 

Low-P 

Feed 

HP 

RO Make-up 

Feed 

Product Water 

Acid Pump 

Acid 

Feed 

RO-2 

Feed 

Inter-Bank 

Booster Pump 

High-P 

Combined 

RO Feed 

RO Feed 

Pump 2 

Feed 

Booster 

Pump 

Figure 5-4. SW-WE-a1 configuration with interstage boost 

Power is then calculated with nominal values for pressure and flow until a value for the total 

power is about 540 kW. This gives a baseline for the configuration. 

Next, the RO membrane steady-state model33 is applied to determine the appropriate 

configuration for the RO part of the configuration. This model uses the feed described in 

section 5.2, and is optimized with the constraints detailed in Table 5-2. These constraints have 

been determined by industry design standards, and the capabilities of the membranes 

manufactured by Toray Membrane America, Inc.33 

52 
Acid tank 

Filter

Feed Seawater

Feed - Well

Filter Pump 

Low-P Brine Out 

Filter 

Filter 

Solids 

RO Feed 

Pump 1 

High-P 

Main 

RO Feed 

RO-1 

Permeate 1 

RO-2 

Permeate 2 

Concentrate 2 

DWEER 

Low-P 

Feed Bypass 

Low-P 

Feed 

HP 

RO Make-up 

Feed 

Product Water 

Acid Pump 

Acid 

Feed 

RO-2 

High-P 

Feed 

Inter-Bank 

Booster Pump 

Combined 

RO Feed 

RO Feed 

Pump 2 

Feed 

Booster 

Pump 

Concentrate 1 

Figure 5-5. SW-WE-a1 configuration with DWEER feed boost

Table 5-2. Membrane Design Parameters 

Parameter Value/Range REMARKS 

Feed Flow Lower limit > 15 gpm on the last element in the 

train 

gpm = gal/min 

Permeate Flux Seawater: 8 < gfd <12 (13−21 lmh) 

Brackish: 10 < gfd < 16 (17−27 lmh) 

gfd = gal/ft

2

/d; lmh 

= liter/m2

/h 

Limits: scaling, feed 

P and osmotic P 

Feed Pressure Seawater: 1000 psig/70 bar 

Brackish: 600 psig/41 bar 

Pressure Drop < 20 psi (1.4 bar)/module 

< 60 psi (4.0 bar)/vessel 

Limitation by 

membrane 

structure 

Permeate < 500 ppm TDS-250 NaCl-0.5 ppm Boron WHO limits42 

RO Recovery Seawater: 35%−45% Brackish: 70%−80% 

Temperature < 45°C (113°F) for operation Element limitations 

Fouling 10% permeate flux decline per year 

Membrane Lifetime 3−5 years 

53 
5.2.1.1 Filter model 

In both designs, the primary feed is from a seawater well, which required filtration of any 

suspended solids. This filter is modeled with a standard design equation24, which is detailed in 

Eq. 5-2. 

2 2A2 (ΔP)

(1−s)

θ ' V + 2AVFV = Eq. 5-2

α'Wμ

Inputs 

V = Filtrate volume – amount of water to be pretreated by filter (m3) 

ΔP = Pressure drop – determined by feed pump power draw as the input pressure, 

and assumes atmospheric pressure after filter. Design based on maximum 

ΔP(N/m2

) 

ρc = Filter cake density (dry solids per volume we filter cake, kg/m3

) 

W = Solids conc. in solution (dry solids per volume solid–free liquid, kg/m3

) 

μ = Solution viscosity (N-s/m2

) 

θ’ = Filtration time – Determined by time for a given filtration. Design based on 

minimum time for filtration (s) 

Constants – Empirically Determined or Use Industrial Correlations 

VF = Filtrate volume constant related to filter cake thickness (m3/m2

ѕ = Compressibility exponent of filter cake (dimensionless) 

α’ = Cake resistance constant = (α)/(ΔP)s (s m2

/kg) 

α = Specific filter cake resistance = C/ρc (s m2

/kg) 

C = Proportionality constant for cake resistance and cake thickness 

Outputs 

A = Filter area (m2) 

Cost = Capital cost for the filter ($) 

The solution to Eq. 5-2 is typically accomplished in two stages. The first is to use empirical 

data from the fluid/solid system to be filtered to determine some of the model parameters. 

Typically, this is done in a laboratory with a small-scale test. In this case, numbers from 

typical filtration systems were used24,43 with the method described in Figure 5-6. 

 For at least two or three values of constant ΔP experimental data, plot θ’ΔP/(V/A) 

versus (V/A) to give slope α’wμ(ΔP)s

/2 and intercept α’wμVF(ΔP)s 

 Log (slope) = s Log ΔP + Log (α’wμ/2) 

 Log (intercept) = s Log ΔP + Log (α’wμVF) 

 Plot ΔP versus Slope to get experimental values of s and α’wμ/2 

 Plot ΔP versus Intercept to get experimental values of s and α’wμVF 

 Check data for consistency and arrive at values of s, α’, and VF 

Figure 5-6. Algorithm for solving first stage of filtration model equation 

54 
The next step is to then apply the known values of variables and constants to Eq. 5-2, and 

then rearrange the equation to solve for the area, A, of the filter required to separate solids 

at a given concentration in a feed fluid, using a defined pressure gradient. This 

rearrangement is shown in Eq. 5-3, where the right-hand term of the equation is subtracted 

from both slides, leading to a quadratic equation, whose solution is given in Eq. 5-4. 

[(2(ΔP)(1-s)θ ')/(α'wμ)] A2 - (2VFV)A - V2 = 0 Eq. 5-3 

(4VF

2V 2) ± {(4VF2V 2) + 4V 2[(2(ΔP)(1−s)

θ ') /(α' wμ)]} 

A = Eq. 5-4

[4(ΔP)

(1−s)

θ '/(α'wμ)] 

The positive value for A is taken as the real solution to the model equation. From the 

power calculations for the SW-WE-a1 configuration, the volumetric flow rate V is given. 

In turn, the surface area, A, of the filter can be calculated from the above equation, and 

then the capital cost of the filter can be determined24,25. This cost is then included in the 

cost model of section 4.1. 

5.2.1.2 Power and reverse osmosis model optimization 

We used the design parameters from Table 5-2 and the flows from the power calculations 

to optimize the steady-state membrane model, which uses software developed by Toray 

Membrane America, Inc.33. Feed inputs are the composition of the feed, the feed flow rate, 

and any feed pretreatment (pH adjustment, scale inhibitor, etc.). The RO unit inputs are 

the type of membrane, the RO recovery, the number of stages, the number of RO elements 

per vessel, the membrane fouling factor, the salt passage rate per year, the age of the 

membrane, and the permeate backpressure. The model then converges to a solution for the 

ion concentrations in the brine and permeate streams by use of the flux equation across a 

membrane shown in Eq. 5-5 and Eq. 5-6. 

J sol = Ksol (Mcb − c p ) Eq. 5-5 tm 

M = cw / cb Eq. 5-6 

where 

Jsol = the flux across the membrane 

Ksol = the permeability of the membrane to the solvent 

tm = the membrane thickness 

M = the polarization modulus 

cb = the bulk ion concentration 

cp = the permeate ion concentration 

cw = the ion concentration at the membrane wall 

55 
The membrane flux, ion concentrations, and stream pressures are determined for each element 

and each stage of the model. Once converged, the model gives a steady-state output from the 

system. These outputs include the overall flows and pressures of each stream, the ion 

concentrations in each stream, and the individual and overall fluxes for the RO membrane 

system. 

At each convergence of the RO model, the output flows and pressures from the membrane 

model were plugged back into the pump power calculations to see if the power was still 

optimal at about 540 kW. Since the feed flow is the largest power draw on the system, if the 

power was too low, the feed flow to the membrane model was increased. If the power was too 

high, the feed flow was decreased. This cycle was iterated until the maximum flow for the 

given power input through an RO system was achieved. Figure 5-7 and Figure 5-8 show the 

results of this optimization for the power calculations that represent the configurations in 

Figure 5-4 and Figure 5-5, respectively. The RO steady-state model outputs are found in 

Appendix A, which refers to the interstage boost case, and data from the DWEER boost case. 

The interstage boost design of Figure 5-4 was optimized for the first stage of 50 vessels by six 

elements per vessel, followed by a second stage of 38 vessels by six elements per vessel. Each 

stage uses a Toray Membrane America, Inc. Model 820-370 seawater membrane. Appendix A 

details the specifications of this type of membrane. The DWEER boost design of Figure 5-5 

was similarly optimized to 50 x 6 and 38 x 6 model configurations. Both design scenarios 

obtain the same optimal RO configuration, as the placement of the boost before the second 

stage or after the DWEER does not affect the overall design. In the case of interstage boost, 

the second stage operates at a higher pressure, with slightly greater recovery of permeate from 

this stage, but since the constraints on the input energy, the membrane flux and feed pressure 

limit the amount of permeate in the second stage, the optimization shows that there is no 

design difference in the RO elements for the two design cases (interstage boost or DWEER 

boost). 

56 
Figure 5-7. Power calculations for SW-WE-a1 design with interstage boost 

Figure 5-8. Power calculations for SW-WE-a1 design with DWEER boost 

57
We used the RO membrane design reports and the power calculations to develop an overall 

process flow diagram for each SW-WE-a1 configuration. The interstage boost case is shown 

in Figure 5-9 with calculations shown in both English and metric units. A similar flow 

diagram is shown for the DWEER boost case in Figure 5-10. English units for flow, pressure, 

and flux are gal/min (gpm), pound-force/in2

 (psia), and gal/ft2/d (gfd), respectively. 

Corresponding metric units are m3

/h (cmh), bar, and liter/m2/h (lmh). 

Acid tank 

1050 GPM 713 GPM 15 PSIA 15 PSIA TDS 255 PPM 0.05 GPM TDS 187 PPM 

Filter Pump 

Seawater 

Feed - Well 

Filter 

Filter 

Feed 

Filter 

Solids 

RO Feed 

Pump 1 

High-P 

Main 

RO Feed 

RO-1 

Permeate 1 

Concentrate 1 

RO-2 

Permeate 2 

Concentrate 2 

DWEER 

Low-P Brine Out 

Low-P 

Feed Bypass 

Low-P 

Feed 

HP 

RO Make-up 

Feed 

Product Water 

Acid Pump 

Acid 

Feed 

RO-2 

Feed 

Inter-Bank 

Booster Pump 

High-P 

Combined 

RO Feed 

RO Feed 

Pump 2 

Feed 

Booster 

Pump 

2625 GPM 

2625 GPM 

45 PSIA 

2625 GPM 

30 PSIA 

1546.6 GPM 

30 PSIA 

1546.6 GPM 

733 PSIA 

1078.4 GPM 

30 PSIA 

2625 GPM 

731 PSIA 

B 0.25 PPM 

337 GPM 

15 PSIA 

TDS 398 PPM 

B 0.43 PPM 

B 0.31 PPM 

1912 GPM 

715 PSIA 1912 GPM 

757 PSIA 

1575 GPM 

742 PSIA 

1575 GPM 

15 PSIA 

27.2% Recovery 

9.27 GFD 

50 x 6 elements 

TM830-370 

17.6% Recovery 

5.76 GFD 

38 x 6 elements 

TM830-370 

30 PSIA 

1078.4 GPM 

731 PSIA 

Acid tank 

238.4 CMH 161.9 CMH 1.03 Bar 1.03 Bar TDS 255 PPM 0.012 CMH TDS 187 PPM 

Filter Pump 

Seawater 

Feed - Well 

Filter 

Filter 

Feed 

Filter 

Solids 

RO Feed 

Pump 1 

High-P 

Main 

RO Feed 

RO-1 

Permeate 1 

Concentrate 1 

RO-2 

Permeate 2 

Concentrate 2 

DWEER 

Low-P Brine Out 

Low-P 

Feed Bypass 

Low-P 

Feed 

HP 

RO Make-up 

Feed 

Product Water 

Acid Pump 

Acid 

Feed 

RO-2 

Feed 

Inter-Bank 

Booster Pump 

High-P 

Combined 

RO Feed 

RO Feed 

Pump 2 

Feed 

Booster 

Pump 

596.2 CMH 

596.2 CMH 

3.1 Bar 

596.2 CMH 

2.07 Bar 

351.3 CMH 

2.07 Bar 

351.3 CMH 

50.5 Bar 

244.9 CMH 

2.07 Bar 

596.2 CMH 

50.4 Bar 

B 0.25 PPM 

76.5 CMH 

1.03 Bar 

TDS 398 PPM 

B 0.43 PPM 

B 0.31 PPM 

434.3 CMH 

49.3 Bar 434.3 CMH 

52.2 Bar 

357.7 CMH 

51.2 Bar 

357.7 CMH 

1.03 Bar 

27.2% Recovery 

15.74 LMH 

50 x 6 elements 

TM830-370 

17.6% Recovery 

9.78 LMH 

38 x 6 elements 

TM830-370 

2.07 Bar 

244.9 CMH 

50.4 Bar 

Figure 5-9. SW-WE-a1 interstage boost flow diagram 

58 
Acid tank 

Filter Pump 

Seawater 

Feed - Well 

Filter 

Filter 

Feed 

Filter 

Solids 

RO Feed 

Pump 1 

High-P 

Main 

RO Feed 

RO-1 

Permeate 1 

Concentrate 1 

RO-2 

Permeate 2 

Concentrate 2 

DWEER 

Low-P Brine Out 

Low-P 

Feed Bypass 

Low-P 

Feed 

HP 

RO Make-up 

Feed 

Product Water 

Acid Pump 

Acid 

Feed 

RO-2 

Feed 

Inter-Bank 

Booster Pump 

High-P 

Combined 

RO Feed 

RO Feed 

Pump 2 

Feed 

Booster 

Pump 

2600 GPM 

2600 GPM 

45 PSIA 

2600 GPM 

30 PSIA 

1532 GPM 

30 PSIA 

1532 GPM 

753 PSIA 

1068 GPM 

30 PSIA 

2600 GPM 

753 PSIA 

743 GPM 

15 PSIA 

TDS 185 PPM 

B 0.25 PPM 

297 GPM 

15 PSIA 

TDS 449 PPM 

B 0.47 PPM 

1040 GPM 

15 PSIA 

TDS 260 PPM 

B 0.31 PPM 

1857 GPM 

737 PSIA 

1560 GPM 

723 PSIA 

1560 GPM 

15 PSIA 

28.6% Recovery 

9.66 GFD 

50 x 6 elements 

TM830-370 

0.05 GPM 

30 PSIA 

1068 GPM 

753 PSIA 

1532 GPM 

715 PSIA 

16.0% Recovery 

5.08 GFD 

38 x 6 elements 

TM830-370 

Acid tank 

Filter Pump 

Seawater 

Feed - Well 

Filter 

Filter 

Feed 

Filter 

Solids 

RO Feed 

Pump 1 

High-P 

Main 

RO Feed 

RO-1 

Permeate 1 

Concentrate 1 

RO-2 

Permeate 2 

Concentrate 2 

DWEER 

Low-P Brine Out 

Low-P 

Feed Bypass 

Low-P 

Feed 

HP 

RO Make-up 

Feed 

Product Water 

Acid Pump 

Acid 

Feed 

RO-2 

Feed 

Inter-Bank 

Booster Pump 

High-P 

Combined 

RO Feed 

RO Feed 

Pump 2 

Feed 

Booster 

Pump 

590.5 CMH 

590.5 CMH 

3.1 Bar 

590.5 CMH 

2.07 Bar 

347.9 CMH 

2.07 Bar 

347.9 CMH 

51.9 Bar 

242.6 CMH 

2.07 Bar 

590.5 CMH 

51.9 Bar 

168.8 CMH 

1.03 Bar 

TDS 185 PPM 

B 0.25 PPM 

67.5 CMH 

1.03 Bar 

TDS 449 PPM 

B 0.47 PPM 

236.3 CMH 

1.03 Bar 

TDS 260 PPM 

B 0.31 PPM 

421.8 CMH 

50.8 Bar 

354.3 CMH 

49.9 Bar 

354.3 CMH 

1.03 Bar 

28.6% Recovery 

16.4 LMH 

50 x 6 elements 

TM830-370 

242.6 CMH 

51.9 Bar 

347.9 CMH 

49.3 Bar 

16.0% Recovery 

8.62 LMH 

38 x 6 elements 

TM830-370 

0.012 CMH 

2.07 Bar 

Figure 5-10. SW-WE-a1 DWEER boost flow diagram 

59 
Based on a comparison of the two configurations, the interstage boost configuration produces 

about 68% of the product in the first stage and 32% in the second stage. In the DWEER boost 

configuration, the first stage produces 71% of the product, with 29% in the second stage. The 

results indicate nearly equal performance of the two configurations in both production amount 

and product quality. 

5.2.1.3 Boron sensitivity analysis 

The level of Boron in permeate water is now set to 0.3-0.5 ppm by WHO42. To understand the 

sensitivity of this configuration to Boron, we increased its feed level to determine what level 

of Boron in the feed would cause it to break through in the permeate to a level of 0.5 ppm . 

We used the steady-state RO membrane model33 to determine that the level of Boron in the 

feed that results in a 0.5-ppm level in the product permeate is 1.8 ppm for the interstage boost 

and DWEER boost designs. Since there is large variation in seawater Boron levels, any 

feedwater with Boron levels higher than 1.8 ppm would require a redesign of the system for a 

specific situation. 

One way is to lower recovery on the current configurations to increase salt rejection, which 

will lower product output. This is the quality/productivity trade-off. For example, lowering 

the overall recovery of the current configurations from 40% to 30% (a 10% decrease), and 

reducing the array configuration to 45 x 6 on the first stage and 30 x 6 on the second stage 

allows for the same permeate flow and power use as the base configurations. In this type of 

configuration, the increase in the feed Boron level is only to about 2 ppm (11% increase) to 

still meet the 0.5 ppm limit. There is little room for improvement in the current design to 

higher Boron levels. Therefore, if Boron levels are higher than 2 ppm, the best design option 

would be to have another RO Boron removal stage for the permeate only. This would require 

extra capital costs and increase energy consumption. Either a smaller production plant or 

larger wind turbine would be required to compensate for the increased energy use. Those 

trade-offs in capital and operating expenses versus productivity would have to be assessed on 

specific high-Boron feed cases. 

5.2.2 Cost of Water Analysis 

Based on the above design, an overall COW is determined by calculating capital and 

operating costs for the configuration as outlined in detail in section 4.1. Because the only real 

difference between the SW-WE-a1 interstage boost configuration and the DWEER boost 

configuration is the placement and size of the booster pump, the capital and operating costs 

for these two configurations are virtually identical. A cost summary that outlines the relevant 

capital and operating costs for the steady state model is shown in Figure 5-11. The model 

assumes an operating year is 350 days, with a permeate flow rate of 5723 m3

/d (1,050 gpm). 

This yields an annual production of 2 x 106 m3

/yr of product water. Rolling up all the capital 

and operating costs for this production level gives an overall steady-state COW of about 

$1.20/m3

. This cost can vary for a site-specific situation, where well construction costs, feed 

concentrations, and waste disposal costs can vary. The steady-state cost model, however, is 

flexible and can make provisions for these cost variances (see section 4.1). 

60 
Figure 5-11. Summary costs for the steady-state SW-WE-a1 configuration 

5.2.3 Design Space Analysis 

We conducted a design space analysis to understand the extent of the operating envelope 

associated with the configuration described in Section 5.2.1. The main purpose of this study is 

to investigate the points in the input space at which the system fails to satisfy all the 

component and system constraints. If the system were operated at these points, where the 

constraints were not met, the potential for membrane degradation through fouling or scaling 

or membrane destruction caused by increased stresses may result. In addition to understanding 

where constraints are violated, the design space study provides some insight into how system 

quantities of interest such as recovery ratio, specific energy consumption, total power and 

permeate flow vary with the choice of input parameters. The qualitative understanding that 

the design space study provides is critical for understanding the potential for system 

optimization. 

For the two-stage configuration shown in Figure 5-12, the input space is defined by the 

parameters listed in Table 5-3. 

61 
Sum 

Flow 

Valve 

FeedwaterInlet

Conditions of

pressure (p0),0

concentration (c0)

and temperature

(t0)

Permeate Exit

p21

V1 16

Brine Exit Pressure P22 DWEEREnergy Recovery 

RO > > 

> RO 

Interstage 

Pump 

Booster Pump 

HP Pump 

1 

2 

3 

4 5 

6 

7 

8 

9 

10 

11 

12 14

17 

13 

N1 

N2 

N3 

19 

S1 S2 

22 

Flow 

Sum 

Flow 

Sum 

RO1 RO2 

V2 Valve 

V4 

Valve 

V3 Valve 

20 

DWEEREnergy Recovery

RO >

>

> RO

mp

1

5

8

9

10

11

12 14

17

13

N1

N2

N3

19

S1 S2

22

Flow

Flow

Sum

Sum

V2 Valve

V3 Valve

20

Brine Exit

Interstage

Pump

Booster Pump

HP Pu

2

3

4

6

7

Sum

Flow

RO1 RO2

V4

Valve

 Pressure P22 DWEEREnergy Recovery

RO >

>

> RO

Interstage

Pump

Booster Pump

HP Pump

1

2

3

4 5

6

7

8

9

10

11

12 14

17

13

N1

N2

N3

19

S1 S2

22

Flow

Sum

Flow

Sum

Flow

Sum

RO1 RO2

V2 Valve

V4

Valve

V3 Valve

20

DWEEREnergy Recovery

RO >

>

> RO

Interstage

Pump

Booster Pump

HP Pump

1

2

3

4 5

6

7

8

9

10

11

12 14

17

13

N1

N2

N3

19

S1 S2

22

Flow

Sum

Flow

Sum

Flow

Sum

RO1 RO2

V2 Valve

V4

Valve

V3 Valve

20

15

18 Valve

Figure 5-12. RO system configuration SWWE-a1 

Table 5-3. Input Parameters for Configuration SWWE-a1 

Parameter Description 

S1 Number of vessels in stage 1 

S2 Number of vessels in stage 2 

N1 High-pressure pump speed 

N2 Booster pump speed 

N3 Interstage pump speed 

V1 Stage 1 permeate recycle valve position 

V2 Stage 1 permeate output valve position 

V3 Stage 2 permeate recycle valve position 

V4 Stage 2 permeate output valve position 

Since the valve positions V1−V4 are mainly used to initiate a recycle flow for very low wind 

power capture conditions, the design space analysis fixes these quantities V1 = V3 = 0 (valve 

closed) and V2 = V4 = 1 (valve fully opened). The aforementioned valve positions indicate 

that there is no recycle of the permeate flow. 

62 
Table 5-4 lists the parameter values investigated in the design space analysis for this 

configuration. 

The steady-state constraints for the RO system are highlighted in Section 5.1.2 and listed in 

Table 5-5. Table 5-5 also lists the index associated with each constraint; this index reference 

is used in the figures associated with the design space analysis to highlight which constraints, 

if any, are being violated at a given point in the input space. 

63 
Table 5-4. Input Space Parameter Ranges for Configuration SWWE-a1 

Parameter Description Units Variation Range 

S1 Vessels in stage 1 - 15–75 

S2 Vessels in stage 2 - 15− 55 

N1 High-pressure pump speed rpm 3000–3900 

N2 Booster pump speed rpm 3000–3900 

N3 Interstage pump speed rpm 3000–3900 

V1 Stage 1 permeate recycle valve % open 0 (fully closed) 

V2 Stage 1 permeate output valve % open 1 (fully open) 

V3 Stage 2 permeate recycle valve % open 0 (fully closed) 

V4 Stage 2 permeate output valve % open 1 (fully open) 

p0 Feedwater pressure psid 20 

p21 Permeate exit pressure psid 15 

p22 Brine exit pressure psid 15 

T0 Feedwater temperature °C 25 

c0 Feedwater dissolved salt 

concentration 

kg/m3 29.6 

Table 5-5. Constraint Definition for Configuration SWWE-a1 

Parameter Value/Range Index Used in Plots 

Element polarization Cm / Cavg < 1.2 1 – Stage 1 

2 – Stage 2 

Element concentration flow Qc > 15 gpm 3 – Stage 1 

4 – Stage 2 

Feedwater pressure Pf < 1,200 psi 5 

Element pressure drop ΔPelm < 10 psid 6 – Stage 1 

8 – Stage 2 

Vessel pressure drop ΔPvessel < 58 

psid 

7 – Stage 1 

9 – Stage 2 

Permeate quality Cp < 500 ppm 10 

Element flux Flux < 20.6 gfd 11 – Stage 1 

12 – Stage 2 

64 
The results of the design space analysis are shown in Figure 5-13–Figure 5-37 for system 

parameters such as permeate flow, total power, specific energy consumption, and recovery 

ratio. The figures associated with these parameters also highlight the constraints violated in 

brackets and the system parameter value at each data point in the analysis. Finally, for each 

combination of input parameters that are presented, the distance to the constraint is identified 

in terms of percentage. The distance in terms of percentage from maximum constraints is 

given in Eq. 5-7 by 

Distance to constraint = Constraint Value − ParameterValue *100 Eq. 5-7 

ConstraintValue 

and the distance in terms of percentage from minimum constraints is given in Eq. 5-8 by 

Distance to constraint = ParameterValue − Constraint Value *100 Eq. 5-8 

ConstraintValue 

Positive numbers in these figures indicate that there are no limiting constraints, and the 

number shown in the figure is the distance to the most restrictive constraint. Negative 

numbers shown in the figures indicate that at least one constraint is being violated, and the 

number shown in the figure indicates the maximum constraint violation. 

Consider the results shown in Figure 5-13–Figure 5-27 for the case where the booster pump 

speed (N2) and interstage pump speed (N3) are set to 3000 rpm, and the number of vessels in 

the second stage, S2, is varied from 15 to 39 to 55. For each value of S2, data associated with 

permeate flow, total power, specific power, recovery ratio, and distance from the constraint 

are shown as a function of high-pressure pump speed (N1) and the number of vessels in stage 

1 (S1). When the number of vessels in the second stage is 15, S2 = 15, the only viable 

operating point is when the number of vessels in stage 1 is large and the high-pressure pump 

speed is at a minimum (Figure 5-13). In fact, in most cases, the constraints associated with a 

membrane element and vessel pressure drop in the second stage are being violated (Figure 

5-16). Also, when the number of vessels in stage 1 is low, the pressure drop constraint 

(element and vessel) is violated (Figure 5-16). 

As the number of vessels in the second stage increases, the available design space that meets 

all the constraints greatly increases (Figure 5-14 and Figure 5-15). However, the distance 

from the constraint in the viable operating space does not change significantly. This would 

suggest that the robustness associated with a particular design point does not improve as the 

number of vessels in stage 2 increases. The results for permeate flow (Figure 5-16–Figure 

5-18) show that as the high-pressure pump speed or the number of vessels in the first stage is 

increased, the permeate flow also increases. However, the rate of increase is higher at larger 

high pressure pump speeds. In addition, the increase rate of permeate flow as a function of 

high-pressure pump speed is larger as the number of stages in S1 increases. With regard to 

total power consumed, the results in Figure 5-19−Figure 5-21 show that at a given N2, N3 

combination, the total power is primarily dictated by the high pressure pump speed. This 

result is expected given that the high pressure pump dominates the system energy 

consumption. 

65 
By coupling the permeate flow results with the total power results, we can investigate the 

variation in specific energy consumption (Figure 5-22–Figure 5-23). The specific energy 

consumption decreases as the number of vessels in the second stage increases, going from a 

minimum value of 2.4 kWh/m3

 to 2.0 kWh/m3. In addition, as the number of vessels in the 

second stage increases, the minimum point for specific energy consumption moves to lower 

high pressure pump speeds. Finally, with regard to recovery ratio (Figure 5-25–Figure 5-27), 

the achievable recovery ratio increases with the number of vessels in the second stage. In 

addition, as the number of vessels in the second stage increases, a line of constant recovery 

ratio would move to the left in the S1–N1 range. 

To consider the impact of changes in the booster pump speed (N2), consider the changes in 

system parameters as booster pump speed is varied from 3,000 rpm to 3,540 rpm for a fixed 

number of vessels in the second stage, S2 = 39, and a fixed interstage pump speed of 3,000 

rpm. The distance from the limiting constraints is not significantly different in the acceptable 

regions of the design space (Figure 5-28). In fact, variations in N2 have little impact on the 

permeate flow of the system or the recovery ratio (Figure 5-29 and Figure 5-32). As expected, 

there is an increase in the total power consumed because of the higher booster pump speed 

(Figure 5-30), which in turn leads to a higher specific energy consumption (Figure 5-31). The 

minimum point for specific energy consumption moves to greater high-pressure pump speeds 

as booster pump speed is increased (Figure 5-31). Although not plotted, similar results were 

obtained at other stage two vessel configurations and other interstage pump speeds. 

To understand the impact of changes in the interstage pump speed (N3), consider the changes 

in the system parameters as the interstage pump speed is varied from 3,000 rpm to 3,540 rpm 

for a fixed number of vessels in the second stage, S2 = 39 and a fixed booster speed of 3,000 

rpm. As in the above case where the booster pump speed is varied, the results with regard to 

the system parameters of interest are similar. The distance from the limiting constraints is not 

significantly different in the acceptable regions of the design space (Figure 5-33). Variations 

in N3 have little impact on the permeate flow of the system and the recovery ratio (Figure 

5-34 and Figure 5-37). As expected, there is an increase in the total power consumed because 

of the higher interstage pump speed (Figure 5-35), which in turn leads to a higher specific 

energy consumption (Figure 5-36). As in the case of N2 variation, the minimum point for 

specific energy consumption moves to greater high-pressure pump speeds as interstage pump 

speed is increased (Figure 5-36). Although not plotted, similar results were obtained at other 

stage two vessel configurations and other booster pump speeds. 

66 
Percentage Distance from Consraint, V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=15 

80 

-39.1 -57.5 -76.4 -100.8 -168.1 -235.9 

-7.4 -17.6 -27.7 -37.8 -47.7 -57.6 

-3 -11.8 -20.6 -29.3 -37.9 -46.4 

0.1 -7. 8 -15.6 -23.2 -30.9 -38.4 

2.5 -4. 9 -12.1 -19.1 -25.9 -32.6 

4.4 -2. 6 -9.4 -16 -22.4 -28.7 

0 

70 

-50 

60 

50 -100 

40 

-150 

30 Stage 1 Number of Vessels 20 -200 

10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-13. Percentage distance from constraint at N2 = 3,000 rpm, 

N3 = 3,000 rpm, and S2 = 15 

Percentage Distance from Consraint, V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=39 

80 

-45.1 -114.5 -193.3 -272.4 -351.6 -431 

13.1 12.7 12.3 11.9 6 -2.1 

12.9 12.4 12 11.6 11.2 10.8 

12.6 12.1 11.7 11.3 10.9 10.5 

12.5 11.9 11.5 11 10.7 10.3 

12.3 11.8 11.3 10.9 10.5 10.1 

0 

-50 

-100 

70 

60

Stage 1 Number of Vessels 

-150 

50 

-200 

40 -250 

30 -300 

-350 20 

-400 

10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-14. Percentage distance from constraint at N2 = 3,000 rpm, 

N3 = 3,000 rpm, and S2 = 39 

Percentage Distance from Consraint, V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=55 

80 0 

-57.7 -138.3 -219 -299.7 -380.6 -461.5 

12.9 12.4 12 11.6 6.1 -2 

13.1 12.7 12.3 11.9 11.5 11.2 

12.9 12.4 12 11.6 11.2 10.9 

12.7 12.2 11.7 11.3 11 10.6 

12 12 11.5 11.1 10.7 10.4 -50 

-100 

-150 

-200 

-250 

70 

60 

50 

40

Stage 1 Number of Vessels 

-300 

30 

-350 

20 -400 

-450 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

10 

Figure 5-15. Percentage distance from constraints at N2 = 3,000 rpm, 

67 
N3 = 3,000 rpm, and S2 = 55 

System Permeate Flow (gpm), V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=15 

80 1100 

[6 7 8 9] 

412.9 

[6 7 8 9] 

492.3 

[6 7 8 9] 

573.5 

[6 7 8 9] 

656.1 

[6 7 8 9 11] 

739. 8 

[6 7 8 9 11] 

824.6 

[8 9] 

497.1 

[8 9] 

588.7 

[8 9] 

681.3 

[8 9] 

774.5 

[8 9] 

868 

[8 9] 

961.7 

[8 9] 

543.1 

[8 9] 

641 

[8 9] 

739.3 

[8 9] 

837.7 

[8 9] 

935. 9 

[8 9] 

1033.8 

[8] 

573 

[8 9] 

674.8 

[8 9] 

776.5 

[8 9] 

877.9 

[8 9] 

978. 7 

[8 9] 

1079 

594 

[8 9] 

698.3 

[8 9] 

802.3 

[8 9] 

905.6 

[8 9] 

1008.1 

[8 9] 

1109.8 

609.6 

[8 9] 

715.6 

[8 9] 

821.1 

[8 9] 

925.7 

[8 9] 

1029.4 

[8 9] 

1132.1 

70 1000 

60 

Number Vessels Stage 1 

900 

800 

700 

600 

500 

50 

40 

30 

20 

10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-16. Permeate flow for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 15 

System Permeate Flow (gpm), V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=39 

80 

[6 7] 

514 

[6 7] 

606.2 

[6 7] 

699.3 

[6 7] 

792.9 

[6 7] 

886. 9 

[6 7] 

981.1 

577 676.8 776.9 876.8 976. 4 

[6] 

1075.7 

607.4 711 814.4 917.3 1019.6 1121.2 

626.8 732.7 838.1 942.8 1046.6 1149.5 

640.5 747.9 854.7 960.5 1065.3 1169.1 

650.8 759.3 866.9 973.5 1079 1183.3 1100 

1000 

900 

800 

700 

600 

70 

60 

50 

40

Number Vessels Stage 1 30 

20 

10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-17. Permeate flow for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 39 

System Permeate Flow (gpm), V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=55 

80 1200 

[6 7] 

548.8 

[6 7] 

644.8 

[6 7] 

741.3 

[6 7] 

838.1 

[6 7] 

935 

[6 7] 

1031.7 

605.8 708.2 810.5 912.5 1013.9 

[6] 

1114.7 

631.6 737 842 946.3 1049.8 1152.5 

647.6 754.8 861.4 967.1 1071.9 1175.6 

658.9 767.3 874.9 981.5 1087 1191.4 

667.4 776.6 884.9 992.1 1098.2 1203 

70 1100 

60 1000 

900 

800 

700 

600 

Number Vessels Stage 1 50 

40 

30 

20 

10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-18. Permeate flow for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 55 

68 
Number Vessels Stage 1 

Total Power [kW], V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=15 

80 

[8 9] [8 9] [8 9] [8 9] [8 9] 550 326.6 365.5 407.9 454.9 507.2 565.8 

70 

[8 9] [8 9] [8 9] [8 9] [8 9] 

60 327.3 366.5 408.9 455.7 507.6 565.6 500 

[8] [8 9] [8 9] [8 9] [8 9] [8 9] 

50 328 367.6 410.2 456.9 508.4 565.6 

450 

[8 9] [8 9] [8 9] [8 9] [8 9] [8 9] 40 

328.5 368.8 411.9 458.6 509.7 566.2 

400 30 [8 9] [8 9] [8 9] [8 9] [8 9] [8 9] 

328.1 369.6 413.6 460.8 512 567.9 

20 

[6 7 8 9] [6 7 8 9] [6 7 8 9] [6 7 8 9] [6 7 8 9 11] [6 7 8 9 11] 350 

322 366.1 412.6 462 514.9 571.8 

10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-19. Total power for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 15 

Total Power [kW], V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=39 

80 

[6 7] 

330.3 

[6 7] 

371.1 

[6 7] 

414.5 

[6 7] 

461.3 

[6 7] 

512. 3 

[6 7] 

568.3 

330.9 370.2 412.5 458.8 510 

[6] 

567 

330 368.8 411 457.5 509. 4 567.4 

329.1 367.6 409.8 456.7 509. 1 568.1 

328.2 366.7 409 456.1 509 568.7 

327.5 365.9 408.2 455.6 509 569.4 

550 

70 

60 

50 

500 

Number Vessels Stage 1 

450 

40 

30 

20 

400 

350 

10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-20. Total power for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 39 

Total Power [kW], V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=55 

80 

[6 7] 

331.1 

[6 7] 

370.9 

[6 7] 

413.6 

[6 7] 

460.1 

[6 7] 

511. 1 

[6 7] 

567.5 

330.9 369.6 411.7 458.1 509. 8 

[6] 

567.6 

329.9 368.3 410.4 457.2 509. 6 568.6 

328.9 367.3 409.5 456.6 509. 7 569.6 

328.1 366.4 408.8 456.2 509. 7 570.4 

327.4 365.7 408.2 455.9 509. 8 571.1 550 

70 

60 500 

Numb er Vessels Stage 1 

50 

450 

40 

30 

20 

400 

350 

10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-21. Total power for N2 = 3000 rpm, N3 = 3000 rpm, and S2 = 55 

69 
System Specific Power [kWh/m 3], V1=0 V2=1 V3=0 V4=1 N2= 3000 N3=3000 S2=15 

80 3.4 

[8 9] [8 9] [8 9] [8 9] [8 9] 

2.4 2.2 2.2 2.2 2.2 2.2

70

3.2 

[8 9] [8 9] [8 9] [8 9] [8 9] 

2.4 2.3 2.2 2.2 2.2 2.2 60 

3 

[8] [8 9] [8 9] [8 9] [8 9] [8 9]

50 2.5 2.4 2.3 2.3 2.3 2.3 

2.8 

[8 9] [8 9] [8 9] [8 9] [8 9] [8 9] 40 

2.7 2.5 2.5 2.4 2.4 2.4 

2.6 

30 [8 9] [8 9] [8 9] [8 9] [8 9] [8 9] 

2.9 2.8 2.7 2.6 2.6 2.6 

2.4 

20

[6 7 8 9] [6 7 8 9] [6 7 8 9] [6 7 8 9] [6 7 8 9 11] [6 7 8 9 11]

3.4 3.3 3.2 3.1 3.1 3.1

10 2.2 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Number Vessels Stage 1 

Figure 5-22. Specific power for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 15 

System Specific Power [kWh/m 3], V1=0 V2=1 V3=0 V4=1 N2= 3000 N3=3000 S2=39 

80 

[6 7] 

2.8 

[6 7] 

2.7 

[6 7] 

2.6 

[6 7] 

2.6 

[6 7] 

2.5 

[6 7] 

2.6 

2.5 2.4 2.3 2.3 2.3 

[6] 

2.3 

2.4 2.3 2.2 2.2 2.2 2.2 

2.3 2.2 2.2 2.1 2.1 2.2 

2.3 2.2 2.1 2.1 2.1 2.1 

2.2 2.1 2.1 2.1 2.1 2.1 

2.8 

70 2.7 

60 

Number Vessels Stage 1 

2.6 

50 2.5 

2.4 40 

30 2.3 

2.2 20 

2.1 

10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-23. Specific power for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 39 

System Specific Power [kWh/m 3], V1=0 V2=1 V3=0 V4=1 N2= 3000 N3=3000 S2=55 

80 

70 

[6 7] 

2.7 

[6 7] 

2.5 

[6 7] 

2.5 

[6 7] 

2.4 

[6 7] 

2.4 

[6 7] 

2.4 

2.4 2.3 2.2 2.2 2.2 

[6] 

2.2 

2.3 2.2 2.1 2.1 2.1 2.2 

2.2 2.1 2.1 2.1 2.1 2.1 

2.2 2.1 2.1 2 2.1 2.1 

2.2 2.1 2 2 2 2.1 

2.5 

2.6 

60 

Number Vessels Stage 1 

2.4 50 

40 2.3 

30 2.2 

20 2.1 

10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-24. Specific power for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 55 

70 
System Recovery Ratio [%]s, V1=0 V2=1 V3= 0 V4= 1 N2=3000 N3= 3000 S2= 15 

80 

70 

38 

[6 7 8 9] 

21.3 

[6 7 8 9] 

23.4 

[6 7 8 9] 

25.2 

[6 7 8 9] 

26.9 

[6 7 8 9 11] 

28.4 

[6 7 8 9 11] 

29.9 

[8 9] 

24.9 

[8 9] 

27.1 

[8 9] 

29.1 

[8 9] 

30.9 

[8 9] 

32.5 

[8 9] 

34 

[8 9] 

27 

[8 9] 

29.3 

[8 9] 

31.4 

[8 9] 

33.2 

[8 9] 

34.9 

[8 9] 

36.4 

[8] 

28.3 

[8 9] 

30.7 

[8 9] 

32.9 

[8 9] 

34.7 

[8 9] 

36.4 

[8 9] 

37.9 

29.3 

[8 9] 

31.8 

[8 9] 

33.9 

[8 9] 

35.8 

[8 9] 

37.5 

[8 9] 

39 

30 

[8 9] 

32.5 

[8 9] 

34.7 

[8 9] 

36.6 

[8 9] 

38.3 

[8 9] 

39.9 

36 

34 

32 

30 

28 

26 

60 

Number Vessels Stage 1 50 

40 

30 

20 24 

22 10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-25: Recovery ratio for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 15 

System Recovery Ratio [%]s, V1=0 V2=1 V3= 0 V4= 1 N2=3000 N3= 3000 S2= 39 

80 

[6 7] 

25.9 

[6 7] 

28.1 

[6 7] 

30.1 

[6 7] 

31.9 

[6 7] 

33.5 

[6 7] 

35 

28.3 30.6 32.7 34.5 36.2 

[6] 

37.6 

29.6 32 34.1 35.9 37.6 39.1 

30.4 32.9 35 36.9 38.6 40.1 

31.1 33.5 35.6 37.5 39.2 40.8 

31.5 34 36.2 38.1 39.8 41.3 40 

70 

38 

60 

Number Vessels Stage 1 

36 

50 

34 

40 32 

30 30 

20 28 

10 26 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-26. Recovery ratio for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 39 

System Recovery Ratio [%]s, V1=0 V2=1 V3= 0 V4= 1 N2=3000 N3= 3000 S2= 55 

80 42 

[6 7] 

27.6 

[6 7] 

29.9 

[6 7] 

31.9 

[6 7] 

33.7 

[6 7] 

35.4 

[6 7] 

36.9 

29.7 32 34.1 35.9 37.6 

[6] 

39.1 

30.7 33.1 35.2 37.1 38.8 40.3 

31.4 33.8 36 37.8 39.5 41.1 

31.9 34.4 36.5 38.4 40.1 41.6 

32.3 34.8 36.9 38.8 40.5 42 40 70 

38 

36 

60 

Number Vessels Stage 1 50 

34 40 

32 30 

30 20 

28 10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-27. Recovery ratio for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 55 

71 
40 

50 

60 

70 

-300 

-250 

-200 

-150 

-100 

-50 

10 

20 

70 

Percentage Distance from Consraint, V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=39 Percentage Distance from Consraint, V1=0 V2=1 V3=0 V4=1 N2=3540 N3=3000 S2=39 

80 

-45.1 -114.5 -193.3 -272.4 -351.6 -431 

13.1 12.7 12.3 11.9 6 -2.1 

12.9 12.4 12 11.6 11.2 10.8 

12.6 12.1 11.7 11.3 10.9 10.5 

12.5 11.9 11.5 11 10.7 10.3 

12.3 11.8 11.3 10.9 10.5 10.1 

80 

-98.6 -177.5 -256.6 -335.9 -415.4 -495.2 

13.1 12.7 12.3 11.9 7.1 -1.1 

12.8 12.3 11.9 11.5 11.1 10.7 

12.5 12 11.6 11.2 10.8 10.4 

12.3 11.8 11.4 10.9 10.5 10.2 

12.2 11.6 11.2 10.7 10.3 10 

0 0

-50 70 

-100 

60 

Number Vessels Stage 1 Stage 1 Number of Vessels 

Stage 1 Number of Vessels 

-150 

50 

-200 

-250 40 

30 -300 30 

-350 -400 

20 20 

-450 -400 

10 10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-28. Distance from constraint comparison for changes in

N2 for fixed N3 and S2

System Permeate Flow (gpm), V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=39 System Permeate Flow (gpm), V1=0 V2=1 V3=0 V4=1 N2=3540 N3=3000 S2=39 

80 80 

[6 7] 

508 

[6 7] 

600.3 

[6 7] 

693.5 

[6 7] 

787.3 

[6 7] 

881. 5 

[6 7] 

975.8 

569.8 669.9 770.2 870.4 970. 3 

[6] 

1069.8 

599.9 703.8 807.4 910.6 1013.2 1115.1 

619.1 725.2 830.9 935.9 1040.1 1143.3 

632.6 740.3 847.3 953.5 1058.6 1162.7 

642.9 751.6 859.5 966.4 1072.2 1176.9 

[6 7] 

514 

[6 7] 

606.2 

[6 7] 

699.3 

[6 7] 

792.9 

[6 7] 

886. 9 

[6 7] 

981.1 

577 676.8 776.9 876.8 976. 4 

[6] 

1075.7 

607.4 711 814.4 917.3 1019.6 1121.2 

626.8 732.7 838.1 942.8 1046.6 1149.5 

640.5 747.9 854.7 960.5 1065.3 1169.1 

650.8 759.3 866.9 973.5 1079 1183.3 1100 70 

1000 60 

50 

60 

Number Vessels Stage 1 

900 50 

40 800 40

30 700 30

20 600 

10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-29. Permeate flow comparison for changes in N2 for fixed N3 and S2 

72 

-350 

600 

700 

800 

900 

1000 

1100 
20 

40 

50 

60 

80 

450 

500 

20 

Total Power [kW], V1=0 V2=1 V3=0 V4=1 N2=3000 N3= 3000 S2= 39 Total Power [kW], V1=0 V2=1 V3=0 V4=1 N2=3540 N3=3000 S2=39 

[6 7] 

330.3 

[6 7] 

371.1 

[6 7] 

414.5 

[6 7] 

461.3 

[6 7] 

512. 3 

[6 7] 

568.3 

330.9 370.2 412.5 458.8 510 

[6] 

567 

330 368.8 411 457.5 509.4 567.4 

329.1 367.6 409.8 456.7 509.1 568.1 

328.2 366.7 409 456.1 509 568.7 

327.5 365.9 408.2 455.6 509 569.4 

80

550

[6 7] 

352 

[6 7] 

394.1 

[6 7] 

438.6 

[6 7] 

486.4 

[6 7] 

538. 2 

[6 7] 

595 

352.6 393 436.4 483.5 535. 5 

[6] 

593 

351.4 391.4 434.5 481.8 534. 3 592.8 

350.3 389.9 433 480.6 533. 6 593 

349.3 388.8 431.9 479.7 533. 1 593.3 

348.4 387.8 431 479 532.8 593.6 

70 70 550

500 60

Number Vessels Stage 1 

Number Vessels Stage 1 

450

50

40

30 400 30

20

350

10 10 350 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-30. Total power consumption comparison for variation in N2 for 

fixed N3 and S2 

System Specific Power [kWh/m 3 System Specific Power [kWh/m ], V1=0 V2=1 V3=0 V4=1 N2= 3540 N3=3000 S2=39 3], V1=0 V2=1 V3=0 V4=1 N2= 3000 N3=3000 S2=39 

80 80 2.8 

[6 7] 

3.1 

[6 7] 

2.9 

[6 7] 

2.8 

[6 7] 

2.7 

[6 7] 

2.7 

[6 7] 

2.7 

2.7 2.6 2.5 2.4 2.4 

[6] 

2.4 

2.6 2.4 2.4 2.3 2.3 2.3 

2.5 2.4 2.3 2.3 2.3 2.3 

2.4 2.3 2.2 2.2 2.2 2.2 

2.4 2.3 2.2 2.2 2.2 2.2 

3

[6 7] 

2.8 

[6 7] 

2.7 

[6 7] 

2.6 

[6 7] 

2.6 

[6 7] 

2.5 

[6 7] 

2.6 

2.5 2.4 2.3 2.3 2.3 

[6] 

2.3 

2.4 2.3 2.2 2.2 2.2 2.2 

2.3 2.2 2.2 2.1 2.1 2.2 

2.3 2.2 2.1 2.1 2.1 2.1 

2.2 2.1 2.1 2.1 2.1 2.1 

70 70 2.7 2.9 

60 60 2.6 

Number Vesse ls Sta ge 1 

Number Vessels Stage 1 Number Vessels Stage 1 

50 50 2.5 

2.4 40 40

2.3 30 30

2.2 20

2.1 10 10 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-31. Specific power consumption comparison for variation in N2 for 

fixed N3 and S2 

System Recovery Ratio [%]s, V1=0 V2=1 V3= 0 V4= 1 N2=3000 N3= 3000 S2= 39 System Recovery Ratio [%]s, V1=0 V2=1 V3=0 V4=1 N2=3540 N3=3000 S2=39 

80

[6 7] 

25.9 

[6 7] 

28.1 

[6 7] 

30.1 

[6 7] 

31.9 

[6 7] 

33.5 

[6 7] 

35 

28.3 30.6 32.7 34.5 36.2 

[6] 

37.6 

29.6 32 34.1 35.9 37.6 39.1 

30.4 32.9 35 36.9 38.6 40.1 

31.1 33.5 35.6 37.5 39.2 40.8 

31.5 34 36.2 38.1 39.8 41.3 

80

40

[6 7] 

25.8 

[6 7] 

28.1 

[6 7] 

30.1 

[6 7] 

31.9 

[6 7] 

33.5 

[6 7] 

35 

28.3 30.6 32.7 34.5 36.2 

[6] 

37.7 

29.6 32 34.1 36 37.6 39.2 

30.4 32.9 35 36.9 38.6 40.1 

31.1 33.5 35.7 37.6 39.3 40.8 

31.6 34 36.2 38.1 39.8 41.4 40

70 70

38 38

60 60

Number Vessels Sta ge 1 

36

50

34

40 32

30 30

28 20

10 26 10 26 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-32: Recovery ratio comparison for variation in N2 for fixed N3 and S2 

73

400 

2.2 

2.3 

2.4 

2.5 

2.6 

2.7 

2.8 

20 

30 

40 

50 

28 

30 

32 

34 

36 
40 

50 

60 

-140 

-120 

-100 

-80 

-60 

10 

20 

70 

Percentage Distance from Consraint, V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=39 Percentage Distance from Consraint, V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3540 S2=39 

80 

-45.1 -114.5 -193.3 -272.4 -351.6 -431 

13.1 12.7 12.3 11.9 6 -2.1 

12.9 12.4 12 11.6 11.2 10.8 

12.6 12.1 11.7 11.3 10.9 10.5 

12.5 11.9 11.5 11 10.7 10.3 

12.3 11.8 11.3 10.9 10.5 10.1 

80 0 

-49.9 -68.4 -87.3 -106.4 -131.8 -214.1 

12.7 12.3 12 11.6 4.4 -3.7 

13.1 12.6 12.2 11.8 11.4 11 

12.9 12.4 11.9 11.5 11.1 10.8 

12.7 12.2 11.7 11.3 10.9 10.6 

12.6 12.1 11.6 11.1 10.7 10.4 

0 

-50 -20 

-40 

70 70 

-100 

Stage 1 Number of Vessels 

60 

50 

40 

30 

Number Vessels Stage 1 Stage 1 Number of Vessels 

-150 

-200 

-250 

30 -300 

-350 20 20 -180 

-400 

10 10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump S peed - rpm 

Figure 5-33. Distance from constraint comparison for changes in N3 for 

fixed N2 and S2 

System Permeate Flow (gpm), V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=39 System Permeate Flow (gpm), V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3540 S2=39 

80 80 

[6 7] 

514 

[6 7] 

606.2 

[6 7] 

699.3 

[6 7] 

792.9 

[6 7] 

886. 9 

[6 7] 

981.1 

577 676.8 776.9 876.8 976. 4 

[6] 

1075.7 

607.4 711 814.4 917.3 1019.6 1121.2 

626.8 732.7 838.1 942.8 1046.6 1149.5 

640.5 747.9 854.7 960.5 1065.3 1169.1 

650.8 759.3 866.9 973.5 1079 1183.3 

[6 7] 

536.7 

[6 7] 

627.4 

[6 7] 

719.1 

[6 7] 

811.5 

[6 7] 

904. 3 

[6 7] 

997.3 

598.3 696.7 795.4 894 992.5 

[6] 

1090.6 

627.9 730.1 832.1 933.8 1034.9 1135.5 

646.6 751.1 855.3 958.7 1061.5 1163.4 

659.9 765.9 871.4 976.1 1079.8 1182.6 

669.8 777 883.4 988.9 1093.3 1196.7 1100 70 

1000 60 

50 

60 

Number Vessels Stage 1 

900 50 

40 800 40

30 700 30

20 600 

10 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-34. Permeate flow comparison for changes in N3 for fixed N2 and S2 

74 

-200 

-160 

600 

700 

800 

900 

1000 

1100 
20 

40 

50 

60 

70 

80 

500 

550 

600 

10 

Total Power [kW], V1=0 V2=1 V3=0 V4=1 N2=3000 N3= 3000 S2= 39 Total Power [kW], V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3540 S2=39 

80

550

70

Number Vessels Stage 1 Number Vessels Stage 1 

[6 7] 

384.7 

[6 7] 

426.5 

[6 7] 

470.9 

[6 7] 

518.6 

[6 7] 

570. 3 

[6 7] 

626.9 

384 424.5 468 515.5 567.7 

[6] 

625.6 

382.2 422.2 465.7 513.5 566. 5 625.6 

380.4 420.3 463.8 512 565.7 625.9 

379 418.7 462.3 510.8 565.1 626.1 

377.8 417.4 461.1 509.8 564. 6 626.3 

[6 7] 

330.3 

[6 7] 

371.1 

[6 7] 

414.5 

[6 7] 

461.3 

[6 7] 

512. 3 

[6 7] 

568.3 

330.9 370.2 412.5 458.8 510 

[6] 

567 

330 368.8 411 457.5 509.4 567.4 

329.1 367.6 409.8 456.7 509.1 568.1 

328.2 366.7 409 456.1 509 568.7 

327.5 365.9 408.2 455.6 509 569.4 

500

30

60

Number Vessels Stage 1 50

40

450

400 30

20

350

10 10

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-35. Total power consumption comparison for variation in N3 for 

fixed N2 and S2 

System Specific Power [kWh/m 3], V1=0 V2=1 V3=0 V4=1 N2= 3000 N3=3000 S2=39 System Specific Power [kWh/m 3], V1=0 V2=1 V3=0 V4=1 N2= 3000 N3=3540 S2=39 

80

[6 7] 

2.8 

[6 7] 

2.7 

[6 7] 

2.6 

[6 7] 

2.6 

[6 7] 

2.5 

[6 7] 

2.6 

2.5 2.4 2.3 2.3 2.3 

[6] 

2.3 

2.4 2.3 2.2 2.2 2.2 2.2 

2.3 2.2 2.2 2.1 2.1 2.2 

2.3 2.2 2.1 2.1 2.1 2.1 

2.2 2.1 2.1 2.1 2.1 2.1 

80 2.8 3.1 

[6 7] 

3.2 

[6 7] 

3 

[6 7] 

2.9 

[6 7] 

2. 8 

[6 7] 

2.8 

[6 7] 

2.8 

2.8 2.7 2.6 2.5 2.5 

[6] 

2.5 

2.7 2.5 2.5 2.4 2.4 2.4 

2.6 2.5 2.4 2.4 2.3 2.4 

2.5 2.4 2.3 2.3 2.3 2.3 

2.5 2.4 2.3 2.3 2.3 2.3 

70 70 2.7 3

60 2.6 60

Number Vessels Stage 1 

50 2.5 50

2.4 40 40

2.3 30 30

2.2 20 20 2.4 

2.1 

10

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-36. Specific power consumption comparison for variation in N3 for 

fixed N2 and S2 

75

400 

450 

2.3 

2.5 

2.6 

2.7 

2.8 

2.9 
10 

20 

40 

50 

60 

80 

32 

34 

36 

40 

System Recovery Ratio [%]s, V1=0 V2=1 V3= 0 V4= 1 N2=3000 N3= 3000 S2=39 System Recovery Ratio [%]s, V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3540 S2=39 

80 

[6 7] 

25.9 

[6 7] 

28.1 

[6 7] 

30.1 

[6 7] 

31.9 

[6 7] 

33.5 

[6 7] 

35 

28.3 30.6 32.7 34.5 36.2 

[6] 

37.6 

29.6 32 34.1 35.9 37.6 39.1 

30.4 32.9 35 36.9 38.6 40.1 

31.1 33.5 35.6 37.5 39.2 40.8 

31.5 34 36.2 38.1 39.8 41.3 40 

[6 7] 

26.4 

[6 7] 

28.6 

[6 7] 

30.5 

[6 7] 

32.2 

[6 7] 

33.8 

[6 7] 

35.2 

28.8 31 33 34.7 36.3 

[6] 

37.8 

30 32.3 34.3 36.1 37.7 39.2 

30.8 33.1 35.2 37 38.7 40.2 

31.4 33.7 35.8 37.7 39.3 40.8 

31.8 34.2 36.3 38.2 39.8 41.4 

70 70 

38 38 

60 

Number Vessels Stage 1 

36 

34 

Number Vessels Stage 1 50 

40 32 

30 30 30 

20 28 

26 10

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-37. Recovery ratio comparison for variation in N3 for fixed N2 and S2 

76 

28 

30 
5.2.4 SWWE-a3 Nominal Design 

In the SW-We-a3 configuration, a single-stage RO system is analyzed to determine the 

optimal design for the given energy and membrane constraints as applied to the SE-WE-a1 

configuration. In this case, since there is only a single stage, there is no interstage boost pump. 

This means the system needs to be a DWEER boost pump, since the brine outlet pressure will 

always be below the feed inlet pressure to the RO system. This configuration is shown 

schematically in Figure 5-38. 

Acid tank 

Filter Pump 

Seawater 

Feed - Well 

Filter 

Filter 

Feed 

Filter 

Solids 

RO Feed 

Pump 

High-P 

Feed 

RO-1 

Permeate Product 

Concentrate 

DWEER 

Low-P Brine Out 

Low-P 

Feed Bypass 

Low-P 

Feed

 Make-up 

Feed 

Acid Pump 

Acid 

Feed 

Booster 

Pump 

High-P 

Make-Up 

Feed 

High-P 

RO Feed 

Figure 5-38. SW-WE-a3 configuration with DWEER feed boost 

5.2.4.1 Power and reverse osmosis model optimization 

As with SW-WE-a1, power is calculated with nominal values for pressure and flow until a 

value for the total power is about 540 kW. This gives a baseline for the configuration. We 

used the design parameters from Table 5-2 and the flows from the power calculations to 

optimize the steady-state membrane model. 

At each convergence of the RO model, the output flows and pressures from the membrane 

model were plugged back into the pump power calculations to see if the power was still 

optimal at about 540 kW. Since the feed flow is the largest power draw on the system, if the 

power was too low, the feed flow to the membrane model was increased. If the power was too 

high, the feed flow was decreased. This cycle was iterated until the maximum flow for the 

given power input through an RO system was achieved. Figure 5-39 shows the results of this 

optimization for the power calculations representing the configurations in Figure 5-38. The 

77 
RO steady state model outputs are found in Appendix A, which refers to the data from the 

DWEER boost case. 

Figure 5-39. Power calculations for SW-WE-a3 design with DWEER boost 

We used the RO membrane design reports and the power calculations to develop an overall 

process flow diagram for the SW-WE-a3 configuration. A flow diagram is shown for the 

DWEER boost case in Figure 5-40. English units for flow, pressure, and flux are gpm, psia, 

and gfd, respectively. Corresponding metric units are cmh, bar, and lmh. 

78 
Acid tank 

Filter Pump 

Seawater 

Feed - Well 

Filter 

Filter 

Feed 

Filter 

Solids 

RO Feed 

Pump 

High-P 

Feed 

RO-1 

Permeate Product 

Concentrate 

DWEER 

Low-P Brine Out 

Low-P 

Feed Bypass 

Low-P 

Feed

 Make-up 

Feed 

Acid Pump 

Acid 

Feed 

Booster 

Pump 

High-P 

Make-Up 

Feed 

High-P 

RO Feed 

2390 GPM 

2390 GPM 

45 PSIA 

2390 GPM 

30 PSIA 

1408 GPM 

30 PSIA 

1408 GPM 

829 PSIA 

982 

GPM 

30 PSIA 982 GPM 

854 PSIA 

2390 GPM 

854 PSIA 

956 GPM 

15 PSIG 

TDS 204 PPM 

B 0.27 PPM 

1434 GPM 

841 PSIG 

1434 GPM 

15 PSIA 

40% Recovery 

10.2 GFD 

52 x 7 elements 

TM820-370 

1408 GPM 

854 PSIA 

0.05 GPM 

30 PSIA 

Acid tank 

Filter Pump 

Seawater 

Feed - Well 

Filter 

Filter 

Feed 

Filter 

Solids 

RO Feed 

Pump 

High-P 

Feed 

RO-1 

Permeate Product 

Concentrate 

DWEER 

Low-P Brine Out 

Low-P 

Feed Bypass 

Low-P 

Feed

 Make-up 

Feed 

Acid Pump 

Acid 

Feed 

Booster 

Pump 

High-P 

Make-Up 

Feed 

High-P 

RO Feed 

542.8 CMH 

542.8 CMH 

3.1 bar 

542.8 CMH 

2.07 bar 

319.8 CMH 

2.07 bar 

319.8 CMH 

57.2 bar 

223 

CMH 

2.07 bar 223 CMH 

58.9 bar 

542.8 CMH 

58.9 bar 

217.1 CMH 

1.03 bar 

TDS 204 PPM 

B 0.27 PPM 

325.7 CMH 

58 bar 

325.7 CMH 

1.03 bar 

40% Recovery 

17.3 LMH 

52 x 7 elements 

TM820-370 

319.8 CMH 

58.9 bar 

0.01 CMH 

2.07 bar 

Figure 5-40. SW-WE-a3 DWEER boost flow diagram 

79 
5.2.4.2 Boron sensitivity analysis 

The level of Boron in permeate water is now set to 0.3−0.5 ppm by WHO42. To understand 

the sensitivity of this configuration to Boron, we increased its feed level to determine what its 

level in the feed would cause it to break through in the permeate to a level of 0.5 ppm. We 

used the steady-state RO membrane model33 to determine that the level of Boron in the feed 

that results in a 0.5-ppm level in the product permeate is 2.05 ppm. Since there is large 

variation in seawater Boron levels, any feedwater with Boron levels higher than 2 ppm would 

require a redesign of the system for a specific situation. 

In this single-stage case, reducing the recovery to 30% for the 52 x 7 element configuration, 

and keeping the same production rate, the feed rate can be increased to 3,187 gpm (724 cmh). 

The energy consumption remains at about 540 kW, as the feed pressure drops to 785 psia 

(54.1 bar) from 854 psia (58.9 bar). The feed level of Boron can be raised to 2.3 ppm (12.2% 

increase), and the product permeate will remain at 0.5 ppm. There is some room for 

improvement in the current design to higher Boron levels. Therefore, if Boron levels are 

higher than 2.3 ppm, the best design option would be to have another RO Boron removal 

stage for the permeate only. This would require extra capital costs and increase energy 

consumption. Either a smaller production plant or a larger wind turbine would be required to 

compensate for the increased energy use. Those trade-offs in capital and operating expenses 

versus productivity would have to be assessed on specific high-Boron feed cases. 

5.2.5 Cost of Water Analysis 

Based on the above design, an overall COW is determined by calculating capital and 

operating costs for the configuration as outlined in detail in section 4.1. This configuration has 

only one stage, so the capital costs for the membrane system are much lower than those of the 

SW-WE-a1 configuration. A summary of the cost is shown in Figure 5-41, which outlines the 

relevant capital and operating costs for the steady-state model. The model assumes an 

operating year is 350 days, with a permeate flow rate of 5,211 m3

/day (956 gpm). This yields 

an annual production of 1.82 x 106 m3

/yr of product water. This single-stage configuration 

produces about 10% less water than the two-stage SW-WE-a1 configuration. Since the first 

stage of the SW-WE-a1 configuration (50 vessels x 6 elements, 15.7 lmh flux) is similar to 

the SW-WE-a3 stage (52 vessels x 7 elements, 17.3 lmh flux), the costs reduced capital costs 

of the single-stage SW-WE-a3 are offset by a 10% lower production rate of water. 

Rolling up all the capital and operating costs for this production level gives an overall steadystate COW of about $1.24/m3

. This cost can vary for a site-specific situation, where well 

construction costs, feed concentrations, and waste disposal costs can vary. The steady-state 

cost model, however, is flexible and can make provisions for these variances (see section 4.1). 

80 
Figure 5-41 Summary costs for the steady-state SW-WE-a3 configuration 

5.2.6 Design Space Analysis 

We conducted a design space analysis to understand the extent of the operating envelope 

associated with the configuration described in Section 5.2.2. As in the previous 

configurations, the main purpose of this study is to investigate the points in the input space at 

which the system fails to satisfy all the component and system constraints. If the system were 

operated at these points, where the constraints were not met, the potential for membrane 

degradation through fouling or scaling or membrane destruction from increased stresses may 

result. In addition to understanding where constraints are violated, the design space study 

provides some insight into how system quantities of interest such as recovery ratio, specific 

energy consumption, total power, and permeate flow vary with the choice of input parameters. 

The qualitative understanding that the design space study provides is critical for 

understanding the potential for system optimization. 

For the single stage configuration shown in Figure 5-42, the input space is defined by the 

parameters listed in Table 5-6. 

81 
Permeate

Exit

Pressure

p15

DWEEREnergy Recovery 

RO > 

>

Booster Pump 

HPPump 

1 

2 

3 

4 5 

6 

7 

8 

9 

11 12 V1 14 

S1 

Brine Exit Pressure, p16 

16 

Flow 

Sum 

Valve 

Flow Sum 

Flow 

Sum 

RO1 

Good permeate 

Bad permeate 

10 

17 

1-V1 

Valve 

N1 

N2 

Feedwater inlet 

(c0), temperature 

DWEEREnergy Recovery

RO >

>

Booster Pump

HPPump

1

2

3

4 5

6

7

8

9

11 12 V1 14

S1

Brine Exit Pressure, p16

16

Flow

Sum

Valve

Flow Sum

Flow

Sum

RO1

Good permeate

Bad permeate

10

17

1-V1

Valve

N1

N2

Feedwater inlet 

(c0), temperature

0

conditions of

pressure (p0),

concentration 

(T0)

Figure 5-42. RO system configuration SWWE-a3 

Table 5-6. Input Parameters for Configuration SWWE-a3 

Parameter Description 

S1 Number of vessels in stage 1 

N1 High-pressure pump speed 

N2 Booster pump speed 

V1 Bad permeate recycle valve position 

Since the valve position V1 is mainly used to initiate a recycle flow for low wind power 

capture conditions, the design space analysis considers only small amounts of recycle given 

by valve positions in the range of 0%–20%. Table 5-7 lists the parameter values investigated 

in the design space analysis for this configuration. 

The steady-state constraints for the RO system were highlighted in Section 5.1.2 and are 

repeated in Table 5-8. Table 5-8 also lists the index associated with each constraint; this index 

reference is used in the design space plots to highlight which constraints, if any, are being 

violated at a given point in the input space. 

82 
Table 5-7. Input Space Parameter Ranges for Configuration SWWE-a3 

Parameter Description Units Variation Range 

S1 Vessels in stage 1 - 15−125 

N1 High pressure pump speed rpm 3,000–3900 

N2 Booster pump speed rpm 3,000–3,900 

V1 Stage 1 permeate recycle valve % open 0%–20% 

p0 Feedwater pressure psid 20 

p15 Permeate exit pressure psid 15 

p16 Brine exit pressure psid 15 

T0 Feedwater temperature °C 25 

c0 Feedwater dissolved salt concentration kg/m3 29.6 

Table 5-8. Constraint definition for configuration SWWE-a3 

Parameter Value/range Index Used in Plots 

Element polarization Cm / Cavg < 1.2 1 

Element concentration flow Qc > 15 gpm 2 

Feedwater pressure Pf < 1200 psi 3 

Element pressure drop �Pelm < 10 psid 4 

Vessel pressure drop �Pvessel < 58 psid 5 

Permeate quality Cp < 500 ppm 6 

Element flux Flux < 20.6 gfd 7 

The results of the design space analysis for the seawater configuration SWWE-a3 are shown 

in Figure 5-43−Figure 5-57 for system parameters such as permeate flow, total power, 

specific energy consumption, and recovery ratio. The figures associated with these parameters 

also highlight the constraints violated in brackets and the system parameter value at each data 

point in the analysis. Finally, for each combination of input parameters that are presented, the 

distance to the constraint is identified in terms of percentage. The distance in terms of 

percentage from maximum constraints is given in Eq. 5-9 by 

Distance to constraint = Constraint Value − ParameterValue *100 Eq. 5-9 

ConstraintValue 

and the distance in terms of percentage from minimum constraints is given in Eq. 10 by 

Distance to constraint = ParameterValue − Constraint Value *100 Eq. 5-10 

ConstraintValue 

83 
Positive numbers in these figures indicate that there are no limiting constraints, and the 

number shown in the figure is the distance to the most restrictive constraint. Negative 

numbers shown in the figures indicate that at least one constraint is being violated, and the 

number shown in the figure indicates the maximum constraint violation. 

Consider the results shown in Figure 5-43–Figure 5-57 for the case where the booster pump 

speed (N2) is varied from 3,000 rpm to 3,900 rpm, and the recycle valve, V1, is varied 

between a fully closed position (V1 = 0) to a partially opened position (V1 = 20%). For each 

value of N2, data associated with permeate flow, total power, specific power, recovery ratio, 

and distance from the constraint are shown as functions of high-pressure pump speed (N1) 

and the number of vessels in RO stage (S1). Considering the results in Figure 5-43, the 

operating points that meet the constraints of the system lie on a diagonal in the S1-N1 input 

space. Essentially, as the high-pressure pump speed is increased, the number of vessels should 

also increase. Figure 5-43−Figure 5-45 show that as the booster pump speed is increased, the 

allowable design space shifts downward toward a lower number of vessels. The impact on the 

design space variation when permeate recycle is introduced is slight. For example, consider 

Figure 5-43 where N2 = 3,000 rpm and the recycle valve is opened from a fully closed 

position to a partially open position. The area of the S1-N1 input space that sees the most 

impact is the lower right hand corner, small number of vessels and larger high pressure pump 

speeds. For this region of the input space, recycle reduces the allowable design space and 

drives the system further away from meeting the constraints. This behavior is also observed at 

other booster speeds (Figure 5-44 and Figure 5-45). 

To better understand the limiting constraints and the impact on additional system parameters, 

consider the permeate flow results shown in Figure 5-46–Figure 5-48. Figure 5-46 shows that 

the primary constraint being violated at large number of vessels is the minimum concentration 

flow. The fact that concentration flow is the limiting factor is reasonable given that the 

feedwater is divided across a larger number of vessels without a significant increase in 

recovery ratio (Figure 5-55). The result is a lower concentration flow in each element, which 

results in a violation of the minimum concentration flow constraint. When the high-pressure 

pump speed is great and the number of vessels is small, the limiting constraint is the flux in an 

element. This behavior is reasonable in that at greater high-pressure pump speeds for a 

specified pressure rise, the larger inlet flow is split across fewer vessels. Hence, the flux in 

each element of the vessel will be larger and result in a violation of the flux constraint. The 

trend in permeate flow for a given booster pump speed depends on the speed of the highpressure pump. At lower speeds, the gradient with number of vessels is approximately 5 

gpm/vessel. However, at higher speeds, the gradient is on the order of 15 gpm/vessel. The 

impact of booster pump speed on permeate flow is that as booster speed is increased, the 

permeate flow decreases by approximately 3%-4% for a 500-rpm increase in booster speed. 

The results in Figure 5-49–Figure 5-51 show that the total power consumed is primarily 

dictated by the high-pressure pump speed. This result is expected given that the high 

pressure pump dominates the system energy consumption. The increase in power 

consumed for a given high-pressure pump speed that is caused by an increase in the 

number of vessels is on the order of 2 kW/vessel at lower values of high-pressure pump 

speed and approximately 7 kW/vessel at higher pump speeds. The power consumption per 

vessel differences at low and high speeds is primarily driven by the increased flow 

capacity at the higher speeds, which corresponds to higher permeate flows at larger high 

84 
20 

40 

60 

80 

100 

120 

pressure pump speeds. By coupling the permeate flow results with the total power 

consumption results, the variation in specific energy consumption can be investigated 

(Figure 5-52−Figure 5-54). The specific energy consumption decreases slightly when the 

number of vessels is increased. In addition, as the booster speed is increased, the area in 

the S1-N1 region that corresponds to minimum specific energy consumption shifts to the 

right, i.e., greater high-pressure pump speeds. The impact of permeate recycle is to 

slightly increase the specific energy consumption that is caused by a reduction in overall 

permeate flow. 

Finally, with regard to system recovery ratio (Figure 5-55−Figure 5-57), the relationship 

between number of vessels and high-pressure pump speed is nonlinear. For example, consider 

the results in Figure 5-55 for a booster pump speed of 3,000 rpm. At each high-pressure pump 

speed, the system recovery ratio initially increases as the number of vessels is increased. 

However, with a large number of vessels, the system recovery ratio does not change 

significantly with further increases in the number of vessels. This behavior would suggest that 

initially the throughput of the system is easily increased with an increasing number of vessels 

without a substantial increase in feedwater flow. However, there is a point of diminishing 

returns where changes in recovery ratio are not easily made. In this case, an increase in 

feedwater flow rates is required for an increase in permeate flow. The number of vessels at 

which the recovery ratio stabilizes is lower as the high-pressure pump speed is increased. The 

impact of booster pump speed on the recovery ratio is to slightly decrease the system recovery 

and incur an increase in power consumption. As expected, the impact of the permeate recycle 

is to drop the overall system recovery rate. 

Percentage Distance From Constraints, Booster speed 3000 rpm Recycle Vale Pos ition 0% Percentage Distance From Cons traints, Booster speed 3000 rpm Recycle Vale Position 20% 

12.2 10.9 9.7 8.6 -2.4 -19.9 

11.7 10.3 9 7.7 5.2 -11.1 

11.4 10 8.6 7. 2 5.9 -5.6 

11.2 9.7 8.3 6.9 5.6 -1.4 

11.1 9.5 8.1 6.7 5.3 2 

9.9 9.4 7.9 6.5 5.2 3.9 

2.5 8.3 7.8 6.4 5 3.7 

-3.2 2.2 7.5 6.3 5 3.7 

-7.7 -2.6 2.4 6.3 4.9 3.6 

-11.3 -6.5 -1.8 2.8 4.9 3.6 

-14.3 -9.7 -5.2 -0.9 3.2 3.6 

-16.8 -12.4 -8.1 -4 -0.1 3.7 

12.1 10.8 9.6 8.4 -4.3 -22 

11.6 10.2 8.9 7.6 3.3 -13.2 

11.3 9.8 8.4 7.1 5.8 -7.7 

11.1 9.6 8.1 6.7 5.4 -3.4 

10.9 9.4 7.9 6.5 5.2 0.1 

9.8 9.3 7.8 6.4 5 3.2 

2.4 8.2 7.7 6.3 4.9 3.6 

-3.3 2.1 7.4 6.2 4.8 3.5 

-7.8 -2.7 2.2 6.1 4.8 3.5 

-11.4 -6.6 -1.9 2.6 4.8 3.5 

-14.4 -9.8 -5.4 -1.1 3 3.5 

10 -16.9 -12.5 -8.3 -4.2 -0.3 3.5 120 

5 100 

Numbe r of Vessels 

Number of Vessels 

0 

-5 

80 

60 

-10 

-15 

40 

20 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-43. Percentage distance from constraint for N2 = 3,000 rpm, recycle valve 

at 0% and 20% opening 

85 

-20 

-15 

-10 

-5 

0 

5 

10 
20 

40 

60 

80 

100 

120 

-5 

0 

5 

10 

20 

40 

60 

80 

100 

120 

80 

100 

120 

Percentage Distance From Constraints, Booster speed 3540 rpm Recycle Vale Pos ition 0% Percentage Distance From Cons traints, Booster speed 3540 rpm Recycle Vale Position 20% 

10 120 

12.5 11.2 10 8.7 0.2 -17.6 

12.1 10.6 9.3 7.9 6.6 -9.1 

11.8 10.3 8.8 7.4 6.1 -3.8 

11.6 10 8.5 7.1 5.7 0.3 

11.4 9.8 8.3 6.9 5.5 3.7 

7.7 9.7 8.2 6.7 5.3 4 

0.5 6.5 8.1 6.6 5.2 3.9 

-5 0.5 5.9 6.6 5.2 3.9 

-9.4 -4.2 0.9 5.8 5.1 3.8 

-12.9 -8 -3.2 1.4 5.1 3.8 

-15.9 -11.2 -6.6 -2.2 2 3.8 

-18.3 -13.8 -9.5 -5.3 -1.3 2.6 

12.6 11.3 10.1 8.9 2 -15.5 

12.2 10.8 9.4 8.1 6.8 -7 

11.9 10.4 9 7.6 6.3 -1.7 

11.7 10.2 8.7 7.3 5.9 2.2 

11.6 10 8.5 7 5.7 4.3 

7.8 9.9 8.3 6.9 5.5 4.2 

0.6 6.6 8.2 6.8 5.4 4.1 

-4.9 0.6 6 6.7 5.3 4 

-9.3 -4.1 1 5.9 5.3 3.9 

-12.9 -7.9 -3.1 1.6 5.2 3.9 

-15.8 -11.1 -6.5 -2.1 2.2 3.9 

-18.2 -13.7 -9.3 -5.1 -1.1 2.8 

5 100 

Numbe r of Vessels 

Number of Vessels 

0 

-5 

80 

60 

-10 

-15 

40 

20 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-44. Percentage distance from constraint for N2 = 3,540 rpm, recycle valve 

at 0% and 20% opening 

Percentage Distance From Constraints, Booster speed 3900 rpm Recycle Vale Pos ition 0% Percentage Distance From Cons traints, Booster speed 3900 rpm Recycle Vale Position 20% 

12.9 11.6 10.3 9.1 5.3 -12.2 

12.5 11.1 9.7 8.3 7 -3.9 

12.3 10.7 9.3 7.9 6.5 1.2 

12.1 10.5 9 7.5 6.2 4.8 

12 10.3 8.8 7. 3 5.9 4.6 

6.2 10.2 8.7 7.2 5.8 4.4 

-0.9 5.2 8.6 7.1 5.6 4.3 

-6.3 -0. 6 4.9 7 5.6 4.2 

-10.6 -5.2 0 4.9 5.5 4.2 

-14.1 -9 -4.1 0.6 5.2 4.2 

-17 -12.1 -7.4 -3 1.4 4.2 

-19.4 -14.7 -10.2 -6 -1.8 2.1 

12.8 11.5 10.2 9 3.5 -14.2 

12.4 10.9 9.5 8.2 6.9 -6 

12.1 10.6 9.1 7.7 6.4 -0.8 

12 10.4 8.8 7.4 6 3.2 

11.8 10.2 8.6 7.2 5.8 4.4 

6.2 10.1 8.5 7 5.6 4.3 

-0.9 5.1 8.4 6.9 5.5 4.2 

-6.4 -0.7 4.8 6.8 5.4 4.1 

-10.7 -5.3 -0.2 4.8 5.4 4.1 

-14.2 -9.1 -4.2 0.5 4.9 4.1 

-17 -12.2 -7.6 -3.1 1.2 4.1 

-19.4 -14.8 -10.4 -6.1 -2 1.9 10 120 

5 100 

Numbe r of Vessels 

Number of Vessels 

0 

-5 

80 

60 

-10 

40 

-15 

20 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-45. Percentage distance from constraint for N2 = 3,900 rpm, recycle valve 

at 0% and 20% opening 

Permeate Flow (gpm), Boos ter speed 3000 rpm Recy cle Vale Position 0% Permeate Flow (gpm), Booster speed 3000 rpm Recycle Vale Position 20% 

173.3 236.7 305.2 378.4 

[7]

456. 2 

[7]

538.5 

245.5 337.6 437.4 544.6 658. 8 

[7]

779.8 

307.5 423.6 549.9 685.8 830. 6 

[7]

983.8 

363.4 500.6 650 810.7 982 

[7] 

1163.2 

415.3 571.4 741.5 924.4 1119.2 1324.1 

464.3 637.9 826.8 1029.7 1245.4 1472.2 

511.5 701 907.2 1128.2 1362.3 1609.4 

[2]

556.9 761.5 983.7 1221.5 1473 1737.7 

[2]

601 

[2]

819.8 1056.9 1310 1577.8 1858.5 

[2]

644.1 

[2]

876.3 

[2]

1127.4 1395.3 1677.4 1972.8 

[2] 

686.3 

[2] 

931.2 

[2] 

1195.6 

[2] 

1476.9 1772.9 2081.5 

[2] 

728.5 

[2] 

985.7 

[2] 

1262.7 

[2] 

1556.8 

[2] 

1865.5 2186.7 

165.6 225.8 290.6 359.7 

[7]

433 

[7]

510.4 

236.9 325.2 420.6 522.7 631. 3 

[7]

745.9 

298.5 410.5 531.9 662.1 800. 5 

[7]

946.7 

354.1 486.9 631.2 785.9 950. 3 

[7] 

1123.8 

405.6 557.3 722 898.5 1086 1282.8 

454.3 623.2 806.5 1002.7 1210.8 1429.1 

500.9 685.5 886.1 1100.3 1326.6 1564.6 

[2]

545.8 745.5 961.7 1192.5 1435.8 1691.1 

[2]

589.4 

[2]

803.1 1034 1280.1 1539 1810.1 

[2]

631.9 

[2]

858.8 

[2]

1103.6 1363.8 1637.2 1922.6 

[2] 

673.4 

[2] 

912.9 

[2] 

1170.7 

[2] 

1444.2 1731.1 2029.4 

[2] 

715.1 

[2] 

966.7 

[2] 

1236.8 

[2] 

1522.8 

[2] 

1822.1 2132.7 

2000 120 

1800 

100 

1600 

Numbe r of Vessels Numbe r of Vessels 

1400 

1200 

1000 

80 

60 

800 

600 

40 

400 

200 

20 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-46. Permeate flow for N2 = 3,000 rpm, recycle valve 

at 0% and 20% opening

86 

-15 

-10 

-15 

-10 

-5 

0 

5 

10 

20 

40 

60 

200 

400 

600 

800 

1000 

1200 

1400 

1600 

1800 

2000 
20 

40 

60 

80 

100 

120 

1000 

1200 

1400 

1600 

1800 

2000 

20 

40 

60 

80 

100 

120 

80 

100 

120 

Permeate Flow (gpm), Boos ter speed 3540 rpm Recy cle Vale Position 0% Permeate Flow (gpm), Booster speed 3540 rpm Recycle Vale Position 20% 

2000 

147.3 207.2 271.7 340.6 413. 8 

[7]

491.1 

210.3 297.8 392.7 494.5 602. 7 

[7]

717.3 

264.9 375.8 496.5 626.1 764. 2 

[7]

910.2 

314.4 445.9 589.1 743.2 907. 2 1080.5 

360.5 510.5 674.1 849.9 1036.9 1233.5 

404.2 571.2 753.3 948.8 1156.4 1374.5 

446.2 629 828.1 1041.5 1267.4 1505.3 

[2]

486.9 684.4 899.3 1129.2 1372.2 1627.5 

[2]

526.4 

[2]

737.9 967.5 1212.8 1471.5 1742.6 

[2]

565.1 

[2]

789.7 

[2]

1033.1 1292.7 1565.9 1851.4 

[2] 

603 

[2] 

840.2 

[2] 

1096.6 

[2] 

1369.5 1656.3 1954.8 

[2] 

641 

[2] 

890.4 

[2] 

1159.2 

[2] 

1444.6 

[2] 

1743.8 2054.8 

154.1 217.1 285.2 358.2 435. 8 

[7]

518 

217.8 309 408.2 515 628. 8 

[7]

749.5 

272.8 387.6 513 648.2 792. 5 

[7]

945.5 

322.6 458.1 606.4 766.4 937. 1 1117.9 

369 523.3 692 874 1068.2 1273.5 

413.2 584.5 771.9 973.9 1189 1415.5 

455.6 642.9 847.2 1067.2 1301.7 1547.9 

[2]

496.7 698.9 919.5 1156.4 1407.4 1671.9 

[2]

536.8 

[2]

753 988.5 1241 1508 1788.6 

[2]

575.9 

[2]

805.6 

[2]

1055.1 1322.1 1604.2 1899.2 

[2] 

614.5 

[2] 

856.8 

[2] 

1119.6 

[2] 

1400.1 1695.8 2004.3 

[2] 

653.1 

[2] 

907.7 

[2] 

1183.1 

[2] 

1476.3 

[2] 

1784.8 2105.9 120 

1800 

100 1600 

1400 

1200 

1000 

Numbe r of Vessels Numbe r of Vessels 

80 

60 

800 

600 40 

400 

200 

20 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-47. Permeate flow for N2 = 3,540 rpm, recycle valve at 0% and 20% opening 

Permeate Flow (gpm), Boos ter speed 3900 rpm Recy cle Vale Position 0% Permeate Flow (gpm), Booster speed 3900 rpm Recycle Vale Position 20% 

133.5 193 257.3 326 399. 1 

[7]

476.4 

190.3 277.1 371.5 472.9 581 

[7]

695.4 

239.6 349.5 469.5 598.7 736. 5 

[7]

882.3 

284.5 414.7 557.2 710.7 874. 3 1047.3 

326.5 475 637.6 812.8 999. 4 1196.5 

366.5 531.9 712.8 907.6 1114.9 1332.8 

[2]

405 586 783.9 996.7 1222.3 1460 

[2]

442.4 

[2]

638.1 851.7 1081 1323.7 1579 

[2]

478.9 

[2]

688.5 

[2]

916.8 1161.5 1419.9 1691.2 

[2]

514.6 

[2]

737.4 

[2]

979.6 1238.5 1511.6 1797.3 

[2] 

549.8 

[2] 

785 

[2] 

1040.3 

[2] 

1312.6 1599.4 1898.2 

[2] 

585.2 

[2] 

832.4 

[2] 

1100.3 

[2] 

1385.2 

[2] 

1684.5 1995.8 

139.5 202.1 270 342.8 420. 3 

[7]

502.3 

197 287.4 386 492.4 606 

[7]

726.5 

246.7 360.4 485 619.6 763. 6 916.3 

291.9 426 573.3 732.6 902. 9 1083.4 

334.2 486.8 654.4 835.6 1029.3 1234.3 

374.6 544.1 730.3 931.4 1146 1372.2 

[2]

413.4 598.8 802 1021.1 1255 1500.9 

[2]

451.4 

[2]

651.5 870.7 1106.7 1357.8 1621.6 

[2]

488.4 

[2]

702.5 

[2]

936.4 1188.2 1454.8 1735.4 

[2]

524.6 

[2]

752 

[2]

1000.2 1266.4 1548.2 1843.2 

[2] 

560.3 

[2] 

800.5 

[2] 

1061.9 

[2] 

1341.6 1637.1 1945.8 

[2] 

596.3 

[2] 

848.6 

[2] 

1122.7 

[2] 

1415.3 

[2] 

1723.6 2044.8 

2000 

1800 

120 

1600 100 

1400 

Numbe r of Vessels Numbe r of Vessels 

80 

60 

1200 

1000 

800 

600 40

400 

20 

200 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-48. Permeate flow for N2 = 3,900 rpm, recycle valve at 0% and 20% opening 

Total Power (kW), Booster speed 3000 rpm Recycle Vale Position 0% Total Power (kW), Booster speed 3000 rpm Recycle Vale Position 20% 

92 127.1 170.5 223.2 

[7]

286. 1 

[7]

360.3 

120.5 169.6 230.4 304 391. 6 

[7]

494.2 

144.9 205.3 279.8 369.6 475. 7 

[7]

598.9 

166.6 236.5 322.3 424.8 545. 1 

[7] 

683.6 

186.5 264.5 359.6 472.5 603. 7 753.5 

204.9 290 392.9 514.2 654 812.7 

222.2 313.4 423 551.1 697. 6 863.5 

[2]

238.4 335.1 450.3 584 736. 2 907.6 

[2]

253.8 

[2]

355.2 475.3 613.6 770. 4 946.6 

[2]

268.3 

[2]

374 

[2]

498.1 640.4 801 981.4 

[2] 

282.1 

[2] 

391.5 

[2] 

519.2 

[2] 

664.7 828. 8 1013.1 

[2] 

295.4 

[2] 

408.1 

[2] 

538.8 

[2] 

687.2 

[2] 

854. 3 1042.8 1000 

120 

900 

800 100 

700 

600 

500 

Numbe r of Vessels 

80 

60 

400 

40 300 

200 20 

100 93.6 129.5 173.8 227.4 

[7]

291. 4 

[7]

366.8 

123.2 173.5 235.7 310.9 400. 2 

[7]

504.5 

148.3 210.3 286.6 378.3 486. 3 

[7]

611.6 

170.7 242.3 330 434.6 556. 9 

[7] 

697.5 

191 270.9 368 482.9 616. 1 767.8 

209.8 296.8 401.7 524.9 666. 7 827.1 

227.3 320.4 432 561.9 710. 2 877.7 

[2]

243.7 342.3 459.4 594.8 748. 6 921.5 

[2]

259.2 

[2]

362.5 484.3 624.3 782. 5 960.2 

[2]

273.9 

[2]

381.3 

[2]

507.1 650.8 812. 8 994.8 

[2] 

287.8 

[2] 

398.8 

[2] 

528 

[2] 

674.9 840. 3 1026.4 

[2] 

301.2 

[2] 

415.5 

[2] 

547.5 

[2] 

697.2 

[2] 

865. 7 1056 

Numbe r of Vessels 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-49. Total power for N2 = 3,000 rpm and recycle valve position 

at 0% and 20% opening

87 

200 

400 

600 

800 

200 

400 

600 

800 

1000 

1200 

1400 

1600 

1800 

20 

40 

60 

100 

200 

300 

400 

500 

600 

700 

800 

900 

1000 
20 

40 

60 

80 

100 

120 

500 

600 

700 

800 

900 

1000 

20 

40 

60 

80 

100 

120 

80 

100 

120 

Total Power (kW), Booster speed 3540 rpm Recycle Vale Position 0% Total Power (kW), Booster speed 3540 rpm Recycle Vale Position 20% 

1000 

95.3 130.1 173.3 225.7 288. 4 

[7]

362.2 

122.2 170.7 231 304.1 391. 3 

[7]

493.5 

145.5 205.2 279.1 368.3 474 

[7]

597.1 

166.6 235.6 320.8 423 543 681.6 

186.1 263.3 357.8 470.5 601. 9 752.3 

204.3 288.7 391.3 512.6 652. 9 812.1 

221.6 312.2 421.6 550 697. 6 864 

[2]

238 334.2 449.6 584 737 909.3 

[2]

253.6 

[2]

354.8 475.3 614.6 772. 3 949.5 

[2]

268.4 

[2]

374.2 

[2]

499 642.4 804. 2 985.4 

[2] 

282.7 

[2] 

392.4 

[2] 

520.9 

[2] 

667.8 833 1017.9 

[2] 

296.4 

[2] 

409.7 

[2] 

541.6 

[2] 

691.3 

[2] 

859. 6 1048.2 

96.7 132.4 176.4 229.8 293. 5 

[7]

368.6 

124.6 174.4 236 310.8 399. 6 

[7]

503.6 

148.6 209.9 285.5 376.7 484. 4 

[7]

609.5 

170.2 241.1 328.2 432.5 554. 6 695.3 

190.1 269.3 365.9 480.7 614. 1 766.2 

208.7 295.1 399.8 523.1 665. 4 826.4 

226.3 318.9 430.5 560.8 709. 9 878.2 

[2]

242.9 341.1 458.5 594.6 749. 3 923.3 

[2]

258.6 

[2]

361.8 484.2 625.1 784. 4 963.1 

[2]

273.7 

[2]

381.2 

[2]

507.8 652.7 815. 9 998.7 

[2] 

288 

[2] 

399.5 

[2] 

529.7 

[2] 

677.9 844. 5 1031 

[2] 

301.9 

[2] 

416.9 

[2] 

550.2 

[2] 

701.3 

[2] 

870. 8 1061.2 120 

900 

100 800 

700 

600 

500 

Numbe r of Vessels 

80 

60

Numbe r of Vessels 

400 

40 

300 

200 20 

100 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-50. Total power for N2 = 3,540 rpm and recycle valve position at 0% and 20% opening 

Total Power (kW), Booster speed 3900 rpm Recycle Vale Position 0% Total Power (kW), Booster speed 3900 rpm Recycle Vale Position 20% 

98.8 134.3 178.1 231.3 294. 9 

[7] 

369.7 

125.3 174.7 236 310.3 398.8 

[7]

502.6 

148.5 209.1 284.3 375.1 482.6 

[7]

607.5 

169.5 239.7 326.4 430.4 552.4 693.2 

189.1 267.6 363.8 478.5 612 764.8 

207.5 293.2 397.7 521.2 663.8 825.4 

[2] 

225 317.1 428.6 559.4 709 878 

[2]

241.7 

[2]

339.5 457.1 593.8 749. 3 924.1 

[2]

257.6 

[2]

360.6 

[2]

483.3 625 785. 3 964.9 

[2] 

272.8 

[2] 

380.5 

[2] 

507.6 653.5 817. 8 1001.4 

[2] 

287.5 

[2] 

399.2 

[2] 

530.2 

[2] 

679.6 847. 3 1034.5 

[2] 

301.8 

[2] 

417.1 

[2] 

551.5 

[2] 

703.9 

[2] 

874. 5 1065.4 

97.5 132.2 175.2 227.4 289. 8 

[7]

363.5 

123.1 171.2 231.1 303.9 390. 7 

[7]

492.6 

145.6 204.7 278.1 367 472. 4 595.2 

166.2 234.6 319.2 421.1 541 679.6 

185.4 261.8 356 468.5 599. 9 750.6 

203.5 287.1 389.5 510.8 651. 4 811.1 

[2]

220.6 310.8 420.1 548.7 696. 7 863.9 

[2]

237.1 

[2]

332.9 448.4 583.2 737. 2 910.2 

[2]

252.9 

[2]

353.9 

[2]

474.6 614.6 773. 3 951.3 

[2]

268 

[2]

373.6 

[2]

499 643.2 806. 1 988.1 

[2] 

282.5 

[2] 

392.3 

[2] 

521.6 

[2] 

669.5 835. 8 1021.5 

[2] 

296.6 

[2] 

410.2 

[2] 

543 

[2] 

694 

[2] 

863. 3 1052.4 1000 

900 

1000 

900 

800 

700 

600 

120 

100 800 Number of Vessels 

700 

600 

500 

Numbe r of Vessels Numbe r of Vessels 

80 

60 500 

400 400 

40 

300 

200 20 

300 

200 

100 100 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-51. Total power for N2 = 3,900 rpm and recycle valve position 

at 0% and 20% opening 

Specific Power (kWh/m 3), Booster speed 3000 rpm Recycle Vale Position 0% Specific Power (kWh/m 3), Booster speed 3000 rpm Rec ycle Vale Position 20%

2.5 2.5 2.6 2.8 

[7]

3 

[7]

3.2 

2.3 2.3 2.5 2.6 2.8 

[7]

3 

2.2 2.3 2.4 2.5 2.7 

[7]

2.8 

2.1 2.2 2.3 2.4 2.6 

[7] 

2.7 

2.1 2.1 2.2 2.4 2.5 2.6 

2 2.1 2.2 2.3 2.4 2.5 

2 2.1 2.1 2.2 2.4 2.5 

[2]

2 2 2.1 2.2 2.3 2.4 

[2]

1.9 

[2]

2 2.1 2.1 2.2 2.3 

[2]

1.9 

[2]

2 

[2]

2 2.1 2.2 2.3 

[2] 

1.9 

[2] 

1.9 

[2] 

2 

[2] 

2.1 2.1 2.2 

[2] 

1.9 

[2] 

1.9 

[2] 

1.9 

[2] 

2 

[2] 

2.1 2.2 

2.3 2.4 2.5 2.6 

[7]

2.8 

[7]

2.9 

2.2 2.2 2.3 2.5 2.6 

[7]

2.8 

2.1 2.1 2.2 2.4 2.5 

[7]

2.7 

2 2.1 2.2 2. 3 2.4 

[7] 

2.6 

2 2 2.1 2. 3 2.4 2.5 

1.9 2 2.1 2.2 2.3 2.4 

1.9 2 2.1 2.2 2.3 2.4 

[2]

1.9 1.9 2 2.1 2.2 2.3 

[2]

1.9 

[2]

1.9 2 2.1 2.1 2.2 

[2]

1.8 

[2]

1.9 

[2]

1.9 2 2.1 2.2 

[2] 

1.8 

[2] 

1.9 

[2] 

1.9 

[2] 

2 2.1 2.1 

[2] 

1.8 

[2] 

1.8 

[2] 

1.9 

[2] 

1.9 

[2] 

2 2.1 120 

100 

2.8 

2.6 

Numbe r of Vessels 

80 

60 

2.4 

2.2 

40 

2 

20 

1.8 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-52. Specific energy consumption for N2 = 3,000 rpm and recycle valve 

position at 0% and 20% opening 

88 

100 

200 

300 

400 

20 

40 

60 

2 

2.2 

2.4 

2.6 

2.8 

3 
20 

40 

60 

80 

100 

120 

2.6 

2.8 

3 

3.2 

20 

40 

60 

80 

100 

120 

Specific Power (kWh/m 3), Booster speed 3540 rpm Recycle Vale Position 0% Specific Power (kWh/m 3), Booster speed 3540 rpm Rec ycle Vale Position 20% 

3 

2.7 2.6 2.7 2.8 2.9 

[7]

3.1 

2.5 2.4 2.5 2.6 2.7 

[7]

2.9 

2.3 2.3 2.4 2.5 2.6 

[7]

2.8 

2.3 2.3 2.3 2.4 2.6 2.7 

2.2 2.2 2.3 2.4 2.5 2.6 

2.2 2.2 2.2 2.3 2.4 2.5 

2.1 2.1 2.2 2.3 2.4 2.5 

[2]

2.1 2.1 2.2 2.2 2.3 2.4 

[2]

2.1 

[2]

2.1 2.1 2.2 2.3 2.3 

[2]

2.1 

[2]

2 

[2]

2.1 2. 1 2.2 2.3 

[2] 

2 

[2] 

2 

[2] 

2 

[2] 

2.1 2.2 2.2 

[2] 

2 

[2] 

2 

[2] 

2 

[2] 

2.1 

[2] 

2.1 2.2 120 

2.9 

2.8 100 

2.7 

2.6 

2.5 

2.4 

2.3 

Numbe r of Vessels 

80 

60 

40 

2.2 

2.1 

2 

20 

2.9 2.8 2.9 3 3.1 

[7]

3.3 

2.6 2.6 2.6 2.8 2.9 

[7]

3.1 

2.5 2.5 2.5 2.6 2.8 

[7]

2.9 

2.4 2.4 2.5 2.6 2.7 2.8 

2.3 2.3 2.4 2.5 2.6 2.7 

2.3 2.3 2.3 2.4 2.5 2.6 

2.2 2.2 2.3 2.4 2.5 2.6 

[2]

2.2 2.2 2.2 2.3 2.4 2.5 

[2]

2.2 

[2]

2.2 2.2 2.3 2.3 2.4 

[2]

2.1 

[2]

2.1 

[2]

2.2 2.2 2.3 2.4 

[2] 

2.1 

[2] 

2.1 

[2] 

2.1 

[2] 

2.2 2.2 2.3 

[2] 

2.1 

[2] 

2.1 

[2] 

2.1 

[2] 

2.1 

[2] 

2.2 2.3 

Numbe r of Vessels 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-53. Specific energy consumption for N2 = 3,540 rpm and recycle valve 

position at 0% and 20% opening 

Specific Power (kWh/m 3), Booster speed 3900 rpm Recycle Vale Position 0% Specific Power (kWh/m 3), Booster speed 3900 rpm Rec ycle Vale Position 20% 

3.1 2.9 2.9 2.9 3 

[7]

3.2 

2.8 2.6 2.6 2.7 2.8 

[7]

3 

2.6 2.5 2.5 2.6 2.7 2.9 

2.5 2.4 2.5 2.5 2.6 2.8 

2.4 2.4 2.4 2.5 2.6 2.7 

2.4 2.3 2.3 2.4 2.5 2.6 

[2]

2.3 2.3 2.3 2.4 2.4 2.5 

[2]

2.3 

[2]

2.3 2.3 2.3 2.4 2.5 

[2]

2.3 

[2]

2.2 

[2]

2.2 2. 3 2.3 2.4 

[2]

2.2 

[2]

2.2 

[2]

2.2 2. 2 2.3 2.4 

[2] 

2.2 

[2] 

2.2 

[2] 

2.2 

[2] 

2.2 2.2 2.3 

[2] 

2.2 

[2] 

2.1 

[2] 

2.1 

[2] 

2.2 

[2] 

2.2 2.3 

3.3 3.1 3 3.1 3.3 

[7]

3.4 

2.9 2.8 2.8 2.9 3 

[7]

3.2 

2.7 2.6 2.7 2.8 2.9 

[7]

3 

2.6 2.5 2.6 2.7 2.8 2.9 

2.6 2.5 2.5 2.6 2.7 2.8 

2.5 2.4 2.5 2.5 2.6 2.7 

[2]

2.4 2.4 2.4 2.5 2.6 2.6 

[2]

2.4 

[2]

2.3 2.4 2.4 2.5 2.6 

[2]

2.4 

[2]

2.3 

[2]

2.3 2.4 2.4 2.5 

[2]

2.3 

[2]

2.3 

[2]

2.3 2.3 2.4 2.5 

[2] 

2.3 

[2] 

2.2 

[2] 

2.2 

[2] 

2.3 2.3 2.4 

[2] 

2.3 

[2] 

2.2 

[2] 

2.2 

[2] 

2.2 

[2] 

2.3 2.4 3.1 120 

3 

100 2.9 

2.8 

2.7 

2.6 

2.5 

Numbe r of Vessels Numbe r of Vessels 

80 

60 

2.4 40 

2.3 

20 2.2 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-54. Specific energy consumption for N2 = 3,900 rpm and recycle valve 

position at 0% and 20% opening 

89 

2.2 

2.4 

2.4 

2.6 

2.8 

3 

3.2 

3.4 
20 

40 

60 

80 

100 

120 

30 

35 

40 

45 

50 

20 

40 

60 

80 

100 

120 

System Recovery Ratio, Booster speed 3000 rpm Recy cle Vale Position 0% System Recovery Ratio, Booster speed 3000 rpm Recycle Vale Position 20% 

50 120 

20.8 25.2 29.1 32.5 

[7]

35.6 

[7]

38.3 

24.8 30 34.4 38.2 41.6 

[7]

44.6 

27.1 32.6 37.3 41.3 44.9 

[7]

47.9 

28.6 34.2 39.1 43.2 46.8 

[7] 

49.9 

29.6 35.3 40.2 44.4 48 51.1 

30.3 36 40.9 45.1 48.7 51.9 

30.8 36.5 41.5 45.6 49.2 52.4 

[2]

31.1 36.9 41.8 46 49.6 52.7 

[2]

31.4 

[2]

37.1 42 46.2 49.8 52.9 

[2]

31.6 

[2]

37.3 

[2]

42.2 46.3 49.9 52.9 

[2] 

31.7 

[2] 

37.4 

[2] 

42.3 

[2] 

46.4 49.9 53 

[2] 

31.9 

[2] 

37.5 

[2] 

42.3 

[2] 

46.4 

[2] 

49.9 52.9 

20 24.3 28.1 31.4 

[7]

34.4 

[7]

37.1 

24.2 29.2 33.5 37.3 40.6 

[7]

43.5 

26.6 31.9 36.5 40.5 44 

[7]

47 

28.1 33.6 38.4 42.4 46 

[7] 

49.1 

29.1 34.8 39.6 43.7 47.3 50.3 

29.8 35.5 40.4 44.5 48.1 51.2 

30.3 36 40.9 45.1 48.6 51.7 

[2]

30.7 36.4 41.3 45.4 49 52 

[2]

31 

[2]

36.7 41.5 45.6 49.2 52.2 

[2]

31.2 

[2]

36.9 

[2]

41.7 45.8 49.3 52.3 

[2] 

31.3 

[2] 

37 

[2] 

41.8 

[2] 

45.9 49.4 52.4 

[2] 

31.5 

[2] 

37.1 

[2] 

41.9 

[2] 

45.9 

[2] 

49.4 52.4 

45 100 

Numbe r of Vessels Numbe r of Vessels 

40 

35 

80 

60 

30 

25 

40 

20 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-55. System recovery ratio for N2 = 3,000 rpm and recycle valve position at 

0% and 20% opening 

System Recovery Ratio, Booster speed 3540 rpm Recy cle Vale Position 0% System Recovery Ratio, Booster speed 3540 rpm Recycle Vale Position 20% 

18.5 23.1 27 30.5 33.7 

[7]

36.4 

22.4 27.8 32.3 36.3 39.8 

[7]

42.9 

24.7 30.4 35.3 39.5 43.1 

[7]

46.3 

26.1 32.1 37.1 41.4 45.1 48.3 

27.1 33.2 38.3 42.6 46.4 49.6 

27.8 33.9 39.1 43.5 47.2 50.4 

28.3 34.4 39.6 44 47.7 51 

[2]

28.7 34.8 40 44.4 48.1 51.3 

[2]

29 

[2]

35.1 40.2 44.6 48.3 51.5 

[2]

29.2 

[2]

35.3 

[2]

40.4 44.8 48.5 51.6 

[2] 

29.4 

[2] 

35.4 

[2] 

40.5 

[2] 

44.8 48.5 51.7 

[2] 

29.5 

[2] 

35.6 

[2] 

40.6 

[2] 

44.9 

[2] 

48.5 51.7 

19.2 23.9 28 31.6 34.8 

[7]

37.7 

23 28.5 33.2 37.3 40.8 

[7]

43.9 

25.2 31.1 36 40.3 44 

[7]

47.2 

26.6 32.6 37.8 42.1 45.9 49.2 

27.6 33.7 38.9 43.3 47.1 50.4 

28.2 34.4 39.6 44.1 47.9 51.1 

28.7 34.9 40.1 44.6 48.4 51.6 

[2]

29.1 35.3 40.5 44.9 48.7 52 

[2]

29.4 

[2]

35.5 40.7 45.1 48.9 52.1 

[2]

29.6 

[2]

35.7 

[2]

40.9 45.3 49 52.2 

[2] 

29.8 

[2] 

35.9 

[2] 

41 

[2] 

45.3 49.1 52.2 

[2] 

29.9 

[2] 

36 

[2] 

41.1 

[2] 

45.4 

[2] 

49.1 52.2 50 120 

45 100 

40 

35

Numbe r of Vessels Numbe r of Vessels 

80 

60 

30 

25 

40 

20 

20 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-56. System recovery ratio for N2 = 3,540 rpm and recycle valve position at 

0% and 20% opening 

90 

25 

20 

25 

30 

35 

40 

45 

50 
20 

40 

60 

80 

100 

120 

30 

35 

40 

45 

50 

System Recovery Ratio, Booster speed 3900 rpm Recy cle Vale Position 0% System Recovery Ratio, Booster speed 3900 rpm Recycle Vale Position 20% 

50 120 

18 22.9 27.2 30.9 34.2 

[7]

37.2 

21.6 27.3 32.2 36.5 40.1 

[7]

43.4 

23.6 29.8 35 39.5 43.3 46.7 

25 31.4 36.7 41.3 45.2 48.6 

25.9 32.4 37.8 42.5 46.4 49.8 

26.6 33.1 38.6 43.2 47.2 50.6 

[2]

27.1 33.6 39.1 43.7 47.7 51.1 

[2]

27.4 

[2]

34 39.4 44.1 48 51.4 

[2]

27.7 

[2]

34.2 

[2]

39.7 44.3 48.2 51.6 

[2]

28 

[2]

34.4 

[2]

39.9 44.4 48.3 51.7 

[2] 

28.1 

[2] 

34.6 

[2] 

40 

[2] 

44.5 48.4 51.7 

[2] 

28.3 

[2] 

34.7 

[2] 

40 

[2] 

44.6 

[2] 

48.4 51.7 

45 

100 

40 

35 

Number of Vessels 

80 

60 

30 

40 

25 

20 

20 17.3 22.1 26.2 29.9 33.1 

[7] 

35.9 

21 26.6 31.4 35.5 39.1 

[7]

42.3 

23.1 29.2 34.3 38.7 42.4 

[7]

45.7 

24.5 30.8 36.1 40.6 44.4 47.8 

25.5 31.9 37.2 41.8 45.7 49.1 

26.2 32.6 38 42.6 46.5 49.9 

[2] 

26.7 33.1 38.6 43.2 47.1 50.4 

[2]

27.1 

[2]

33.5 39 43.5 47.4 50.8 

[2]

27.4 

[2]

33.8 

[2]

39.2 43.8 47.6 51 

[2] 

27.6 

[2] 

34 

[2] 

39.4 43.9 47.8 51.1 

[2] 

27.8 

[2] 

34.2 

[2] 

39.5 

[2] 

44 47.8 51.1 

[2] 

28 

[2] 

34.3 

[2] 

39.6 

[2] 

44.1 

[2] 

47.9 51.1 

Numbe r of Vessels 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-57. System recovery ratio for N2 = 3,900 rpm and recycle valve position at 

0% and 20% opening 

91 

20 

25 
5.3 Brackish Water 

The seawater RO design objective is to obtain a viable commercial wind-RO system 

configuration that can provide purified product water at a cost that is competitive with 

traditionally powered RO systems. Because there is a plentiful supply of brackish water in 

many remote areas that have no power infrastructure or where energy costs are high, a windpowered RO system that can produce competitively priced water is desirable. The challenges 

are that brackish water dissolved solids can vary even more than those of seawater; other solid 

contaminants also pose an issue, as they must be removed by settling or filtration before RO 

treatment. Because of the great variation in brackish feedwater, the model configuration 

represents an example case study. Since the model is robust to the feedwater input 

concentrations, it can easily be adjusted to optimize a configuration for a site-specific 

application of the wind-powered RO system. Even on a specific site, individual well sources 

of brackish water may vary greatly in composition. For these specific cases, a homogenizing 

feed tank may be desirable to average the concentration of the feed so the membrane does not 

incur wide swings in ionic feed concentrations. This would require additional capital. 

In addition, brackish water is moderately corrosive and has varying compositions of brackish 

water, so construction materials are important. For the brackish water system to be 

considered, the TDS of the feedwater is taken as ~5,000 ppm. Table 5-9 shows the breakdown 

of cations and anions in the model brackish water considered. 

Table 5-9. Model Brackish Water Feed Composition 

Component Concentration 

(ppm) 

CATIONS 

Sodium 1,370 

ANIONS 

Bicarbonate 3,626 

Chlorine 0.41 

Carbonate 3.61 

NON-VALENT 

Carbon Dioxide 486 

TDS 5,000 

pH 7.0 

92 
We took this input and the methodology outlined in section 5.1.1 to develop a steady-state 

model for a two-stage RO system. The design goals were to provide the maximum amount of 

water for the given power input (product yield) and to meet WHO standards

42 for product 

quality. Because product yield and quality typically are at odds with one another, several RO 

system sizes and pressure and pumping schemes were considered for the power requirements. 

5.3.1 BW-WE-a1 Nominal Design 

Based on the single- and two-stage analysis and optimization for seawater, the two-stage 

system can maximize production of a given feed stream. Because brackish water has typically 

six to seven times less TDS, the two-stage RO system was chosen as the base design. The first 

design considered was a two-stage RO system, with energy recovery and the option of 

interstage pumping to boost pressure in the second stage. This model is designated BW-WEa1. The BW refers to brackish water, the WE is for work exchanger (energy recovery), and 

the a1 design is a two-stage system. The system is depicted schematically in Figure 5-58. In 

performing the power calculations as outlined in section 5.1.1, two design options concerned 

the interstage boost and the ERD DWEER described in section 3.2.6: (1) provide a pump to 

boost the brine outlet pressure from the first stage before it enters the second stage; and (2) 

provide a booster pump to the feed, which has already recovered energy from the DWEER, 

but is still at a lower pressure than the main feed system to the RO unit. Based on a power and 

pressure study of each of these possible configurations, we determined that there were only 

two viable alternatives. Because the brackish water is much lower in brine content, the TDS 

of the brine outlet from the first stage is at high enough pressure for further recovery of 

permeate. Since the seawater model showed little difference in the SW-WE-a1 and SW-WEa3 configurations, we decided to look at the DWEER boost case for brackish water as the 

viable option. 

Power was calculated with nominal values for pressure and flow until a value for the total 

power is about 540 kW. This gives a baseline for the configuration. 

Next, the RO membrane steady-state model33 is applied to determine the appropriate 

configuration for the RO portion of the configuration. This model uses the feed described 

earlier in this section and is optimized using the constraints detailed in Table 5-10. These 

constraints have been determined by industry design standards, and the capabilities of the 

membranes manufactured by Toray Membrane America, Inc.33. 

93 
Acid tank 

Permeate 1 Product Water 

Filter Pump 

Brackish Water 

Feed - Well 

Filter 

Filter 

Feed 

Filter 

Solids 

RO Feed 

Pump 1 

High-P 

Main 

RO Feed 

RO-1 

Low-P 

Feed 

HP 

RO Make-up 

Feed 

Acid Pump 

Acid 

Feed High-P 

Combined 

RO Feed 

RO Feed 

Pump 2 

Permeate 2 

RO-2 

Feed 

RO-2 

RO Feed

Pump 3 DWEER 

Concentrate 2 Feed

Booster

Pump

Low-P 

Feed Bypass Low-P Brine Out 

Figure 5-58. BW-WE-a1 configuration with DWEER boost

Table 5-10. Membrane Design Parameters 

Parameter Value/Range REMARKS 

Feed Flow Lower limit > 15 gpm on the last 

element in the train 

gpm = gal/min 

Permeate Flux Brackish: 10 < gfd <16 (17−27 lmh) gfd = gal/ft

2

/d; lmh = l/m2/h 

Limits: scaling, feed P, and 

osmotic P 

Feed Pressure Brackish: 600 psig/41 bar 

Pressure Drop < 20 psi (1.4 bar)/module 

< 60 psi (4.0 bar)/vessel 

Limitation by membrane 

structure 

Permeate < 500 ppm TDS, 250 Na, Cl-0.5 

ppm Boron 

WHO limits42 

RO Recovery Brackish: 70%−80% 

Temperature < 45°C (113°F) for operation Element limitations 

Fouling 10% permeate flux decline per year 

Membrane Lifetime 3−5 years 

5.3.1.1 Filter model 

In this design, the primary feed is from a brackish water well, which required suspended 

solids to be filtrated. This filter is modeled with a standard design equation24

, which is 

detailed in section 5.2.1. The volumetric flow rate V is given from the power calculations for 

94 
the BW-WE-a1 configuration. In turn, the surface area, A, of the filter can be calculated from 

this equation, then the capital cost of the filter can be determined24,25. This cost is then 

included in the cost model of section 4.1. 

5.3.1.2 Power and reverse osmosis model optimization 

We used the design parameters from Table 5-10 and the flows from the power calculations to 

optimize the steady-state membrane model. The steady-state model for the RO membranes 

uses software developed by Toray Membrane America, Inc.33. Feed inputs are composition, 

feed, flow rate, and any pretreatment (pH adjustment, scale inhibitor, etc). The RO unit inputs 

are the type of membrane, the RO recovery, the number of stages, the number of RO elements 

per vessel, the membrane fouling factor, the salt passage rate per year, the age of the 

membrane, and the permeate backpressure. The model then converges a solution for the ion 

concentrations in the brine and permeate streams by use of the flux equation across a 

membrane shown in Eq. 5-5 and Eq. 5-6. 

The membrane flux, ion concentrations, and stream pressures are determined for each element 

and each stage of the model. Once converged, the model gives a steady-state output form the 

system. These outputs include the overall flows and pressures of each stream, the ion 

concentrations in each stream, and the individual and overall fluxes for the RO membrane 

system. 

At each convergence of the RO model, the output flows, and pressures from the membrane 

model were plugged back into the pump power calculations to see if the power was still 

optimal at about 540 kW. Since the feed flow is the largest power draw on the system, if the 

power was too low, the feed flow to the membrane model was increased. If the power was too 

high, the feed flow was decreased. This cycle was iterated until the maximum flow for the 

given power input through an RO system was achieved. Figure 5-59 shows the results of this 

optimization for the power calculations representing the configurations in Figure 5-58. The 

RO steady-state model outputs are found in Appendix A, which shows data from the DWEER 

boost case. 

The DWEER boost design of Figure 5-58 was optimized for the first stage of 82 vessels by 

seven elements per vessel, followed by a second stage of 39 vessels by seven elements per 

vessel. Each stage uses a Toray Membrane America, Inc. Model 720-370 seawater membrane. 

Appendix A details the specifications of this type of membrane. 

95 
Figure 5-59. Power calculations for BW-WE-a1 design with DWEER boost 

We used the RO membrane design reports and the power calculations to develop an overall 

process flow diagram of the BW-WE-a1 configuration. A flow diagram is shown for the 

DWEER boost case in Figure 5-60. English units for flow, pressure, and flux are gpm, psia, 

and gfd, respectively. Corresponding metric units are cmh, bar, and lmh. 

96 
Acid tank 

Filter Pump 

Brackish Water 

Feed - Well 

Filter 

Filter 

Feed 

Filter 

Solids 

RO Feed 

Pump 1 

High-P 

Main 

RO Feed 

RO-1 

Permeate 1 

RO-2 

Permeate 2 

Concentrate 2 

DWEER 

Low-P Brine Out 

Low-P 

Feed Bypass 

Low-P 

Feed 

HP 

RO Make-up 

Feed 

Product Water 

Acid Pump 

Acid 

Feed 

RO-2 

Feed 

High-P 

Combined 

RO Feed 

RO Feed 

Pump 2 

Feed 

Booster 

Pump 

RO Feed 

Pump 3 

3900 GPM 

3900 GPM 

45 PSIA 

3900 GPM 

30 PSIA 

689 GPM 

30 PSIA 

689 GPM 

269 PSIA 

3211 GPM 

30 PSIA 

3900 GPM 

268 PSIA 

2686 GPM 

15 PSIA 

TDS 74.9 PPM 

512 GPM 

15 PSIA 

TDS 433 PPM 

3198 GPM 

15 PSIA 

TDS 132 PPM 

1214 GPM 

258 PSIA 

702 GPM 

252 PSIA 

702 GPM 

15 PSIA 

68.9% Recovery 

18.2 GFD 

82 x 7 elements 

TM720-370 

42.2% Recovery 

7.31 GFD 

39 x 7 elements 

TM720-370 

1.0 GPM 

30 PSIA 

3211 GPM 

268 PSIA 

Acid tank 

Filter Pump 

Brackish Water 

Feed - Well 

Filter 

Filter 

Feed 

Filter 

Solids 

RO Feed 

Pump 1 

High-P

Main 

RO Feed 

RO-1 

Permeate 1 

RO-2 

Permeate 2 

Concentrate 2 

DWEER 

Low-P Brine Out 

Low-P 

Feed Bypass 

Low-P 

Feed 

HP 

RO Make-up 

Feed 

Product Water 

Acid Pump 

Acid 

Feed 

RO-2 

Feed 

High-P 

Combined 

RO Feed 

RO Feed 

Pump 2 

Feed 

Booster 

Pump 

RO Feed 

Pump 3 

886 CMH 

886 CMH 

3.1 Bar 

886 CMH 

2.07 Bar 

156.7 CMH 

2.07 Bar 

156.7 CMH 

18.5 Bar 

729.3 CMH 

2.07 Bar 

886 CMH 

18.5 Bar 

610.3 CMH 

1.03 Bar 

TDS 74.9 PPM 

116.3 CMH 

1.03 Bar 

TDS 433 PPM 

726.6 CMH 

1.03 Bar 

TDS 132 PPM 

275.7 CMH 

17.8 Bar 

159.4 CMH 

17.4 Bar 

159.4 CMH 

1.03 Bar 

0.2 CMH 

2.07 Bar 

729.3 CMH 

18.5 Bar 

68.9% Recovery 

30.9 LMH 

82 x 7 elements 

TM720-370 

42.2% Recovery 

12.4 LMH 

39 x 7 elements 

TM720-370 

Figure 5-60. BW-WE-a1 DWEER boost flow diagram 

5.3.1.3 Boron sensitivity analysis 

The level of Boron in permeate water is now set to 0.3−0.5 ppm by WHO42. To understand 

the sensitivity of this configuration to Boron, we increased its feed level to determine what its 

level in the feed would cause it to break through in the permeate to a level of 0.5 ppm. We 

used the steady-state RO membrane model33 to determine that the level of Boron in the feed 

that results in a 0.5-ppm level in the product permeate is 0.7 ppm. Since there is large 

97 
variation in brackish water Boron levels, any feedwater with Boron levels higher than 0.7 

ppm would require a redesign of the system for a specific situation. 

One way is to lower recovery on the current configurations to increase salt rejection, which 

lowers product output. This is the quality/productivity trade-off. For example, lowering the 

overall recovery of the current configurations from 82% to 70% (12% decrease), and allowing 

for the same permeate flow and power use as the base configurations, the increase in the feed 

Boron level is only to about 0.8 ppm (14% increase) to still meet the 0.5-ppm limit. There is 

little room for improvement in the current design to higher Boron levels. Therefore, if Boron 

levels are higher than 0.8 ppm, the best design option would be to have another RO Boron 

removal stage for the permeate only. This would require extra capital costs and increase 

energy consumption. Either a smaller production plant or a larger wind turbine would be 

required to compensate for the increased energy use. Those trade-offs in capital and operating 

expenses versus productivity would have to be assessed for specific high-Boron feed cases. 

5.3.2 Cost of Water Analysis 

Based on the above design, an overall COW is determined by calculating capital and 

operating costs for the configuration as outlined in detail in section 4.1. A summary of the 

cost is shown in Figure 5-61, which outlines the relevant capital and operating costs for the 

steady-state model. The model assumes an operating year of 350 days, with a permeate 

flowrate of 17,432 m3

/day (3,198 gpm). This yields an annual production of 6.1 x 106 m3/yr of 

product water. Rolling up all the capital and operating costs for this production level gives an 

overall steady-state COW of about $0.60/m3

. This cost can vary for a site-specific situation, 

where well construction costs, feed concentrations, and waste disposal costs can vary. The 

steady-state cost model, however, is flexible and can make provisions for these cost variances. 

98 
Figure 5-61. Summary costs for the steady-state BW-WE-a1 configuration 

5.3.3 Design Space Analysis 

We conducted a design space analysis to understand the extent of the operating envelope 

associated with the configuration described in Section 5.3.1. As in the previous 

configurations, the main purpose of this study is to investigate the points in the input space at 

which the system fails to satisfy all the component and system constraints. If the system were 

operated at these points, the potential for membrane degradation through fouling or scaling or 

membrane destruction caused by increased stresses may result. In addition to helping us 

understand where constraints are violated, the design space study provides some insight into 

how recovery ratio, specific energy consumption, total power, and permeate flow vary with 

the choice of input parameters. The qualitative understanding that the design space study 

provides is critical for understanding the potential for system optimization. 

99 
For the two-stage configuration shown in Figure 5-62, the input space is defined by the 

parameters listed in Table 5-11. 

Permeate

Exit Pressure

Feedwaterinlet

conditions of

pressure (p0),

concentration (c0), 

temperature (T0)

0

DWEEREnergy Recovery 

RO > > 

> RO 

Interstage 

Pump 

Booster 

Pump 

HPPump 

1 

2 

3 

4 5 

6 

7 

8 

9 

10 

11 

14 15 

16 

12 

18 17

13 

N1 

N2 

N3 

V1 

19 

S1 S2 

22 

Flow 

Sum 

Valve 

Flow 

Sum 

Flow 

Sum 

RO1 RO2 

V2 Valve 

V4 

Valve 

V3 Valve 

20 

DWEEREnergy Recovery

RO >

>

> RO

Interstage

Pump

Booster

Pump

HPPump

1

2

3

4 5

6

7

8

9

10

11

14 15

16

12

18 17

13

N1

N2

N3

V1

19

S1 S2

22

Flow

Sum

Valve

Flow

Sum

Flow

Sum

RO1 RO2

V2 Valve

V4

Valve

V3 Valve

20

DWEEREnergy Recovery

RO >

>

> RO

DWEEREnergy Recovery

p21 

Brine Exit Pressure p22 

p2

Interstage

Pump

Booster

Pump

HPPump

1

2

3

4 5

6

7

8

9

10

11

14 15

16

12

18 17

13

N1

N2

N3

V1

19

S1 S2

22

Flow

Sum

Valve

Flow

Sum

Flow

Sum

RO1 RO2

V2 Valve

V4

Valve

V3 Valve

20

RO >

>

> RO

Interstage

Pump

Booster

Pump

HPPump

1

2

3

4 5

6

7

8

9

10

11

14 15

16

12

18 17

13

N1

N2

N3

V1

19

S1 S2

22

Flow

Sum

Valve

Flow

Sum

Flow

Sum

RO1 RO2

V2 Valve

V4

Valve

V3 Valve

20

1

Brine Exit Pressure p22

Figure 5-62. RO system configuration BWWE-a1

Table 5-11. Input Parameters for Configuration BWWE-a1 

Parameter Description 

S1 Number of vessels in stage 1 

S2 Number of vessels in stage 2 

N1 High pressure pump speed 

N2 Booster pump speed 

N3 Interstage pump speed 

V1 Stage 1 permeate recycle valve position 

V2 Stage 1 permeate output valve position 

V3 Stage 2 permeate recycle valve position 

V4 Stage 2 permeate output valve position 

Since the valve positions V1−V4 are mainly used to initiate a recycle flow for very low wind 

power capture conditions, the design space analysis fixes these quantities V1 = V3 = 0 (valve 

closed) and V2 = V4 = 1 (valve fully opened). These valve positions indicate that there is no 

recycle of the permeate flow. 

Table 5-12 lists the parameter values investigated in the design space analysis for this 

configuration. 

100 
Table 5-12. Input Space Parameter Ranges for Configuration BWWE-a1 

Parameter Description Units Variation 

Range 

S1 Vessels in stage 1 - 40–120 

S2 Vessels in stage 2 - 20–70 

N1 High pressure pump speed rpm 3,000–3,900 

N2 Booster pump speed rpm 3,000–3,900 

N3 Interstage pump speed rpm 3,000–3,900 

V1 Stage 1 permeate recycle valve % open 0 (fully closed) 

V2 Stage 1 permeate output valve % open 1 (fully open) 

V3 Stage 2 permeate recycle valve % open 0 (fully closed) 

V4 Stage 2 permeate output valve % open 1 (fully open) 

p0 Feedwater pressure psid 20 

p21 Permeate exit pressure psid 15 

p22 Brine exit pressure psid 15 

T0 Feedwater temperature °C 25 

c0 Feedwater dissolved salt concentration kg/m3 4.8 

The steady-state constraints for the RO system are highlighted in Section 5.1.2 and listed in 

Table 5-13, which also lists the index associated with each constraint. This index reference is 

used in the figures associated with the analysis to highlight which constraints, if any, are 

being violated at a given point in the input space. 

Table 5-13. Constraint Definition for Configuration BWWE-a1 

Parameter Value/Range Index Used in Plots 

Element polarization Cm / Cavg < 1.2 1 – Stage 1 

2 – Stage 2 

Element concentration flow Qc > 15 gpm 3 – Stage 1 

4 – Stage 2 

Feedwater pressure Pf < 600 psi 5 

Element pressure drop ΔPelm < 10 psid 6 – Stage 1 

8 – Stage 2 

Vessel pressure drop ΔPvessel < 58 psid 7 – Stage 1 

9 – Stage 2 

Permeate quality Cp < 500 ppm 10 

Element flux Flux < 28.3 gfd 11 – Stage 1 

12 – Stage 2 

101 
The results of the design space analysis for the brackish water configuration BWWE-a1 are 

shown in Figure 5-63–Figure 5-87 for system parameters such as permeate flow, total power, 

specific energy consumption, and recovery ratio. The figures associated with these parameters 

also highlight the constraints violated in brackets and the system parameter value at each data 

point in the analysis. Finally, for each combination of input parameters that are presented, the 

distance to the constraint is identified in terms of percentage. The distance in terms of 

percentage from maximum constraints is given in Eq. 5-11 by 

Distance to constraint = Constraint Value − ParameterValue *100 Eq. 5-11 

ConstraintValue 

and the distance in terms of percentage from minimum constraints is given in Eq. 5-12 by 

Distance to constraint = ParameterValue − Constraint Value *100 Eq. 5-12 

ConstraintValue 

Positive numbers in these figures indicate that there are no limiting constraints, and the 

number shown in the figure is the distance to the most restrictive constraint. Negative 

numbers shown in the figures indicate that at least one constraint is being violated, and the 

number shown in the figure indicates the maximum constraint violation. 

Consider the results shown in Figure 5-63–Figure 5-77 for the case where the booster pump 

speed (N2) and interstage pump speed (N3) are set to 3,000 rpm, and the number of vessels in 

the second stage, S2, is varied from 20 to 40 to 60. For each value of S2, data associated with 

permeate flow, total power, specific power, recovery ratio, and distance from the constraint 

are shown as a function of high-pressure pump speed (N1) and the number of vessels in stage 

1 (S1). Figure 5-63 shows that when the number of vessels in the second stage is 20, S2 = 20, 

the available design space that meets all the constraints lies in a diagonal band across the N1, 

S1 input space. In particular, the results indicate that at low high-pressure pump speeds, the 

number of vessels in S1 must be limited to the lower values. As the high-pressure pump speed 

is increased, the region in which there is an allowable design space increases with the number 

of vessels in S1. At very large N1, e.g., 3,900 rpm, constraint violation occurs with a small 

number of vessels in stage 1. As the number of vessels in stage 2 increases, S2 = 40, the 

design space is slightly reduced at low high-pressure pump speeds (Figure 5-64). At larger 

values of N1, the number of vessels in S1 that fall into the allowable design space increases 

compared to the case when S2 = 20. Hence, as the number of vessels is increased from 20 to 

40, there is an increase in the allowable operating envelope of the configuration. Finally, at S2 

= 60 (Figure 5-65), there are no viable operating points in the N1-S1 input space for N2 = 

3,000 rpm, N3 = 3,000 rpm. Thus, as the number of stages is increased from 20 to 40 to 60, 

there is a potential for defining an optimal configuration that maximizes the allowable 

operating envelope. 

To better understand the limiting constraints, and the impact on additional system parameters, 

consider the permeate flow results shown in Figure 5-66−Figure 5-68. Figure 5-66 shows that 

the primary constraint being violated is the minimum concentration flow in the first stage. To 

understand this behavior, consider the situation when N1 = 3,000 rpm. For the range of S1, 

the total permeate flow is not vastly different. If the recovery ratio were essentially the same, 

102 
Figure 5-75, the larger number of vessels would indicate a reduction in the feedwater flow to 

each vessel. Consequently, as the number of vessels in S1 is increased, the concentration flow 

at each vessel is expected to decrease. At great high-pressure pump speeds, N1 = 3,900 rpm, 

the maximum flux constraint is violated in the second stage. This would suggest that the 

number of vessels in the second stage is too small for the system flow that results from the 

values of N1, N2, N3, S1 and S2. As the number of vessels in S2 is increased from 20 to 40 to 

60, Figure 5-67 and Figure 5-68, the limiting constraints are the concentration flow 

requirements for both stage 1 and stage 2. Again the previous argument can be used to 

understand this trend. With regard to the permeate flow itself, for a given N1 the magnitude of 

the change in permeate flow with an increase in S1 vessels diminishes. Finally, for a given S1, 

permeate flow increases with increased N1 because of the higher flow capabilities of the 

pump at higher speeds for the same pressure rise. However, the magnitude of the change in 

flow is greater for an increased number of vessels. 

The results in Figure 5-69–Figure 5-71 show that at a given N2, N3 combination, the total 

power consumed is primarily dictated by the high-pressure pump speed. This result is 

expected given that the high-pressure pump dominates the system energy consumption. The 

increase in the power consumed for a given N1 caused by an increase in S1 is slight. In fact 

the power consumption decreases slightly at first and then increases. At large S1, the power 

consumption levels off. By coupling the permeate flow results with the total power 

consumption results, the variation in specific energy consumption can be investigated (Figure 

5-72–Figure 5-74). The specific energy consumption decreases slightly, approximately 0.1 

kWh/m3

, at some S1-N1 combinations as the number of vessels in the second stage increases. 

In addition, as the number of vessels in the second stage increase, the range of S1−N1 

combinations where specific energy consumption is low increases. Finally, with regard to 

recovery ratio (Figure 5-75–Figure 5-77), the achievable recovery ratio increases with the 

number of vessels in the second stage. In addition, as the number of vessels in the second 

stage increases, a line of constant recovery ratio moves to the lower right in the S1–N1 range. 

To understand the impact of changes in the booster pump speed (N2), consider the changes in 

system parameters as booster pump speed is varied from 3,000 rpm to 3,540 rpm for a fixed 

number of vessels in the second stage, S2 = 40, and a fixed interstage pump speed of 3,000 

rpm. The distance from the limiting constraints is not significantly different in the acceptable 

regions of the design space (Figure 5-78). However, at the limiting boundary between the 

allowable and nonallowable design space, an increase in the constraint violation is observed. 

When considering permeate flow (Figure 5-79) as well as recovery ratio (Figure 5-82), 

variations in N2 have little impact. As expected, there is an increase in the total power 

consumed caused by the higher booster pump speed (Figure 5-80), which in turn leads to a 

higher specific energy consumption (Figure 5-81). The S1-N1 region with lower specific 

energy consumption expands into regions associated with larger high pressure pump speeds as 

booster pump speed is increased (Figure 5-81). Although not plotted, similar results were 

obtained at other interstage pump speeds and the two-stage vessel size. 

To understand the impact of changes in the interstage pump speed (N3), consider the changes 

in the system parameters as the interstage pump speed is varied from 3,000 rpm to 3,540 rpm 

for a fixed number of vessels in the second stage, S2 = 40 and a fixed booster speed of 3,000 

rpm. As the interstage pump speed is increased, the applicable design space increases; 

however, at each viable operating point, the degree of robustness is reduced (Figure 5-83), 

103 
which is evident from a reduction in the distance from the limiting constraint. Variation in N3 

also impacts the permeate flow in that the permeate flow is increased anywhere from 

approximately 3% at great high-pressure pump speeds to 5% at low high-pressure pump 

speeds (Figure 5-84). The increase in permeate flow, however, comes at a price of higher 

power consumption of approximately 50–60 kW over the S1−N1 input space (Figure 5-85). 

The recovery ratio, on the other hand, increases slightly, typically 0.1%, at most combinations 

of S1-N1 (Figure 5-87). The recovery is increases slightly, but the increase in power 

consumption offsets the increased permeate flow translating into a slight increase in the 

specific energy consumption as N3 is increased (Figure 5-86). Although not plotted, similar 

results were obtained at other two-stage vessel configurations and other booster pump speeds. 

Percentage Distance from Consraint, V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=20 

120 

5.3 4.9 4.5 2.6 -5.6 -14.1 

5.8 5.3 4.8 4.4 -2.7 -11.3 

5.7 5.6 5.1 4.6 0 -8.8 

-6.8 5.6 5.4 4.8 2.3 -6.7 

-20.8 -6. 1 5.6 5 4.3 -4.8 

-31.4 -18.2 -5.5 5.1 4.6 -3.2 

-39.5 -27.7 -16.3 -5.1 4.7 -1.8 

-46 -35.3 -24.9 -14.8 -4.8 -0.6 

-51.3 -41.5 -32 -22.7 -13.5 -4.6 0 

-10 

-20 

-30 

-40 

-50 

110 

100 

90 

80 

70

Stage 1 Number of Vessels 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-63. Percentage distance from constraint at N2 = 3,000 rpm, 

N3 = 3,000 rpm, and S2 = 20

Percentage Distance from Consraint, V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=40 

120 

110 

100 

-13.5 0.6 2.9 2.8 2.6 2.4 

-13.5 0.2 3.1 2.9 2.7 2.5 

-13.7 -0. 3 3.2 3 2.8 2.5 

-13.8 -0. 6 3.4 3.1 2.8 2.6 

-14 -0. 9 3.5 3.2 2.9 2.6 

-23 -6. 4 3.7 3.3 3 2.7 

-32.6 -17.5 -3.1 3.4 3.1 2.7 

-40.1 -26.4 -13.3 -0.7 3.1 2.8 

-46.2 -33.7 -21.7 -10.1 1 2.8 0 

-5 

-10 

-15 

-20 

-25 

-30 

-35 

-40 

-45 

Stage 1 Number of Vessels 

90 

80 

70 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-64. Percentage distance from constraint at N2 = 3,000 rpm, 

N3 = 3,000 rpm, and S2 = 40

104 
Percentage Distance from Consraint, V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=60 

120 

110 

-5 

-45.6 -36.9 -27.8 -18.5 -9.2 0 

-45.4 -36.9 -28.1 -19.1 -10.1 -1.1 

-45.4 -37 -28.4 -19.7 -10.9 -2.1 

-37.9 -37.1 -28.7 -20.1 -11.5 -2.9 

-45.4 -37.2 -28.9 -20.5 -12 -3.5 

-45.4 -37.2 -29.1 -20.8 -12.5 -4.1 

-45.5 -37.3 -29.3 -21.1 -12.8 -4.5 

-45.5 -37.4 -29.4 -21.3 -13.1 -4.9 

-45.6 -37.4 -29.5 -21.5 -13.4 -5.2 

-10 

-15 

-20 

-25 

-30 

-35 

-40 

-45 

Stage 1 Number of Vessels 

100 

90 

80 

70 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-65. Percentage distance from constraint at N2 = 3,000 rpm, 

N3 = 3,000 rpm, and S2 = 60 

System Permeate Flow (gpm), V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=20 

1650. 9 1855.9 2055 2250.6 

[12] 

2444.5 

[11 12] 

2637.7 

1722. 3 1945.3 2159.7 2368.6 

[12] 

2574.4 

[12] 

2778.3 

1770. 2 2007.2 2233.1 2451.7 

[12] 

2665.8 

[12] 

2877.1 

[3] 

1803.3 2052.1 2286.7 2512.9 2733.3 

[12] 

2950 

[3] 

1826.8 

[3] 

2084.6 2327.1 2559.4 2784.9 

[12] 

3005.8 

[3] 

1843.9 

[3] 

2109.5 

[3] 

2358.5 2595.8 2825.4 

[12] 

3049.7 

[3] 

1856.7 

[3] 

2128.4 

[3] 

2383.2 

[3] 

2624.9 2857.9 

[12] 

3085.1 

[3] 

1866.7 

[3] 

2144.1 

[3] 

2403.1 

[3] 

2648.5 

[3] 

2884.5 

[12] 

3114.1 

[3] 

1874.5 

[3] 

2156.4 

[3] 

2419.3 

[3] 

2668 

[3] 

2906.7 

[3] 

3138.4 3000 

2800 

2600 

2400 

2200 

2000 

1800 

120 

110 

100 

Number Vessels Stage 1 

90 

80 

70 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-66. Permeate flow for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 20 

System Permeate Flow (gpm), V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=40 

[4] 

1859. 3 2099.4 2325.2 2542 2753.6 2962.4 

[4] 

1914. 5 2175.2 2418.9 2651.1 2876.3 3097.2 

[4] 

1948 

[4] 

2225.2 2482.1 2725.6 2960.3 3189.5 

[4] 

1971.4 

[4] 

2259.8 2527 2779.1 3021 3255.7 

[3 4] 

1986.3 

[4] 

2284.6 2560.2 2819.2 3066.7 3306.9 

[3 4] 

1996.5 

[3 4] 

2302.8 2582 2850.1 3102.3 3346.3 

[3 4] 

2002.6 

[3 4] 

2316.7 

[3] 

2605.1 2874.5 3130.7 3377.7 

[3 4] 

2008.8 

[3 4] 

2327.4 

[3] 

2620.7 

[3] 

2894.3 3153.7 3403.4 

[3 4] 

2011. 1 

[3 4] 

2335.9 

[3] 

2633.4 

[3] 

2911.1 3172.7 3424.8 

3400 

3200 

3000 

2800 

2600 

2400 

2200 

2000 

120 

110 

100 

90 

80 

70

Number Vessels Stage 1 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-67. Permeate flow for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 40 

105 
System Permeate Flow (gpm), V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=60 

3500 120 

110 

100 

[4] 

1945 

[4] 

2205.9 

[4] 

2448.5 

[4] 

2677.7 

[4] 

2898.4 

[4] 

3114.4 

[4] 

1993.3 

[4] 

2274.5 

[4] 

2535.9 

[4] 

2781.9 

[4] 

3017.5 

[4] 

3246.5 

[4] 

2022. 7 

[4] 

2318.4 

[4] 

2593.4 

[4] 

2851.5 

[4] 

3097.6 

[4] 

3335.6 

[4] 

2118. 2 

[4] 

2348.3 

[4] 

2633.5 

[4] 

2900.7 

[4] 

3154.6 

[4] 

3399.4 

[3 4] 

2053. 6 

[4] 

2369.5 

[4] 

2662.7 

[4] 

2937.1 

[4] 

3197.1 

[4] 

3447.2 

[3 4] 

2061. 9 

[3 4] 

2385 

[4] 

2684.8 

[4] 

2964.9 

[4] 

3229.9 

[4] 

3484.1 

[3 4] 

2067. 6 

[3 4] 

2396.7 

[4] 

2701.8 

[4] 

2986.7 

[4] 

3255.8 

[4] 

3513.4 

[3 4] 

2071. 5 

[3 4] 

2405.6 

[3 4] 

2715.3 

[4] 

3004.2 

[4] 

3276.8 

[4] 

3537.3 

[3 4] 

2074. 4 

[3 4] 

2412.5 

[3 4] 

2726.1 

[3 4] 

3018.5 

[4] 

3294 

[4] 

3557 

3000 

2500 

2000 

Number Vessels Stage 1 

90 

80 

70 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-68. Permeate flow for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 60 

Total Power [kW], V1=0 V2=1 V3=0 V4= 1 N2=3000 N3= 3000 S2= 20 

120 

110 

100 

373.1 441.2 513.8 591.8 

[12] 

676. 1 

[11 12] 

767.2 

374.9 444 517.4 596.1 

[12] 

680. 8 

[12] 

772.2 

375.3 445.2 519.1 598.1 

[12] 

683. 1 

[12] 

774.7 

[3] 

375.1 445.6 519.9 599.2 684. 3 

[12] 

776.1 

[3] 

374.7 

[3] 

445.6 520.2 599.8 685 

[12] 

776.8 

[3] 

374.2 

[3] 

445.4 

[3] 

520.3 600 685. 4 

[12] 

777.2 

[3] 

373.7 

[3] 

445.2 

[3] 

520.3 

[3] 

600.1 685. 6 

[12] 

777.5 

[3] 

373.2 

[3] 

444.9 

[3] 

520.2 

[3] 

600.1 

[3] 

685. 7 

[12] 

777.6 

[3] 

372.7 

[3] 

444.7 

[3] 

520 

[3] 

600.1 

[3] 

685. 7 

[3] 

777.6 750 

700 

650 

600 

550 

500 

450 

400 

Number Vessels Stage 1 

90 

80 

70 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-69. Total power consumed at N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 20 

Total Power [kW], V1=0 V2=1 V3=0 V4= 1 N2=3000 N3= 3000 S2= 40 

120 

110 

100 

[4] 

387.4 455.3 527.1 604.2 687.4 777.8 

[4] 

387.3 456.2 528.7 606.1 689.5 779.8 

[4] 

386.4 

[4] 

456.2 529.1 606.8 690. 2 780.5 

[4] 

385.3 

[4] 

455.7 529.1 606.9 690. 5 780.8 

[3 4] 

384.2 

[4] 

455.1 528.8 606.9 690. 5 780.8 

[3 4] 

383.1 

[3 4] 

454.5 528.5 606.7 690. 4 780.7 

[3 4] 

382 

[3 4] 

453.8 

[3] 

528.1 606.5 690. 3 780.5 

[3 4] 

381.1 

[3 4] 

453.2 

[3] 

527.7 

[3] 

606.3 690. 1 780.4 

[3 4] 

380.3 

[3 4] 

452.7 

[3] 

527.4 

[3] 

606.1 689. 9 780.2 750 

700 

650 

600 

550 

500 

450 

400 

Number Vessels Stage 1 

90 

80 

70 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-70. Total power consumed at N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 40 

106 
Total Power [kW], V1=0 V2=1 V3=0 V4= 1 N2=3000 N3= 3000 S2= 60 

120 

110 

750 

700 

[4] 

391.6 

[4] 

459.1 

[4] 

530.4 

[4] 

606.8 

[4] 

689. 6 

[4] 

779.8 

[4] 

391 

[4] 

459.5 

[4] 

531.3 

[4] 

608 

[4] 

690. 8 

[4] 

780.7 

[4] 

389.9 

[4] 

459.2 

[4] 

531.4 

[4] 

608.3 

[4] 

691 

[4] 

780.8 

[4] 

392 

[4] 

458.5 

[4] 

531.2 

[4] 

608.2 

[4] 

691 

[4] 

780.7 

[3 4] 

387.3 

[4] 

457.8 

[4] 

530.8 

[4] 

608 

[4] 

690. 9 

[4] 

780.4 

[3 4] 

386.1 

[3 4] 

457.1 

[4] 

530.4 

[4] 

607.8 

[4] 

690. 6 

[4] 

780.2 

[3 4] 

385 

[3 4] 

456.4 

[4] 

530 

[4] 

607.5 

[4] 

690. 4 

[4] 

779.9 

[3 4] 

384 

[3 4] 

455.8 

[3 4] 

529.6 

[4] 

607.2 

[4] 

690. 2 

[4] 

779.6 

[3 4] 

383.1 

[3 4] 

455.2 

[3 4] 

529.2 

[3 4] 

607 

[4] 

690 

[4] 

779.4 

650 

600 

550 

500 

450 

400 

100 

Number Vessels Stage 1 

90 

80 

70 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-71. Total power consumed at N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 60 

System Specific Power [kWh/m 3], V1=0 V2=1 V3=0 V4=1 N2= 3000 N3=3000 S2=20 

120 

110 

100 

1 1 1.1 1.2 

[12] 

1.2 

[11 12] 

1.3 

1 1 1.1 1.1 

[12] 

1.2 

[12] 

1.2 

0.9 1 1 1.1 

[12] 

1.1 

[12] 

1.2 

[3] 

0.9 1 1 1 1.1 

[12] 

1.2 

[3] 

0.9 

[3] 

0.9 1 1 1.1 

[12] 

1.1 

[3] 

0.9 

[3] 

0.9 

[3] 

1 1 1.1 

[12] 

1.1 

[3] 

0.9 

[3] 

0.9 

[3] 

1 

[3] 

1 1.1 

[12] 

1.1 

[3] 

0.9 

[3] 

0.9 

[3] 

1 

[3] 

1 

[3] 

1 

[12] 

1.1 

[3] 

0.9 

[3] 

0.9 

[3] 

0.9 

[3] 

1 

[3] 

1 

[3] 

1.1 1.25 

1.2 

1.15 

1.1 

1.05 

1 

0.95 

0.9 

Number Vessels Stage 1 

90 

80 

70 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-72: Specific power consumption at N2 = 3,000 rpm,

N3 = 3,000 rpm, and S2 = 20 

System Specific Power [kWh/m 3], V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=40 

120 

110 

100 

[4] 

0.9 1 1 1 1.1 1.2 

[4] 

0.9 0.9 1 1 1.1 1.1 

[4] 

0.9 

[4] 

0.9 0.9 1 1 1.1 

[4] 

0.9 

[4] 

0.9 0.9 1 1 1.1 

[3 4] 

0.9 

[4] 

0.9 0.9 0. 9 1 1 

[3 4] 

0.8 

[3 4] 

0.9 0.9 0. 9 1 1 

[3 4] 

0.8 

[3 4] 

0.9 

[3] 

0.9 0. 9 1 1 

[3 4] 

0.8 

[3 4] 

0.9 

[3] 

0.9 

[3] 

0. 9 1 1 

[3 4] 

0.8 

[3 4] 

0.9 

[3] 

0.9 

[3] 

0. 9 1 1 

1.15 

1.1 

1.05 

1 

0.95 

0.9 

0.85 

Number Vessels Stage 1 

90 

80 

70 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-73. Specific power consumption at N2 = 3,000 rpm,

N3 = 3,000 rpm, and S2 = 40 

107 
System Specific Power [kWh/m 3], V1=0 V2=1 V3=0 V4=1 N2= 3000 N3=3000 S2=60 

1.1 

120 

110 1.05 

[4] 

0.9 

[4] 

0.9 

[4] 

1 

[4] 

1 

[4] 

1 

[4] 

1.1 

[4] 

0.9 

[4] 

0.9 

[4] 

0.9 

[4] 

1 

[4] 

1 

[4] 

1.1 

[4] 

0.8 

[4] 

0.9 

[4] 

0.9 

[4] 

0.9 

[4] 

1 

[4] 

1 

[4] 

0.8 

[4] 

0.9 

[4] 

0.9 

[4] 

0.9 

[4] 

1 

[4] 

1 

[3 4] 

0.8 

[4] 

0.9 

[4] 

0.9 

[4] 

0.9 

[4] 

1 

[4] 

1 

[3 4] 

0.8 

[3 4] 

0.8 

[4] 

0.9 

[4] 

0.9 

[4] 

0.9 

[4] 

1 

[3 4] 

0.8 

[3 4] 

0.8 

[4] 

0.9 

[4] 

0.9 

[4] 

0.9 

[4] 

1 

[3 4] 

0.8 

[3 4] 

0.8 

[3 4] 

0.9 

[4] 

0. 9 

[4] 

0.9 

[4] 

1 

[3 4] 

0.8 

[3 4] 

0.8 

[3 4] 

0.9 

[3 4] 

0.9 

[4] 

0.9 

[4] 

1 

1 

0.95 

0.9 

0.85 

100 

Number Vessels Stage 1 

90 

80 

70 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-74. Specific power consumption at N2 = 3,000 rpm,

N3 = 3,000 rpm, and S2 = 60 

System Recovery Ratio [%]s, V1=0 V2=1 V3= 0 V4= 1 N2=3000 N3= 3000 S2= 20 

120 

110 

100 

74 73.5 73 72.7 

[12] 

72.5 

[11 12] 

72.3 

75 74.6 74.2 73.9 

[12] 

73.7 

[12] 

73.5 

75.6 75.3 75 74.7 

[12] 

74.5 

[12] 

74.4 

[3] 

76.1 75.8 75.6 75.4 75.2 

[12] 

75 

[3] 

76.4 

[3] 

76.2 76 75.8 75.6 

[12] 

75.5 

[3] 

76.6 

[3] 

76.5 

[3] 

76.4 76.2 76 

[12] 

75.8 

[3] 

76.8 

[3] 

76.7 

[3] 

76.6 

[3] 

76.4 76.3 

[12] 

76.1 

[3] 

77 

[3] 

76.9 

[3] 

76.8 

[3] 

76.7 

[3] 

76.5 

[12] 

76.4 

[3] 

77.1 

[3] 

77.1 

[3] 

77 

[3] 

76.9 

[3] 

76.7 

[3] 

76.6 

77 

76.5 

76 

75.5 

75 

74.5 

74 

73.5 

73 

72.5 

Number Vessels Stage 1 

90 

80 

70 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-75. System recovery ratio for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 20 

System Recovery Ratio [%]s, V1=0 V2=1 V3= 0 V4= 1 N2=3000 N3= 3000 S2= 40 

120 

110 

100 

[4] 

78.2 77.7 77.1 76.6 76.2 75.8 

[4] 

78.7 78.4 77.9 77.5 77.2 76.8 

[4] 

79 

[4] 

78.8 78.5 78.1 77.8 77.5 

[4] 

79.2 

[4] 

79.1 78.9 78.6 78.3 78 

[3 4] 

79.4 

[4] 

79.3 79.2 78.9 78.7 78.4 

[3 4] 

79.5 

[3 4] 

79.5 79.3 79.2 78.9 78.7 

[3 4] 

79.6 

[3 4] 

79.6 

[3] 

79.6 79.4 79.2 79 

[3 4] 

79.6 

[3 4] 

79.7 

[3] 

79.7 

[3] 

79.6 79.4 79.1 

[3 4] 

79.7 

[3 4] 

79.8 

[3] 

79.8 

[3] 

79.7 79.5 79.3 79.5 

79 

78.5 

78 

77.5 

77 

76.5 

76 

Number Vessels Stage 1 

90 

80 

70 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-76. System recovery ratio for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 40 

108 
40 

50 

60 

70 

80 

90 

110 

120 

80 

90 

110 

120 

System Recovery Ratio [%]s, V1=0 V2=1 V3= 0 V4= 1 N2=3000 N3= 3000 S2= 60 

82 

81.5 

120 

110 

[4] 

79.9 

[4] 

79.5 

[4] 

79 

[4] 

78.5 

[4] 

78 

[4] 

77.6 

[4] 

80.2 

[4] 

80 

[4] 

79.7 

[4] 

79.3 

[4] 

78.9 

[4] 

78.5 

[4] 

80.4 

[4] 

80.3 

[4] 

80.1 

[4] 

79.8 

[4] 

79.4 

[4] 

79.1 

[4] 

82.1 

[4] 

80.6 

[4] 

80.4 

[4] 

80.1 

[4] 

79.8 

[4] 

79.5 

[3 4] 

80.7 

[4] 

80.7 

[4] 

80.6 

[4] 

80.4 

[4] 

80.2 

[4] 

79.9 

[3 4] 

80.8 

[3 4] 

80.9 

[4] 

80.8 

[4] 

80.6 

[4] 

80.4 

[4] 

80.1 

[3 4] 

80.8 

[3 4] 

80.9 

[4] 

80.9 

[4] 

80.8 

[4] 

80.6 

[4] 

80.3 

[3 4] 

80.9 

[3 4] 

81 

[3 4] 

81 

[4] 

80.9 

[4] 

80.7 

[4] 

80.5 

[3 4] 

80.9 

[3 4] 

81.1 

[3 4] 

81.1 

[3 4] 

81 

[4] 

80.9 

[4] 

80.7 

81 

80.5 

80 

79.5 

79 

78.5 

78 

100 

Number Vessels Stage 1 

90 

80 

70 

60 

50 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm 

Figure 5-77. System recovery ratio for N2 = 3,000 rpm, N3 = 3,000 rpm, and S2 = 60 

Percentage Distance from Consraint, V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=40 Percentage Distance from Consraint, V1=0 V2=1 V3=0 V4=1 N2=3540 N3=3000 S2=40 

-13.5 0.6 2.9 2.8 2.6 2.4 

-13.5 0.2 3.1 2.9 2.7 2.5 

-13.7 -0. 3 3.2 3 2.8 2.5 

-13.8 -0. 6 3.4 3.1 2.8 2.6 

-14 -0. 9 3.5 3.2 2.9 2.6 

-23 -6. 4 3.7 3.3 3 2.7 

-32.6 -17.5 -3.1 3.4 3.1 2.7 

-40.1 -26.4 -13.3 -0.7 3.1 2.8 

-46.2 -33.7 -21.7 -10.1 1 2.8 

-17.6 -4.2 2.8 2. 7 2.6 2.4 

-17.7 -4.5 3 2. 8 2.6 2.4 

-17.7 -4.6 3.2 2. 9 2.7 2.5 

-17.8 -5 3.3 3. 1 2.8 2.5 

-18.4 -5.1 3.5 3. 2 2.9 2.6 

-30 -12.8 3.7 3. 3 3 2.7 

-39 -23.5 -8.5 3. 4 3.1 2.7 

-45.9 -31.9 -18.3 -5.2 3.1 2.8 

-51.5 -38.7 -26.3 -14.3 -2.7 2.8 

100 

120 0 

-5 110

-10 100

Stage 1 Number of Vessels 

Stage 1 Nu mber of Vessels 

-15 90 

80 

70 

-20 

-25 

-30 

-35 

60 

-40 

50 

-45 40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-78: Distance from constraint comparison for changes in N2 for fixed N3 and S2 

System Permeate Flow (gpm), V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=40 System Permeate Flow (gpm), V1=0 V2=1 V3=0 V4=1 N2=3540 N3=3000 S2=40 

3400 

[4] 

1859. 3 2099.4 2325.2 2542 2753.6 2962.4 

[4] 

1914. 5 2175.2 2418.9 2651.1 2876.3 3097.2 

[4] 

1948 

[4] 

2225.2 2482.1 2725.6 2960.3 3189.5 

[4] 

1971. 4 

[4] 

2259.8 2527 2779.1 3021 3255.7 

[3 4] 

1986. 3 

[4] 

2284.6 2560.2 2819.2 3066.7 3306.9 

[3 4] 

1996. 5 

[3 4] 

2302.8 2582 2850.1 3102.3 3346.3 

[3 4] 

2002. 6 

[3 4] 

2316.7 

[3] 

2605.1 2874.5 3130.7 3377.7 

[3 4] 

2008. 8 

[3 4] 

2327.4 

[3] 

2620.7 

[3] 

2894.3 3153.7 3403.4 

[3 4] 

2011. 1 

[3 4] 

2335.9 

[3] 

2633.4 

[3] 

2911.1 3172.7 3424.8 

[4] 

1827 

[4] 

2080.3 2316 2539.5 2755.4 2967 

[4] 

1860.2 

[4] 

2145.1 2400.5 2641 2871.7 3096.2 

[4] 

1892.9 

[4] 

2185 2456.3 2709.3 2950.6 3184.2 

[3 4] 

1906.3 

[4] 

2213.9 2495.1 2757.9 3007.2 3247.7 

[3 4] 

1913.8 

[4] 

2231.7 2523.1 2793.7 3049.6 3295.4 

[3 4] 

1917.7 

[3 4] 

2244.6 2543.9 2818.3 3082.2 3332.4 

[3 4] 

1916 

[3 4] 

2253.8 

[3] 

2559.7 2842.4 3108.1 3361.8 

[3 4] 

1920.4 

[3 4] 

2260.4 

[3] 

2571.9 

[3] 

2859.4 3128.9 3385.7 

[3 4] 

1921.1 

[3 4] 

2265.3 

[3] 

2581.5 

[3] 

2873.1 

[3] 

3146 3405.5 

100 

120 

110 3200 

3000 100 

Number Vessels Stage 1 

Number Vessels Stage 1 

90 

80 

70 

2800 

2600 

2400 

60 

50 

2200 

2000 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-79. Permeate flow comparison for changes in N2 for fixed N3 and S2 

109 

-50 

-45 

-40 

-35 

-30 

-25 

-20 

-15 

-10 

-5 

0 

40 

50 

60 

70 

2000 

2200 

2400 

2600 

2800 

3000 

3200 

3400 
40 

50 

60 

70 

80 

90 

100 

110 

120 

600 

650 

700 

750 

40 

50 

60 

70 

80 

90 

110 

120 

Total Power [kW], V1=0 V2=1 V3=0 V4=1 N2=3000 N3= 3000 S2= 40 Total Power [kW], V1=0 V2=1 V3=0 V4=1 N2=3540 N3= 3000 S2= 40 

[4] 

387.4 455.3 527.1 604.2 687. 4 777.8 

[4] 

387.3 456.2 528.7 606.1 689. 5 779.8 

[4] 

386.4 

[4] 

456.2 529.1 606.8 690. 2 780.5 

[4] 

385.3 

[4] 

455.7 529.1 606.9 690. 5 780.8 

[3 4] 

384.2 

[4] 

455.1 528.8 606.9 690. 5 780.8 

[3 4] 

383.1 

[3 4] 

454.5 528.5 606.7 690. 4 780.7 

[3 4] 

382 

[3 4] 

453.8 

[3] 

528.1 606.5 690. 3 780.5 

[3 4] 

381.1 

[3 4] 

453.2 

[3] 

527.7 

[3] 

606.3 690. 1 780.4 

[3 4] 

380.3 

[3 4] 

452.7 

[3] 

527.4 

[3] 

606.1 689. 9 780.2 

[4] 

391.1 

[4] 

461.7 535.8 614.8 699. 8 791.7 

[4] 

391.4 

[4] 

462 536.9 616.4 701. 5 793.4 

[4] 

388.5 

[4] 

461.5 537 616.8 702. 1 793.9 

[3 4] 

386.7 

[4] 

460.7 536.7 616.8 702. 2 794 

[3 4] 

385 

[4] 

459.7 536.2 616.5 702. 1 793.9 

[3 4] 

383.5 

[3 4] 

458.8 535.7 616.2 701. 9 793.7 

[3 4] 

382 

[3 4] 

457.9 

[3] 

535.2 615.9 701. 6 793.5 

[3 4] 

380.9 

[3 4] 

457.1 

[3] 

534.7 

[3] 

615.6 701. 4 793.3 

[3 4] 

379.9 

[3 4] 

456.4 

[3] 

534.2 

[3] 

615.2 

[3] 

750 701. 1 793 120 

110 

700 

100 

Number Vessels Stage 1 

650 

600 

550 

Number Vessels Stage 1 

90 

80 

70 

500 60 

450 50 

400 40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-80. Total power consumption comparison for variation in N2 for fixed N3 and S2 

System Specific Power [kWh/m 3], V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=40 System Specific Power [kWh/m 3], V1=0 V2=1 V3=0 V4=1 N2= 3540 N3=3000 S2=40 

[4] 

0.9 1 1 1 1.1 1.2 

[4] 

0.9 0.9 1 1 1.1 1.1 

[4] 

0.9 

[4] 

0.9 0.9 1 1 1.1 

[4] 

0.9 

[4] 

0.9 0.9 1 1 1.1 

[3 4] 

0.9 

[4] 

0.9 0.9 0. 9 1 1 

[3 4] 

0.8 

[3 4] 

0.9 0.9 0. 9 1 1 

[3 4] 

0.8 

[3 4] 

0.9 

[3] 

0.9 0. 9 1 1 

[3 4] 

0.8 

[3 4] 

0.9 

[3] 

0.9 

[3] 

0. 9 1 1 

[3 4] 

0.8 

[3 4] 

0.9 

[3] 

0.9 

[3] 

0. 9 1 1 

[4] 

0.9 

[4] 

1 1 1. 1 1.1 1.2 

[4] 

0.9 

[4] 

0.9 1 1 1.1 1.1 

[4] 

0.9 

[4] 

0.9 1 1 1 1.1 

[3 4] 

0.9 

[4] 

0.9 0.9 1 1 1.1 

[3 4] 

0.9 

[4] 

0.9 0.9 1 1 1.1 

[3 4] 

0.9 

[3 4] 

0.9 0.9 1 1 1 

[3 4] 

0.9 

[3 4] 

0.9 

[3] 

0.9 1 1 1 

[3 4] 

0.9 

[3 4] 

0.9 

[3] 

0.9 

[3] 

0. 9 1 1 

[3 4] 

0.9 

[3 4] 

0.9 

[3] 

0.9 

[3] 

0. 9 

[3] 

1 1 

1.15 

120 

1.1 110

100 100

Number Vessels Stage 1 

1.05 

1 

0.95 

Number Vessels Stage 1 

90 

80 

70 

60 

50 

0.9 

0.85 40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-81. Specific power consumption comparison for variation in N2 for fixed N3 and S2 

110 

400 

450 

500 

550 

0.9 

0.95 

1 

1.05 

1.1 

1.15 
40 

50 

60 

70 

80 

90 

100 

110 

120 

40 

50 

60 

70 

80 

90 

110 

120 

System Recovery Ratio [%]s, V1=0 V2=1 V3=0 V4=1 N2=3540 N3=3000 S2=40 

80 120 

System Recovery Ratio [%]s, V1=0 V2=1 V3= 0 V4= 1 N2=3000 N3= 3000 S2= 40 

[4] 

78.7 

[4] 

78.4 77.9 77.4 76.9 76.5 

[4] 

79.1 

[4] 

78.9 78.6 78.2 77.8 77.4 

[4] 

79.3 

[4] 

79.3 79.1 78.7 78.4 78.1 

[3 4] 

79.4 

[4] 

79.5 79.4 79.1 78.9 78.6 

[3 4] 

79.5 

[4] 

79.7 79.6 79.4 79.2 78.9 

[3 4] 

79.6 

[3 4] 

79.8 79.8 79.6 79.4 79.2 

[3 4] 

79.6 

[3 4] 

79.9 

[3] 

79.9 79.8 79.7 79.4 

[3 4] 

79.7 

[3 4] 

79.9 

[3] 

80 

[3] 

80 79.8 79.6 

[3 4] 

79.7 

[3 4] 

80 

[3] 

80.1 

[3] 

80.1 

[3] 

80 79.8 

[4] 

78.2 77.7 77.1 76.6 76.2 75.8 

[4] 

78.7 78.4 77.9 77.5 77.2 76.8 

[4] 

79 

[4] 

78.8 78.5 78.1 77.8 77.5 

[4] 

79.2 

[4] 

79.1 78.9 78.6 78.3 78 

[3 4] 

79.4 

[4] 

79.3 79.2 78.9 78.7 78.4 

[3 4] 

79.5 

[3 4] 

79.5 79.3 79.2 78.9 78.7 

[3 4] 

79.6 

[3 4] 

79.6 

[3] 

79.6 79.4 79.2 79 

[3 4] 

79.6 

[3 4] 

79.7 

[3] 

79.7 

[3] 

79.6 79.4 79.1 

[3 4] 

79.7 

[3 4] 

79.8 

[3] 

79.8 

[3] 

79.7 79.5 79.3 

110 

79.5 

100 

79 

79 

78 

78 

77 

77 

Number Vessels Stage 1 

79 

78.5 

78 

90 

80 

70 

Stage 1 Number of Vessels Number Vessels Stage 1 

77.5 60 

77 50

40 76.5 

76 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

76 HP Pump Speed - rpm 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900

HP Pump Speed - rpm

Figure 5-82. Recovery ratio comparison for variation in N2 for fixed N3 and S2 

Percentage Distance from Consraint, V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=40 Percentage Distance from Consraint, V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3540 S2=40 

-13.5 0.6 2.9 2.8 2.6 2.4 

-13.5 0.2 3.1 2.9 2.7 2.5 

-13.7 -0. 3 3.2 3 2.8 2.5 

-13.8 -0. 6 3.4 3.1 2.8 2.6 

-14 -0. 9 3.5 3.2 2.9 2.6 

-23 -6. 4 3.7 3.3 3 2.7 

-32.6 -17.5 -3.1 3.4 3.1 2.7 

-40.1 -26.4 -13.3 -0.7 3.1 2.8 

-46.2 -33.7 -21.7 -10.1 1 2.8 

-4.4 2.5 2.4 2. 4 2.2 2 

-4.5 2.5 2.5 2. 4 2.2 2 

-4.7 2.6 2.7 2. 4 2.3 2 

-4.9 2.8 2.6 2. 5 2.3 2.1 

-5 2.9 2.7 2. 5 2.3 2.1 

-5.1 3 2.8 2. 6 2.4 2.2 

-14.6 -1.3 2.9 2. 6 2.4 2.2 

-23.7 -11.6 0.1 2. 7 2.5 2.2 

-31.2 -20.1 -9.3 1. 2 2.5 2.2 

100 

120 0 

-5 110

-10 100

Stage 1 Nu mber of Vessels 

-15 

-20 

-25 

-30 

90 

80 

70 

60 

-35 

50 

-40 

40 -45 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-83. Distance from constraint comparison for changes in N3 for fixed N2 and S2 

111 

-30 

-25 

-20 

-15 

-10 

-5 

0 
40 

50 

60 

70 

80 

90 

100 

110 

120 

2600 

2800 

3000 

3200 

3400 

40 

50 

60 

70 

80 

90 

System Permeate Flow (gpm), V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=40 System Permeate Flow (gpm), V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3540 S2=40 

3400 

3200 

120 

[4] 

1859. 3 2099.4 2325.2 2542 2753.6 2962.4 

[4] 

1914. 5 2175.2 2418.9 2651.1 2876.3 3097.2 

[4] 

1948 

[4] 

2225.2 2482.1 2725.6 2960.3 3189.5 

[4] 

1971. 4 

[4] 

2259.8 2527 2779.1 3021 3255.7 

[3 4] 

1986. 3 

[4] 

2284.6 2560.2 2819.2 3066.7 3306.9 

[3 4] 

1996. 5 

[3 4] 

2302.8 2582 2850.1 3102.3 3346.3 

[3 4] 

2002. 6 

[3 4] 

2316.7 

[3] 

2605.1 2874.5 3130.7 3377.7 

[3 4] 

2008. 8 

[3 4] 

2327.4 

[3] 

2620.7 

[3] 

2894.3 3153.7 3403.4 

[3 4] 

2011. 1 

[3 4] 

2335.9 

[3] 

2633.4 

[3] 

2911.1 3172.7 3424.8 

[4] 

2050.5 2265.2 2472.4 2675 2875.5 3075.1 

[4] 

2116.9 2349.5 2572.4 2789 3001.8 3212.6 

[4] 

2160.5 2406.4 2650.1 2867.3 3088.5 3307.2 

[4] 

2190.3 2446.7 2690.1 2924.1 3152 3376 

[4] 

2211.5 2476.5 2727 2966.9 3199.8 3428.1 

[3 4] 

2226.9 2499 2755.4 3000.2 3237.2 3468.8 

[3 4] 

2238.3 

[3] 

2516.4 2777.8 3026.7 3267 3501.4 

[3 4] 

2246.8 

[3] 

2530.1 2795.8 3048.3 3291.4 3528.2 

[3 4] 

2253.5 

[3] 

2541.1 

[3] 

2810.5 3066 3311.6 3550.4 

110 

3000 100 

Number Vessels Stage 1 

Number Vessels Stage 1 

90 

80 

70 

2800 

2600 

2400 

60 

50 

2200 

2000 

40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-84. Permeate flow comparison for changes in N3 for fixed N2 and S2 

Total Power [kW ], V 1=0 V2=1 V3=0 V4= 1 N2=3000 N3= 3000 S2= 40 Total Power [kW ], V 1=0 V2=1 V3=0 V4=1 N2=3000 N3= 3540 S2= 40 

120 750 120 

110 110 

700 

[4] 

387.4 455.3 527.1 604.2 687. 4 777.8 

[4] 

387.3 456.2 528.7 606.1 689. 5 779.8 

[4] 

386.4 

[4] 

456.2 529.1 606.8 690. 2 780.5 

[4] 

385.3 

[4] 

455.7 529.1 606.9 690. 5 780.8 

[3 4] 

384.2 

[4] 

455.1 528.8 606.9 690. 5 780.8 

[3 4] 

383.1 

[3 4] 

454.5 528.5 606.7 690. 4 780.7 

[3 4] 

382 

[3 4] 

453.8 

[3] 

528.1 606.5 690. 3 780.5 

[3 4] 

381.1 

[3 4] 

453.2 

[3] 

527.7 

[3] 

606.3 690. 1 780.4 

[3 4] 

380.3 

[3 4] 

452.7 

[3] 

527.4 

[3] 

606.1 689. 9 780.2 

[4] 

448.7 516 588 665.5 749. 1 839.7 

[4] 

447.6 515.8 588.4 666.2 750. 1 840.8 

[4] 

446 514.9 588.3 666.1 750. 1 840.9 

[4] 

444.4 513.8 587.3 665.6 749. 8 840.6 

[4] 

442.8 512.7 586.5 665.1 749. 4 840.2 

[3 4] 

441.3 511.6 585.7 664.5 748. 9 839.7 

[3 4] 

439.9 

[3] 

510.6 584.9 663.9 748. 4 839.3 

[3 4] 

438.7 

[3] 

509.7 584.2 663.4 748 838.9 

[3 4] 

437.6 

[3] 

508.9 

[3] 

583.6 662.9 747. 6 838.5 

100 100 

Number Vessels Stage 1 

650 

600 

550 

Number Vessels Stage 1 

90 

80 

70 

500 60 

450 50 

400 40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-85. Total power consumption comparison for variation in N3 for fixed N2 and S2 

112 

2200 

2400 

450 

500 

550 

600 

650 

700 

750 

800 
40 

50 

60 

70 

80 

90 

100 

110 

120 

1 

1.05 

1.1 

1.15 

1.2 

40 

50 

60 

70 

80 

90 

110 

120 

System Specific Power [kWh/m 3], V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3000 S2=40 System Specific Power [kWh/m 3], V1=0 V2=1 V3=0 V4=1 N2= 3000 N3=3540 S2=40 

1.15 

120 

[4] 

0.9 1 1 1 1.1 1.2 

[4] 

0.9 0.9 1 1 1.1 1.1 

[4] 

0.9 

[4] 

0.9 0.9 1 1 1.1 

[4] 

0.9 

[4] 

0.9 0.9 1 1 1.1 

[3 4] 

0.9 

[4] 

0.9 0.9 0. 9 1 1 

[3 4] 

0.8 

[3 4] 

0.9 0.9 0. 9 1 1 

[3 4] 

0.8 

[3 4] 

0.9 

[3] 

0.9 0. 9 1 1 

[3 4] 

0.8 

[3 4] 

0.9 

[3] 

0.9 

[3] 

0. 9 1 1 

[3 4] 

0.8 

[3 4] 

0.9 

[3] 

0.9 

[3] 

0. 9 1 1 

[4] 

1 1 1 1. 1 1.1 1.2 

[4] 

0.9 1 1 1. 1 1.1 1.2 

[4] 

0.9 0.9 1 1 1.1 1.1 

[4] 

0.9 0.9 1 1 1 1.1 

[4] 

0.9 0.9 0.9 1 1 1.1 

[3 4] 

0.9 0.9 0.9 1 1 1.1 

[3 4] 

0.9 

[3] 

0.9 0.9 1 1 1.1 

[3 4] 

0.9 

[3] 

0.9 0.9 1 1 1 

[3 4] 

0.9 

[3] 

0.9 

[3] 

0.9 1 1 1 

1.1 110

100 

Number Vessels Stage 1 

1.05 

1 

0.95 

Number Vessels Stage 1 

90 

80 

70 

60 

50 

0.9 

0.85 40 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-86. Specific power consumption comparison for variation in N3 for fixed N2 and S2 

System Recovery Ratio [%]s, V1=0 V2=1 V3= 0 V4= 1 N2=3000 N3= 3000 S2= 40 System Recovery Ratio [%]s, V1=0 V2=1 V3=0 V4=1 N2=3000 N3=3540 S2=40 

[4] 

78.2 77.7 77.1 76.6 76.2 75.8 

[4] 

78.7 78.4 77.9 77.5 77.2 76.8 

[4] 

79 

[4] 

78.8 78.5 78.1 77.8 77.5 

[4] 

79.2 

[4] 

79.1 78.9 78.6 78.3 78 

[3 4] 

79.4 

[4] 

79.3 79.2 78.9 78.7 78.4 

[3 4] 

79.5 

[3 4] 

79.5 79.3 79.2 78.9 78.7 

[3 4] 

79.6 

[3 4] 

79.6 

[3] 

79.6 79.4 79.2 79 

[3 4] 

79.6 

[3 4] 

79.7 

[3] 

79.7 

[3] 

79.6 79.4 79.1 

[3 4] 

79.7 

[3 4] 

79.8 

[3] 

79.8 

[3] 

79.7 79.5 79.3 

[4] 

78.1 77.6 77.1 76.6 76.2 75.9 

[4] 

78.7 78.3 77.9 77.5 77.2 76.9 

[4] 

79.1 78.8 78.6 78.2 77.9 77.6 

[4] 

79.3 79.2 78.9 78.6 78.3 78.1 

[4] 

79.5 79.4 79.2 79 78.7 78.5 

[3 4] 

79.6 79.6 79.4 79.2 79 78.8 

[3 4] 

79.7 

[3] 

79.8 79.6 79.4 79.2 79 

[3 4] 

79.8 

[3] 

79.9 79.8 79.6 79.4 79.2 

[3 4] 

79.9 

[3] 

80 

[3] 

79.9 79.7 79.5 79.3 

100 

79.5 120 

110 

79 

100 

Number Vessels Stage 1 

Number Vessels Stage 1 

78.5 

78 

77.5 

90 

80 

70 

77 60 

76.5 50 

40 76 

3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 

HP Pump Speed - rpm HP Pump Speed - rpm 

Figure 5-87. Recovery ratio comparison for variation in N3 for fixed N2 and S2 

113 

0.9 

0.95 

76 

76.5 

77 

77.5 

78 

78.5 

79 

79.5 
6 Wind Desalination Design Optimization 

Typically, RO desalination technology has been developed for operation at nearly constant 

conditions, except for trimming plant set points to account for long-term variations in 

membrane degradation and changes in water temperature and salinity. 

Where grid power is not available or is cost prohibitive, the hybrid RO system uses only wind 

energy and needs to operate under wide variations in available power. The economic viability 

of the wind desalination technology in a grid-isolated topology largely depends on the ability 

of the RO plant to produce water efficiently in most of this range. 

The configurations proposed in the previous section are meant to provide a great degree of 

flexibility to operate the wind desalination system in a wide range of conditions dictated by 

available power and feedwater state. In this section we use the physical and economic models, 

in combination with optimization techniques, to define plant size and the location in the 

operating space to minimize the resulting COW. For example, we provide a rigorous method 

to address a fundamental design problem: to define the relative size of the power generation 

subsystem with respect to the desalination subsystem. Also, since the proposed configurations 

rely on the ability to change the desalination capacity by partially activating RO banks, we 

propose methodologies to calculate optimal RO capacities and the corresponding pump 

speeds as a function of the available power. 

6.1 Overview of Wind Desalination Topologies 

The grid topologies analyzed in this section are grid isolated, where the RO system operates 

with the wind power and, occasionally, from energy storage devices; and a grid-connected 

topology where the RO system operates with wind power, grid power, or both. 

The analysis has focused on two problems that are fundamental in the design and operation of 

a wind desalination plant: 

1. Given the available energy for desalination, calculate the RO set points for maximum 

water production. 

2. Given an RO plant and local grid energy prices, decide whether wind power is 

economically viable to produce water. 

The optimization studies were performed for the single-stage seawater configuration (SWWEa3) only, although the same techniques can be applied to the other two configurations 

proposed in Section 2. 

6.1.1 Grid-Isolated and Design Choices/Optimization Opportunities 

The grid-isolated configuration consists in the RO configuration SWWE-a3 (see Figure 5-40) 

powered by a 1.5-MW wind turbine that operates with class II winds. To evaluate the COW 

for this configuration, the size of the RO subsystem, operating strategy, and energy storage 

size have to be defined, for which we have taken the following steps. 

1. Solved an optimization problem for the range of possible power levels from a 1.5-MW 

wind turbine to obtain the maximum water production subject to all the operating 

114 
constraints. As a result, the upper bound of number of RO vessels was obtained, as 

well as the optimal set points for associated operating strategies. 

2. Obtained the optimal number of vessels by calculating the COW for every RO 

plant size (assuming an optimal operation as given by step 1, assuming an energy 

storage size), and selecting the lowest one. 

3. Suggested a procedure to size the energy storage based on wind statistical information. 

6.1.2 Grid-Connected and Design Choices/Optimization Opportunities 

Given the greater flexibility of a grid-connected topology, there are many opportunities for 

optimal design and optimal operation calculations. For the grid-connected case, we focused 

on analyzing viability of a wind-powered RO technology and understanding its preferred 

conditions over an RO plant that is powered with grid energy only. We chose a simple 

operating strategy to compute a detailed COW for this topology. In addition, we suggested an 

optimal operation strategy for dealing with the energy management between wind power, grid 

power, and the energy storage subsystem. 

6.2 Grid-Isolated Results 

6.2.1 Plant Sizing Analysis with Regard to Cost of Water 

We analyzed a single-stage RO water desalination plant (configuration SWWE-a3). This 

analysis assumed that the wind turbine is the sole energy source for the plant; i.e., that the 

plant is isolated from the power grid, and that no energy storage is available. In this case, the 

size of the plant is of interest, in terms of RO vessels installed, that leads to a minimum 

average SCOW over one year of operation, taking into account the variability of the energy 

source. Detailed COW evaluations for two-stage configurations (like SWWE-a1 and BWWEa1) can be evaluated with the same methodology. 

6.2.1.1 Design Process 

The size of the RO plant, given by the maximum number of RO vessels, has been defined to 

obtain the minimal COW when the power is produced for a 1.5-MW wind turbine. For this 

purpose, we: 

1. Defined the generic operation of the RO plant at different power levels. 

2. Given the generic operation in step 1, computed the expected COW (taking into 

account the wind speed statistics) that correspond to RO plants in a range of possible 

sizes. 

3. Selected the size for which minimum COW is achieved. 

Generic Operation of Reverse Osmosis Plant 

Defining the plant operation consists of calculating the set points of the available control 

knobs that will lead to minimal COW at all possible power levels. Regarding RO 

configuration, this involves calculating the optimal number of active RO vessels in the RO 

bank, S, the optimal speed of the high-pressure pump, N1 , and of the booster pump, N2 , the 

optimal valve opening for permeate recycle, V1 in the range of 70 kW to 1500 kW of 

115 
consumed power. To achieve minimum COW, we used the maximization of water production 

as the optimization criterion. Therefore, the RO operating set points were defined by 

maximizing the permeate flow-rate subject to the following constraints: 

• RO operational constraints as described in Section 5.1.2. 

• The power consumed by the pumps is fixed. 

This optimization problem has been solved for a set of power levels of 70−1500 kW. The 

results of these calculations are presented in Figure 6-1−Figure 6-7 and Table 6-1. For most 

values of available power, the maximum permeate flow is achieved when the last element 

concentrate flow has the lowest value allowed by the constraints. This is consistent with the 

analysis of the operational space presented in Section 5.2.6 (see Figure 5-52). 

6000 

5000 

Permeate Flow, gpm 

Feed Flow, gpm 

4000 

3000 

2000 

1000

0

0 500 1000 1500 

Available Power, kW 

Figure 6-1. Maximum permeate flow as a function of available power for plant SWWE-a3 

116 
4500 200 

4000 

Boo

ster Pu

mp rpm 

Num

ber of ve

ssels (S) 

HP Pump rp

m

100 

3500 

3000 

0 

0

500 1000 1500 0 

4500 

4000 

500 1000 1500 

R

ecycl

e of perm

e

ate 

1 

0.5 

0 

3500 

3000 

0 500 1000 1500 0 500 1000 1500 

Available Power, kW Available Power, kW 

Figure 6-2. Optimal operating parameters as a function of available power, plant 

SWWE-a3; dotted lines represent the available parameter variation ranges 

0.6 

0.55 

0.5 

0.45 

0.4 

0.35 

0.3 

0.25 

0.2 

R

ecovery rate 

0 500 1000 1500 

Available power, kW 

Figure 6-3. Recovery of a function of available power for optimal results 

(configuration SWWE-a3) 

117 
0 

5 

10 

15 

20 

25 

Perm

e

ate flux, gfd 

Upper bound 

1st element 

last element 

average 

0 500 1000 1500

Available Power, kW

Figure 6-4. Permeate flux for optimal results on configuration SWWE-a3 

0.1 

0.2 

0.3 

0.4 

0.5 

T

D

S, k

g/m3 

0 

50 

100

F

eed flowrate, gpm

1st elem 

0 500 1000 1500 0 500 1000 1500

0 500 1000 1500

400 

600 

800 

1000 

1200 

RO Feed pressur

e, psi 

0 500 1000 1500 

0 

20 

40 

60 

80

C

o

n

centrate flow, gpm 

Last element 

Available Power, kW Available Power, kW

Figure 6-5. Constrained variables for optimal results on configuration SWWE-a3 

118
0 500 1000 1500 

1.05 

1.1 

1.15 

1.2 

Cm/Cbar 

Element 1 

Element 2 

Element 3 

Element 4 

Element 5 

Element 6 

Element 7 

Available Power, kW 

Figure 6-6. Concentration polarization for optimal results on RO configuration 

SWWE-a3 

0 

20 

40 

60

Pressur

e drop, psi

RO vessel 

0 

5 

10

Pressur

e drop, psi

1st RO element 

0 500 1000 1500 0 500 1000 1500

1.8 

2 

2.2 

2.4 

2.6 Specific consumption, kWh/m3 

0 500 1000 1500

Available Power, kW

Figure 6-7. RO pressure drop and specific energy consumption for optimal results 

on configuration SWWE-a3 

119
Table 6-1. Optimal Operating Parameters for Plant SWWE-a3 

Available 

Power, kW 

Optimal 

N1, rpm 

Optimal 

N2, rpm 

Optimal 

S (vessels) 

Optimal 

Recycle 

Maximum Permeate 

Flow, gpm 

Optimal 

Recovery 

70 3,000.0 3,000 9 0 117.37 0.16168 

120 3,000.0 3,000 25 0 244.16 0.24751 

170 3,040.3 3,000 41 0 364.94 0.29296 

220 3,072.0 3,000 58 0 487.22 0.32123 

270 3,070.6 3,000 83 0 623.15 0.33394 

320 3,146.8 3,000 88 0 734.04 0.35931 

370 3,216.1 3,000 92 0 842.85 0.38077 

420 3280.2 3,000 96 0 950.15 0.39927 

470 3,340.0 3,000 100 0 1,056.8 0.41567 

520 3,396.7 3,000 103 0 1,162.7 0.43022 

570 3,450.7 3,000 107 0 1,268.2 0.44332 

620 3,502.4 3,000 110 0 1,373.4 0.4552 

670 3,552.2 3,000 113 0 1,478.5 0.46605 

720 3,600.2 3,000 117 0 1,583.2 0.476 

770 3,646.6 3,000 120 0 1,687.7 0.48517 

820 3,691.5 3,000 123 0 1,791.6 0.49363 

870 3,735.0 3,000 126 0 1,894.9 0.50147 

920 3,777.1 3,000 129 0 1,997.2 0.50872 

970 3,817.9 3,000 132 0 2,098.4 0.51545 

1,020 3,857.3 3,000 135 0 2,198.2 0.52169 

1,070 3,895.4 3,000 138 0 2,296.2 0.52748 

1,120 3,932.1 3,000 140 0 2,392.3 0.53285 

1,150 3,953.5 3,000 142 0 2,449.0 0.53589 

1,200 3,988.0 3,000 144 0 2,541.5 0.54066 

1,250 4,021.2 3,000 147 0 2,631.6 0.54508 

1,300 4,053.0 3,000 149 0 2,719.1 0.54919 

1,350 4,083.4 3,000 152 0 2,803.9 0.55301 

1,400 4,112.5 3,000 154 0 2,885.9 0.55656 

1,450 4,140.2 3,000 156 0 2,965.2 0.55986 

1,500 4,166.7 3,000 158 0 3,041.8 0.56294 

120 
This calculation assumed that the capacity of the ERD depends linearly on the number of 

RO vessels, according to the relation in Eq. 6-1: 

Cpe = 1+0.0087(S -51) Eq. 6-1 

This law of variation was determined by accounting for the capacity of the pressure exchanger 

used at the nominal design point of the plant (where 35% of the nominal power of the turbine 

is available) and the capacity of the ERD necessary to cope with the maximum capacity of the 

plant (when the turbine generates 1.5 MW). The increased cost incurred by using a larger 

capacity ERD is accounted for in the cost model. 

Expected Cost of Water for Reverse Osmosis Plants of Different Sizes 

As a second step in determining the optimal plant RO size, the expected COW was calculated 

for all plant sizes (ranging from nine vessels to 158 vessels) with the COW model described 

in Section 4.2. 

We considered a location with a yearly average wind speed (at a 10-m standard height) of 7 

m/s (Class II wind). The parameters characterizing the Weibull probability density function 

for mean wind speeds at standard height are in this case A10m = 7.9 and k = 2. At hub height, 

hhub = 70m (corresponding to the GE 1.5-MW turbine), the yearly average wind speed is 9.24 

m/s (Eq. 4-3), and the parameters of the Weibull probability density function are Ahub = 10.43 

and k = 2. The probabilities of n = 28 mean wind speeds (0−27 m/s) at hub height, occurring 

in a one year period, as computed from the Weibull probability density function, are presented 

in Figure 6-8. 

Probability 

0 5 10 15 20 25 

Mean wind speed, m/s 

Figure 6-8. Probability of mean wind speeds at turbine hub height, A = 10.43, k = 2 

0 

0.01 

0.02 

0.03 

0.04 

0.05 

0.06 

0.07 

0.08 

121 
The available power at each wind speed was calculated with a GE 1.5 turbine power curve 

(Section 3.2.2). A plot of the available power at different (hub height) wind speeds is 

presented in Figure 6-9. 

0 

500 

1000 

1500 

Generated p

o

wer, kW 

0 5 10 15 20 25 

Mean wind speed at hub height, m/s 

Figure 6-9. Generated power as a function of wind speed 

(measured at 70 m above the ground) 

Once the available power for each wind speed was computed, the optimal operating points for 

each wind speed were determined by using the results in Table 6-1. 

The average yearly SCOW considering plants with different numbers of installed RO vessels, 

was computed following the procedure presented in Section 4. In this case (Eq. 4-2), 

ROPower = Pj., i.e., the power available to the RO plant varies in time and is, in fact, the 

power generated by the wind turbine, corresponding to the mean wind speed Vj . 

A plot of the SCOW as a function of the number of RO vessels installed in the plant is 

presented in Figure 6-10. 

122 
1.5 

2 

2.5 

3 

3.5 

4 

4.5 

5 

5.5 

Co

st of w

ater, $/m3 

20 40 60 80 100 120 140 

Number of vessels used 

Figure 6-10. Annual average COW for plant SWWE-a3, operated as grid isolated, as a 

function of the number of RO vessels installed 

Optimal Plant Size 

From results in Figure 6-10, the average COW is minimized for a plant size of 158 

vessels. 

6.2.1.2 Results 

The optimal plant size for RO configuration SWWE-a3 is given by 158 vessels. The 

corresponding performance indexes, computed using weighted averaging calculations 

similar to those in Section 4.2, are given in Table 6-2. 

Table 6-2. Performance of Optimal Wind-RO Plant 

Maximum wind turbine power 1,500 kW 

RO plant size 158 vessels 

Average COW 1.111 $/m3 

Average recovery rate 39.45% 

Average permeate flow rate 1,686 gpm 

Average permeate flow per maximum power 1.12 gpm/kW 

Even though SminCOW = 158 vessels are physically installed in the plant, they may not be used 

at all times. Depending on the level of power available to operate the plant, vessels may be 

connected and disconnected; the speed of the pumps and the recycle rate may also be adjusted 

to ensure a maximum flow rate of permeate for the power available. The above calculations 

indicate that on average over one year (the period considered in computing the Weibull 

distribution) the SCOW produced by a plant that has 158 vessels installed is the lowest of all 

the plant configurations considered (see also Table 6-1). 

123 
The contributions of the factors considered in developing the cost model (Section 4) to the 

SCOW produced by the optimal grid-isolated desalination plant (operating at full capacity), 

158 vessels connected to a 1,500-kW wind turbine are presented in Figure 6-11. 

Water cost components, 158-vessel wind-powered plant 

72% 

11% 

13% 

1% 

2% Fixed charges RO 

Fixed charges WT

 Maintenance RO 

Maintenance WT 

Raw materials 

Figure 6-11. Contribution to the COW for an optimal grid-isolated RO plant 

powered by a wind turbine 

The design procedure and results in this section assume that the plant operator would produce 

as much water as possible for the available wind power. There was no attempt to deal with 

changes in water demand or distributions constraints. If this assumption is not satisfied, the 

design procedure can be adjusted accordingly, and the optimal size and performance may 

differ from those presented in this section. 

6.2.2 Sizing energy storage 

Energy storage is useful in a grid-isolated topology to keep the RO system in operation even 

without wind power. The following parameters should be understood to quantify the 

economic benefits of using a battery to reduce shutdowns: 

• Statistical information on the period of time for which the RO plant lacks power to be 

operative. This magnitude depends on the local wind characteristics and in the 

minimum number of vessels that can be active in the RO plant. 

• The effect of an RO shutdown on the COW, including effects of lack of water 

production during shutdown and increased use of chemicals. 

124 
A preliminary battery size can be determined from the maximum period of time to operate the 

minimum set of vessels in the RO plant. This consideration leads to the minimum battery 

power rating and the maximum battery capacity. 

The wind statistical description can be used to find an optimal battery sizing. In fact, we can 

use wind statistics to determine the effect of “blackouts” on battery life as a function of 

battery size (smaller batteries will cycle more often and will exhaust their lives sooner than 

larger batteries). An optimal battery size can be calculated by a trade-off analysis between a 

battery’s size and its economic impact on the COW. 

Since the required wind statistical description for optimal battery sizing is not available, we 

sized the battery so it provides 100 kW during four hours of continuous operation, which is 

enough to operate at least nine vessels during that time (according to Table 6-1). 

6.2.3 Plant operation concepts 

The operational strategy suggested by the optimization results in Section 6.2.1 indicates that, 

whenever the available wind power is 70−1500 kW, the plant set points should be as close as 

possible to the optimal values in Table 6-1. If the wind is such that the available power is 

outside this range, the following operational modes should be taken into account. 

• If the wind power is below 70 kW, the plant can operate if the battery charge is above 

the minimum charge level. A threshold on minimum wind speed should be defined to 

bring the RO plant up again. This threshold should be greater than the cut-in wind 

speed. 

• When wind power is available, it can be used to produce water and charge the energy 

storage device, if it is not at full charge. A possible strategy to operate the plant is to 

use a threshold on wind speeds (or wind power) for battery charging. If wind power is 

below the threshold, the wind power will be used only to produce water. If wind 

power exceeds the threshold and battery is not at full capacity, the excess of power 

will be used to charge the battery until it is at full capacity. If wind power is above a 

threshold and battery is full, all the wind power will be used to produce water. The 

optimal value for the power threshold depends on the local wind statistics, the local 

water demand, or constraints in the water distribution. The optimal set point could be 

calculated with the methods outlined in Section 6.3.3. 

Using the optimal operating set points given in the previous section would require the ability 

to switch individual vessels on and off. Building an RO plant with this capability may be 

impractical; in a more likely scenario, the RO plant will be able to connect groups of vessels 

instead of individual vessels. 

If the RO vessels can only be connected in groups, the optimal set points can be calculated 

with the methodology described earlier, but must explicitly include the limitations on the RO 

operation. Irrespective of the restrictions in the vessel connections, Table 6-1 gives the 

maximum number of vessels that can be connected for any given power. That is, if the current 

wind power is such that the optimal number of vessels cannot be used, the plant should 

operate with fewer vessels (most available, fewer than the optimal). For example, if the wind 

turbine is producing 1 MW and the RO vessels can be connected only in groups of 20, only 

120 vessels should be active. Connecting 140 vessels would lead to violations of constraints 

125 
on minimum concentrate. The interaction between specific energy consumption, number of 

active vessels, and constraint violation should be clear from the design space analysis in 

Section 5.2.6 (see, for example, Figure 5-52) and the results in Section 6.2. 

Because of membrane degradation considerations, vessels should avoid being inactive and 

filled of seawater for more than 12 hours. To handle this constraint, the plant operation should 

cycle the active vessels if the wind power is not enough to operate all the available vessels. 

6.3 Grid-Connected Results 

6.3.1 Wind-Reverse Osmosis Viability Analysis 

The availability of a power grid connection increases the flexibility of an RO water 

desalination plant design. We analyzed two possible designs with the same RO capital 

expenditure (given by a size of 158 vessels) to evaluate the viability of the wind-RO 

technology in a grid-connected topology: 

• The RO plant is operated at full capacity solely with grid power (in which case capital 

expenditures decrease without a wind turbine). 

• The RO plant is operated at full capacity with both grid and wind power. 

In designing a grid-connected wind-RO plant, the goal was to improve on the operation of the 

grid-isolated plant described in Section 6.2. Thus, we considered that the plant is operated at a 

constant set point, namely, using the plant parameters that lead to the lowest average COW in 

the grid-isolated case. During periods of low wind speeds, when the wind power is not enough 

to operate the RO plant at full capacity, the remaining power is purchased from the grid. This 

operating strategy is “robust” with respect to grid blackouts, since in the case unavailable grid 

power, the plant can be operate on wind power alone, and water would be, even under these 

circumstances, produced at a minimum cost. 

Specifically, parameters chosen for the operation of the plant are (also, see Table 6-1). 

Number of RO SminCOW = 158 

vessels 

HP pump speed N1,min COW = 4,166 rpm 

Booster pump speed N 2 ,min COW = 3,000 rpm 

Power Pmin COW = 1,500 Kw 

Permeate flow Qp,min COWl = 3,041.8 gpm 

To maintain the plant operation at the constant set point above, energy is assumed to be 

purchased from the grid at a price $buy when the generated power Pgen is less than Pmin COW . 

The average SCOW was computed according to the method presented in Section 4, 

considering that the energy purchase price is $0.02/kWh−$0.2/kWh. 

126 
6.3.2 COW Results 

The SCOW obtained for the two RO plants described in the previous sections and 

summarized in Figure 6-12 presents COW for wind-powered and grid-connected windpowered plants for various energy purchase prices. 

0.65 

0.7 

0.75 

0.8 

0.85 

0.9 

0.95 

1 

Co

st of w

ater, $/m3 

COW with grid power only 

COW with grid and wind power 

0.05 0.1 0.15 0.2 

Energy Buy Price, $/kWh 

Figure 6-12. Comparison of the SCOW for a grid-connected wind-powered 

desalination plant and its grid-powered counterpart 

The SCOW generated with grid power only is lower at low energy costs, and becomes higher 

than that of the water generated by the grid-connected wind-powered RO desalination plant as 

the cost of buying energy from the grid increases. The “break even” point (where the cost of 

water generated by the two plants considered is the same) occurs when the energy buy price is 

$buy = 0.0664$ / kWh . In this price range it can be understood by considering that the COE 

generated by the wind-turbine considered in the present project (GE 1.5 MW, in a Class II 

wind location) is $0.0664/kWh. As such, the wind-powered grid-connected plant is expected 

to become a viable alternative to the grid-only plant when the cost of grid energy exceeds the 

COE generated by the wind turbine. Since the plant is designed to operate at the maximum 

power provided by the wind turbine (1.5 MW), no power is sold to the grid; hence, the energy 

sale price does not influence the COW. The SCOW generated by the grid-connected windpowered plant is less dependent on the cost of energy purchased from the grid. Specifically, 

the COW produced by the grid-connected wind-powered plant exhibits a change of less than 

30% over the range of variation of energy prices considered; the variation of the specific 

COW produced by the grid-powered plant is close to 65% over the same range. Thus, when 

high fluctuations in the grid energy purchase price are anticipated, resorting to a windpowered grid connected desalination plant would lead to smaller fluctuations in the 

production COW than in the case of a grid-powered plant. 

Table 6–3 and Table 6–4 summarize the performance of the two plants analyzed in this 

section. Figure 6-13 gives the structure of COW for a grid-connected wind-RO plant, 

assuming an average cost of grid energy of $0.08/kWh. Figure 6-14 gives COW structure for 

127 
the 158-vessel desalination plant, powered only with grid energy, assuming a $0.08/kWh 

energy cost. 

Table 6-3. Performance of a Grid-Connected Wind-RO Plant 

Maximum wind turbine power 1,500 kW 

RO plant size 158 vessels 

Average cost of water (COE at $0.04/kWh) 0.69 $/m3 

Average cost of water (COE at $0.12/kWh) 0.77 $/m3 

Average recovery rate 56.3 % 

Average permeate flow rate 3,042 gpm 

Average permeate flow per maximum power 2.03 gpm/kW 

W ater co st com pone nts, 158-v esse l wind-po wered grid-con nected p 

3% 

6 1% 

10% 

15% 

1% 

1 1% Fix ed charg es RO 

Fix ed charg es W T 

Ma inte na nce RO 

Ma inte na nce W T 

Grid E nergy 

Raw m ateria ls 

Figure 6-13. COW structure for the 158-vessel grid-connected wind-RO 

desalination plant, assuming $0.08/kWh grid energy cost 

128 
Table 6-4. Performance of an RO Plant Using Only Grid Power 

Maximum wind turbine power 1,500 kW 

RO plant size 158 vessels 

Average COW (COE at $0.04/kWh) 0.66 $/m3 

Average COW (COE at $0.12/kWh) 0.83 $/m3 

Average recovery rate 56.3 % 

Average permeate flow rate 3,042 gpm 

Average permeate flow per maximum power 2.03 gpm/kW 

Water cost components, 158-vessel grid-powered plant 

3% 

60% 

14% 

23% 

Fixed charges RO 

Maintenance RO 

Grid Energy 

Raw materials 

Figure 6-14. COW structure for the 158-vessel desalination plant, powered only 

with grid energy, assuming a $0.08/kWh energy cost 

The average SCOW in the case of a grid-connected wind-powered desalination plant is 

lower than that in the similar plant operated in a grid-isolated mode (considered in Section 

6.2). This reduction is owed to the more efficient use of equipment; namely, the cost of 

power purchased from the grid to run the plant at full capacity (with no RO vessels idling 

at any time) is smaller than the fixed (annualized) cost of the RO vessels that would 

remain unused when the power generated by the turbine is insufficient for running the RO 

plant at full capacity. This occurs for any (currently reasonable) cost of the energy 

purchased from the grid. However, for a very large COE, this balance may not stay true, 

and operating a grid-connected wind-powered RO desalination plant will become less 

advantageous than the operation of a similar, but grid-isolated configuration. 

129 
6.3.3 Plant operation concepts 

The constant operation of a wind-RO plant analyzed in Section 6.3.1 is one of many 

possible operating strategies. Clearly, for the same capital expenditure, the plant operator 

may prefer to produce less water when grid power is expensive (decreasing the operating 

costs) and increase water production when wind is available. Accordingly, the “optimal” 

size of RO plant is closely dependent on the chosen strategy. 

For a grid-connected operation, the plant set points include not only the grid-isolated 

topology set points (water pump speeds, number of active vessels, recirculation flows), 

but also those that correspond to the power management: power used by the RO plant, 

power bought or sold to the grid, and power drawn from or stored in the batteries (if 

available). 

The operation of a wind-RO plant can take into account the forecast for wind speeds, and 

energy prices to make well-informed decisions to manage the energy storage. One 

possible way to achieve this is to use receding horizon techniques that continuously 

correct the operating set points to maximize a performance criterion. In the context of a 

grid-connected wind-RO plant this strategy can be defined by solving optimization 

problems in Table 6-5. 

Table 6-5. Receding Horizon Approach for Wind-RO Operating Strategies 

Minimize ∑=

N 

k 

COWk 

1 

Subject to RO operational constraints (Sections 3.2.4−3.2.5) 

Energy storage constraints (Section 3.2.8) 

S < Smax (RO plant size) 

Qp > Q p demand 

C p < C p max 

Where the optimization is performed with respect to the wind-RO plant set points, during a

period of time spanning N steps, COWk is the SCOW at the step k, Smax is the maximum

number of vessels in the RO plant, Qp and Cp are respectively, the average permeate flow and 

permeate concentration during the following N steps, and the limits Qp min and Cp max

depend on the local water regulations. 

Model predictive control strategies as defined in Table 6-5 have been subjected to extensive 

use in industry for process control (see Rossiter 200344 and Maciejowski 200245).

130 
7 Conclusions 

A systematic approach to address fundamental problems in the integration of wind energy and 

desalination systems was presented. The basic technological challenge for integrating RO 

desalination with renewable energy sources relies on the interaction between a power 

generation characterized by significant time fluctuations with a desalination technology that is 

typically designed for a steady operation and possesses a multiplicity of restrictive operational 

limits. 

The design of a wind-RO system and its operational strategy requires an understanding of the 

physical limits that constrain the desalination operation and the way they are affected by 

power variations. To address this issue, a physics-based model has been developed to simulate 

the integrated wind-desalination system accounting effects such as: 

• Changes in pressures, concentrations, and flows throughout the RO plant generated by 

changes in pump speeds, feedwater concentration, pressure and temperature, valve 

openings, and connection of RO vessels during operation 

• Changes in the pump efficiencies caused by changes in water flows and pump speeds 

• Changes in the electrical motor loads caused by changes in pump speed and flow 

rates 

• Changes in the available power caused by changes in wind speeds 

• Analyzing physical constraints (of all the components in the system) for any value 

of pump speed, valve position, vessel connection, and feedwater properties. 

An integrated COW model was developed to evaluate the economic viability of various 

wind-desalination configurations and perform trade-off analyses. The integrated model 

accounts for the stochastic nature of wind and its economic effects on water production. 

The operational flexibility is regarded as an important concern to operate RO plants in a 

wide range of available powers. This issue has been addressed first, by defining a set of 

desalination configurations with the ability to operate in a wide range of settings; then, a 

rigorous analysis has been performed using the physical models, to obtain the actual 

operating space allowed by the system constraints and to understand the trade-offs 

between operational constraints and desalination performance. 

A preliminary cost analysis has been presented for two seawater desalination 

configurations and one brackish water configuration, which showed that the resulting 

COW had the potential to be viable. These configurations were defined considering that a 

1.5-MW wind turbine provides the power. 

One RO configuration was selected for further analysis to understand its performance and 

economics in grid-connected and grid-isolated electrical topologies. The detailed analyses 

include: 

• The definition and calculation of an optimal operational strategy for a grid-isolated 

topology 

131 
• Definition and calculation of optimal plant size 

• Detailed COW calculation of the resulting grid-isolated topology 

• Definitions and calculation of an operating strategy for grid-connected topology 

• Detailed COW calculation for resulting grid-connected topology, including a 

sensitivity analysis with respect to the cost of grid energy 

• Definition of optimal operating strategies for grid-connected topologies. 

The results showed that a wind-RO-integrated technology can produce water at 

competitive prices. For example, the analysis of seawater desalination powered by a 1.5­

MW wind turbine, predicted a levelized annual cost of $1.11/m3

 in a grid-isolated 

topology, and a cost of $0.77/m3

 for a grid-connected topology with energy prices of 

$0.12/kWh. 

The systematic approach presented in this report should prove useful to pursue more 

detailed system design, trade-off analysis, and optimal operation strategies definition on 

similar systems and to analyze other hybrid desalination system with renewable energy 

sources. 

132 
8 Future Work 

Many problems that can be considered as parts of a natural continuation of the approach 

presented in this report, and can benefit the understanding and design procedures for 

wind/RO systems. Some of them are listed here. 

1. Use the physics and economical models in the proposed approach to investigate 

the potential technological improvements that have the largest impact on the COW 

for wind/RO desalination (or other hybrid desalination technologies). Methods to 

reduce the CO include 

a. Improve pump efficiencies. 

b. Improve energy recovery efficiencies. 

c. Relax RO membrane constraints by redesigning spiral wound elements. 

d. Augment the operational flexibility of ERDs. 

2. Calculate optimal strategies to account for switching behavior of vessels and 

ERDs. The current strategy (as indicated in section 6.2.3) assumes that vessels can 

be individually activated or deactivated. An optimal strategy that accounts for 

restrictions in vessel and ERD operation should be used for more detailed analysis. 

As a by-product, a method to determine the optimal size of membrane and energy 

recovery banks will be obtained. 

3. Define optimal operating strategies for efficient operation of wind-RO plants, 

taking into account local water distribution constraints. The approach, which was 

outlined in Section 6.3.3, takes into account the dynamics of the energy storage 

system and forecasted wind speeds and energy prices (if connected to the grid). 

4. Obtain control strategies that account for damaging effects of membrane pressure 

fluctuations. This problem is more critical with grid-isolated configurations, and 

requires a good understanding of membrane degradation as a function of pressure 

fluctuations. The fluctuation in membrane caused by changes in wind speed (and 

electrical power fed to the water pumps) could be absorbed by the energy storage 

system. 

5. Operating strategy will not follow exactly the table of optimal results. Instead the 

pump speed command should use a filter to mitigate pressure fluctuations in the 

range of frequencies that most affect membrane life. In this case the mismatch 

between wind power and used power can be absorbed by the energy storage. 

6. Trip design: in cases when the fluctuations in power are large enough so that there 

is not time to implement switching strategies in RO banks or even dissipate extra 

power, there should be protective logic to prevent membrane damage. Threshold 

on the wind fluctuations can be defined to trigger a plant shutdown. 

133 
9 Toray Membrane America Design Guidelines 

134
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135 
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136 
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137 
Appendix A 

Toray Reverse Osmosis, Brackish Water, and 

Seawater Elements 

The following documents are used with permission from Toray Membrane America, Inc. 

 138
TorayRO v 2.0.28 File: SW-WE-a1-3-06-06-05.tro 06 Jun 2005 

Project: 

Comments: 

Prepared For: 

Location: 

Prepared By: 

Date Prepared: 

System Results 

Flow Rates Gal/min Concentrations mg/l 

RO Feed 2600 RO Feed TDS 35098 

Permeate 1040 Permeate TDS 260 

Concentrate 1560 Concentrate TDS 58323 

Total Feed 2600 Total Feed TDS 35106 

Total Product 1040 Total Product TDS 260 

System Details Single Stage Design 

Temperature: 25.0 Deg C Water Type: Seawater -well 

System Recovery: 40.0 % 

Pass 1 Units: Pressure - Psi Flow - Gal/min TDS - mg/l 

Array 1 Recovery: 40.0% Concentrate TDS: 58323 Concentrate Flow: 1560 

Total Total Element Feed Perm Feed Delta Perm 

Bank Vessels Elements Model Flow Flow Press Press TDS 

TM820- 1 50 300 2600 743 753 14.2 185 370 

TM820- 2 38 228 1857 297 737 14.5 449 370 

Total 88 528 2600 1040 260 

Concentration, Saturation and pH Data mg/l 

Ion Permeate Treated Feed Feed Concentrate 

Ca 0.96 408 408 679 

Mg 3.07 1298 1298 2161 

Na 92.6 10768 10768 17885 

K 3.77 388 388 644 

Ba 0.0 0.0 0.0 0.0 

Sr 0.0 0.0 0.0 0.0 

NH4 0.0 0.0 0.0 0.0 

Fe 0.0 0.0 0.0 0.0 

HCO3 1.26 101 143 168 

Cl 149 19380 19380 32200 

SO4 8.6 2738 2702 4558 

NO3 0.0 0.0 0.0 0.0 

F 0.0 0.0 0.0 0.0 

B 0.31 1.1 1.1 1.63 

Toray Incorporated © 2002 Page 1 
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Ion Permeate Treated Feed Feed Concentrate 

SiO2 0.16 15.0 15.0 24.9 

PO4 0.0011 0.5 0.5 0.83 

CO3 4.12E-06 0.0814 2.29 0.26 

CO2 34.0 34.0 2.4 34.0 

TDS 260 35098 35106 58323 

pH 4.76 6.5 7.8 6.7 

Saturation Data (%) 

CaSO4 0.0027 21.8 21.5 41.6 

CaPO4 0.0 0.0732 10000 174 

CaF2 0.0 0.0 0.0 0.0 

BaSO4 0.0 0.0 0.0 0.0 

SiO2 0.12 14.0 11.7 23.8 

SrSO4 0.0 0.0 0.0 0.0 

LSI -7.62 -0.74 0.72 0.0899 

SDSI -6.56 -1.57 -0.11 -1.08 

Toray Incorporated © 2002 Page 2 
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System Summary 

System Configuration 

System Type: 

Feed Predosing?: Yes 

Feed Afterdosing?: No 

Interpass Dosing?: No 

Product Dosing?: No 

Feed CO2 Stripping?: No 

Interpass CO2 Stripping?: No 

Product CO2 Stripping?: No 

Raw Feed Bypass?: No 

First Pass Recycle?: No 

Interpass Pumping?: No 

Feed Information 

Water Type: Seawater -well 

Temperature, Deg C: 25.0 

Feed pH: 7.8 

Silt Density Index: 5.5

 Feed Ion Concentration (mg/l)

Ca 408

Mg 1298

Na 10768

K 388

Ba 0.0

Sr 0.0

NH4 0.0

Fe 0.0

HCO3 143

Cl 19380

SO4 2702

NO3 0.0

F 0.0

B 1.1

SiO2 15.0

PO4 0.5

CO3 2.29

CO2 2.4

System Flux, Flows and Recoveries 

Average System Flux: 7.68 Gal/ft2/day 

Feed Flow: 2,600.00 Gal/min 

Product Flow: 1,040.00 Gal/min 

Concentrate Flow: 1,560.00 Gal/min 

First Pass Recovery: 40.0 % 

System Recovery: 40.0 % 

Toray Incorporated © 2002 Page 3 
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First Pass Array 

Interbank Pressure Drop: 

Interbank Pressure Boost 

Bank 1-2: 

Bank 1 Back Pressure: 

Bank 2 Back Pressure: 

Number of Banks: 2

Bank

2.0 Psi

0.0 Psi

15.0 Psi

15.0 Psi

Total Elements: 528

# Vessels # Elements/Vessel Element Type

1 50 6

2 38 6

Element Age

TM820-370 3

TM820-370 3

Chemical Treatment 

Station Chemical Target pH

Feed Pre-Treat Sulfuric Acid 6.5

Toray Incorporated © 2002 Page 4
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Process Data 

Flow Units: Gal/min 

Pressure Units: psi 

Feed

 2600 

Concentrate

 1560 

Product

 1040 

Net Feed

 2600 

40.0% 

System Recovery 

Flow Rates Gal/min Concentrations mg/l 

RO Feed 2600 RO Feed TDS 35098 

Permeate 1040 Permeate TDS 260 

Concentrate 1560 Concentrate TDS 58323 

Total Feed 2600 Total Feed TDS 35106 

Total Product 1040 Total Product TDS 260 

System Data Single Stage Design 

Temperature: 25.0 Deg C 

Stage 1 

Fouling Allowance 85.0 % 

Salt Passage Increase Per Year 10.0 % 

Feed Pressure 753 Psi 

Interbank Loss 2.0 Psi 

Element Age 3.0 Years 

Interbank Boost Pressure Stage 1 

Banks 1-2 0.0 Psi 

Chemical Usage Chemical lb/day kg/day Target pH 

Feed Pre-Treat Sulfuric Acid 1156 525 6.5 

40.0% 

Toray Incorporated © 2002 Page 5 
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Stream Data 

Units: Pressure - psi Flow - Gal/min TDS - mg/l Saturation - % 

System Predosed 1st Pass Total System 

Stream ---> Feed Feed Feed Permeate Product 

Ca 408 408 408 0.96 0.96 

Mg 1298 1298 1298 3.07 3.07 

Na 10768 10768 10768 92.6 92.6 

K 388 388 388 3.77 3.77 

Ba 0.0 0.0 0.0 0.0 0.0 

Sr 0.0 0.0 0.0 0.0 0.0 

NH4 0.0 0.0 0.0 0.0 0.0 

Fe 0.0 0.0 0.0 0.0 0.0 

HCO3 143 101 101 1.26 1.26 

Cl 19380 19380 19380 149 149 

SO4 2702 2738 2738 8.6 8.6 

NO3 0.0 0.0 0.0 0.0 0.0 

F 0.0 0.0 0.0 0.0 0.0 

B 1.1 1.1 1.1 0.31 0.31 

SiO2 15.0 15.0 15.0 0.16 0.16 

PO4 0.5 0.5 0.5 0.0011 0.0011 

CO3 2.29 0.0814 0.0814 4.12E-06 4.12E-06 

CO2 2.4 34.0 34.0 34.0 34.0 

TDS 35106 35098 35098 260 260 

pH 7.8 6.5 6.5 4.76 4.76 

LSI 0.72 -0.74 -0.74 -7.62 -7.62 

Stiff-Davis -0.11 -1.57 -1.57 -6.56 -6.56 

BaSO4 Sat 0.0 0.0 0.0 0.0 0.0 

CaSO4 Sat 21.5 21.8 21.8 0.0027 0.0027 

CaPO4 Sat 10000 0.0732 0.0732 0.0 0.0 

CaF2 Sat 0.0 0.0 0.0 0.0 0.0 

SrSO4 Sat 0.0 0.0 0.0 0.0 0.0 

SiO2 Sat 11.7 14.0 14.0 0.12 0.12 

Flow 2600 2600 2600 1040 1040 

Temp, Deg C 25.0 25.0 25.0 25.0 25.0 

Pressure 753 753 753 0.0 0.0 

Osm Pressure 368 368 368 3.07 3.07 

Toray Incorporated © 2002 Page 6 
TorayRO v 2.0.28 File: SW-WE-a1-3-06-06-05.tro 06 Jun 2005 

Units: Pressure - psi Flow - Gal/min 

System 

Stream ---> Concentrate 

Ca 679 

Mg 2161 

Na 17885 

K 644 

Ba 0.0 

Sr 0.0 

NH4 0.0 

Fe 0.0 

HCO3 168 

Cl 32200 

SO4 4558 

NO3 0.0 

F 0.0 

B 1.63 

SiO2 24.9 

PO4 0.83 

CO3 0.26 

CO2 34.0 

TDS 58323 

pH 6.7 

LSI 0.0899 

Stiff-Davis -1.08 

BaSO4 Sat 0.0 

CaSO4 Sat 41.6 

CaPO4 Sat 174 

CaF2 Sat 0.0 

SrSO4 Sat 0.0 

SiO2 Sat 23.8 

Flow 1560 

Temp, Deg C 25.0 

Pressure 723 

Osm Pressure 603 

TDS - mg/l Saturation - % 

Toray Incorporated © 2002 Page 7 
TorayRO v 2.0.28 File: SW-WE-a1-3-06-06-05.tro 06 Jun 2005 

Element Data 

Pass 1, Bank 1 Units: Pressure - psi, Flow - Gal/min, TDS - mg/l, Saturation - %, Flux - gal/ft2/day 

Bank Permeate Back Pressure: 15.0 

Elem 1 Elem 2 Elem 3 Elem 4 Elem 5 Elem 6 

Permeate Ions 

Ca 

Mg 

Na 

K 

Ba 

Sr 

NH4 

Fe 

HCO3 

Cl 

SO4 

NO3 

F 

B 

SiO2 

PO4 

CO3 

CO2 

TDS 

pH 

LSI 

Stiff-Davis 

Conc Saturation 

BaSO4 Sat 

CaSO4 Sat 

CaF2 Sat 

SrSO4 Sat 

SiO2 Sat 

Flow 

Feed 

Permeate 

Pressure 

Feed 

Net Driving 

Pressure Drop 

Feed Osmotic 

Other Parameters 

% Recovery 

B Conc Pol 

A Value 

B Value 

Flux 

0.48 

1.53 

46.5 

1.89 

0.0 

0.0 

0.0 

0.0 

0.63 

74.9 

4.3 

0.0 

0.0 

0.19 

0.0807 

0.0005 

9.82E-07 

34.0 

130 

4.47 

-9.4 

-7.43 

0.0 

23.5 

0.0 

0.0 

14.9 

52.0 

3.07 

753 

330 

2.83 

368 

5.9 

1.08 

2.56E-09 

2.06E-08 

12.0 

0.55 

1.75 

53.1 

2.16 

0.0 

0.0 

0.0 

0.0 

0.72 

85.6 

4.91 

0.0 

0.0 

0.21 

0.0925 

0.0006 

1.30E-06 

34.0 

149 

4.52 

-9.29 

-7.26 

0.0 

25.3 

0.0 

0.0 

15.8 

48.9 

2.83 

751 

305 

2.62 

390 

5.79 

1.08 

2.57E-09 

2.06E-08 

11.0 

0.63 

2.02 

61.0 

2.48 

0.0 

0.0 

0.0 

0.0 

0.83 

98.4 

5.65 

0.0 

0.0 

0.23 

0.11 

0.0007 

1.73E-06 

34.0 

171 

4.58 

-9.17 

-7.09 

0.0 

27.2 

0.0 

0.0 

16.8 

46.1 

2.59 

748 

279 

2.43 

413 

5.63 

1.07 

2.58E-09 

2.05E-08 

10.1 

0.73 

2.33 

70.6 

2.87 

0.0 

0.0 

0.0 

0.0 

0.96 

114 

6.54 

0.0 

0.0 

0.26 

0.12 

0.0008 

2.34E-06 

34.0 

198 

4.64 

-9.06 

-6.9 

0.0 

29.1 

0.0 

0.0 

17.8 

43.5 

2.35 

746 

253 

2.27 

437 

5.41 

1.07 

2.58E-09 

2.04E-08 

9.18 

0.85 

2.72 

82.1 

3.34 

0.0 

0.0 

0.0 

0.0 

1.12 

133 

7.61 

0.0 

0.0 

0.3 

0.14 

0.0009 

3.21E-06 

34.0 

231 

4.71 

-8.94 

-6.71 

0.0 

31.2 

0.0 

0.0 

18.9 

41.1 

2.12 

743 

227 

2.12 

462 

5.15 

1.06 

2.59E-09 

2.04E-08 

8.26 

1.02 

3.24 

97.8 

3.98 

0.0 

0.0 

0.0 

0.0 

1.33 

158 

9.08 

0.0 

0.0 

0.34 

0.17 

0.0011 

4.63E-06 

34.0 

275 

4.78 

-7.23 

-6.49 

0.0 

33.2 

0.0 

0.0 

19.9 

39.0 

1.89 

741 

202 

1.99 

486 

4.84 

1.06 

2.60E-09 

2.07E-08 

7.37 

Toray Incorporated © 2002 Page 8 
TorayRO v 2.0.28 File: SW-WE-a1-3-06-06-05.tro 06 Jun 2005 

Pass 1, Bank 2 Units: Pressure - psi, Flow - Gal/min, TDS - mg/l, Saturation - %, Flux - gal/ft2/day 

Bank Permeate Back Pressure: 15.0 

Bank Boost Pressure: 0.0 

Elem 1 Elem 2 Elem 3 Elem 4 Elem 5 Elem 6 

Permeate Ions 

Ca 

Mg 

Na 

K 

Ba 

Sr 

NH4 

Fe 

HCO3 

Cl 

SO4 

NO3 

F 

B 

SiO2 

PO4 

CO3 

CO2 

TDS 

pH 

LSI 

Stiff-Davis 

Conc Saturation 

BaSO4 Sat 

CaSO4 Sat 

CaF2 Sat 

SrSO4 Sat 

SiO2 Sat 

Flow 

Feed 

Permeate 

Pressure 

Feed 

Net Driving 

Pressure Drop 

Feed Osmotic 

Other Parameters 

% Recovery 

B Conc Pol 

A Value 

B Value 

Flux 

1.17 

3.72 

112 

4.57 

0.0 

0.0 

0.0 

0.0 

1.53 

182 

10.4 

0.0 

0.0 

0.37 

0.19 

0.0013 

6.21E-06 

34.0 

316 

4.84 

-6.75 

-6.31 

0.0 

34.7 

0.0 

0.0 

20.6 

48.9 

1.71 

737 

183 

2.65 

510 

3.49 

1.05 

2.59E-09 

2.09E-08 

6.65 

1.35 

4.31 

130 

5.29 

0.0 

0.0 

0.0 

0.0 

1.77 

210 

12.1 

0.0 

0.0 

0.41 

0.22 

0.0015 

8.43E-06 

34.0 

365 

4.9 

-6.42 

-6.13 

0.0 

36.3 

0.0 

0.0 

21.3 

47.2 

1.53 

735 

165 

2.54 

528 

3.24 

1.04 

2.59E-09 

2.10E-08 

5.96 

1.57 

5.0 

151 

6.13 

0.0 

0.0 

0.0 

0.0 

2.05 

244 

14.0 

0.0 

0.0 

0.46 

0.26 

0.0017 

1.15E-05 

34.0 

424 

4.96 

-6.16 

-5.94 

0.0 

37.7 

0.0 

0.0 

22.0 

45.6 

1.36 

732 

148 

2.44 

545 

2.99 

1.04 

2.57E-09 

2.11E-08 

5.31 

1.83 

5.82 

175 

7.12 

0.0 

0.0 

0.0 

0.0 

2.38 

283 

16.3 

0.0 

0.0 

0.5 

0.29 

0.002 

1.58E-05 

34.0 

493 

5.02 

-5.92 

-5.76 

0.0 

39.1 

0.0 

0.0 

22.7 

44.3 

1.21 

730 

132 

2.36 

561 

2.73 

1.03 

2.56E-09 

2.13E-08 

4.71 

2.13 

6.78 

204 

8.29 

0.0 

0.0 

0.0 

0.0 

2.77 

330 

19.0 

0.0 

0.0 

0.56 

0.34 

0.0023 

2.18E-05 

34.0 

573 

5.08 

-5.7 

-5.57 

0.0 

40.4 

0.0 

0.0 

23.3 

43.1 

1.07 

727 

117 

2.28 

576 

2.48 

1.03 

2.54E-09 

2.14E-08 

4.16 

2.49 

7.91 

238 

9.65 

0.0 

0.0 

0.0 

0.0 

3.22 

384 

22.2 

0.0 

0.0 

0.61 

0.39 

0.0027 

3.02E-05 

34.0 

668 

5.15 

-5.5 

-5.38 

0.0 

41.6 

0.0 

0.0 

23.8 

42.0 

0.94 

725 

104 

2.21 

590 

2.24 

1.03 

2.53E-09 

2.16E-08 

3.67 

Toray Incorporated © 2002 Page 9 
TorayRO v 2.0.28 File: SW-WE-a1-3-06-06-05.tro 06 Jun 2005 

Errors & Warnings 

Warning - High LSI. LSI > zero. Concentrate CaCO3 greater than saturation. Scale inhibitor required. 

The feed water analysis was balanced with added Na or Cl. 

Database version used for design : 2.028 

WARRANTY DISCLAIMER. NO WARRANTIES ARE GIVEN IN CONNECTION WITH THIS SOFTWARE OR ITS USE. THIS SOFTWARE IS NOT WARRANTED 

FOR MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. This software is provided as an aid for the design of reverse osmosis systems 

incorporating membrane elements sold by Toray Industries, Inc., Toray Membrane America, Inc. and ROPUR AG. Such companies do not assume any 

responsibilities or liability in connection with this software or any results obtained or damages incurred in connection with its use. The user of the software shall be 

solely responsible for any designs created using the software and therefore should have the necessary technical skills and experience to design reverse osmosis 

systems. Although it is anticipated that system designs will be reviewed by application engineers of one of the companies mentioned above, such companies do not 

assume any responsibility or liability arising out of such review. Any warranty of systems or system designs will be provided only as expressly stated in a written 

document signed by an authorized representative of the company issuing the warranty. 

Toray Industries, Inc. Membrane Products Dept. TEL: (+81) 47-350-6030 

8-1, Mihama 1-chome, Urayasu, Chiba 279-8555, Japan Fax: (+81) 47-350-6066 

TORAY Membrane America, Inc. ROPUR AG 

USA, South America, Canada Europe, Middle East and Africa Tel: +41 (61) 415 87 10 

12520 High Bluff Drive, Suite 120 Tel: +1 (858) 523 0476 Grabenackerstrasse 8 

San Diego, CA 92130, USA Fax: +1 (858) 523 0861 CH-4142 Munchenstein 1, Switzerland Fax: +41 (61) 415 87 20 

Toray Incorporated © 2002 Page 10 
TorayRO v 2.0.28 File: SW-WE-a1-4-06-06-05.tro 06 Jun 2005 

Project: 

Comments: 

Prepared For: 

Location: 

Prepared By: 

Date Prepared: 

System Results 

Flow Rates Gal/min Concentrations mg/l 

RO Feed 2625 RO Feed TDS 35098 

Permeate 1050 Permeate TDS 255 

Concentrate 1575 Concentrate TDS 58327 

Total Feed 2625 Total Feed TDS 35106 

Total Product 1050 Total Product TDS 255 

System Details Single Stage Design 

Temperature: 25.0 Deg C Water Type: Seawater -well 

System Recovery: 40.0 % 

Pass 1 Units: Pressure - Psi Flow - Gal/min TDS - mg/l 

Array 1 Recovery: 40.0% Concentrate TDS: 58327 Concentrate Flow: 1575 

Total Total Element Feed Perm Feed Delta Perm 

Bank Vessels Elements Model Flow Flow Press Press TDS 

TM820- 1 50 300 2625 713 731 14.6 187 370 

TM820- 2 38 228 1912 337 757 14.9 398 370 

Total 88 528 2625 1050 255 

Concentration, Saturation and pH Data mg/l 

Ion Permeate Treated Feed Feed Concentrate 

Ca 0.94 408 408 679 

Mg 3.0 1298 1298 2161 

Na 90.7 10768 10768 17886 

K 3.69 388 388 644 

Ba 0.0 0.0 0.0 0.0 

Sr 0.0 0.0 0.0 0.0 

NH4 0.0 0.0 0.0 0.0 

Fe 0.0 0.0 0.0 0.0 

HCO3 1.23 101 143 168 

Cl 146 19380 19380 32202 

SO4 8.42 2738 2702 4558 

NO3 0.0 0.0 0.0 0.0 

F 0.0 0.0 0.0 0.0 

B 0.31 1.1 1.1 1.63 

Toray Incorporated © 2002 Page 1 
TorayRO v 2.0.28 File: SW-WE-a1-4-06-06-05.tro 06 Jun 2005 

Ion Permeate Treated Feed Feed Concentrate 

SiO2 0.16 15.0 15.0 24.9 

PO4 0.001 0.5 0.5 0.83 

CO3 3.95E-06 0.0814 2.29 0.26 

CO2 34.0 34.0 2.4 34.0 

TDS 255 35098 35106 58327 

pH 4.75 6.5 7.8 6.7 

Saturation Data (%) 

CaSO4 0.0026 21.8 21.5 41.6 

CaPO4 0.0 0.0732 10000 175 

CaF2 0.0 0.0 0.0 0.0 

BaSO4 0.0 0.0 0.0 0.0 

SiO2 0.12 14.0 11.7 23.8 

SrSO4 0.0 0.0 0.0 0.0 

LSI -7.88 -0.74 0.72 0.09 

SDSI -6.58 -1.57 -0.11 -1.08 

Toray Incorporated © 2002 Page 2 
TorayRO v 2.0.28 File: SW-WE-a1-4-06-06-05.tro 06 Jun 2005 

System Summary 

System Configuration 

System Type: 

Feed Predosing?: Yes 

Feed Afterdosing?: No 

Interpass Dosing?: No 

Product Dosing?: No 

Feed CO2 Stripping?: No 

Interpass CO2 Stripping?: No 

Product CO2 Stripping?: No 

Raw Feed Bypass?: No 

First Pass Recycle?: No 

Interpass Pumping?: No 

Feed Information 

Water Type: Seawater -well 

Temperature, Deg C: 25.0 

Feed pH: 7.8 

Silt Density Index: 5.5

 Feed Ion Concentration (mg/l)

Ca 408

Mg 1298

Na 10768

K 388

Ba 0.0

Sr 0.0

NH4 0.0

Fe 0.0

HCO3 143

Cl 19380

SO4 2702

NO3 0.0

F 0.0

B 1.1

SiO2 15.0

PO4 0.5

CO3 2.29

CO2 2.4

System Flux, Flows and Recoveries 

Average System Flux: 7.75 Gal/ft2/day 

Feed Flow: 2,625.00 Gal/min 

Product Flow: 1,050.00 Gal/min 

Concentrate Flow: 1,575.00 Gal/min 

First Pass Recovery: 40.0 % 

System Recovery: 40.0 % 

Toray Incorporated © 2002 Page 3 
TorayRO v 2.0.28 File: SW-WE-a1-4-06-06-05.tro 06 Jun 2005 

First Pass Array 

Interbank Pressure Drop: 

Interbank Pressure Boost 

Bank 1-2: 

Bank 1 Back Pressure: 

Bank 2 Back Pressure: 

Number of Banks: 2

Bank

2.0 Psi

42.0 Psi

15.0 Psi

15.0 Psi

Total Elements: 528

# Vessels # Elements/Vessel Element Type

1 50 6

2 38 6

Element Age

TM820-370 3

TM820-370 3

Chemical Treatment 

Station Chemical Target pH

Feed Pre-Treat Sulfuric Acid 6.5

Toray Incorporated © 2002 Page 4
TorayRO v 2.0.28 File: SW-WE-a1-4-06-06-05.tro 06 Jun 2005 

Process Data 

Flow Units: Gal/min 

Pressure Units: psi 

Feed

 2625 

Concentrate

 1575 

Product

 1050 

Net Feed

 2625 

40.0% 

System Recovery 

Flow Rates Gal/min Concentrations mg/l 

RO Feed 2625 RO Feed TDS 35098 

Permeate 1050 Permeate TDS 255 

Concentrate 1575 Concentrate TDS 58327 

Total Feed 2625 Total Feed TDS 35106 

Total Product 1050 Total Product TDS 255 

System Data Single Stage Design 

Temperature: 25.0 Deg C 

Stage 1 

Fouling Allowance 85.0 % 

Salt Passage Increase Per Year 10.0 % 

Feed Pressure 731 Psi 

Interbank Loss 2.0 Psi 

Element Age 3.0 Years 

Interbank Boost Pressure Stage 1 

Banks 1-2 42.0 Psi 

Chemical Usage Chemical lb/day kg/day Target pH 

Feed Pre-Treat Sulfuric Acid 1167 531 6.5 

40.0% 

Toray Incorporated © 2002 Page 5 
TorayRO v 2.0.28 File: SW-WE-a1-4-06-06-05.tro 06 Jun 2005 

Stream Data 

Units: Pressure - psi Flow - Gal/min TDS - mg/l Saturation - % 

System Predosed 1st Pass Total System 

Stream ---> Feed Feed Feed Permeate Product 

Ca 408 408 408 0.94 0.94 

Mg 1298 1298 1298 3.0 3.0 

Na 10768 10768 10768 90.7 90.7 

K 388 388 388 3.69 3.69 

Ba 0.0 0.0 0.0 0.0 0.0 

Sr 0.0 0.0 0.0 0.0 0.0 

NH4 0.0 0.0 0.0 0.0 0.0 

Fe 0.0 0.0 0.0 0.0 0.0 

HCO3 143 101 101 1.23 1.23 

Cl 19380 19380 19380 146 146 

SO4 2702 2738 2738 8.42 8.42 

NO3 0.0 0.0 0.0 0.0 0.0 

F 0.0 0.0 0.0 0.0 0.0 

B 1.1 1.1 1.1 0.31 0.31 

SiO2 15.0 15.0 15.0 0.16 0.16 

PO4 0.5 0.5 0.5 0.001 0.001 

CO3 2.29 0.0814 0.0814 3.95E-06 3.95E-06 

CO2 2.4 34.0 34.0 34.0 34.0 

TDS 35106 35098 35098 255 255 

pH 7.8 6.5 6.5 4.75 4.75 

LSI 0.72 -0.74 -0.74 -7.88 -7.88 

Stiff-Davis -0.11 -1.57 -1.57 -6.58 -6.58 

BaSO4 Sat 0.0 0.0 0.0 0.0 0.0 

CaSO4 Sat 21.5 21.8 21.8 0.0026 0.0026 

CaPO4 Sat 10000 0.0732 0.0732 0.0 0.0 

CaF2 Sat 0.0 0.0 0.0 0.0 0.0 

SrSO4 Sat 0.0 0.0 0.0 0.0 0.0 

SiO2 Sat 11.7 14.0 14.0 0.12 0.12 

Flow 2625 2625 2625 1050 1050 

Temp, Deg C 25.0 25.0 25.0 25.0 25.0 

Pressure 731 731 731 0.0 0.0 

Osm Pressure 368 368 368 3.01 3.01 

Toray Incorporated © 2002 Page 6 
TorayRO v 2.0.28 File: SW-WE-a1-4-06-06-05.tro 06 Jun 2005 

Units: Pressure - psi Flow - Gal/min 

System 

Stream ---> Concentrate 

Ca 679 

Mg 2161 

Na 17886 

K 644 

Ba 0.0 

Sr 0.0 

NH4 0.0 

Fe 0.0 

HCO3 168 

Cl 32202 

SO4 4558 

NO3 0.0 

F 0.0 

B 1.63 

SiO2 24.9 

PO4 0.83 

CO3 0.26 

CO2 34.0 

TDS 58327 

pH 6.7 

LSI 0.09 

Stiff-Davis -1.08 

BaSO4 Sat 0.0 

CaSO4 Sat 41.6 

CaPO4 Sat 175 

CaF2 Sat 0.0 

SrSO4 Sat 0.0 

SiO2 Sat 23.8 

Flow 1575 

Temp, Deg C 25.0 

Pressure 742 

Osm Pressure 603 

TDS - mg/l Saturation - % 

Toray Incorporated © 2002 Page 7 
TorayRO v 2.0.28 File: SW-WE-a1-4-06-06-05.tro 06 Jun 2005 

Element Data 

Pass 1, Bank 1 Units: Pressure - psi, Flow - Gal/min, TDS - mg/l, Saturation - %, Flux - gal/ft2/day 

Bank Permeate Back Pressure: 15.0 

Elem 1 Elem 2 Elem 3 Elem 4 Elem 5 Elem 6 

Permeate Ions 

Ca 

Mg 

Na 

K 

Ba 

Sr 

NH4 

Fe 

HCO3 

Cl 

SO4 

NO3 

F 

B 

SiO2 

PO4 

CO3 

CO2 

TDS 

pH 

LSI 

Stiff-Davis 

Conc Saturation 

BaSO4 Sat 

CaSO4 Sat 

CaF2 Sat 

SrSO4 Sat 

SiO2 Sat 

Flow 

Feed 

Permeate 

Pressure 

Feed 

Net Driving 

Pressure Drop 

Feed Osmotic 

Other Parameters 

% Recovery 

B Conc Pol 

A Value 

B Value 

Flux 

0.49 

1.57 

47.7 

1.94 

0.0 

0.0 

0.0 

0.0 

0.65 

76.8 

4.4 

0.0 

0.0 

0.19 

0.0837 

0.0005 

1.03E-06 

34.0 

134 

4.48 

-9.38 

-7.4 

0.0 

23.4 

0.0 

0.0 

14.8 

52.5 

2.95 

731 

310 

2.86 

368 

5.61 

1.08 

2.62E-09 

2.04E-08 

11.5 

0.56 

1.79 

54.3 

2.21 

0.0 

0.0 

0.0 

0.0 

0.74 

87.5 

5.02 

0.0 

0.0 

0.21 

0.0956 

0.0006 

1.36E-06 

34.0 

152 

4.53 

-9.27 

-7.24 

0.0 

25.1 

0.0 

0.0 

15.7 

49.6 

2.72 

729 

286 

2.67 

389 

5.48 

1.07 

2.63E-09 

2.03E-08 

10.6 

0.65 

2.05 

62.2 

2.53 

0.0 

0.0 

0.0 

0.0 

0.85 

100 

5.76 

0.0 

0.0 

0.24 

0.11 

0.0007 

1.80E-06 

34.0 

175 

4.59 

-9.16 

-7.06 

0.0 

26.8 

0.0 

0.0 

16.7 

46.8 

2.49 

726 

262 

2.49 

411 

5.31 

1.07 

2.63E-09 

2.03E-08 

9.7 

0.74 

2.37 

71.7 

2.92 

0.0 

0.0 

0.0 

0.0 

0.98 

116 

6.64 

0.0 

0.0 

0.27 

0.13 

0.0008 

2.42E-06 

34.0 

201 

4.65 

-9.05 

-6.88 

0.0 

28.7 

0.0 

0.0 

17.6 

44.3 

2.26 

723 

237 

2.33 

433 

5.1 

1.06 

2.64E-09 

2.02E-08 

8.81 

0.86 

2.75 

83.0 

3.38 

0.0 

0.0 

0.0 

0.0 

1.13 

134 

7.7 

0.0 

0.0 

0.3 

0.15 

0.0009 

3.29E-06 

34.0 

233 

4.71 

-8.93 

-6.69 

0.0 

30.5 

0.0 

0.0 

18.5 

42.1 

2.04 

721 

214 

2.18 

456 

4.84 

1.06 

2.64E-09 

2.01E-08 

7.94 

1.02 

3.24 

98.0 

3.98 

0.0 

0.0 

0.0 

0.0 

1.33 

158 

9.09 

0.0 

0.0 

0.34 

0.17 

0.0011 

4.65E-06 

34.0 

275 

4.78 

-7.23 

-6.49 

0.0 

32.4 

0.0 

0.0 

19.5 

40.1 

1.82 

719 

191 

2.05 

478 

4.55 

1.05 

2.65E-09 

2.04E-08 

7.1 

Toray Incorporated © 2002 Page 8 
TorayRO v 2.0.28 File: SW-WE-a1-4-06-06-05.tro 06 Jun 2005 

Pass 1, Bank 2 Units: Pressure - psi, Flow - Gal/min, TDS - mg/l, Saturation - %, Flux - gal/ft2/day 

Bank Permeate Back Pressure: 15.0 

Bank Boost Pressure: 42.0 

Elem 1 Elem 2 Elem 3 Elem 4 Elem 5 Elem 6 

Permeate Ions 

Ca 

Mg 

Na 

K 

Ba 

Sr 

NH4 

Fe 

HCO3 

Cl 

SO4 

NO3 

F 

B 

SiO2 

PO4 

CO3 

CO2 

TDS 

pH 

LSI 

Stiff-Davis 

Conc Saturation 

BaSO4 Sat 

CaSO4 Sat 

CaF2 Sat 

SrSO4 Sat 

SiO2 Sat 

Flow 

Feed 

Permeate 

Pressure 

Feed 

Net Driving 

Pressure Drop 

Feed Osmotic 

Other Parameters 

% Recovery 

B Conc Pol 

A Value 

B Value 

Flux 

1.03 

3.29 

99.5 

4.05 

0.0 

0.0 

0.0 

0.0 

1.35 

161 

9.23 

0.0 

0.0 

0.34 

0.17 

0.0011 

4.80E-06 

34.0 

279 

4.79 

-7.15 

-6.47 

0.0 

34.0 

0.0 

0.0 

20.3 

50.3 

1.92 

757 

209 

2.75 

500 

3.81 

1.05 

2.55E-09 

2.10E-08 

7.47 

1.2 

3.8 

115 

4.67 

0.0 

0.0 

0.0 

0.0 

1.56 

185 

10.7 

0.0 

0.0 

0.38 

0.19 

0.0013 

6.49E-06 

34.0 

323 

4.85 

-6.69 

-6.28 

0.0 

35.7 

0.0 

0.0 

21.0 

48.4 

1.73 

754 

189 

2.62 

519 

3.57 

1.05 

2.54E-09 

2.11E-08 

6.73 

1.39 

4.41 

133 

5.41 

0.0 

0.0 

0.0 

0.0 

1.81 

215 

12.4 

0.0 

0.0 

0.42 

0.22 

0.0015 

8.86E-06 

34.0 

374 

4.91 

-6.38 

-6.1 

0.0 

37.2 

0.0 

0.0 

21.8 

46.7 

1.55 

751 

170 

2.51 

538 

3.31 

1.04 

2.53E-09 

2.13E-08 

6.03 

1.61 

5.14 

155 

6.29 

0.0 

0.0 

0.0 

0.0 

2.11 

250 

14.4 

0.0 

0.0 

0.46 

0.26 

0.0018 

1.22E-05 

34.0 

435 

4.97 

-6.11 

-5.91 

0.0 

38.8 

0.0 

0.0 

22.5 

45.1 

1.38 

749 

153 

2.41 

556 

3.05 

1.04 

2.52E-09 

2.15E-08 

5.36 

1.88 

5.99 

180 

7.33 

0.0 

0.0 

0.0 

0.0 

2.45 

292 

16.8 

0.0 

0.0 

0.51 

0.3 

0.0021 

1.68E-05 

34.0 

507 

5.03 

-5.88 

-5.72 

0.0 

40.2 

0.0 

0.0 

23.2 

43.7 

1.22 

747 

136 

2.32 

573 

2.79 

1.03 

2.50E-09 

2.16E-08 

4.75 

2.2 

7.0 

211 

8.56 

0.0 

0.0 

0.0 

0.0 

2.86 

340 

19.6 

0.0 

0.0 

0.57 

0.35 

0.0024 

2.34E-05 

34.0 

592 

5.1 

-5.66 

-5.53 

0.0 

41.6 

0.0 

0.0 

23.8 

42.5 

1.08 

744 

121 

2.24 

589 

2.53 

1.03 

2.48E-09 

2.18E-08 

4.19 

Toray Incorporated © 2002 Page 9 
TorayRO v 2.0.28 File: SW-WE-a1-4-06-06-05.tro 06 Jun 2005 

Errors & Warnings 

Warning - High LSI. LSI > zero. Concentrate CaCO3 greater than saturation. Scale inhibitor required. 

The feed water analysis was balanced with added Na or Cl. 

Database version used for design : 2.028 

WARRANTY DISCLAIMER. NO WARRANTIES ARE GIVEN IN CONNECTION WITH THIS SOFTWARE OR ITS USE. THIS SOFTWARE IS NOT WARRANTED 

FOR MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. This software is provided as an aid for the design of reverse osmosis systems 

incorporating membrane elements sold by Toray Industries, Inc., Toray Membrane America, Inc. and ROPUR AG. Such companies do not assume any 

responsibilities or liability in connection with this software or any results obtained or damages incurred in connection with its use. The user of the software shall be 

solely responsible for any designs created using the software and therefore should have the necessary technical skills and experience to design reverse osmosis 

systems. Although it is anticipated that system designs will be reviewed by application engineers of one of the companies mentioned above, such companies do not 

assume any responsibility or liability arising out of such review. Any warranty of systems or system designs will be provided only as expressly stated in a written 

document signed by an authorized representative of the company issuing the warranty. 

Toray Industries, Inc. Membrane Products Dept. TEL: (+81) 47-350-6030 

8-1, Mihama 1-chome, Urayasu, Chiba 279-8555, Japan Fax: (+81) 47-350-6066 

TORAY Membrane America, Inc. ROPUR AG 

USA, South America, Canada Europe, Middle East and Africa Tel: +41 (61) 415 87 10 

12520 High Bluff Drive, Suite 120 Tel: +1 (858) 523 0476 Grabenackerstrasse 8 

San Diego, CA 92130, USA Fax: +1 (858) 523 0861 CH-4142 Munchenstein 1, Switzerland Fax: +41 (61) 415 87 20 

Toray Incorporated © 2002 Page 10 
1 

TorayRO v 2.0.28 File: SW-WE-a3-3-06-08-05.tro 09 Jun 2005 

Project: SW-WE-a3 

Comments: 

Prepared For: 

Location: 

Prepared By: 

Date Prepared: 08 June 2005 

System Results 

Flow Rates Gal/min Concentrations mg/l 

RO Feed 2390 RO Feed TDS 35102 

Permeate 956 Permeate TDS 204 

Concentrate 1434 Concentrate TDS 58367 

Total Feed 2390 Total Feed TDS 35106 

Total Product 956 Total Product TDS 204 

System Details Single Stage Design 

Temperature: 77.0 Deg F Water Type: Seawater -well 

System Recovery: 40.0 % 

Pass 1 Units: Pressure - Psi Flow - Gal/min TDS - mg/l 

Array 1 Recovery: 40.0% Concentrate TDS: 58367 Concentrate Flow: 1434 

Total Total Element Feed Perm Feed Delta Perm 

Bank Vessels Elements Model Flow Flow Press Press TDS 

TM820- 52 364 2390 956 854 12.8 204 370 

Total 52 364 2390 956 204 

Concentration, Saturation and pH Data mg/l 

Ion Permeate Treated Feed Feed Concentrate 

Ca 0.76 408 408 679 

Mg 2.4 1298 1298 2162 

Na 72.7 10768 10768 17898 

K 2.96 388 388 645 

Ba 0.0 0.0 0.0 0.0 

Sr 0.0 0.0 0.0 0.0 

NH4 0.0 0.0 0.0 0.0 

Fe 0.0 0.0 0.0 0.0 

HCO3 1.17 120 143 200 

Cl 117 19380 19380 32221 

SO4 6.69 2723 2702 4534 

NO3 0.0 0.0 0.0 0.0 

F 0.0 0.0 0.0 0.0 

B 0.27 1.1 1.1 1.66 

SiO2 0.12 15.0 15.0 24.9 

Toray Incorporated © 2002 Page 1 
TorayRO v 2.0.28 File: SW-WE-a3-3-06-08-05.tro 09 Jun 2005 

Ion Permeate Treated Feed Feed Concentrate 

PO4 0.0008 0.5 0.5 0.83 

CO3 5.88E-06 0.19 2.29 0.62 

CO2 20.2 20.2 2.4 20.2 

TDS 204 35102 35106 58367 

pH 4.95 6.8 7.8 7.0 

Saturation Data (%) 

CaSO4 0.0017 21.6 21.5 41.4 

CaPO4 0.0 5.04 10000 9994 

CaF2 0.0 0.0 0.0 0.0 

BaSO4 0.0 0.0 0.0 0.0 

SiO2 0.0915 14.6 11.7 24.9 

SrSO4 0.0 0.0 0.0 0.0 

LSI -6.89 -0.36 0.72 0.47 

SDSI -6.49 -1.19 -0.11 -0.7 

Toray Incorporated © 2002 Page 2 
TorayRO v 2.0.28 File: SW-WE-a3-3-06-08-05.tro 09 Jun 2005 

System Summary 

System Configuration 

System Type: 

Feed Predosing?: Yes 

Feed Afterdosing?: No 

Interpass Dosing?: No 

Product Dosing?: No 

Feed CO2 Stripping?: No 

Interpass CO2 Stripping?: No 

Product CO2 Stripping?: No 

Raw Feed Bypass?: No 

First Pass Recycle?: No 

Interpass Pumping?: No 

Feed Information 

Water Type: Seawater -well 

Temperature, Deg F: 77.0 

Feed pH: 7.8 

Silt Density Index: 5.5

 Feed Ion Concentration (mg/l)

Ca 408

Mg 1298

Na 10768

K 388

Ba 0.0

Sr 0.0

NH4 0.0

Fe 0.0

HCO3 143

Cl 19380

SO4 2702

NO3 0.0

F 0.0

B 1.1

SiO2 15.0

PO4 0.5

CO3 2.29

CO2 2.4

System Flux, Flows and Recoveries 

Average System Flux: 10.2 Gal/ft2/day 

Feed Flow: 2,390.00 Gal/min 

Product Flow: 956.00 Gal/min 

Concentrate Flow: 1,434.00 Gal/min 

First Pass Recovery: 40.0 % 

System Recovery: 40.0 % 

Toray Incorporated © 2002 Page 3 
TorayRO v 2.0.28 File: SW-WE-a3-3-06-08-05.tro 09 Jun 2005 

First Pass Array 

Interbank Pressure Drop: 0.0 Psi 

Bank 1 Back Pressure: 15.0 Psi 

Number of Banks: 1 Total Elements: 364 

Bank # Vessels # Elements/Vessel Element Type Element Age 

1 52 7 TM820-370 3 

Chemical Treatment 

Station Chemical Target pH 

Feed Pre-Treat Sulfuric Acid 6.8 

Toray Incorporated © 2002 Page 4 
TorayRO v 2.0.28 File: SW-WE-a3-3-06-08-05.tro 09 Jun 2005 

Process Data 

Flow Units: Gal/min 

Pressure Units: psi 

Feed

 2390 

Concentrate

 1434 

Product

 956 

Net Feed

 2390 

40.0% 

System Recovery 

Flow Rates Gal/min Concentrations mg/l 

RO Feed 2390 RO Feed TDS 35102 

Permeate 956 Permeate TDS 204 

Concentrate 1434 Concentrate TDS 58367 

Total Feed 2390 Total Feed TDS 35106 

Total Product 956 Total Product TDS 204 

System Data Single Stage Design 

Temperature: 77.0 Deg F 

Stage 1 

Fouling Allowance 85.0 % 

Salt Passage Increase Per Year 10.0 % 

Feed Pressure 854 Psi 

Interbank Loss 0.0 Psi 

Element Age 3.0 Years 

Interbank Boost Pressure Stage 1 

Chemical Usage Chemical lb/day kg/day Target pH 

Feed Pre-Treat Sulfuric Acid 619 282 6.8 

40.0% 

Toray Incorporated © 2002 Page 5 
TorayRO v 2.0.28 File: SW-WE-a3-3-06-08-05.tro 09 Jun 2005 

Stream Data 

Units: Pressure - psi Flow - Gal/min TDS - mg/l Saturation - % 

System Predosed 1st Pass Total System 

Stream ---> Feed Feed Feed Permeate Product 

Ca 408 408 408 0.76 0.76 

Mg 1298 1298 1298 2.4 2.4 

Na 10768 10768 10768 72.7 72.7 

K 388 388 388 2.96 2.96 

Ba 0.0 0.0 0.0 0.0 0.0 

Sr 0.0 0.0 0.0 0.0 0.0 

NH4 0.0 0.0 0.0 0.0 0.0 

Fe 0.0 0.0 0.0 0.0 0.0 

HCO3 143 120 120 1.17 1.17 

Cl 19380 19380 19380 117 117 

SO4 2702 2723 2723 6.69 6.69 

NO3 0.0 0.0 0.0 0.0 0.0 

F 0.0 0.0 0.0 0.0 0.0 

B 1.1 1.1 1.1 0.27 0.27 

SiO2 15.0 15.0 15.0 0.12 0.12 

PO4 0.5 0.5 0.5 0.0008 0.0008 

CO3 2.29 0.19 0.19 5.88E-06 5.88E-06 

CO2 2.4 20.2 20.2 20.2 20.2 

TDS 35106 35102 35102 204 204 

pH 7.8 6.8 6.8 4.95 4.95 

LSI 0.72 -0.36 -0.36 -6.89 -6.89 

Stiff-Davis -0.11 -1.19 -1.19 -6.49 -6.49 

BaSO4 Sat 0.0 0.0 0.0 0.0 0.0 

CaSO4 Sat 21.5 21.6 21.6 0.0017 0.0017 

CaPO4 Sat 10000 5.04 5.04 0.0 0.0 

CaF2 Sat 0.0 0.0 0.0 0.0 0.0 

SrSO4 Sat 0.0 0.0 0.0 0.0 0.0 

SiO2 Sat 11.7 14.6 14.6 0.0915 0.0915 

Flow 2390 2390 2390 956 956 

Temp, Deg F 77.0 77.0 77.0 77.0 77.0 

Pressure 854 854 854 0.0 0.0 

Osm Pressure 368 368 368 2.41 2.41 

Toray Incorporated © 2002 Page 6 
TorayRO v 2.0.28 File: SW-WE-a3-3-06-08-05.tro 09 Jun 2005 

Units: Pressure - psi Flow - Gal/min 

System 

Stream ---> Concentrate 

Ca 679 

Mg 2162 

Na 17898 

K 645 

Ba 0.0 

Sr 0.0 

NH4 0.0 

Fe 0.0 

HCO3 200 

Cl 32221 

SO4 4534 

NO3 0.0 

F 0.0 

B 1.66 

SiO2 24.9 

PO4 0.83 

CO3 0.62 

CO2 20.2 

TDS 58367 

pH 7.0 

LSI 0.47 

Stiff-Davis -0.7 

BaSO4 Sat 0.0 

CaSO4 Sat 41.4 

CaPO4 Sat 9994 

CaF2 Sat 0.0 

SrSO4 Sat 0.0 

SiO2 Sat 24.9 

Flow 1434 

Temp, Deg F 77.0 

Pressure 841 

Osm Pressure 604 

TDS - mg/l Saturation - % 

Toray Incorporated © 2002 Page 7 
TorayRO v 2.0.28 File: SW-WE-a3-3-06-08-05.tro 09 Jun 2005 

Element Data 

Pass 1, Bank 1 Units: Pressure - psi, Flow - Gal/min, TDS - mg/l, Saturation - %, Flux - gal/ft2/day 

Bank Permeate Back Pressure: 15.0 

Elem 1 Elem 2 Elem 3 Elem 4 Elem 5 Elem 6 Elem 7 

Permeate Ions 

Ca 

Mg 

Na 

K 

Ba 

Sr 

NH4 

Fe 

HCO3 

Cl 

SO4 

NO3 

F 

B 

SiO2 

PO4 

CO3 

CO2 

TDS 

pH 

LSI 

Stiff-Davis 

Conc Saturation 

BaSO4 Sat 

CaSO4 Sat 

CaF2 Sat 

SrSO4 Sat 

SiO2 Sat 

Flow 

Feed 

Permeate 

Pressure 

Feed 

Net Driving 

Pressure Drop 

Feed Osmotic 

Other Parameters 

% Recovery 

B Conc Pol 

A Value 

B Value 

Flux 

0.45 

1.42 

42.9 

1.75 

0.0 

0.0 

0.0 

0.0 

0.69 

69.1 

3.94 

0.0 

0.0 

0.18 

0.0715 

0.0005 

1.97E-06 

20.2 

120 

4.73 

-9.16 

-7.16 

0.0 

23.9 

0.0 

0.0 

15.8 

46.0 

3.53 

854 

419 

2.39 

368 

7.68 

1.1 

2.32E-09 

2.12E-08 

13.8 

0.52 

1.66 

50.2 

2.04 

0.0 

0.0 

0.0 

0.0 

0.81 

80.9 

4.62 

0.0 

0.0 

0.2 

0.084 

0.0006 

2.73E-06 

20.2 

141 

4.8 

-9.03 

-6.96 

0.0 

26.4 

0.0 

0.0 

17.2 

42.4 

3.24 

852 

385 

2.16 

397 

7.64 

1.1 

2.33E-09 

2.12E-08 

12.6 

0.62 

1.96 

59.4 

2.42 

0.0 

0.0 

0.0 

0.0 

0.96 

95.7 

5.46 

0.0 

0.0 

0.23 

0.0996 

0.0007 

3.87E-06 

20.2 

167 

4.87 

-7.78 

-6.75 

0.0 

29.1 

0.0 

0.0 

18.7 

39.2 

2.94 

850 

349 

1.96 

429 

7.51 

1.09 

2.34E-09 

2.11E-08 

11.5 

0.74 

2.35 

71.0 

2.89 

0.0 

0.0 

0.0 

0.0 

1.15 

114 

6.53 

0.0 

0.0 

0.27 

0.12 

0.0008 

5.60E-06 

20.2 

199 

4.94 

-6.96 

-6.52 

0.0 

32.0 

0.0 

0.0 

20.2 

36.2 

2.63 

848 

313 

1.78 

463 

7.27 

1.09 

2.34E-09 

2.10E-08 

10.3 

0.91 

2.9 

87.8 

3.57 

0.0 

0.0 

0.0 

0.0 

1.42 

142 

8.09 

0.0 

0.0 

0.31 

0.14 

0.001 

8.73E-06 

20.2 

247 

5.03 

-6.49 

-6.25 

0.0 

35.1 

0.0 

0.0 

21.8 

33.6 

2.32 

846 

276 

1.62 

498 

6.91 

1.08 

2.34E-09 

2.15E-08 

9.06 

1.14 

3.63 

110 

4.46 

0.0 

0.0 

0.0 

0.0 

1.77 

177 

10.1 

0.0 

0.0 

0.37 

0.18 

0.0013 

1.39E-05 

20.2 

308 

5.13 

-6.12 

-5.97 

0.0 

38.3 

0.0 

0.0 

23.4 

31.3 

2.01 

844 

241 

1.49 

534 

6.41 

1.07 

2.32E-09 

2.18E-08 

7.82 

1.44 

4.59 

138 

5.63 

0.0 

0.0 

0.0 

0.0 

2.23 

223 

12.8 

0.0 

0.0 

0.43 

0.22 

0.0016 

2.27E-05 

20.2 

389 

5.22 

-5.78 

-5.68 

0.0 

41.4 

0.0 

0.0 

24.9 

29.3 

1.7 

843 

209 

1.38 

570 

5.82 

1.06 

2.29E-09 

2.22E-08 

6.64 

Toray Incorporated © 2002 Page 8 
TorayRO v 2.0.28 File: SW-WE-a3-3-06-08-05.tro 09 Jun 2005 

Errors & Warnings 

Warning - High LSI. LSI > zero. Concentrate CaCO3 greater than saturation. Scale inhibitor required. 

The feed water analysis was balanced with added Na or Cl. 

Database version used for design : 2.028 

WARRANTY DISCLAIMER. NO WARRANTIES ARE GIVEN IN CONNECTION WITH THIS SOFTWARE OR ITS USE. THIS SOFTWARE IS NOT WARRANTED 

FOR MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. This software is provided as an aid for the design of reverse osmosis systems 

incorporating membrane elements sold by Toray Industries, Inc., Toray Membrane America, Inc. and ROPUR AG. Such companies do not assume any 

responsibilities or liability in connection with this software or any results obtained or damages incurred in connection with its use. The user of the software shall be 

solely responsible for any designs created using the software and therefore should have the necessary technical skills and experience to design reverse osmosis 

systems. Although it is anticipated that system designs will be reviewed by application engineers of one of the companies mentioned above, such companies do not 

assume any responsibility or liability arising out of such review. Any warranty of systems or system designs will be provided only as expressly stated in a written 

document signed by an authorized representative of the company issuing the warranty. 

Toray Industries, Inc. Membrane Products Dept. TEL: (+81) 47-350-6030 

8-1, Mihama 1-chome, Urayasu, Chiba 279-8555, Japan Fax: (+81) 47-350-6066 

TORAY Membrane America, Inc. ROPUR AG 

USA, South America, Canada Europe, Middle East and Africa Tel: +41 (61) 415 87 10 

12520 High Bluff Drive, Suite 120 Tel: +1 (858) 523 0476 Grabenackerstrasse 8 

San Diego, CA 92130, USA Fax: +1 (858) 523 0861 CH-4142 Munchenstein 1, Switzerland Fax: +41 (61) 415 87 20 

Toray Incorporated © 2002 Page 9 
TorayRO v 2.0.28 File: BW-WE-a1-06-14-05.tro 15 Jun 2005 

Project: Starting Configuration BW 5000ppm TDS 

Comments: Feasible Configuration for Brackish Water with 5000 ppm TDS 

Prepared For: 

Location: 

Prepared By: Markus Forstmeier 

Date Prepared: 31 May 2005 

System Results 

Flow Rates Gal/min Concentrations mg/l 

RO Feed 3900 RO Feed TDS 4807 

Permeate 3198 Permeate TDS 132 

Concentrate 702 Concentrate TDS 26151 

Total Feed 3900 Total Feed TDS 5000 

Total Product 3198 Total Product TDS 132 

System Details Single Stage Design 

Temperature: 25.0 Deg C Water Type: Seawater -well 

System Recovery: 82.0 % 

Pass 1 Units: Pressure - Psi Flow - Gal/min TDS - mg/l 

Array 1 Recovery: 82.0% Concentrate TDS: 26151 Concentrate Flow: 702 

Total Total Element Feed Perm Feed Delta Perm 

Bank Vessels Elements Model Flow Flow Press Press TDS 

TM720- 1 82 574 3900 2686 268 9.98 74.9 370 

TM720- 2 39 273 1214 512 258 6.97 433 370 

Total 121 847 3900 3198 132 

Concentration, Saturation and pH Data mg/l 

Ion Permeate Treated Feed Feed Concentrate 

Ca 0.0 0.0 0.0 0.0 

Mg 0.0 0.0 0.0 0.0 

Na 36.9 1370 1370 7438 

K 0.0 0.0 0.0 0.0 

Ba 0.0 0.0 0.0 0.0 

Sr 0.0 0.0 0.0 0.0 

NH4 0.0 0.0 0.0 0.0 

Fe 0.0 0.0 0.0 0.0 

HCO3 89.3 3626 3626 14671 

Cl 0.0084 0.41 0.41 2.24 

SO4 6.12 0.0 0.0 3998 

NO3 0.0 0.0 0.0 0.0 

F 0.0 0.0 0.0 0.0 

B 0.0 0.0 0.0 0.0 

Toray Incorporated © 2002 Page 1 
TorayRO v 2.0.28 File: BW-WE-a1-06-14-05.tro 15 Jun 2005 

Ion Permeate Treated Feed Feed Concentrate 

SiO2 0.0 0.0 0.0 0.0 

PO4 0.0 0.0 0.0 0.0 

CO3 0.0006 3.61 3.61 41.7 

CO2 1141 486 486 1139 

TDS 132 4807 5000 26151 

pH 5.09 6.5 7.0 7.16 

Saturation Data (%) 

CaSO4 0.0 0.0 0.0 0.0 

CaPO4 0.0 0.0 0.0 0.0 

CaF2 0.0 0.0 0.0 0.0 

BaSO4 0.0 0.0 0.0 0.0 

SiO2 0.0 0.0 0.0 0.0 

SrSO4 0.0 0.0 0.0 0.0 

LSI -6.62 -3.8 -3.17 -2.44 

SDSI 0.0 0.0 0.0 0.0 

Toray Incorporated © 2002 Page 2 
TorayRO v 2.0.28 File: BW-WE-a1-06-14-05.tro 15 Jun 2005 

System Summary 

System Configuration 

System Type: 

Feed Predosing?: Yes 

Feed Afterdosing?: No 

Interpass Dosing?: No 

Product Dosing?: No 

Feed CO2 Stripping?: No 

Interpass CO2 Stripping?: No 

Product CO2 Stripping?: No 

Raw Feed Bypass?: No 

First Pass Recycle?: No 

Interpass Pumping?: No 

Feed Information 

Water Type: Seawater -well 

Temperature, Deg C: 25.0 

Feed pH: 7.0 

Silt Density Index: 5.5

 Feed Ion Concentration (mg/l)

Ca 0.0

Mg 0.0

Na 1370

K 0.0

Ba 0.0

Sr 0.0

NH4 0.0

Fe 0.0

HCO3 3626

Cl 0.41

SO4 0.0

NO3 0.0

F 0.0

B 0.0

SiO2 0.0

PO4 0.0

CO3 3.61

CO2 486

System Flux, Flows and Recoveries 

Average System Flux: 14.7 Gal/ft2/day 

Feed Flow: 3,900.00 Gal/min 

Product Flow: 3,198.00 Gal/min 

Concentrate Flow: 702.00 Gal/min 

First Pass Recovery: 82.0 % 

System Recovery: 82.0 % 

Toray Incorporated © 2002 Page 3 
TorayRO v 2.0.28 File: BW-WE-a1-06-14-05.tro 15 Jun 2005 

First Pass Array 

Interbank Pressure Drop: 

Interbank Pressure Boost 

Bank 1-2: 

Bank 1 Back Pressure: 

Bank 2 Back Pressure: 

Number of Banks: 2

Bank

0.0 Psi

0.0 Psi

15.0 Psi

15.0 Psi

Total Elements: 847

# Vessels # Elements/Vessel Element Type

1 82 7

2 39 7

Element Age

TM720-370 3

TM720-370 3

Chemical Treatment 

Station Chemical Target pH

Feed Pre-Treat Sulfuric Acid 6.5

Toray Incorporated © 2002 Page 4
TorayRO v 2.0.28 File: BW-WE-a1-06-14-05.tro 15 Jun 2005 

Process Data 

Flow Units: Gal/min 

Pressure Units: psi 

Feed

 3900 

Concentrate

 702 

Product

 3198 

Net Feed

 3900 

82.0% 

System Recovery 

Flow Rates Gal/min Concentrations mg/l 

RO Feed 3900 RO Feed TDS 4807 

Permeate 3198 Permeate TDS 132 

Concentrate 702 Concentrate TDS 26151 

Total Feed 3900 Total Feed TDS 5000 

Total Product 3198 Total Product TDS 132 

System Data Single Stage Design 

Temperature: 25.0 Deg C 

Stage 1 

Fouling Allowance 85.0 % 

Salt Passage Increase Per Year 10.0 % 

Feed Pressure 268 Psi 

Interbank Loss 0.0 Psi 

Element Age 3.0 Years 

Interbank Boost Pressure Stage 1 

Banks 1-2 0.0 Psi 

Chemical Usage Chemical lb/day kg/day Target pH 

Feed Pre-Treat Sulfuric Acid 34669 15759 6.5 

82.0% 

Toray Incorporated © 2002 Page 5 
TorayRO v 2.0.28 File: BW-WE-a1-06-14-05.tro 15 Jun 2005 

Stream Data 

Units: Pressure - psi Flow - Gal/min TDS - mg/l Saturation - % 

System 1st Pass Total System System 

Stream ---> Feed Feed Permeate Product Concentrate 

Ca 0.0 0.0 0.0 0.0 0.0 

Mg 0.0 0.0 0.0 0.0 0.0 

Na 1370 1370 36.9 36.9 7438 

K 0.0 0.0 0.0 0.0 0.0 

Ba 0.0 0.0 0.0 0.0 0.0 

Sr 0.0 0.0 0.0 0.0 0.0 

NH4 0.0 0.0 0.0 0.0 0.0 

Fe 0.0 0.0 0.0 0.0 0.0 

HCO3 3626 2711 89.3 89.3 14671 

Cl 0.41 0.41 0.0084 0.0084 2.24 

SO4 0.0 725 6.12 6.12 3998 

NO3 0.0 0.0 0.0 0.0 0.0 

F 0.0 0.0 0.0 0.0 0.0 

B 0.0 0.0 0.0 0.0 0.0 

SiO2 0.0 0.0 0.0 0.0 0.0 

PO4 0.0 0.0 0.0 0.0 0.0 

CO3 3.61 0.85 0.0006 0.0006 41.7 

CO2 486 1148 1141 1141 1139 

TDS 5000 4807 132 132 26151 

pH 7.0 6.5 5.09 5.09 7.16 

LSI -3.17 -3.8 -6.62 -6.62 -2.44 

Stiff-Davis 0.0 0.0 0.0 0.0 0.0 

BaSO4 Sat 0.0 0.0 0.0 0.0 0.0 

CaSO4 Sat 0.0 0.0 0.0 0.0 0.0 

CaPO4 Sat 0.0 0.0 0.0 0.0 0.0 

CaF2 Sat 0.0 0.0 0.0 0.0 0.0 

SrSO4 Sat 0.0 0.0 0.0 0.0 0.0 

SiO2 Sat 0.0 0.0 0.0 0.0 0.0 

Flow 3900 3900 3198 3198 702 

Temp, Deg C 25.0 25.0 25.0 25.0 25.0 

Pressure 268 268 0.0 0.0 251 

Osm Pressure 41.5 38.5 1.12 1.12 203 

Toray Incorporated © 2002 Page 6 
TorayRO v 2.0.28 File: BW-WE-a1-06-14-05.tro 15 Jun 2005 

Element Data 

Pass 1, Bank 1 Units: Pressure - psi, Flow - Gal/min, TDS - mg/l, Saturation - %, Flux - gal/ft2/day 

Bank Permeate Back Pressure: 15.0 

Elem 1 Elem 2 Elem 3 Elem 4 Elem 5 Elem 6 Elem 7 

Permeate Ions 

Ca 

Mg 

Na 

K 

Ba 

Sr 

NH4 

Fe 

HCO3 

Cl 

SO4 

NO3 

F 

B 

SiO2 

PO4 

CO3 

CO2 

TDS 

pH 

LSI 

Stiff-Davis 

Conc Saturation 

BaSO4 Sat 

CaSO4 Sat 

CaF2 Sat 

SrSO4 Sat 

SiO2 Sat 

Flow 

Feed 

Permeate 

Pressure 

Feed 

Net Driving 

Pressure Drop 

Feed Osmotic 

Other Parameters 

% Recovery 

B Conc Pol 

A Value 

B Value 

Flux 

0.0 

0.0 

9.42 

0.0 

0.0 

0.0 

0.0 

0.0 

22.5 

0.0021 

1.51 

0.0 

0.0 

0.0 

0.0 

0.0 

3.39E-05 

1141 

33.4 

4.5 

-7.83 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

47.6 

5.8 

268 

202 

2.51 

38.6 

12.2 

1.22 

7.74E-09 

4.76E-08 

22.6 

0.0 

0.0 

11.5 

0.0 

0.0 

0.0 

0.0 

0.0 

27.6 

0.0026 

1.85 

0.0 

0.0 

0.0 

0.0 

0.0 

5.12E-05 

1141 

40.9 

4.59 

-7.64 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

41.8 

5.52 

266 

193 

2.06 

43.8 

13.2 

1.23 

7.75E-09 

4.82E-08 

21.5 

0.0 

0.0 

14.4 

0.0 

0.0 

0.0 

0.0 

0.0 

34.6 

0.0032 

2.33 

0.0 

0.0 

0.0 

0.0 

0.0 

8.14E-05 

1141 

51.3 

4.69 

-7.44 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

36.2 

5.2 

264 

181 

1.67 

50.3 

14.4 

1.24 

7.75E-09 

4.90E-08 

20.3 

0.0 

0.0 

18.6 

0.0 

0.0 

0.0 

0.0 

0.0 

44.8 

0.0042 

3.02 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0001 

1141 

66.4 

4.8 

-7.21 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

31.0 

4.82 

262 

168 

1.32 

58.6 

15.5 

1.24 

7.76E-09 

4.98E-08 

18.8 

0.0 

0.0 

24.8 

0.0 

0.0 

0.0 

0.0 

0.0 

60.1 

0.0056 

4.06 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0003 

1141 

88.9 

4.92 

-6.96 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

26.2 

4.37 

261 

153 

1.03 

69.0 

16.7 

1.24 

7.76E-09 

5.08E-08 

17.0 

0.0 

0.0 

34.6 

0.0 

0.0 

0.0 

0.0 

0.0 

83.9 

0.0079 

5.69 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0005 

1141 

124 

5.07 

-6.67 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

21.8 

3.83 

260 

134 

0.79 

82.4 

17.5 

1.23 

7.76E-09 

5.20E-08 

14.9 

0.0 

0.0 

50.5 

0.0 

0.0 

0.0 

0.0 

0.0 

123 

0.0115 

8.34 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0011 

1141 

181 

5.23 

-6.35 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

18.0 

3.2 

259 

112 

0.6 

99.3 

17.8 

1.22 

7.76E-09 

5.33E-08 

12.5 

Toray Incorporated © 2002 Page 7 
TorayRO v 2.0.28 File: BW-WE-a1-06-14-05.tro 15 Jun 2005 

Pass 1, Bank 2 Units: Pressure - psi, Flow - Gal/min, TDS - mg/l, Saturation - %, Flux - gal/ft2/day 

Bank Permeate Back Pressure: 15.0 

Bank Boost Pressure: 0.0 

Elem 1 Elem 2 Elem 3 Elem 4 Elem 5 Elem 6 Elem 7 

Permeate Ions 

Ca 

Mg 

Na 

K 

Ba 

Sr 

NH4 

Fe 

HCO3 

Cl 

SO4 

NO3 

F 

B 

SiO2 

PO4 

CO3 

CO2 

TDS 

pH 

LSI 

Stiff-Davis 

Conc Saturation 

BaSO4 Sat 

CaSO4 Sat 

CaF2 Sat 

SrSO4 Sat 

SiO2 Sat 

Flow 

Feed 

Permeate 

Pressure 

Feed 

Net Driving 

Pressure Drop 

Feed Osmotic 

Other Parameters 

% Recovery 

B Conc Pol 

A Value 

B Value 

Flux 

0.0 

0.0 

61.1 

0.0 

0.0 

0.0 

0.0 

0.0 

148 

0.014 

10.1 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0016 

1141 

220 

5.31 

-6.18 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

31.1 

2.91 

258 

102 

1.4 

120 

9.34 

1.14 

7.77E-09 

5.47E-08 

11.3 

0.0 

0.0 

77.0 

0.0 

0.0 

0.0 

0.0 

0.0 

187 

0.0177 

12.8 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0026 

1140 

277 

5.41 

-5.99 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

28.2 

2.53 

257 

88.7 

1.22 

132 

8.96 

1.12 

7.77E-09 

5.53E-08 

9.87 

0.0 

0.0 

98.0 

0.0 

0.0 

0.0 

0.0 

0.0 

238 

0.0225 

16.4 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0044 

1140 

352 

5.51 

-5.78 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

25.7 

2.16 

256 

75.9 

1.07 

144 

8.42 

1.11 

7.77E-09 

5.58E-08 

8.43 

0.0 

0.0 

126 

0.0 

0.0 

0.0 

0.0 

0.0 

305 

0.0289 

21.1 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0074 

1140 

452 

5.61 

-5.58 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

23.5 

1.82 

255 

63.8 

0.95 

157 

7.72 

1.1 

7.77E-09 

5.63E-08 

7.09 

0.0 

0.0 

162 

0.0 

0.0 

0.0 

0.0 

0.0 

394 

0.0375 

27.4 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0126 

1140 

583 

5.72 

-5.36 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

21.7 

1.5 

254 

52.8 

0.85 

170 

6.92 

1.09 

7.78E-09 

5.67E-08 

5.86 

0.0 

0.0 

210 

0.0 

0.0 

0.0 

0.0 

0.0 

510 

0.0487 

35.7 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0218 

1140 

755 

5.83 

-5.15 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

20.2 

1.22 

253 

43.1 

0.77 

182 

6.06 

1.07 

7.78E-09 

5.71E-08 

4.77 

0.0 

0.0 

272 

0.0 

0.0 

0.0 

0.0 

0.0 

660 

0.0633 

46.7 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0379 

1140 

979 

5.93 

-4.93 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

19.0 

0.99 

252 

34.8 

0.71 

193 

5.2 

1.06 

7.78E-09 

5.74E-08 

3.85 

Toray Incorporated © 2002 Page 8 
TorayRO v 2.0.28 File: BW-WE-a1-06-14-05.tro 15 Jun 2005 

Errors & Warnings 

The feed water analysis was balanced with added Na or Cl. 

Database version used for design : 2.028 

WARRANTY DISCLAIMER. NO WARRANTIES ARE GIVEN IN CONNECTION WITH THIS SOFTWARE OR ITS USE. THIS SOFTWARE IS NOT WARRANTED 

FOR MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. This software is provided as an aid for the design of reverse osmosis systems 

incorporating membrane elements sold by Toray Industries, Inc., Toray Membrane America, Inc. and ROPUR AG. Such companies do not assume any 

responsibilities or liability in connection with this software or any results obtained or damages incurred in connection with its use. The user of the software shall be 

solely responsible for any designs created using the software and therefore should have the necessary technical skills and experience to design reverse osmosis 

systems. Although it is anticipated that system designs will be reviewed by application engineers of one of the companies mentioned above, such companies do not 

assume any responsibility or liability arising out of such review. Any warranty of systems or system designs will be provided only as expressly stated in a written 

document signed by an authorized representative of the company issuing the warranty. 

Toray Industries, Inc. Membrane Products Dept. TEL: (+81) 47-350-6030 

8-1, Mihama 1-chome, Urayasu, Chiba 279-8555, Japan Fax: (+81) 47-350-6066 

TORAY Membrane America, Inc. ROPUR AG 

USA, South America, Canada Europe, Middle East and Africa Tel: +41 (61) 415 87 10 

12520 High Bluff Drive, Suite 120 Tel: +1 (858) 523 0476 Grabenackerstrasse 8 

San Diego, CA 92130, USA Fax: +1 (858) 523 0861 CH-4142 Munchenstein 1, Switzerland Fax: +41 (61) 415 87 20 

Toray Incorporated © 2002 Page 9 
TM800


Type Diameter Membrane Area Salt Rejection Product Flow Rate 

inch ft2 (m2) % gpd (m3/d) 

TM820-370 8" 370 (34) 99.75 6,000 (23) 

TM820-400 8" 400 (37) 99.75 6,500 (25) 

1. Membrane Type Cross Linked Fully Aromatic Polyamide Composite 

2. Test Conditions 

Feed Water Pressure 

Feed Water Temperature 

Feed Water Concentration 

Recovery Rate 

Feed Water pH 

800 psi (5.52 MPa) 

77  ̊F (25  ̊C) 

32,000 mg/l NaCl 

8% 

7 

3. Minimum Salt Rejection 99.5 % 

4. Minimum Product Flow Rate 4,800 gpd ( 18 m3/d) (TM820-370) 

5,200 gpd ( 20 m3/d) (TM820-400) 

Dimensions 

All dimensions shown in inches (millimeter). 

Feed Water 

Concentrated Brine 

Flow direction 

TM820-370 

TM820-400 

40 (1016) 

1.125 (29)

7.9 (201) 

TM800 
Maximum Operating Pressure 1000 psi (6.9 MPa) 

Maximum Feed Water Temperature 113  ̊F (45  ̊C) 

Maximum Feed Water SDI15 5 

Feed Water Chlorine Concentration Not Detectable 

Feed Water pH Range, Continuous Operation 2-11 

Feed Water pH Range, Chemical Cleaning 1-12 

Maximum Pressure Drop per Element 20 psi (0.14 MPa) 

Maximum Pressure Drop per Vessel 60 psi (0.4 MPa) 

Operating Information

1.	 For the recommended design range, please consult the latest Toray technical bulletin, de

guidelines, computer design program, and/or call an application specialist. If the opera

limits given in this Product Information Bulletin are not strictly followed, the Limited Warranty 

be null and void. 

2.	 All elements are wet tested, treated with a 1% by weight percent sodium bisulfite storage solut

and then vacuum packed in oxygen barrier bags. To prevent biological growth during s

term storage, shipment, or system shutdown, it is recommended that Toray elements be imme

in a protective solution containing 500 - 1,000 ppm of sodium bisulfite (food grade) dissolve

permeate. 

3.	 Permeate from the first hour of operation shall be discarded. 

4.	 The customer is fully responsible for the effects of chemicals that are incompatible with 

elements. Their use will void the element Limited Warranty. 

Notice 

1.	 Toray accepts no responsibility for results obtained by the application of this information or 

safety or suitability of Toray's products, either alone or in combination with other products. U

are advised to make their own tests to determine the safety and suitability of each pro

combination for their own purposes. 

2.	 All data may change without prior notice, due to technical modifications or production changes. 

Asia and Oceania: 

Toray Industries, Inc. 

Membrane Products Department 

8-1, Mihama 1-chome 

Urayasu, Chiba 279-8555, Japan 

Te l : +81 47 350 6030 

Fax: +81 47 350 6066 

http://www.toray-membrane.com 

Americas: 

Toray Membrane America, Inc. 

Sales Office 

12520 High Bluff Drive, Suite 120 

San Diego, CA 92130, U.S.A. 

Te l : +1 858 523 0476 

Fax: +1 858 523 0861 

Europe, Middle East and Afri

Toray Membrane Europe A

Grabenackerstrasse 8 

CH-4142 Münchenstein 1, Switzerla

Te l : +41 61 415 87 10 

Fax: +41 61 415 87 20 

TM800 
TM700


Type Diameter Membrane Area Salt Rejection Product Flow Rate 

inch ft2 (m2) % gpd (m3/d) 

TM710 4" 87 (8) 99.7 2,400 (9.1) 

TM720-370 8" 370 (34) 99.7 9,500 (36) 

TM720-400 8" 400 (37) 99.7 10,200 (39) 

TM720-430 8" 430 (40) 99.7 11,000 (42) 

1. Membrane Type Cross Linked Fully Aromatic Polyamide Composite 

2. Test Conditions 

Feed Water Pressure 

Feed Water Temperature 

Feed Water Concentration 

Recovery Rate 

Feed Water pH 

225 psi (1.55 MPa) 

77  ̊F (25  ̊C) 

2,000 mg/l NaCl 

15 % 

7 

3. Minimum Salt Rejection 99.0 % 

4. Minimum Product Flow Rate 2,000 gpd (7.6 m3/d) (TM710) 

7,500 gpd ( 28 m3/d) (TM720-370) 

8,200 gpd ( 31 m3/d) (TM720-400) 

8,800 gpd ( 33 m3/d) (TM720-430) 

Dimensions 

All dimensions shown in inches (millimeter). 

Feed Water 

Concentrated Brin

TM710 

Flow direction 

Flow direction 

40 (1016) 

40 (1016) 

0.75 (19)

4 (101) 

1.05 (26) 

1.125 (29)

7.9 (201)

TM720-370 

TM720-400 

TM720-430 
Maximum Operating Pressure 600 psi (4.1 MPa) 

Maximum Feed Water Temperature 113  ̊F (45  ̊C) 

Maximum Feed Water SDI15 5 

Feed Water Chlorine Concentration Not Detectable 

Feed Water pH Range, Continuous Operation 2-11 

Feed Water pH Range, Chemical Cleaning 1-12 

Maximum Pressure Drop per Element 20 psi (0.14 MPa) 

Maximum Pressure Drop per Vessel 60 psi (0.4 MPa) 

Operating Information

1.	 For the recommended design range, please consult the latest Toray technical bulletin, de

guidelines, computer design program, and/or call an application specialist. If the opera

limits given in this Product Information Bulletin are not strictly followed, the Limited Warranty 

be null and void. 

2.	 All elements are wet tested, treated with a 1% by weight percent sodium bisulfite storage solut

and then vacuum packed in oxygen barrier bags. To prevent biological growth during s

term storage, shipment, or system shutdown, it is recommended that Toray elements be imme

in a protective solution containing 500 - 1,000 ppm of sodium bisulfite (food grade) dissolve

permeate. 

3.	 Permeate from the first hour of operation shall be discarded. 

4.	 The customer is fully responsible for the effects of chemicals that are incompatible with 

elements. Their use will void the element Limited Warranty. 

Notice 

1.	 Toray accepts no responsibility for results obtained by the application of this information or 

safety or suitability of Toray's products, either alone or in combination with other products. U

are advised to make their own tests to determine the safety and suitability of each pro

combination for their own purposes. 

2.	 All data may change without prior notice, due to technical modifications or production changes. 

Asia and Oceania: 

Toray Industries, Inc. 

Membrane Products Department 

8-1, Mihama 1-chome 

Urayasu, Chiba 279-8555, Japan 

Te l : +81 47 350 6030 

Fax: +81 47 350 6066 

http://www.toray-membrane.com 

Americas: 

Toray Membrane America, Inc. 

Sales Office 

12520 High Bluff Drive, Suite 120 

San Diego, CA 92130, U.S.A. 

Te l : +1 858 523 0476 

Fax: +1 858 523 0861 

Europe, Middle East and Afri

Toray Membrane Europe A

Grabenackerstrasse 8 

CH-4142 Münchenstein 1, Switzerla

Te l : +41 61 415 87 10 

Fax: +41 61 415 87 20 
F1146-E(12/2004) 

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1. REPORT DATE (DD-MM-YYYY)

October 2006 

2. REPORT TYPE

Subcontract report 

3. DATES COVERED (From - To)

10/11/2004 - 7/29/2005 

5a. CONTRACT NUMBER

DE-AC36-99-GO10337 

5b. GRANT NUMBER

4. TITLE AND SUBTITLE

Integrated Wind Energy/Desalination System 

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

NREL/SR-500-39485 

5e. TASK NUMBER

WER6.7502 

6. AUTHOR(S)

GE Global Research 

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GE Gobal Research 

Niskayuna, New York 

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REPORT NUMBER

YAM-4-33200-09 

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13. SUPPLEMENTARY NOTES

NREL Technical Monitor: Scott Schreck 

14. ABSTRACT (Maximum 200 Words)

This study investigates the feasibility of multiple concepts for integrating wind turbines and reverse osmosis 

desalination systems for water purification. 

15. SUBJECT TERMS

wind energy; water purification; desalination 

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