Abstract:
The invention relates to a method and apparatus that shares the cost and areal footprint of the barge floatation platform for a floating power platform (FPP) with the cost and aerial footprint of the high pressure vessels of the compressed air energy storage (CAES) system. The integration of these two systems provides cost savings and energy consumption savings with potential for desalination.

Description:
RELATED PATENT AND PENDING PATENTS 
       [0001]    Enis B. and Lieberman P., TITLE: “Method and Apparatus for Using Wind Energy or Solar Energy for an Underwater and/or for an Under Seabed Compressed Air Energy Storage System” 
         [0002]    1. Application Ser. No. 13/610,440, ISSUE DATE Sep. 11, 2012 
         [0003]    Enis B. and Lieberman P., TITLE: “Wind Turbine Station and Tower with Vertical Storage Tanks” 
         [0004]    1. U.S. PROVISIONAL PATENT APPLICATION—PENDING 
         [0005]    Enis B. and Lieberman P., TITLE: “Method and Apparatus for Using Wind Turbines to Generate and Supply Uninterrupted Power to Locations Remote from the Power Grid” 
         [0006]    1. U.S. Pat. No. 6,927,503, ISSUE DATE: Aug. 9, 2005 
         [0007]    2. U.S. Pat. No. 7,067,937, ISSUE DATE Jun. 27, 2006 
         [0008]    3. U.S. Pat. No. 7,250,691, ISSUE DATE Jul. 31, 2007 
         [0009]    Enis B. and Lieberman P., TITLE: “A Method of Coordinating and Stabilizing the Delivery of Wind Generated Energy” 
         [0010]    1. U.S. Pat. No. 6,963,802, ISSUE DATE: Nov. 8, 2005 
         [0011]    2. U.S. Pat. No. 7,308,361 B2, ISSUE DATE: Dec. 11, 2007 
         [0012]    Enis B. and Lieberman P., TITLE: “A Method and Apparatus for Storing and Using Energy to Reduce the End-User Cost of Energy” 
         [0013]    1. U.S. Pat. No. 7,155,912 
         [0014]    Enis B. and Lieberman P., TITLE: “Method of Transporting and Storing Wind Generated Energy Using a Pipeline” 
         [0015]    1. U.S. patent Ser. No. 11/700,503, ISSUE DATE: Jan. 31, 2007 
         [0016]    2. U.S. Pat. No. 7,504,739 B2. ISSUE DATE: Mar. 17, 2009 
         [0017]    Enis B. and Lieberman P., TITLE: “Desalination Method and System Using Compressed Air Energy Systems.” 
         [0018]    1. U.S. patent application—PENDING 
         [0019]    Enis B. and Lieberman P., TITLE: “Desalination Method and System Using a Continuous Helical Slush Removal System 
         [0020]    1. U.S. patent application—PENDING 
         [0021]    Enis B. and Lieberman P., TITLE: “The Use of the Compressor-Turbocompressor-Turboexpander (CTT) Device to Increase the Efficiency of a Gas Turbine, Steam Turbine and Electricity Generator Set” 
         [0022]    1, U.S. PROVISIONAL PATENT APPLICATION—PENDING 
         [0023]    Enis B. and Lieberman P., TITLE: “Method and Apparatus for Using Solar Energy to Enhance the Operation of a Compressed Air Energy Storage System” 
         [0024]    1. U.S. PROVISIONAL PATENT APPLICATION—PENDING
       61/062,149, filed on Jan. 24, 2008   61/068,170, filed on Mar. 5, 2008,   61/195,418, filed on Oct. 7, 2008       
 
         [0028]    2. U.S. patent application
       Ser. No. 12/321,689 filed: Jan. 26, 2009       
 
         [0030]    Enis B. and Lieberman P., TITLE: “Enhanced Operation of Gas-Driven and Steam-Driven Generator Sets by Coupling with Output of T-CAES System” 
         [0031]    1. U.S. PROVISIONAL PATENT APPLICATION—PENDING 
         [0032]    Enis B. and Lieberman P., TITLE: “Method and Apparatus for Using Compressed Air to Increase the Efficiency of a Fuel Driven Turbine Generator.” 
         [0033]    1. U.S. Provisional Application Ser. No. 61/195,418 
     
    
     BACKGROUND OF THE INVENTION 
     Floating Power Plant (FPP) 
       [0034]    In the early 2000s, the capacity of the floating power plant (FPP) was pushed to a much higher level with the design and construction of a 220 MW combined cycle power barge that was installed in India. This barge used aero-derivative gas turbine technology with heat recovery, inlet air chilling and a steam turbine generator producing a highly efficient plant that initially used naphtha as a fuel. Herein, we intend to use the similar type gas turbine generator set but with a much higher intensity of inlet air cooling. 
         [0035]    Floating power barge designs are now charting new territory with projects on the boards with capacities up to 550 MW using technologies that include combined cycle with industrial and aero-derivative gas turbines and Integrated Gasification combined cycle (IGCC) schemes. Greater consideration is also being given to emissions and different fuels, particularly as the cost of oil increases to higher levels. LNG, CNG and coal fueled projects are now being considered for installation on FPPs. 
         [0036]    The FPP is not designed to sit in waters that are aggravated by waves. The FPP is not made to sail like a vessel at sea but rather it is designed for service in protected inland waters such as rivers, lagoons, or ports. 
         [0037]    One of the more significant differences of a floating power plant to a land based plant is its transportability being capable of moving the unit from one location to another. This is achieved with the use of submersible heavy lift ships, designed to move very large structures around the world weighing upwards of 60,000 tons. 
         [0038]    A total of about four self-propelled power ships are currently deployed around the world, while there are over 75 power barges worldwide, including over 600 MW of generation capacity in New York City. Power barges can be built very quickly in comparison to a power ship or a land based plant. A 100 MW gas turbine power barge can be built in about 3 months and be ready for deployment.[citation 
         [0039]    The following is a list of the special advantages available from the floating power plant (or power barge or power ship):
       A floating power plant can be moved from one location to another in a matter of weeks and connected to the grid to alleviate local shortages   Simple and straight forward location of power station where power is required   Fast supply of electricity to areas with limited infrastructure   Installation possible in areas with poor logistic infrastructure   Independent from soil quality   Provides additional safety in earth quake and flooding areas   Where land space is limited, large site area not needed   Mobile asset for the owner, possibility to trade   Constructed in shipyards under controlled conditions   Minimal environmental impact as only a small area of coastal or up-river land is required.   Relatively fast construction dependent upon equipment availability   Short building times: for example 70 MW power station can be installed in less than 12 months.   Can utilize any electrical generating technologies   Transportable power; large capacity can be moved to areas of need quickly   Fuels can be supplied by ocean transport and stored in adjacent barges   Financially viable asset for installation in developing countries   Floating power stations can take advantage of financing incentives from shipbuilding regions   Minimum operator&#39;s investment risk due to the mobility, versatility and adaptability of this type of plant.   Supports rapid infrastructure development in remote regions   Independence from local infrastructure   Reduced reliance on poor or nonexistent local capabilities.   Unaffected by landslides and earthquakes.   The floating power station is supplied with surrounding water heat exchange (especially useful for the compressed air energy storage system pressure vessel operation       
 
       Transportable Compressed Air Energy Storage (T-CAES) System 
       [0063]    The conventional compressed air energy storage (CAES) systems have used inexpensive night time commercial power, air compressors, and an underground cavern as a pressure vessel for energy storage. During the daytime when the electricity power rates and energy rates are more expensive fuel and the compressed air from the cavern are combined in combustion driven electric generator set that results in a cost savings. 
         [0064]    More recent designs have taken suggested the use of wind turbine farms and/or solar farms to supply the excess (not immediately used by the local grid) electrical power from these green power sources to drive the compressors whenever the excess power is available. In all cases combustion is used to drive the generator set. 
         [0065]    The key cost savings feature of the underground cavern pressure vessel storage is the availability of existing deep underground caverns or initial deep underground caverns that can be enlarged by inexpensive mining . . . especially in the case of salt caverns. On the other hand, after locating a site and expending funds and times the cavern may reveal itself to be flawed as in the case of the CAES system intended for Iowa. Furthermore, not every naturally occurring cavern is located near a city that requires its use or located near a high wind zone. 
         [0066]    The authors (Dr. Ben Enis and Dr. Paul Lieberman) have introduced a variation of the CAES system wherein the pressure vessel is a (1) Thick walled steel storage tank, (2) Miles-long thick steel walled pipeline, (3) Underwater reinforced concrete series of storage tanks with metal output pipes or a (4) Thick walled vertical mast of a tall wind turbine. The objective of the CAES system was to not only store the input energy as high pressure air but also for the thick walled steel pressure vessel to release its heat content when the internal air pressure drops when the compressed air is continuously discharged to the turboexpander that powers the electric generator set. No combustion is used to drive the turboexpander/generator set. 
         [0067]    The net result is that the green energy sources such as wind and solar photovoltaic energies are used to produce electricity without combustion. There are no greenhouse gases emitted. The lack of combustion also provides more than 50 year lifetime because high temperature and corrosion atmospheres are eliminated in the electricity generating equipment. 
         [0068]    Another result is that for every 1 MW of electricity produced there is 1 MW of thermal energy produced. The thermal energy exists in the form of a high mass flow of super-chilled air (−170° F. to −180° F.) are exhausted from the turboexpander expansion impeller. 
         [0069]    In June 2004, a 75 kWe version of the Enis/Lieberman Compressed Air Energy Storage System (CAES) was tested at National Technical Systems in Santa Clarita, Calif. The CAES system was comprised of a compressor, piping system, high pressure storage vessels and a turboexpander/generator set ( FIG. 1 ). General Electric supplied the turboexpander/generator set and S2M of St. Marcel, France supplied the special high speed (28,000 RPM) bearing. S2M is the world&#39;s biggest producer of magnetic bearings. The control system, sensors, instrumentation and recorders were set to display the generation of 75 kW of electrical power and 75 kW of thermal power. The thermal power was the high mass flow of super-chilled (−175° F.) air. Hot water was collected from the (1) Inter-stage condensation of the air compressor (2) Coolant water of the compressor and (3) Coolant water of the electricity generator. 
         [0070]    The California Energy Commission sponsored Dr. Paul Lieberman for a series of heat transfer tests that provided the design data required to specify the pressure vessel diameter and pressure vessel steel wall thickness to assure that the expulsion of the compressed air does not produce an excessive pressure drop in the expanding air being released from the pressure vessel. The heat release from the room temperature walls of the thick walled pressure vessel had to be sufficiently rapid to compete with the temperature drop in the expanding air for a specified expulsion rate of air. 
         [0071]    The advantage of the Enis/Lieberman CAES system is that it is not limited by geography or geology in its choice of location as is the case of the underground cavern CAES systems. 
         [0072]    As mentioned earlier, the impressive cost savings for the underground cavern version of the CAES system is the availability of the nearly pre-existing pressure vessel . . . the deep underground cavern. This cost savings becomes available to the Enis/Lieberman version of the CAES system in the scenario of the floating power plant where the thick walled steel pressure vessels become the required strong back of the floating platform and also supply the required buoyancy force. Thus integration of the Enis/Lieberman pressure vessels with the barge structure places the Enis/Lieberman CAES system as price competitive and brings along the transportable asset not available to fixed deep underground caverns. 
         [0073]    There is also the availability of the surrounding seawater or surrounding sweet-water in contact with the steel pressure vessel that is strongly useful for efficient operation of the thermal heat exchange process that occurs between the steel walls and the expanding air exhausting from the storage tanks to provide a near uniform air temperature delivery to the turboexpander in the turboexpander/generator set. 
         [0074]    The conventional safety factor for pressure vessels of a factor of 4.0 for above ground tanks in the areas where there are personnel in the area may be reduced when the pressure vessel is (1) Under water and (2) Away from personnel that will not potentially experience air blast or high speed flying steel fragments. This is another important cost savings factor. 
       Enhanced Performance of Turbocompressor-Driven Generator Sets 
       [0075]    The basic theory of inlet air cooling for gas turbines is simple enough. Combustion Turbines (CT) are constant volume machines—at a given shaft speed they always move the same volume of air—but the power output of a turbine depends on the flow of mass through it. That&#39;s why on hot days, when air is less dense, power output falls off. By feeding cooler air into the CT, mass flow is increased, resulting in higher output. 
         [0076]    Another factor is the power consumed by the CT&#39;s compressor. About ⅔ of the combustion energy is used by the CT and the remaining ⅓ of the combustion energy is used to generate electricity. The work required to compress air is directly proportional to the temperature of the air, so reducing the inlet air temperature reduces the work of compression and there is more work available at the turbine output shaft. 
         [0077]    Many technologies are commercially available for Turbine Inlet Cooling (TIC). These Technologies can be divided into the following major categories or groups:
       Evaporative: wetted media, fogging, and wet compression/overspray   Refrigeration: mechanical and absorption chillers without or with thermal energy storage (TES)   Special Application Technologies i.e., re-vaporization of liquefied natural gas (LNG)   Hybrid Systems: a mix of mechanical and absorption chillers       
 
         [0082]    The above systems typically reduce the intake air temperature to no less than 44° F. to avoid icing in the turbo-compressor blades first stage of compression. All technologies listed above have advantages and disadvantages. We move the +59° F. and +44° F. to −22° F. for enhanced performance. 
         [0083]    Many published articles are available on these technologies. Many Combustion Turbine (CT) plants across the U.S. and around the world are using various TIC technologies that improve their performance and economics. A database of some of these installations is available in the Experience Database section of the Turbine Inlet Cooling Association website. 
         [0084]    The super-chilled air from the Compander, T-CAES system, TL-CAES system or UW-CAES underwater system fed to the Turbo-compresor will use 30% less natural to produce the same amount of electricity. 
         [0085]    There is a strong enhanced performance of turbocompressor-driven generator sets introduced by reducing the turbo compressor input air temperature from +100° F. to +59° F. or to +44° F. as is done for many generator sets. In the patent disclosure herein it is proposed to further reduce the air intake temperature to −22° F. Many of the commercial Gensets are already tested at −25° F. for use in arctic regions. 
         [0086]    The Turbo Compressor Generator (TCG) Set consumes 30% less natural gas to generate the same electricity when it is operated at the proposed −22° F. rather than at the typical power plant enclosure at +100° F. The cold dense air will combust with the natural gas and allocate more energy to the production of electricity and less energy to drive the turbine. The current state of the art for many facilities is to cool the Turbo Compressor intake air from +100° F. down to +59° F. and sometimes down to +44° F. using water. This lowering of inlet air temperature reduces the consumption of natural gas. LRA proposes to drop the intake temperature down to −22° F. where the Turbo Compressor is already designed for arctic operation at −25° F. and to thereby save use of natural gas in hot and temperate climates. 
         [0087]    The acceptance of −22° F. intake air by a combustion turbine driven Generator Set has been demonstrated by the Caterpillar Company, Solar Turbine Model MARS 100 (˜11 MW) system. 
         [0088]    Military standard MIL-STD-810 standard describes environmental management and engineering processes that is of enormous value to generate confidence in the environmental worthiness and overall durability of a system design. Mil-Std-810 G, Method 502.5, entitled, Low Temperature Testing: Environmental Engineering Considerations and Laboratory tests, Part One Annex C, Table C-I, “Summary of Climatic Conditions and Daily Cycles of Temperature, Solar radiation, and Relative humidity” specifies that the military requires −25° F. for vendors to qualify for arctic “cold” environments. 
         [0089]    Thus the system presented herein places no additional mechanical stresses on Genset hardware. The MARS 100, Titan 130 and Centaur 40 and other Gensets have already been tested for their guaranteed performance during their Mil-Std-810 G, Method 502.5 Low Temperature Testing. 
         [0090]    Note that typical power plant facility buildings are often at 100° F. even though the outside ambient temperature is 70° F. Baldor Generators, 3815 Oregon Street, Oshkosh, Wis. 54902 recommends that when evaluating performance of their Gensets assume room ambient of 100° F. This conforms to my personal experience when I toured the power plant facility at University of California, San Diego campus. The comfortable 65° F. ambient temperature at that seaside location still resulted in my sweating in an indoor environment of the order of 100° F. The HVAC and generator coolant system were not effective in handling the waste heat output from the more than 28,000 kWe turbo generators. 
       Eutectic Freeze Crystallization Via the T-CAES System for Desalination. 
       [0091]    With fresh water becoming more and more in demand, the use of desalination systems become more attractive. For example, for San Clemente Island it costs almost as much to deliver water by barge to the island as it does to deliver the fuel to power the island. Eutectic Feed Crystallization (EFC) is more robust than the typical reverse osmosis desalination technique when there are severe pollutants in the water. Eutectic Freeze Crystallization has been developed for purifying not only saltwater but water runoff from pig farms and from waste water drained from radioactive piles. The Dutch (NIRO) has pioneered the basic parameters of the process and Canadian researchers have applied EFC purification to severely polluted drain water. 
         [0092]    The Dutch NIRO company has perfected a EFC process using refrigeration systems, refrigeration coils and scrapers. Their refrigeration temperatures are relatively warm (just below the freezing point of salt water) and when compared to the −170° F. to −180° F. air temperatures that reside alongside a spray of seawater droplets that are flash frozen so that when they are deposited at the bottom of the spray column, the fresh ice water floats above dense brine. The disadvantages of the refrigeration coils and scrapers are eliminated in the spray chamber version of Eutectic Freeze Crystallization. 
         [0093]    One approach is to feed the air intake of the turbo-compressor of the Genset via an educator that sucks in ambient air (˜+100° F.) and mixes the turboexpander exhaust air (˜−180° F.) to supply dry air at −22° F. 
         [0094]    The other approach is to feed the turboexpander exhaust air (˜−180° F.) to a salt water spray chamber to generate fresh water along with a continuous flow of air at −22° F. This air may contain ice fragments that need removal by centrifugal forces available by placing a double bend pipe setup in the path of the particle laden air so that only dry −22° F. air is supplied to the Genset air intake.
       The centrifuge will remove and save the large ice particles, while the safe and useful small ˜10 microns diameter particles will be permitted as intake to the combustion turbine. The small 10 micron diameter ice particles track the air flow between the high speed compressor turbine blades doing no impact damage but actually vaporize and further cool the intake air to enhance its compressor efficiency.
 
Integrated on-Shore Green Power Sources with Compressed Air Energy Storage System Aboard a Floating Power Plant
       
 
         [0096]    The floating power plant aboard a barge contains turbocompressor driven electricity generators, smoke stacks with waste heat recovery boiler and silencer, electricity power output control equipment, step-up transformers, control room and administration facilities. There is also storage space for oil and fuel. All these facilities are located on a floating barge with airtight compartments below the deck to provide buoyancy. 
         [0097]    A typical 72 MW Floating Diesel Power Station is about 180 feet long, 100 feet wide and 16 feet deep. The barge is must navigate through waters greater than 10 feet depth. 
         [0098]    If the Enis/Lieberman CAES system is integrated into a barge design, all the pressure vessels will be paced below the barge deck to provide the required stored high pressure air volume and to also supply the strong back for the barge structure and to supply most of the buoyancy force. 
         [0099]    In a completely green scenario, the barge would be located offshore adjacent to a wind farm or a solar photovoltaic farm where these farms are designed oversized to the immediate power demand. All the excess electrical power would be fed to the barge via power lines as long as the winds and/or sun power supplies are active. The electrically powered multistage air compressor, air mass control valve, turboexpander/generator set, electric power conditioning equipment, air ducting for the high mass flow of super-chilled air and cold storage facilities are on deck. The net product is electrical power, high mass flow of super-chilled air and hot water. 
         [0100]    In a partially green (hybrid) scenario #1, the barge would be located offshore adjacent to a wind farm or a solar photovoltaic farm where these farms are designed oversized to the immediate power demand. All the excess electrical power would be fed to the barge via power lines as long as the winds and/or sun power supplies are active. The electrically powered multistage air compressor, air mass control valve, turboexpander/generator set, electric power conditioning equipment, air ducting for the high mass flow of super-chilled air, educator, centrifuge ducting and turbocompressor Genset are on deck. The net product is electrical power, hot water and reduced consumption of natural gas. 
         [0101]    In a partially green (hybrid) scenario #2, the barge would be located offshore adjacent to a wind farm or a solar photovoltaic farm where these farms are designed oversized to the immediate power demand. All the excess electrical power would be fed to the barge via power lines as long as the winds and/or sun power supplies are active. The electrically powered multistage air compressor, air mass control valve, turboexpander/generator set, electric power conditioning equipment, air ducting, desalination facility, centrifuge ducting and turbocompressor Genset are on deck. The net product is electrical power, desalinated water, hot water and reduced consumption of natural gas. 
         [0102]    In a partially green (hybrid) scenario #3, the barge would be located offshore. Compressed air available on the barge powers a compander that uses the compressed air to generate a high air mass flow of super-chilled (−180° F.) air. The coolant water for the two stages of turbocompression in the compander becomes heated. The compander, air ducting, desalination facility, centrifuge ducting and turbocompressor Genset are on deck. The net product is electrical power from the onboard turbocompressor driven Genset, desalinated water, hot water and reduced consumption of natural gas. 
         [0103]    For a 180 feet long and 100 feet wide barge deck it is anticipated that there will be a manifold that connects a set of about 25 pipes in the uppermost layer of pressurized pipes and as many as 4 layers of these pipes. If the barge is to operate in very shallow waters, the length of the pipes will be doubled and the layers will be halved. 
         [0104]    The multi-layered bank of high air pressure pipes will not only supply the strong back basis for the structure of the barge, but also supply much of the buoyancy requirements. 
       SUMMARY OF THE INVENTION 
       [0105]    The Enis/Lieberman version of the Compressed Air Energy Storage (CAES) system uses high air pressure, thick steel wall, pipes to store its compressed air. Green power (wind and/or solar) sources or commercial grid electric power source to drive a multi-stage air compressor when the green power is available or when the commercial power is less expensive that pressurizes a pressure vessel. At a later time, when this stored energy is required the pressurized air is metered via an air mass control valve to drive the turboexpander of a turboexpander/generator set to generate electricity. Since there is no fuel combusted the pressurized air flow input at near room temperature exhausts a high mass flow of super-chilled (−180° F.) air. This super-chilled air can simply be used for HVAC or for cold storage facilities. Or this super-chilled air can be used to reduce the fuel consumption of a nearby turbocompressor driven Genset by as much as 30%. Or, in a more advanced version, this super-chilled air can be used to desalinate saltwater or brackish water and to also reduce the fuel consumption of a nearby turbocompressor driven Genset. 
         [0106]    One of the factors limiting the Enis/Lieberman version of the Compressed Air Energy Storage (CAES) system is the payback period after the system installation. The Time-Of-Use schedules dictate payback periods of 5 to 7 years depending upon the city utility rates as to daytime versus night time and summer time versus winter time. The major contributing factor is the cost of the thick steel wall pressure vessels required for the energy storage. 
         [0107]    In the barge scenario for the floating power plant the expense associated with the construction of the barge itself with all its submerged air compartments will be shared with the construction of the Enis/Lieberman CAES system pressure vessels. Thus the payback period for the Enis/Lieberman CAES system is reduced to 3 to 5 years. Also the fundamental cost of power for many of the island and isolated locations is about three-fold more expensive than populated areas so that payback periods are further shortened. 
         [0108]    The deep underground cavern CAES systems not only are geographically and geologically limited but they have long study periods and long installation periods associated with 5 to 10 years. This compares to typical FPP and Enis/Lieberman CAES system installation period of less than 1 year. 
         [0109]    Not only does the Enis/Lieberman CAES system versus the cavern system avoid burning fuel in its generation of electricity but also has high mass flow of super-chilled air output that reduces the fuel consumption of nearby turbocompressor driven Gensets. 
         [0110]    The isolated locations of these islands also have greater use of refrigeration facilities for their fish processing and storage facilities. The high mass flow of superchilled air from the turboexpander exhaust is of immediate use in that scenario. This all-fresh-air configuration avoids the need for the typical ammonia refrigeration facilities that have a history of toxic plume release as the ammonia storage tanks age. 
         [0111]    In summary, the integration of the FPP and Enis/Lieberman CAES system creates a portable (shippable) facility for delivering electric power and high mass flow of super-chilled air to remote locations in a short installation time and with reduced need for fuel combustion. There is also the potential to introduce desalination as a step in the overall process. Payback periods in isolated areas where energy cost rates are high will result in payback periods less than 3 years. It is the integration of the cost of the barge construction and the pressure vessel construction that permits these advantages. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0112]      FIG. 1  describes the Enis/Lieberman Compressed Air Energy Storage (CAES) system that uses either commercial power from the grid when the T-O-U schedule is to our advantage or uses green power to drive a multistage air compressor to pressurize the air in the pressure vessel wherein the energy is stored for later usage. The impeller wheel of the turboexpander is shown in an exploded view. The turboexpander drives the electric generator to produce electricity at the time it is demanded and as a byproduct it exhausts useful high mass flow of superchilled air. 
           [0113]      FIG. 2  shows the performance chart for the Caterpillar Company, Solar Turbine Division, MARS 100 Genset driven by natural gas. At the high ambient air temperature intake the Genset produces only 9,200 kW of electricity. Commercial air intake coolers attempt to supply the denser air associated with 59° F. (10,300 kWe) or even denser air at 44° F. (11,000 kWe). The patent concept disclosed herein will supply air at the −22° F. (13,000 kWe) that the Genset is capable of achieving as demonstrated during its Mil Std Environmental tests at −25° F. 
           [0114]      FIG. 3  shows the cost savings for four different commercial inlet air cooling systems. These cost figures were developed in the presentation entitled, “Effect of Turbine Inlet Air Cooling Technology on Capital Cost for Incremental Capacity”. This chart was for the 317 MW Cogeneration System Snapshot at 95° F. Dry Bulb and 80° F. Wet Bulb Ambient Air Temperature as reported by Punwami et al ASHRAE Winter Meeting, January 2001. 
           [0115]      FIG. 4  show that the physics of water evaporation controls the limit of the available commercial systems. If the ambient air is 100° F., the 15° F. and 25° F. temperature drops result in air intake temperatures are 85° F. and 75° F. that do result in enhanced electrical power output. If the ambient air is 100° F., the 45° F. temperature drop results in air intake temperatures are 55° F. that does result in more enhanced electrical power output. 
           [0116]    On the other hand, if the ambient air is 100° F., the 122° F. temperature drop results in air intake temperatures are −22° F. that does result in most enhanced electrical power output . . . by a large margin! 
           [0117]      FIG. 5  shows the air temperatures from the exhaust of a turboexpander impeller wheel. 
           [0118]      FIG. 6  shows the schematic drawing of the internal components of a compander. 
           [0119]      FIG. 7  shows an example of a barge FPP that EnRevo Pyro has developed for generating electrical power from pyrolysis of waste material. Their “house” air is between 102 and 105 psig (114.67 and 119.67 psia) so that it is more than sufficient than the compander shown in  FIG. 5  to obtain even lower air temperatures. 
           [0120]      FIG. 8  shows the complete system wherein the Enis/Lieberman CAES system is integrated with the floating power plant (FPP) barge. In this version of the CAES and FPP integrated system a turboexpander/generator system is powered to generate electricity and to create the high mass flow of super chilled air to be consumed by the turbocompressor driven Genset 
           [0121]      FIG. 9  shows the centrifuge performance in the rejection of the larger glass particles in a specific pipe cross section, air mass flow, pipe cross-sectional area and air temperature after it transits a 90 degree bend in the pipe. 
           [0122]      FIG. 10  shows the detailed coupling between the exhaust air from the turboexpander to the intake of the turbocompressor that is combusted with the fuel in the Genset. The path of the superchilled air from the turboexpander extends through a Eutectic Freeze Crystallization chamber that desalinates seawater or brackish water. 
           [0123]      FIG. 11  is the end view of an actual FPP barge floatation arrangement. The steel walls of the pressure vessels are in contact with the water for purposes of safety and heat exchange between the surrounding water and the steel outer surface as well as for floatation. 
           [0124]      FIG. 12  is the end view of the FFP barge flotation arrangement using layers of an array of high air pressure cylindrical pipes. 
           [0125]      FIG. 13  shows operation of the complete integration of the CAES system and the FPP system to provide electrical power at remote sites adjacent to waterways. This system is shippable to another site when needed. There are additional components that provide desalination and less use of fuel in turbocompressor driven Genset. 
           [0126]    There is also the configuration wherein the chilled air is used directly to chill a cold storage facility as well supply more electricity. One variation is to supply chilled air to a cold storage facility without the supply of electricity. 
           [0127]      FIG. 14  shows the lengths of four 10 inch inside diameter steel pipes that flow the 200 psig compressed air from the reinforced concrete pressure vessels under the barge to the 5,000 or 1,000 kWe turboexpander/generator set on the barge. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0128]    The following discussion contains a narrative of the invention that integrates the CAES system and its variations with the FPP system. The narrative is followed by a calculation that sizes a specific system as an example. 
         [0000]    a. Narrative 
         [0129]    The electric utility supply power system is comprised of (1) Transportable Compressed Air Energy Storage (T-CAES) system and its specific versions described herein and (2) Floating Power Plant (FPP) barge. 
         [0130]    1. Transportable Compressed Air Energy Storage (T-CAES) System 
         [0131]      FIG. 1  describes the Enis/Lieberman Compressed Air Energy Storage (CAES) system that uses either commercial power from the grid when the T-O-U schedule is to our advantage or uses green power to drive a multistage air compressor to pressurize the air in the pressure vessel wherein the energy is stored for later usage. When the energy is needed, the air mass control valve releases the pressure in the pressure vessel and feeds the steady high mass of near room temperature air to the input of a turboexpander impeller wheel (shown in an exploded view). The expansion process in the two-stage turboexpander releases the compressed air to the ambient pressure at very low temperatures (minus 180° F.). The torque from the turboexpander/impeller wheel drives the electricity generator. A complete 2.5 MW turboexpander/generator system is shown on its shipping pallet. 
         [0132]      FIG. 1  shows the schematic of the basic transportable compressed air energy storage (T-CAES) system. It is comprised of:
       Electrical power source   Green Energy
               Wind Turbine(s)   Photovoltaic solar panel(s)   Other       Waste Energy Power Plant   Utility Electric Power Grid during the Inexpensive periods of Time-Of-Use Multi-Stage High Air Pressure Compressor   Multi-Stage for high efficiency   
           Lowest acceptable thermodynamic efficiency at 2.0 SCFM/HP   Water cooled for recovery of waste heat   Hot water condensed from the moist air will be collected for recovery of waste heat   More than one compressor, each efficient for the available input power when input electric power is not steady   Pressure Vessel
           Air pressure sufficiently high
               To condense most of the moisture in the input air   To reduce the area footprint   
               Thick steel walls
               To safely contain internal high air pressure   To contain sufficient thermal capacity to supply the required heat to continuously warm expanding air as it is exhausted from the pressure vessel   
               
           Air Mass Control Valve
           Will deliver a constant air mass flow to the input of the turboexpander   Will adjust the output pressure for the slow decrease in air temperature received from the pressure vessel   
           No fuel for combustion is added!   Turboexpander
           No more than 100 psig as input to a one-stage turboexpander because of flow separation on the impeller blades   No more than 200 psig as input to a two-stage turboexpander because of flow separation on the impeller blades   
           Generator
           The electricity generator is driven by the shaft of the turboexpander   Water coolant water will be passed through a waste recovery circuit   
           Control System for Turboexpander/Generator set
           Generated electricity is condition for voltage and frequency control   Rotational speeds of turboexpander and generator measured for safety cut-off   Vibration and acceleration sensors are monitored for safety cut-off   Air mass flow of turboexpander is monitored
               Mass flow   Temperature   Pressure   
               
           Control System for overall T-CAES system
           Only excess power from the power source(s) is used for the compressor   System shuts down when there is not sufficient demand   
               
 
         [0173]    All other available commercial systems burn fuel with the pressurized air from the pressure vessel. Thus these systems generate electricity and an exhaust of high mass flow of hot combustion gases. 
         [0174]    This T-CAES system does not burn fuel with the pressurized air from the pressure vessel. It is unique in this characteristic. Thus the T-CAES system generates electricity and an exhaust of high mass flow of super chilled air. It is the use of this super chilled air that results in the following two families of useful power systems: (1) Green and (2) Hybrid 
         [0175]    The green (wind, solar, geothermal . . . ) systems use no fuel. The high mass flow of super chilled air from the turboexpander exhaust is fed to HVAC or cold storage facilities or to desalination facilities. 
         [0176]    The hybrid system burns fuel in its last step in the power system process. The last step is the fuel driven turbocompressor generator set that generates more and more electricity with colder and colder air intake. Many commercial systems already use water vapor systems and refrigeration to bring high ambient air temperatures down to about 59° F. to produce more electricity for the same fuel consumption ( FIGS. 2 and 3 ). In this invention we have the advantage of bringing 100° F. ambient air temperatures down to −22° F. or for a temperature change of 122° F. ( FIG. 4 ). 
         [0177]    When there is no wind or no sun a community will still need its electric power. The hybrid system provides reduced use of fuel when the natural power sources are strong or when the pressure vessel is not on empty. On the other hand, the hybrid system uses its planned fuel consumption when the natural power sources are weak or when the pressure vessel is on empty. 
         [0178]      FIG. 2  shows the performance chart for the Caterpillar Company, Solar Turbine Division, MARS 100 Genset driven by natural gas. At the high ambient air temperature intake the Genset produces only 9,200 kW of electricity. Commercial air intake coolers attempt to supply the denser air associated with 59° F. (10,300 kWe) or even denser air at 44° F. (11,000 kWe). The patent concept disclosed herein will supply air at the −22° F. (13,000 kWe) that the Genset is capable of achieving as demonstrated during its Mil Std Environmental tests at −25° F. 
         [0179]      FIG. 3  shows the cost savings for four different commercial inlet air cooling systems. These cost figures were developed in the presentation entitled, “Effect of Turbine Inlet Air Cooling Technology on Capital Cost for Incremental Capacity”. This chart was for the 317 MW Cogeneration System Snapshot at 95° F. Dry Bulb and 80° F. Wet Bulb Ambient Air Temperature as reported by Punwami et al ASHRAE Winter Meeting, January 2001. 
         [0180]      FIG. 4  show that the physics of water evaporation controls the limit of the available commercial systems. If the ambient air is 100° F., the 15° F. and 25° F. temperature drops result in air intake temperatures are 85° F. and 75° F. that do result in enhanced electrical power output. If the ambient air is 100° F., the 45° F. temperature drop results in air intake temperatures are 55° F. that does result in more enhanced electrical power output. 
         [0181]    On the other hand, if the ambient air is 100° F., the 122° F. temperature drop results in air intake temperatures are −22° F. that does result in most enhanced electrical power output . . . by a large margin! 
         [0182]      FIG. 2  shows that many commercial turbocompressor driven Gensets are already tested to Mil Std Environmental Cold Climate test operation at −25° F. Thus there are no questions as to the ability of the commercial system to perform at this temperature and produce more electricity without degrading any of the internal components. 
         [0183]      FIG. 5  shows examples of the superchilled air temperatures in the exhaust of several turboexpander configurations. The first row shows the cold temperature value (−104° F.) attained in a typical single stage turboexpander/generators.  FIG. 5  shows the air temperatures from the exhaust of a turboexpander impeller wheel. For one stage of air expansion it is only possible to drop from 114.67 psia (100 psig) to 19.67 psia (5 psig) and avoid flow air flow separation from its channeling impeller blades. At about 85% thermal efficiency the expansion results in the intake air at 100° F. to expand to −104° F. 
         [0184]      FIG. 5  shows the second and third rows show the cold temperature value (−56° F. after first stage and −104° F. after second stage) attained in a typical two stage turboexpander/generators. There are a multitude of companies that produce these generators. Turboexpander/generator sets generate both electricity and super chilled air from a high pressure air input. For two stages of air expansion it is only possible to drop from 300 psia to 85 psia and avoid flow air flow separation from its channeling impeller blades in the first stage; to drop from 80 psia to 15 psia and avoid flow air flow separation from its channeling impeller blades in the second stage. At about 85% thermal efficiency the expansion results in the intake air at 77° F. to expand to −181° F. 
         [0185]      FIG. 5  also shows examples of the superchilled air temperatures in the exhaust of a typical two-stage, free spooling compander. The last two rows show the cold temperature value (−82° F. after first stage and −174.5° F. after second stage) attained in a typical two stage free spooling compander. There is now only one company in the USA and the other in France that produce a compander. The compander does not generate electricity only super chilled air from a low pressure air input. 
         [0186]    In the above examples of commercial turboexpander/generator sets that are available in the 100 kWe to 40 MWe both electricity and a high mass flow of super chilled air are generated. 
         [0187]    In the case where there are two stages of turbocompression followed by two stages of turboexpansion via connection of a specific turbocompressor and turboexpander coupled to each other at one rotational speed and another specific turbocompressor and turboexpander coupled to each other at another rotational speed we have the creation of a two-stage, free-spooling, compander. The 90 psia and 70° F. intake air is exhausted at 20 psia and −174° F. . . . and there is no electricity generated. Only super-chilled air and hot water are the products. This device is used when there is “house” compressed air available at 90 psia. 
         [0188]      FIG. 6  shows the schematic drawing of the internal components of a compander. The 90 psia air can be delivered via the T-CAES system pressure vessels or from typical commercial “house” pressurized compressed air. The air initially flows through the path indicated by steps  1  through  7  to start the compander rotating. Thereafter the system of impeller wheels accelerate until the steady state (free-wheeling) state is achieved. 
         [0189]    In step  1 , the pressurized air is first fed through the series of turbocompressor #1, turbocompressor #2, turboexpander #1 and then turboexpander #2. This forced flow through the series of impeller wheels start the system rotating. Over a short period of time each impeller wheel starts to assume more and more of its own role that it will have at its steady state operation. The enthalpy changes across the dedicated pair of turbocompressor and turboexpander on their common shaft achieve a rotational speed wherein the enthalpies delivered and consumed are matched. This steady state condition is call “free-spooling. The detailed design of the four impeller wheels are designed to handle the same air mass flow throughout the system so that one set of free-spooling turbocompressor and turboexpander will rotate at a different speed than the other set to assure that the increase in enthalpy is matched by the relevant decrease in enthalpy in each rotating set. 
         [0190]    The air from the turbocompressor #1 is hot and is cooled prior to its transfer to turbocompressor #2. The air from the turbocompressor #2 is hot and is cooled prior to its transfer to turboexpander #1. Thus the system not only cools input air but also heats output water. 
         [0191]    The net results are the temperatures shown in  FIG. 5  and also hot water is generated as a byproduct. 
         [0192]      FIG. 7  shows an example of a barge FPP that EnRevo Pyro has developed for generating electrical power from pyrolysis of waste material. Their “house” air is between 102 and 105 psig (114.67 and 119.67 psia) so that it is more than sufficient than the compander shown in  FIG. 5  to obtain even lower air temperatures. 
         [0193]    The exhaust air from the compander is above atmospheric and the compressor turbine operates with suction upstream of its first stage of compression. This pressure difference across the educator pipe draws in the hot moist ambient air. After several pipe diameters downstream the mixing is complete between hot moist annular flowing air and the inner cylindrical core of the flowing super chilled compander air. There is then created a mixture of ice particle laden air at −22° F. The mixed flow is forced through two 135 degree bends in the ducting to assure that no large ice particles are fed into the path of the high speed blades of the turbocompressor. 
         [0194]    The large diameter ice particles accumulate and are continuously removed by a process not completely shown in  FIG. 7  but is completely shown in  FIG. 8 . 
         [0195]      FIG. 8  shows the complete system wherein the Enis/Lieberman CAES system is integrated with the floating power plant (FPP) barge. In this version of the CAES and FPP integrated system a turboexpander/generator system is powered to generate electricity and to create the high mass flow of super chilled air to be consumed by the turbocompressor driven Genset. The net result is the same electricity power output with a strongly decreased use of input fuel. The net result is thus electricity output from the turboexpander/generator set and electricity output from the Genset. 
         [0196]    The accumulated ice is continuously thawed to recover fresh potable water as a product. 
         [0197]    The flowing warm water discharged from the multi-stage air compressor cooling system is used to thaw the accumulating ice masses and then returned to again cool the multi-stage air compressor. 
         [0198]    The electric power transmission lines and their towers that deliver the electric power from the barge to the island is also used to place power lines from the wind turbine farm and/or solar photovoltaic farm to the barge for powering the multi-stage air compressor. 
         [0199]    The multi-stage air compressor pressurizes the steel pressure vessels below the barge deck. It is in these pressure vessels that the incoming power is delivered over time to store its energy as compressed air. 
         [0200]    The next  FIGS. 9 through 12  present details of the components of the hardware mentioned as centrifuge, desalination, compander and layered underwater pressure vessels. Thereafter,  FIG. 13  combines all the separate components of the system. 
         [0201]      FIG. 9  shows the centrifuge performance in the rejection of the larger glass particles in a specific pipe cross section, air mass flow, pipe cross-sectional area and air temperature after it transits a 90 degree bend in the pipe. The specific spherical diameter of particle is plotted. Although the results are somewhat generalized by the stated values of Reynolds Number and Stokes Number. 
         [0202]    For a Reynolds Number of 3 (laminar flow) about 15% of all the glass particles (density of glass is about three times that of ice) were deposited prior to a 90 degree turn in the duct. 
         [0203]    We use 135 degree bend that is more severe than a 90 degree bend so that the centrifugal forces are more severe, and we use two such bends. 
         [0204]    Another favorable physics effect that we use is that the air pressurized to 1,200 psig in the pressure vessel can support only 3*10̂−4 pounds of water per pound of air so that all the water in excess of that is condensed and drained. Note that at even 100% relative humidity the air at 75° F. and 0 psig can support 2*10̂−2 pounds of water per pound of air. Thus the air from the turboexpander is extremely dry. This mass flow of dry air mixes with the hot humid ambient air prior to encountering the double bend centrifuge. 
         [0205]      FIG. 10  shows the detailed coupling between the exhaust air from the turboexpander to the intake of the turbocompressor that is combusted with the fuel in the Genset. 
         [0206]    The 5,500 pounds per minute of −170° F. exhaust air from the 10,000 kWe turboexpander/generator set is combined with 194 gallons per minute of sweater at 70° F. so that the seawater spray is flash frozen to form a mixture of ice particles and air at −22° F. 
         [0207]    The temperature drop for the seawater droplets is extreme (+70° F. to −22° F.) so that the time delay for the freezing process to occur throughout the seawater droplet is short. 
         [0208]    Furthermore the pressure drop across the spray nozzle and the diameter of the orifices in the nozzle head are designed to produce a fine particle spray to assure that the resultant ice particles are small in diameter. The dwell time in the desalination chamber is so short that the ice particles have little time to grow in diameter during its downward flight (or fall). 
         [0209]    The heavy ice particles accumulate in the hopper at the bottom of the desalination chamber. The high density salt water drains to the bottom and the low density ice floats to the top of the salt water surface. At these low temperatures some of the other salts, other than NaCl, as well as minerals will deposit as solid particulates at the bottom of the brine solution. These materials are continuously collected by any of several commercial separation processes. 
         [0210]    The turboexpoander/generator and/or compander system supply of high mass flow of super chilled air to a desalination chamber provides Eutectic Freeze Crystallization (EFC) of seawater or brackish water at such an extreme temperature difference that desalination occurs over a shorter residence time and over a smaller path so that a smaller facility is possible compared to the conventional refrigeration coils systems. Furthermore, there are no scraper coils in the disclosed desalination system as is used in conventional refrigeration systems. 
         [0211]    The −22° F. air, free of large ice particles, is fed to the turbocompressor that drives the Genset. 
         [0212]    Note that a 10,000 kWe turboexpander/generator set fed sufficient cold air to produce 22,700 kWe from a pair of MARS 100 Gensets at a 30% fuel savings . . . plus 194 gallons per minute of seawater desalination. 
         [0213]    2. Floating Power Plant (FPP) Barge 
         [0214]    A typical 72 MW Floating Diesel Power Station is about 180 feet long, 100 feet wide and 16 feet deep. The barge is must navigate through waters greater than 10 feet depth. There are more than 60 floating power plants (FPPs) operating around the world. 
         [0215]    The objective is to consider that the strong back and the floatation systems of these FPPs ( FIG. 11 ) provide an excellent opportunity to hide the cost of the high pressure compressed air storage (CAES) system pipes as part of the strong back and floatation system of the FPP. Thus the most expensive portion of the T-CAES system is thereby excluded from the cost of the T-CAES system and its payback period shrinks from 5 to 7 to 11 years (depending upon Time-Of-Use schedules of a particular utility) to 3 to 5 to 7 years. 
         [0216]      FIG. 11  is the end view of an actual FPP barge floatation arrangement. This arrangement supports a 72 MW power plant that includes all the necessities of generators, smoke stacks, smoke stack scrubbers, heat recovery system from the smoke stack, electric power conditioning equipment, lubricant oil storage, fuel storage, compressed air system, administration offices, sewage tanks, ballast tanks, etc. 
         [0217]      FIG. 12  is the end view of the FFP barge flotation arrangement using layers of an array of high air pressure cylindrical pipes. These pipes are connected via a manifold that feeds compressed air into the pipes and later exhausts air from the pipes. 
         [0218]    This view shows the barge when it is not heavily loaded down with much of the required stored liquids and gases. When fully loaded it is desired that all the pipes be under water for efficient heat exchange operation of the CAES system. Thus it is expected that additional flotation will be provided between the deck and the pipes. This flotation will be constructed of less costly materials. 
         [0219]    For operation in depths less than 20 feet deep, it will be necessary to use a barge twice the shown length and half the number of pipe layers. 
         [0220]      FIG. 13  shows operation of the complete integration of the CAES system and the FPP system to provide electrical power at remote sites adjacent to waterways. This system is shippable to another site when needed. 
         [0221]    There are additional components that provide desalination and less use of fuel in turbocompressor driven Genset. 
         [0222]    There is also the configuration wherein the chilled air is used directly to chill a cold storage facility as well supply more electricity. One variation is to supply chilled air to a cold storage facility without the supply of electricity. 
         [0223]      FIG. 14  considers the steel wall pressure vessels considered in the CAES systems discussed in this disclosure. The thick steel wall not only contains sufficient heat capacity and high thermal diffusivity in the metal mass to supply the heat required by the expanding compressed air exhausting from the fixed volume storage pressure vessel so that the discharged air does not drop excessively in air temperature prior to arrival at the turboexpander input port. This temperature drop limit is further sustained by the presence of the steel pressure vessels direct contact with the water under the barge. 
         [0224]    However, there are sites where thick wall steel pressure vessels are not readily available. Thus there is T-CAES system configuration that uses concrete that it readily available. There are commercial pipe companies that have successfully transferred 500-psig water over long distances using reinforced concrete that contains not only the usual reinforcement bar network but also use a thin metal liner. The key to their commercial success has been the special end configuration of each pipe that permits the end to end attachment of separately manufactured lengths of pipes. This special end coupling is required for the tens of miles of pipe above ground exposed to heat and cold and to hills and valleys. This special end coupling is not required for reinforced concrete pipes 200 feet in length exposed to nearly the same temperature all the time and with no changes in elevation. 
         [0225]    Another reinforced concrete pipe company mixes in short lengths of high strength fiber in the concrete to enhance concrete&#39;s notorious poor tensile strength. 
         [0226]    The T-CAES system would then need to operate at a lower pressure vessel pressure, say, 600 psig. The turboexpander/generator set would operate with a one-stage turboexpander at 100 psig pressure input. 
         [0227]    In order for the system to operate with a reinforced concrete thick wall pressure vessel there is now necessary to arrange for heat transfer to the expanding air that is dropping in temperature as the pressure vessel progressively discharges its air to assure near constant temperature delivery of the 100 psig compressed air to the turboexpander input port. 
         [0228]    The compressed air discharged from the pressure vessel is piped onto the barge deck, pipe to the mass control valve on the barge deck, enters a set of four parallel pipes that are underwater alongside the 200 feet long barge, heated by the surrounding water alongside the barge and then fed to the turboexpander input port. A 400 feet required pipe length would require that the pipe be fed back and forth below the barge. 
         [0229]      FIG. 14  shows that at the beginning of the discharge when the air from the pressure vessel is still above 30° F., only a short length of the set of pipes perform the warming. But as the air from the pressure vessel gets colder and colder, more and more of the total available pipe length is used to assure the required heat exchange. 
         [0230]    The cold pressurized air from the pressure vessel starts flowing through a pipe at an initial air temperature and the air is then heated by the water surrounding the pipe. The pipe is maintained at the same temperature by the ambient water surrounding its outside surface. The minimum pipe length (L) required to assure that the heat transfer to the air given by: 
         [0000]        Q  dot= M  dot*Cp*( T   final   −T   initial ) 
         [0231]    The heat transfer from the pipe to the air in the pipe is also given by: 
         [0000]        Q  dot= h*pi ( )* D*L* ( T water− T   LMTD air )
 
         [0232]    These two equations, the boundary temperatures at the inlet of the pipe and outlet of the pipe, and at the outside of the pipe in the water as well as the Logarithmic Mean Temperature Difference (LMTD) for the heat exchanger configuration permit the determination of the pipe length. However, the heat transfer coefficient “h” is required. 
         [0233]    The value of “h” is determined from the air flow requirement from the turboexpander, pipe diameter and air properties as follows: 
       Reynolds Number: 
       [0000]    
       
         
           
             ρ is density of the flowing fluid. 
             μ is viscosity of the flowing fluid. 
             L is a characteristic length of the problem. For pipe flow L=D, where D is the pipe diameter. 
             U is a characteristic axial velocity 
           
         
       
     
         [0000]    
       
      
       Re=ρUD/ρ 
      
     
       PrandtI Number: 
       [0000]    
       
         
           
             Cp is the constant-pressure specific heat of the flowing fluid. 
             k is the conductivity of the flowing fluid. 
           
         
       
     
         [0000]        Pr =Cp μ/ k  
 
       Nusselt Number: 
       [0000]    
       
         
           
             h is the heat transfer coefficient. 
           
         
       
     
         [0000]    
       
      
       Nu=hL/k  
      
     
       Correlation for Turbulent Flow (Dittus-Boelter): 
       [0241]        h=k/D* 0.023* Re   0.8   Pr   n          n=0.33 heating   n=0.40 cooling   0.65≦Pr≦160         
         [0245]    The air pressure in the pipe and the permissible pressure drop determine the permitted pipe length. The pressure drop formula is given by: 
         [0000]      Δ P=f*L/D *(0.5 ρ U   2 )
       f is the friction factor ˜0.02 for many commercial       
 
         [0247]    The pipe length calculations shown is  FIG. 14  are slightly conservative in that the heat transfer coefficient, h=50 BTU/(Hr SqFt F) at −50° F. is used rather than the enhanced h=53 BTU/(Hr SqFt F) at +60° F. for the 5,000 kWe turboexpander input; that the heat transfer coefficient, h=13.9 BTU/(Hr SqFt F) at −50° F. is used rather than the enhanced h=14.6 BTU/(Hr SqFt F) at +60° F. for the 1,000 kWe turboexpander input. 
         [0248]    The reinforced concrete material pressure vessel is not a complete thermal insulator. The internal thin wall metal steel liner and network of metal reinforcement bars provide heat transfer. The direct contact of the concrete outer surface with the water also assures some heat exchange to the expanding air. 
         [0249]    The pressure vessel made of reinforced concrete also results in a net buoyancy force to assist the barge floatation. 
       Specific Example of T-CAES System and FPP System Integration 
       [0250]    The steps required to size the integrated CAES and FPP system are:
       Define the electric power requirement of the Genset (say, 11,350 kWe)   Define the electrical power requirement (say, 2,000 kWe)   Define the number of hours of the electrical power discharge (say, 8 hours)   Calculate the pressure vessel volume required   Define the length of the pressure vessel or length of barge (say, 200 feet lengths)   Define the inside diameter of the pressure vessel (pipe) (say, 4 feet)   Calculate the outside diameter of the pressure vessel   Define the space between horizontal pressure vessels (say, 0.5 feet)   Define the space between vertical pressure vessels (say, 0 feet)   Define the width of the array of pressurized pipes or width of barge (110 feet)   Calculate the layers of pipes below the barge deck   Calculate the weight of the pressurized pipes   Calculate the buoyancy force   Calculate the educator inflow air mass   Calculate the size of the compressor       
 
         [0266]    Genset Power and Airflow Intake
       Caterpillar Company, Solar Turbines, MARS 100 Genset
           11,350 kWe   73,727 SCFM intake air   
               
 
         [0270]    Turboexpander Power
       2,000 kW   2,681 HP   11.9 SCFM/HP (15% thermodynamic efficiency)   31,903 SCFM required       
 
         [0275]    Turboexpander Power Discharge Time
       8 hours   480 minutes   15,313,673 SCF required       
 
         [0279]    Calculate the required Pressure Volume
       4 ft diameter   18,000 feet length cylinder   226,195 CU FT water volume   18,728,826 SCF at 1,214.67 psia (start of operation)   3,309,967 SCF at 214.67 psia (end of operation)   15,418,860 SCF available air volume to drive turboexpander       
 
         [0286]    Define the length of each Pipe Cylinder based on Barge Length
       200 feet lengths or 62 meters length   90 cylinders required for 18,000 total pipe length       
 
         [0289]    Calculate the wall thickness required of the Pipe Cylinder
       40,000 psi stainless steel 316 tensile yield strength   1,200 psig internal pressure   48 inches internal diameter   0.72 inches wall thickness required for safety factor=1.0   1.44 inches wall thickness required for safety factor=2.0   The pressure vessel will be under water and there will be no nearby personnel so that a safety factor=2.0 is recommended.       
 
         [0296]    Calculate the outside diameter required of the Pipe Cylinder
       50.88 inches outside diameter   4.24 feet outside diameter   0.5 ft spacing between cylinders       
 
         [0300]    Calculate the number of cylinders in a layer
       23 cylinders per layer   109 feet width (or 33.2 meters wide)       
 
         [0303]    Calculate the number of layers
       90 cylinders required for 18,000 total pipe length   23 cylinders per layer   4 layers       
 
         [0307]    Calculate the weight of the cylinders (excluding the weight of end domes and manifold)
       495 pounds per cubic feet of steel   48 inches internal diameter   1.44 inches wall thickness   18,000 feet total pipe length   14,098,261 pounds of all pipes   7,049 tons as downward weight force when not underwater       
 
         [0314]    Calculate the buoyancy force
       64 pounds per cubic feet of salt water displaced   50.88 inches outside diameter   18,000 feet total pipe length   8,133 tons of upward buoyancy force       
 
         [0319]    Calculate the educator inflow rate of ambient air using Genset air intake requirement
       11,350 kWe Genset   91.8 pounds of air intake per second   0.075 pounds/cu ft at STP   73,440 SCFM   100 deg F. input air temperature   −22 deg F. output air temperature   39,028 SCFM ambient air   −170 deg F. input turboexpander exhaust air   −22 deg F. output air temperature   31,903 SCFM turboexpander air   70,931 SCFM total air flow from eductor to Genset (almost matched to 73,440, repeat calculation until matched       
 
         [0331]    Calculate the compressor size
       2,750 kW   3,686 HP   2.2 SCFM/HP   8,110 SCFM required       
 
         [0000]    
       
         
               
               
               
             
               
               
               
             
           
               
                   
               
               
                 Air Pressure 
                 Thermodynamic 
                 Thermodynamic 
               
               
                 (psia) 
                 Efficiency (%) 
                 Efficiency (SCF/HP) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 205 
                 75 
                 3.75 
               
               
                 394 
                 75 
                 3.0 
               
               
                 726 
                 70 
                 2.50 
               
               
                 1,253 
                 63 
                 2.14 
               
               
                   
               
             
          
         
       
       
         
           
             Use 2.2 SCFM/HP in this calculation to assure a conservative selection for the air compressor. This value is conservative because the operational cycle consists of compressing the pressure vessel from 214.67 psia to 1,214.67 psia in each cycle.
           16 hours   960 minutes   7,785,523 SCF required   4 feet inside diameter   9,100 feet length cylinder   114,354 CU FT water volume   9,468,462 SCF at 1,214.67 psia   1,673,372 SCF at 214.67 psia   7,795,090 SCF available (matched)   
         
           
         
       
     
         [0346]    The above set of calculations can be used for sizing other combinations of compressor, pressure vessels, turboexpander/generator set, educator and turbocompressor driven Genset. 
         [0347]    The embodiments discussed and shown herein are merely exemplary and are by no means intended to be limiting. The present invention contemplates various methods and systems that can be adapted that can carry out the intents and purposes of the invention, which may be a variation of the embodiments disclosed herein.