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# Optimum Values of Process Parameters of the "Wet Limestone Flue Gas Desulfurization System"
By lerzy Warych and Marek Szymanowski* In this article the method of cost optimization of the "Wet Limestone Flue Gas Desulfurization System" is presented. The optimizationcalculationsinclude process andcostmodels.Theprocessmodeldescribes themostimportantstageofS02removal that runs in the absorber and in the holding tank. It includes absorption of sulfur dioxide, oxidation of**SO~~** dissolution of limestone, and crystallization ofgypsum. The model was applied to calculate indispensable parameters for estimating costs and thentominimize capital andoperatingcosts. Costs ofallimportantequipmentwere estimated, such as S02removal systems with the absorber andtheholding tank,reagentfeed systemwiththeballmill anddewateringgypsum slurry system. Optimumvalues ofthe process parameters for different conditions of running flue gas desulfurization system were found. The process and cost model can be useful when designing the wet limestone FGD systems and carrying out economic analysis of the flue gas desulfurization plants.


### 1 Introduction

The dominating flue gas desulfurization (FGD) technology is based on absorption of S02 in limestone slurry. The efficiency of S02 removal is higher than 90 % for different working conditions, but FGD capital cost is very high and investmentcostreaches20- 30 % oftheinvestmentcostofthe whole power plant. Operating costs are high, too.

Research and development of the FGD technology aim at improving desulfurization efficiency, increasing a sorbent conversion, minimizing water and energy consumption, and waste production, but first of all at cuttingthe desulfurization cost.

NewdevelopmentsinFGDtechnology substantiallyreduce the investment and operating costs [1]. Simplifications of the system configuration are: current design eliminates the prescrubber, oxidation of sulfite, and limestone dissolution and gypsumcrystallizationthattakeplaceinthe sameholding tank. New corrosion- and erosion-resistant materials, such as rubber and fiberglass reinforced polyester piping, are used instead of high alloy materials. More developed process chemistry and control systems increase the S02 removal efficiency and improve the quality of gypsum. The use of larger and more efficient pumps, fans, oxidation systems and dewatering equipment also reduces the desulfurization cost. Simplification of the system configuration, improved corrosion materials, and improved process chemistry and control reduce redundancy requirements, especially the spare absorber.

The use of optimization procedure during the construction process could reduce the investment cost, and during operation it could reduce the operation cost. To calculate optimum process parameters, it is necessary to work out a
[*J J. Warych, M. Szymanowski, Warsaw University of Technology, Department of Chemical and Process Engineering, Warynskiego 1, 00-645 Warsaw, Poland. E-mail: szymanow@ichip.pw.edu.pl process model and a cost model of the FGD systems. In the process model, the reaction running in various apparatus of the systems should be described in detail.

It is hard to describe such a complicate system, as few processes run simultaneously in a holding tank and an absorber. A number of investigators have studied these processes for different working conditions, but a complex approach is necessary for optimization. There are a few complex models presented in the literature. FGDPRISM simulating model can be used as a design tool [2]. S02 absorption was describedby the stagnant-film theory, andthe assumptionofthermodynamicequilibriuminthe solutionwas used. Calibrating is necessary in order to estimate the mass transfer coefficient. The stagnant-film theory was used in the model of Eden, Luckas [3], and the model describes the absorption of SOb HCl, HF, and CO2, Eden, Heiting, and Luckas [4] presented a simple correlation to calculate the desulfurization efficiency. The correlation is a function ofthe LlG rate, the gas velocity inside the absorber, the pH of the solution, the concentration of S02 in gas, and the concentration ofchlorine and magnesia inliquid. Penetrationmodels to describe S02 absorption are used, too [5]. Kiil et al. 

### [6] describe processes which run in the absorber and in the holding tank using balance equation for every important component. Experiments were carried out in a packed absorber. In the literature, no calculation is presented of the optimal process parameters with are based on a complex process and cost model. The S02AdvancedRetrofit (SOAR) Methodology developed by the Electric Power Research Institute (EPRI) was used as a design tool to optimize the process parameters andselectthe materialofconstruction [7]. The methodologyusedEPRI'sFGDCOST,FGDPRISM, and FGD-RAM computer programs.

The aim of this work is to develop a complex cost and process model of the wet limestone flue gas desulfurization systems and optimize process parameters for various working conditions.

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## 2 Methodology ofCost Optimization
2.1 Objective function

The Net Present Value (NPV) was chosen as an objective function (OF) to solve the optimization task. The NPV is the sum of the discounted initial investment cost and the discounted annual operating cost over live years of the FGD plants.

Objective function 1):

n 1 max OF = max NPV = 

## L --t

. CFt t=O 

### (1+r) (1)
The Net Present Value calculation was based on the real discountrate andits value was estimated accordingto the rate of a long-term credit.

The value ofthe objective function (OF) changes according totheflow offlue gas, 

### S02, andthe HClconcentrationingases, desulfurization efficiency, numbers of operation hours over a year. Thequality ofcoal, the environmentallaw acts, andtotal operation time of the combustion over a year and load ofthe combustion determine the value of these parameters. The value of these parameters changes during operation of FGD plants. These parameters were included in the objective function as initial data. The investment cost was calculated according to the maximum value of flue gas, 

### S02 and HCl concentration, and the operating cost was calculated according to the mean value of these parameters. At final decision, the variables of the objective function are as follows:

Max OF

### =f(velocityofgases inthe absorber, average slurry residence time in the holding tank, LlG ratio, 

### Ca/S ratio, the limestone particle size distribution, pH of the slurry, concentration of Cl- in the slurry)

2.2 Limitations ofthe Decision Variable

In order to obtain a reasonable value of the optimum process parameters, limitations of the decision variable have been used. The limitations were as follows:

- maximumchlorideconcentrationintheslurry-O.5 kmollm3

- maximum limestone concentration in the slurry - 2 kg/m3

- maximum LlG ratio -16 dm3/m3

- range of the slurry pH

- 5.2

- 5.9

- minimal average residence time in the holding tank

- 12 h

- maximum gas velocity in the absorber

- 3.5 m/s

The scheme of searching procedure of the optimal parameters is presented in Fig. 1.

1) List of symbols at the end of the paper. 428 © WILEY·VCH Verlag GmbH, D·69469 Weinheim, 2002 Process model

Limitations of tile decision variable Input data: flue gases: - concentration of S02 and He!

- moisture

- temperature -flux desuifurizaiion efficiency limestone composition

max OF = f(LiG, vg , Ca/S, slurry pH, "HT, concentration of CI**~**

limestone article size)

Figure 1. Scheme of searching procedure.

2.3 Estimation ofInvestment and Operating Cost
2.3.11nvestment Cost

The total investment cost includes costs of all systems of FGD plant: the absorber, the holding tank, recirculation systems, reagent storage and handling systems, preparation andstorage ofthe limestone slurry, flue gas systemwithreheat systems, gypsum dewatering, and wastewater treatment. Procedures of EPRI were used to calculate the total investment cost [8]. Purchase cost of general apparatus and equipment was estimated based on different technical publications. Costs of auxiliary equipment, installing cost, andindirectcostwerecalculatedaccordingtofactors basedon costs of general apparatus and equipment. For increasing the prices of apparatus and equipment over time the Chemical Engineering Cost Index was used.

2.3.2 Operating Costs

The operating costs comprise two elements: variable cost andfixed cost. The fixed operatingcosts arefully independent of the gas throughput and they were not included in optimization calculation except the change of depreciation tax. Atthe endofthe calculations, thefixed costwere addedin order to estimate the total desulfurization cost.

The variable operating cost consists of the following detailed costs of:

- limestone

- raw materials: water, compressed air

- electricity

- reheating of flue gases,

- wastewater treatment

- maintenance: materials and replacement parts

Chern. Eng. Techno!. 25 (2002) 4Both lower environmental duties, regarding the reduction of S02 emission and sale of gypsum reduce the cost of desulfurization.

To estimate the operating costs, it is necessary to calculate material and energy balance. The material balance was calculated for limestone, water, compressed air, wastewater and gypsum. Total electricity consumption was determined as the sum of electricity consumption on all systems of the desulfurization plants.

2.4 Economic Criteria

Calculation year - second half of 1998 yr Discount rate
- 6.5 % Book live

- 30 years Electric power - 30 $/MWh Limestone

- 25.5 $/ton Water consumption

- 0.75 $/m3 Cost ofwastewater treatment
- 1.5 $/m3 Steam

- 6.3 $/t Environmental payment:

- S02 emission

- 0.094 $/kg

- HCI emission

- 0.22 $/kg

- Waste disposal- 2.0 $/ton

2.5 Process Model

The absorber and the holding tank are the most important apparatus where reactions take place. The model describes processes that take place in both apparatus. In the holding tank, the following processes take place: oxidation of sulfite, limestone dissolution and gypsum crystallization. In an absorber, the following processes take place, first of all absorption of S02 and HCl.

2.5.1 Holding Tank Limestone dissolution

Limestone dissolution takes place according to the dissolution reaction on the surface of CaC0 3 and diffusion transportation of reaction products. The flux of limestone dissolution is calculated by the film theory. The dominating stage is diffusive transportation of ions, and a thermodynamic equilibrium is achieved on the particle surface.

In this work, the limestone dissolution in the holding tank has been described according to the Borgren and Karlsson model [9]. The holding tank and the scrubber have been regarded as a continuous stirred tank reactor and used as a model in the process description; also the residence time distribution function of the slurry in the reactor has been used. Sulfite oxidation C .J)E T Full Paper <X

In order to calculate the rate of sulfite oxidation, the assumption has been made that the order of the oxidation reaction is 112 with respect to the manganese ion concentration, 3/2 with respect to the sulfite concentration and zero order with respect to the oxygen concentration.

In order to calculate operating cost, it is also necessary to determine the flux ofoxidation air to the holding tank. Gypsum crystallization

Many different elements influence the gypsum crystallization and crystal size distribution: temperature, presence ofother substances, mixing strength, thus it is very difficult to determine the rate of crystallization constant. The size of the gypsum crystals mustbe large enough for separate systems to workproperly and so that gypsum couldbe used as a building material. There should be enoughresidence time in a holding tanktokeeptherelativesupersaturationbelow 1.4,becausefor this conditioncrystallizationtakesplaceonthegypsumsurface rather than on the apparatus surface. These conditions are obtained when the average residence time in a holding tank equals 10-15h. In thestudy,thegypsumcrystallizationhasnot beenmodeled,but a conditionofan average residence time of slurry inthe holding tank ofnotless than 12 h has beenused.

2.5.2 Absorber

Absorption of S02 in a limestone slurry runs as follows: transport of S02 to the liquid surface, dissolution of SOb generation of the ions: H+, HSO:i, and sottransportation of the ions inside the liquid, dissolution of CaC03 , oxidation of sulfite, reaction of Ca2 +with**SO~~** and gypsum crystallization. Mostreactions thatrunduring sulfurdioxide absorption are instantaneous and they attain thermodynamic equilibrium. Still, dissolution and crystallization processes require more time to attain equilibrium.

An assumption of thermodynamic equilibrium in the solution has been used. Equilibrium calculation includes the following ions: OH-,HSO:;,**SO~~HSO:i,** SOtHCO:i,**CO~~Cl-,** Mg2+, Ca2 +, H+, and the dissolved gases S02 and CO2, Basic assumptions of absorption S02 in slurry droplets are the following:

- Resistance ofmass transport is in the gas andliquidphases.

- The drop shape is spherical.

- There are equal conditions in every point inside a drop,

which make an ideal mixing state.

- The absorber has been divided into two parts: the first

region is the height ofthe absorberfrom the top edge ofthe inletgases ducttothe spray systems, andthesecondregionis the height of the inlet gases duct.

- Both regions have been divided into a few layers.

- For the first region the concentration of S02 in the gases

change with the height of the absorption zone and the equilibrium inside the drop was calculated according to the condition at the beginning of the layer.

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- For the second region inside the drops, the same assumptions as those for the first region were used and an assumption of gas ideal mixing in the layer was used.

- Oxidation ofsulfite and limestone dissolution in droplets is

considered. The model can describe multiple-level spray systems. The results of this model agree with the data from the flue gas desulfurization plant [10] installed. Warych and Szymanowski [11] have described the process model in detail.

2.6 Neural Network

The process model ofthe FGD systems is complicated, and numerous iterations have been made when calculating the desulfurization efficiency. The objective function contains six decision variables and solving the optimization task requires to make numerous iterations. It is time-consuming to use the process model to calculate the optimum process parameters for many different initial data. In order to solve the optimization task, the neural network model has been developed to predict the results ofthe process model (Fig. 1). The network composed of three layers, including the hidden one, was used. The hidden layer included 19 neurons.

Inputs of the network were:

- height ofthe absorber

- height ofinlet duct of the flue gases

- velocity of gases in the absorber

- LlG ratio

- pH of the slurry

- concentration of

## crin the slurry

- concentration of S02 in the flue gases

- concentration ofHCI in the flue gases

The output of the network was desulfurization efficiency. The training and testing data were produced by the process model. The training set contained 700 vectors of data. The neural network was trained using Levenberg-Marquardt method (Neural Network Development Tool). Finally, the total sum square error equalled 0.13 %.

2.7 Method ofSolving the Optimization Task

Calculations of the optimal process parameters were made using the Matlab Optimization Toolbox. Function "constr" is a function to solve the optimization task with nonlinear limitations. The function "constr" is based on the BroydenFletcher-Godfarb-Shamio (BFGS) method.


### 3 Results ofthe Optimization Calculations 3.1 General Conclusions

Thebestadvantageis todesignanabsorberwithmaximumgas velocity, limited by the drop entrainment. A growth ofthe gas
430 © WILEY·VCH Verlag GmbH, D·69469 Weinheim, 2002 velocity to this value increases the desulfurization efficiency, reduces the dimension of the absorber, and the rise of costs connectedwith anincrease ofresistance ofgas flow is nothigh.

The optimum values ofthe otherparameters depend onthe S02 and HCI concentrations, stream of the flue gases, and economic parameters (e.g., price of sorbents and electricity, cost of apparatus, and installing cost).

TheLlGratio dependsonthe desulfurizationefficiency and S02 concentration. The optimum values of this parameter reach a maximum value for almosteveryworkingconditionof the FGD system.

The heightof absorption section strongly depends oninitial data. The optimum value equals 9.8

- 16.5 m. The process model does notdescribe coalescence ofdrops inthe absorber, and average drop diameters were used to calculate a mass transfer coefficient. The coalescence process and drops colliding with the pipe of spray systems could influence the optimum value of both parameters (LiG ratio, height of absorption section).

The Ca/S ratio in optimum condition of direction of the desulfurization process equals 1.03 to 1.05, and the pH of the slurry equals 5.5 to 5.7. Both parameters are correlated. The rate ofthe limestonedissolutiondependsonthe slurrypH, and the pH of the slurry is kept constant by the flow of dissolved Ca2 + ions. Itis very difficult to keep the value ofthe Ca/S ratio constant. The capacity ofthe holding tank is very big and the pH slurry changes very slowly, even when the Ca/S ratio rises or decreases considerably.

3.2 Effect ofInput Data on the Optimum Value ofthe Process Parameters 3.2.1 Flow of the Flue Gas The flow of the flue gases does not influence the process parameters. The optimum value of chloride concentration, slurry pH, LlG ratio, and Ca/S ratio stays nearly constant for various values of the flue gas stream. For the S02 concentration

- 3000 mglNm3 and HCI

- 200 mg/Nm3

, Ca/S ratio and LlG ratio obtain maximum value, and equal limitations (Ca/S 

### = 1.05 and LlG 

### = 16 dm3/m3).

3.3 Concentration ofS02 in the Flue Gases

Tab. 1 shows the optimum value of the process parameters for different S02 concentrations.

The concentration of S02 is the most important parameter that influences the cost of desulfurization and the optimum value ofthe decision variable. When the concentrationofS02 rises, then the throughput of all systems of the FGD plants rises, too. The height of absorber rises from 10.4 m to 16.6 m when the S02 concentration rises from 1000 to 5000 mglNm3• The optimum value ofchloride concentration decreases from 0.31 kmol/m3 to 0.28 kmol/m3 for the same range of S02

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Table 1. Optimum value of the decision variable (flow of flue gas 1380 Nm3/h. desulfurization efficiency 90 %). Concentration of S02 

## ! mgINm3 1000 2000 

## ! 3000 Height of the absorption section 

## ! m 10.4 10.9 

## ! 13.0 Concentration of Cl- in slurry 

## ! kmollm3 0.310 0.305 

## ! 0.300 LlG ratio 

## ! dm3/m3 14.4 16.0 

## ! 16.0

concentration. LowconcentrationofCl- reduces thepHofthe slurry and it is positive to the rate of S02 absorption.

3.4 Concentration ofHCI in the Flue Gases

Concentration of HCl in the flue gases influences the optimum value of chloride concentration in the slurry. The concentration of Cl- rises from 0.27 kmol/m3 to 0.31 kmollm3 for the range of HCl concentration from 50

- 300 mglNm3• Chlorides are removed from the slurry with wastewater, then the wastewater flow rises along with the rise of HCl concentration. The flow of wastewater is a linear function of HCl concentration (Fig. 2). The optimum height of the absorption section rises along with the rise of the HCl concentration. The height of absorber changes from 12.2 m to 13.6 m for the analyzed range ofHCl concentration.
14 0.35 

## 2 12 0.30 Cll 

### '0 5: 10 0.25 C 2 c 

## :s**<~,** 0 ()) 8 0.20**~** Ui E rn:E 5:**M~** 

## S

.**~** 

# -
. '0 ::: 6 0.15 c ()) 0 <l.l (j) E E (J -0 

## "'" OJ 4 0.10 c "§ 

### e:: 0 u 

### :c US 2 0.05 II 0 0.00

0 100 200 300 Concentration of HCI in fiue gases mg/N rn 3 Figure 2. Optimum value of the wastewater stream and the concentration of chlorides in the slurry.

3.5 Desulfurization Efficiency

Animpactofthedesulfurizationefficiencywas analyzedfor the range of S02 concentration 1000

- 5000 mg/Nm3• The optimum values of the decision variable are described in Tab. 2. The desulfurization efficiency influences mostly the height of the absorption section and LlG ratio. The value of both parameters rises along with increasing desulfurization efficiency. Figs. 3 and 4 show the optimum value of the absorption section height and LlG ratio.

The optimum value of the Ca/S ratio is lower than the maximum value onlyfor low desulfurization efficiency. When the Ca/S ratio is low, then the decreased pH ofthe slurry and decreased rate of S02 absorption is noted. 4000 5000 15.1 16.6 0.295 0.285 16.0 16.0

3.6 Effect ofEconomic Parameters on the Optimum Value of the Process Parameters

The most important elements that have an impact on the desulfurization cost are the prices of sorbent, electricity, and water.Theimpactoftheseelementswas analyzedfortheprice range from -30 % to +30 % of the basic price.

Any change in the prices of these elements influences the optimum value of the process parameters as follows:

- rise of the sorbent price

- slight decrease of the Ca/S rate

value,

- rise ofpriceofelectricity

- decreaseofvalue oftheLlGratio

and rise of the absorber height,

- rise ofthe waterprice-riseofCl- concentrationintheslurry

and decrease the waste water flux. An impact of costs of purchasing and installing the main apparatus of desulfurization systems was also analyzed. The change of these elements influences the desulfurization cost and the value ofthe objective function, butdoes notinfluence the optimum value of the process parameters.


### 4 Conclusions

The process, the cost model, and optimization procedure can be useful when designing the wetlimestoneFGD systems as well as for the control of the desulfurization plants. The model can also be useful in economic analysis of desulfurization plants.

The optimum values of the process parameters depend on numerous parameters, particularly on flux of gases, concentration of S02 and HCl and value ofeconomic parameters.

This article was presented at the US EPA/DOE/EPRI Combined Power Plant Air Pollutant Control Symposium: "The Mega Symposium", August20-23,2001, Chicago, IL. Received: July 17, 2001 [CET 1456] 

### Symbols used CF annual operating cost or investment cost, cash flow n total years of life and buildings of the FGD systems NPV net present value ON objective function r discount rate year

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Table 2. Optimum value of the decision variable as a function of the desulfurization efficiency.

Concentration Desulfurization Concentration Height CalS of S02 efficiency Slurry pH of Cl- of absorption LlG ratio ratio section mgINm3

- - kmollm3 m

4000 0.60 5.50 0.305 9.75 0.70 5.57 0.300 9.75 0.80 5.51 0.300 12.30 0.90 5.60 0.295 15.05 0.95 5.77 0.290 16.40 3000 0.60 5.53 0.310 9.75 0.70 5.64 0.305 9.75 0.80 5.71 0.305 10.50 0.90 5.72 0.300 13.00 0.95 5.75 0.295 14.70 2000 0.60 5.51 0.310 9.75 0.70 5.64 0.310 9.75 0.80 5.73 0.310 9.75 0.90 5.76 0.305 10.90 0.95 5.74 0.300 12.80 1000 0.60 5.62 0.315 9.75 0.70 5.72 0.315 9.75 0.80 5.72 0.315 9.75 0.90 5.76 0.310 10.40 0.95 5.80 0.305 13.20

Figure 3. Optimum height of the absorption section as a function of the desulfurization efficiency (flue gas flow

- 1380 X 103 Nm3/h).


### References
[1] Takeshita. M.• Air Pollution Control Costs for Coal-Fired Power Stations. lEA Coal Research. London. Jan. 1995. [2] Noblett. J. G.; Hebets. M. 1.; Moser. R. E.• EPA/EPRI Symp. on Flue Gas Desulfurisation. New Orleans 1990. pp. 7BI27-7BI44. [3] Eden

. D.; Luckas. M. A. Chem. Eng. Techno!. 21 (1998) pp. 56-60. [4] Eden

. D.; Heiting. B.; Luckas. M.• VGB Kraftwerkstechnik 77 (1997) pp. 505-511. [5] Brogren. Ch.; Karlsson. H. T.. Chem. Eng. Sci. 52 (1997) pp. 3085-3090. [6] Kiil. S.; Michael. L.; Michelsen. M. L.; Dam-Johansen. K.. Ind. Eng. Chem. Res. 37 (1998) pp. 2792-2806.

432 © WILEY-VCH Verlag GmbH

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17.0 16.0 15.0 

### E 14.0 

# ii '" ·13.0· 0 

# ., 12.0 

### r: Cl 11.0· :J 10.0 9.0 8.0

0.60 0.65 - 1.031 1.035 1.035 1.038 1.050 1.033 1.042 1.049 1.050 1.050 1.032 1.041 1.050 1.050 1.050 1.040 1.050 1.050 1.050 1.050

i-III- Concentration of S02
- 3000 rng/Nrn31

!

......... Concentration of S02
- 2000 mg/Nm3 !

0.70 0.75 0.80 0.85 0.90 Desulfurization efficency 0.65
Figure4. Optimum LlGratio as a function ofthe desulfurization efficiency (flue gas flow: 1380 x 103 Nm3 /h).

[7] Colley. 1. D.; Meadows. M. L.; Torstrick. R. L.; Mitchell. G. J.; Smigielski. 1. E.• FGD System Design Optimizing Using EPRI'S S02 Advanced Retrofit SOAR Methodology, Proceedings of ASME Joint Int. Power Generation Conf., ASME Paper, Phoenix 1994, pp. 1-8. [8] Keeth, R. J.; Baker, D. L.; Tracy, P. E.; Ogden, G. E.; Ireland, P. A., Economic Evaluation ofFlue Gas Desulfurization, United Engineers and Constructors, INC., EPRI, 1991. [9] Brogren, Ch.; Karlsson, H. T., Ind. Eng. Chem. Res. 36 (1997) pp. 3889- 3897. [10] Szymanowski, M., Ph. D. Thesis, Warsaw University of Technology 1999. [11] Warych, 1.; Szymanowski, M., Ind. Eng. Chem. Res. (2001), in press.

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