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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 

optimization calculations include process and cost models. The process model describes the most important stage of S02 removal 

that runs in the absorber and in the holding tank. It includes absorption of sulfur dioxide, oxidation of SO~~ dissolution of 

limestone, and crystallization of gypsum. The model was applied to calculate indispensable parameters for estimating costs and 

then to minimize capital and operating costs. Costs of all important equipment were estimated, such as S02 removal systems with 

the absorber and the holding tank, reagent feed system with the ball mill and dewatering gypsum slurry system. Optimum values 

of the 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 

investment cost reaches 20- 30 % of the investment cost of the 

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 cutting the desulfurization 

cost. 

New developments in FGD technology substantially reduce 

the investment and operating costs [1]. Simplifications of the 

system configuration are: current design eliminates the 

pre scrubber, oxidation of sulfite, and limestone dissolution 

and gypsum crystallization that take place in the same holding 

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 described by the stagnant-film theory, and the 

assumption of thermodynamic equilibrium in the solution was 

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 of the 

LlG rate, the gas velocity inside the absorber, the pH of the 

solution, the concentration of S02 in gas, and the concentration of chlorine and magnesia in liquid. Penetration models 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 S02 Advanced Retrofit (SOAR) 

Methodology developed by the Electric Power Research 

Institute (EPRI) was used as a design tool to optimize the 

process parameters and select the material of construction [7]. 

The methodology used EPRI's FGDCOST, 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 of Cost 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 

discount rate and its value was estimated according to the rate 

of a long-term credit. 

The value of the objective function (OF) changes according 

to the flow of flue gas, S02, and the HCl concentration in gases, 

desulfurization efficiency, numbers of operation hours over a 

year. The quality of coal, the environmental law acts, and total 

operation time of the combustion over a year and load of the 

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 (velocity of gases in the 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 of the 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 of Investment 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 

and storage of the limestone slurry, flue gas system with reheat 

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, 

and indirect cost were calculated according to factors based on 

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 

and fixed cost. The fixed operating costs are fully independent 

of the gas throughput and they were not included in 

optimization calculation except the change of depreciation 

tax. At the end of the calculations, the fixed cost were added in 

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) 4 
Both 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 of wastewater 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 CaC03 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 

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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 of oxidation air to the holding tank. 

Gypsum crystallization 

Many different elements influence the gypsum crystallization and crystal size distribution: temperature, presence 

of other substances, mixing strength, thus it is very difficult to 

determine the rate of crystallization constant. The size of the 

gypsum crystals must be large enough for separate systems to 

work properly and so that gypsum could be used as a building 

material. There should be enough residence time in a holding 

tank to keep the relative supersaturation below 1.4, because for 

this condition crystallization takes place on the gypsum surface 

rather than on the apparatus surface. These conditions are 

obtained when the average residence time in a holding tank 

equals 10-15 h. In the study, the gypsum crystallization has not 

been modeled, but a condition of an average residence time of 

slurry in the holding tank of not less than 12 h has been used. 

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 sot transportation of 

the ions inside the liquid, dissolution of CaC03, oxidation of 

sulfite, reaction of Ca2

+ with SO~~ and gypsum crystallization. 

Most reactions that run during sulfur dioxide 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 of mass transport is in the gas and liquid phases. 

- 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 of the absorber from the top edge of the 

inlet gases duct to the spray systems, and the second region is 

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 of sulfite 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 of the 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 of the 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 of the absorber 

- height of inlet duct of the flue gases 

- velocity of gases in the absorber 

- LlG ratio 

- pH of the slurry 

- concentration of cr in the slurry 

- concentration of S02 in the flue gases 

- concentration of HCI 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 of Solving 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 of the Optimization Calculations 

3.1 General Conclusions 

The best advantage is to design an absorber with maximum gas 

velocity, limited by the drop entrainment. A growth of the 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 

connected with an increase of resistance of gas flow is not high. 

The optimum values of the other parameters depend on the 

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). 

The LlG ratio depends on the desulfurization efficiency and 

S02 concentration. The optimum values of this parameter 

reach a maximum value for almost every working condition of 

the FGD system. 

The height of absorption section strongly depends on initial 

data. The optimum value equals 9.8 - 16.5 m. The process 

model does not describe coalescence of drops in the 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 of the limestone dissolution depends on the slurry pH, and 

the pH of the slurry is kept constant by the flow of dissolved 

Ca2+ ions. It is very difficult to keep the value of the Ca/S ratio 

constant. The capacity of the 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 of Input Data on the Optimum Value of the 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 of S02 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 of the decision variable. When the concentration of S02 

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 of chloride 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. Low concentration of Cl- reduces the pH of the 

slurry and it is positive to the rate of S02 absorption. 

3.4 Concentration of HCI 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 of HCl concentration. 

14 0.35 

2 12 0.30 

Cll '0 5: 10 0.25 C 

2 c 

0 :s <~, ()) 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 

An impact of the desulfurization efficiency was analyzed for 

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 only for low desulfurization efficiency. When 

the Ca/S ratio is low, then the decreased pH of the 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 of Economic 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. The impact of these elements was analyzed for the price 

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 of price of electricity - decrease of value of the LlG ratio 

and rise of the absorber height, 

- rise of the water price -rise of Cl- concentration in the slurry 

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 of the objective function, but does not influence 

the optimum value of the process parameters. 

4 Conclusions 

The process, the cost model, and optimization procedure 

can be useful when designing the wet limestone FGD 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 of economic parameters. 

This article was presented at the US EPA/DOE/EPRI 

Combined Power Plant Air Pollutant Control Symposium: 

"The Mega Symposium", August 20-23,2001, 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). 

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Chem. Res. 37 (1998) pp. 2792-2806. 

432 © WILEY-VCH Verlag GmbH. D-69469 Weinheim. 2002 

dm3/m3 

13.23 

16.00 

16.00 

16.00 

16.00 

12.03 

14.36 

16.00 

16.00 

16.00 

10.59 

12.59 

14.74 

16.00 

15.79 

8.89 

10.51 

12.65 

14.39 

12.67 

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 

Figure 4. Optimum LlG ratio as a function of the desulfurization efficiency (flue 

gas flow: 1380 x 103 Nm3

/h). 

[7] Colley. 1. D.; Meadows. M. L.; Torstrick. R. L.; Mitchell. G. J.; Smigielski. 

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and Constructors, INC., EPRI, 1991. 

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3897. 

[10] Szymanowski, M., Ph. D. Thesis, Warsaw University of Technology 

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[11] Warych, 1.; Szymanowski, M., Ind. Eng. Chem. Res. (2001), in press. 

Chem. Eng. Techno!. 25 (2002) 4