Model of the Wet Limestone Flue Gas Desulfurization Process for Cost

The results of this model are in agreement with data from flue gas ... Operating costs are high, too. Optimum process parameters calcu- lation can dec...
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Ind. Eng. Chem. Res. 2001, 40, 2597-2605

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PROCESS DESIGN AND CONTROL Model of the Wet Limestone Flue Gas Desulfurization Process for Cost Optimization Jerzy Warych and Marek Szymanowski* Faculty of Chemical and Process Engineering, Warsaw University of Technology, Waryn˜ skiego 1, 00-645 Warsaw, Poland

A detailed process model of the wet limestone flue gas desulfurization system has been presented. This model can be used to calculate indispensable parameters for estimating costs and next to minimize capital and operating costs. The process model describes most important stage of SO2 removal running in an absorber and a holding tank. It includes absorption of sulfur dioxide, oxidation of SO3-, dissolution of limestone, and crystallization of gypsum. An assumption of thermodynamic equilibrium in the solution has been used. SO2 removal and limestone dissolution calculation has been based on stagnant-film theory. The model has been used for predicting the SO2 removal efficiency in the spray scrubber for process parameters, e.g., L/G, droplet diameter, stoichiometric ratio Ca/S, height of the absorption section, gas velocity, concentration in liquidphase ions of Mg2+ and Cl-, and liquid pH. This model could be used to describe a multilevel spray system, too. The results of this model are in agreement with data from flue gas desulfurization installation at the Bełchato´w Power Plant (Poland). Introduction The dominating flue gas desulfurization (FGD) technology is based on absorption of SO2 in a limestone slurry. The efficiency of SO2 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. Optimum process parameters calculation can decrease the cost of desulfurization. The process model is necessary to solve the optimization task. The limestone FGD technology is a complex system and consists of many apparatuses. Before the scrubber, dust is precipitated in a dust collector. The next gases are directed to the scrubber where slurry is sprayed and SO2 is removed. Outlet gas, saturated with moisture, is reheated. The slurry is collected in the holding tank. In the tank take place the following: oxidation of SO32-, limestone dissolution, and crystallization of gypsum. Limestone slurry is prepared in a reagent feed system (with ball mill). Slurry from the holding tank is directed to the dewatering gypsum slurry system. Two kinds of dewatering systems are often used: hydrocyclones for the first step of dewatering and centrifugal separator or thickener and belt filter. After dewatering, gypsum contains 10% of moisture. It is hard to describe such a complicated system, because a few processes run simultaneously in a holding tank and an absorber. Models of SO2 absorption in water droplets were presented by Roberts and Friedlander,1 Chang and Rochelle,2 Chang et al.,3 and Hsu et al.4 In limestone desulfurization technology, SO2 is absorbed * Corresponding author. Tel.: +48-22-6236564. Fax: +4822-251410. E-mail: [email protected].

into a slurry containing particles of sorbent, sulfites, and sulfates. Uchida and Ariga5 used a two-reaction zone model. A liquid film near the gas-liquid interface was divided into three regions, and the assumption that all reactions in the liquid are instantaneous was used. Pasiuk-Bronikowska and Rudzinski6 described absorption of SO2 into slurries of Ca(OH)2 and CaSO3 by a stagnant-film theory. Calculation of the ions concentration on the interface surface and in liquid makes it possible to estimate the enhancement factor. Lancia et al.7 studied the rate of SO2 absorption into a slurry of limestone and Gerard et al.8 that into a slurry of CaSO3. Limestone dissolution, oxidation of sulfite, and gypsum crystallization are very important processes. 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. A FGDPRISM simulating model can be used as a design tool.9 SO2 absorption was described by the stagnant-film theory, and the assumption of thermodynamic equilibrium in the solution was used. Calibrating it was necessary in order to estimate the mass-transfer coefficient. The stagnant-film theory was used in the model of Eden and Luckas10 that describes absorption of SO2, HCl, HF, and CO2. Eden et al.11 presented a simple correlation to the calculation efficiency of desulfurization. The correlation is a function of the L/G rate, the gas velocity inside the absorber, the pH of the solution, the concentration of SO2 in the gas, and the concentration of chlorine and magnesia in liquid. Penetration models to describe SO2 absorption are used too.12 Chang and Rochelle13 studied the impact of organic acid on SO2 absorption using the surface renewal theory. Stergrasek et al.14 carried out experiments with a spray absorber and estimated the liquid-side mass-transfer coefficient for the Higbie

10.1021/ie0005708 CCC: $20.00 © 2001 American Chemical Society Published on Web 05/19/2001

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model. Kiil et al.15 describe processes which run in the absorber and in the holding tank using a balance equation for every important components. Experiments were carried out in a packet absorber. The aim of this work is to develop a complex model of the wet limestone FGD process. The model has been used to predict the SO2 removal efficiency in the spray scrubber and to calculate values of parameters necessary to estimate overall costs, e.g., L/G, droplet diameter, stoichiometric ratio Ca/S, height of the absorption section, gas velocity, concentration in the liquid phase of Cl- and Ca2+, solution pH, and capacity of the holding tank.

cations and anions, and the flux of charge is equal zero; therefore

JSO2 + JHSO3- + JSO32- ) 0

(3)

JHSO4- + JSO42- ) 0

(4)

JMg2+ ) 0

(5)

JCl- ) 0

(6)

Jan ) 0

(7)

Jcat ) 0

(6a)

∑k zkJk ) 0

(8)

Process Model of the FGD Systems The absorber and the holding tank are the most important apparatuses where reactions take place. The model describes processes which take place in both apparatuses. In the holding tank take place the following: oxidation of sulfite, limestone dissolution, and gypsum crystallization. In an absorber, first of all the following takes place: absorption of SO2 and HCl. Holding Tank. (i) Limestone Dissolution. Limestone dissolution takes place according to the dissolution reaction on the surface of CaCO3 and diffusion transport of reaction products. The dissolution is influenced by different species. Dissolved metals (zinc, magnesium, manganese, and copper) and their salts can decrease the rate of dissolution. Van Tonder and Schutte16 have shown that the presence of these ions is insignificant when their concentration is not higher than 80-100 mg/ dm3. Metals precipitate with gypsum, and the ion concentration is not very high. For conditions in a holding tank, the presence of sulfite can change the rate of limestone dissolution.17 When oxidation of sulfite takes place in a holding tank, the influence of sulfite presence on the dissolution can be disregarded. Dissolved CO2 can hydrolyze and change the rate of dissolution, but it is insignificant when buffering species are present. The flux of limestone dissolution is calculated by the film theory. The dominating stage is diffusive transport of ions, and a thermodynamic equilibrium is achieved on the particle surface. The mass balance described by the differential equation around the particle is

1 r2

(∑ ) ∂(r2Jk) ∂r2

k

)0

(1)

where k indicates different components. The equation includes a balance of the following components: sulfite (SO2, HSO3-, and SO32), sulfate (HSO4- and SO42-), carbonate (HCO3- and CO32-), magnesium, chlorine, and calcium ions. An additional equation is necessary for a balance of the net charge. Brogren and Karlsson18 have shown that the effect of the potential gradient can be neglected when the pH of the slurry is above 3. Therefore, the flux balance is as follows:

1

(∑ )

r2

∂(r2Jk)

zk

k

∂r2

)0

The following equations express the condition of surface equilibrium with CaCO3, and the flux of calcium must be equal to the flux of total carbonate:

Ks ) [Ca2+][CO32-]

(9)

JHCO3- + JCO32- ) JCa2+

(10)

The limestone particle size distribution is a very important parameter to calculate the rate of limestone dissolution. The particle size changes during dissolution in the holding tank. The flux of Ca2+ could change with the shrinking particle diameter. The change in flux has been modeled using a correction factor R:19 in

()

JdCas ) JdCas

R

ds

(11)

din s

In this work the limestone dissolution in the holding tank has been described according to the Borgren and Karlsson model.19 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. The degree of limestone conversion f can be expressed as the ratio between the limestone leaving the holding tank Ms and that being added to the tank Mso. The degree of limestone conversion can be calculated as a function of average residence time, τ, and the particle size distribution:

f)1-

Ms Min s n

∑ i)1

)1-

[

in in (F(ds,i ) - F(ds,i-1 ))

∫0

∞

() ] ds,i

in ds,i

3

1 -t/τ dt (12) e τ

The limestone for FGD is prepared in a ball mill. The particle size distribution after grinding in the ball mill can be described with the Rosin-Rammler function.

F(di) ) 1 - exp[-(di/L*)n]

(13)

(2)

On the surface of the limestone particle, there is no net flux of sulfite, sulfate, magnesia, chlorine, and other

An analysis of a few the limestone particle size distributions showed that the function of RosinRammler could be successfully used. During the analysis it has been observed that parameter n stays almost

Ind. Eng. Chem. Res., Vol. 40, No. 12, 2001 2599

constant for the same limestone and different grinding times. Frances et al.20 observed the same effects for grinding of Al(OH)3. When parameter n is known, only one parameter L* is necessary to describe the particle size distribution. It is very useful to determine the optimum particle size and time of grinding, because only one parameter L* describes the particle size distribution of different grinding times. Brogren and Karlsson19 have shown that flux of calcium JCa does not change with the particle diameter (R ) 0, eq 11). Calculations of the limestone dissolution for different values of correction factor R confirm this conclusion. The constant value of the film thickness δs for this assumption was found, δs ) 3.5 µm. Changing particle size of CaCO3 during dissolution when the flux of Ca2+ does not depend on the particle diameter is described by the equation

ds 2MCa ds t ∂ds 2MCa ds J w )1J (14) )∂t Fs Ca din Fs Ca din s

s

The limestone conversion is equal to n

f)1-

∑ i)1

{

[ ( )[ ( ) ] ( ) ]}

in in [F(ds,i ) - F(ds,i-1 )] 6

1 +1+6

B

in ds,i

B

in ds,i

3

τ

2

τ

exp -

in ds,i

-

Bτ

B -3 τ in ds,i

(15)

where

B)

Fs 2MCaJdCas

s ; JdNa )

DCa ([Ca2+]s - [Ca2+]l) δs

(ii) Sulfite Oxidation. Changes of the sulfite and oxygen concentrations influence the oxidation rate. A few authors found that the reaction is zero-order or firstorder with respect to the oxygen concentration. Sulfite precipitation takes place, and the rate of oxidation is limited by sulfite dissolution. When forced oxidation takes place, the concentration of sulfite in the slurry is low and sulfite precipitation is limited. The presence of a metal catalyst influences the oxidation. The biggest source of metal ions (copper, cobalt, iron, and manganese) in the slurry is limestone dissolution. The copper, iron, and cobalt quickly precipitate with gypsum, and the influence of these ions can be neglected.15 The concentration of Mn2+ is sufficiently high to influence the rate of oxidation. In the presence of a catalyst, it is very difficult to establish an order of reaction. Various authors assume different values of the order of the oxidation reaction.21-23 To calculate the rate of sulfite oxidation, an assumption has been made that the order of the oxidation reaction is 1/2 order with respect to the manganese ion concentration, 3/2 order with respect to the sulfite concentration, and zero order with respect to the oxygen concentration:24

-

d[SIV] ) kox[SIV]1.5[Mn2+]0.5 dt

(16)

To calculate operating costs, it is necessary to determine the flux of oxidation air to a holding tank. The flux of oxygen absorption (eq 17) has to be equal to 1/2 of the flux of the SO2 absorption. In the slow reaction

regime

RO2 ) k1aApp,htHox[O2]*

(17)

kla is calculated according to the Akita-Yoshida equation:25

( )( )( )

3 DO2,1 ν1 k1a ) g db db DO2,1 g )

1/2

gdb3

1/4

ν12

1 0.35 F1σ 2+ Uox 72

gdb2F1 σ

( )( )

1/3

3/8

(18)

(19)

(iii) Gypsum Crystallization. The rate of gypsum crystallization is a function of the relative supersaturation Rs:

Rgp ) agpVhtkgp(Rs - 1)

(20)

It is very difficult to determine the rate crystallization constant, and the results given by various authors do not comply. There are no models that describe the gypsum crystal size distribution, and the results of laboratory-scale research works cannot be used to describe crystallization in full-scale installations. Many different elements influence the gypsum crystallization and crystal size distribution: temperature, presence of other substances, mixing strength, etc. The size of the gypsum crystals must be large enough to work properly in separate systems 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 no less than 12 h has been used. Scrubber. Absorption of SO2 in a limestone slurry runs as follows: transport of SO2 to the liquid surface, dissolution of SO2, generation of the ions H+, HSO3-, and SO32-, transport of the ions inside the liquid, dissolution of CaCO3, oxidation of sulfite, reaction of Ca2+ with SO42-, and gypsum crystallization. Most of the 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-, HSO4-, SO42-, HSO3-, SO32-, HCO3-, CO32-, Cl-, Mg2+, Ca2+, H+, and dissolved gases SO2 and CO2. Basic assumptions of absorption SO2 in slurry droplets are the following: (i) Resistance of mass transport is in the gas and liquid phases. (ii) The drop shape is spherical. (iii) There are the same conditions in every point inside a drop, which make an ideal mixing state. (iv) The absorber has been divided into two parts (Figure 1): the first region is the height of the absorber from the top edge of the inlet gases duct to the spray

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Figure 1. Scheme of division of the absorber into two regions and layers.

systems; the second region is the height of the inlet gases duct. (v) Both regions have been divided into a few layers. (vi) For the first region the concentration of SO2 in the gases changes 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. (vii) 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. (viii) Oxidation of sulfite and limestone dissolution in droplets is considered. The model could describe multiple-level spray systems. In this condition, the balance of SO2 absorbing for every layer in the first region is described by the following equation:

ugFm dps P

dz

[

n

) -ad

Kig(ps - po,i ∑ s ) i)1

After integration

-

∆zPad u g Fm

n

∑ i)1

ps,j+1

) ln

n

ps,j

n

i Kg,j

-

∑ i)1

]

i o,i Kg,j ps,j

n

i i o,i Kg,j - ∑(Kg,j ps,j ) ∑ i)1 i)1

For the second region

/

(21)

and zj-1, V˙ g,j is the flux of the gas into the absorber below a height of zj, and

hdc - (z - hab) V˙ g,j ) V˙ g hdc

(24)

∆z / ) V˙ g V˙ g,j hdc

(25)

Values of kl and kg were calculated according to the local gas velocity. The balance equation for chlorides is the same as that for SO2, but the overall mass-transfer coefficient is equal to the gas-side transfer coefficient HCl HCl ) kg,j . Kg,j Balance equations describe the changing concentration of sulfite, sulfate, and calcium in succeeding layers. i i - [SIV]ij) ) RSO - kox([SIV]ij)1,5[Mn2+]0.5V˙ il V˙ il([SIV]j+1 2,j (26)

V˙ g(ps,j+1 - ps,j) RT n

i Kg,j ∑ i)1

(22)

dc ) Kg,j(ps,j - pSO2,j)∆zApp,abad ) RSO 2,j / V˙ g,j (pjin ˙ g,j(ps,j+1 - ps,j) s - ps,j) + V (23) RT

where i is the number of spray system levels, j is the / number of calculating layers, V˙ g,j is the flux of the gas into the absorber between a height of the inlet duct zj

n

)

i RSO ∑ ,j i)1 2

i [SIV]j+1 - [SIV]ij ) kox([SIV]ij)1,5[Mn2+]0.5

(27) (28)

For high SO2 concentration in gases, dominant resistance to mass transfer is on the liquid side, but for low SO2 concentration, resistance on the gas side is important. The gas-side mass-transfer coefficient has been calculated according to the Frossling equation:

Shg ) 2 + 0.6Re0.5Scg0.333

(29)

It is more difficult to estimate the liquid-side masstransfer coefficient. A number of different models were developed for the liquid-side mass-transfer coefficient. The models and experimental data are not in good agreement.26 An equation by Hsu and Shih27 has been

Ind. Eng. Chem. Res., Vol. 40, No. 12, 2001 2601

used in order to calculate kl:

k1 ) 0.88xfoD1; fo )

8σ x3πm

(30)

The overall mass-transfer coefficient is

HSO2 1 1 ) + i Kg,j kg k1βij

(31)

where βj is the mass-transfer enhancement factor, which has been calculated for equilibrium inside the drops and at the interface at the beginning of the jth layer. The ion concentration inside the drops was calculated according to equations of thermodynamic balance including constants of reactions and electroneutrality condition. Calculation of the equilibrium ion concentration at the interface was based on the stagnant-film theory, and diffusion coefficients were modified to approximate the surface-renewal theory. To solve the problem, the following boundary condition was accepted: no net flux of calcium, magnesium, and sulfate, flux of charge equal to zero, SO2 transport to the interface equal to sulfite transport inside the liquid, and flux of HCl to the interface equal to chloride transport inside the drop. The concentration of the carbonate is close to equilibrium with the CO2 concentration in the gas.

Jan ) 0

(32)

Jcat ) 0

(33)

JMg2+ ) 0

(34)

JCa2+ ) 0

(35)

JHSO4- + JSO42- ) 0

(36)

∑k zkJk ) 0

(37)

JSO2 + JHSO3- + JSO32- ) ks(ps - p/s )

(38)

Jg,HCl ) J1,Cl-

(39)

Equilibrium constants were calculated by correlation of Brewer28 and activity coefficients by the equation of Davies.29 Henry’s constants were modified by data of Weisenberger and Schumpe.30 Analysis of Model Calculation Results Figure 2 shows modeled values of efficiency desulfurization versus FGD plant data. The wet limestone with force oxidation and a gypsum byproduct FGD plant was installed in the Bełchato´w Power Plant on four units (360 MW capacity each). Equipment absorbers (one absorber was installed on one power unit) include a spray system with four recirculation pumps (delivery of 9500 m3/h each). Comparison was made for different operation conditions: gas flux, 1 × 106-3 × 106 Nm3/h; SO2 concentration in the inlet gases, 1000-4000 mg/Nm3; pH solution, 5.2-5.6. For the remaining parameters, constant values were chosen: chloride concentrations, 0.1 kmol/m3; sulfite concentration in a holding tank, 0.2 mol/m3;

Figure 2. Modeled values of desulfurization efficiency versus FGD systems (installed at the Bełchato´w Power Plant) data.31

limestone in the slurry, 3.0 kg/m3; average drop diameter, 2900 µm. The average difference between data from the FGD plant and modeled results equals 1-3% of the desulfurization efficiency, with a standard deviation equal to 2.45% and a 95% confidence interval equal to 4.7%. For extreme conditions (high or little SO2 concentration in the inlet gases), differences equal 5%. For the outlet of the SO2 concentration, 200-250 ppm maximum differences are no higher than 80 ppm. The reason for higher differences for few data could be subject to the assumed constant value of magnesia, and the chloride concentration in solution, and the limestone concentration in the slurry. Magnesia, chloride, and limestone concentrations influence the desulfurization efficiency, but these parameters were measured only once per week and an average constant value was chosen for every data point. For more detailed data (limestone, magnesia, and chloride concentrations), the value of a statistical parameter of the model error will be superior and the standard deviation and confidence interval values will be lower. Average drop diameter sprays in absorbers for FGD systems are equal to 1500-2000 µm. The drop diameter equal to 2900 µm was chosen in every calculation. A bigger drop diameter results from coalescence in the absorber and a risk of the worst work of a nozzle that was used a long time (the worst distribution of the drop diameter). When the drops collide with a pipe of the spray system, the diameters are changed, too. The drop diameter is the calibrating parameter and collects all mistakes of the model. Nevertheless, only one calibrating parameter can adjust the modeled result to data from FGD plants. Influence of Process Parameters on the Desulfurization Efficency The use of the model desulfurization efficiency for different process parameter values was compared. This analysis was made for following parameters: pH solution, chloride concentration in solution, drop diameter, height of the absorption section, L/G rate, inlet SO2 concentration, and velocity of the gas in the absorber. The Ca/S rate was not included. The model describes a

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Table 1. Relations between the Desulfurization Efficiency and Process Parameters31 parameter

units

range of param value

min and max efficiency value [%]

changing the efficiency for a given range [%]

slurry pH drop diameter height of the absorption section magnesium concentration chloride concentration inlet SO2 concentration gas velocity L/G ratio

µm m kmol/m3 kmol/m3 ppm m/s dm3/m3

5.2-5.8 2000-3000 6-18 0.03-0.13 0.1-0.3 1500-5000 2-4 8-15

86.4-93.5 74.5-99.3 66.5-99.7 66.4-95.0 83.6-93.4 73.4-97.0 90.0-98.9 68.3-97.7

7.6 25.0 33.4 30.1 10.5 24.3 8.9 30.1

Table 2. Impact of the Process on the Desulfurization Efficiency31 process

average difference [%]

max difference [%]

limestone dissolution; concentration of CaCO3 1000 g/m3 concentration of CaCO3 5000 g/m3 oxidation of sulfite absorption of HCl; concentration of HCl in inlet gases 20 mg/Nm3 200 mg/Nm3 simplification of the model: mixing of drops for different spray levels average height of the absorption section

+0.15-1.0 +1.5-3.0 below 0.1 -0.2 -1.0-2.0 +0.2-0.4 +0.5-1

+2.5 +7.3

reaction running in a holding tank. Conditions in a holding tank determine equilibrium in the inlet solution to the absorber, and the Ca/S rate determines the concentration of limestone in the slurry. The influence of limestone dissolution on the desulfurization efficiency was analyzed in the next paragraph. The process parameters and range that were chosen for this analysis are included in Table 1. The SO2 removal efficiency was calculated for succeeding boundary values and average values of the remaining parameters. The strongest influence in given ranges was observed for the L/G ratio, height of the absorption section, and drop diameter and the lowest for the slurry pH, chloride concentration, and linear gas velocity. This analysis describes only a general dependence between efficiency and parameters because changes in the efficiency depend on a chosen range of parameters. Calculation of suitable parameter values makes it possible to optimize operation of a desulfurization plant. One of the most important parameters is the drop diameter. The drop diameter has to be correlated with the gas velocity in an absorber. These parameters are important for the rate of mass transfer in an absorber. The drop diameter and the gas velocity determine the time of phase contact, surface mass transport, and values of the mass-transfer coefficient on gas-phase side and liquid-phase side (for circulating drops). The value of the mass-transfer coefficient increases with the growth of the gas velocity, but the velocity has to be limited according to drop entrainment. The best advantage is to design an absorber with a maximum gas velocity, limited by drop entrainment. A growth of the gas velocity to this value increases the desulfurization efficiency and reduces the dimension of the absorber, and the rise in cost connected with the increase of resistance of gas flow is not high. There are numerous relationships between process parameters, and calculations of optimum values have to be treated on a broad basis. Impact of Different Processes on the SO2 Removal Efficiency An impact of a few processes on the absorption of SO2, for the range of parameters shown in Table 1, has been made. This analysis includes the absorption of HCl,

-0.5 -4.8 +0.6 +1.9

oxidation of sulfite and limestone dissolution in the absorption zone, and simplification of the model. Sulfite Oxidation. Usually, the degree of the sulfite oxidation within the tower is only in the range of 2030% of absorbed SO2. Oxidation of sulfite reduces the SO3- ion concentration and this is positive to the absorption, but it increases the pH too and this is negative. Results of the calculation have shown that oxidation changes the desulfurization efficiency by no more than 0.2%. Limestone Dissolution. When the concentration of limestone in a slurry equals 5000-10 000 g/m3, the limestone dissolution is an advantage to the rate of SO2 absorption. The limestone particle size distribution is very important for this process because it determines the value of the mass-transfer surface. CaCO3 dissolution has strong influences on the SO2 absorption on the bottom part of the absorber, where slurry pH is low and the rate of dissolution is high. In this part of the absorber, dissolution of CaCO3 increases the slurry pH and the rate of SO2 absorption. When the pH of the slurry in a holding tank is higher, the influence of dissolution on the desulfurization efficiency is lower. In a FGD plant with gypsum byproduct, the concentration of limestone is no higher than 1500-2000 g/m3 and the impact of dissolution is low. Dissolution of limestone in drops increases SO2 removal efficiency by 0.5-1% (maximum 2.5%; see Table 2). Absorption of HCl. If the concentration of HCl in flue gases amounts to 20 mg/Nm3, absorption of HCl does not influence the rate of SO2 removal. For higher HCl concentration, the influence of this process is higher. If the concentration of HCl equals 200 mg/Nm3, the rate of SO2 absorption decreases by 1-5% (Table 2). Absorption of HCl indirectly influences the desulfurization efficiency too. The average residential time in a holding tank equals dozen or so, and chlorides are cumulated in the slurry. A high concentration of chloride changes the equilibrium in the slurry and reduces the pH of the slurry and the desulfurization efficiency. It is necessary to use the rate of HCl absorption to calculate the chloride balance and flux of wastewater. Simplification of the Model. Two simplifications of the scrubber calculation with multilevel spray systems have been analyzed: (i) the assumption that drops from different levels of spray systems are mixed up was

Ind. Eng. Chem. Res., Vol. 40, No. 12, 2001 2603

Figure 3. Enhancement factor β and concentration of sulfite inside the drops profiles.

used, and the equilibrium in all drops is the same. (ii) Multilevel spray systems were replaced by one spray system, and average height of the absorption section was used; the average height was determined from all levels of a spray system. Both simplifications do not influence the rate of SO2 absorption. The desulfurization efficiency increased by 0.6% when the first simplification was used. For the second simplification, a maximum change of the desulfurization efficiency equals 2%, but if the drop diameter was increased by 1%, the difference equaled 0.10.6%. The model does not describe coalescence of the drops. The rate of this process grows with an increase of the L/G ratio and so the influence of simplifications on model results will be stronger. An average height of the absorption section is useful in the optimization calculation. The application of this parameter reduces the number of variable parameters, and only one parameter, i.e., the average height of the absorption section, could be used instead of the absorption section height and the number of spray system levels. Distribution of Process Parameters with the Height of the Absorption Section Several calculations of process parameter distributions with the height of the absorption section have been made. Calculation was made for the following values of parameters: pH, 5.5; drop diameter, 2900 µm; chloride and sulfite concentration in the slurry, 0.1 kmol/m3 and 0.2 mol/m3; inlet SO2 concentration, 1000 ppm; inlet HCl concentration, 200 mg/Nm3; limestone concentration in the slurry, 1.0 kg/m3; and countercurrent flux. Mass-transfer resistance on the gas side is high on the top of an absorber where the partial pressure of SO2 is low. The resistance on the gas side decreases on the bottom of the absorption section to the value of 20%. The enhancement factor β profile is shown in Figure 3. Values of β are high on the top of an absorber and quickly decrease together with the height of the absorption section. The concentration of sulfite and the pH of the slurry influence the value of the enhancement factor. In Figure 3, profile of the sulfite concentration is shown. Figure 4 shows distribution of the SO2 absorption flux and the pH of the slurry as a function of the absorption height. Flux of the sulfur dioxide absorption attains a maximum value on the height of the absorption section equal to 6-7 m. The reason for the flux distribution is a rise of the mass transport driving force in the gas phase and a decrease of the force in the liquid phase. The pH decreases very quickly in the top part of an absorber, while in the bottom part the drop is considerably slower and pH stays about constant. The gas-side

Figure 4. Flux of SO2 absorption and pH slurry profiles.

Figure 5. Gas-phase-side resistance to mass transfer and partial pressure of SO2 profiles.

mass-transfer resistance and partial pressure of SO2 is shown in Figure 5. The shape of the parameter profiles changed for different inlet conditions, and the presented distribution of parameter values can be taken as an example. Conclusions The process model describes in detail the processes running in absorption systems. The results of this model agree with data from the installed FGD plant, and only one model calibrating parameter (drop diameter) is good enough. The analyses showed that all processes, which ran in an absorber and a holding tank, influenced the rate of SO2 absorption. The process model could be used to calculate the desulfurization efficiency and the rate of HCl absorption for different values of process parameters. The cost model of the FGD system along with the process model was used in order to determine optimum values of decision variables for different conditions of the running FGD system. List of Symbols App ) area of the cross section, m2 a ) specific surface area, m2/m3 D ) diffusivity, m2/s d ) diameter, m F(ds,i) ) cumulative mass fraction of the product, the size of which is smaller than di f ) degree of limestone conversion fo ) frequency of drop oscillation,1/s g ) acceleration of gravity, m2/s H ) Henry’s constant, kPa‚m3/kmol Hox ) height of liquid aeration, m hdc ) height of the inlet duct to the absorber, m J ) absorption rate, kmol/s‚m2 Kg ) mass-transfer coefficient, kmol/(m2‚s‚kPa) Ks ) thermodynamic equilibrium constant, kmol2/m6 kg ) gas-side mass-transfer coefficient, kmol/(m2‚s‚kPa)

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kgp ) rate constant of gypsum crystallization, kmol/(m2‚s) kl ) liquid-side mass-transfer coefficient, m/s kox ) rate constant of sulfite oxidation, m3/(kmol‚s) L* ) characteristic diameter, eq 13, m Mi ) molar weight of component i, kg/kmol Ms ) amount of limestone leaving a reaction tank, kg/s Msin ) amount of limestone added to a reaction tank, kg/s m ) drop mass, kg n ) distribution modulus P ) overall pressure, kPa ps ) partial pressure of SO2, kPa R ) constant, kJ/kg‚K RO2 ) flux of O2, kmol/s Re ) Reynolds number Rgp ) rate of gypsum crystallization, kmol/m3‚s Rs ) relative saturation RSO2 ) flux of SO2, kmol/s r ) distance from the center of the limestone particle, m Sc ) Schmidt number Sh ) Sherwood number SIV ) sulfites t ) time, s Uox ) superficial gas-phase velocity in a holding tank, m/s ug ) gas velocity in the absorber, m/s uk ) drop velocity in the relation apparatus, m/s V˙ g,j ) flux of the gas into the absorber below a height of zj, m3/s / V˙ g,j ) flux of the gas into the absorber between a height of inlet duct zj and zj-1, m3/s V˙ 1 ) liquid flux, m3/h z ) charge or height of the actual calculation, m [k] ) concentration of component k, kmol/m3 Greek Letters R ) correction factor, eq 11 β ) enhancement factor ∆z ) height of a layer, m δs ) film thickness, m g ) gas holdup µ ) dynamic viscosity, Pa‚s ν ) kinematic viscosity, m2/s Fi ) density of component i, kg/m3 Fm ) molar density, kmol/m3 σ ) surface of tension, N/m τ ) average slurry residence time, s Subscripts ab ) absorber an ) anions b ) bubbles cat ) cations d ) drops dc ) inlet duck of gas to absorber g ) gas phase gp ) gypsum ht ) holding tank j ) jth layer k ) component k l ) liquid phase ox ) oxidation of sulfite s ) particle of limestone Superscripts i ) ith spray level or the ith fraction of limestone in ) corresponding to the limestone feed ° ) inside the liquid phase / ) equilibrium on the gas-liquid interface

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Received for review June 13, 2000 Accepted November 17, 2000 IE0005708