Experimental Investigation and Modeling of a Wet Flue Gas


A detailed model for a wet flue gas desulfurization (FGD) pilot plant, based on the packed tower concept, has been developed. All important rate-deter...
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Ind. Eng. Chem. Res. 1998, 37, 2792-2806

Experimental Investigation and Modeling of a Wet Flue Gas Desulfurization Pilot Plant Søren Kiil, Michael L. Michelsen, and Kim Dam-Johansen* Department of Chemical Engineering, Technical University of Denmark, Building 229, DK-2800 Lyngby, Denmark

A detailed model for a wet flue gas desulfurization (FGD) pilot plant, based on the packed tower concept, has been developed. All important rate-determining steps, absorption of SO2, oxidation of HSO3-, dissolution of limestone, and crystallization of gypsum were included. Population balance equations, governing the description of particle size distributions of limestone in the plant, were derived. Model predictions were compared to experimental data such as gas-phase concentration profiles of SO2, slurry pH profiles, solids content of the slurry, liquid-phase concentrations, and residual limestone in the gypsum. Simulations were found to match experimental data for the two limestone types investigated. A parameter study of the model was conducted with the purpose of validating assumptions and extracting information on wet FGD systems. The modeling tools developed may be applicable to other wet FGD plants. Introduction Sulfur dioxide (SO2) is evolved from coal-fired combustion through oxidation of sulfur (S) contained in the fuel. The SO2 has a number of hazards to human health and contributes to the formation of acid rain. Consequently, many countries have imposed strict regulations on coal-fired power plants. This has, since the beginning of the 1970s, created a market for SO2-reducing technologies, of which many types are presently available (Takeshita and Soud, 1993). The dominating flue gas desulfurization (FGD) technology, however, is absorption of SO2 in a limestone slurry, known as wet scrubbing. A number of different types of wet scrubbers have been developed in the past 20 years. Common examples include spray scrubbers, packed towers, jet bubbling reactors, and double-loop towers (Takeshita and Soud, 1993). The most commonly used and best studied wet scrubber is the countercurrent spray scrubber employing liquid distribution at different levels in the absorber. Simulations of complete wet FGD spray scrubber systems have been conducted by Gage (1989) and by Agarwal and Rochelle (1993). Their models used, among other parameters, a fixed limestone feed flow rate and slurry solids concentration as model inputs. The model contained submodels for the individual rate-determining steps, and some of these were empirical and others of a more fundamental nature. The Electric Power Research Institute (EPRI) (Harries, 1993; Noblett et al., 1993) has developed a commercial simulation model (FGDPRISM) which can be used as a design tool and to evaluate laboratory and pilot-scale data for a spray scrubber and changes to an existing full-scale system. Olausson et al. (1993) developed a detailed, yet sufficiently simple, model for a spray scrubber to allow a low computation time. They included most of the rate-determining steps and used the liquid film thickness as a fitting parameter to match simulations and experimental data taken from the literature. Gerbec et al. (1995) developed a transient * Corresponding author. Telephone: 45 45 25 28 45. Fax: 45-45882258. E-mail: [email protected]

Figure 1. Schematic illustration of a full-scale wet FGD packed tower employing co-current gas-slurry contacting.

model of absorption of SO2 into droplets of slurry in a spray scrubber. They included internal mixing in the droplets and were able to predict pilot-plant data. Limestone dissolution and sulfite oxidation were modeled using empirical relationships based on pilot-plant data. Recently, Brogren and Karlsson (1997b) modeled the transient absorption of SO2 into a single droplet of limestone slurry in a spray scrubber including all ratedetermining steps. Their work showed that the rate of absorption of SO2 in this absorber type to a large extent is liquid-side mass-transfer-controlled. However, their model predictions, which included a number of adjustable parameters such as mass-transfer coefficients and the enhancement factor of O2 absorption, were not verified against experimental data. Wet FGD scrubbers, different from the spray type, have not received as much attention in the literature. One of these is the packed tower absorber using plastic grid packing. This type of absorber, shown schematically in Figure 1, was developed by Mitsubishi Heavy Industries (Muramatsu et al., 1984; Takeshita and Soud, 1993) and has been installed at oil- or coal-fired power plants in many

S0888-5885(97)00944-5 CCC: $15.00 © 1998 American Chemical Society Published on Web 05/27/1998

Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998 2793

Figure 2. Schematic illustration of wet FGD chemistry and mass-transport phenomena in plants using forced oxidation mode.

countries. It usually employs cocurrent gas-liquid contacting, giving rise to a low flue gas pressure drop. By distributing the whole amount of circulating slurry evenly from the upper part of the absorber, the packed grid in the lower section is completely wetted and sufficient slurry holdup is secured. In the compact grid packing, a high SO2-removal performance is attained by effective gas-liquid contacting. The byproduct is high-grade gypsum. The objective of the present work was to develop a detailed reactor model for a wet FGD pilot plant based on the packed tower concept. The model takes into account all important rate-determining steps as well as population balance equations for the limestone particles and is verified against a large volume of experimental data. Outline of Wet FGD Chemistry and Mass Transport Phenomena Wet FGD plants employing an in situ forced oxidation mode are three-phase reactors with process efficiencies dependent on up to four rate-determining steps. These are absorption of SO2, oxidation of HSO3-, dissolution of limestone, and crystallization of gypsum, all of which are shown schematically in Figure 2. The overall reaction can be written as

CaCO3(s) + SO2(g) + 1/2O2(g) + 2H2O(l) f CaSO4‚2H2O(s) + CO2(g) (1) Absorption of SO2 may be influenced by gas- and liquid-phase mass transport. When SO2 is absorbed in aqueous solutions, reactions I and II in Figure 2 are at equilibrium throughout the liquid phase. These two instantaneous, reversible reactions enhance the liquidphase mass transport of SO2 by allowing transport of SO2(aq) in the forms of HSO3- and SO32-. The HSO3ions produced may be oxidized to SO42- ions, reaction III, provided sufficient O2(aq) is present. The latter is absorbed from the flue gas in the absorber and from air injected in the holding tank. Depending on the process conditions, the reaction rate may be O2 liquid-phase mass transport and/or reaction controlled. H+ ions, produced from the absorption of SO2 and oxidation of HSO3-, react with the limestone particles, thereby producing Ca2+ ions. The dissolution process is masstransfer-controlled with participation of various ions present in the liquid bulk. The dissociation of CO2, reaction V, has a finite rate (Wallin and Bjerle, 1989).

Figure 3. Schematic illustration of the wet FGD pilot plant based on the falling film principle.

In our model development we assumed, due to its slowness, that the reaction takes place in the liquid bulk only. The forward rate of reaction is given by

Rf,CO2 ) kCO2[CO2] and the reverse by

Rr,CO2 )

( ) kCO2

KCO2

[HCO3-][H+]

(2)

(3)

The Ca2+ ions produced react with SO42- ions, according to reaction VIII, and crystallize as gypsum (CaSO4‚ 2H2O). Experimental Setup Wet FGD Pilot Plant. The main components of the experimental setup are the falling film column (absorber), the holding tank, and the natural gas burner (Figure 3). All pipes and vessels are made of PVC, glass, or stainless steel coated with nylon. The absorber simulates a single vertical channel of the tower packings (grid) used in full-scale wet FGD plants based on the falling film principle (Figure 1). The column is a vertical, transparent PVC tube, 5 m in length (compa-

2794 Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998 Table 1. Chemical Analyses of the Limestones Used in the Wet FGD Experiments BET area (m2/g) CaCO3 (wt %) MgCO3 (wt %) SiO2 (wt %) Al2O3 (wt %) Fe2O3 (wt %) MnO (wt %) K2O (wt %) P2O5 (wt %) S (wt %) moisture (wt %) residual (wt %)

Faxe Bryozo

Mikrovit (chalk)

0.687 96.9 1.2 0.8 0.15 0.08 0.02

2.2 97.9 0.7 0.4 0.1 0.04 0.01 0.04 0.12 0.03 0.05 0.61

0.04 0.08 0.73

rable to full-scale grid height) and with an inner diameter of 3.3 cm. The inlet and outlet sections of a full-scale plant are not included in the setup, leading to lower rates of SO2 removal than observed in full-scale. The holding tank is made of PVC and has a volume of 110 L, of which up to about 40 L can be slurry. The tank is equipped with four baffles, a stirrer, a bottom air inlet in the center of the tank, and a flow loop allowing measurements of temperature and pH and withdrawal of slurry samples. The feed gas is supplied from the burner. The gas mixture enters the heat exchanger, where it is preheated or cooled to the desired temperature and saturated with water. To simulate a coal gas, SO2 is added to the saturated natural flue gas just before it enters the absorber. The absorption of SO2 takes place primarily in the absorber. Slurry and flue gas flow from the absorber into the holding tank. Here, air is supplied for oxidation of HSO3- and the purified flue gas is led from the holding tank to the stack. Most of the slurry from the holding tank is recycled to the top of the absorber via the film distributor which ensures the formation of a more or less uniform falling film. The film distributor is made of glass and has an inner diameter of 10 cm (for details, see Nielsen et al., 1998). The pH of the holding tank is on/off controlled at a fixed level (typically 5.5) by addition of limestone slurry (limestone in distilled water). Finally, some slurry (water with gypsum containing residual limestone) is removed as a product. Probes. Gas samples can be withdrawn through probes (for details, see Nielsen et al., 1998) and analyzed (SO2, CO2, and O2) on-line at six positions in the column tube (1/2, 1, 2, 3, 4, and 5 m from the column top) and at the gas inlet and outlet. In the absorber, the pH of the slurry can be measured at positions 1/2, 1, 2, 3, and 4 m by means of a thin, pencil-shaped pH probe inserted directly into the slurry through holes with diameters of 1.4 cm. Analyses. Concentrations of Ca2+, Mg2+, and SO42in slurry samples, withdrawn from the holding tank and filtrated, were measured by ion chromatography. The amounts of residual limestone in gypsum samples from the holding tank were determined by TGA analysis. Finally, the solid contents (gypsum with residual limestone) of the holding tank samples were determined by evaporation (40 °C) and subsequent weighing. Particle size distributions (PSD) of limestone and gypsum were measured on a Malvern analyzer (laser diffraction) using as dispersants tap water (additive to avoid agglomeration: Na4P2O7‚10H2O) and ethanol, respectively. Chemical compositions of the two limestones used are given in Table 1.

Mathematical Modeling The mathematical wet FGD model of the pilot plant in Figure 3 is comprised of submodels for the four ratedetermining steps and an overall reactor model. Ideal solutions are assumed, and the following species are considered in the model: SO2(g and aq), HSO3-, SO32-, HSO4-, SO42-, CO2(g and aq), HCO3-, CO32-, Ca2+, CaCO3(s), Mg2+, Mn2+, O2(g and aq), CaSO4‚2H2O(s), H+, and OH-. Absorption of CO2, O2, and SO2 (Gas-Liquid Mass Transport). (a) Absorber. The gas-liquid mass transport of CO2 and O2 can, due to the relatively low solubilities of these species, be considered liquidphase mass-transport-controlled (Levenspiel, 1993). The rate of absorption is given by

NB )

EBkL,B°aA(pB/HB - [B]o) fL

(4)

where B ) CO2 or O2. As mentioned earlier, the dissociation rate for CO2 in water is slow and the enhancement factor for CO2 is taken to be 1. Some oxidation of HSO3- may take place in the liquid film but is assumed here to take place entirely in the liquid bulk (i.e., an enhancement factor of unity for O2). This is a reasonable approximation, as will be shown later. The mass transfer of SO2 from the bulk gas to the bulk liquid phase can be written as

NSO2 )

KG,SO2aA(pSO2 - HSO2[SO2]o) fL

(5)

where

1 KG,SO2

)

1 kG,SO2

+

HSO2 ESO2kL,SO2°

(6)

The enhancement factor for SO2 can be expressed as (Kiil, 1998) ESO2 ) 1 + DL,HSO3-([HSO3-]i - [HSO3-]o) + DL,SO32-([SO32-]i - [SO32-]o) DL,SO2([SO2]i - [SO2]o)

(7) The interfacial concentrations are determined from a balance on local charge

DL,H+∇x2[H+] - DL,HSO3-∇x2[HSO3-] 2DL,SO32-∇x2[SO32-] - DL,OH-∇x2[OH-] ) 0 (8) with boundary conditions given by known bulk phase concentrations and interfacial partial pressure of SO2 and by a condition of zero charge flux at the gas-liquid interface. The interfacial partial pressure of SO2 is determined from a mass balance over the interface

kG,SO2(pSO2 - pSO2,i) - ESO2kL,SO2°([SO2]i - [SO2]o) ) 0 (9) where

pSO2,i ) HSO2[SO2]i

(10)

Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998 2795

The above submodel for SO2 mass transport is solved iteratively, at any position in the absorber, using the equilibria I, II, and VII. (b) Holding Tank. Here, air is injected, leading to absorption of O2 and desorption of CO2. The rate of absorption is given by

NB ) EBkL,B°aT(pB/HB - [B]o)

(11)

where B ) CO2 or O2. It was found experimentally that some SO2 (typically 10-15% of the total SO2 removal) is absorbed in the holding tank when the flue gas passes from the outlet of the absorber to the stack (see Figure 3). The rate of absorption is empirically assumed to follow

NSO2 ) KG,SO2aT(pSO2 - HSO2[SO2]o)

(12)

where KGaT is an adjustable parameter, the significance of which is discussed in a later paragraph. Oxidation of Sulfite. (a) Kinetics. The rate of oxidation of HSO3- and SO32- in the presence of a catalyst (typically transition metals) has been studied by several authors (Linek and Vacek, 1981; Lancia et al., 1996), but the kinetics are still in dispute. This is due mainly to the extreme sensitivity of the reactions with respect to the experimental conditions. However, the following rate equation appears to be the most common in use for Mn2+-catalyzed oxidation of HSO3at pH values of 4.5-5.5 (where the concentration of SO32- is negligible)

-rHSO3- ) Rox ) kox[HSO3-]3/2[Mn2+]1/2[O2]

(13)

though some authors have found a zero-order dependency of the rate with respect to the concentration of O2(aq). Hjuler and Dam-Johansen (1994) found the concentration dependency of the rate with respect to O2(aq), using Mn2+ as catalyst, to be close to unity. The wet FGD model was tested and found practically insensitive to the reaction order (zero or unity) of O2(aq), and a reaction order of one was chosen. The Mn2+ ions originate from MnO (treated here as MnCO3) impurities in the limestone (see Table 1). Metals other than Mn2+, such as Co+, Fe3+, and Cu2+, may catalyze the rate of oxidation (Linek and Vacek, 1981). However, these ions precipitate rapidly with the gypsum (Clarke, 1993) and are therefore assumed not to influence the rate of oxidation. (b) Absorber. In the absorber, the rate of oxidation of HSO3- can be mass transport and/or reaction controlled depending on the process conditions. The local concentrations of O2(aq) and Mn2+ are determined from differential mass balances with inlet values given by the holding tank values (Kiil, 1998). (c) Holding Tank. Here, air is injected to obtain complete oxidation of HSO3-. The concentrations of O2(aq) and Mn2+ are calculated from the overall mass balances. Dissolution of Limestone. (a) Particle Model. An aqueous slurry of limestone particles is fed directly into the holding tank in order to maintain a constant pH. The particles subsequently dissolve in the holding tank as well as in the absorber. Modeling of this dissolution process is essential for a good description of a wet FGD plant. In the past 20 years, a number of dissolution mechanisms and models, some of which are

referenced by Brogren and Karlsson (1997a), have been published. However, the more recent mass-transfer models (e.g. Wallin and Bjerle, 1989; Lancia et al., 1991; Gage and Rochelle, 1992) appear to give the best descriptions. Thus, we have based the dissolution model of this work on such a model. The rate of dissolution of a spherical limestone particle of radius rj (assuming it dissolves according to a shrinking particle model) is given in terms of the rate of mass transfer of Ca2+ ions from the particle surface to the liquid bulk

JCa2+j ) -DL,Ca2+ × 4πrj2∇rj[Ca2+]|rj

(14)

The spatial concentration gradient of Ca2+ ions over the solid-liquid film is determined from a differential mass balance for Ca2+, leading, under the assumption of a stagnant medium (i.e., δj f ∞), to

JCa2+j ) DL,Ca2+ × 4πrj([Ca2+]s - [Ca2+]o)

(15)

The surface concentration of Ca2+ is determined from a mass-transfer model (Kiil, 1998) using total component mass balances (Olander, 1960), the equilibria I, II, IV, VI, and VII, and the solubility product of CaCO3. Reaction V is, due to its slow reaction rate (Brogren and Karlsson, 1997b), omitted, and electric potential gradients in the liquid are neglected. It is worth mentioning that the solution to the mass-transfer model is particle size independent so that the equations need only be solved once for given bulk phase concentrations. Furthermore, the rate of dissolution, J j, needs only to be calculated for one particle size because J j/rj is independent of particle size. Population Balance Equations (PBE) for Limestone Particles. In both the absorber and holding tank, limestone particles dissolve when SO2 is absorbed. The dissolution process is mass-transport-controlled, and the particles shrink at a size-dependent rate. Thus, a reactor model for a wet FGD plant must include population balance equations (PBE) for the limestone particles in order to calculate the local dissolution rate given by

RCaCO3 )

∑j JCa

2+

j

Nj

(16)

where Nj is the number of particles of size dj per unit liquid volume. MgCO3, which is the major impurity (1 wt %) in CaCO3, is assumed to dissolve at the same rate as CaCO3, yielding

RMgCO3 ) θMgCO3RCaCO3

(17)

and similarly with MnO (treated as MnCO3)

RMnCO3 ) θMnCO3RMnCO3

(18)

(a) Absorber. It is assumed that limestone particles do not dissolve in the liquid film but only in the liquid bulk of the slurry liquid film. The rate of change of the PSD of limestone in the absorber can, in the case of a stagnant medium surrounding the particles (i.e., ShLS ) 2), be determined in a simple way using the concept of a cumulative concentration transform (Del Borghi et al., 1976). Consider a single spherical limestone particle of size dj. The rate of dissolution can, using eq 15, be written as

2796 Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998

fCaCO3(1 - CaCO3)FCaCO3(1/2πdj2)(-∇tdj) MCaCO3

) DL,Ca2+ ×

2πdj([Ca2+]s - [Ca2+]o) (19) which is rearranged to

∇tdj )

-4DL,Ca2+MCaCO3 FCaCO3(1 - CaCO3)dj fCaCO3

([Ca2+]s - [Ca2+]o) (20)

Rgypsum ) kgypsum(RSgypsum - 1)

(21)

where RSgypsum is the relative saturation of gypsum given by

with initial condition

t ) 0 (or z ) 0):

dj ) djo

Integration of eq 20 yields, in terms of dimensionless position z in the absorber

dj2 ) djo2 -

8DL,Ca2+τAMCaCO3 FCaCO3(1 - CaCO3)fCaCO3

λ

(22)

where the cumulative concentration transform, λ, is given by

λ)

∫0z([Ca2+]s - [Ca2+]0) dz

(23)

Thus, the current size of any limestone particle can be determined from eq 22 provided the local value of λ is known. λ is determined from eq 24 which is derived by differentiation of eq 23

dλ ) ([Ca2+]s - [Ca2+]0) dz

λ)0

(25)

accumulation ) input - output + net generation (26) or

(30)

The gypsum crystallization rate constant, kgypsum, was determined from experimental data. A consequence of using this simple, empirical model is that the amount of gypsum only and not the PSD can be predicted. However, detailed nucleation and growth rate kinetics, presently not available, would be needed for a more elaborate description. Knowledge of the PSD of gypsum may be important for the prediction of dewatering properties of a given gypsum product, but that topic was not considered in this work. Olausson et al. (1993) and Agarwal and Rochelle (1993) also used empirical relationships in their models for the prediction of the rate of crystallization.

The reactor model for the wet FGD pilot plant is a steady-state model comprised of a plug-flow reactor (the absorber) and a well-mixed reactor (the holding tank) combined through a recycle stream from the outlet of the tank to the inlet of the absorber (see Figure 3). Liquid volumes in the absorber and the holding tank were taken, due to low volume concentrations of solids, as the slurry volumes. Absorber. The differential component mass balances for the absorber are all of the general form

d[i]

( ) ( ) ()

R h jNj Qin QF Qo dNj + NjF Nj + ) Njin dt VT VT VT Vj - Vj-1 R h j+1Nj+1 (27) Vj+1 - Vj where the two generation terms account for particles of the current size, dj, dissolving to size dj-1 and larger particles of size dj+1 dissolving to size dj, respectively. For the largest particle size, Nj+1 ) 0, and for the smallest, Vj-1 ) 0. The particle diameters at the outlet of the absorber were rescaled on a volumetric basis to match the holding tank particle discretization. The number of particles of size dj per unit liquid volume in the feed stream, NjF, is calculated from

wjFH2OwCaCO3

[Ca2+][SO42-] Lgypsum

Reactor Model

(b) Holding Tank. The holding tank is modeled as a well-mixed reactor. The conservation equation based on the number of limestone particles for the holding tank looks like

NjF )

RSgypsum )

(29)

(24)

with initial condition

z ) 0:

The weight fraction of particles of size dj for the particular limestone sample used as sorbent, wj, was obtained from PSD measurements. The model required discretization with respect to 40-60 particle classes (equal weight fractions in each class), depending on the process conditions, for convergence of output variables, such as the steady-state PSD, to be established. Crystallization of Gypsum. We model the rate of crystallization of gypsum by the empirical expression

F F

FCaCO3(1 - CaCO3)Vj(1 - wCaCO3 )

(28)

dz

) τA



Rl

(31)

l)reac.

with the inlet condition given by the holding tank value. The following total component mass balances (Olander, 1960) were used in the calculation of the spatial derivatives.

Balance for sulfurous species d ([SO2] + [HSO3-] + [SO32-] + [SO42-] + dz [HSO4-]) ) τA(NSO2 - Rgypsum) (32) Balance for SO2, HSO3-, and SO32d ([SO2] + [HSO3-] + [SO32-]) ) τA(NSO2 - Rox) dz (33)

Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998 2797

Balance for carbon species, Ca2+, Mg2+, and Mn2+

Transient balance for sulfurous species

d ([CO2] + [HCO3-] + [CO32-] - [Ca2+] - [Mg2+] dz [Mn2+]) ) τA(NCO2 + Rgypsum) (34)

d ([SO2]o + [HSO3-]o + [SO32-]o + [SO42-]o + dt [HSO4-]o) ) THSO3- + TSO2 + TSO32- + TSO42- + THSO4- + NSO2 - Rgypsum (43)

Balance for all ions

Balance for SO2, HSO3-, and SO32- species

d ([H+] + 2[Ca2+] + 2[Mg2+] + 2[Mn2+] dz [HSO3-] - 2[SO32-] - [HSO4-] - 2[SO42-] [HCO3-]

-

2[CO32-]

-

- [OH ]) ) 0 (35)

Balance for sulfate and carbon species d ([CO2] + [HCO3-] + [CO32-] + [SO42-] + dz [HSO4-]) ) τA(NCO2 - Rgypsum + Rox + RCaCO3 + RMgCO3 + RMnCO3) (36) For CO2 one has

Balance for carbon species, Ca2+, Mg2+, and Mn2+ d ([CO2]o + [HCO3-]o + [CO32-]o - [Ca2+]o dt [Mg2+]o - [Mn2+]o) ) THCO3- + TCO2 + TCO32- TCa2+ - TMg2+ - TMn2+ + NCO2 + Rgypsum (45) Total component balance for ions

d[CO2] ) τA(Rr,CO2 - Rf,CO2 + NCO2) dz

(37)

and for Mg2+

d[Mg2+] ) τARMgCO3 dz

(38)

Five additional equations in terms of the unknown spatial derivatives are supplied by spatial differentiation of the equilibria I, II, IV, VI, and VII. Initial conditions are given in terms of known inlet (holding tank) concentrations. The above system of equations is solved with respect to the spatial derivatives, and these are subsequently used in the plug-flow component mass balances to solve the absorber model. Furthermore, for the gas phase a differential mass balance yields

( )

(39)

yB ) yB,i

(40)

NBL dyB ) -τA dz G

z ) 0:

where B ) SO2(g), CO2(g), or O2(g). The concentration of gypsum is determined from a differential mass balance with the initial condition given by the holding tank value. Holding Tank. The general transient mass balance equation for a well-mixed reactor is given by

d[i]o dt

) Ti +



Rl

(41)

l)reac.

where

1 (Q [i] + QF[i]F - Qo[i]o) VT in in

d ([H+]o + 2[Ca2+]o + 2[Mg2+]o + 2[Mn2+]o dt [HSO3-]o - 2[SO32-]o - [HSO4-]o - 2[SO42-]o [HCO3-]o - 2[CO32-]o - [OH-]o) ) TH+ + 2TCa2+ + 2TMg2+ + 2TMn2+ - THSO3- - 2TSO32- - THSO4- 2TSO42- - THCO3- - 2TCO32- - TOH- (46) Balance for sulfate and carbon species d ([CO2]o + [HCO3-]o + [CO32-]o + [SO42-]o + dt [HSO4-]o) ) TSO42- + THSO4- + TCO2 + THCO3- + TCO32- + (NCO2 - Rgypsum + Rox + RCaCO3 + RMgCO3 + RMnCO3) (47) For CO2 one has

d[CO2]o ) TCO2 + (Rr,CO2 - Rf,CO2 + NCO2) (48) dt

with initial condition

Ti )

d ([SO2]o + [HSO3-]o + [SO32-]o) ) THSO3- + TSO2 + dt TSO32- + NSO2 - Rox (44)

(42)

Also for this reactor, total component mass balances are used.

and for Mg2+

d[Mg2+]o ) TMg2+ + RMgCO3 dt

(49)

d[Mn2+]o ) TMn2+ + RMnCO3 dt

(50)

and Mn2+

Also for this reactor, five additional equations in the unknown temporal derivatives are supplied by differentiation of equilibria I, II, IV, VI, and VII. The gasphase concentration of CO2 in the air stream, after injection, is calculated from a gas-phase mass balance for CO2 over the holding tank. The air stream is subsequently mixed with the purified flue gas upon leaving the holding tank. The outlet SO2 concentration in the purified flue gas is found from a mass balance

2798 Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998

over the gas phase. The liquid-phase concentrations in the limestone feed stream were taken as those calculated for a saturated solution of CaCO3 in distilled water. The gypsum concentration is calculated from a steady-state balance over the holding tank, and an overall mass balance for water is also included. Solution Procedure. The steady-state absorber equations were solved by the integration routine SIRUKE of Villadsen and Michelsen (1978). The steady-state solution to the holding tank equations is found by the method of false transients. Finally, the steady-state solution to the complete (absorber and holding tank combined) model is found by adjusting the limestone feed flow rate after each recycle loop so as to match a fixed specified holding tank pH using PI-control expressed by

QF ) Qset + KP(pHset - pHT) + KPKI



(pHset - pHT) (51)

recycles

The calculations were terminated when the relative error in the overall atom balances for Ca, S, and H were less than 0.1%. The computation time, at typical process conditions (i.e., L ) 4.9 L/min and yi ) 1000 ppmv), was about 45 min (2500 recycles) on a Pentium 166-MHz PC. Low inlet gas-phase concentrations of SO2 and/or high recycle flow rates required longer computation times. The computation time is largely determined by the time required to reach a steady-state distribution of the limestone particles. Estimation of Model Parameters The wet FGD model requires a number of physical and chemical constants. These were taken from various literature sources and are available as Supporting Information. Equilibrium constants for reactions I, II, and IV-VII and the solubility product of gypsum were taken from Brewer et al. (1982). Liquid-phase diffusion coefficients were taken from Gage (1989) and extrapolated to other temperatures using the Stokes-Einstein relation (Gage, 1989). Gas-phase diffusion coefficients were calculated from Reid et al. (1987). Henry’s constants for SO2, CO2, and O2 were found in Wilhelm et al. (1977), and the solubility product of limestone was taken from Plummer and Busenberg (1982) as recommended by Gal et al. (1996). Dimensionless correlations for the gas-phase and physical liquid-phase mass transport coefficients of the absorber (falling film column) were determined in our earlier work (Nielsen et al., 1998). Volumetric gas-liquid mass transport coefficients for O2 and CO2 in the holding tank were calculated by the correlation of Yagi and Yoshida (1975). The effect of limestone and gypsum particles on the gas-liquid-phase mass transport coefficients was assumed to be negligible. No correlation was available for the overall volumetric mass transport coefficient of SO2 from the flue gas to the slurry in the holding tank. However, a universal value which could be used in all simulations was determined to 8 mol/(m3‚s‚atm) by adjusting this parameter so that holding tank simulations matched the experimental outlet concentration of SO2 (i.e., the value measured in the stack). The value of the holding tank gas-liquid mass transport coefficient only has a negligible influence on the simulated rate of absorption in the absorber. The reason for this

Table 2. Input (Process) Parameters to the Wet FGD Model and Pilot Plant (Base Case) parameter flue gas flow rate (L/min (STP)) inlet flue gas concentration of SO2 (ppmv) inlet flue gas concentration of CO2 (vol %) inlet flue gas concentration of O2 (vol %) height of the absorber (m) inner diameter of the absorber (m) limestone content of feed stream (wt %) temperature (K) slurry recycle flow rate (L/min) air flow rate to the holding tank (L/min (STP)) slurry volume in the holding tank (L) stirrer speed in the tank (s-1) diameter of the holding tank (m) pressure in the plant (atm) diameter of the impeller in the holding tank (m) holding tank pH porosity of limestone limestone type (PSD and chemical analysis) proportional control gain (model only) integral control gain (model only) setpoint flow rate for the PI controller (L/h) (model only)

315 1014 9.3 4.8 5 0.033 8.1 327 4.9 12.8 30 7 0.4 1 0.25 5.5 0.0 Faxe Bryozo 0.2 0.2 0.6

is that the pH of the slurry being recycled from the holding tank to the absorber inlet is fixed and so the slurry composition is practically unaffected by an increased absorption in the holding tank. The only outputs affected by the adjustable parameter are the limestone feed flow rate to the holding tank and the gypsum production rate. The physical liquid film thickness, δA, in the falling film column (absorber) was calculated from the correlation of Feind (1960), assuming this correlation to be valid for slurry flow. Liquid viscosities and densities were taken from DIPPR Tables (1983). The rate constant and activation energy for reaction V was taken from Wallin and Bjerle (1989). It was not possible to find a reliable rate constant for reaction III, but experimentally no HSO3- could be detected, suggesting that the reaction is very fast. Simulations were found to be insensitive to the value of the rate constant for kox > 2000 (m3/mol)2‚s-1, and therefore an accurate value was not needed. Computing time was only somewhat sensitive to the value of kox. The gypsum rate constant and the porosity of limestone are discussed in the Results and Discussion section. Results and Discussion To verify the wet FGD model, five experimental series were conducted in the pilot plant. The first involved using pure water as the absorbent and no recycle of the liquid phase. The second, referred to in the following as Base Case, was a complete wet FGD experiment with parameters as specified in Table 2. The last three experiments involved perturbations from Base Case with respect to three important parameters: slurry recycle flow rate (increased from 4.9 to 9.1 L/min), inlet gas-phase concentration of SO2 (reduced from 1000 to 200 ppmv), and limestone type (a chalk, Mikrovit, was used in place of Faxe Bryozo limestone). Other parameters in Table 2, such as flue gas flow rate and gasphase concentrations, deviate a few percentages among experiments. It should be noticed in Table 2 that the pH of the holding tank is a model input. This is due to the fact that the pH of the holding tank is maintained at a fixed value by PI control. Thus, the limestone feed flow rate is calculated as part of the model solution. This approach has not been used in earlier models but is a

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Figure 4. Simulations (lines) and experimental data (symbols) of absorption of SO2 in distilled (304 K) and tap (323 K, 19° dH ) 190 mg of CaO/L) water (no recycle). L ) 4.5 L/min. Flue gas flows are 315 L/min (STP) for yi ) 1000 ppmv and 272 L/min (STP) for yi ) 200 ppmv, respectively.

necessary step toward simulation of FGD plants where holding tank pH is indeed maintained at a specified value by control of the limestone feed flow rate. Degree of Desulfurization. In Figure 4 are shown two cases of absorption of SO2 in distilled water (304 K, no recycle). Good agreement is seen between experimental and predicted degrees of desulfurization. In this experiment, the only rate-determining step is the gasliquid-phase mass transport of SO2. Thus, the results of Figure 4 confirm that our submodel for the enhancement factor of SO2 is satisfactory. The pH profile in the absorber (not shown) was also predicted very well. Experimental results from absorption of SO2 in tap water (323 K, no recycle, 19° dH ) 190 mg of CaO/L) are also shown in this figure. In this case, the HCO3-/ CO32- buffer, present in natural waters in east Denmark, completely counteracts the pH drop in the absorber, making the absorption gas film controlled with a resulting high removal rate of SO2. Results of wet FGD pilot-plant studies are shown in Figure 5. Here, experimental data and simulations of Base Case and L ) 9.1 L/min are compared. The model predicts the experimental data very well. Increased absorption is seen when the recycle flow rate is increased. This is due to two effects: larger gas-liquid mass-transfer coefficients and shorter slurry residence time. The latter results in more sorbent capacity available in the absorber and thereby a smaller pH drop. For the sake of comparison, model predictions of absorption of SO2 in distilled water (no recycle) and in dilute NaOH (entirely gas-phase mass-transport-controlled) are also shown. One may notice the expected increased removal rate of SO2 in wet FGD and NaOH systems compared to distilled water. In Figure 6 are shown results for yi ) 200 ppmv and Mikrovit. Small deviations are seen between experimental data and simulations, but the agreements seem satisfactory considering the system complexity. The effect of lowering the inlet gas-phase concentration of SO2 is, due to increased sorbent capacity available, a higher rate of absorption. It is apparent from Figure 6b that when Faxe Bryozo is substituted with the chalk Mikrovit, the removal rate of SO2 is still predicted very well. In fact, the chalk and the limestone result in the same degree of desulfurization. As we shall see later, the predicted steady-state average chalk

Figure 5. Simulations and experimental data of absorption of SO2 in the wet FGD pilot plant (effect of slurry recycle flow rate), NaOH, and distilled water (no recycle). Parameters are given in Table 2.

particle size in the plant is smaller than that for limestone, but at the same time less residual limestone is present in the gypsum (and thereby in the absorber), apparently giving rise to more or less the same degree of desulfurization. Thus, switching to a finer grinded limestone may not necessarily be an efficient means of increasing the rate of SO2 removal but a good choice if very low residual limestone content in the gypsum is required. Predicted Ca/S molar ratios (based on feed streams) were also found to match experimental data though some scatter was seen in the measured values. Slurry pH Profiles. When validating chemical reactors as complex as wet FGD plants, it is essential to consider and measure several concentrations and not just an outlet concentration. In Figure 7 are shown simulated and measured slurry pH profiles for Base Case and L ) 9.1 L/min. The pH of the slurry at the inlet of the absorber is the pH of the holding tank. We see that an increased recycle flow rate, due to increased sorbent capacity (shorter slurry residence time), results in a smaller pH drop than for the Base Case even though the degree of desulfurization is higher for L ) 9.1 L/min. It is also apparent that a larger pH drop occurs for the once-through (i.e., no recycle) simulation with distilled water than for Base Case. The experimental data in Figure 7a are somewhat more scattered than those in Figure 7b. The reason for this is that the data in Figure 7a are taken from several independent experiments, conducted over 2 months, whereas those of Figure 7b are obtained within a short period of time. Figure 8 show pH profiles for yi ) 200 ppmv and for Mikrovit. The simulations are seen to match the

2800 Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998

Figure 6. Simulations and experimental data of absorption of SO2 in the wet FGD pilot plant. The effects of inlet SO2 concentration and limestone type can be seen. Parameters are given in Table 2.

Figure 7. Simulations and experimental data of slurry pH profiles in the wet FGD pilot plant (effect of slurry recycle flow rate). Parameters are given in Table 2.

experimental data. It is worth noticing that, due to reasons stated earlier, the limestone and the chalk give rise to the same pH profile. Solid Concentrations. In Figure 9 are shown transient experimental data of solids concentrations in the slurry from all four wet FGD experiments and model predictions by the steady-state model. It appears that only Base Case and perhaps L ) 9.1 L/min and Mikrovit could be considered in steady state when the experiments were halted after 8 days. For yi ) 200 ppmv, the pilot plant had only received about 20% of the SO2 that Base Case had received when it was interrupted, and thus a much longer time to reach steady state is expected. For Base Case, L ) 9.1 L/min, and Mikrovit, the model appears to give good predictions of the steadystate solid concentrations, whereas for yi ) 200 ppmv, it is not possible to decide from the present data whether this is the case. According to simulations, more or less the same steady-state solid concentration is expected for all four cases. Relative Saturations (Concentrations of Ca2+ and SO42-). During the experimental periods, slurry samples were withdrawn from the holding tank, filtrated, and analyzed for the concentrations of Ca2+ and SO42-. In Figure 10 are shown experimental and predicted relative saturations of gypsum, defined in eq 30, for the four wet FGD cases. The rate constant for the gypsum crystallization was obtained by fitting simulations to the experimental data shown in Figure 10 and determined to 4.5 × 10-4 mol/(m3‚s), and this value was used in all simulations. However, it can be seen that a complete match was not possible, indicating

that our submodel for the crystallization process is too simple. To test the importance of this, simulations were also performed with values of kgypsum determined individually for each experiment. The predicted values of important parameters such as the degree of desulfurization, slurry pH profiles, residual limestone in gypsum, etc., were found to be practically unchanged. Thus, the simple empirical model for the crystallization process appears to be adequate for the purpose of this work. According to Randolph and Larson (1988), crystallization kinetics may be reactor dependent and should preferably be determined for each individual plant. Furthermore, since ideal solutions were assumed in the model of this work, any nonidealities may be lumped into the value of kgypsum, making it applicable for simulations of our particular pilot plant only. The overall rate of crystallization is not affected by the choice of crystallization model since satisfaction of the overall mass balances requires that the amount of gypsum produced corresponds to the amount of SO2 absorbed. Concentrations of Mg2+ and Other Ions. Mg2+ and other ions in the slurry solution may influence the solution chemistry. Mg2+ is present in most limestones as MgCO3 (see Table 1) and is liberated to the slurry solution upon dissolution of the limestone. If Mg2+ does not subsequently precipitate, it will accumulate in the slurry solution (Clarke, 1993). In Figure 11 is shown the transient accumulation of Mg2+ for the four cases as well as model predictions. It is apparent that the predicted concentrations are too high. This means that some Mg2+ must precipitate with the gypsum, and a gypsum analysis confirmed this expectation. To account for this, the content of MgCO3 in the limestone, used

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Figure 10. Steady-state simulations (lines) and transient experimental data (symbols) of relative saturations in the holding tank for the four cases. Parameters are given in Table 2.

Figure 8. Simulations and experimental data of slurry pH profiles in the wet FGD pilot plant. The effects of inlet SO2 concentration and limestone type can be seen. Parameters are given in Table 2.

Figure 11. Steady-state simulations (lines) and transient experimental data (symbols) of concentrations of Mg2+ in the holding tank for the four cases. Parameters are given in Table 2.

Figure 9. Steady-state simulations (lines) and transient experimental data (symbols) of solids contents of the slurry in the holding tank for the four cases. Parameters are given in Table 2.

as model input, was modified to match the measured concentration. This modification had some influence on the concentrations of Ca2+ and SO42- but not on any important model outputs. Other elements, such as Al, Fe, and Si (also present as impurities in limestone), are removed from wet FGD plants mainly with the gypsum

(Clarke, 1993). The total concentration of HSO3-/SO32-/ SO2 was also measured in the holding tank, using the method of Greenberg et al. (1992), and, as predicted by the model, found to be negligible. Finally, the concentration of O2(aq) was measured using an O2 probe, and 100% saturation of the slurry in the holding tank, in good agreement with model predictions, was found. Residual Limestone in the Gypsum. An essential parameter in the operation of a wet FGD plant is the amount of residual limestone in the gypsum. There are two reasons for this: good utilization of the sorbent (limestone) and a saleable gypsum product (i.e., less than 3 wt % residual limestone; Ibæk, 1996). In Figure 12 are shown transient experimental data and steadystate simulations for the Base Case and Mikrovit. Excellent agreement (steady state) is seen for Mikrovit. For the Base Case, the model also gives a reasonable prediction of experimental data. Similar results were

2802 Ind. Eng. Chem. Res., Vol. 37, No. 7, 1998

Figure 12. Simulations (lines) and experimental data (symbols) of residual limestone contents in the gypsum for Base Case and Mikrovit (chalk). Parameters are given in Table 2.

Figure 14. Simulation (steady state) of PSD of residual limestone particles and experimental data of transient development of PSD of gypsum for Base Case. Parameters are given in Table 2.

Figure 13. Simulations of PSDs of residual limestone (RL) and measured PSDs of fresh limestone for Base Case and Mikrovit. Parameters are given in Table 2.

Figure 15. Comparison of PSDs of fresh limestone and steadystate gypsum samples for Base Case. Parameters are given in Table 2.

found for L ) 9.1 L/min and yi ) 200 ppmv, though the experimental data were not in a steady state. As mentioned earlier, the chalk (Mikrovit), due to its smaller particles and thereby higher dissolution rate, results in less residual limestone and this improved gypsum quality. Another advantage of finely grinded limestone particles is that the holding tank volume, due to the shorter residence times required for the limestone particles to dissolve, can be reduced. Additionally, it may also be possible to operate the plant at a higher holding tank pH (>5.5), leading to higher rates of SO2 removal. PSDs of Limestone and Gypsum. The incorporation of population balance equations for the limestone particles makes it possible to predict the steady-state size distribution of limestone particles in the residual limestone. Simulations and initial PSDs (measured) for the two limestones used are shown in Figure 13. It is apparent that Faxe Bryozo residual limestone contains larger particles than residual limestone of Mikrovit, but none of the residual limestones contain particles less than about 1 µm. In Figure 14 is shown the transient development (experimental) of the PSD of gypsum for Base Case. It was confirmed from several independent

slurry samples that quite large gypsum crystals were formed during the first day of operation. After approximately 2 days (48 h) the PSD of gypsum was fully developed, as shown in Figure 14. For comparison the simulated steady-state PSD of residual limestone is shown. It can be seen that some (or perhaps all) of the larger particles of the gypsum samples must originate from residual limestone. In Figure 15 are shown experimental data of steady-state gypsum samples from Base Case and Mikrovit experiments. The important result here is that the two gypsum samples have very similar PSDs. The two samples appear to differ only for particle sizes larger than about 100 µm. This deviation can be explained by considering the two fresh limestone samples, also depicted in Figure 15, from which it is clear that the particles above about 100 µm, in the case of Faxe Bryozo gypsum, must originate from residual limestone. Thus, gypsum dewatering difficulties are not expected when using finer grinded limestones (chalks) instead of Faxe Bryozo. However, this problem was observed by Ibæk (1996) during full-scale operation of a wet FGD packed tower using another Danish chalk. He was able to dewater the gypsum

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Figure 16. Simulated ratio of liquid- to gas-phase mass-transport resistances in the absorber for the four cases. Parameters are given in Table 2.

Figure 17. Simulated concentration profiles for sulfurous species and O2(aq) in the absorber. Notice the scaling factors. Parameters are given in Table 2.

crystals originating from a chalk, but longer centrifuge times were needed. Gas-Liquid Mass-Transport Resistances and Enhancement Factors. An interesting question in relation to the design of a wet FGD plant is the ratio of the liquid to gas mass-transfer resistance defined as

Concentration Profiles in the Absorber. In Figure 17 are shown concentration profiles (Base Case) for S species and O2(aq). Initially, O2(aq) is abundant in the absorber but is consumed as HSO3- builds up. For absorber heights larger than about 0.7 m, the rate of oxidation becomes entirely mass-transport-controlled. Furthermore, SO2(aq) and HSO4- accumulate in the absorber. SO42- ions are formed when HSO3- ions are oxidized and removed as gypsum. Simulations of concentration profiles for carbon species and Ca2+ were also performed (not shown). The concentrations of HCO3- and CO32- are, due to the low pH, very low in the absorber. CO2 is desorbed in the holding tank when air is injected and produced in the absorber when limestone dissolves. Some CO2 may also be absorbed from the gas phase. Ca2+ ions are formed when limestone dissolves and are consumed by gypsum crystallization. The concentration of Ca2+ is practically constant (about 14 mol/m3) in the absorber. Temperature. The effect of temperature on the degree of desulfurization for a temperature range of 313-333 K (pertinent for wet FGD packed towers) was simulated. Only a limited sensitivity (less than 5% relative deviation from the Base Case) was seen, with the lower temperature, due to the increased solubility of SO2 in water, giving higher rates of SO2 removal. For comparison, simulations in the same temperature interval for the system SO2-distilled water were produced and a stronger temperature dependence than for the slurry system was observed. Whether operation at a lower temperature is economically feasible depends on other plant aspects such as the cost of cooling and subsequently heating of the flue gas before emission to the atmosphere. pH of Holding Tank. As already discussed, the pH of the holding tank is a model input. Its effect on the degree of desulfurization and residual limestone in gypsum is shown in Figure 18. Lowering the holding tank pH results in low residual limestone contents in the gypsum at the cost of reduced removal rates of SO2. Thus, a holding tank pH of 5-5.5 (also employed in fullscale FGD packed towers) appears to be a reasonable compromise with respect to the degree of desulfurization and residual limestone in the gypsum. Convective Contribution to Liquid-Solid Mass Transport. Liquid-solid mass transport was assumed to involve no convective contribution (i.e., ShLS ) 2).

RLG )

HSO2kG,SO2 ESO2kL,SO2°

(52)

In Figure 16 is shown how this ratio varies with absorber height for the four cases. It can be seen that, for Base Case and Mikrovit, the ratios are more or less the same and that the liquid-phase resistance is 1222% of the gas-phase resistance. For L ) 9.1 L/min and yi ) 200 ppmv, the liquid-phase resistance is less than about 10% of the gas-phase resistance. Thus, while the gas-phase resistance is the dominating resistance, the liquid-phase resistance cannot be neglected. The rate of SO2 removal is best improved by creating more turbulence in the gas phase and thereby higher gasphase mass-transport coefficients or by increasing the surface area available for mass transport. Simulations of the enhancement factors for SO2 showed values between 10 and 25 (depending on absorber position and process conditions) for Base Case, L ) 9.1 L/min, and Mikrovit. For yi ) 200 ppmv, the enhancement factor varied between 30 and 90 in the absorber. For low gasphase concentrations of SO2, the large enhancement factors result in small liquid-phase mass-transport resistances. Where Does the Limestone Dissolve? The slurry volume in the absorber is about 1% of that in the holding tank in our pilot plant. However, the pH of the holding tank is typically 5.5, whereas the pH in the absorber may drop from 5.5 to below 4 (see Figures 7 and 8). Calculations showed that somewhere between 15 and 32% of the limestone dissolves in the absorber depending on the process conditions. This result may be important when considering, in the design of packed towers, where to add the fresh limestone. Adding fresh limestone to the recycling slurry at the inlet of the absorber is expected to be more efficient than adding it directly to the holding tank. The small particles are thereby utilized in the absorber where a high rate of dissolution is more important than in the holding tank.

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Figure 18. Model predictions of degrees of desulfurization (at the outlet of the absorber) and residual limestone contents in gypsum for various values of pH in the holding tank. Other parameters are given in Table 2.

This assumption was investigated, independently for the absorber and the holding tank, by artificially increasing the effective mass-transfer coefficient by a constant factor. For the holding tank, the effect was a reduction in the residual limestone content of the gypsum and, due to a decreased amount of limestone in the absorber, a lower degree of desulfurization. For the absorber, the effect of introducing convection was increased SO2 removal but also a smaller pH drop deviating from the experimentally observed pH values. Thus, liquid-solid convection seems to be unimportant in the holding tank as well as in the absorber, for the experiments conducted in the pilot plant. Enhancement Factor for O2 Absorption. The liquid-phase mass transport of O2 in the absorber may be enhanced by the oxidation of HSO3-. In our model, the enhancement factor was assumed equal to unity. To test this assumption, simulations were performed with enhancement factors between 1 and 10. The degree of desulfurization was somewhat sensitive to this parameter, but again the simulated pH profiles did not match the experimental values for enhancement factors larger than unity. The pH (and other model outputs) in the absorber is sensitive to the enhancement factor because H+ ions are formed when HSO3- is oxidized. Based on this analysis, the enhancement factor for O2 was estimated to be unity in the pilot plant. Increasing the liquid-phase mass-transfer coefficient or partial pressure of O2 in the flue gas would have an effect similar to that of the enhancement factor (i.e., higher removal rate of SO2). Finally, it should be mentioned that in the absorber only the concentration of HSO3and not the degree of desulfurization is sensitive to the oxidation reaction (assuming an enhancement factor of unity for O2). However, in the holding tank all HSO3must be oxidized and the reaction cannot be omitted. Solubility Product of CaCO3. Considerable disparity exists in the literature for the reported values of the solubility product of CaCO3 (calcite). The thermodynamic database of Brewer (1982), for instance, gives a value of 3 × 10-2 (mol/m3)2 (323 K), whereas Plummer and Busenberg (1982) have reported 2.2 × 10-3 (mol/ m3)2 at this temperature. According to Gal et al. (1996), the most suitable value, which was used in this work, is that of Plummer and Busenberg (1982). The effect of using the higher value of the solubility product is

similar to that of the convective contribution to liquidsolid mass transfer discussed above. Porosity of Limestone. The porosity of limestone was set to zero in our simulations, because the correct values to use are presently unknown. It is possible to determine the porosity for the larger limestone particles, but for small particles the porosity is hard to measure and may well be negligible. The same could be true for large particles that have partly dissolved. The effect, however, of porosity on simulations is similar, as can be seen from eq 22, to that of the convective contribution to liquid-solid mass transfer discussed above. We therefore chose to neglect porosity for the two limestones used. It should be stressed, however, that this may not be valid for all limestone types. Sensitivity Analysis. A sensitivity analysis of the model (Base Case) with respect to all the physical and chemical parameters mentioned in our model development has been performed. The following parameters were identified to influence the model simulations (i.e., degree of desulfurization at the outlet of the absorber and residual limestone in the gypsum) with relative deviations from the Base Case between 2 and 10% when varied (20% around their estimated values: the gasand liquid-phase mass-transport coefficients of SO2 in the absorber, Henry’s constant for SO2, the liquid-phase diffusion coefficients of HSO4- and H+, the equilibrium constant for reaction I, the absorber slurry film thickness, and the solubility product of CaCO3. Of these parameters, only the diffusion coefficients, the absorber slurry film thickness, and the solubility product of CaCO3 are not known with a high accuracy. However, even with errors of up to 20% in the latter values, model predictions are still in good quantitative agreement with experimental data. Other Model Assumptions. The wet FGD model was based on four simplifying assumptions that have not been verified. In the absorber, it was assumed that limestone particles do not dissolve in the liquid film but only in the liquid bulk. The advantage of making this assumption is that the calculations of dissolution of limestone are decoupled from those of the enhancement factor. For both the absorber and the holding tank, ideal solutions were, contrary to that of many other wet FGD models, assumed. Furthermore, it was assumed that gypsum and limestone particles, present in the liquid phase, do not influence the mass-transport coefficients. Finally, electric potential gradients in the liquid were, due to the high ionic strength of FGD liquids, assumed to be negligible. These four assumptions could not be directly validated from the experimental data. However, considering the limited accuracy of the experimental data and the uncertainties of many key physical parameters (such as diffusion coefficients and solubility products), these added complexities are not expected to improve the model predictions. Additionally, incorporation of the above phenomena would make our model very complex and lead to substantially increased computing times. Conclusions A wet FGD pilot plant, based on the packed tower concept, was modeled. All important rate-determining steps, gas-liquid mass transport of SO2, oxidation of HSO3-, dissolution of limestone, and crystallization of gypsum, were included. Simulations were found to match the experimental data well. The modeling tools

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developed may be adapted to other wet FGD plants employing different reactor configurations, but values for plant-specific parameters, such as gas-liquid masstransport coefficients, should preferably be measured in the pertinent plant or else sought in the literature. Scaleup of the reactor model is needed for it to be applicable as a design tool for full-scale plants. This would include modeling of the inlet and outlet sections of a full-scale absorber. Further work with the model involves experimental studies and modeling of the effects of HCl, organic acid buffers, and co-firing of coal and biomass on the plant performance. Acknowledgment The authors thank Thomas Wolfe for experimental assistance. S. K. is grateful to Dr. Suresh Kumar Bhatia for the many valuable discussions during his stay at University of Queensland. This work, which was a part of the CHEC Research Program, was supported by the Danish Ministry of Energy, Elsam (the Jutland-Funen Electricity Consortium), Elkraft (the Zealand Electricity Consortium), and the Danish Technical Research Council. Notation aA ) specific gas-liquid interfacial area in the absorber, 4/dt, m2/m3 aT ) specific gas-liquid interfacial area in the holding tank, m2/m3 dj ) particle diameter of particles of size j, m dt ) inner diameter of the absorber, m D ) molecular diffusion coefficient, m2/s E ) enhancement factor fk ) weight fraction of component k in limestone fL ) volume of slurry in the absorber to volume of the absorber, 4δA/dt G ) molar flow rate of flue gas or air, mol/s hA ) height of the absorber, m H ) Henry’s constant, atm‚m3 of liquid/mol Jj ) rate of dissolution of particles of size dj, mol/s k ) rate constant, s-1 or s-1‚(m3 of liquid/mol)2 kG ) gas-phase mass-transport coefficient, mol/(m2 of surface‚atm‚s) kL° ) physical liquid-phase mass-transport coefficient, m/s K ) equilibrium constant, mol/m3 or (mol/m3)2 KG ) overall mass-transport coefficient on a gas basis, mol/ (m2 of surface‚atm‚s) KI ) integral control gain KP ) proportional control gain L ) slurry recycle flow rate, m3/s Lk ) solubility product of species k, (mol/m3)2 M ) molar mass, kg/mol N ) rate of absorption, mol/(m3 of liquid‚s) Nj ) number of particles of size dj per unit liquid volume, m-3 pB ) partial pressure of component B, yBP, atm P ) total pressure in the plant, atm Q ) liquid flow rate, m3/s r ) radius of limestone particle, m, or rate of reaction, mol/ m3‚s R ) rate of reaction, mol/(m3 of liquid‚s) R h j ) rate of dissolution (volumetric basis) of particles of size dj, m3 of CaCO3/s RLG ) ratio of liquid to gas mass-transfer resistances in the absorber RS ) relative saturation t ) time, s Ti ) defined in eq 42, mol/m3 of liquid‚s

Vj ) volume of limestone particles of size dj, m3 VT ) volume of slurry in the holding tank, m3 wj ) weight fraction of particles of size dj in the limestone sample wkF ) weight fraction of component k in a feed stream x ) spatial coordinate in the liquid film (gas-liquid twofilm theory), m y ) gas-phase mole fraction z ) dim. spatial coordinate in the absorber, t/τA [i] ) concentration of component i, mol/m3 Greek Letters δA ) thickness of slurry film in the absorber, m δj ) thickness of solid-liquid (two-film theory) film surrounding particles of size dj, m  ) porosity λ ) cumulative concentration transform, defined in eq 23, mol/m3 θk ) molar ratio of species k to CaCO3 in limestone F ) density, kg/m3 τA ) residence time of slurry in the absorber, πhAdtδA/L, s Subscripts A ) absorber B ) CO2, O2, or SO2 C ) current value (in the absorber) f ) forward F ) feed G ) gas-phase value i ) interface value or inlet to absorber in ) value at the inlet to the holding tank from the absorber j ) particle size j L ) liquid-phase value o ) bulk phase value, outlet of the holding tank, or initial diameter ox ) oxidation reaction r ) reverse s ) surface value set ) setpoint T ) holding tank value Superscripts F ) inlet slurry feed stream in ) value at the inlet to the holding tank j ) value for particles of size j Mathematical Operations ∇ ) “del” or “nabla” operator

Supporting Information Available: Physical and chemical constants used in the simulations (3 pages). Ordering information is given on any current masthead page. Literature Cited Argarwal, R. S.; Rochelle, G. T. Chemistry of Limestone Slurry Scrubbing. 1993 SO2 Control Symposium, Boston, 1993; U.S. Environmental Protection Agency, Research and Development: Research Triangle Park, NC, 1993; Vol. 3, p 78; EPA600/R-95-015. Brewer, L. Thermodynamic Values for Desulfurization Processes. ACS Symp. Ser., 1982, 188, 1. Brogren, C.; Karlsson, H. T. A Model for Prediction of Limestone Dissolution in Wet Flue Gas Desulfurization Applications. Ind. Eng. Chem. Res. 1997a, 36, 3889. Brogren, C.; Karlsson, H. T. Modelling the Absorption of SO2 in a Spray Scrubber using the Penetration Theory. Chem. Eng. Sci. 1997b, 52, 3085. Clarke, L. B. Management of FGD Residues; IEA CR/62; IEA Coal Research: London, 1993.

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Received for review December 30, 1997 Revised manuscript received April 1, 1998 Accepted April 2, 1998 IE9709446