Ind. Eng. Chem. Res. 1997, 36, 197-203
197
Modeling of SO2 Absorption into Limestone Suspensions Amedeo Lancia,*,† Dino Musmarra,‡ and Francesco Pepe§ Dipartimento di Ingegneria Chimica, Universita` di Napoli “Federico II”, P. le Tecchio 80, 80125 Napoli, Italy, Istituto di Ricerche sulla Combustione, CNR, P. le Tecchio 80, 80125 Napoli, Italy, and Facolta` di Scienze Ambientali, Seconda Universita` di Napoli, Via Arena 22, 81100 Caserta, Italy
The wet limestone flue gas desulfurization process, and more specifically absorption of SO2 limestone suspensions, was studied. Experiments of SO2 absorption were carried out using a bubbling reactor with a mixture of sulfur dioxide and nitrogen in the gas phase and an aqueous limestone suspension in the liquid phase. The SO2 absorption rate was measured at different compositions of both gas and liquid phases and at different gas flow rates and agitator speeds. A model based on the film theory was proposed to describe liquid-side mass transfer. It was assumed that the liquid-phase diffusional resistance is concentrated in a layer, the thickness of which depends on fluid dynamics, but is independent of the nature of the reactions taking place. The equations considered by the model describe conditions of thermodynamic equilibrium as well as material and electrical balances and use the experimentally determined gas- and liquidside mass-transfer coefficients, rather than empirical parameters. Model calculations and experimental results were compared, and a good consistency was found. Eventually the model was used to evaluate the absorption enhancement factor as a function of gas- and liquid-phase composition. Introduction Combustion of fossil fuels for power generation gives rise to large emissions of SO2 and NOx. Such pollutants are responsible for acid rain and, therefore, have to be removed from combustion flue gas. Among the flue gas desulfurization (FGD) treatments which have reached industrial scale, the most common is the wet limestone process (Klingspor and Cope, 1987). In this process SO2 removal is realized by scrubbing the flue gas with a limestone suspension in a spray or packed tower. High SO2 removal efficiency, low cost, and wide availability of the absorbing reagent are the main features which have determined the success of the treatment (Rochelle, 1983). While wet limestone FGD has been in commercial application since the early 1970s, still many problems exist with regard to the modeling of the elementary stages of the process, which are SO2 absorption, limestone dissolution, sulfite oxidation, and sulfite/sulfate crystallization. In particular, concerning SO2 absorption, reliable models for the evaluation of the absorption rate for given gas- and liquid-phase compositions are required with the aim of efficiently describing the whole process (Rochelle and King, 1977; Olausson et al., 1993). Absorption of pure SO2 in water and in aqueous solutions of HCl, NaHSO3, and NaCl was studied by Lynn et al. (1995a-c), who used the penetration theory. Later Danckwerts (1968) studied SO2 absorption in water and showed that it could be regarded as a process of absorption with instantaneous reaction, so that the adsorption rate could be calculated considering a “total” driving force, obtained by adding together the contributions of unreacted SO2(aq) and of its reacted forms (HSO3- and SO32- ions). Also, Hikita et al. (1977) and Teramoto et al. (1978) used the penetration theory to model SO2 absorption in water or in aqueous solutions of NaOH and Na2SO3, and in particular they pointed out that one or two reactions planes exist in the masstransfer boundary layer. †
Universita` di Napoli “Federico II”. CNR. § Seconda Universita ` di Napoli. ‡
S0888-5885(96)00236-9 CCC: $14.00
On the other hand, Chang and Rochelle (1982) showed that a very good approximation to the results of the penetration theory could be obtained by making use of the film theory and replacing the diffusivity ratios by their square roots. Furthermore, the same authors (Chang and Rochelle, 1985) showed that, in conditions of interest for FGD applications (i.e., low SO2 partial pressure), the reversibility of the SO2 hydration reaction has to be taken into account in order to predict the gasliquid mass-transfer rate. Another problem related to modeling of SO2 absorption stems from the fact that the suspensions into which absorption is carried out contain relevant quantities of ionic solids, mainly calcium carbonate, sulfite, and sulfate. Sada and co-workers (1979, 1981a,b, 1982) showed that, in the presence of rather specific experimental conditions (suspension of very fine particles with very high concentration), solid dissolution in the gasliquid mass-transfer boundary layer has to be taken into account. Therefore, according to these authors, the theory proposed by Uchida and co-workers (Uchida et al., 1975; Uchida and Ariga, 1985), which describes absorption of a gas into a slurry containing sparingly soluble solid particles, has to be used. On the other hand Pasiuk-Bronikowska and Rudzinski (1991) showed that, if the solid concentration is relatively low, SO2 absorption into aqueous systems could be successfully modeled, neglecting the solid dissolution into the gasliquid mass-transfer boundary layer. In their work Pasiuk-Bronikowska and Rudzinski considered conditions in which solid Ca(OH)2 or CaSO3 was present and used the film theory to predict the rate of SO2 absorption and the value of the enhancement factor. More recently, Lancia et al. (1994) focused their attention on the effect of the electric potential on ionic diffusion in the masstransfer boundary layer. They studied SO2 absorption in CaCO3-containing systems by means of the film theory and determined the concentration profiles of the different species in liquid film. The purpose of the present paper is to study SO2 absorption in diluted limestone suspensions using a laboratory-scale bubbling reactor, with different SO2N2 mixtures in the gas phase and solid concentrations © 1997 American Chemical Society
198 Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997
Figure 1. Sketch of the experimental apparatus.
in the liquid phase. The experimental results are compared with those obtained by means of a model capable of describing the process of absorption and simultaneous chemical reactions. The model proposed, which is similar to the one set up by Lancia et al. (1994), takes into account the coupling between mass-transfer and simultaneous ionic reactions in a stagnant liquid film adhering to the gas-liquid interface, with an approach derived from the one proposed by Olander (1960). However, the main characteristic of the model, compared to the one described by Lancia et al. (1994), is that it contains no adjustable parameter, so that in order to evaluate the SO2 absorption rate it only requires the experimentally determined values of the gas- and liquid-side mass-transfer coefficients. Experimental Apparatus and Procedure A sketch of the experimental apparatus is presented in Figure 1. The absorber is a thermostated stirred vessel with continuous feeding of both gas and liquid phases, and in all the experimental runs the temperature of the thermostatic bath was kept at 25 °C. The reactor, made of Pyrex glass, is a jacketed, 0.13 m i.d. cylinder with a hemispherical bottom, fitted with two vertical baffles and a liquid overflow. An axial twoblade stirrer, with speed (n) adjustable from 0 to 15 s-1, is used to mix the liquid phase. The gas phase was a mixture of SO2 in N2 taken from cylinders of certified composition. It was laminated, passed through a rotameter, and bubbled at the bottom of the reactor. Its volumetric flow rate (G) was kept at 1.43 × 10-4 m3/s in most runs; however, a few runs were carried out with flow rates of 0.94 or 2.52 × 10-4 m3/s. Different SO2 partial pressures in the gas phase were used, namely, of 48.6, 99.3, 150.0, and 190.0 Pa. The liquid phase was prepared by mixing bidistilled water and a proper amount of reagent-grade CaCO3 powder, so as to obtain solid concentrations of 0.10, 0.30, 0.44, 0.70, and 1.00 kg/m3. A peristaltic pump was used to feed the liquid phase, and the flow rate was kept at about 1.20 × 10-6 m3/s. Furthermore, in order to evaluate the gas- and liquid-side mass-transfer coefficients, few experimental runs were performed by absorbing SO2 containing gas into aqueous solutions of NaOH or HCl. Preliminary stimulus-response experiments (Logoteta, 1988) had shown that the liquid phase is well mixed with n g 5 s-1 and that the system is at steady
state after a time larger than 3τ has elapsed, where τ is the mean residence time of the liquid phase. Therefore, it was decided to operate with n varying in the range of 5-15 s-1, and the following experimental procedure was adopted: at the beginning of each experiment, as soon as the liquid in the reactor reached the overflow, agitation was started and the gas stream was introduced. After a time of about 5τ the steady state was considered attained, and the SO2 absorption rate was evaluated by measuring the SO2 concentration in the outlet gas stream using an UV analyzer (Hartmann and Brown Radas 1G). Afterward, the dissolved Ca2+ ion concentration in the outlet liquid stream from the reactor was measured by EDTA titration using muresside as an indicator. The sulfur material balance was checked by measuring the total sulfite concentration in the outlet liquid stream by iodometric titration using starch as an indicator; such balance indicated an error smaller than 7%. Results and Discussion A number of preliminary experimental runs were carried out to assess the relevant physical characteristics of the gas-liquid contacting device employed, namely, liquid hold (V) and gas- and liquid-side masstransfer coefficents. In particular, the product between the gas-side and mass-transfer coefficient and the interfacial area per unit volume (kga) was evaluated by absorbing the SO2-containing gas into 0.1 kmol/m3 NaOH aqueous solution, since at very high pH values SO2(aq) is instantaneously depleted at the gas-liquid interface and therefore the liquid-side resistance can be neglected. On the other hand, the product between the liquid-side mass-transfer coefficient and the interfacial area per unit volume (kL°a) was evaluated by absorbing SO2-containing gas into 1 kmol/m3 HCl. In such conditions it is possible to neglect SO2(aq) dissociation, and therefore it may be assumed that only physical absorption takes place. However, both the gas-side and the liquid-side resistances have to be taken into account, so that the evaluation of the liquid-side mass-transfer coefficient has to go through the evaluation of an overall (gas- or liquid-side) mass-transfer coefficient. The experimental results for SO2 absorption into diluted limestone suspensions are summarized in Tables 1 and 2. Since limestone dissolution does not constitute the object of the present work, its rate was not evaluated. Rather, limestone dissolution was taken into account by measuring the Ca2+ ion concentration in the outlet stream from the reactor. In Tables 1 and 2 for each run there are reported inlet and outlet SO2 partial pressure (pSO2|in and pSO2|out, respectively), SO2 absorption rate (rSO2), outlet Ca2+ concentration (cCa2+), V, kga, and kL°a. Table 1 refers to a group of runs in which, keeping G and n constant, SO2 partial pressure and limestone concentration were varied. The experimental results indicate that an increase of any of these variables causes an increase of both the SO2 absorption rate and the limestone dissolution rate. Table 2 refers to groups of runs performed with the aim of exploring the effect of fluid dynamic conditions on the absorption for a constant limestone concentration in the suspension fed to the reactor. Again, the experimental results indicate that an increase of either the agitator speed or the gas flow rate causes an increase of both rSO2 and cCa2+. With the aim of modeling gas-liquid mass transfer, it is necessary to examine the dependence of the
Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 199 Table 1. Experimental Results for SO2 Absorption into Limestone Suspensionsa experiment
limestone conc. (kg/m3)
pSO2|in (Pa)
pSO2|out (Pa)
rSO2 (mol/m3s)
cCa2+ (mol/m3)
V (m3)
kga (mol/m3 s Pa)
kL°a (s-1)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.10 0.10 0.10 0.10 0.30 0.30 0.30 0.30 0.44 0.44 0.44 0.44 0.70 0.70 0.70 0.70 1.00 1.00 1.00 1.00
48.64 99.30 149.96 190.49 48.64 99.30 149.96 191.50 48.64 99.30 149.96 190.49 48.64 99.30 149.96 190.49 48.64 99.30 149.96 190.49
7.90 34.05 64.85 91.19 3.70 17.02 40.23 62.42 3.65 15.81 35.67 47.01 3.45 14.19 25.94 40.53 2.43 11.75 24.32 38.50
5.61 × 10-3 8.99 × 10-3 1.17 × 10-2 1.37 × 10-2 6.19 × 10-3 1.13 × 10-2 1.51 × 10-2 1.78 × 10-2 6.19 × 10-3 1.15 × 10-2 1.57 × 10-2 1.98 × 10-2 6.22 × 10-3 1.17 × 10-2 1.71 × 10-2 2.06 × 10-2 6.36 × 10-3 1.21 × 10-2 1.73 × 10-2 2.09 × 10-2
0.80 0.95 1.00 1.00 1.15 2.15 2.70 2.90 1.30 2.30 3.10 3.90 1.60 2.45 3.40 4.45 1.80 2.60 3.60 4.60
4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4 4.18 × 10-4
4.84 × 10-4 4.48 × 10-4 4.84 × 10-4 4.84 × 10-4 4.84 × 10-4 4.84 × 10-4 4.84 × 10-4 4.84 × 10-4 4.84 × 10-4 4.84 × 10-4 4.84 × 10-4 4.84 × 10-4 4.84 × 10-4 4.84 × 10-4 4.84 × 10-4 4.84 × 10-4 4.84 × 10-4 4.85 × 10-4 4.85 × 10-4 4.84 × 10-4
1.99 × 10-2 1.99 × 10-2 1.99 × 10-2 1.99 × 10-2 1.98 × 10-2 1.97 × 10-2 1.98 × 10-2 1.97 × 10-2 2.03 × 10-2 2.04 × 10-2 2.04 × 10-2 2.03 × 10-2 2.03 × 10-2 2.06 × 10-2 2.09 × 10-2 1.99 × 10-2 2.02 × 10-2 2.12 × 10-2 2.12 × 10-2 1.98 × 10-2
a
Experiments performed with G ) 1.43 × 10-4 m3/s and n ) 5 s-1.
absorption rate on the gas-liquid driving force for absorption, ∆pSO2. If the hypothesis is made that the gas bubbles undergo an essentially plug flow within the reactor, ∆pSO2 can be evaluated, taking pSO2|av, the logarithmic average between pSO2|in and pSO2|out, as representative of gas-phase composition and the SO2(aq) concentration as representative of liquid-phase composition. Therefore, the following expression was used:
∆pSO2 ) pSO2|av - HSO2cSO2(aq)
(1)
where HSO2 is Henry’s constant for SO2, the value of which is 82.5 m3 Pa/mol at 25 °C (Goldberg and Parker, 1985), and cSO2(aq) is the SO2(aq) concentration in the liquid bulk. The SO2(aq) concentration in the liquid bulk, together with other concentrations, was calculated by making the hypothesis that CO2 stripping does not occur and therefore by using the following equations: (i) The equations describing conditions of thermodynamic equilibrium of the following reactions:
SO2(aq) + H2O ) H+ + HSO32-
K ) 6.50 × 10
HSO3 ) H + SO3 -
+
-5
H2CO3 ) H+ + HCO3HCO3- ) H+ + CO32H2O ) H + OH +
+
K ) 13.9 mol/m2 (2) mol/m
3
(3)
K ) 4.25 × 10-4 mol/m3 (4) K ) 4.57 × 10-8 mol/m3 (5)
K ) 1.00 × 10
-8
2
mol /m
6
(6)
where the values of the thermodynamic constants K at 25 °C are calculated from data reported in the literature (Brewer, 1982; Goldberg and Parker, 1985). (ii) The electroneutrality equation:
∑I zIcI ) 0
(7)
where cI and zI are respectively the concentration and the number of elementary charges of the I species.
(iii) The stoichiometric equations for sulfite and carbonate:
cS(IV) ) cSO2(aq) + cHSO3- + cSO32-
(8)
cCa2+ ) cCO2(aq) + cHCO3- + cCO32-
(9)
where cS(IV) and cCa2+ are the experimentally measured concentrations of sulfite and calcium in the outlet liquid stream from the reactor. In Figures 2 and 3 the experimental results are reported as a plot of the SO2 absorption rate rSO2 vs the absorption driving force. In particular, Figure 2 refers to the runs of Table 1, while Figure 3 refers to the runs of Table 2. In each figure, together with the experimental results, there are also reported a couple of straight lines representing the upper and lower limits for the absorption rate. The upper line describes conditions of gas film control (no liquid-side resistance) and is obtained by means of the following equation:
rSO2 ) kga(pSO2|av - HSO2cSO2(aq))
(10)
The lower line is representative of conditions in which only physical absorption occurs and is obtained by means of the following equation:
rSO2 )
1
(p | - HSO2cSO2(aq)) HSO2 SO2 av 1 + kga kL°a
(11)
It has to be observed that, while for all the runs of Table 1 there is just a single couple of limiting lines for the conditions of gas film control and physical absorption (Figure 2), for the runs reported in Table 2 there are four couples of such lines (Figures 3a-d). This is due to the fact that in Table 2 there are reported experimental runs carried out with different fluid dynamic conditions and therefore with different values of kga and kL°a. Figures 2 and 3 show that for most of the experiments carried out neither conditions of gas film control nor conditions of physical absorption were found. In particular, Figure 2 shows that for low absorption driving force and high limestone concentration the absorption
200 Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 Table 2. Experimental Results for SO2 Absorption into Limestone Suspensionsa experiment
G (m3/s)
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
1.43 × 1.43 × 10-4 1.43 × 10-4 1.43 × 10-4 1.43 × 10-4 1.43 × 10-4 1.43 × 10-4 1.43 × 10-4 9.44 × 10-5 9.44 × 10-5 9.44 × 10-5 9.44 × 10-5 2.52 × 10-4 2.52 × 10-4 2.52 × 10-4 2.52 × 10-4
a
10-4
n (s-1) pSO2|in (Pa) pSO2|out (Pa) rSO2 (mol/m3 s) cCa2+ (mol/m3) 10 10 10 10 15 15 15 15 5 5 5 5 5 5 5 5
48.64 95.25 149.96 191.50 51.07 95.25 149.96 191.50 51.07 97.27 149.96 191.50 51.07 97.27 149.96 191.50
1.22 4.46 11.86 21.89 0.81 1.62 5.67 12.16 1.42 4.46 10.13 16.01 5.27 15.00 30.56 46.93
8.12 × 1.55 × 10-2 2.36 × 10-2 2.90 × 10-2 9.77 × 10-3 1.82 × 10-2 2.80 × 10-2 3.49 × 10-2 4.33 × 10-3 8.10 × 10-3 1.22 × 10-2 1.53 × 10-2 1.18 × 10-2 2.12 × 10-2 3.08 × 10-2 3.73 × 10-2 10-3
1.90 2.65 3.65 4.65 1.95 2.70 3.80 4.70 1.40 2.09 2.70 3.40 2.35 3.50 4.90 5.75
V (m3)
kga (mol/m3 s Pa)
kL°a (s-1)
3.37 × 3.37 × 10-4 3.37 × 10-4 3.37 × 10-4 2.96 × 10-4 2.96 × 10-4 2.96 × 10-4 2.96 × 10-4 4.37 × 10-4 4.37 × 10-4 4.37 × 10-4 4.37 × 10-4 3.95 × 10-4 3.95 × 10-4 3.95 × 10-4 3.95 × 10-4
7.68 × 7.68 × 10-4 7.68 × 10-4 7.68 × 10-4 1.01 × 10-3 1.01 × 10-3 1.01 × 10-3 1.01 × 10-3 3.33 × 10-4 3.33 × 10-4 3.33 × 10-4 3.33 × 10-4 8.09 × 10-4 8.09 × 10-4 8.09 × 10-4 8.09 × 10-4
2.50 × 10-2 2.49 × 10-2 2.50 × 10-2 2.49 × 10-2 2.87 × 10-2 2.87 × 10-2 2.91 × 10-2 2.91 × 10-2 5.31 × 10-3 5.35 × 10-3 5.31 × 10-3 5.34 × 10-3 1.17 × 10-1 1.19 × 10-1 1.20 × 10-1 1.20 × 10-1
10-4
10-4
Experiments performed with inlet limestone concentration of 0.70 kg/m3.
According to the model, sulfur dioxide absorption requires the removal of aqueous SO2 from the gasliquid interface. The reaction with the species produced by limestone dissolution allows the concentration of SO2(aq) to decrease. As a consequence SO2 absorption takes place due to the transport of the species which are originally present at the surface and of those produced by reaction (2-6). The phenomena of mass transfer and accompanying instantaneous chemical reactions described above were modeled using the film theory. The equations taken into account are the total material balances (Olander, 1960) for sulfite, carbonate, and calcium:
dNSO2(aq) Figure 2. SO2 absorption rate vs absorption driving force with G ) 1.43 × 10-4 m3/s, n ) 5 s-1. Limestone concentrations (kg/ m3): (3) 0.10; (O) 0.30; (0) 0.40; (]) 0.70; (4) 1.0. Upper line: absorption rate with gas film control (no liquid-side resistance). Lower line: physical absorption rate (no liquid-phase reactions).
rate is mainly controlled by the gas-side resistance and that the liquid-side resistance becomes progressively more important as the absorption driving force increases and the limestone concentration decreases. Figure 3 shows that, as the agitator speed or the gas flow rate increase, the liquid-side resistance tends to become more important, since both these variables have a positive influence on the contact between bubbles and the liquid phase. This effect is particularly strong for the gas flow rate, to the point out that for the higest gas flow rate considered the absorption process could almost be considered as a physical absorption (Figure 3d). The results reported in Figures 2 and 3 suggest that neither eq 10 nor eq 11 can be used to evaluate the absorption rate. Therefore, with the aim of calculating the rate of SO2 absorption into limestone suspensions, it is necessary to take into account the interactions between mass-transfer and chemical reactions which take place during SO2 absorption. In this work a model is proposed which is partly based on the work of PasiukBronikowska and Rudzinski (1991) and furthermore takes into account the suggestions made by Rochelle (1992). Such a model assumes that the diffusion of ions and molecules is the limiting step in the absorption process, that diffusional resistances are confined in a thin layer around the gas bubbles rising in the liquid, and that thermodynamic equilibrium exists between the species involved.
dx
dNHSO3+
dNH2CO3 dx
dx
dNSO32-
dNHCO3+
dx
dx
+
dNCO32+
dNCa2+ )0 dx
dx
)0
(12)
)0
(13)
(14)
where NI is the molar flux of the I species and x is the normal coordinate in a system having its origin at the gas-liquid interface. At the gas-liquid interface (x ) 0) the boundary conditions for such a system take into account the continuity of the SO2 flux through the interface and the fact that there is no flux of calcium and carbonate from or to the gas bubble. On the other hand, at the interface between the gas-liquid film and the liquid bulk (x ) δ, where δ is the film thickness), the boundary conditions link film and liquid bulk concentrations. The solution of the system of eqs 12-14 is made complex by the fact that, when charged species diffuse, the flux of each species depends on the fluxes of the other species through the electric potential of diffusion (Vinograd and McBain, 1941). Therefore, the transport equations are highly coupled, and their resolution is cumbersome (Lancia et al., 1994). On the other hand, as pointed out by Glasscock and Rochelle (1989; see also Rochelle, 1992), a small error is introduced if the contribution of the electric potential to the mass-transfer rate is neglected, and the electroneutrality condition in the film is relaxed. Following this approach, the condition of electroneutrality (eq 7) is substituted by the
Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 201
Figure 3. SO2 absorption rate vs absorption driving force with a limestone concentration of 0.70 kg/m3: (a) G ) 1.43 × 10-4 m3/s, n ) 10 s-1; (b) G ) 1.43 × 10-4 m3/s, n ) 15 s-1; (c) G ) 9.44 × 10-5 m3/s, n ) 5 s-1; (d) G ) 2.52 × 10-4 m3/s, n ) 5 s-1. Upper lines: absorption rate with gas film control (no liquid-state resistance). Lower lines: physical absorption rate (no liquid-phase reactions). Table 3. Diffusivities in Water at 298 K species
D × 103 (mm2/s)
species
D × 103 (mm2/s)
H+ OHSO2(aq) HSO3SO32-
9.30a 5.27a 1.76b 1.33a 0.77a
H2CO3 HCO3CO32Ca2+
2.0a 1.20a 0.70a 0.79a
a From Rochelle et al. (1983). b From Pasiuk-Bronikowska and Rudzinski (1991).
condition that no net charge transport takes place between the gas and the liquid:
d
∑I zINi) ) 0
(
dx
(15)
and the simple Fick’s law is used to express the flux of each species in eqs 12-15:
NI ) -Di
dcI dx
(16)
where DI is the diffusivity of the I species, the value of which is reported in Table 3. The system of eqs 12-15, once eq 16 is used to express fluxes in terms of concentrations, can be analytically integrated, leading to a set of four algebraic equations. Such equations, together with the five equilibrium equations associated with reactions (2 - 6), can be used to evaluate the nine unknown interfacial concentrations of SO2(aq), HSO3-, SO32-, H2CO3, HCO3-, CO32-, Ca2+, H+, and OH-. The solution of the system of eqs 12-15 allows the evaluation of the rate of SO2 mass transfer for given experimental conditions and therefore makes possible a comparison between the model proposed and the experimental results. Such a comparison is shown in Figure 4 in the form of a “parity plot” of theoretical results vs experimental results. The plot shows that the model is capable of predicting the experimental results quite accurately, even though it contains no adjustable parameter and is based only on independently measured physical constants. However, it appears
that some discrepancies exist between model and experimental results and, namely, that the model slightly overpredicts the SO2 absorption rate. As pointed out by Rochelle et al. (1983) with reference to limestone dissolution, the discrepancies could be attributed to the fact that the model considers reaction (4), through the HCO3- is consumed to produce H2CO3, as instantaneous, while in the literature some results have been presented in conflict with this assumption (e.g., see Astarita et al., 1983). Indeed, if reaction (4) were not instantaneous, the interfacial HCO3- concentration would be higher, the interfacial pH would be lower, and therefore the SO2 absorption rate would be lower than predicted. The model results can be expressed in a more general way by reporting the enhancement factor for chemical absorption as a function of liquid bulk composition. According to Astarita et al. (1983; p 99), the enhancement factor E is defined as the ratio between the actual absorption rate and the rate which would be observed under the same driving force if no chemical reactions took place, and therefore sulfite diffused only as SO2(aq), according to the following equation:
E)
NSO2(aq) + NHSO3- + NSO32NSO2(aq)
(17)
The trend of E versus the driving force is reported in Figure 5 for different values of the total concentration of sulfite and of Ca2+ ion concentration. The curves obtained are consistent with the one reported by Astarita et al. (1983; p 165) for the case of large driving force. As expected (Danckwerts, 1970; section 5.14), the higher the Ca2+ ion concentration and the lower the total concentration of sulfite, the higher the enhancement factor. Conclusions SO2 absorption in spray or packed towers is a relevant step of wet limestone FGD. Despite the large amount of experimental work carried on this subject, still the need exists of numerical models capable of reliably
202 Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 K ) thermodynamic equilibrium constant kg ) gas-side mass-transfer coefficient, mol/m2 s Pa kL° ) liquid-side mass-transfer coefficient, m/s N ) molar flux, mol/m2 s n ) agitator speed, s-1 pSO2 ) SO2 partial pressure, Pa rSO2 ) SO2 absorption rate, mol/m3 s V ) liquid holdup, m3 x ) normal coordinate in the film, m z ) number of elementary charges, dimensionless Greek Symbols ∆pSO2 ) driving force for SO2 absorption, Pa δ ) film thickness, m τ ) liquid phase residence time, s Subscripts
Figure 4. Comparison between model and experimental results for SO2 absorption rate: (‚‚‚) (20% limit.
av ) average I ) I species in ) inlet out ) outlet
Literature Cited
Figure 5. Enhancement factor vs absorption driving force for different sulfite and Ca2+ concentrations in the liquid bulk: (s) cCa|b ) 1.2 mol/m3; cS|b ) 2.5 mol/m3; (- -) cCa|b ) 1.2 mol/m3; cS|b ) 3.5 mol/m3; (‚‚‚) cCa|b ) 1.5 mol/m3; cS|b ) 2.5 mol/m3.
calculating the SO2 absorption rate. The process involves chemical absorption of SO2 in the instantaneous reaction regime and simultaneous limestone dissolution. In the present work the attention was focused on SO2 absorption, and a diffusive model based on the film theory was developed. Some experiments of SO2 absorption in limestone suspensions were carried out using a bubbling reactor with continuous feeding of both gas and liquid phases. Model and experimental results were compared, and it was shown that, using independently calculated values of gas- and liquid-side masstransfer coefficients, the model fits well the experimental results and furthermore that it allows one to calculate the enhancement factor as a function of the absorption driving force and of the liquid bulk composition. List of Symbols a ) gas-liquid specific interfacial area, m-1 c ) concentration, mol/m3 D ) diffusivity, m2/s E ) enhancement factor, dimensionless G ) gas flow rate, m3/s H ) Henry’s constant, m3 Pa/mol
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Received for review April 22, 1996 Revised manuscript received September 25, 1996 Accepted October 1, 1996X IE9602365
X Abstract published in Advance ACS Abstracts, December 1, 1996.
