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SO2 absorption in a bubbling reactor using limestone suspensions
Pergamon
Chemical Engineerin0 Science, Vol. 49, No. 24A, pp. 4523-4532, 1994 Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0009-2509/94 57.00+0.00
0009-2509(94)00355-6
SO2 ABSORPTION IN A BUBBLING REACTOR USING LIMESTONE SUSPENSIONS A. LANCIA,* D. M U S M A R R A , t F. P E P E * and G. V O L P I C E L L I *;t * Dipartimento di lngegneria Chimica, Universit;i di Napoli "Federico II", P~le Tecchio 80, 80125 Napoli, Italy * Istituto di Ricerche sulla Combustione, C.N.R., P.le Tecchio 80, 80125 Napoli, Italy (Received 24 May 1994; accepted for publication 5 October 1994)
Abstract--In the present work attention was focused on a wet flue gas desulfurization process using limestone suspensions, which is the most common method used to reduce SO2 emissions from power plant exhaust gases. The SO2 absorption rate was measured varying both the SOz concentration in the gas phase and the limestone concentration in the suspension. The experiments were performed by bubbling mixtures of sulfur dioxide and nitrogen in the continuous limestone aqueous suspension. The absorption phenomenon was studied by making use of the film theory to describe the 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 which 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. Furthermore, they take into account the effect of the gradient of the electric potential of diffusion on the diffusive transport of ions and molecules in the film surrounding the gas-liquid interface. The SO2 absorption rate and the limestone dissolution rate experimentally determined were used to integrate the model equations, yielding the value of the film thickness, and allowing the determination of the concentration profiles of the different species in the liquid film and of the enhancement factor for chemical absorption. Consistency between model and experimental results, on the basis of the hypothesis of the model, was found.
INTROD UCTION Treatment of flue gases from power plants is required in order to satisfy the stringent emission limits, particularly to reduce the SOd emission into the atmosphere. A desulfurization process that has reached industrial scale and world-wide diffusion is the wet limestone process. In this process the SO2 scrubbing is realized by contacting the flue gases with a limestone suspension in a spray or packed tower. High SO2 absorption removal efficiency, low cost and wide availability of the absorbing reagent are the principal features that have determined the success of the treatment_ On the other hand, the very large sizes of the absorbing towers and the difficulties related to the safe disposal of the sludge produced are the main disadvantages of such a removal process. The search for different contact conditions between the polluted gas and the absorbing suspension has been the object of a good deal of attention. In particular it has been suggested (ldemura et al., 1978) that SOd could be absorbed in bubbling reactors, in which the gas containing SO~ is bubbled through the scrubbing suspension. The use of such contacting devices would, in fact, allow reduced dimensions for the gas treating plants and reduced capital investments.
•*To whom correspondence should be addressed.
SO 2 absorption in water has been regarded as a process of absorption with instantaneous reaction by Danckwerts (1968), who showed that the absorption rate could be calculated by means of the penetration theory equations, considering a " t o t a l " driving force, obtained by adding the contributions of unreacted SO21~q~ and of its reacted forms (HSO3 and S O l ions). Later Hikita et al. (1977) and Teramoto et al. (1978) modeled results relative to SO2 absorption in water or in aqueous solutions of N a O H and Na2SO 3 using the equations of the penetration theory with instantaneous irreversible reactions, assuming that one or two reaction planes exist in the mass transfer boundary layer. Chang and Rochelle (1985) showed that in the conditions of interest for F G D applications (i.e_ low SO2 partial pressure), the reversibility of the SO 2 hydration reaction has to be taken into account. Furthermore the same authors (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. Sada et al. (1979, 1981a,b, 1982) showed that, in the presence of rather specific experimental conditions (solid made of very fine particles with very high concentration), solid dissolution in the gas-liquid mass transfer boundary layer has to be taken into account. Therefore, according to these authors, the
4523
A. LANCIAet al.
4524
theory proposed by Uchida and coworkers (Uchida et al., 1975; Uchida and Ariga, 1985) for the absorption
of a gas into a slurry containing sparingly soluble solid particles has to be used_ More recently, Pasiuk-Bronikovska and Rudzinski (1991) modeled the SO 2 absorption into aqueous systems neglecting the solid dissolution into the gas-liquid mass transfer boundary layer, and obtained satisfactory results. In their model Pasiuk-Bronikowska and Rudzinski (1991) considered the presence of reacting solids Ca(OH) 2 and CaSO3, and used the film theory to predict the rate of SO2 absorption and the value of the enhancement factor. The model equations take into account the material and charge balances for diffusing ionic species, without considering the effect of the electric potential gradient on the ions diffusion. This approach was criticized by Rochelle (1992), who pointed out that neglecting the effect of the electric potential gradient gives rise to a non-zero flux of charge into the liquid film. To avoid this discrepancy, Rochelle found that it is more accurate to make the explicit assumption that the charge flux is zero, without including any relationship forcing charge balance at the interface_ According to Rochelle's approach, ion diffusion is not influenced by the gradient of the electric potential, yet the error introduced in the evaluation of the mass transfer fluxes and the enhancement factor is negligible (Glasscock and Rochelle, 1989). The purpose of the present study is to propose a rigorous model for the absorption of sulfur dioxide and to compare the model prediction with the experimental measurements of the SO2 absorption rate in a limestone aqueous suspension with a pH ranging from 3.6 to 6. This model, which is similar to the one set up by Lancia et al_ (1991) to study calcium carbonate dissolution, takes into account the coupling between mass transfer and simultaneous ionic reactions that take place in a stagnant liquid film adhering to the gas-liquid interface, with an approach similar to that proposed by Olander (1960). In accordance with Sherwood and Wei (1955), the transport of charged species was studied considering the effect of the electric potential of diffusion_ The only parameter of the model is the thickness of the liquid film surrounding the bubble, the gas-liquid specific interfacial area being calculated using relationships available from the literature. The film thickness is evaluated by numerically integrating the model equations once the SO2 absorption rate and the limestone dissolution rate are experimentally determined. The integration of the model equations leads to the assessment of the concentration profiles of the different species in the liquid film and of the enhancement factor.
EXPERIMENTAL APPARATUS
A sketch of the apparatus used in the experiments of sulfur dioxide absorption by diluted limestone suspensions is given in Fig. 1. The absorber is a
thermostated stirred vessel with continuous feeding of both gas and liquid phase, and in all the experimental runs the temperature of the thermostatic bath was kept at 298 K_ The reactor, made of Pyrex glass, is a jacketed 0.13m i.d. cylinder with a hemispherical bottom, fitted with two vertical baffles and a liquid overflow. An axial two-blade stirrer was used to provide thorough mixing in the liquid phase. The gas phase was a mixture of SO2 in N 2 taken from cylinders of certified composition. It was laminated, passed through a rotameter, and bubbled at the bottom of the reactor with a volumetric flow rate (G) of 1.43 x 10 -4 ma/s. The experiments were carried out at atmospheric pressure with different SO2 partial pressures in the gas phase, namely of 48.6, 99.3, 150 and 190 Pa. The suspension was prepared by mixing bidistilled water and a proper amount of reagent grade CaCO3 powder (average diameter 50 #m), to obtain solid concentrations of 0.30, 0.44, 0.70 or 1.00 kg/m a. A peristaltic pump was used to feed the suspension, and the flow rate was kept at about 1.2 x 10 -6 ma/s. Using a stirrer speed of 5 s-1 the liquid hold-up (V) is 4.1 x 1 0 - 4 m a, corresponding to a mean residence time for the continuous phase z of 340 s. Stimulus-response experiments (Logoteta, 1988) indicated that the liquid phase is well mixed. The product between the gas-side mass transfer coefficient and the gas-liquid specific interracial area (koa) was estimated at 4.81 x 10 -4 mol/m 3 sPa (Esposito, 1991). 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. It was assumed that a steady state was reached after a time larger than 53 had elapsed. The SO2 absorption rate at a steady state was evaluated by measuring the SO2 concentration in the outlet gas stream by means of a UV analyzer (Hartmann and Brown Radas 1G). Furthermore, the dissolved Ca 2+ 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%.
THEORY
SO2 absorption into basic suspensions can be regarded as a process involving the following elementary steps: (a) diffusion of the gas toward the gas-liquid interface; (b) diffusion in the liquid film; (c) chemical reaction; (d) dissolution of the solid reagent. The coupling between diffusion and liquid-phase chemical reaction is generally referred to as chemical absorption. In particular, the reactions accompanying SO2 absorption are ionic, and as such are much faster than the concomitant diffusive transfer_ As indicated by Astarita et al. (1983), such a condition is referred to as the
SO2 absorption in a bubbling reactor
4525 "~
"' An
T
R Reactor F Feed tank D Discharge tank C Temperature controller An S O 2 a n a l y z e r T Water trap
I c,
C
Fig. l. Sketch of the experimental apparatus.
instantaneous reaction regime, and the assumption can be made that the reacting species are at thermodynamic equilibrium throughout the liquid. On the other hand, dissolution of the solid reagents is a process which can take place either in series with or parallel to chemical absorption, depending on the size and the concentration of solid particles. Ramachandran and Sharma (1969) showed that chemical absorption and solid dissolution are processes in series if the following relationship is satisfied: ksa, D 2 -
-
4(k~.)2D,
~
I
(0
where ks is the mass transfer coefficient for solid dissolution, a, is the liquid-solid specific interfacial area, DL is the diffusivity of the dissolved gas, k~ is the liquid-side mass transfer coefficient for gas absorption in the absence of chemical reaction and Ds is the diffusivity of the dissolved solid. Generally, the value of ks for solid particles of the size considered here is in the range of 10-5-10 -4 m/s (Armenante and Kirwan, 1989), while k~. may vary between 10-* and 5.0 × 10 - 4 m / s (Astarita et al., 1983, p. 133). Assuming that the ratio D~/D~ is in the order of 10 -9 m2/s, inequality (1) is largely fulfilled for the particle size and the solid concentration used in the present work, so that the SO2 chemical absorption and the limestone dissolution can be considered as
steps in series. In particular, with the attention being focused on SO2 absorption, in order to avoid taking into account the solid dissolution resistance, the Ca z+ concentration in the outlet liquid stream from the reactor was directly measured. Diffusive model The description of SO2 absorption was carried out by making use of the film theory to describe the 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 which is independent of the reactions taking place. The equations considered by the model describe conditions of thermodynamic equilibrium and material and electrical balances as well as diffusive transport of ions and molecules in the film surrounding the gas-liquid interface. In order to obtain one-dimensional transfer equations, the film thickness was assumed to be negligible with regard to the diameter of bubbles. Moreover, the concentrations in the liquid film were assumed to be stationary, and the CO2 desorption was neglected. The total material balances approach (Olander. 1960) was followed, writing the following conservation equations for calcium, carbonates and suifites:
dNc'~" - 0 dx
(2)
A. LANCIA et al.
4526
while the equilibrium equations are those relative to the following reactions (see Appendix):
Table 1. Diffusivities in water at 298 K Species
D x 103 (rnm2/s)
H+ OH SO2~,q~ HSO3 SO~3-
9.30* 5.27* 1.761 1.33' 0.77*
H2CO 3
2.0*
HCO~ C O 2Ca 2+
1.20' 0.70* 0.79*
H2CO 3 = H + + HCO~HCO~- = H + +CO32-
dNnco; dx
+
dNco~dx
+ - -
HzO=H++OH
-
0
(3)
d~
'
R--T z t c ,
d~b
d~
(6)
I
gives for the gradient of electric potential the following equation: ~1 zl Ol de--! dx
d~b -
-
(7)
=
dx
F
~ z~~T c,
from which it is obtained that the gradient of electric potential is not zero since the diffusivities are not all equal among them (Vinograd and McBain, 1941). The system of eqs (2)-(4) can be solved subject to the conditions that both equilibrium and electroneutrality are respected everywhere in the film. Namely, the electroneutrality equation can be expressed as follows: z, e, = I
0
K = 1.39 × 10 -2
(8)
+
K = 6 . 5 0 x l0 -a K=l.00x
l0 -14
(12) (13)
Nca~. = 0
(14a)
NH2COj + NHCO/ + Nco ]- = 0
(14b)
Nso ..... + NHSO; + Nso~- = kg(Pso: - Hso2Cso..... ) (14c) at x = di, where ~ is the film thickness: CCa2"1~=6 = Cc~[b
(5)
with 1 = Ca 2÷, H +, O H - , H2CO 3, H C O 3 , CO 2-, SO2t,q, HSO3, SO 2-. In eq. (5) c~ and zl are respectively the concentration and the number of elementary charges of the I species, D~ is the diffusivity of the I species (the value of which is reported in Table i), F is the Faraday constant, R is the gas constant, T is the absolute temperature and @ is the electric potential of diffusion. It is worth noting that in transport processes involving charged species, even if there is no applied potential, the condition that there is no net current expressed as: z,N I = 0
(10)
where the values of the thermodynamic constants are calculated from data reported in the literature (Brewer, 1982; Goldberg and Parker, 1985)_ The boundary conditions for the system of eqs (2)-(4) are the following: at x = 0:
(4)
where N~ 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. According to Onsager and Fuoss (1932), Nl is given by: N, =
SO2~aq) + H 2 0 = H + + HSO~-
HSO~- = H + + S O ~ -
dNs° ..... + dNHso; + dNso~- - 0 dx dx dx
- D d c l - F DI
K = 4 . 5 7 x l0 - ~
(9)
(ll)
*Rochelle et al. (1983). ~Pasiuk-Bronikowska and Rudzinski (1991). dNH,co~ - dx
K = 4.25 x l0 -7
(14d)
CH2co~[~=6+C.co;l~=6+Cco~ I~=~=cclb
(14e)
Cso..... [,~=,~ + CHSO;I.~=,~ + Cso]-]~=6 = Cslb
(14f)
In eqs (14a)-(14f) /-/so~ is the Henry's constant for SO2, the value of which is 82.5 m 3 Pa/mol (Goldberg and Parker, 1985), cll~= 6 is the molar concentration of the I species at x = ~, and cc,]b, Cc[b, Cs[b, are the total concentrations of calcium, carbonates and sulfites in the liquid bulk. The boundary conditions (14a) and (14b) state that there is no flux of calcium and carbonates from or to the gas bubble, while condition (14c) is representative of the continuity of the SO 2 flux at the gas-liquid interface. On the other hand, conditions (14d)-(14f) relate film and liquid bulk concentrations at their interface_ Bubbling reactor
The model proposed enables us to calculate the S O 2 mass transfer rate, provided that the value of 6 and the liquid concentrations in the outlet stream are known. On the other hand, the value of 6 can be taken as the parameter of the model and can be determined starting from experimentally determined values of the SO2 gas-liquid mass transfer rate_ With the aim of determining 6 and of calculating the concentration profiles in the liquid film, a number of experimental runs of SO2 absorption in limestone suspension was carried out in a bubbling reactor, using different SO2 concentrations in the gas mixture and different limestone concentrations in the suspension. The absorption reactor was modeled assuming that a piston flow model holds for the motion of each bubble and the surrounding liquid film while they rise
SOz absorption in a bubbling reactor vertically in the well-mixed liquid phase_ With such an assumption, the concentrations of the different species in the liquid bulk can be calculated using the equations of model described above, in which the concentrations of sulfites and Ca 2+ ion are experimentally measured values, and the concentration of carbonates is considered equal to that of Ca 2+ ion, since CO2 desorption has been neglected. On the other hand, for the gas phase a balance on SO2 yields:
nd 2 - NsaRT dy 4 G dps02
one, or that, in other words, it is: f pso~lo., 1 Nss dPs°2 -
,1t'so21,.
so~ll.
-
4~y
(16)
In order to evaluate the integral on the left-hand side of eq. (16), it is necessary to know the value of Ns as a function of Pso~. This can be done, once a value for 6 is assigned, using the equations of the model, which can be numerically integrated. The choice of 6 can be checked using the condition that at the reactor outlet the SO 2 partial pressure calculated from eq. (16) has to be equal to the experimentally measured
0.025 ME
0.020 o
E
[3
0.015
0.010
tl 0.005 0
, 0
I 50
(17)
G
RESULTS AND DISCUSSION
(15)
nRTad2
RTaV
The experimental results for the SO2 absorption into aqueous limestone suspensions are shown in Figs 2 and 3. Figure 2 shows the SO2 absorption rate per unit volume of liquid (rso2) as a function of SO2 partial pressure in the inlet gas for different values of limestone concentration in the suspension fed to the reactor. For the limestone concentrations considered, the absorption rate increases nearly linearly with SO2 partial pressure, and depends weakly on limestone concentration. In Fig. 3 the dissolved calcium concentration is reported again versus SO2 partial pressure in the inlet gas and for different values of limestone concentration in the suspension fed to the reactor. It is worth noting that the Ca 2+ concentration is also strongly influenced by the SO2 concentration in the inlet gas, while only a weak dependence on limestone concentration is observed. The experimental values for SO2 absorption rate and Ca 2 + concentration reported in Figs 2 and 3 were used to integrate the model equations, allowing the calculation of the parameter 6 using eq. (17) with a trial and error procedure. The integration, performed for each experimental run, yielded values of 6 ranging around 51/am, with a standard deviation of 8 gin. This is in agreement with the physical meaning of 6, which, according to the film theory, at fixed hydrodynamic conditions should be independent of concentration levels. Figure 4 shows the comparison between the model results, obtained using the 51 ~m average value for the film thickness 6, and the experimental results, in
where Pso~ is the SO2 partial pressure, y is the coordinate along the reactor axis in a system having its origin at the bottom of the reactor, Ns is the sum of the fluxes of SO2t~q,, HSO3 and SO32-, d is the reactor internal diameter and a is the gas-liquid specific interfacial area, which can be calculated using the correlation reported by Shridar and Potter (1980). For the experimental conditions considered, the specific interfacial area can be estimated at 1.0 cm- ~. Equation (15) can be integrated by separating variables with the condition that at y = 0 it is Pso, = Pso~l~,, where Pso2l~. is the SO2 partial pressure of the gas fed to the reactor:
fp's°2 ~sdpso
4527
,
I 100
,
I 150
200
Pso21in (Pa) Fig. 2. SO2 absorption rate versus SO2 inlet partial pressure for different limestone concentrations: O, 0.30 kg/ma; D, 0_44kg/m3; A, 0.70 kg/m~; O, 1.0 kg/m3.
4528
A. LANCIA et al.
5.0
H
4.0
[]
o
0
E
A []
+
~* 3.0
0
2.0
o A
El
1.0
0
~
I
0
,
I
50
,
I
100
,
150
200
Pso21in (Pa) Fig. 3. Dissolved calcium concentration versus SOz inlet partial pressure for different limestone concentrations: ©, 0.30 kg/m3; ~ , 0.44 kg/m3; A, 0.70 kg/m3; O, 1.0 kg/m 3.
70 60 50 []
40
O ,.-t
__O
8
30
r/'J-
20 10 0 0
I
I
10
20
,
I
30
,
I
40
,
1
50
~
I
60
,
70
Pso21out experimental (Pa) Fig. 4. Comparison between SO2 partial pressure in the outlet stream as experimentally detected and as calculated by the model for 6 = 51/am. Limestone concentration in the suspension: O, 0.30 kg/m3; 1:3, 0.44 kg/m3; A, 0.70 kg/m3; O, 1.0 kg/m 3.
terms of SO, partial pressure in the outlet gas stream from the reactor. Good agreement between model and experimental results is outlined in Fig. 4, even though some discrepancies can be observed for the higher values of SO2 partial pressure. Figures 5(a) and 5(b) show the profiles in the liquid film of the concentrations of the different species, as well as of the gradient of the electrical potential of diffusion dd~/dx, as obtained at the gas inlet section of the reactor (y = 0) by integrating the equations of the model. The figures refer to two different SO2 partial pressures in the inlet gas stream 548.6 Pa in Fig. 5(a) and 190 Pa in Fig. 5(b)] and to the same limestone concentration in the suspension fed to the
reactor (1.0 kg/m3). Due to their order of magnitude the concentrations of C O l - and O H - are not reported. The profile of the gradient of the electric potential of diffusion in the film can be explained considering that it tends to contrast charge separation, and globally depends on the concentration gradients of the ions present. In particular, in the zone of the film closer to the gas-liquid interface, it slows down the diffusion of H + ion, which has the highest diffusivity between the ions involved in the process, while its sign changes when the H + concentration becomes low. The non-zero gradient of the concentration profile of Ca 2+, which is not transported from or to the gas
SO2 absorption in a bubbling reactor
4529
50 .~...4~HSO3"
E -~
5
~
4
~ -
/2 "~ -.. ~
ii
0
-50 <
/
3 U e-" 0
C a 2+
Z
"~.
2
0
0.2
0.4
0.6
0.8
1.0
x/5 (-) (a)
2O
5O
E
!
0
"-6 16
.-:2
12
,~.
r-,
=
0
-50
J HSO3
Ca2+
< Z v
"~. -~.
8
e
s
4
H2CO3
_..~~y/O2(aq)
~
~
~
~
~
~
H~,.~)a"~<-- -
H+
0 0
0.2
0.4
0.6
0.8
I .0
x/B (-) (b) Fig. 5. Concentration profiles of the different species and profile of the gradient of the electric potential of diffusion in the film at the reactor inlet (y = 0). (a) SO2 partial pressure 48.6 Pa and limestone concentration in the suspension 1 kg/m ~. (b) SO2 partial pressure 190 Pa and limestone concentration in the suspension l kg/m 3. phase and is not involved in any reaction, is the resultant effect of the electric potential. Moreover, the profiles reported in Figs 5(a) and (b) enable the identification of a reaction zone in the film in which the following reactions take place: H + + SO~- = HSO~ SO21aq)+SO 2- + H 2 0 = 2 H S O
K = 1.53 x 107 ~
(17)
K = 2 . 1 3 x 105
(18) H + + HCO~" = H 2 C O 3
K = 2.35 x 106
(19)
These reactions consume H ÷ and SO21,q) coming
from the interface, and SO] - and H C O 3 coming from the liquid bulk, to produce H S O ~ and H 2 C O 3. As a consequence, the concentrations of H +, SO2~,q), S O l and HCO~- become practically zero at the reaction zone, while H 2 C O 3 has a maximum and the H S O 3 concentration profile, which depends on both the net sulfur transport from the gas-liquid interface and reactions (17) and (18), changes its slope in the reaction zone. Moreover, the model results show that the reaction zone gets closer to the gas-liquid interface as the sulfur concentration increases. This trend is shown by a comparison of Figs 5(a) and 5(b). The model results enable us to evaluate the
A. L A N O ^ et al.
4530
50
40 o
30
2o ~
.
.
~
-.. . . ..
1o l
,
,
i
0
i
[
i
i
L
0.1 c
~
I
0.2 -c
S02(aq)i
,
t
S()201q)h
i
I
i
,
0.3 (mol/m 3)
i
[
i
,
,
0.4
L
0.5
Fig. 6. Enhancement factor versus absorption driving force for different sulfite and Ca 2+ concentrations in the liquid bulk. - - , Cc.lb= 1.2 mol/m 3, Cslb = 2.5 mol/m3; . . . . . , Cc,lb = 1.2 mol/m 3, Cslb = 3_5 mol/m3; . . . . . . , CCBIb= 1.5 mol/m 3, cslb = 2.5 mol/m 3.
enhancement factor for chemical absorption at assigned 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 that would be observed with the same driving force in the absence of chemical reaction: E=
N5 (Dso2,,q,/f)(Cso2,.q,l~=o
(20)
interaction between limestone dissolution and SO2 transport, and to describe the influence on the SO 2 absorption rate of different species that can be added to the liquid to enhance SO 2 removal. Acknowled#ements--Ing. D. Karatza, Ing. L. Esposito and
Mr C. Rossi should be credited for the help given in carrying out the experimental work_
- Cso2,.,,Ix=a)
The trend of E versus the driving force is reported in Fig_ 6 for different values of the total concentration of sulfites and of Ca 2 + 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), the higher the Ca 2+ ion concentration and the lower the total concentration of sulfites, the higher the enhancement factor. CONCLUSIONS
SO2 absorption in bubbling reactors is a promising technique for flue gas desulfurization. The process involves chemical absorption of SO2 in the instantaneous reaction regime and limestone dissolution. In the present work chemical absorption has been studied and a diffusive model based on the film theory has been developed. It has been shown that such a model fits well the experimental results of SO2 absorption in a bubbling reactor and enables us to evaluate the enhancement factor as a function of the driving force for absorption and of the liquid bulk composition_ Moreover, the concentration profiles in the liquid film were evaluated, leading to the identification of a reaction zone. The knowledge of concentration profiles in the liquid-side mass transfer boundary layer may allow us to ascertain the
NOTATION a
as
A B ¢1
d
1), E F FI G
Hso2 ko
kt ks K
/v, Ns Pso~ rsoz
R T V X
gas-liquid specific interfacial area, m - 1 liquid-solid specific interracial area, m-1 Debye-Hiickel constant, m 3/2 mol- 1/2 Debye-Hiickel parameter concentration of the I species, mol/m 3 reactor diameter, m diffusivity of the I species, mZ/s diffusivity of the absorbed gas, m2/s diffusivity of the dissolved solid, m2/s enhancement factor, dimensionless Faraday constant, s A/mol ionic strength, mol/m 3 gas flow rate, m3/s SO2 Henry's constant, m~Pa/mol gas-side mass transfer coefficient, mol/mZsPa liquid-side mass transfer coefficient, m/s solid-liquid mass transfer coefficient, m/s thermodynamic equilibrium constant flux of the 1 species, mol/m2s total flux of sulfites, mol/m2s SO 2 partial pressure, Pa SO2 absorption rate, mol/m3s gas constant, J/mol K absolute temperature, K liquid hold-up, m 3 normal coordinate in the film, m
SO2 absorption in a bubbling reactor Y ZI
normal coordinate along the reactor axis, m number of elementary charges of the I species, dimensionless
Greek letters th activity of the I species, m o l / m 3 Yl activity coefficient of the I species, dimensionless 6 film thickness, m vl stoichiometric coefficient of the I species, dimensionless ~b electric potential, J/s A liquid phase residence time, s
REFERENCES Abdulsattar, A. H., Shridar, S_ and Bromley, L. A_, 1977, Thermodynamics of the sulfur dioxide-seawater system. A.I.Ch.E.J. 23, 62-68. Armenante, P. M. and Kirwan, D. J., 1989, Mass transfer to microparticles in agitated systems. Chem. Engng Sci. 44, 2781-2796. Astarita, G., Savage, D. W_ and Bisio, A_, 1983, Gas Treating with Chemical Solvents. Wiley lnterscience, New York_ Brewer, L., 1982, Thermodynamic values for desulfurization processes, in Flue Gas Desulfurization (Edited by J. L. Hudson and G. T. Rochelle), pp. 1-39. ACS Syrup., Set., 188. Chang, C. S. and Rochelle, G. T., 1982, SO2 absorption into aqueous solutions. A.I.Ch.E.J. 27, 261-266. Chang, C. S. and Rochelle, G. T., 1985, SO2 absorption into NaOH and Na2SO3 aqueous solutions. Ind. Eno- Chem. Fundam. 24, 7-11. Colin, E., Clarke, W. and Glew, D. N. 1980, Evaluation of Debye-H~ckel limiting slopes for water between 0 ° and 150°C. J. Chem. Sac_ Faraday Trans. 76, 1911-1916. Danckwerts, P. V., 1968, Gas absorption with instantaneous reaction. Chem. Engng Sci. 23, 1045-1051. Danckwerts, P. V., 1970, Gas-Liquid Reactions. McGrawHill, New York, Chap. 5.14. Esposito, L_, 1991, Assorbimento di SOz in sospensioni di calcare ed in soluzioni di idrossido di calcio. Graduation thesis, University of Naples "Federico II". Glasscock, D. A. and Rochelle, G. T., 1989, Numerical simulation of theories for gas absorption with chemical reaction. A.I.Ch.E.J. 35, 1271-1281. Goldberg, R. N. and Parker, V. B., 1985, Thermodynamic of solution of SO2c~) in water and of sulfur dioxide solutions. J. Res. Nat. Bur. Stan. 90, 341-358. Hikita, H., Satoru. A. and Tsuji., T., 1977, Absorption of sulfur dioxide into sodium hydroxide and sodium sulfite solutions. A.I.Ch.E.J. 23, 538-544. ldemura, H., Kanai, T. and Yanagioka, H., 1978, Jet bubbling flue gas desulfurization. Chem. Engng Prog. 74(2), 46-50. Lancia, A., Musmarra, D., Pepe, F. and Volpicelli, G., 1991, Concentration profiles in the diffusional film in the calcium carbonate dissolution process. Chem. Engn# Sci. 46, 2507-2512. Logoteta, G., 1988, Stadi limitanti nel processo di desolforazione dei fumi di combustione--Studio sperimentale. Graduation thesis, University of Naples "Federico II". Olander, D. R_, 1960, Simultaneous mass transfer and equilibrium chemical reaction. A.I.Ch.E_ J. 6, 233-239. Onsager, L. and Fuoss, R. M., 1932, Irreversible processes in electrolytes. Diffusion, conductance and viscous flow in arbitrary mixtures of strong electrolytes. J. Phys. Chem. 36, 2689-2778.
4531
Pasiuk-Bronikowska, W. and Rudzinski, K_ J., 1991, Absorption of SO2 into aqueous systems. Chem. Engno. Sci. 46, 2281-2291. Ramachandran, P. A. and Sharma, M. M., 1969, Absorption with fast reaction in a slurry containing sparingly soluble fine particles. Chem. Engng Sci_ 24, 1681-1686. Rochelle, G. T., 1992, Comments on absorption of SO2 into aqueous systems. Chem. Enon 0 Sci. 27, 3169-3171_ Rochelle, G. T., Chan, P. K. R. and Toprac, A. T., 1983, Limestone Dissolution in Flue Gas Desulfurization Process. U.S. EPA-6/7-83-043, Washington, DC_ Sada, E., Kumazawa, H. and Butt, M. H_, 1979, Single and simultaneous absorption of lean SO2 and NO2 into aqueous slurries of Ca(OH)2 or Mg(OH) 2 particles. J. Chem. Eng. Japan 12, 111-117. Sada, E., Kumazawa, H., Sawada, Y_ and Hashizume, I., 198 la. Kinetics of absorption of lean sulphur dioxide into aqueous slurry of calcium carbonate and magnesium hydroxide_ Chem. Engng Sci. 36, 149-155. Sada, E., Kumazawa, H., Hashizume, I. and Kamishima, M., 1981b_ Desulfurization by limestone slurry with added magnesium sulfate. Chem. Eng. J. 22, 133-141_ Sada, E., Kumazawa, H., Hashizume, I_ and Nishimura, H., 1982, Absorption of dilute SO2 into aqueous slurries of CaSO 3. Chem. Engng Sci. 37, 1432-1435. Sherwood, T. K. and Wei, J. C., 1955, Ion diffusion in mass transfer between phases. A_I.Ch.E.J. 1, 522-527_ Shridar, T. and Potter, O_ E, 1980, Interfacial area in gas-liquid stirred vessels. Chem. Engng Sci., 35, 683-695. Teramoto, M., Nagamochi, M., Hiramine, S., Fujii, N. and Teranishi, H., 1978, Simultaneous absorption of SO2 and CO2 in aqueous Na2SO3 solutions_ Int. Chem. Engno 18, 250-257. Uchida, S. and Ariga, O., 1985, Absorption ofsulphur dioxide into limestone slurry in a stirred tank. Can. J_ Chem. Engng 63, 778-782. Uchida, S., Koide, K. and Shindo, M_, 1975, Gas absorption with fast reaction into a slurry containing fine particles. Chem_ Engng Sci. 30, 644-646. Vinograd, J. R. and McBain, J. W., 1941, Diffusion of electrolytes and the ions in their mixtures. J. Am. Chem. Soc. 63, 2008-2015.
APPENDIX
The chemical reactions taken into account by the model can be written in the following general form: vfl = 0
(A.I)
I
where vI is the stoichiometric coefficient of the I species and is assumed positive for the reactants and negative for the products. The equilibrium condition for reaction (A.I) is K = I~ ~'; ~'
(A.2)
I
where at is the activity of the ! species. The activity ,vt is related to the molar concentration by: a l = ctyt
where )'t is the activity coefficient.
(A.3)
A. LANCIA et al.
4532
Values of the activity coefficients for anions (M) and cations (x) can be calculated using the extended version of the Debye-Hiickel theory proposed by Bromley and coworkers (Abdulsattar et al., 1977). According to those authors it is: log(~'M)
=
A~zu(FI)l/2 1 + ( F I ) ~/2
(A.6)
FI = ½ ~, z~c, I
The values of the Debye-Hiickel parameters N are reported in Table 2, taken from Abdulsattar et al. (1977).
+a,~c~+y'a,~c~ x
(A.4)
Iog(T~) =
equation:
Ayz~(FI) x12 1 + (FI) 1/2 b B~ ~M cM + ~u BMC~
(A.5) In these equations Av is the Debye-Hfickel constant, the value of which is 5.62 x 1 0 - 2 m 3/2 mol-t/2 (Colin et al., 1980), and FI is the ionic strength, which can be evaluated by means of the following
Table 2. Debye-H/ickel parameters for eqs. (A.3) and (A.4). From Abdulsattar et al. (1977) Species
B
H+ OH HSO~ SO~ HCO~
0.087 -0.012 -0.013 -0.087 -0.039
co~-
-0087
Ca z +
- 0.035
Chemical Engineerin0 Science, Vol. 49, No. 24A, pp. 4523-4532, 1994 Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0009-2509/94 57.00+0.00
0009-2509(94)00355-6
SO2 ABSORPTION IN A BUBBLING REACTOR USING LIMESTONE SUSPENSIONS A. LANCIA,* D. M U S M A R R A , t F. P E P E * and G. V O L P I C E L L I *;t * Dipartimento di lngegneria Chimica, Universit;i di Napoli "Federico II", P~le Tecchio 80, 80125 Napoli, Italy * Istituto di Ricerche sulla Combustione, C.N.R., P.le Tecchio 80, 80125 Napoli, Italy (Received 24 May 1994; accepted for publication 5 October 1994)
Abstract--In the present work attention was focused on a wet flue gas desulfurization process using limestone suspensions, which is the most common method used to reduce SO2 emissions from power plant exhaust gases. The SO2 absorption rate was measured varying both the SOz concentration in the gas phase and the limestone concentration in the suspension. The experiments were performed by bubbling mixtures of sulfur dioxide and nitrogen in the continuous limestone aqueous suspension. The absorption phenomenon was studied by making use of the film theory to describe the 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 which 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. Furthermore, they take into account the effect of the gradient of the electric potential of diffusion on the diffusive transport of ions and molecules in the film surrounding the gas-liquid interface. The SO2 absorption rate and the limestone dissolution rate experimentally determined were used to integrate the model equations, yielding the value of the film thickness, and allowing the determination of the concentration profiles of the different species in the liquid film and of the enhancement factor for chemical absorption. Consistency between model and experimental results, on the basis of the hypothesis of the model, was found.
INTROD UCTION Treatment of flue gases from power plants is required in order to satisfy the stringent emission limits, particularly to reduce the SOd emission into the atmosphere. A desulfurization process that has reached industrial scale and world-wide diffusion is the wet limestone process. In this process the SO2 scrubbing is realized by contacting the flue gases with a limestone suspension in a spray or packed tower. High SO2 absorption removal efficiency, low cost and wide availability of the absorbing reagent are the principal features that have determined the success of the treatment_ On the other hand, the very large sizes of the absorbing towers and the difficulties related to the safe disposal of the sludge produced are the main disadvantages of such a removal process. The search for different contact conditions between the polluted gas and the absorbing suspension has been the object of a good deal of attention. In particular it has been suggested (ldemura et al., 1978) that SOd could be absorbed in bubbling reactors, in which the gas containing SO~ is bubbled through the scrubbing suspension. The use of such contacting devices would, in fact, allow reduced dimensions for the gas treating plants and reduced capital investments.
•*To whom correspondence should be addressed.
SO 2 absorption in water has been regarded as a process of absorption with instantaneous reaction by Danckwerts (1968), who showed that the absorption rate could be calculated by means of the penetration theory equations, considering a " t o t a l " driving force, obtained by adding the contributions of unreacted SO21~q~ and of its reacted forms (HSO3 and S O l ions). Later Hikita et al. (1977) and Teramoto et al. (1978) modeled results relative to SO2 absorption in water or in aqueous solutions of N a O H and Na2SO 3 using the equations of the penetration theory with instantaneous irreversible reactions, assuming that one or two reaction planes exist in the mass transfer boundary layer. Chang and Rochelle (1985) showed that in the conditions of interest for F G D applications (i.e_ low SO2 partial pressure), the reversibility of the SO 2 hydration reaction has to be taken into account. Furthermore the same authors (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. Sada et al. (1979, 1981a,b, 1982) showed that, in the presence of rather specific experimental conditions (solid made of very fine particles with very high concentration), solid dissolution in the gas-liquid mass transfer boundary layer has to be taken into account. Therefore, according to these authors, the
4523
A. LANCIAet al.
4524
theory proposed by Uchida and coworkers (Uchida et al., 1975; Uchida and Ariga, 1985) for the absorption
of a gas into a slurry containing sparingly soluble solid particles has to be used_ More recently, Pasiuk-Bronikovska and Rudzinski (1991) modeled the SO 2 absorption into aqueous systems neglecting the solid dissolution into the gas-liquid mass transfer boundary layer, and obtained satisfactory results. In their model Pasiuk-Bronikowska and Rudzinski (1991) considered the presence of reacting solids Ca(OH) 2 and CaSO3, and used the film theory to predict the rate of SO2 absorption and the value of the enhancement factor. The model equations take into account the material and charge balances for diffusing ionic species, without considering the effect of the electric potential gradient on the ions diffusion. This approach was criticized by Rochelle (1992), who pointed out that neglecting the effect of the electric potential gradient gives rise to a non-zero flux of charge into the liquid film. To avoid this discrepancy, Rochelle found that it is more accurate to make the explicit assumption that the charge flux is zero, without including any relationship forcing charge balance at the interface_ According to Rochelle's approach, ion diffusion is not influenced by the gradient of the electric potential, yet the error introduced in the evaluation of the mass transfer fluxes and the enhancement factor is negligible (Glasscock and Rochelle, 1989). The purpose of the present study is to propose a rigorous model for the absorption of sulfur dioxide and to compare the model prediction with the experimental measurements of the SO2 absorption rate in a limestone aqueous suspension with a pH ranging from 3.6 to 6. This model, which is similar to the one set up by Lancia et al_ (1991) to study calcium carbonate dissolution, takes into account the coupling between mass transfer and simultaneous ionic reactions that take place in a stagnant liquid film adhering to the gas-liquid interface, with an approach similar to that proposed by Olander (1960). In accordance with Sherwood and Wei (1955), the transport of charged species was studied considering the effect of the electric potential of diffusion_ The only parameter of the model is the thickness of the liquid film surrounding the bubble, the gas-liquid specific interfacial area being calculated using relationships available from the literature. The film thickness is evaluated by numerically integrating the model equations once the SO2 absorption rate and the limestone dissolution rate are experimentally determined. The integration of the model equations leads to the assessment of the concentration profiles of the different species in the liquid film and of the enhancement factor.
EXPERIMENTAL APPARATUS
A sketch of the apparatus used in the experiments of sulfur dioxide absorption by diluted limestone suspensions is given in Fig. 1. The absorber is a
thermostated stirred vessel with continuous feeding of both gas and liquid phase, and in all the experimental runs the temperature of the thermostatic bath was kept at 298 K_ The reactor, made of Pyrex glass, is a jacketed 0.13m i.d. cylinder with a hemispherical bottom, fitted with two vertical baffles and a liquid overflow. An axial two-blade stirrer was used to provide thorough mixing in the liquid phase. The gas phase was a mixture of SO2 in N 2 taken from cylinders of certified composition. It was laminated, passed through a rotameter, and bubbled at the bottom of the reactor with a volumetric flow rate (G) of 1.43 x 10 -4 ma/s. The experiments were carried out at atmospheric pressure with different SO2 partial pressures in the gas phase, namely of 48.6, 99.3, 150 and 190 Pa. The suspension was prepared by mixing bidistilled water and a proper amount of reagent grade CaCO3 powder (average diameter 50 #m), to obtain solid concentrations of 0.30, 0.44, 0.70 or 1.00 kg/m a. A peristaltic pump was used to feed the suspension, and the flow rate was kept at about 1.2 x 10 -6 ma/s. Using a stirrer speed of 5 s-1 the liquid hold-up (V) is 4.1 x 1 0 - 4 m a, corresponding to a mean residence time for the continuous phase z of 340 s. Stimulus-response experiments (Logoteta, 1988) indicated that the liquid phase is well mixed. The product between the gas-side mass transfer coefficient and the gas-liquid specific interracial area (koa) was estimated at 4.81 x 10 -4 mol/m 3 sPa (Esposito, 1991). 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. It was assumed that a steady state was reached after a time larger than 53 had elapsed. The SO2 absorption rate at a steady state was evaluated by measuring the SO2 concentration in the outlet gas stream by means of a UV analyzer (Hartmann and Brown Radas 1G). Furthermore, the dissolved Ca 2+ 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%.
THEORY
SO2 absorption into basic suspensions can be regarded as a process involving the following elementary steps: (a) diffusion of the gas toward the gas-liquid interface; (b) diffusion in the liquid film; (c) chemical reaction; (d) dissolution of the solid reagent. The coupling between diffusion and liquid-phase chemical reaction is generally referred to as chemical absorption. In particular, the reactions accompanying SO2 absorption are ionic, and as such are much faster than the concomitant diffusive transfer_ As indicated by Astarita et al. (1983), such a condition is referred to as the
SO2 absorption in a bubbling reactor
4525 "~
"' An
T
R Reactor F Feed tank D Discharge tank C Temperature controller An S O 2 a n a l y z e r T Water trap
I c,
C
Fig. l. Sketch of the experimental apparatus.
instantaneous reaction regime, and the assumption can be made that the reacting species are at thermodynamic equilibrium throughout the liquid. On the other hand, dissolution of the solid reagents is a process which can take place either in series with or parallel to chemical absorption, depending on the size and the concentration of solid particles. Ramachandran and Sharma (1969) showed that chemical absorption and solid dissolution are processes in series if the following relationship is satisfied: ksa, D 2 -
-
4(k~.)2D,
~
I
(0
where ks is the mass transfer coefficient for solid dissolution, a, is the liquid-solid specific interfacial area, DL is the diffusivity of the dissolved gas, k~ is the liquid-side mass transfer coefficient for gas absorption in the absence of chemical reaction and Ds is the diffusivity of the dissolved solid. Generally, the value of ks for solid particles of the size considered here is in the range of 10-5-10 -4 m/s (Armenante and Kirwan, 1989), while k~. may vary between 10-* and 5.0 × 10 - 4 m / s (Astarita et al., 1983, p. 133). Assuming that the ratio D~/D~ is in the order of 10 -9 m2/s, inequality (1) is largely fulfilled for the particle size and the solid concentration used in the present work, so that the SO2 chemical absorption and the limestone dissolution can be considered as
steps in series. In particular, with the attention being focused on SO2 absorption, in order to avoid taking into account the solid dissolution resistance, the Ca z+ concentration in the outlet liquid stream from the reactor was directly measured. Diffusive model The description of SO2 absorption was carried out by making use of the film theory to describe the 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 which is independent of the reactions taking place. The equations considered by the model describe conditions of thermodynamic equilibrium and material and electrical balances as well as diffusive transport of ions and molecules in the film surrounding the gas-liquid interface. In order to obtain one-dimensional transfer equations, the film thickness was assumed to be negligible with regard to the diameter of bubbles. Moreover, the concentrations in the liquid film were assumed to be stationary, and the CO2 desorption was neglected. The total material balances approach (Olander. 1960) was followed, writing the following conservation equations for calcium, carbonates and suifites:
dNc'~" - 0 dx
(2)
A. LANCIA et al.
4526
while the equilibrium equations are those relative to the following reactions (see Appendix):
Table 1. Diffusivities in water at 298 K Species
D x 103 (rnm2/s)
H+ OH SO2~,q~ HSO3 SO~3-
9.30* 5.27* 1.761 1.33' 0.77*
H2CO 3
2.0*
HCO~ C O 2Ca 2+
1.20' 0.70* 0.79*
H2CO 3 = H + + HCO~HCO~- = H + +CO32-
dNnco; dx
+
dNco~dx
+ - -
HzO=H++OH
-
0
(3)
d~
'
R--T z t c ,
d~b
d~
(6)
I
gives for the gradient of electric potential the following equation: ~1 zl Ol de--! dx
d~b -
-
(7)
=
dx
F
~ z~~T c,
from which it is obtained that the gradient of electric potential is not zero since the diffusivities are not all equal among them (Vinograd and McBain, 1941). The system of eqs (2)-(4) can be solved subject to the conditions that both equilibrium and electroneutrality are respected everywhere in the film. Namely, the electroneutrality equation can be expressed as follows: z, e, = I
0
K = 1.39 × 10 -2
(8)
+
K = 6 . 5 0 x l0 -a K=l.00x
l0 -14
(12) (13)
Nca~. = 0
(14a)
NH2COj + NHCO/ + Nco ]- = 0
(14b)
Nso ..... + NHSO; + Nso~- = kg(Pso: - Hso2Cso..... ) (14c) at x = di, where ~ is the film thickness: CCa2"1~=6 = Cc~[b
(5)
with 1 = Ca 2÷, H +, O H - , H2CO 3, H C O 3 , CO 2-, SO2t,q, HSO3, SO 2-. In eq. (5) c~ and zl are respectively the concentration and the number of elementary charges of the I species, D~ is the diffusivity of the I species (the value of which is reported in Table i), F is the Faraday constant, R is the gas constant, T is the absolute temperature and @ is the electric potential of diffusion. It is worth noting that in transport processes involving charged species, even if there is no applied potential, the condition that there is no net current expressed as: z,N I = 0
(10)
where the values of the thermodynamic constants are calculated from data reported in the literature (Brewer, 1982; Goldberg and Parker, 1985)_ The boundary conditions for the system of eqs (2)-(4) are the following: at x = 0:
(4)
where N~ 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. According to Onsager and Fuoss (1932), Nl is given by: N, =
SO2~aq) + H 2 0 = H + + HSO~-
HSO~- = H + + S O ~ -
dNs° ..... + dNHso; + dNso~- - 0 dx dx dx
- D d c l - F DI
K = 4 . 5 7 x l0 - ~
(9)
(ll)
*Rochelle et al. (1983). ~Pasiuk-Bronikowska and Rudzinski (1991). dNH,co~ - dx
K = 4.25 x l0 -7
(14d)
CH2co~[~=6+C.co;l~=6+Cco~ I~=~=cclb
(14e)
Cso..... [,~=,~ + CHSO;I.~=,~ + Cso]-]~=6 = Cslb
(14f)
In eqs (14a)-(14f) /-/so~ is the Henry's constant for SO2, the value of which is 82.5 m 3 Pa/mol (Goldberg and Parker, 1985), cll~= 6 is the molar concentration of the I species at x = ~, and cc,]b, Cc[b, Cs[b, are the total concentrations of calcium, carbonates and sulfites in the liquid bulk. The boundary conditions (14a) and (14b) state that there is no flux of calcium and carbonates from or to the gas bubble, while condition (14c) is representative of the continuity of the SO 2 flux at the gas-liquid interface. On the other hand, conditions (14d)-(14f) relate film and liquid bulk concentrations at their interface_ Bubbling reactor
The model proposed enables us to calculate the S O 2 mass transfer rate, provided that the value of 6 and the liquid concentrations in the outlet stream are known. On the other hand, the value of 6 can be taken as the parameter of the model and can be determined starting from experimentally determined values of the SO2 gas-liquid mass transfer rate_ With the aim of determining 6 and of calculating the concentration profiles in the liquid film, a number of experimental runs of SO2 absorption in limestone suspension was carried out in a bubbling reactor, using different SO2 concentrations in the gas mixture and different limestone concentrations in the suspension. The absorption reactor was modeled assuming that a piston flow model holds for the motion of each bubble and the surrounding liquid film while they rise
SOz absorption in a bubbling reactor vertically in the well-mixed liquid phase_ With such an assumption, the concentrations of the different species in the liquid bulk can be calculated using the equations of model described above, in which the concentrations of sulfites and Ca 2+ ion are experimentally measured values, and the concentration of carbonates is considered equal to that of Ca 2+ ion, since CO2 desorption has been neglected. On the other hand, for the gas phase a balance on SO2 yields:
nd 2 - NsaRT dy 4 G dps02
one, or that, in other words, it is: f pso~lo., 1 Nss dPs°2 -
,1t'so21,.
so~ll.
-
4~y
(16)
In order to evaluate the integral on the left-hand side of eq. (16), it is necessary to know the value of Ns as a function of Pso~. This can be done, once a value for 6 is assigned, using the equations of the model, which can be numerically integrated. The choice of 6 can be checked using the condition that at the reactor outlet the SO 2 partial pressure calculated from eq. (16) has to be equal to the experimentally measured
0.025 ME
0.020 o
E
[3
0.015
0.010
tl 0.005 0
, 0
I 50
(17)
G
RESULTS AND DISCUSSION
(15)
nRTad2
RTaV
The experimental results for the SO2 absorption into aqueous limestone suspensions are shown in Figs 2 and 3. Figure 2 shows the SO2 absorption rate per unit volume of liquid (rso2) as a function of SO2 partial pressure in the inlet gas for different values of limestone concentration in the suspension fed to the reactor. For the limestone concentrations considered, the absorption rate increases nearly linearly with SO2 partial pressure, and depends weakly on limestone concentration. In Fig. 3 the dissolved calcium concentration is reported again versus SO2 partial pressure in the inlet gas and for different values of limestone concentration in the suspension fed to the reactor. It is worth noting that the Ca 2+ concentration is also strongly influenced by the SO2 concentration in the inlet gas, while only a weak dependence on limestone concentration is observed. The experimental values for SO2 absorption rate and Ca 2 + concentration reported in Figs 2 and 3 were used to integrate the model equations, allowing the calculation of the parameter 6 using eq. (17) with a trial and error procedure. The integration, performed for each experimental run, yielded values of 6 ranging around 51/am, with a standard deviation of 8 gin. This is in agreement with the physical meaning of 6, which, according to the film theory, at fixed hydrodynamic conditions should be independent of concentration levels. Figure 4 shows the comparison between the model results, obtained using the 51 ~m average value for the film thickness 6, and the experimental results, in
where Pso~ is the SO2 partial pressure, y is the coordinate along the reactor axis in a system having its origin at the bottom of the reactor, Ns is the sum of the fluxes of SO2t~q,, HSO3 and SO32-, d is the reactor internal diameter and a is the gas-liquid specific interfacial area, which can be calculated using the correlation reported by Shridar and Potter (1980). For the experimental conditions considered, the specific interfacial area can be estimated at 1.0 cm- ~. Equation (15) can be integrated by separating variables with the condition that at y = 0 it is Pso, = Pso~l~,, where Pso2l~. is the SO2 partial pressure of the gas fed to the reactor:
fp's°2 ~sdpso
4527
,
I 100
,
I 150
200
Pso21in (Pa) Fig. 2. SO2 absorption rate versus SO2 inlet partial pressure for different limestone concentrations: O, 0.30 kg/ma; D, 0_44kg/m3; A, 0.70 kg/m~; O, 1.0 kg/m3.
4528
A. LANCIA et al.
5.0
H
4.0
[]
o
0
E
A []
+
~* 3.0
0
2.0
o A
El
1.0
0
~
I
0
,
I
50
,
I
100
,
150
200
Pso21in (Pa) Fig. 3. Dissolved calcium concentration versus SOz inlet partial pressure for different limestone concentrations: ©, 0.30 kg/m3; ~ , 0.44 kg/m3; A, 0.70 kg/m3; O, 1.0 kg/m 3.
70 60 50 []
40
O ,.-t
__O
8
30
r/'J-
20 10 0 0
I
I
10
20
,
I
30
,
I
40
,
1
50
~
I
60
,
70
Pso21out experimental (Pa) Fig. 4. Comparison between SO2 partial pressure in the outlet stream as experimentally detected and as calculated by the model for 6 = 51/am. Limestone concentration in the suspension: O, 0.30 kg/m3; 1:3, 0.44 kg/m3; A, 0.70 kg/m3; O, 1.0 kg/m 3.
terms of SO, partial pressure in the outlet gas stream from the reactor. Good agreement between model and experimental results is outlined in Fig. 4, even though some discrepancies can be observed for the higher values of SO2 partial pressure. Figures 5(a) and 5(b) show the profiles in the liquid film of the concentrations of the different species, as well as of the gradient of the electrical potential of diffusion dd~/dx, as obtained at the gas inlet section of the reactor (y = 0) by integrating the equations of the model. The figures refer to two different SO2 partial pressures in the inlet gas stream 548.6 Pa in Fig. 5(a) and 190 Pa in Fig. 5(b)] and to the same limestone concentration in the suspension fed to the
reactor (1.0 kg/m3). Due to their order of magnitude the concentrations of C O l - and O H - are not reported. The profile of the gradient of the electric potential of diffusion in the film can be explained considering that it tends to contrast charge separation, and globally depends on the concentration gradients of the ions present. In particular, in the zone of the film closer to the gas-liquid interface, it slows down the diffusion of H + ion, which has the highest diffusivity between the ions involved in the process, while its sign changes when the H + concentration becomes low. The non-zero gradient of the concentration profile of Ca 2+, which is not transported from or to the gas
SO2 absorption in a bubbling reactor
4529
50 .~...4~HSO3"
E -~
5
~
4
~ -
/2 "~ -.. ~
ii
0
-50 <
/
3 U e-" 0
C a 2+
Z
"~.
2
0
0.2
0.4
0.6
0.8
1.0
x/5 (-) (a)
2O
5O
E
!
0
"-6 16
.-:2
12
,~.
r-,
=
0
-50
J HSO3
Ca2+
< Z v
"~. -~.
8
e
s
4
H2CO3
_..~~y/O2(aq)
~
~
~
~
~
~
H~,.~)a"~<-- -
H+
0 0
0.2
0.4
0.6
0.8
I .0
x/B (-) (b) Fig. 5. Concentration profiles of the different species and profile of the gradient of the electric potential of diffusion in the film at the reactor inlet (y = 0). (a) SO2 partial pressure 48.6 Pa and limestone concentration in the suspension 1 kg/m ~. (b) SO2 partial pressure 190 Pa and limestone concentration in the suspension l kg/m 3. phase and is not involved in any reaction, is the resultant effect of the electric potential. Moreover, the profiles reported in Figs 5(a) and (b) enable the identification of a reaction zone in the film in which the following reactions take place: H + + SO~- = HSO~ SO21aq)+SO 2- + H 2 0 = 2 H S O
K = 1.53 x 107 ~
(17)
K = 2 . 1 3 x 105
(18) H + + HCO~" = H 2 C O 3
K = 2.35 x 106
(19)
These reactions consume H ÷ and SO21,q) coming
from the interface, and SO] - and H C O 3 coming from the liquid bulk, to produce H S O ~ and H 2 C O 3. As a consequence, the concentrations of H +, SO2~,q), S O l and HCO~- become practically zero at the reaction zone, while H 2 C O 3 has a maximum and the H S O 3 concentration profile, which depends on both the net sulfur transport from the gas-liquid interface and reactions (17) and (18), changes its slope in the reaction zone. Moreover, the model results show that the reaction zone gets closer to the gas-liquid interface as the sulfur concentration increases. This trend is shown by a comparison of Figs 5(a) and 5(b). The model results enable us to evaluate the
A. L A N O ^ et al.
4530
50
40 o
30
2o ~
.
.
~
-.. . . ..
1o l
,
,
i
0
i
[
i
i
L
0.1 c
~
I
0.2 -c
S02(aq)i
,
t
S()201q)h
i
I
i
,
0.3 (mol/m 3)
i
[
i
,
,
0.4
L
0.5
Fig. 6. Enhancement factor versus absorption driving force for different sulfite and Ca 2+ concentrations in the liquid bulk. - - , Cc.lb= 1.2 mol/m 3, Cslb = 2.5 mol/m3; . . . . . , Cc,lb = 1.2 mol/m 3, Cslb = 3_5 mol/m3; . . . . . . , CCBIb= 1.5 mol/m 3, cslb = 2.5 mol/m 3.
enhancement factor for chemical absorption at assigned 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 that would be observed with the same driving force in the absence of chemical reaction: E=
N5 (Dso2,,q,/f)(Cso2,.q,l~=o
(20)
interaction between limestone dissolution and SO2 transport, and to describe the influence on the SO 2 absorption rate of different species that can be added to the liquid to enhance SO 2 removal. Acknowled#ements--Ing. D. Karatza, Ing. L. Esposito and
Mr C. Rossi should be credited for the help given in carrying out the experimental work_
- Cso2,.,,Ix=a)
The trend of E versus the driving force is reported in Fig_ 6 for different values of the total concentration of sulfites and of Ca 2 + 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), the higher the Ca 2+ ion concentration and the lower the total concentration of sulfites, the higher the enhancement factor. CONCLUSIONS
SO2 absorption in bubbling reactors is a promising technique for flue gas desulfurization. The process involves chemical absorption of SO2 in the instantaneous reaction regime and limestone dissolution. In the present work chemical absorption has been studied and a diffusive model based on the film theory has been developed. It has been shown that such a model fits well the experimental results of SO2 absorption in a bubbling reactor and enables us to evaluate the enhancement factor as a function of the driving force for absorption and of the liquid bulk composition_ Moreover, the concentration profiles in the liquid film were evaluated, leading to the identification of a reaction zone. The knowledge of concentration profiles in the liquid-side mass transfer boundary layer may allow us to ascertain the
NOTATION a
as
A B ¢1
d
1), E F FI G
Hso2 ko
kt ks K
/v, Ns Pso~ rsoz
R T V X
gas-liquid specific interfacial area, m - 1 liquid-solid specific interracial area, m-1 Debye-Hiickel constant, m 3/2 mol- 1/2 Debye-Hiickel parameter concentration of the I species, mol/m 3 reactor diameter, m diffusivity of the I species, mZ/s diffusivity of the absorbed gas, m2/s diffusivity of the dissolved solid, m2/s enhancement factor, dimensionless Faraday constant, s A/mol ionic strength, mol/m 3 gas flow rate, m3/s SO2 Henry's constant, m~Pa/mol gas-side mass transfer coefficient, mol/mZsPa liquid-side mass transfer coefficient, m/s solid-liquid mass transfer coefficient, m/s thermodynamic equilibrium constant flux of the 1 species, mol/m2s total flux of sulfites, mol/m2s SO 2 partial pressure, Pa SO2 absorption rate, mol/m3s gas constant, J/mol K absolute temperature, K liquid hold-up, m 3 normal coordinate in the film, m
SO2 absorption in a bubbling reactor Y ZI
normal coordinate along the reactor axis, m number of elementary charges of the I species, dimensionless
Greek letters th activity of the I species, m o l / m 3 Yl activity coefficient of the I species, dimensionless 6 film thickness, m vl stoichiometric coefficient of the I species, dimensionless ~b electric potential, J/s A liquid phase residence time, s
REFERENCES Abdulsattar, A. H., Shridar, S_ and Bromley, L. A_, 1977, Thermodynamics of the sulfur dioxide-seawater system. A.I.Ch.E.J. 23, 62-68. Armenante, P. M. and Kirwan, D. J., 1989, Mass transfer to microparticles in agitated systems. Chem. Engng Sci. 44, 2781-2796. Astarita, G., Savage, D. W_ and Bisio, A_, 1983, Gas Treating with Chemical Solvents. Wiley lnterscience, New York_ Brewer, L., 1982, Thermodynamic values for desulfurization processes, in Flue Gas Desulfurization (Edited by J. L. Hudson and G. T. Rochelle), pp. 1-39. ACS Syrup., Set., 188. Chang, C. S. and Rochelle, G. T., 1982, SO2 absorption into aqueous solutions. A.I.Ch.E.J. 27, 261-266. Chang, C. S. and Rochelle, G. T., 1985, SO2 absorption into NaOH and Na2SO3 aqueous solutions. Ind. Eno- Chem. Fundam. 24, 7-11. Colin, E., Clarke, W. and Glew, D. N. 1980, Evaluation of Debye-H~ckel limiting slopes for water between 0 ° and 150°C. J. Chem. Sac_ Faraday Trans. 76, 1911-1916. Danckwerts, P. V., 1968, Gas absorption with instantaneous reaction. Chem. Engng Sci. 23, 1045-1051. Danckwerts, P. V., 1970, Gas-Liquid Reactions. McGrawHill, New York, Chap. 5.14. Esposito, L_, 1991, Assorbimento di SOz in sospensioni di calcare ed in soluzioni di idrossido di calcio. Graduation thesis, University of Naples "Federico II". Glasscock, D. A. and Rochelle, G. T., 1989, Numerical simulation of theories for gas absorption with chemical reaction. A.I.Ch.E.J. 35, 1271-1281. Goldberg, R. N. and Parker, V. B., 1985, Thermodynamic of solution of SO2c~) in water and of sulfur dioxide solutions. J. Res. Nat. Bur. Stan. 90, 341-358. Hikita, H., Satoru. A. and Tsuji., T., 1977, Absorption of sulfur dioxide into sodium hydroxide and sodium sulfite solutions. A.I.Ch.E.J. 23, 538-544. ldemura, H., Kanai, T. and Yanagioka, H., 1978, Jet bubbling flue gas desulfurization. Chem. Engng Prog. 74(2), 46-50. Lancia, A., Musmarra, D., Pepe, F. and Volpicelli, G., 1991, Concentration profiles in the diffusional film in the calcium carbonate dissolution process. Chem. Engn# Sci. 46, 2507-2512. Logoteta, G., 1988, Stadi limitanti nel processo di desolforazione dei fumi di combustione--Studio sperimentale. Graduation thesis, University of Naples "Federico II". Olander, D. R_, 1960, Simultaneous mass transfer and equilibrium chemical reaction. A.I.Ch.E_ J. 6, 233-239. Onsager, L. and Fuoss, R. M., 1932, Irreversible processes in electrolytes. Diffusion, conductance and viscous flow in arbitrary mixtures of strong electrolytes. J. Phys. Chem. 36, 2689-2778.
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Pasiuk-Bronikowska, W. and Rudzinski, K_ J., 1991, Absorption of SO2 into aqueous systems. Chem. Engno. Sci. 46, 2281-2291. Ramachandran, P. A. and Sharma, M. M., 1969, Absorption with fast reaction in a slurry containing sparingly soluble fine particles. Chem. Engng Sci_ 24, 1681-1686. Rochelle, G. T., 1992, Comments on absorption of SO2 into aqueous systems. Chem. Enon 0 Sci. 27, 3169-3171_ Rochelle, G. T., Chan, P. K. R. and Toprac, A. T., 1983, Limestone Dissolution in Flue Gas Desulfurization Process. U.S. EPA-6/7-83-043, Washington, DC_ Sada, E., Kumazawa, H. and Butt, M. H_, 1979, Single and simultaneous absorption of lean SO2 and NO2 into aqueous slurries of Ca(OH)2 or Mg(OH) 2 particles. J. Chem. Eng. Japan 12, 111-117. Sada, E., Kumazawa, H., Sawada, Y_ and Hashizume, I., 198 la. Kinetics of absorption of lean sulphur dioxide into aqueous slurry of calcium carbonate and magnesium hydroxide_ Chem. Engng Sci. 36, 149-155. Sada, E., Kumazawa, H., Hashizume, I. and Kamishima, M., 1981b_ Desulfurization by limestone slurry with added magnesium sulfate. Chem. Eng. J. 22, 133-141_ Sada, E., Kumazawa, H., Hashizume, I_ and Nishimura, H., 1982, Absorption of dilute SO2 into aqueous slurries of CaSO 3. Chem. Engng Sci. 37, 1432-1435. Sherwood, T. K. and Wei, J. C., 1955, Ion diffusion in mass transfer between phases. A_I.Ch.E.J. 1, 522-527_ Shridar, T. and Potter, O_ E, 1980, Interfacial area in gas-liquid stirred vessels. Chem. Engng Sci., 35, 683-695. Teramoto, M., Nagamochi, M., Hiramine, S., Fujii, N. and Teranishi, H., 1978, Simultaneous absorption of SO2 and CO2 in aqueous Na2SO3 solutions_ Int. Chem. Engno 18, 250-257. Uchida, S. and Ariga, O., 1985, Absorption ofsulphur dioxide into limestone slurry in a stirred tank. Can. J_ Chem. Engng 63, 778-782. Uchida, S., Koide, K. and Shindo, M_, 1975, Gas absorption with fast reaction into a slurry containing fine particles. Chem_ Engng Sci. 30, 644-646. Vinograd, J. R. and McBain, J. W., 1941, Diffusion of electrolytes and the ions in their mixtures. J. Am. Chem. Soc. 63, 2008-2015.
APPENDIX
The chemical reactions taken into account by the model can be written in the following general form: vfl = 0
(A.I)
I
where vI is the stoichiometric coefficient of the I species and is assumed positive for the reactants and negative for the products. The equilibrium condition for reaction (A.I) is K = I~ ~'; ~'
(A.2)
I
where at is the activity of the ! species. The activity ,vt is related to the molar concentration by: a l = ctyt
where )'t is the activity coefficient.
(A.3)
A. LANCIA et al.
4532
Values of the activity coefficients for anions (M) and cations (x) can be calculated using the extended version of the Debye-Hiickel theory proposed by Bromley and coworkers (Abdulsattar et al., 1977). According to those authors it is: log(~'M)
=
A~zu(FI)l/2 1 + ( F I ) ~/2
(A.6)
FI = ½ ~, z~c, I
The values of the Debye-Hiickel parameters N are reported in Table 2, taken from Abdulsattar et al. (1977).
+a,~c~+y'a,~c~ x
(A.4)
Iog(T~) =
equation:
Ayz~(FI) x12 1 + (FI) 1/2 b B~ ~M cM + ~u BMC~
(A.5) In these equations Av is the Debye-Hfickel constant, the value of which is 5.62 x 1 0 - 2 m 3/2 mol-t/2 (Colin et al., 1980), and FI is the ionic strength, which can be evaluated by means of the following
Table 2. Debye-H/ickel parameters for eqs. (A.3) and (A.4). From Abdulsattar et al. (1977) Species
B
H+ OH HSO~ SO~ HCO~
0.087 -0.012 -0.013 -0.087 -0.039
co~-
-0087
Ca z +
- 0.035