Ind. Eng. Chem. Res. 1993,32, 553-563
Citrate-Based Contained Liquid Membranes for Flue Gas Desulfurization Neeraj R. Pakala, Sasidhar Varanasi,' and Steven E. LeBlanc Department of Chemical Engineering, The University of Toledo, Toledo, Ohio 43606
The steady-state SO2 fluxes across aqueous sodium citrate and sulfite films were measured, using a flat liquid film sandwiched between polymer sheets and also a hollow-fiber contained liquid membrane device (HFCLM). Nonequilibrium boundary layer analysis (NEBLA) for the transport of SO2 through sulfite films was modified for citrate films and compared to the experimental data. The agreement between the measured fluxes and model predictions is excellent. SO2 transport rates acrosa citrate films were found to be higher by a t least a factor of 4 compared to those across sulfite films, a t all reagent concentrations studied. The observed enhancement in SO2 flux across aqueous sulfite or citrate films stems from the "dynamic role" played by these weak-acid reagents as "carriers" for H+ ions across the film. A weak acid with a pK close to the arithmetic mean of the pH values a t the two faces of the liquid film is expected to provide the maximum enhancement in SO2 flux.
Introduction Removal of SO2 from stack gases has probably been the subject of more research than any other gas purification process, because of the detrimental effect of SO2 on the environment. A great number of flue gas desulfurization (FGD) processes have been developed throughout the world. Many of these processes are reviewed by Crynes (1977)and Kohl and Riesenfeld (1985). The widelypracticed FGD processes involve scrubbing of flue gases with aqueous solutions containing chemical reagents that enhance SO2 absorption; the spent reagents are subsequently discarded (throwaway processes) or regenerated (regenerableprocesses). Lime/limestone-based scrubbing is the most popular in the category of throwaway processes and the (sulfite-bisulfite based) Wellman-Lord process leads in the regenerable systems category (Astarita et al., 1983). The throwaway processes pose several operational problems such as fouling of the scrubber and disposal of large amounts of solid waste generated. These problems can, in turn, add significantly to the cost of operation (Oxley et al., 1979), and also lead to environmental pollution. Hence, regenerable processes are of much interest. The Flakt-Boliden process (Erga, 1980) is another regenerable process that has been commercialized to date, in addition to the Wellman-Lord process. In the former process an aqueous solution of the sodium salt of the polyfunctional organic acid, citric acid, is used for SO2 absorption, while inorganic alkali metal sulfite-bisulfite salt solutions (viz., NaHS03 and Na2S03) are employed in the latter. Although the Wellman-Lord process has attracted more commercialinterest than the Flakt-Boliden process, Astarita et al. (1983)have pointed out that the polyfunctional organic acid additives often lead to better absorption-regeneration characteristics over a wider pH range (pH 3 6 )compared to alkali metal sulfite solutions. It is also pertinent to note that the addition of weak organic acids to the scrub solution in lime/limestone scrubbing is known to improve SO2 absorption rates considerably (Hatfield and Potta, 1971;Rochelle and King, 1977;Chang and Rochelle, 1982). In both the above-mentioned regenerable processes, the absorption of SO2 and the regeneration of the spent reagent are achieved in separate units.
* To whom correspondence should be addressed.
It has long been known that liquid membrane processes, which are based on the principle of "carrier-facilitated transport", are capable of accomplishing absorption and regeneration in a single step, thus eliminating the costs associated with solvent pumping (Ward, 1970;Schultz et al., 1974;Way et al., 1982;Matson et al., 1983). In these systems, a reagent (carrier) that undergoes a specific and reversible chemical reaction with the gaseous component is incorporated into the liquid film. When a partial pressure difference of the permeating gas is maintained across the liquid film, the carrier "facilitates" the permeant's transport across the film, by binding with it at one end and releasing it at the other. Clearly, to achieve the best permeation rates, the binding and the releasing rates of the permeant with (by) the carrier should be large and comparable in magnitude. This implies that the equilibrium constant of the carrier-permeant reaction should have an optimal value. While this brief description outlines the basic principle of carrier-facilitatedtransport, in a number of systems of practical interest, the reactiondiffusion phenomena become complicated when multiple chemical reactions are involved (Schulz et al., 1974). Traditionally, carrier facilitated transport processes are carried out using immobilized liquid membranes (ILMs) obtained by impregnating thin porous polymeric sheets with carrier solutions. However, ILMs are prone to some serious operational problems such as evaporation of the carrier liquid and film instability (Matson et al., 1983; Teramoto et al., 1989). These difficulties have so far prevented liquid membrane processes from being commercialized. An alternate method of preparing the liquid films-suggested by Sirkar and co-workers (Sengupta and Sirkar, 1986) and referred to as the contained liquid membrane (CLM) technique-is to contain the liquid in the thin gap formed between two nonwetting microporous polymeric membranes. To employ the CLMs for industrial-scale separations, one has to package a very large membrane area per unit volume. Sirkar's research group has used the so-called dual hollow fiber contained liquid membrane (HFCLM) technique to achieve this objective (seethe experimental section for a description of HFCLM). These authors demonstrated that this approach overcomes many of the operational problems of traditional ILMs, and hence revives the prospects for the commercialization of liquid membrane processes (Majumdaret al., 1988,1989; Sengupta et al., 1988;Guha et al., 1991).
0888-5885/93/2632-0553$04.00/0 1993 American Chemical Society
554 Ind. Eng. Chem. Res., Vol. 32, No. 3, 1993
recirculation in case of HFCLM
Calibration Gas
Manifold for
Figure 1. Exnerimental setun for SO?removal: MFC. mass flow controller; SV,shut-off valve; PG, pressure gauge; H,hollow-fiber humidifier. . HFCLMs can form a competitive alternative to the existing regenerable processes, if carriers could be identified that effectively facilitate the transport of SO2 from the flue gas mixture. Indeed, the additives employed in both the Wellman-Lord and the Flakt-Boliden processes could, in principle, facilitate SO,transport across aqueous films via their participation in the multiple acid-base reactions involving dissolved SOz. Roberts and Friedlander (1980h) and more recently Sengupta et al. (1990) have studied SO2 transport across aqueous ILMs containing dissolved sodium sulftelbisulfte mixtures. However, as shown later, the sulfite systems appear to he a poor choice hecause of the nature of the acid-base equilibria involved. To the best of our knowledge, there are no reports to date concerning the performance of organic acids as carriers. The previously mentioned observation of Astarita et al. (1983) regarding the absorption-regeneration chemistry of weak organic acids and their success as additives in limestone scrubbing (Chang and Rochelle, 1982) lends hope that sodium citrate films couldmake better carrier mediated transport system than sulfite films. The twomain objectivesof this investigation are (i) to perform a comparative experimental evaluation of SO2 transport across sodium citrate vs sulfite films in order to identify the better carrier and (ii) to model the facilitated transport of SOz across flat citrate films and compare the predictionsofthe modelagainst experimental data obtained in a well-characterized CLM device. In our experiments, we used two kinds of CLM devices. Firstly, we have measured SO2 transport across a "model CLM device" which we refer to as a flat-plate contained liquid membrane (FPCLM) contactor. In this device, a liquid film of the reagent solution, the thickness of which can be controlled precisely, was sandwiched between two hydrophobic microporouspolymer sheets. This contador, while does not provide appreciable membrane area, allows a rigorous comparison of the model predictions with the experimental data due to its simple geometry. In view of the fact that HFCLMs are more practical devices, we also carried out anexperimentalcomparisonofthe performance of citrate versus sulfite films in an HFCLM module. The goal of these latter studies is to evaluate the potential of HFCLMs as viable altemativestothe existing regenerable FGD processes. Experimental System and Measurements The steady-state flux of SO2 across aqueous films of knowncompositions was measured with the experimental apparatus shown in Figure 1. The test cell in the figure
gas
Brass O-rings used to change
membrane
Liquid OUt
I
I
Figure 2. Sketch of flabplate contained liquid'membrane contractor: (1) microporow polymeric sheets; (2) gas chambers for feed and sweepstreams; (3) flexiblegssketathatensureasnugfitofthecasing with the two halves (stainless skel blocks) forming the cell.
was either a FPCLM or HFCLM. All gas flow rates, including SOZ, were controlled by FMA-700 series mass flow controllers (OMEGA Enginee:ing, Inc., Stamford, CT). The simulated flue gas feed was prepared by mixing the appropriate amount of SO2 with air using mass flow controllers. Compressed air was used as the sweep stream. Both the feed andsweepgasstream wereprehumidifid, prior to entering the cell. A portion of each gas outlet stream was sent to an SO1 analyzer (Model 40, Pulsed Fluorescent SO2 analyzer, Thermo Environmental Instruments Inc., Franklin, MA) for continuous monitoring of the SO2 concentration. The analyzer was calibrated after each experiment using a certified gas mixture (SO2 and air). The calibration gas cylinders were supplied by LINDE Specialty Gases, Toledo, OH. The sodium citrate and sodium sulfite chemicals used for the preparation of reagent solution were purchased from Fisher Scientific. The details regarding the test cells used in this study and their operating parameters are presented below. FPCLM Operating Parameters. An outline drawing of the FPCLM contractor is shown in Figure 2. The cell consists of three stainless steel parts: a casing and two halves. Two microporous polypropylene (Celgard 2500, Hoechst Celanese, Charlotte, NC) sheets, one for each half
Ind. Eng. Cham. Res., Vol. 32, No. 3,1993 555 Back pressure Valve
Membrane Liquid Feed Tank
Membrane Liquid Outlet
t
Peristaltic Pump Inlet
Tw Hoil ins
Hollow Fibers Canying Feed Strea
Fiber Characteristics Celgardo X-IO
Sweep Outlet
Type
I
Wall Tlickness
microporous polypropylene 30pm
Diameter
240pm
Effective Pore Size
0 . 0 5 ~
Porosity Number of Fibers Effective Fiber Length EffectiveSurfaceArea
0.30 700 (350bundle)
Material Membrane Liquid
Beween Two Sets of Hollow Fibers
25.4cm 0.14m1
OoSsSeelimlView of the fib” Bundle
Figure 3. Outline diagram of the hollow-fiber contained liquid membrane device and varioua flow patterns including a crass-sectional view of the fiber bundle.
cell, are mounted by means of a sliding ring (not shown in figure) and six screws. These halves are mounted in thecasing asshown i n t h e f w e . Propertiesofthe polymer sheet are also given in Figure 1. The exposed surface area of each polymeric sheet is 18.7 cm2, and the volume of each of the gas chambers formed is about 5.4 cm3. The thickness of the liquid membrane can be adjusted from 100 to 1700 pm by using brass O-rings of different thicknesses. The thickness employed in the present study was 200 pm. The cell has the provision to flow the reagent solution between the two polymeric sheets. However, in allourexperimenta,the reagent solutionwas heldstagnant. As already noted, evaporative losses of liquid film were minimized by prehumidifying the gas streams entering the device. HFCLM Operating Parameters. The HFCLM module (commercially known as LIQUI-CEL) was manufactured by Hoechst Celanese, Charlotte, NC. An outline sketch of the module and flow paths of the gas and liquid streams involved are shown in Figure 3. Also shown, in cross-sectional view, is the fiber bundle which consists of two sets of microporous hollow fibers enclosed in a casing (shell). Feed gas flows through one set of fibers, and the sweep gas flows through the other set of fibers. The two sets of fibers are well-mingled throughout the length of the bundle (so that, on the average,any feed-carryingfiber has one or more sweep-carrying fibers in its immediate vicinity). The sets are separated at the ends of the casing to form inlet and outlet ports for both the sweep and feed streams. The membrane liquid fills the shell of the device and occupies the interstitial region between the two kinds offihers. SO:!permeatesfromfeedfibersintosweepfibers across this liquid film present in the intervening space. A very large membrane area can be attained per unit volume in the HFCLM module. It is also possible to easily recirculate the liquid film in this device, which would improve the mass-transfer characteristics. A back-pressure valve installed in the recirculation loop (Figure 3) allows us to maintain the shell-side liquid at a slightly
Hydmphobic Mimpomus Polymeric Sheets with Gas Filled Pores
F-1 Figure 4. Schematic diagram of the contained liquid membrane.
higher pressure than the tube-side gases, thus preventing themixingof feed and sweep streams. Thecharaderiatics of the hollow fibers used in the construction of the module arealsoshowninFigure3. Inourexperiments,thereagent solution was recirculated at a nominal flow rate of 2.5 cm3/min using a computer-driven peristaltic pump. Both feed and sweep gas flow rates were 2000 cm3/min, at a pressure of about 1.1atm. The exit gas streams were also nearly at atmospheric pressure. The feed gas SO2 concentration was 3500 ppm. Model Development Consider the schematic diagram of the contained liquid membraneshowninFigure4. Liquid, containmgdissolved sodium citrate, is sandwiched between two microporous polymeric sheets. The liquid film is exposed to the flue gas mixture (SO2 3500 ppm) on one side ( x = 0 ) and to a sweep stream, free of SOZ,on the opposite side (x = L). Since the concentration of SO2 is higher on the feed side, we expect the transport of SO2 from x = 0 to x = L.
-
556 Ind. Eng. Chem. Res., Vol. 32, No. 3, 1993 Table I. Possible Reactions in SO2-Sodium Citrate System. equilibrium coeff (25 "C) reaction symbol value reference K1 0.014 rnol/L Roberts (1979) SO2 = H20 ~9 H+ = HS03Dean (1985) K2 1.008 X H20 I$ H+ = OHmo12/L2 K3 1.194 mol/L estd (Fuoss, 1958) Na3R NaZR- = Na+ K4 0.958 mol/L estd (Fuoss, 1958) NaRZ-= Na+ Na& Na@- I$ R3- = Na+ Ks 0.886 mol/L estd (Fuoss, 1958) K6 7.447 X Dean (1985) RHo RH2- = H+ mol/L K7 1.734 X Dean (1985) RH2- RH*- = H+ mol/L RHZ- e* R3- = H+ Ks 4.018 X Dean (1985) mol/L
-Q
a
R3- indicates CH,-COOHO-C
I -COOI
NNv(x=O)= 0 and N,,(x=L) = 0 (3a) The following boundary conditions can be written for
so2:
[
F
Cgo, = H::so2]
and Cko, =
[
S
pso2
Hso,Yso,
]
(3b)
The Henry solubility constant, Hso,, has been measured as 0.824 atm/M at 25 OC (Rabe and Harris, 1963). If there are N species in solution, it can be shown, following the approach suggested by Schultz et al. (19741, that not all of the 2(N- 1)boundary conditions represented by eq 3a are physically independent. Therefore, in order to define the system uniquely, one must also specify the following integral constraints which state that the total amounts of (i) sodium atoms, (ii) R3- radicals, and (iii) charge contained in the reagents initially added to the film remain undestroyed during the reaction-diffusion processes taking place in the film:
CH, -COO-
~ o L c Cdxm= LC,
Our goal is to estimate the steady-state SO2 flux (NsoJ across the liquid film, given the citrate concentration in the film and SO2 concentration in the gas streams on both sides of the film. (Since the high feed and sweep flow rates employed in our experiments ensured good mixing in the gas chambers on either side of the liquid membrane, in the following analysis we have ignored the gas-film resistance to SO2 transport. The resistance offered by the gas filling the pores of the polymer films was also deemed insignificant since the diffusion coefficient of SO2 is orders of magnitude higher in gases than in liquids.) Modeling the liquid membrane transport requires the knowledge of the different species present in the liquid system and their interconversions when the film is exposed to SO*. The possible reactions and their equilibrium Coefficients for the SOz-sodium citrate system are given in Table I. The equilibrium constant for the dissociation of bisulfite ion to form sulfite is small enough to make the concentration of sulfite ions insignificant for pH values less than 6. As shown later, the maximum pH within the membrane liquid was always less than 6 for this system. Therefore, the sulfite formation reaction was omitted. Governing Equations. In the flat-plate CLM, mass transport takes place only in the direction perpendicular to the membrane (i.e., =x" direction), and hence the equation of continuity for any of the species, i, can be written as dN,/dx = ri (1) where Ni and r, denote the flux and the rate of formation of species i at any location in the film, respectively. Nl can be related to its local concentration gradient by the following form of Fick's law of diffusion in the absence of convective transport: dCi Ni = -D, dx where Di is the diffusion coefficient of species i. The electrical potential term for ion transport has been omitted from eq 2 because of the high totalsodium concentrations (Nat.,,t 1 0.03 M) employed in this study (Roberte and Friedlander, 1980a). All species involved in the process, except S02, are nonvolatile and remain confined to the liquid film, so they must satisfy the following boundary conditions:
m
and ~ L ~ z dx i C=i0
(6)
1
Expression for SO2 Facilitation Factor. From the stoichiometry of reaction 1in Table I-the only reaction in which dissolved SO2 participates-one may note that at any location in the film rSO,
= -rHS03-
(7)
From eqs 1,2,3, and 7, one can derive the net flux of SO2 across the liquid film as
Diffusion coefficients of both SO2 and HS03- at 20 "C cm2/s (Eriksen, 1967). were reported to be 1.48 X The flux enhancement factor or facilitation factor (F) may then be defined as
where NOrepresents the flux of SO2 in the absence of chemical reactions. In order to find NSO,and F from eqs 8 and 9, we need to know the concentrations of dissolved SO2 and HS03ions at both the boundaries of the film. To determine these concentrations, in principle, one has to solve numerically the system of differential equations described by eqs l and 2 subject to the boundary and integral constraints provided by eqs 3-6. When the forward as well as the backward rates of all the governing reactions are "fast" compared to the rates of diffusion of the species involved, the reactions approach equilibrium through most of the film, except in two boundary layers adjoining each of the faces of the film. The thickness of these boundary layers is governed by the magnitude of a Damkohler number, 4, defined as the ratio of the characteristic time of diffusion of the permeant through the film to that of its reaction with the carrier. Within the
Ind. Eng. Chem. Res., Vol. 32, No. 3, 1993 557 nonequilibrium boundarylayers, the diffusion and reaction rates will be comparable in magnitude. The boundary layers become progressively thinner as 4 becomes larger; in the limit of m, they become vanishingly thin and one may assume that all the reactions are at equilibrium everywhere in the film. This limit is known as the “equilibrium approximation”. However, in most of the carrier mediated transport processes, this limit is not valid and hence one has to account for the presence of the boundary layers in computing the permeant flux for the near-equilibrium regime (Kreuzer and Hoofd, 1972; Schultz et al., 1974; Roberts and Friedlander, 1980a). In what follows, we shall predict the SO2 flux across citrate films first in the equilibrium limit and then by using the nonequilibrium boundary approximation (NEBLA), proposed by Roberta and Friedlander. Equilibrium Approximation. Here it is assumed that the reaction rates are so fast that the chemical equilibria are instantaneously established at any point in the film for all the reactions = 1, 2, ..., 8) listed in Table I.
-
The equilibrium approximation simplifies the effort involved in predicting the permeant flux immensely becauseone now has to solve a system of nonlinear algebraic equations represented by eq 10 subject to the integral constraints and the boundary conditions on the permeant listed before, instead of the system of differential equations given in eqs 1and 2. The model can be further simplified, if one assumes that the diffusion coefficients of all the ionic species present in appreciable concentrations are approximately the same (H+and OH- are present at very low concentrations). Therefore, we assume that the diffusion coefficients of the remaining ionic species (excluding H+ and OH-) can be replaced with that of the bisulfite ion, as was done by Roberts (1979). This allows one to replace the threeglobal constraints given in eqs 4-6 by the following three equations which represent, respectively, the conservation of sodium atoms, R3-radical, and electrical charge locally in the film. (11)
in
&Ci
=0
I
Equations 11and 12 imply that the total molarities of sodium and R3- species at the boundaries are equal to their respective original molarities in the liquid film preparation. Therefore, to obtain the concentrations of the various species at each boundary of film, it is enough to determine separately the liquid-phase composition that results when the corresponding gas phase is equilibrated with a sodium citrate solution of molarity CO. SO2 Equilibrium with a Bulk Solution of Sodium Citrate. The activity of the species appearing in the equilibrium relations (eq 10) can be related to their concentrations by activity coefficients. These coefficients for all the species other than SO2 were computed using the extended Davies model (Davies, 1962). The activity coefficient of SO2 and the activity of water were computed using the relations given by Harned and Owen (1958) and Johnstone and Blankmeyer (19381, respectively. The set of model equations constitute a system of 38 simultaneous algebraic equations. This system of equa-
tions can be solved numerically for the 38 unknowns (12 C1’s,12 al’s, 12 yl’s,UH,O, and I). This was accomplished using the IMSL subroutine DNEQNF on the VAX/VMS system. The input parameters for these equilibrium computations were psol in the gas phase, and the amount of reagent added to the bulk liquid. Knowing pso, on both sides of the film and sodium citrate concentration, CO, in the film, the concentrations of species at the boundaries can be computed. The C$oz, Ckof, @Hso3.,and Chso -values thus obtained can be substituted into eqs 8 and 9‘ to determine NSO,and F, respectively. Nonequilibrium Boundary Layer Analysis (NEBLA). Since the forward step of the hydrolysis reaction of the dissolved SO2 (reaction 1,Table I) requires a finite amount of time, the SO2 molecule, after its dissolution, diffuses a certain distance before undergoing any reaction. This distance corresponds to the width of the boundary layer on the feed side of the film in the NEBLA of Roberts and Friedlander. Clearly, within the boundary layer, the permeant transport occurs only by physical diffusion. A similar phenomenon occurs (in the reverse direction) at the other boundary of the film; i.e., SO2 transport takes place only by physical diffusion over a distance that is determined by setting the diffusion time of the HS03equal to time needed for the reverse step of the hydrolysis to occur. Accordingly, the boundary layer thickness on the feed and the sweep sides (60and aL) can be determined on the basis of the characteristic reaction times for the forward and reverse reactions of reaction 1: 6’ = [Ds0l/kl]li2
(14)
aL = [DHso,~/k-lC*l”2
(15)
The value of kl has been measured as 3.4 X lo6 s-l at 20 OC (Eigen et al., 1961). As is the case with all other boundary layer analyses, it is assumed that at the boundary layer/core interfaces ( x = 6O and (L- aL)) all chemical reactions are at local equilibrium. Since all chemical reactions are “frozen” within the boundary layers, the concentrations of all the nonvolatile species remain uniform within each boundary layer at their values at the correspondingboundary layer/core interface. Therefore, the H+ ion concentration (C*)appearing in the definition of aL will be its value at the sweep-side boundary layer/ core interface. From the physical parameters of the system under consideration, it was found that the ratio (aL/60) is about 10“103, and hence 6O was neglected in the following analysis. This implies that the equilibrium core extends right up to the gas-liquid interface on the feed side of the film. The flux across the boundary layer on the sweep side is the Fickian diffusion of SOz(aq). Therefore,
(CigL
Nso, = (Dsol/aL) - CioOs) (16) In the core region of the film, the expression for steadystate flux of SO2 is the same as that given by eq 8, but the concentrations of both the SOZ(aq)and HS03- on the lowpressure side must be evaluated at x = L - SL. Thus, eq 8 becomes
Under steady-sgte conditions, the flux of SO2 across the boundary layer and that across the core region must be the same, and hence eqs 16 and 17 should yield the same NSO,values. Since the feed-side boundary layer
558 Ind. Eng. Chem. Res., Vol. 32,No. 3, 1993
thickness is negligible, at x = 0, the liquid-phase Ci's are in equilibrium with feed flue gas SO2 concentration. Thus, the feed-side Ci values are computed as described in equilibrium calculations. However, the sweep-side calculations must be performed iteratively because of the existence of the boundary layer. One method for these calculations is the following algorithm. (i) Assume a value for C&2*L. (ii) Compute Cf-*Lusing the equilibrium model. (iii) Use eq 15 to calculate aL and eqs 16 and 17 to obtain two values of Nso,. (iv) If the difference between the two NSO, values obtained in step iii is within a specified tolerance limit, stop the computations. Otherwise,guess a different value for C!&2*L and repeat steps ii-iv. The above completes the model development for SO2 transport across aqueous sodium citrate films. The results obtained from these computations can be compared with experiments and are presented below.
Results and Discussion FPCLM Results and Theoretical Predictions. In all FPCLM experiments, the SO2 concentration in the feed flue gas was 3500 ppm, and the incoming sweep gas was air, free of S02. The feed and sweep gases were fed to the device at a rate of 4000 cm3/min. The operating pressure was atmospheric on both sides of the cell, and the process was carried out at room temperature (25"C). The high gas flow rates used ensured good mixing in the gas chambers. Experimentswere conducted using aqueous films of both sodium sulfite and citrate. The reagent concentrations studied varied from 0 to 0.66M for sodium citrate, and from 0 to 1 M for sodium sullite. In a typical experiment, the SO2 concentration in the two gas streams leaving the device was monitored continuously at specified values of the feed and sweep gas flow rates, feed SO2 concentration, liquid film thickness, and reagent concentration in the liquid. The time needed for the system to attain steady-state conditions ranged from 1 to 4 h. The measured steady-state partial pressure of SO2 in the sweep-stream was related to the SO2 flux across the film (Nso,,exp) by the relation
@to,,
Nso,, exp = Qs@&IR7')Js~
(18)
This flux was compared to the SO2 flux predicted by the model (NsoJ when the two faces of the membrane are exposed to SO2 partial pressures equal to those in the two streams leaving the FPCLM device. SO2 Transport across W n t - F r e e Aqueous Films. For a reagent-free aqueous film (pure water) the measured partial pressures of SO2 on the feed and sweep sides of the PFCLM device at steady state are 3467 and 33 ppm, respectively. The correspondingNso2,exp (computed from eq 18)is 1.07 X lo-* mol/(cm2-s). It is important to note that, even in pure water, transport of SO2 does not take place by physical diffusion alone, but is facilitated by the HSO3- ion formed by the hydrolysis reaction (reaction 1, Table I). For the above-mentioned SO2 partial pressure difference across the water film, the flux resulting from SO2 transfer by physical diffusion only (NO) is computed as5.34 X 10"3moV(cm2*s).Clearly,the extent of facilitation in water is small (- 1). In order to release SO2, HSO3- has to recombine with a H+ ion on the sweep side of the film. The rate of this recombination, under steady-state conditions, is determined by the fluxes of HSO3- and H+ ions across the film. By the stoichiometry of reaction 1 (Table
feed gas flow rate = 4000 cc/min
-
/
J
1
0.1 Sodium sulfite concentration (M)
1
Figure 5. Variation of sulfur dioxide flux with sodium sulfite concentration in the FPCLM contactor. The liquid film thicknesa is 200 pm.
I), the fluxes of these two species should be equal under steady transport conditions. However, the driving force that determines the physical diffusion of H+ in pure water films is the pH difference across the film. Therefore, H+ ion flux in water films tends to be very small, and so will be the flux of HSO3- ions. This leads to the observed low facilitation factors in pure water films. Obviously, reagents that can facilitate the transport ofH+ions across the film should lead to a concomitant increase in the flux of HSOsions, and hence to larger SO2 facilitation factors. Indeed, commonly used weak-acid pH buffers were shown to be effective in accomplishing proton transport facilitation in immobilized enzyme systems (Engasser and Horvath, 1974)and the facilitated transport of C02 across aqueous films (Gros et al., 1976;Meldon et al., 1977). In these studies it was identified that both the binding constant (pK) of the weak acid and its concentration determine its ability to function as an effective proton facilitationagent. Engasser and Horvath also observed that there exista a weak acid with an optimum pK that leads to maximum proton facilitation. In the following subsections, we shall evaluate sodium sulfite and sodium citrate as proton carriers. We expect their behavior to be different since the former is monoprotic (pK 7.2)while the latter is polyproticwith closely spaced pICs (pK1 = 3.1, pK2 = 4.76,and pK3 = 6.4). SO2 Transport across Sodium Sulfite Films. Figure 5 shows the variation of the observed flux, Nso,, with different concentrations of sodium sulfite in the liquid film. For all the runs in Figure 5, the liquid film thickness and the SO2 partial pressure in the incoming flue gas were held fixed at 200 pm and 3500 ppm, respectively. The steady-state fluxes predicted by the model (both equilibrium approximation and NEBLA), are also plotted in Figure 5 as flux vs reagent concentration. Clearly, the NEBLA predictions are in much better agreement with the experimental data than those employing the equilibrium approximation. This observation corroborates the previous conclusions of Roberts and Friedlander (1980) and Sengupta et al. (1990). It may also be noted from Figure 5 that the addition of sulfite to the aqueous film, while leading to SO2 fluxes larger than in pure water as expected at concentrations higher than 0.1 M, actually lowers the flux slightly at smaller concentrations. This anomaly results from the important role played by the diffusional potential on SO2 flux at low ionic strengths, as noted earlier by Roberta and Friedlander.
-
Ind. Eng. Chem. Res., Vol. 32, No. 3, 1993 519 Table 11. Boundary pH Values and Their Arithmetic Averages Calculated Using NEBLA for Sulfite Films' sulfite concn (mol/L) pHo pHL (pH0 = pHL)/2 0.015 2.61 4.43 3.52 0.0375 2.94 4.87 3.91 0.075 3.21 5.07 4.14 0.15 3.48 5.14 4.31 0.75 4.03 5.22 4.63 1.0 4.10 5.23 4.67
SULFITE SOLUTION DIFFUSION PATH
a
..........................................................
I
CITRATE SOLUTION DIFFUSION PATH
j
I
-Bo;
I
I
I
Figure 6, (a, top) Simple model of SO2 permeation across sodium sulfte films. HS03-is mainly responsible for the facilitated transport of Son. HS03-/S032-conjugateacid-basereactionforma the-shuttle" that facilitates the transport of H+ ions. (b, bottom) Schematic of the mechanism of SO2 transport acroee citrate fiis. The cloee spacing of the three pKs of citricacid permits proton transport by more than one form of the conjugate base species, at any given reagent concentration. Of the three paths shown (RH3,RH2-, and RH*-),the fraction of protons carried in each form cfi, f2, and f s ) is determined by the pH values at the ends of the film. The double-headed arrows on the two path, RH2- and RHZ-, imply that these forms of the reagent can either be conveying H+ions to the sink, or be serving as unbound carriers moving toward the source. Their actual direction of motion is determined by the pH values at the ends of the film. When these species are moving toward the proton source the corresponding f s will become zero.
As already mentioned, the observed increase in SO2 flux at high sulfite cmcentrations can be attributed to the proton transport facilitation by the sulfite (so32-) ions, which bind H+ ions at the feed side of the film and release them on the sweep side according to the following reversible reaction: 50;- + H+ o H S O i
aS032-aH+
K = -- 6.2 X loW8M OHSO,-
(19) On the basis of the above role of the sulfite ion, one can visualizethe transport mechanim schematically displayed in Figure 6a to be operative in sodium sulfite films. As observed by Roberta and Friedlander, in addition to SO2 hydrolysis, the formation of other sulfur-containingspecies may become important at very high reagent concentrations. (The formation of these compounds is accounted for during comparison of our experiments with NEBLA as well as the equilibrium approximation.) Nevertheless, HSO3- remains the dominant carrier of SO?,and thus the schematic shown in Figure 6a makes it easier to envision
Experimental gas-phase SO2 partial pressures were used.
the physicochemical phenomena involved in SO2 transport across sulfite films. One may also note from Figure 5 that, while the addition of sulfite improves the SO2 flux across the film, the increase is only 3-fold (compared to the pure water case) even at the highest sulfite concentration studied (1 M). In Wellman-Lord process, the sulfite concentrations used are typically -0.6 M. Higher concentrations are known to lead to operational problems such as high viscosity of the solution and decreased SO2 solubility due to the "salting-out" phenomenon. Also, the trend of the flux vs sulfite concentration behavior predicted by NEBLA (Figure 5) indicates that increasing sulfite concentration beyond 1M may not lead to any appreciable increase in SO2 flux. An explanation for this marginal performance of sulfite films can be sought in light of the mechanism shown in Figure 6a. The performance of the reagent is directly related to the ability of the s0s2-to serve as a proton carrier. As noted before, this effectiveness of S032is determined by ita pK. From Schultz et al.'s analysis of carrier mediated transport systems (1974, p 4381, one can expect a conjugate acid-base pair with a pK which is the arithmetic mean of the pH values of the proton "source" (feed-side interface in our case) and "sink" (sweep-side boundary layer/core interface) to provide maximum proton facilitation. The pH values at the proton source and the sink, along with their arithmetic mean, are shown in Table I1 for the six sulfite runs. The experimentally observed feed- and sweep-side SO2 partial pressures are used along with NEBLA to compute these pH values. Comparison of the average pH values with the pK of sulfite (-7.21, see eq 19) indicates that so32-is not a very effective proton carrier in this partial pressure range. Indeed, it is incapable of releasing the bound protons on the sweep side due to ita high pK. This implies an inadequate supply of "free carriers" which can shuttle back to the feed side to combine with more protons. From the equilibrium solubility data of SO2 in sulfite solutions, one can verify that at extremely low feed- and sweep-side SO2 partial pressures (
