200
Ind. Eng. Chem. Res. 1993,32,200-206
Sorption of Dibasic Acids on Weak Base Resins Vinay M. Bhandari, Vinay A. Juvekar,* and Suresh R. Patwardhan Department of Chemical Engineering, Indian Institute of Technology, Bombay 400 076,India
Higher rates of uptake of dibasic acids by weak base anion exchange resins, in comparison to those of monobasic acids, have been satisfactorily explained on the basis of dual site adsorption of divalent anion on the protonated resin sites. Due to dual site sorption, divalent anions are strongly bound to the resin matrix, thereby neutralizing the positive charges on the protonated pore surface. Hence, there is practically no exclusion of co-ions from the pores of the resin. The extent of reversibility of sorption is considerably less as a result of less repulsion of H+ions from the pore surface than that observed in monobasic acids. A theoretical model is developed and successfully validated using the experimental data of our work and those in the literature on batch sorption dynamics of sulfuric acid on weak base resins.
Introduction It is a well-established fact that sorption of polybasic acids on weak base resins proceeds at a much faster rate than that of monobasic acids (Adams et al., 1969; Rao and Gupta, 1982; Helfferich and Hwang, 1985). Although a number of explanations have been offered for this phenomenon, apparently the most reasonable explanation is that of Helfferich and Hwang (1985). These authors proposed a mechanism of proton transfer in which anion HS04-acta as a latent carrier of H+, which is required for the protonation of the ionogenic groups. This mechanism, however, does not accurately predict the rates of sorption. The regressed value of the pore diffusivity of the rate controlling ion (HS04-)obtained using this model is significantly higher than that derived from ita free diffusivity in solution after applying an appropriate tortuosity correction. In our opinion, the difference between the rates of sorption of a monobasic and a dibasic acid stems from the following two reasons. (a) It is reasonable to expect that divalent anions are more strongly anchored on the protonated resin sites than monovalent anions. This is due to the fact that they simultaneously neutralize two sites, and hence the free energy change accompanying their sorption is high. The electric potential of the protonated resin surface is therefore considerably weakened by these strongly sorbed anions of the acid. Such a surface offers a very weak Donnan barrier and hence the extent of exclusion of H+ from the resin pores is expected to be very small. (b) The sorption of monobasic acids on resins, in general, shows reversibility. This reversibility is due to the exclusion of H+ from the vicinity of a positively charged resin surface as a result of electrostatic repulsion (Bhandari et al., 1992a,b). The extent of reversibility depends upon the nature of the ionogen. For the same ionogen, the extent of reversibility is much lower if dibasic acid is used. This again is due to suppression of the surface charge by the strongly adsorbed divalent anion. This charge suppression makes the resin surface much more accessible to H+. As a result of a, H+ also contribute, in a significant proportion, to the diffusive flux of the acid. A lesser extent of reversibility of sorption, as discussed in b, implies that polybasic acids will show higher uptake rates due to a higher driving force for the uptake. A model which takes both these factors into account can explain more accurately the differences in the dynamics characteristics of the resin toward monobasic and dibasic acids. In this work, we have attempted to develop such a model. In the development of the model, it is assumed that the divalent anion of the acid is so strongly sorbed on the protonated resin surface that the surface potential is practically reduced to zero.
Table I. Resin Characteristics and Operating Conditions Dowex Amberlite WGR-2 IRA-93 capacity based on pore volume, 10.1 4.67 kmol/m3 2.45 x 10-4 2.25 x 10-4 bead size, Rb, m form free base free base temperature, O C 27f1 27*1 speed of agitation, rev/min 450 450
The resin surface therefore acts as a neutral surface and allows the co-ion to diffuse freely inside the pore. For experimental verification of the model, we have studied the equilibria and dynamics of sorption of H2S04on the free base form of weak base resins (Dowex WGR-2 and Amberlite IRA-93). A good fit of the model with these experiments as well as those of Helfferich and Hwang (1985) on sorption of H2S04on Amberlite IRA-68 substantiates the theoretical framework of the model.
Experimental Work In the present study we have used two resins, viz.,Dowex WGR-2 (epoxyamine resin supplied by Dow Chemical Co.) and Amberlite IRA-93 (polystyrene resin supplied by Rohm and Haas Co.), in their free base form. Resin samples were characterized for their size and shape, the capacity and the water content as per the procedure described in our earlier work (Bhandari et al., 1992a). Sulfuric acid used in this study was of analytical reagent grade. Studies on the sorption equilibria were carried out by equilibrating known weights of resin with the acid solutions of known concentrations. The quantity of the sorbed acid was obtained from the difference between the initial and the equilibrium extraparticle acid concentrations. Appropriate correction for the free acid present in the pores was incorporated. The sorption dynamics was studied in a batch reactor by adding a known weight of resin sample to an acid solution of known concentration. The change in the concentration of H+ in the solution at different times was then measured using the pH meter. The range of H2S04concentration studied was from 5 X 104 to 1 X kmol/m3. The details of the experimental procedure are as described in our earlier work cited above. The resin characteristics and the operating conditions used in the experiments are listed in Table I. The total concentration of the acid in the solution was obtained from its pH by accounting for the extent of dissociation of the acid. For sulfuric acid, the first dissociation (H$04 H+ + HS04-)can be assumed to be complete while the value kmol/m3 was used for the second dissociation of 1.2 X (HS04- H++ S042-)constant, Ka2.The concentration
-
-
o a a a - ~ a a ~ ~ ~ ~ ~ ~ ~ ~ ~ -1993 o ~ American o o ~ o ~ Chemical . o o ~ oSociety
Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 201
1
I
Id'
#,,',t,l 10 4
1
16'
#
I
,
,
I 10-1
I,,,
1
4 IO
Cnl, k m o i / m) Figure 2. Sorption equilibria on Dowex WGR-2.
I 10-1
I
1
I 1 1 1 1 1 1
10-b
I
I 1 1 1 1 1 1 1
I
10-3
1
I 1 1 1 1 1 1
I
10-2
,,"d 5.01
I
01
[HI, kmol/d
Figure 1. Plot of sorbed acid concentration vs [HI.
of H+ can be related to the total concentration of sulfuric acid ([H2S041T)by the following expression:
I/
Sorption Equilibria Figure 1shows the plots of the concentration of H2S04 sorbed by the resins v8 the concentration of H+ in solution at equilibrium. The concentrations of the sorbed acid are based on the pore volume of the resin. The asymptotic value of the sorbed acid concentration at high concentrations of H+ represents the capacity of the resin. The capacities of the resins, Dowex WGR-2 and Amberlite IRA93, for H2S04are seen to be 5.00 and 2.30 kmol/m3, respectively. The corresponding capacities of these resins for the sorption of monobasic acids as seen from Table I are 10.1 and 4.67 kmol/m3, respectively. The comparison between these values clearly indicate that the capacity of a resin for H 8 O 4 is halfof that for monobasic acids. This leads us to conclude that each of the sorbed acid molecules occupies two sites on the resin surface. This means that H2S04will be adsorbed as a divalent 502- anion as depicted below:
1.0 1
I
d
I
L
,
I
I 1 1 1 , l
I
Io-'
to-'
[H],b mol / m'
4
, 1 1 1 1 1 1
Io-
*
I
I
,
I ,
lo-'
Figure 3. Sorption equilibria on Amberlite IRA-93.
acid as a special case. For convenience, the following abbreviations are used in the model equations: H2A = divalent acid molecule (e.g., H#04); HA = monovalent acidic anion (e.g., HS04-); A = divalent anion (sorbed species) (e.g., SO,?-);H = H+ ion; RH = protonated species of the resin (e.g., RH+). The extraparticle and intraparticle species are distinguished from each other by writing an overbar on the notations of the intraparticle species. The concentrations of all the species are expressed in molar units. The intraparticle concentrations are based on the volume of the pore phase. The first and the second dissociation of the acid in the interior of the resin particle may be described by the following set of reactions:
-
Such a dual site sorption requires that sites on the resin surface are sufficiently closely packed so that two sites are O:-. This is plausimultaneouslyaccessible to a single S sible in view of the high surface site density of these resins. Such behavior may be expected to be shown by all types of ion exchange resins, in general, and weak base/acid resins in particular. On the basis of the dual site sorption mechanism, the concentration of the protonated ionogens, RH+, can now be obtained by doubling the sorbed acid concentration. Figures 2 and 3 are the equilibrium plota of [RH+]v8 [H+]. It is evident that the extent of reversibility in the case of monobasic acids (Bhandari et al., 1992a,b) is substantially higher than that observed in the sorption of polybasic acids.
Sorption Dynamics: Generalized Mathematical Treatment In this section the generalized mathematical model for the sorption of dibasic acid on weak base resins has been developed. It is then applied to the sorption of sulfuric
H2A H + H A (3) HAeH+A (4) (The same equations without overbar are valid in the extraparticle solution.) These reactions are instantaneous and reversible. The concentration based equilibrium constants of these reactions can be expressed as
Since the resin surface is assumed to be electrically neutral, the condition of electroneutrality exists at each and every point in the pore phase and can be expressed as [R) = + 2[A] (7) This electroneutrality condition, when suitably combined with the dissociation equilibria (eqs 5 and 6) and -simplified, yields the following expressions for [H2A], [HA], and
[rn]
202 Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993
Eliminating V 4 from the set of eq 19 using eq 21, we get the following expression for the fluxes of H and HA in the pore phase.
[A] in terms of [HI.
-
[Hi3 [HzA1= Ka,(2Ka2+ [HI)
The corresponding equations in the extraparticle solution could be obtained by removing overbars from the notations for concentration in eqs 8-10. In developing the model, we have neglected the liquid film resistance, and hence the sorption dynamics would be governed by diffusion of species H, HA, A, and H2A through the resin pores. For writing unsteady-state continuity equations for different species in the pore phase, we consider the following fast but reversible rate processes H , A &r2 H + H A -
(11)
r
H A J H + A 74
r5
-
R + H S R H r6
Equations 22 and 23 can be simplified by expressing [HA] and [A] in terms of [HI using eqs 9 and 10 to yield
(12)
(13)
The continuity equations for the following species can now be written as
(1+ HA
+ 2(Ka2/[H])(2a~+ 1))(2(K,2/[H]) + 1)’ (27)
a[RH] --
-
r5 - r6 at Eliminating the terms containing ris from eqs 14-17, we get a[H] a[HA] a[RH] +2-= at at at at
+-
+-
a[m]
The ionic fluxes, J H , JHA, and J A , may be expressed by the Nernst-Planck equation as
Further, the no current condition (CziJi= 0) requires J H - J H A - WA = 0 (20) Substitution of the expressions for fluxes of species, H, HA, and A from eq 19 into eq 20 and subsequent rearrangement yields the following expression for the electrical potential gradient
(YHA and LYA in the above equations are diffusivity ratios defined as (YHA = DHA/DH and (YA = DA/DH (28)
The flux of molecular species H2A is expressed by Fick’s law as
Substituting the above expressions for the fluxes into eq 18, we get the following expression:
where the derivatives d [ m ] / a [ R l and a[ml/a[Rl can be obtained using eqs 8 and 9, respectively, while a [ m ] / d [ R l can be obtained from the slope of the sorption equilibrium curve. The boundary conditions and the initial condition associated with eq 30 are at r = o (31) a[H]/ar = O [HI = [HI [R] = 0
at r = Rb at t = O
(32) (33)
Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 203 Equation 33 indicates that the resin is in free base form at the start of the experiment. Batch sorption dynamics also involves changes in the extraparticle acid concentration with time. The material balance in the extraparticle fluid yields d[HI + d[HAI 4H2Al +2-= dt
dt
dt
4rRb2efl(JHlr=Rb
+ JHAlr=Rb + 2JH2Alr=Rb) (34)
Substitution of the expressions for the fluxes in eq 34 using eqs 24, 25, and 29 yields d[HI + d[HAI dt
dt
4H2Al +2-= dt
2t
I
I
I
0’
2
L
6
T i m e , ks
Figure 4. Fit of the model using the experimental data on sorption dynamics.
where [H2A]’ represents the initial acid concentration and is given by and W is the dimensionless resin loading defined as
W =
total resin capacity 2(total initial acid content)
,,Q - ~ / ~ I ~ R ~ N V E(37) 2[H2A]T
[HA] and [H2A]in eq 35 can be written in terms of [HI using the eqs 8 and 9 without overbar. The initial condition to eq 35 is [HI = [HIi
at t = O
(38)
Application of the Model to the Sorption of H2S04 The generalized mathematical treatment of the above section can now be applied to the sorption of sulfuric acid on weak base resins. As mentioned earlier, the first dissociation of H#04 can be assumed to be complete. In such a cam, the molecular species, H A , does not exist and hence eq 30 can be simplified to the following form.
(
I+-+d[m] d[H]
-- -
d[m])d[A] d[R] dt
Boundary conditions to eq 39 are given by eqs 31 and 32 while the initial condition is given by eq 33. Similarly, the extraparticle acid balance can be rewritten by simplifying eq 35 as d[HI +-= dt
dt
The initial condition to eq 40 is given by eq 38.
Method of Solution The orthogonal collocation technique was used to convert the partial differential equations (PDEs) into a set of ordinary differential equations (OD&) which were then solved using the IMSL routine IVPAG. The method of solution is discussed in detail in our earlier work.
11 0
I
I
I
2
L
6
l i m e , ks
Figure 5. Fit of the model using the experimental data on sorption dynamics. Table 11. Regressed Values WGR-IL&SOI) IH,SO,lT. kmol/m3 5.5 x 10-4 2.2 x 10-3 4.5 x 10-3 1.05 X
of DB(System: Dowex
W 2.21 1.12 1.09 0.85
D,
X
lo9.m2/s 4.77 4.65 4.65 4.65
The values of the individual free ionic diffusion coefficient for H+, HSO,, and SO4” in solution are 9.31 X lP, 1.33 X and 1.06 X m2/s, respectively (Cussler, 1986; Dean, 1985). Theae values of the diffusion coefficient have been used in evaluating the constants, LYHA( = D H A / DH)and LYA ( = D A / D H ) on the basis of the assumption that the tortuosity factor for diffusion through the pore phase is the same for all the species. The value of D H , diffusivity of H+ in the pore phase, was regressed by using a least squares fit of eq 39 to the experimental data on sorption dynamics of sulfuric acid on Dowex WGR-2 and Amberlite IRA-93 resins (shown in Figures 4-11). The regressed values of D H are reported in Tables I1 and 111.
Results and Discussion The values of D H reported in Tables I1 and I11 compare very well with 4.65 X lo4 m2/s, a value which is obtained
a
204 Ind. Eng. Chem. Res., Vol. 32,No. 1, 1993 WGR-2
OOWCX
/H2S04
[ H ~ S O L ] ~ = L . S X I Okmol/m3 -~
w
0
-
D
1.09
0
4 -
Fit 0 1 the model
n
E 6
I R A - 9 3 / HZ 5 0 4 = 2 . 2 a10-' k mol/m3
Amberlite [H2SOr]:
-
W
i
1.19
Fit o f the model
n
I
U
0
i 6
2
8
Figure 6. Fit of the model using the experimental data on sorption dynamics. Oowca
I
I
1
2
4 Time, k s
6
Figure 9. Fit of the model using the experimen-taldata on sorption dynamics.
WGR-2 IH2SO4
[HzS04]:=
1 ~ 0 5 ~ 1 0k m - ~d / m 3
-
20
0
0
ks
Time
Fit o t the model
I
I
I
2
L
6
8
0'
Time, k s
I
I
I
2
4
6
Time, k s
Figure 7. Fit of the model using the experimental data on sorption dynamics.
. I'
r
Figure 10. Fit of the model using the experimental data on sorption dynamics.
~
Ambcrlitc
0
-
16
I R A - 9 3 /H2s04
HI SO^]:: 5 . 5 x l O - ' w
kmol/m)
1.95
Fit of the model
12
*I
0 I
--
n
E
0
Y 0
E
-I
n
I
T
U
Time, k s
Figure 8. Fit of the model using the experimental data on sorption dynamics.
by applying Wheeler's (1951)tortuosity correction factor of 2 to the free diffusivity of H+. Figures 4-11 compare the experimental data of the H+ concentration vs time with the simulated profiles. The
L
0
I
I
I
2
4
6
Time, ks
Figure 11. Fit of the model using the experimental data on sorption dynamics.
simulated profiles are based on the best fit values of DH. It can be seen that the fit of the model is excellent over the entire range of resin conversion. The maximum de-
Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 205 Table IV. Estimated Valuer of DBUsing Shrinking Core Model (System: Amberlite IRA-68/H2S0,. Q = 3.71 kmol/m* Bawd on Pore Volume) slope of the plot [HISO,], integral Z DH X lo9, kmol/m3 (referred in eq 51) of eq 47 mz/s 0.05 0.2616 0.02521 6.41 0.1 0.5208 0.05071 6.35 0.5 2.488 0.2587 5.96
Table 111. Rearerred Valuer of D n (System: Amberlite IRA-93/HZS0;) W DH X log,m2/s [H,SO,] 7, kmol/ m3 5.5 x 10-4 1.95 3.88 2.2 x 10-3 1.19 4.45 4.5 x 10-3 1.20 4.14 1.00 x 10-2 0.53 4.14 I
-
viation between the predicted concentration and the corresponding experimental concentration, for any run, was less than 10%. The excellent match between the theoretical and experimental results clearly supports the assumptions of the model. It is therefore concluded that there is practically no exclusion of co-ions from the pore phase mainly due to the very strong adsorption of SO:- ions on the protonated pore surface. Irreversible Sorption of H2S04. For some weak base resins the extent of reversibility of protonation is very small. Under these conditions the dynamic behavior can be more conveniently analyzed using the shrinking core model since it yields an analytical expression relating resin conversion with the elapsed time. For the sorption of H2S04,the s h r i i g core model m a y be derived as follows. The continuity equation over the reacted shell region under the pseudo-steady-state condition can be derived from eq 18 as
Substitution of JHand JHA from eqs 24 and 25 results in the following expression
Equation 42 can be solved using the following two boundary conditions. [R] = 0 at r = rc (43) [R] = [HI at P=Rb (44) where rc is the radius of the unreacted core. Solution of eq 42 yields the following relation between the local concentration of H+ in the pore and the location r.
The concentration gradient at r = rc can be obtained by differentiating eq 45 as
since [HI= 0 at r = rc and w2 = 0 (from eq 27), and hence we obtain
(49) substituting a[H]/arlr,r, from eq 46 into eq 49 and noting the following relation between the fractional conversion of resin X and the core radius rc
x
1- ( r ~ / R b ) ~
(50)
we obtain the desired expression for the shrinking core model under the condition when the extraparticle concentration of H+ is constant.
+
6D,It/QRb2 = 1 - 3(1 - x)2/32(1 -
A plot of 1 - 3(1-
x)
m2I3+
2(1- X ) v8 t should be a straight line passing through the origin with a slope equal to 6DHI/QRb2.From the value of the slope, the diffusivity DH can be estimated. Verification of Shrinking Core Model. Verification of the model developed in the previously section is attempted by using the data of Helfferich and Hwang (1985) on sorption of H2SO4 on Amberlite IRA-68. Our investigation on the sorption equilibria of this resin have confirmed that the sorption is practically irreversible over the entire concentration range used in their investigation (0.05-0.5 kmol/m3). The value of the diffusivity of H+ for each of the three concentrations used by these authors has been regressed using eq 51. The slopes of the relevant plots and the regressed value of diffusivity, DH, are listed in Table IV. Validity of the model is evident from the fact that the values of DH are practically the same for all three concentrations. Further, these values are comparable with, although somewhat higher than, the value of 4.65 X lo4 m2/s (DH obtained through Wheeler's (1951) tortuosity correction).
Conclusions Sorption studies of this work have indicated that the dynamics of sorption of H8O4 on weak base resins can be best correlated if we assume that the pore surface is electrically neutral and offers practically no barrier for exclusion of co-ions from the pore phase. The proposed mechanism satisfactorily explains the high rates of the sorption of polybasic acids.
where Z is defined as
I = l [ 0H 1 ( w l + wz)d[R]
Nomenclature (47)
This integral can be analytically evaluated. The analytical expression is given in the Appendix. Taking the material balance of H+ at the core-shell boundary (i.e., r = re),we obtain the following expression
(51)
A- = divalent anion species [A] = concentration of divalent anion, kmol/m3 C = concentration, kmol/m3 Ci= concentration of species i, kmol/m3 DA = pore diffusivity of divalent anion, mz/s DH = pore diffusivity of H+ion, m2/s DHA = pore diffusivity of monovalent anion, mz/s Di = pore diffusivity of species i, m2/s D, = pore diffusivity of molecule, m2/s
206 Ind. Eng. Chem. Res.,Vol. 32, No. 1, 1993
F = Faraday constant, C/mol H+ = hydrogen ion species [HI= concentration of H+ ion, kmol/m3 HA = monovalent anion species [HA] = concentration of HA, kmol/m3 H2A = undissociated acid species [H2A]= concentration of H2A,kmol/m3 [H2AIT= total concentration of acid in solution, kmol/m3 Z = integral as defined by eq 47 J A = flus of A, kmol/(m2 s) J H = flux of H+ ions, kmol/(m2 s) J H A = flux of HA, kmol/(m2 8 ) JH,A = flux of H2A,kmol/(m2 e) Ji = flux of species i , kmol/(m2 8 ) K,, = first dissociation constant of acid, kmol/m3 K,, = second dissociation constant of acid, kmol/m3 N = number of resin particles per unit volume of extraparticle fluid Q = resin capacity based on pore volume, kmol/m3 Rb = radius of resin bead, m R = gas constant, J/(mol K) RH = protonated species on the resin [RH] = concentration of RH, km0i/m3 rl-r6 = rates of reactions presented in eqs 11-13 r = radial distance measured from the center of bead, m rc = unreacted core radius, m T = absolute temperature, K t = time, s V = solution volume, m3 W = dimensionless resin loading X = fractional conversion of resin z = valence of ion
Greek Letters aA= diffusivity ratio as defined by eq 28 = diffusivity ratio as defined by eq 28 tp = fractional pore volume based on total resin volume 4 = electrical potential, V w1 and w2 = quantities defined by eqs 26 and 27 Subscripts i = initial value i = any species
Bar above the species refers to pore phase. Appendix. Analytical Solution for Integral I of Equation 47
z = z1 + 1 2
where
ZI = &["'al d[R] = -[ ~[ UHI H@ A
1 + HA
+ F) + E ( f - c ) In
and
=
(+)
"--[
+
[HI- cA In [HI+
1 + &HA
where A=
b - cu (d -
+ c2,, D=
B=l-
+
b - CQ c2 (d - c ) ~
ad - b - d 2 d-c
and
d = 2Ka2; f = 3Ka2; g =
2Ka2ffA -
HA
Literature Cited Adams, G.; Jones, P. M.; Miller, J. R. Kinetics of acid uptake by weak base anion exchangers. J. Chem. SOC.A 1969, 2543. Bhandari, V.M.; Juvekar, V. A,; Patwardhan, S. R. Sorption studies on ion exchange resins. 1. Sorption of strong acids on weak base resins. Ind. Eng. Chem. Res. 1992a, 31, 1060. Bhandari, V. M.; Juvekar, V. A.; Patwardhan, S. R. Sorption studies on ion exchange resins. 2. Sorption of weak acids on weak base resins. Ind. Eng. Chem. Res. 19928,31, 1073. Cussler, E. L. Diffusionmass transfer in fluid systems; Cambridge University Press: Oxford, U.K., 1986. Dean, J. A. Lunge's Handbook of Chemistry, 13th ed.; McGraw-Hik New York, 1985. Helfferich, F. G.; Hwang, Y. L. Kinetics of acid uptake by weak base anion exchangers. Mechanism of proton transfer. AIChE Symp. Ser. 1985, 81 (No. 242), 17. Rao, M. G.; Gupta, A.K. Kinetics of ion exchange in weak baee anion exchange resins. AIChE Symp. Ser. 1982,78 (No. 219), 96. Wheeler, A. Reaction rates and selectivity in catalyst pores. Adu. Catal. 1951, 3, 249. Received f o r review June 24, 1992 Accepted October 16,1992
