Ind. Eng. Chem. Res. 1990, 29, 116-121
116
Amine Recovery by Ligand Exchange: Pore Diffusion Model Wayne B. Boldent and Frank R. Groves, Jr.* Chemical Engineering Department, Louisiana State University, Baton Rouge, Louisiana 70803
This paper presents data on the removal of butylamine from a dilute aqueous solution by complexing with copper ion immobilized on an ion-exchange resin. The process, called ligand exchange, is much like ion exchange or adsorption. Data are presented both for batch and fixed bed continuous operation. A mathematical model based on control of the process by diffusion of amine in the resin pores is derived and solved numerically by an orthogonal collocation method. The fixed bed results are successfully modeled using effective diffusivity and equilibrium data from separate batch experiments.
Introduction Ligand exchange is a separation process in which a solute is removed from solution by complexing with metal ion immobilized on an ion exchange resin. For example, a carboxylic acid ion-exchangeresin loaded with copper(I1) ion can be used to remove aliphatic amines from a dilute aqueous solution by complexing with the copper. This separation method can be used in a fixed bed continuous configuration much like conventional ion exchange or adsorption. When the bed is loaded with amine, it is regenerated by treatment with steam or hot water which recovers the amine in a more concentrated solution. The process has the advantage of selectivity since only materials that complex with the metal ion are removed. It may have the advantage of greater capacity as compared to ion exchange since each metal ion may complex multiple ligands. Aliphatic amines are used in the oil and chemical industries as solvents in absorbers for acid gas remove1 from process streams. Fugitive amine emissions from these units can overload biological treatment facilities. Since amines can form carcinogenic nitrosamines, it is important that they may be removed from wastewater before discharge. Ligand exchange offers interesting possibilities for removing and recovering amines from wastewater. Ligand exchange has been used successfully in analytical chemistry but has not been applied on a commercial scale. This paper presents experimental data and a computer simulation for the complexation of butylamine with copper(I1) ion held on a carboxylic acid type ion-exchange resin. The computer simulation treats both a batch sorber and a continuous fixed bed. The rate of the process is governed by unsteady-state diffusion in the pores of the ion-exchange resin.
Previous Work Helfferich (1962) did the earliest basic work on the theory and practice of ligand exchange. Dawson (1974), Dobbs et al. (1975),and Dobbs (1976) developed a process for ammonia removal from waste streams by complexation with copper held on a hydrous zirconium oxide ion exchanger. They demonstrated the regeneration of the ligand-exchange fixed bed using low-pressure steam. Jeffrey (1977) found that Cu(I1) on a carboxylic acid ion-exchange resin was effective in removing ammonia from salt solutions produced during catalyst manufacture. Groves and White (1984) correlated ammonia removal data by means of the Thomas model (1944), an analytical solution for fixed bed adsorption. Groves (1984) demonstrated aliphatic amine removal from an aqueous solution using
* To whom correspondence should be addressed.
Present address: Shell Development Company, Houston, TX
77001. 0888-5885/90/2629-0116$02.50/0
copper ion and correlated the fixed bed results by using the Thomas model. The use of the Thomas model for ligand exchange is not entirely satisfactory. Since complexation of amines with copper is a fast process, the rate of ligand exchange is controlled by mass transfer-convective mass transfer in the boundary layer at the surface of the ion-exchange particles and diffusion in the pores of the particles. The diffusion is accompanied by equilibrium between complexed amine and free amine in the pores. The Thomas model is based on second-order kinetics for the exchange process and has to be modified empirically to handle mass-transfer control. One of the objectives of the present work is to develop a more rigorous simulation based on convective mass transfer and internal diffusion and incorporate the nonlinear ligand-exchange equilibrium relation. HOll and Sontheimer (1977) developed a similar pore diffusion model for batch ion exchange of hydrogen ions with metal ions on spherical resin particles.
Theory Solute transport in porous media is usually modeled by the classical Fick law for unsteady-state diffusion. In the pore diffusion model of the amine recovery process, the amine is assumed to diffuse into the pores of the ion-exchange resin. Complexed amine is held stationary in the resin phase. Equilibrium is assumed at each point in the ion-exchange particle between amine in the pore liquid and complexed amine fixed to copper ions in the resin matrix. For a single spherical resin pellet, the unsteady-state diffusion equation is
The equilibrium equation q = fWP) relates the resin phase, q(r,t), and pore liquid phase, Cp(r,t), concentrations at any point r in the resin pellet. The initial and boundary conditions are Cp=q=O att=O f o r O - < r < R (3) aCp/ar = aq/ar = 0
at r = 0
for t I O
(4)
and
&,dCp/ar = kf(Cb - C,)
at r = R , t > 0 (5)
The pore diffusion model described above gives a rigorous description of the ligand-exchange process assuming only that the complexation reaction is rapid compared to the mass-transfer processes. Yoshida et al. (1986) present a similar pore diffusion model for complexation of metal ions with a chelating resin. Their model includes chemical 0 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 1, 1990 117 250
In Z
1 I
W
a 200-
a
0
(3 \
0
(3
E
150
E
-
0
a
4
a
I-
W
a -0.50
I-
t loow
u
z
0
v)
0
z -
z5
a 50
0
-
Data L a n qmuir Model
W
- 0.25 g 5
In
0
w 30
60
120
90
SOLUTION CONCENTRATION,
1500.00
MG / L
Figure 1. Butylamine equilibrium a t 295 K.
reaction effects, which, however, were negligible in their studies for resin beads greater than 0.02 cm in diameter. Since the complexation of amines with copper is known to proceed rapidly and the beads used in this work were 0.06 cm in diameter, it is reasonable to neglect the chemical reaction effects. Equilibrium Relation. In this research, we have represented the equilibrium data empirically by a Langmuir equilibrium equation UCP
q=m
aU
(7)
For ligand exchange of amine solutions of -0.1 M and higher concentration, the equilibrium curve can be approximated by a step function. The pore diffusion model then predicts shrinking core behavior for the sorption process with a fully complexed shell at the surface of the resin bead sharply separated from an uncomplexed region that shrinks toward the center of the bead. For this special case, the mathematical treatment is simplified by using the pseudo-steady-state shrinking core approximation (Dana and Wheelock, 1974). For the dilute amine solutions used in this work, the governing portion of the equilibrium curve (Figure 1)does not conform to a step function, and the more rigorous unsteady-state pore diffusion model is appropriate. Batch Sorber Model. The batch sorber consists of an isothermal, well-mixed volume of solution, V, suddenly subjected to a volume, V,, of ligand-exchange sorbent. The composition, cb, of the bulk fluid is related to the volume-average sorbent concentration, qa, by the material balance
with initial conditions Cb = Co and qa = 0. This can be written in dimensionless form dub - = - -1 dQa (9) dt dt which integrates to
L
J
where the dimensionless equilibrium curve Q g ( U ) = a U / [ l + ( a - 1)U] (13) has been used to eliminate Q. At the stirrer speeds used in the batch sorber experiments, the external mass-transfer resistance proved negligible. Hence, the boundary condition of eq 5 was replaced by a material balance on the resin pellet:
which becomes dr
(6)
This can be expressed in dimensionless form with respect to reference values, qo and Co, of the concentration: = 1 + ( a - 1)U
(10) u b = 1 - Qa/5 This relation can be used along with the single-pellet mass-transport model, 1-5, to predict the variation with time of the bulk solution concentration, ub, during the course of a batch sorber experiment. By comparing the predicted concentration variation with experimental data, the value of the effective pore diffusivity, D,, can be determined. The symmetry condition, eq 4, is first satisfied automatically by the transformation z = (r/R)2 (11) The resin pellet diffusion relation, eq 1, is then expressed in dimensionless form
when transformed to dimensionless coordinates. These model equations were solved by orthogonal collocation (Villadsen and Michelsen, 1978). The particle diffusion equation (12) was discretized at N interior collocation points along the radius of the pellet to give N+ 1
dU,i/dT = 11 + g ’ ( U , i ) / ~ ] - C ~ [TijUpj]
15 i 5
N
j=l
(16) When eq 15 was discretized, the result was N+ 1
dQa/dT = 67 C A N + I , jupj j=1
(17)
+
The N 1 equations, eq 16 and 17, were solved simultaneously along with the material balance, eq 10, to obtain the N + 2 unknowns Upl, U 2, ..., UpN+l,Q, as functions of time. Note that ub = for the special case of negligible external mass-transfer resistance. The LSODE Livermore Solver routine was used to obtain the solution numerically. Eight collocation points were used. Fixed Bed Model. The material balance equation for the fixed bed is Cb acf/ax + pb aq,/atr = o (18)
gN+l
where t’= t - x / u . The inherent assumptiom are (a) radial and angular symmetry of the bed, (b) neglect of axial dispersion, and (e) small particle diameter in comparison with the overall bed length. The initial and boundary conditions are c f =c,; x = 0, t’> 0 qa =o;
c,=o;
O I X
IL, t ’ = O
O l X l L , t’=O (19) The second term in eq 18 is the volume-average accumulation rate in the exchanger sorbent. It couples the
118 Ind. Eng. Chem. Res., Vol. 29, No. 1, 1990
liquid-phase material balance to that of the sorbent phase. For ligand exchange of amines with copper, this rate is governed by diffusion in the resin particles and by mass transfer in the boundary layer at the particle surface. The equation describing diffusion within the particles is eq 1 used earlier for the batch sorber model. As in that model, we assume equilibrium between the liquid phase and the resin phase at every point in the particle. With this assumption, the resin-phase concentration q ( r , t ) can be eliminated by using the equilibrium relation, eq 6 and 7. The particle-phase average amine accumulation rate is related to boundary layer mass transfer at the particle surface by Pb L’q,/L’t’ = k@I(Cf - C p ) ; r = R , t’ > O, X L O (20) In dimensionless form, eq 18 becomes du,/ap + ?&o[Uf- U*] = 0
(21)
The liquid-phase concentrations in the bed at t’= 0, UT (x,O), were obtained analytically from this equation. At t ’ = 0, q,(x,O) = 0 everywhere in the bed, so U* = 0. Thus, eq 21 can be integrated analytically with the boundary condition Uf = U , at p = 0 to give Uf(P,O) = U , exp(-wB) (22) The solution of the fixed bed problem was completed by a numerical method using orthogonal collocation. Equation 21 was discretized using M axial interior collocation points and two boundary points, B = 0 and = 1: M+l
2 DlkUfk+ vllcp[Uf, - Uj*] = 0;
15 j
