Ind. Eng. Chem. Res. 1996,34, 4040-4048
4040
A Kinetic Model for Cationic-Exchange-ResinRegeneration Vikram Chowdiah and Gary L. Foutch* School of Chemical Engineering, Oklahoma State University, Stillwater, Oklahoma 74078
Equilibrium models are typically used to describe ion-exchange-resin regeneration. These models are accurate for most applications due to the high concentration of regenerant used. However, for ultrapure water applications, where regeneration efficiencies must exceed 99.9% (sites in the hydrogen or hydroxide form), equilibrium models underpredict the total chemical contact time required. One approach to correct this modeling deficiency is to replace the equilibrium assumption with a kinetic expression. This paper describes kinetic modeling of ion-exchangeresin regeneration using both the Nernst-Planck and Fick's Law approaches. The model compares favorably with literature data.
Introduction Large-scale applications for high-purity water production are found in the power and microelectronics industries. Although water quality standards for high-purity water differ among industries, generally, water approaching 0.055 pSlcm conductivity (25 "C) and ionic content of Na+, C1-, and S O F less than 1 ppb (parts per billion) is desired. A mixed bed of cationic and anionic resin is widely used in high-purity water technology. The H+-formresin exchanges hydrogen ions for other cations in the bulk liquid, while the OH--form resin exchanges hydroxide ions for other anions. This mode of mixed-bed operation is the service cycle. In reverse mode, the regeneration cycle, ions loaded during the service cycle are replaced with H+or OH- ions. Mixed-bed regeneration requires separation of the cationic and anionic resin, usually by backwashing. Anionic resins are lighter than cationic resins, hence backwashing results in stratification. Separated resins may be transferred to different vessels where they are regenerated with concentrated solutions (e.g., 10%HCl for cationic resin and 10% NaOH for anionic resin). Regenerated resins are rinsed thoroughly with highpurity water before being transferred back to the service vessel and air mixed. Resin separation is critical, especially for sub-partsper-billion ionic concentrations. Cross contamination (cationic resin in the anionic resin during regeneration and vice versa) results in increased impurity leakage during the service cycle (strauss, 1991). Regeneration efficiency is also one of the parameters controlling the lower limit of service-cycle water quality. The need for extremely high regeneration efficiencies can be seen by example. Ambersep 252, with a cation regeneration efficiency of 99.8% (percentage of sites in the hydrogen form), will have an equilibrium leakage of 1.0 ppb when placed in service. An efficiency of 99.84% will give a leakage of 0.8 ppb (Bates et al., 1993). With many of these industries requiring ionic contamination of less than 0.1 ppb, the need for even higher regeneration efficiencies can be seen. System parameters affecting regeneration efficiency can be studied using a regeneration model. Improper or incomplete regeneration leads to ionic leakage from the bed into the treated water. Problems in regeneration may also be due to insufficient contact time andor resin fouling (davies, 1994). During regeneration the contact time required is determined by
* Author
t o whom correspondence should be sent. 0888-5885/95/2634-4040$09.00/0
nomographs or equations supplied by the respective resin manufacturer. This information does not usually include the proprietary data used to develop the nomographs, and in general, the amount of chemical indicated is excessive in order to guarantee a conservative estimate of the expected water quality in service. Most operators modify these estimated contact times and chemical use as they become acquainted with their facilities, thereby attempting to minimize chemical use and still achieve the desired service-cycle water purity. The cost of regeneration is a major expense in ion exchange (Kuriychuk and Gallupe, 1990). Frequent regenerations require the purchase of large quantities of chemical regenerant. After regeneration, large volumes of high-purity rinse water are needed to displace regenerant from the ' resin. In addition, disposal is required for the used regenerant and rinse water. The performance of an ion-exchange operation is governed by a combination of stoichiometric, equilibrium, and rate relationships and the process configuration. A regeneration model can be used to study the effects of different parameters on resin regeneration. Hence, the model can be used as a process optimization tool. This paper presents a model development for resinregeneration kinetics of strong cationic resin with monovalent binary exchange of ions. Since the regenerants are in high concentration, resin-phase diffusion is the rate-controlling step. This has been confirmed experimentally by Helfferich (1962). Helfferich (1958) used the Nernst-Planck equation to model resin-phase kinetics. The equation was solved using a finitedifference scheme. Helfferich (1962) presented an analytical solution for solid-phase kinetics using a constant diffusion coefficient. The system modeled here is sodium ions (in the resin phase) exchanging with hydrogen ions from the bulk solution. At high regenerant concentrations the system exhibits a nonlinear equilibrium relationship. The exchanging ions have significantly different mobilities. Solid-phase ionic flux is described by either (a) the Nernst-Planck model or (b) Fick's law. The NernstPlanck model leads to a concentration-dependent diffusion coefficient. Since it is appropriate to model ionic fluxusing the Nernst-Planck model, a matching effective-diffusion coefficient is used in the Fick's law approach. Computational results from the two models are compared. At the resin boundary, concentration variation is described considering the internal-to-external resistance ratio. A column process model is developed t o study regeneration of a cationic resin as binary
0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 11,1995 4041 sodium-hydrogen exchange. The model may then be used to analyze system parameter effects on resin regeneration (flow rate, bed depth, contact time, and regenerant concentration), as well as to predict effects of regenerant concentration on regeneration efficiency.
Background In addition to ultrapure water applications, resin regeneration is used in other processes, e.g., the recovery of gold from plating waste solutions. A two-step regeneration was developed for this process. The regenerants are concentrated potassium chloride followed by potassium thiocyanate solution (Sapjeta et al., 1987). Ionexchange resins used to remove nitrate from drinking water are regenerated with concentrated sodium chloride (Hoek and Klapwijk, 1989). A nonaqueous solution of HC1 is used to regenerate cation-exchange resins that remove nitrogen compounds from hydrocarbon oils (Yan and Shu, 1987). Helfferich (1965) derived kinetic expressions for ion exchange accompanied by a reaction (neutralization, association, or complex formation). Much of this work is the basis to explain ion-exchange kinetics of weak anionic or cationic resins, which contain incompletely dissociated groups, leading to association or complex formation reactions in the resin. Dana and Wheelock (1974) studied acid elution of a cupric-amine complex from a cation exchanger and obtained rate data and solute movement characteristics within the bead using photography. They analyzed the kinetics as a moving boundary problem. To model the process they used Fick’s law with a constant effective-diffusioncoefficient. HOll and Kirch (1978)modeled the regeneration of weakbase ion-exchange resins. They used a reaction-diffusion coupled model with a constant effective-diffusion coefficient. Colwell and Dranoff (1969) considered nonlinear equilibrium and axial mixing effects on sorption in ionexchange beds. The solid phase was modeled with a constant effective diffusivity. The effective-diffusion coefficient was obtained by a curve fit of the experimental data. Kataoka et al. (1977) modeled breakthrough behavior of an ion-exchange column operating under particle diffusion controlled conditions. They defined an equilibrium constant based on the law of mass action. Tien and Thodos (1959) considered the effects of liquid-film resistance and particle diffusion for nonequilibrium relationships, assuming a constant effective diffusivity in the resin. Kinetics of ion exchange in concentrated buffer solutions have been studied by Koloini et al. (1990). They assumed only film diffusion as the important process and used an effective-film mass-transfer coefficient to model their system. The liquid-phase diffusion coefficients were derived from infinite-dilution values. Use of diffusion coefficients calculated from infinite-dilution conductances is not correct at the high reagent concentrations used during regeneration. In concentrated electrolyte solutions ion-ion interactions become important. Ionic conductances are not additive, hence the Nernst-Hartley expression cannot be used to obtain diffusion coefficients. Miller (1966) studied the transport properties of HC1 in solutions of varying strength and presented the HC1 diffusion coefficient as a function of solution normality. A minimum cm2/sis observed a t diffusion coefficient of 3.05 x 0.2 N. At lower concentrations the value rises to 3.35 x cm2/s at infinite dilution. Above 0.3 N a near-
linear relationship exists up to a value of 4.6 x cm2/s at 3.0 N. Liberti and Passino (1982) modeled ion exchange under idealized conditions assuming equilibrium. The model was solved under favorable and unfavorable equilibrium conditions. Tondeur and Bailly (1986) modeled ion-exchange columns assuming equilibrium between the solid and liquid phase at all points in the column. For kinetically controlled exchange they suggested that accurate quantitative data fitting must be undertaken. They conducted a limited number of experiments to fit their model. Durao et al. (1992) modeled regeneration as an equilibrium process and incorporated shrinkinghwelling behavior of the resin bead. Mass-transfer effects were absent. The model deviated considerably from their experimental data, predicting an earlier breakthrough than observed. In these previous models, concentration at the resinfilm boundary has been assumed constant. However, this is true for infinite solution volume only. Since regeneration is performed in columns, the concentration at the resin boundary varies and is a function of bulk concentration and equilibrium at the resin surface. Also, a t the resin surface, the ratio of internal-toexternal resistance needs to be considered. This change in boundary condition affects mass transfer into the resin and, hence, the average resin concentration.
Model Development and Numerical Solution Sorption of ionic and nonionic solutes on ion-exchange beds has been studied extensively. Experimental breakthrough data have been fit to both equilibrium and rate models. Initially, equilibria nonlinearities were assumed t o be due to axial mixing and density gradients in the liquid phase. Helfferich (1962) applied the Nernst-Planck expression t o describe the transport of electrolytes in ion-exchange resins. The Nernst-Planck expression incorporates the effect of an electric-potential gradient caused by the differences in the self-diffusivity of the ions. This modeling approach accounted for some of the nonlinearity noticed earlier. Intraparticle diffusion is rate controlling in resin regeneration since the regenerant concentration is high (1-2 N solution strength). The following assumptions have been made to model resin kinetics: (1)The resin bead is a uniform sphere. This is a reasonable assumption since monosphere resins with tight size distributions are available. (2) Ion exchange is not accompanied by volume changes in the sphere. Experiments by Kataoka et al. (1975)found that there is little shrinking or swelling of resin when sodium is exchanged for hydrogen ions. (3) Individual diffusion coefficients in the resin are constant. The bidisperse nature of the ion exchanger is not considered. Experimentally, variation in the diffusion coefficients within the resin is difficult to evaluate. (4) Fluxes of the ions are coupled by the electric field only. (5) The concentration profile within the bead, before exchange, is constant. (6) Co-ions are excluded from the resin phase. An experimental investigation of Patell and Turner (1979)has shown that the amount of co-ion sorbed by the ion exchanger, at high external-solution concentrations, is negligibly small. When the external solution was 1 N HC1, the sorbed concentration was 0.04 N. Ion-exchange rate was not affected by co-ion intrusion when the sorbed-phase concentration of co-ion was low, and the resin-phase diffusivity ratio of the co-ion to the ion initially present in the resin was less than 10 (Kataoka et al., 1978).
4042 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995
The Nernst-Planck Approach. The NernstPlanck equation for flux of ion i is written as
(10) T'O
(1) The following constraints also apply (Helfferich, 19621, n
Cici= Q
(electroneutrality)
(2)
i=l n
&Ji = 0
(no electric current)
(3)
The average resin-phase concentration of hydrogen is given by
i=l
i = 1, ..., n
(12) (different ionic species involved)
The fluxes of the independent ions are combined using eqs 2 and 3 t o eliminate the electric-potential term. The flux expression is used in the material balance for a sphere to obtain (for sodium exchanging with hydrogen)DN,DH,CH, and CN, are quantities defined for the resin
phase. Equation 4 is subject to the following initial and boundary conditions:
Equations 9- 12 are solved numerically. The Fick's Law Approach. Fick's law can be used t o model this system with a constant diffusion coefficient.
The fly expression, eq 13, combined with a material balance for a sphere gives (for hydrogen)
t=O
(14)
O
