Multicomponent ion exchange column dynamics

Abstract

Simple model equations which consider different rate control mechanisms are formulated for fixed bed multicomponent ion exchange processes. Efficient and accurate numerical methods are developed for solving these equations for liquid phase, solid phase or combined phase control. The algorithms are applicable to both ion exchange and liquid adsorption and are shown to be extendable to a general form of isotherms. The accuracy of the numerical algorithm is evidenced by the fact that the asymptotic limiting equilibrium solutions are closely approached as the dimensionless length parameter is increased, regardless of the rate control mechanism. Numerical examples for ion exchange applications are presented. These examples included multicomponent elution and purification problems. The effect of mass transfer resistance was also examined. Other examples examine the validity of a model reduction assumption and the comparison of equilibrium theory with the results obtained using the present finite mass transfer rate model.

Multicomponent biosorption in fixed beds

“…The approaches used for modeling ion exchange in ®xed beds by Hiester and Vermeulen (1952) for single solute, and by Helerich (1967) and by Klein et al (1967) for multicomponent mixtures, are restricted to systems with constant separation factors and/or to in®nitely long ®xed beds for which the assumption of a local equilibrium is valid. The most universal approach seems to be the one adopted by Tan and Spinner (1994) who numerically solved a mixed system of partial dierential, ordinary dierential, and algebraic equations describing the dynamics of multicomponent ion exchange in a ®xed-bed. In this work, the model of Tan and Spinner (1994) has been adopted as outlined earlier which is restricted to binary systems, i.e.…”

“…The most universal approach seems to be the one adopted by Tan and Spinner (1994) who numerically solved a mixed system of partial dierential, ordinary dierential, and algebraic equations describing the dynamics of multicomponent ion exchange in a ®xed-bed. In this work, the model of Tan and Spinner (1994) has been adopted as outlined earlier which is restricted to binary systems, i.e. single solute ion exchange, which allows us to test the approach for the case of biosorption while reducing the number of equations to a minimum.…”

Optimizing Cu removal/recovery in a biosorption column

“…It is known that the "favorable isotherm" leads to the development of a self-sharpening exchange zone in the fixed-bed adsorber, whereas the "unfavorable isotherm" gives rise to a broadening dynamic sorption zone (Helfferich, 1962;Coulson and Richardson, 1991). As an alternative to ion-exchange isotherms, tables of values of separation factors for the compositions existing in an adsorber can be used to represent the equilibrium for the purpose of computer simulation of the fixed bed (Tan and Spinner, 1994).…”

“…The approaches used for modeling ion exchange in fixed beds by Hiester and Vermeulen (1952) for single solute and by Helfferich (1967) and Klein et al (1967) for multicomponent mixtures are restricted to systems with constant separation factors and/or to infinitely long fixed beds for which the assumption of a local equilibrium is valid. The most universal approach seems to be the one adopted by Tan and Spinner (Tan and Spinner, 1994) who numerically solved a mixed system of partial differential, ordinary differential and algebraic equations describing the dynamics of multicomponent ion exchange in a fixed bed. In the present work, the model of Tan and Spinner (1994) has been adopted with the following modifications.…”

“…Although the process of Cu biosorption in a fixed-bed column is influence by both the sorption equilibrium and the mass transfer, the present column experimental data were interpreted mainly through the concept of ion-exchange equilibrium isotherms calculated from a model originally developed for biosorption by algal biomass (Schiewer and Volesky, 1995b). The effect of mass transfer was not studied; however, some of the column data were used for fitting a fixed-bed ion-exchange model recently used by Tan and Spinner (Tan and Spinner, 1994). The literature on modeling of biosorption in a fixed bed is rather scarce, and the few models that were applied (Trujillo et al, 1991;Volesky and Prasetyo, 1994) approached the biosorption process as the adsorption on activated carbon.…”