A NONEQUILIBRIUM ADSORPTION MODEL SATISFYING ELECTRO-NEUTRALITY CONDITION FOR ION-EXCHANGE CHROMATOGRAPHY

Abstract

In species exchange processes (e.g., ion-exchange chromatography), nonequilibrium adsorption models with conventional linear driving force (LDF) approximation describe mass transfer (or exchange) between liquid and solid phases in the presence of liquid concentrations (or active regions), where adsorption isotherms are often expressed as a function of the liquid concentrations. This study addresses whether the nonequilibrium adsorption model with LDF approximation satisfying the electro-neutrality condition can produce unphysical solutions in the absence of liquid concentrations (or inactive regions). The reason of the unphysical behavior of the model is elucidated numerically and theoretically. In this article, a generalized LDF rate model is proposed, without losing the generality of the conventional LDF model, to handle the active and inactive regions simultaneously. The limiting-component constraint (LCC) describing phenomenological observation on liquid concentrations is constructed on the basis of the nonnegative liquid concentration constraint. The generalized adsorption rate model in continuous and discontinuous forms is derived from the LCC for multicomponent systems. For illustration, an ideal three-component ion-exchange problem with inactive initial condition is solved. An ion-exchange/ion-exclusion simulated moving bed (SMB) process is also illustrated as its successful implementation, comparing it with in situ experimental data.

Keywords:

• Electro-neutrality condition
• Ion-exchange chromatography
• Linear driving force (LDF) approximation
• Nonequilibrium adsorption model
• Simulated moving bed (SMB)
• Virtual desorption

Acknowledgments

This work was supported by grant No. R01-2006-000-10786-0 from the Basic Research Program of the Korea Science & Engineering Foundation (KoSEF). Thanks go to Professor S. B. J⊘rgensen for his constructive advice.

Notes

^a Dry resin density is assumed to be 0.65 g/mL. Original resin capcity = 5.173 meqv/g (Dranoff and Lapidus, 1961).

^b Overall diffusivity coefficients estimated from Ernest et al. (1997) data: 4.60 × 10⁻⁵ (H⁺), 3.15 × 10⁻⁵ (Na⁺), and 3.39 × 10⁻⁵ (Ag⁺) cm²/min.

^a One backwashing column is not taken into account.

^b has a unit [eqv/L] on the basis of the particle volume, where n _{T, bed volume} (= 2.0±0.1) is on the basis of the bed volume.

^a .

^b .

^c .

^d .

^a Resin utility = (% in K⁺-form)_{V2 column} − (% in K-form)_{V1 column}.