Efficient simulation and equilibrium theory for adsorption processes with implicit adsorption isotherms – Mass action equilibria

Abstract

An efficient method for the simulation of packed bed adsorbers is presented. It is based on equilibrium models and can be applied to any implicit adsorption isotherm. It uses a method of lines approach, avoids explicit differentiation of the adsorption isotherm, and exploits standard numerics for the simultaneous solution of the resulting ordinary differential and implicit algebraic equations. Application is illustrated for stoichiometric ion exchange, which also admits an analytical approach using equilibrium theory. Classical theoretical results from equilibrium theory are summarized, further extended and compared to the numerical calculations for different scenarios. Focus is on selectivity reversals and their influence on process operation. It is shown that the selectivity reversal may introduce multiple solutions.

Numerical Short-Cut Design of Simulated Moving Bed Chromatography for Multicomponent Nonlinear Adsorption Isotherms: Nonstoichiometric Langmuir Model

“…However, the FDEs do not have any analytical solution if there are more than three components in the feed. The general FDEs for the N -component system are, To solve the above given complex system of polynomial equations, many mathematical methods, such as the solution of an eigenvalue problem or, more specific, for the case of Langmuir adsorption isotherms, the ω-transformation were introduced.…”

“…Solutions for a very flexible extension to a generalized Langmuir isotherm model are also available . More recently Fechtner and Kienle discussed equilibrium theory for stoichiometric ion exchange with an implicit sorption isotherm and extended triangle theory to ion exchange SMB processes …”

Efficient simulation and equilibrium theory for adsorption processes with implicit adsorption isotherms – Ideal adsorbed solution theory

“…Particular challenging are implicit adsorption isotherms. For the efficient simulation of equilibrium models of packed bed adsorbers with implicit adsorption isotherms, we recently proposed a new approach [1]. It is based on a reformulation of the underlying partial differential equations, uses a method of lines (MOL) approach (see e.g.…”

“…To overcome the challenges and restrictions of previous approaches, the new methodology introduced in [1] is used and extended accordingly in the present paper. The outline of the paper is as follows: First, the model equations are briefly summarized and some structural properties that are essential for the new approach are proven.…”