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. (C) 2017 Elsevier Ltd. All rights reserved.