An equilibrium theory simulator (Esim) for the simulation of cyclic adsorption processes is presented. The equations are solved with a Godunov upwind flux scheme that does not require either the evaluation of characteristics or shock equations or the imposition of a numerical entropy condition to track shocks. Esim is able to simulate non-trace and non-isothermal adsorption systems with any adsorption isotherm. Esim has been validated against gPROMS based simulations that use the full set of governing equations (including mass and heat transfer resistances and axial dispersion) carried out under conditions close to the limits where equilibrium theory is valid. Esim enables the establishment of bounds for the optimal performance of an equilibrium driven separation and requires only the measurement of adsorption isotherms. (C) 2016 Elsevier Ltd. All rights reserved.