In this work we present a comparison of different discretization techniques, in the context of finite volume formulation, for the solution of separation processes involving adsorption, absorption and permeation. The mathematical model developed assumes axially dispersed plug-flow, uniform bed/sorbent/membrane properties along the axial coordinate and negligible radial gradients. The algorithm used enforces both local and global flux conservation in space and time. The discretization of convection terms is made using unbounded schemes and bounded high-resolution schemes. We use the same strategy for simulating three different separation processes: membrane permeation, pressure swing adsorption and simulated moving bed. In the case of membrane permeation we present simulation results of air separation using a polysulfone membrane and compare to ones of Coker et al. [Coker, D. T., Freeman, B. D., & Fleming, G. K. (1998). Modeling multicomponent gas separation using hollow-fiber membrane contactors. AIChE Journal, 44, 1289]. In the case of pressure swing adsorption we study a small pressure swing adsorption unit for air separation as described by Santos et al. [Santos, J. C., Portugal, A. F., Magalhaes, F. D., & Mendes, A. (2004). Simulation and optimization of small oxygen pressure swing adsorption units. Industrial and Engineering Chemistry Research, 43, 8328]. In the case of simulated moving bed we consider the glucose/fructose separation as described by Leao and Rodrigues [Leao, C. P., & Rodrigues, A. E. (2004). Transient and steady-state models for simulated moving bed processes: Numerical solutions. Computers and Chemical Engineering, 28, 1725]. Our simulated results are particularly interesting for the case of transient highly convective separation problems, where standard procedures may lead to the appearance of unphysical oscillations in the computed solution due to the existence of sharp moving fronts. (c) 2005 Elsevier Ltd. All rights reserved.