Concentration and/or space-dependent diffusive and convective mass transport, through capillary, anisotropic membrane layer, dense or porous membrane, were investigated. A quasi-analytical solution is presented in order to estimate the concentration distribution in the membrane layer and the total mass transfer rates, namely the sum of the diffusive and convective ones. These properties have been given in closed, explicit, mathematical forms which make the calculation process very simple. The diffusion coefficient can vary with the concentration and/or space coordinate, while the convective velocity can vary with the space coordinate. It was shown that the change of the Pe-number can have strong effect on the mass transport process, thus its effect must not be neglected. The model developed can be applied by any mathematical function of the variation of the mass transport parameters. (C) 2009 Elsevier B.V. All rights reserved.