The numerical prediction of mass transfer rates in the mass boundary layer over a membrane separation requires the use of a very dense grid. In this work, a simple logarithmic variable transformation applied to the solute transport equation improves the well-known finite difference scheme, allowing the use of a larger grid spacing without loss of accuracy. This method is applied to solve laminar flow and solute transport equations in a parallel plate device with permeable walls. The concentration profiles along the membrane surface and in the mass boundary layer are predicted. For high permeate velocity, the grid spacing can increase four times without loss of accuracy. The method applied has several advantages comparatively to the optimized grid spacing method that can be used in alternative.