In this paper, by adopting a "half-channel" model, a mass exchange process (presented in the therapy of hemodialysis) between two opposite running flows is numerically simulated. The flows are confined inside channels and separated by intercalary porous membranes. In the simulation, two types of flows, channel flow and ultra-filtration flow, are physically described, respectively, by Navier-Stokes equations and Kedem-Katchalsky (K-K) equations. By further adopting "SimpleR" algorithm, the velocity fields inside the channels are determined, meanwhile, solute mass distributions are predicted by concentration equation. The solid computation in this paper perfectly explored the process of hemodialysis, its results: (1) displayed the flow and solute distribution patterns inside channels; (2) described the ultra-filtration profiles along the surface of the porous membrane; and (3) disclosed an existent nano-scale reverse osmosis problem. (C) 2010 Elsevier Ltd. All rights reserved.