A Non-Dimensional Lattice Boltzmann Method (NDLBM) based on a multiple zone porous medium model is extended to simulate fluid flow and mass transfer inside multiple layer water filters. Comparative studies based on two basic design models (permeable and semipermeable membrane model) are carried out to investigate the flow and mass transport inside cylindrical multiple layer water filters. In the permeable membrane design model, the water is purified by passing multiple units with sandwich like structures. In the semipermeable membrane model, macromolecules such as suspended particulates cannot pass the semipermeable membranes, while micromolecules can pass the porous semipermeable membranes. The quasi-steady state velocity distributions are obtained. The transient concentrations of suspended particulates captured by porous solid structures and left in water are compared for the two design models. Different dimensionless governing parameters and the porosities for the membranes are studied to understand the underlying mechanism of the purification procedure and to compare performance of the two models.