The transient fields of fluid flow and concentrations of polluted maters carried in water inside a multiple layer water filter have been simulated by a new Lattice Boltzmann Method. This new Lattice Boltzmann Method speed up the simulation of flow and mass transfer through the complex geometries, which make the present simulations of real flow in water filter structures possible. The water is purified by this filter by passing multiple units of sandwich like porous medium structures. A new porous medium model is introduced to model different structures and materials inside the filter as multiple zone porous medium with different porosity and microscopic geometry. The new porous medium model which fit for the new LBM numerical method can be applied in irregular microscopic structures based on a geometry factor. This geometry factor is independent of porosity which represents how widely the solid is distributed in the fluid. Based on this model, the conjugate simulations of the complex flow and concentration distributions inside the water filter can be modeled by three lattice Boltzmann governing equations in a uniform simple form. The volume averaged drag forces vary with the porosity and structures for each layer of the sandwich structures. The transient flow and concentration governing equations have been solved by define dynamic relaxation time for both flow and concentration lattice Boltzmann equations. The semipermeable films are modeled as reactors, which track the large molecular maters as a mass sink. The simulations have been performed in wide range of the governing parameters obtained by scaling analysis to obtain a better design based on the flow characteristics. The transient streamlines, concentration of larger size molecular in water and attached on films of the sandwich solid structures have been presented to show the transient procedure of purification of the water.