This project concerns the effects of membrane fouling on membrane filtration operations. The most significant modes of fouling (pore constriction, pore blocking, and cake formation) are considered, and two mathematical models for these effects are considered. A combined model is presented, along with simple numerical simulation results for a test case.. This project will focus on the study of mathematical and numerical methods to describe filtration processes through membranes for industrial applications such as in food or pharmaceutical industry.The aim of the project is to propose suitable models to describe correctly the physical processes taking place through the membranes and to perform simulations of simple significant test cases using finite elements