Mathematics is an effective tool to study and model the world in which we live. Schematically, a model is the representation of a system or a process obtained by substituting to the real phenomenon another one in a more familiar field through simplifications, abstractions and analogies. In this book the authors introduce tools needed to carry out computer simulations of membrane reactors. These simulations serve as a complement to conventional experiments, enabling us to learn something new, something that cannot be found out in other ways. This book emphasises the utility of mathematical modelling as an effective tool for predicting/simulating various membrane reactors processes working under different scenarios. The book is divided in 11 chapters dealing with the approach to different membrane reactors. The separation properties of the membranes are introduced first and used in simple simulations in which no reaction takes place. Afterwards, different approaches for simulation of different membrane reactors (porous, dense, zeolitic, metallic and polymeric, photocatalytic, bio- membrane reactors) are introduced and used is base case studies. Finally, the last chapter briefly introduces new numerical techniques applied to membrane and membrane reactors with particular attention to some aspects of quantum mechanics.