In this book, the author presents a detailed complex mathematical and computational model for the simulation of fluid flow in reservoirs. The research was conducted in collaboration with Dr. John M. Tyler of LSU and was funded by the United States Department of Energy. The results were published in a Ph.D. dissertation and at several international conferences. Reservoir simulation is used by oil and gas companies in the development of new fields and in developed fields where production forecasts are needed to help make investment decisions. The simulation is also used to predict the available reserves of oil or gas underground and to identify opportunities to increase oil production in heavy oil deposits.