Single-phase flow in layered porous media with applications to reservoir simulation

In this thesis we explore the use of finite differences in solving second order differential equations. Both initial value problems and boundary value problems are investigated. Numerical schemes for both second order and fourth order methods are derived from first principles. A detailed order analysis is performed to validate the numerical approximations.;We also consider the flow of fluid through porous media with constant and variable permeability. We show how to solve a single phase pressure equation using SINTEF MRST software. We successfully compare the results obtained from the software with the code we developed for solving differential equations.