| dc.description.abstract | The work in this thesis focuses equally on two main topics. The first of these subjects deals with development of criteria for monotonicity of con- trol volume methods. These methods are important and frequently used for solving the pressure equation arising in porous media flow. First we consider homogeneous parallelogram grids, and subsequently general logical Cartesian grids in hetrogeneous media. This subject is concluded by the development of a new class of Multi Point Flux Approximation methods, motivated by the monotonicity results obtained. The second topic of this thesis is the development of analytical and semi- analytical solutions to the problem of leakage through abandoned wells. More specifically, we look at a set of aquifers, separated by impermeable layers (aquicludes), where injection of water or CO2 takes place in some or all the aquifers. The aquifers and aquicludes are frequently penetrated by aban- doned wells from oil exploration, and our problem consists of finding solutions to flow and leakage through these wells. The goal is to obtain expressions for leakage rates that may be evaluated quickly enough such that Monte Carlo realizations over statistical distributions of properties for abandoned wells can be performed. | en_US |
