Reservoir simulation with imposed flux continuity conditions on heterogeneous and anisotropic media for general geometries, and the inclusion of hysteresis in forward modeling

Centre) have been advisors for me, and Norsk Hydro has provided the funding for the work. The thesis' main research part is the five papers A-E, and four of these have been published in conference proceedings and journals. The main focus of these papers is on issues related to reservoir simulation with improved reliability, and in particular discretization methods which should be valid for complex geometry. The governing equations for fluid flow in oil and gas reservoirs can be classified according to conventional theory of applied mathematics. This does not mean that all issues regarding reservoir simulation have been solved. Reliable reservoir simulation is a complicated field, and many issues are still not known to a satisfactory level. The oil and gas reservoirs are very complex physical media, and the level of heterogeneity seen in real sandstones can sometimes overwhelm the novice mathematician. Sandstones may have rapidly varying structure, porosity and permeability on a small scale. It can sometimes be hard to convince oneself that it is possible to model enormous amounts of fluids on a large scale when being faced with such complexity. Regardless of these complexities, applied reservoir simulation does study movement of fluids in complex media. The goal for scientists is to include as much information as possible in the models for both the fluid flow as well as the physical media themselves. At multi discipline research centres, geologists, geophysicists, physicists and mathematicians work together with this drive. Each group may work with their own 'small' problem, but all these pieces should eventually be woven together. For the most complex reservoirs one might never be able to perform accurate and detailed predictions of the future performance. But being able to see 'the main trends' is very useful, and this is really the goal even the scientist should aim for. The contributions in this thesis are mainly in the mathematical and numerical modelling of fluid flow in oil and gas reservoirs. For a person not directly involved, even the field of numerical modelling may seem like a very narrow issue to focus on, and merely a detail in the big picture of oil exploration and production. We, however argue that this is not the case. For future prediction of the performance of an oil reservoir, one has to build a mathematical model. This model should be reliable for a wide range of input, such as rock types, well …