Models for water flooding, imbibition and coupled fracture-matrix flow in a fractured reservoir

Abstract

The study of reservoir performance during waterflooding is important to reservoir engineers. Numerous analytical, semi-analytical and numerical flow models with different assumptions have been submitted over the years, aiming to model and describe reservoir behavior and flow dynamics during an oil/water displacement process. Studying the effect that controlling forces such as viscous, gravity and capillary forces have on water saturation profiles, breakthrough time and oil recovery are important features of these models. In this thesis a derivation and an analytical solution procedure of the Buckley-Leverett equation is presented. A Buckley-Leverett model that includes capillary pressure is derived and solved numerically. The effect capillary forces have on saturation profiles, breakthrough time and oil recovery will be illustrated for different capillary pressures correlations and by varying a dimensionless number consisting of controlling flow parameters such as injection flow rate, fluid viscosity, length of porous media and capillary pressure. Also a derivation and numerical solution of a model for coupled fracture-matrix flow in fractured reservoir will be presented. Modified Buckley-Leverett theory including a time dependent transfer term that takes into account fluid exchange rate between matrix and fracture is used to simulate this waterflooding process. A demonstration of fracture, matrix and total oil recovery will be illustrated for a given case. Additionally, some effects that strong versus weak spontaneous imbibition have on fracture saturation profiles, breakthrough time and oil recovery will be investigated.