Analysis of Buckley-Leverett Problem for Water Flooding in Oil Reservoir Rock: Analytical and Numerical Modeling

The Buckley-Leverett (BL) displacement theory gives a simplified formulation of governing equations controlling oil-water flow in an oil reservoir rock. Formulated under some specific hypothesis, the BL problem has the advantages of being analytically solvable for invading fluid saturation. This paper sheds the light on the Buckley-Leverett problem through analytical and numerical resolutions. An overview on basic mathematical formulations was presented. Then a 1D example was detailed in order to plot the saturation profile of the wetting phase by combining the analytical solution of the front equation with the Welge construction method. Additionally a COMSOL Multiphysics model was built and both numerical and analytical results were compared. Furthermore, the numerical model was extended for a 2D example and obtained wetting saturation profiles plotted along the length of the domain were compared with previous literature outcomes. Two different modules of COMSOL Multiphysics were used to build numerical models. The 1D model reposes on the coefficient form PDE module that permits writing governing equations under matrix form and then solving for the unknown saturation. For the 2D model the capability of COMSOL Multiphysics in coupling different modules has served to implement the model through using both modules viz. phase transport in porous media and Darcy’s law.