Numerical Simulation of Radial Non-Newtonian Foam Flow in a Reservoir

Abstract

Non-Newtonian foam flow in a reservoir can be modeled numerically by discretization of the corresponding analytical formulas. The injection of foam is compared to the injection of water by comparing the injection pressures, which is represented as a dimensionless pressure rise at the injection well. The model first applies the forward-difference method to compute the changes in water saturation over space and time as the foam is injected. These changes in water saturation are related, via Darcy’s Law, to changes in dimensionless pressure. The non-Newtonian foam behavior is implemented in the model by making the gas relative permeability a function of position in radial flow, based on the exponent defined for a power law fluid.
The validity of the model is assessed by a comparison with an analytical model using the method of characteristics to simulate Newtonian foam flow. This model was created by A.H. Al Ayesh. From this comparison, it follows that the numerical model converges to a correct solution for sufficient fine discretizations. Finer discretizations do however introduce drawbacks, such as long computation times and high computer-memory requirements. Another drawback of the numerical model is the inevitable error that is introduced by a numerical artifact in the computation of the total relative mobility in each grid block at the front as foam advances. This error can only be reduced by even-finer discretizations.
The validity of the model for non-Newtonian foam flow simulations is not assessed directly in this thesis. But the model is expected to have similar or coarser grid-refinement criteria for shear-thinning foam flow, and finer or similar grid refinement criteria for shear-thickening foam flow.