Computing sand production under foamy oil flow in porous media via least-squares finite elements

Abstract

Tiny gas bubbles together with sand grains are produced whenever a pressure drawdown is induced in an oil well. The resulting foamy oil flow and sand production seem to enhance the production of oil under certain conditions and environments such as the heavy oil solution gas drive reservoirs in Western Canada and Venezuela. The purpose of this paper is to propose a mathematical model in which gas exsolution and gas bubble dispersions together with sand production are described in a multiphasic porous medium. Gas bubble formation and dispersion are described in a macroscopic manner through equations of states and relaxation, whereas sand production is viewed as an erosional hydrodynamics problem with geomechanical considerations. The formulation of the proposed model leads to a set of highly non-linear governing equations with primary field unknowns such as reservoir fluid pressure, volume fraction of dispersed gas bubbles, concentration of fluidized solid, porosity and solid displacement. The numerical solutions of these equations are challenging and require special treatment such as least-squares finite element techniques in order to ensure stability and accuracy in results. Numerical examples in which foamy oil flow occurs with concomitant sand production and failure are presented to demonstrate the performance of the proposed model.