Modelling sand production with foamy oil: A mechanistic and numerical approach

The motivation for studying sand production and foamy oil flow stems from the fact that a number of heavy oil solution gas drive reservoirs in Western Canada and Venezuela have consistently shown anomalously good primary performance, high oil production rates, and high primary recovery factors. We thus propose a mathematical model to investigate the intertwined behaviour between foamy oil flow and sand production explicitly. A new sand production model with sand failure (dilation) and foamy oil flow was developed as a geomechanical/hydrodynamical/erosional problem. Gas bubble exsolution in the foamy oil flow formulation is described in a macroscopic manner through equations of states and relaxation equations. The effect of porosity change due to sand failure and sand production is also included.; The formulation of the proposed model leads to a set of highly non-linear governing equations. The numerical solutions of these equations are challenging and require special treatment. A selective application of numerical schemes was developed to solve each governing equation based on its form and the underlying physics. Governing equations containing a second order differential operator were solved using Galerkin's method, while those containing a first order differential operator (first order hyperbolic type) were solved via a least-squares finite element technique. As such numerical oscillations that are notorious to the solution of hyperbolic type of equations are eliminated.; The proposed foamy oil model was verified against available foamy oil experimental data. It is found that computed cumulative oil production and pressure evolutions can be matched very well with experimental results. In particular, the phenomenon of "pressure rebound" was captured. The proposed sand production model was also validated as both sand production rate and sand failure zone agreed well with experimental data. Numerical examples in which foamy oil flow occurs with concomitant sand production and failure are further presented to demonstrate the viability of the proposed model in a practical case. The numerical results are very consistent with the physics of gas bubble exsolution and sand production as the reservoir fluid pressure is depleted. It was found that this pressure maintenance helps towards improving oil production significantly through development of high pressure gradients in the reservoir during pressure drawdown. Increasing the depletion rate can improve both foamy oil flow and sand production contributions to the enhancement of oil production. (Abstract shortened by UMI.)...