Numerical Analysis of Water Coning for the Recovery of Petroleum: an Enriched BEM Approach

Abstract

The scope of this thesis focuses on enrichment techniques applied to the water coning problem, a numerical simulation solved with the enriched Boundary Element Method (BEM) for potential problems. The problem consists on a time dependent two-zone model with a pumping sink causing the extraction of hydrocarbons. A time dependent two-zone model implicates a moving interface between the zones and since a numerical simulation is performed, a refined discretization of the interface is necessary thus a high amount of Degrees of Freedom (DoF) are needed for its solution. Enrichment schemes reduce the numbers of DoF on the interface, in theory optimising computer effort. The Boundary Integral Equation (BIE) solved for this problem.
In this work, the physical aspects of the model and the enrichment scheme are described in order to perform tests that would result in the best enrichment function possible that captures reliable results regardless of the conditions of the model. The enrichment scheme is compared to the classical (unenriched) BEM that is used as a reference solution. The change of scheme results in achieving the same accuracy with 8% of the original number of equations. The results allow us to predict the computational improvements that might be achieved when this technique is applied to 3D or the conditions of the model change. These results suggest that simulations would be over 20,000 times faster without loss in accuracy. This presents industry with a strategy to prevent water to be drawn into an oil well, eliminating an expensive oil-water separation process.