Semi-Elimination Methodology for Simulating High Flow Features in a Reservoir

Despite the rapid rise of computing power and advances in computational techniques in past decades, it is still challenging in reservoir simulation to model complex and detailed features that are represented by small cells with large permeability values, for example, fractures, multi-segment wells, etc. While those features may carry a large amount of flow and thus have a significant impact on the performance prediction, the combination of small volume and large permeability unfortunately leads to well-known time stepping and convergence difficulties during Newton iteration. We address this issue of high flow through small cells by developing a new semi-elimination computational technique. At the beginning of simulation, we construct a set of pressure basis which is a mapping from pressures at surrounding cells in the bulk of reservoir to pressures at those small cells. Next, we start the time-stepping scheme. For each time step or iteration within a time step, small cells are first employed to provide an accurate computation of flow rates and derivatives using upstream weighting and a flow partitioning scheme. Afterwards, small cells are eliminated and a linear system of equations is assembled and solved involving only bulk cells. This semi-elimination technique allows us to fundamentally avoid the drawbacks caused by including small cells in the global system of equations, while capturing their effect on the flow of hydrocarbon in the reservoir. One of the advantages of the proposed techniques over other existing methods is that it is fully implicit and preserves upstream weighting and compositions of the flow field even after small cells are eliminated, which enhances numerical stability and accuracy of simulation results. Application of this technique to several synthetic and field models demonstrates significant performance and accuracy improvement over standard approaches. This method thus offers a practical way to model complex and dynamic flow behaviors in important features without incurring penalties in speed and robustness of the simulation.