Development and Application of Fast Simulation Based on the PSS Pressure as a Spatial Coordinate

Recent studies have shown the utility of the Fast Marching Method and the Diffusive Time of Flight for the rapid simulation and analysis of Unconventional reservoirs, where the time scale for pressure transients are long and field developments are dominated by single well performance. We show that similar fast simulation and multi-well modeling approaches can be developed utilizing the PSS pressure as a spatial coordinate, providing an extension to both Conventional and Unconventional reservoir analysis. We reformulate the multi-dimensional multi-phase flow equations using the PSS pressure drop as a spatial coordinate. Properties are obtained by coarsening and upscaling a fine scale 3D reservoir model, and are then used to obtain fast single well simulation models. We also develop new 1D solutions to the Eikonal equation that are aligned with the PSS discretization, which better represent superposition and finite sized boundary effects than the original 3D Eikonal equation. These solutions allow the use of superposition to extend the single well results to multiple wells. The new solutions to the Eikonal equation more accurately represent multi-fracture interference for a horizontal MTFW well, the effects of strong heterogeneity, and finite reservoir extent than those obtained by the Fast Marching Method. The new methodologies are validated against a series of increasingly heterogeneous synthetic examples, with vertical and horizontal wells. We find that the results are systematically more accurate than those based upon the Diffusive Time of Flight, especially as the wells are placed closer to the reservoir boundary or as heterogeneity increases. The approach is applied to the Brugge benchmark study. We consider the history matching stage of the study and utilize the multi-well fast modeling approach to determine the rank quality of the 100+ static realizations provided in the benchmark dataset against historical data. The multi-well calculation uses superposition to obtain a direct calculation of the interaction of the rates and pressures of the wells without the need to explicitly solve flow equations within the reservoir model. The ranked realizations are then compared against full field simulation to demonstrate the significant reduction in simulation cost and the corresponding ability to explore the subsurface uncertainty more extensively. We demonstrate two completely new methods for rapid reservoir analysis, based upon the use of the PSS pressure as a spatial coordinate. The first approach demonstrates the utility of rapid single well flow simulation, with improved accuracy compared to the use of the Diffusive Time of Flight. We are also able to reformulate and solve the Eikonal equation in these coordinates, giving a rapid analytic method of transient flow analysis for both single and multi-well modeling.