Fast-Marching Methods for Complex Grids and Anisotropic Permeabilities: Application to Unconventional Reservoirs

摘要

Unconventional reservoirs are characterized by sufficiently low permeabilities so that the pressure depletion from a producing well may not propagate far from the well during the life of a development. This is in contrast to conventional plays where the pressure transients may probe the entire reservoir in weeks to months. The concept of depth of investigation and its application to unconventional reservoirs provide the understanding necessary to describe and optimize the interaction between complex multi-stage fractured wells, reservoir heterogeneity, drainage volumes, pressure depletion, well rates, and the estimated ultimate recovery. Previous studies have performed unconventional reservoir analysis using more conventional reservoir simulation techniques. High resolution local PEBI grids and global corner point grids have been used to represent complex fracture geometry and conductivity and estimate subsequent well performance. However, these techniques do not provide the more geometric understanding provided by the depth of investigation and drainage volumes. The application of the depth of investigation to heterogeneous reservoirs can be obtained from an asymptotic expansion of the diffusivity equation leading to the Eikonal equation which describes the propagation of the pressure front. This equation is solved using a Fast Marching Method to calculate a diffusive time of flight at every location within the domain. The diffusive time of flight is directly related to pressure front propagation. Unlike in a reservoir simulator, this frontal propagation is determined in a single non-iterative calculation, which is extremely fast. Once the pressure fronts are determined spatially, we may apply a pseudo-steady state pressure approximation within the moving front to determine pressure depletion and well rates. In the current study, we extend the Fast Marching Method for solution of the Eikonal equation to complex simulation grids including corner point and unstructured grids. This allows the rapid approximation of reservoir simulation results without the need for flow simulation, and also provides the time-evolution of the well drainage volume for visualization. Understanding the drainage volume alone is useful for well spacing and multi-stage fracture spacing optimization. Additional potential applications include well trajectory and hydraulic fracture location optimization, reservoir model screening and ranking, matrix/fracture parameter estimation, uncertainty analysis and production data integration.