From Streamlines to Fast Marching: Rapid Simulation and Performance Assessment of Shale Gas Reservoirs Using Diffusive Time of Flight as a Spatial Coordinate
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AbstractCurrent industry practice for characterization and assessment of unconventional reservoirs mostly utilizes empirical decline curve analysis or analytic rate and pressure transient analysis. High resolution numerical simulation with local PEBI grids and global corner point grids has also been used to examine complex non-planar fracture geometry, interaction between hydraulic and natural fractures and implications on the well performance. While the analytic tools require many simplified assumptions, numerical simulation techniques are computationally expensive and do not provide the more geometric understanding derived from the depth of investigation and drainage volume calculations.We propose a novel approach for rapid field-scale performance assessment of shale gas reservoirs. Our proposed approach is based on a high frequency asymptotic solution of the diffusivity equation in heterogeneous reservoirs and serves as a bridge between simplified analytical tools and complex numerical simulation. The high frequency solution leads to the Eikonal equation which is solved for a diffusive time of flight that governs the propagation of the pressure front in the reservoir. The Eikonal equation can be solved using the Fast Marching Method to determine the diffusive time of flight, which generalizes the concept of depth of investigation to heterogeneous and fractured reservoirs. It provides an efficient means to calculate drainage volume, pressure depletion and well performance and can be significantly faster than conventional numerical simulation. More importantly, in a manner analogous to streamline simulation, the diffusive time of flight can also be used as a spatial coordinate to reduce the 3-D diffusivity equation into a 1-D equation, leading to a comprehensive simulator for rapid performance prediction of shale gas reservoirs (Patent Pending, 2013). The speed and versatility of our proposed method makes it ideally suited for high resolution reservoir characterization through integration of static and dynamic data.The major advantages of our proposed approach are its simplicity, intuitive appeal and computational efficiency. We demonstrate the power and utility of our method using a field example that involves history matching, uncertainty analysis and performance assessment of a shale gas reservoir located in East Texas. A sensitivity study is first carried out to systematically identify the heavy hitters impacting the well performance. This is followed by a history matching and uncertainty analysis to identify the fracture parameters and the stimulated reservoir volume. A comparison of model predictions with the actual well performance shows that our approach is able to reliably predict the pressure depletion and rate decline.
