Depth of Investigation and Depletion Behavior in Unconventional Reservoirs Using Fast Marching Methods (SPE 154532)

The concept of depth of investigation is fundamental to well test analysis. Much of current well test analysis relies on solutions based on homogeneous or layered reservoirs. Well test analysis in spatially heterogeneous reservoirs is complicated by the fact that GreenC"s function for heterogeneous reservoirs is difficult to obtain analytically. In this paper, we introduce a novel approach for computing the depth of investigation and pressure response in spatially heterogeneous and fractured reservoirs based on a semi-analytic construction of the GreenC"s function. In our approach, we first present an asymptotic solution of the diffusion equation in heterogeneous reservoirs. Considering terms of highest frequencies in the solution, we obtain two equations: the Eikonal equation that governs the propagation of a pressure C"frontC" and the transport equation that describes the pressure amplitude as a function of space and time. The Eikonal equation generalizes the depth of investigation for heterogeneous reservoirs and provides a convenient mechanism to construct the GreenC"s function. A major advantage of our approach is that the Eikonal equation can be solved very efficiently using a class of front tracking method called the Fast Marching Method. Thus, transient pressure response can be obtained in multimillion cell geologic models in seconds without resorting to reservoir simulators. We validate our approach by comparison with analytic solutions for homogeneous and composite reservoirs. We apply the technique using a high resolution full field geologic model of a tight gas reservoir from the Rocky Mountain region to predict the depth of investigation and pressure depletion. The computation is orders of magnitude faster than conventional simulation and provides a foundation for future work in reservoir characterization and field development optimization.