Depth of Investigation and Depletion Behavior in Unconventional Reservoirs Using Fast Marching Methods
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AbstractThe concept of depth of investigation is fundamental to well test analysis. Much of the 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 Greens function for heterogeneous reservoirs is difficult to obtain analytically (Deng and Horne 1993). In this paper, we introduce a novel approach for computing the depth of investigation and pressure response in spatially heterogeneous and fractured reservoirs.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 front 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 way to calculate drainage volume. From drainage volume calculations, we estimate a generalized pressure solution based on a geometric approximation of the drainage volume. A major advantage of our approach is that the Eikonal equation can be solved very efficiently using a class of front tracking methods called the Fast Marching Methods (FMM). Thus, transient pressure response can be obtained in multimillion cell geologic models in seconds without resorting to reservoir simulators.We first visualize depth of investigation and pressure solution for a homogeneous reservoir with multi-stage transverse fractures and identify flow regimes from pressure diagnostic plot. And then, we apply the technique to a heterogeneous reservoir to predict depth of investigation and pressure behavior. The computation is orders of magnitude faster than conventional numerical simulation and provides a foundation for future work in reservoir characterization and field development optimization.
