The Fast Marching Method (FMM) has been applied to characterize the transient drainage volume and to simulate flow as a function of time in porous media using the concept of the “diffusive time of flight” (DTOF). The DTOF (τ) provides a spatial coordinate which reduces the three dimensional pressure diffusivity equation to an equivalent one dimensional formulation. It is obtained from the solution to the Eikonal equation via the FMM. Previous applications of this approach have solved the flow equations numerically or by using an analytic asymptotic approximation. Both solution approaches rely upon three characteristics. (1) Accurate solution for the DTOF irrespective of the degree of heterogeneity within a reservoir model. (2) The approximation of the three dimensional pressure solution in terms of the τ coordinate. (3) Accurate representation and discretization of the drainage volume, on which the asymptotic and numerical flow simulations are based. The second and third of these characteristics are specific to reservoir engineering applications, and provide the focus of this study. Analysis of the drainage volume shows that the near well region requires special treatment, leading to a composite discretization for the drainage volume. This discretization has a direct impact upon the calculation of the well test pressure derivative when the asymptotic approximation is used for pressure transient interpretation. For flow simulation, the discretization directly impacts the calculation of the well index and the intercell transmissibility computed in the τ coordinate, and places additional constraints on the discretization of the drainage volume. These new results are validated by comparison with a commercial finite difference flow simulator, and are shown to be more accurate than earlier computational approaches.

快速行进法 (FMM) 已用于表征瞬态排水量，并使用“扩散飞行时间”(DTOF) 的概念模拟多孔介质中随时间变化的流动。DTOF ( τ ) 提供了一个空间坐标，它将三维压力扩散方程简化为等效的一维公式。它是通过 FMM 从 Eikonal 方程的解中获得的。这种方法的先前应用已经以数值方式或通过使用解析渐近近似来求解流动方程。两种解决方法都依赖于三个特征。(1) DTOF 的准确解，与储层模型内的非均质性程度无关。(2) 三维压力解的近似τ坐标。(3) 排水量的精确表示和离散化，这是渐近和数值流动模拟的基础。这些特征中的第二个和第三个是特定于油藏工程应用的，并且是本研究的重点。对排水量的分析表明，近井区域需要特殊处理，导致对排水量进行复合离散化。当渐近近似用于压力瞬态解释时，这种离散化对试井压力导数的计算有直接影响。对于流动模拟，离散化直接影响井指数的计算和τ 中计算的单元间传输率协调，并对排水量的离散化施加额外的约束。这些新结果通过与商业有限差分流量模拟器的比较得到验证，并且比早期的计算方法更准确。