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Time-Dependent Shape Factors for Uniform and Non-Uniform Pressure Boundary Conditions

机译：均匀和非均匀压力边界条件的时间相关形状因子

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摘要

Matrix-fracture transfer functions are the backbone of any dual-porosity or dual-permeability formulation. The chief feature within them is the accurate definition of shape factors. To date, there is no completely accepted formulation of a matrix-fracture transfer function. Many formulations of shape factors for instantly-filled fractures with uniform pressure distribution have been presented and used; however, they differ by up to five times in magnitude. Based on a recently presented transfer function, time-dependent shape factors for water imbibing from fracture to matrix under pressure driven flow are proposed. Also new matrix-fracture transfer pressure-based shape factors for instantly-filled fractures with non-uniform pressure distribution are presented in this article. These are the boundary conditions for a case for porous media with clusters of parallel and disconnected fractures, for instance. These new pressure-based shape factors were obtained by solving the pressure diffusivity equation for a single phase using non-uniform boundary conditions. This leads to time-dependent shape factors because of the transient part of the solution for pressure. However, approximating the solution with an exponential function, one obtains constant shape factors that can be easily implemented in current dual-porosity reservoir simulators. The approximate shape factors provide good results for systems where the transient behavior of pressure is short (a case commonly encountered in fractured reservoirs).
机译：基质裂缝传递函数是任何双孔隙率或双渗透率配方的基础。其中的主要特征是形状因数的准确定义。迄今为止，还没有完全接受的矩阵-断裂传递函数公式。已经提出并使用了许多具有均匀压力分布的即时填充裂缝的形状因子公式；但是，它们之间的差异最多可达五倍。基于最近提出的传递函数，提出了随时间变化的形状因数，用于水在压力驱动的流动下从裂缝吸入基质。本文还针对压力分布不均匀的即时填充裂缝，提出了基于基质裂缝传递压力的新形状因子。例如，对于具有平行和不连续裂缝簇的多孔介质，这些是边界条件。这些新的基于压力的形状因子是通过使用非均匀边界条件求解单相的压力扩散系数方程而获得的。由于压力解决方案的过渡部分，这导致了随时间变化的形状因数。然而，用指数函数近似解，可以得到恒定的形状因子，可以在当前的双孔隙度油藏模拟器中轻松实现。近似形状因数为短时压力瞬变行为的系统（在裂缝性储层中经常遇到的情况）提供了良好的结果。

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