The principle purpose of this work is to formulate an accurate mathematical model to evaluate the transient pressure behavior of a well intercepted by a partially penetrating vertical fracture (PPVF) with non-Darcy flow effect. Fracture conductivity is taken into account by coupling the three-dimensional flow in reservoir and the two-dimensional flow within fracture; the Barree-Conway model is incorporated into the model to analyze non-Darcy flow behavior in fracture, which leads to the nonlinearity of the governing equations. A high-effective iterative algorithm using a combined technique of fracture-panel discretization and dimension transform is developed to render the nonlinear equations amenable to analytical linear treatment. On the basis of the solutions, the pressure response and its derivative type curves were generated to identify the evolution of flow regimes with time. Furthermore, the influences of fracture conductivity, penetration ratio, and non-Darcy characteristic parameters on pressure response are investigated. The results show that PPVF exhibits five typical flow regimes, and analytical solutions for each flow regime are similar to that for a fully penetrating vertical fracture (FPVF) that can be correlated with the penetration ratio and apparent conductivity. The non-Darcy flow effect is found to have more significant effect on the low and moderate conductivity, especially in early-stage flow regimes. When the penetration ratio is smaller than 0.5, the pressure behavior exhibit a more remarkable variation with penetration ratio. This study provides a better insight into understanding the influence of non-Darcy flow on flow regime identification.

中文翻译：

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非达西流效应部分贯穿裂缝与直井相交的瞬态压力求解修正

这项工作的主要目的是建立一个准确的数学模型来评估被具有非达西流效应的部分穿透垂直裂缝 (PPVF) 截获的井的瞬态压力行为。将储层三维流动与裂缝内二维流动耦合，考虑裂缝导流能力；Barree-Conway 模型被纳入模型来分析裂缝中的非达西流动行为，这导致控制方程的非线性。开发了一种高效的迭代算法，该算法使用裂缝面板离散化和维数变换的组合技术，使非线性方程易于解析线性处理。在解决方案的基础上，生成压力响应及其衍生类型曲线以识别流态随时间的演变。此外，研究了裂缝导流能力、穿透率和非达西特征参数对压力响应的影响。结果表明，PPVF 表现出五种典型的流态，每个流态的解析解类似于完全穿透垂直裂缝 (FPVF) 的解析解，可以与穿透比和表观传导率相关联。发现非达西流动效应对低和中等电导率具有更显着的影响，特别是在早期流动状态中。当针入度小于 0.5 时，压力行为随针入度变化更显着。