Fluid injection in porous rock occurs in a variety of hydrogeological operations including wastewater disposal, CO₂ sequestration, enhanced oil recovery, and geothermal energy extraction. Influx of fluid into the host rock is usually accompanied by induced permeability enhancement due to increased pore fluid pressure and consequent dilation of the pore volume. The effect would, in turn, enhance the well injectivity index. This paper presents an analytical solution to the nonlinear problem of underground fluid injection in a disk‐shaped reservoir while accounting for the induced permeability enhancement. The host rock permeability is considered to depend on the rock total stress and pore fluid pressure. For this purpose, the rock stress is formulated as a nonlocal function of disturbances in the pore fluid pressure using the fundamental solution for a nucleus of strain in an elastic half space. Alongside, the nonlinear fluid transport equation that incorporates stress‐sensitive rock permeability is analytically solved using a perturbation technique. The good match with finite difference solution to the same problem verifies the validity and accuracy of the perturbation solution. Parametric study on a test case problem is conducted to examine the influence of different parameters on well injectivity. Findings reveal the higher vulnerability of shallower host reservoirs to stress‐induced permeability variations. The effect of rock poroelastic properties on fluid transport process is discussed.

中文翻译：

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应变引起的渗透率变化的地下岩石非线性注入的多孔弹性解

多孔岩中的流体注入发生在各种水文地质作业中，包括废水处理，CO ₂封存，提高石油采收率和地热能提取。由于孔隙流体压力的增加以及孔隙体积的扩大，通常会导致流体涌入基质岩中，从而引起渗透率的提高。反过来，该效果将提高井注入指数。本文提出了一种圆盘状油藏地下流体非线性问题的解析解，同时考虑了诱导渗透率的提高。主岩渗透率被认为取决于岩石的总应力和孔隙流体压力。为此，使用弹性半空间中的应变核的基本解，将岩石应力公式化为孔隙流体压力扰动的非局部函数。旁边 使用摄动技术对包含应力敏感岩石渗透率的非线性流体传输方程进行了解析求解。与有限差分法对同一问题的良好匹配证明了摄动解的有效性和准确性。对测试用例问题进行了参数研究，以检验不同参数对油井注入率的影响。研究结果表明，较浅的宿主油藏更容易受到应力引起的渗透率变化的影响。讨论了岩石孔隙弹性性质对流体输运过程的影响。对测试用例问题进行了参数研究，以检验不同参数对油井注入率的影响。研究结果表明，较浅的宿主油藏更容易受到应力引起的渗透率变化的影响。讨论了岩石孔隙弹性性质对流体输运过程的影响。对测试用例问题进行了参数研究，以检验不同参数对油井注入率的影响。研究结果表明，较浅的宿主油藏更容易受到应力引起的渗透率变化的影响。讨论了岩石孔隙弹性性质对流体输运过程的影响。