Unintentional variations of fluid pressure within a hydraulic fracture will disturb the surrounding stress state, affect the stability of fracture propagation and complicate the fracture intersections during the process of hydraulic fracturing. However, little attention has been paid to the effect of nonuniform fluid pressure inside the hydraulic fracture. This paper presents a semianalytical solution for a Griffith crack nonuniformly pressurized by internal fluid in an impermeable elastic plane. The fluid pressure is hypothetically designated as a general polynomial with respect to the location of the fluid, such that the effect of an arbitrary form of fluid pressure distribution can be explored by polynomial fitting. The semianalytical solution is capable of being degenerated into constant pressure forms which confirms that the solution is an extension of classic constant pressure. In addition, the critical propagation conditions and stress distributions (e.g., σ xx ) under constant and nonuniform pressures are compared and discussed. The comparison results indicate that the effect of nonuniform fluid pressure accumulated by the number of polynomial terms increases the magnitude of stress (or displacement) but does not change its distribution. Subsequently, the semianalytical solution is validated by comparing the fracture intersection predicted by the semianalytical solution with the laboratory experimental observations and published predictions under constant fluid pressure. Good agreement with the experiments and sufficient advantages over previous predictions are observed. Finally, a sensitivity analysis of existing parameters in the semianalytical solution, including crack length, initial pressure, number of terms and number of subintervals, is conducted to evaluate their influence on surrounding stresses and critical propagation conditions, which further demonstrates the applicability and reliability of the presented semianalytical solution. The new solution enriches hydraulic fracturing theory by considering the nonuniform fluid pressure effect and provides important reference for fracture network design during hydraulic fracturing.

中文翻译：

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内流体非均匀加压格里菲斯裂纹的半解析解

在水力压裂过程中，水力裂缝内流体压力的无意变化会扰乱周围的应力状态，影响裂缝扩展的稳定性，并使裂缝交汇处复杂化。然而，很少有人关注水力压裂内部不均匀流体压力的影响。本文提出了一种非渗透弹性平面中由内部流体非均匀加压的格里菲斯裂纹的半解析解。假设流体压力被指定为相对于流体位置的一般多项式，从而可以通过多项式拟合来探索任意形式的流体压力分布的影响。半解析解能够退化为恒压形式，这证实了该解是经典恒压的延伸。此外，还比较和讨论了恒定和非均匀压力下的临界传播条件和应力分布（例如，σ xx ）。比较结果表明，多项式项数累积的非均匀流体压力的影响会增加应力（或位移）的大小，但不会改变其分布。随后，通过将半解析解预测的裂缝交叉点与实验室实验观察和恒定流体压力下已发表的预测进行比较，验证半解析解。观察到与实验的良好一致性和优于先前预测的足够优势。最后，对半解析解中现有参数进行敏感性分析，包括裂纹长度、初始压力、项数和子区间数，以评估它们对周围应力和临界传播条件的影响，进一步证明了该方法的适用性和可靠性。提出的半解析解。新方案通过考虑非均匀流体压力的影响，丰富了水力压裂理论，为水力压裂过程中的缝网设计提供了重要参考。进行项数和子区间数以评估它们对周围应力和临界传播条件的影响，这进一步证明了所提出的半解析解的适用性和可靠性。新方案通过考虑非均匀流体压力的影响，丰富了水力压裂理论，为水力压裂过程中的缝网设计提供了重要参考。进行项数和子区间数以评估它们对周围应力和临界传播条件的影响，这进一步证明了所提出的半解析解的适用性和可靠性。新方案通过考虑非均匀流体压力的影响，丰富了水力压裂理论，为水力压裂过程中的缝网设计提供了重要参考。