Hydraulic fracturing (HF) is a widely employed technique for determining in situ stress. A critical aspect of this technique is the interpretation of the shut-in pressure to ascertain the magnitude of the minimum principal stress. Existing interpretation methods primarily focus on the pressure decay rate or its simple transformation, and an effective physical model has not yet been established to quantitatively characterize the crack closure process, resulting in a certain degree of ambiguity in determining the shut-in pressure. This paper introduces a new approach of determining shut-in pressure based on the Total System Stiffness (TSS). The objective of the TSS method is to better account for fracture responses by decomposing the pressure decay rate and estimating fluid leakage volume, thereby converting the pressure decay curve into a total system stiffness curve. The performance of this method is rigorously evaluated through comparisons with existing methods, utilizing several shut-in curves obtained from field HF experiments. The results demonstrate that the TSS method can serve as a feasible alternative for determining shut-in pressure. The variations of total system stiffness following shut-in can be divided into three main stages, the characteristics of which may be used to identify the upper and lower bounds of shut-in pressure. The primary advantage of the proposed TSS method is that it provides clear physical interpretations for both the beginning and end of the fracture closure process. Consequently, shut-in pressure determined by this method exhibits reduced sensitivity to time window selection compared with conventional approaches. Moreover, the TSS method relies solely on the pressure data, without any fitting or extrapolation. The TSS method is anticipated to have a wide range of applications for the analysis of in-situ stress associated with hydraulic fracturing.

中文翻译：

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在水力压裂应力测量中确定关进压力的总系统刚度方法

水力压裂 （HF） 是一种广泛采用的确定原位应力的技术。该技术的一个关键方面是解释关合压力，以确定最小主应力的大小。现有的解释方法主要集中在压力衰减速率或其简单变换上，尚未建立有效的物理模型来定量表征裂纹闭合过程，导致在确定关合压力时存在一定程度的模糊性。本文介绍了一种基于总系统刚度 （TSS） 确定关进压力的新方法。TSS 方法的目标是通过分解压力衰减速率和估计流体泄漏量来更好地解释断裂响应，从而将压力衰减曲线转换为总系统刚度曲线。通过与现有方法的比较，利用从现场 HF 实验中获得的几条关进曲线，严格评估该方法的性能。结果表明，TSS 方法可以作为确定关合压力的可行替代方案。关切后总系统刚度的变化可以分为三个主要阶段，其特性可用于确定关切压力的上限和下限。所提出的 TSS 方法的主要优点是它为裂缝闭合过程的开始和结束提供了清晰的物理解释。因此，与传统方法相比，通过该方法测定的关内压力对时间窗口选择的敏感性降低。此外，TSS 方法仅依赖于压力数据，没有任何拟合或外推。 预计 TSS 方法将广泛用于分析与水力压裂相关的原位应力。