In this work we propose a method for mini-frac analysis via the direct numerical modeling for permeability and closure stress determination. The idea is to adjust the model parameters to match the simulated and field pressure curves by the virtue of the optimization algorithm to automatize the routine. To this end, the Planar 3D hydraulic fracturing model is improved to take into account the wellbore storage, fracture initiation and pumping through a finite perforation interval. The reservoir mechanical behavior is based on Biot’s equations naturally coupled with the mass conservation law and force balance in the fracture and wellbore. This model is capable to describe all the pressure curve features from the fracture initiation up to the after closure filtration. The optimization workflow is based on Levenberg–Marquardt algorithm with Jacobi matrix calculated via a direct differentiation method. The numerical stability and performance of the inverse problem solution is verified. The pressure curve sensitivity analysis is conducted and the impact of the parameters’ uncertainties on the pressure change is calculated. The proposed method is applied to a field case and compared with classical mini-frac methods. We demonstrate that the wellbore storage impact governs the pressure increase during the fracture initiation and prevents the steep pressure decline after closure. We also show that the shortening of the perforation length generates additional pressure support at the end of and after the fracture closure. The recovered permeability and closure stress appears to be stable in presence of uncertainties in Young’s modulus and Biot’s coefficient.

在这项工作中，我们提出了一种通过渗透率和闭合应力确定的直接数值模拟进行微型压裂分析的方法。其思路是通过优化算法调整模型参数以匹配模拟和现场压力曲线，以实现例程的自动化。为此，Planar 3D 水力压裂模型进行了改进，以考虑井眼储存、裂缝起始和通过有限射孔间隔的泵送。储层力学行为基于 Biot 方程，自然结合质量守恒定律和裂缝和井眼中的力平衡。该模型能够描述从裂缝开始到闭合后过滤的所有压力曲线特征。优化工作流程基于 Levenberg-Marquardt 算法，Jacobi 矩阵通过直接微分方法计算。验证了逆问题解的数值稳定性和性能。进行压力曲线敏感性分析，计算参数不确定性对压力变化的影响。将所提出的方法应用于现场案例并与经典的微型压裂方法进行了比较。我们证明，井筒储存影响控制着裂缝开始期间的压力增加，并防止关闭后压力急剧下降。我们还表明，穿孔长度的缩短会在裂缝闭合结束时和之后产生额外的压力支持。