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.
Предметные области OECD FOS+WOS
- 1.05 НАУКИ О ЗЕМЛЕ И СМЕЖНЫЕ ЭКОЛОГИЧЕСКИЕ НАУКИ
- 2.01 СТРОИТЕЛЬСТВО И АРХИТЕКТУРА
- 1.05.KY ГЕОЛОГИЯ
- 2.07.IX ИНЖЕНЕРИЯ, ГЕОЛОГИЧЕСКАЯ