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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.

This paper presents an analytic self-similar solution describing an equilibrium of a planar semi-infinite hydraulic fracture in a poroelastic medium. The equilibrium of the fracture is sustained by a balance between the pressure of fluid within the fracture and the confining stress due to elasticity of nearby poroelastic material satisfying the Biot model assumptions. Propagation of fluid in the fracture, leakoff through the fracture’s walls and filtration in the poroelastic medium towards the fracture’s tip form a dipole-type pattern of flow. The solution is used for the verification of a numerical algorithm developed earlier for the pressure transient analysis in water injection wells.

The paper addresses the problem of modeling a fracture propagation in linear elastic porous media driven by injection of non-Newtonian power-law fluid. The model involves the lubrication theory equation expressing the mass conservation of fluid and a nonlocal singular integral relation for the fracture aperture as a functional of the fluid pressure. We assume only the viscosity-dominated case in which the fracture toughness is neglected. This allows considering the fracture as an opened part of a preexisting closed fracture of larger length. The numerical method consists in solving equations of the model over the whole length of the preexisting fracture without distinguishing the tip region of the opened part. The problem is solved via the finite element method. The weak formulation of the solution allows pressure singularity with the required asymptotics near the fracture tip. Comparison of the numerical and the exact self-similar solutions in the case of a constant flow rate, zero fluid leakoff, and zero fracture toughness reveals the accuracy of the approximate solution to at least O(h1/2), where h is the maximal linear size of the grid cells. As an illustration, we also demonstrate the numerical experiments with periodic fluid injection and variable fluid efficiency.

In the paper a model for description of a hydraulic fracture propagation in inhomogeneous poroelastic medium is proposed. Among advantages of the presented numerical algorithm, there are incorporation of the near-tip analysis into the general computational scheme, account for the rock failure criterion on the base of the cohesive zone model, possibility for analysis of fracture propagation in inhomogeneous reservoirs. The numerical convergence of the algorithm is verified and the agreement of our numerical results with known solutions is established. The influence of the inhomogeneity of the reservoir permeability to the fracture time evolution is also demonstrated.