On modeling hydraulic fracture in proper variables: Stiffness, accuracy, sensitivity

Abstract

The problem of hydraulic fracture propagation is considered by using its recently suggested modified formulation in terms of the particle velocity, the opening in the proper degree, appropriate spatial coordinates and e-regularization. We show that the formulation may serve for significant increasing the efficiency of numerical tracing the fracture propagation. Its advantages are illustrated by re-visiting the Nordgren problem. It is shown that the modified formulation facilitates (i) possibility to have various stiffness of differential equations resulting after spatial discretization, (ii) obtaining highly accurate and stable numerical results with moderate computational effort, and (iii) sensitivity analysis. The exposition is extensively illustrated by numerical examples.?Peer reviewe

Universal hydrofracturing algorithm for shear-thinning fluids: Particle velocity based simulation

“…Combining (41) and (33) with (46), after some algebra and integration, gives the following relation, which is valid for any real κ:…”

“…Such an approach for the 1D PKN model has already been presented in [32,46,68] while its generalization, introducing explicit relations between crack tip asymptotics and crack propagation speed for all classical 1D models, can be found in [69]. It was shown that, when properly combined with other numerical devices, the algorithm represents an accurate and universal tool, which allows one to circumvent the main problems found in classical approaches used to establish the crack tip position.…”

“…Some of the aforementioned elements were already presented in [32,46,68], where one can find a broad analysis on the application of proper independent and dependent variables and regularization techniques. The theoretical background of the mechanism of fracture front tracing together with a detailed description of the techniques of its application was given in [69].…”

Temperature effect on low permeability porous media filled with water at high pressures

“…The present study is not concerned with the modelling of the fracture propagation (see, for instance [7][8][9][10][11]) or with the fluid flow (e.g. [12][13][14][15][16][17][18][19]).…”

Simulating the Hele-Shaw flow in the presence of various obstacles and moving particles

“…This type of problem is most notably encountered in hydraulic fracturing technologies, with respect to the slurry flow inside the fracture (see, e.g., [6,7] and references therein).…”