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

Details On modeling hydraulic fracture in proper variables: stiffness, accuracy, sensitivity On modeling hydraulic fracture in proper variables: stiffness, accuracy, sensitivity

2012-03-26

arxiv.org/abs/1203.5691v1

Physics

Geophysics

18 pages, 4 figures

Scientific paper

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 $\varepsilon$-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.

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