Seminar: “Using a multiscale tip asymptotic solution for a numerical modeling of a hydraulic fracture growth”

Egor Dontsov

Professor Egor Dontsov

Skoltech Center for Hydrocarbon Recovery is pleased to invite you to a seminar by professor Egor Dontsov from the Department of Civil and Environmental Engineering, University of Houston.

The topic of the seminar is “Using a multiscale tip asymptotic solution for a numerical modeling of a hydraulic fracture growth”.

Seminar Abstract:
Hydraulic fracturing is a method for stimulating oil and gas wells, in which a viscous fluid is injected into a rock formation to produce high conductivity channels. Modeling of the hydraulic fracturing includes fluid balance inside the crack, fluid leak-off into the formation, elastic equilibrium of cracked rock, and a propagation criterion. One peculiar feature of this problem is the multiscale behavior in the crack tip region. In particular, the applicability region of the classical square root solution stemming from the linear elastic fracture mechanics is often smaller than the typical mesh size, which occurs due to the presence of a viscous fluid. As a result, in order to obtain an accurate numerical solution on a relatively coarse mesh, there is a necessity to use the tip asymptotic solution, which has an increased validity region as compared to the classical solution.

This tip asymptotic solution that captures the near-tip behavior can be obtained by solving the problem of a semi-infinite hydraulic fracture that propagates steadily under plane strain elastic conditions. A closed form approximate solution for such problem, which describes the multiscale near tip behavior for the case of a Newtonian fluid and Carter’s leak-off model, has been obtained in Dontsov&Peirce, JFM (2015). This development allowed us to implement the multiscale asymptotic solution as a propagation condition in a numerical simulator to obtain accurate results. In particular, the obtained asymptote is used for a single planar fracture, and for a multiple planar hydraulic fractures that propagate simultaneously from a single wellbore.

The numerical scheme utilizes a fixed rectangular mesh, level set method for tracking the moving fracture front, and an implicit time integration scheme. Results indicate the necessity of using the tip asymptote for obtaining accurate numerical solution, since qualitatively different asymptotes are used in various parts of the same fracture that propagate with different velocities.

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