Sunder H. Advani

Finite Element Model Simulations Associated With Hydraulic Fracturing

This study presents methodology and results pertinent to hydraulic fracture modeling for the U.S. DOEs Eastern Gas Shales Program (EGSP). The presented finite-element model simulations extend available modeling efforts and provide a unified framework for evaluation of fracture dimensions and associated responses. Examples illustrating the role of multilayering, in-situ stress, joint interaction, and branched cracks are given. Selected comparisons and applications also are discussed. 30 refs.

A fixed grid finite element method for nonlinear diffusion problems with moving boundaries

A comprehensive formulation for a class of diffusion problems with non-linear conductivities is derived by unifying and combining the freezing index and Kirchhoff transformation concepts. The transformed equations have appropriate continuity characteristics across the unknown moving boundary. The applicability of the fixed grid algorithm for the total solution domain is, accordingly, demonstrated. Associated finite element formulations and solution procedures for the transformed equations are detailed. In addition, selected numerical results for single and two phase Stefan type problems as well as fluid flow in a prescribed cavity are presented for solution verification and illustration.

Fracture criteria and stress intensity factors including the effect of crack closure

Two- and three-dimensional thermo-mechanical failure criteria, including the effects of crack/cavity closure, are developed in terms of thermal and mechanical loading by extending the work of McClintock and Walsh. General 2- and 3-D fracture criteria in terms of soley stress intensity factors are developed and it is shown that they are expressed in the single relation, (k2k2c)2 + k1k1c = 1, on the basis of Griffith theory and fracture mechanics. General expressions of stress intensity factors in 3-D crack problems under arbitrary thermo-mechanical loading with the effect of crack closure are also deduced.

Three-dimensional analysis of an arbitrary shaped pressurized crack traversing a bi-material interface

Abstract A method for analysing the fracture responses of an arbitrarily shaped planar crack traversing a perfectly bonded bi-material interface is presented. Using the Greens functions for two welded elastic half-spaces, two-dimensional singular integral equations are derived. The solutions to these equations characterize the opening displacement of the three-dimensional crack. Crack opening displacement profiles for an example illustrated by pressurized elliptical cracks of different aspect ratios, with the major axis of the ellipse aligned with the bi-material interface, are given. Corresponding stress intensity factors and energy release rates are also computed.

Fluid flow and structural response modeling associated with the mechanics of hydraulic fracturing

A review of hydraulic-fracture modeling is given. Equations governing pertinent fluid-flow, structural, and fracture-mechanics responses are presented. The finite-element method is used to discretize the field equations and to compute the fracture dimensions, fluid leakoff, and stress intensity factors. In addition, the effects of fracture-fluid properties, layered strata, and in-situ stresses are characterized, and numerical examples are presented.

Hydraulic Fracture Configuration Modeling: Numerical Evaluations

Salient features of a three-dimensional hydraulic fracture finite element simulator are identified. Selected comparisons associated with a penny-shaped model are presented.

An Iterative Solution Method for Frictional Contact Problems

A combination of a direct method (LU decomposition, for example) and the Gauss-Seidel iterations is employed to solve finite element equations subjected to frictional contact conditions. Developed solutions algorithm appears to be very efficient attaining a rapid convergence at a fractional increase in computing time over the conventional elastic solutions. It is found that Coulomb’s law must be applied in an incremental form for an adequate representation of the friction.

The Role of Rock Mechanics in Optimizing Devonian Gas Production From the Appalachian Basin

The dominant role of the in situ stresses and formation mechanical properties for reservoir site selection and hydraulic fracture treatment are quantified in this paper. An illustration of basement-sedimentary cover interaction and salient mechanisms responsible for stress reorientation and tectonic relief in the Rome trough region of the Appalachian Plateau is given. In addition, examples detailing hydraulically induced fracture dimension evaluations along with a discussion of factors governing fracture width, vertical fracture migration and fracture length are presented. Finally, the suitability of different stimulation treatments is discussed. 52 refs.