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This paper describes a numerical algorithm for solving the classic problem of a plane strain (KGD) fracture propagating in an impermeable elastic medium with zero toughness. The method, which takes advantage of the self-similar nature of the solution, combines a domain-based scheme to solve the elasticity equations and a finite volume method to solve the nonlinear lubrication equation. This work represents a first step towards developing a model able to account for pore pressure diffusion in the medium and corresponding poroelastic effects, noting that these processes are more efficiently solved using a domain-based rather than a boundary integral method. To enhance the efficiency and accuracy of the numerical scheme, the far-field crack asymptotics is embedded in the discretized elastic relationship between the fluid pressure and the crack opening, while the coupled fluid-solid tip asymptote is enforced in a weak form when solving the nonlinear lubrication equation. The proposed technique yields results that closely match the analytical solution, even with a coarse mesh. This approach offers potential for addressing more complex hydraulic fracturing problems in the future. [ABSTRACT FROM AUTHOR]

The fundamental solution of a continuous line source, injecting fluid at a constant rate over the thickness of a poroelastic reservoir bounded by infinite impermeable elastic layers, is derived in this paper. This idealized problem has applications in hydrogeology and in petroleum engineering, as it can be used to assess the mechanical perturbations caused by injection or withdrawal of fluid in the subsurface through a vertical well. Construction of the solution takes advantage of the uncoupling of the pore pressure field, which, in this particular case, is given by the classical singular solution of the diffusion equation for an infinite line source. The mechanical fields then are determined by solving an elasticity-like problem with a body force field proportional to the time-dependent pore pressure gradient. On account of the problem symmetries, the Navier equations of elasticity reduce to two uncoupled partial differential equations for the radial and vertical (axial) displacement components, which are solved by a twofold application of Fourier and Hankel transforms. The solution exhibits different regimes at small, intermediate, and large times. When the diffusion radius, proportional to the square root of time, is smaller than or comparable to the thickness of the permeable layer, the induced deformation is confined to a region with a characteristic dimension of the same order as the diffusion radius. At large time, when the diffusion radius is large compared with the permeable layer thickness, the deformation rate in the reservoir is essentially oedometric (uniaxial). The different regimes of solutions are justified with a conceptual model based on identifying the evolving characteristics of complementary interior and exterior domain problems. The derived solution can serve as a valuable benchmark for coupled reservoir simulators. It also provides insights in to such problems as waterflooding, shearing at reservoir/cap rock interfaces, and stress redistribution around producing wells. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: The development of reliable experimental techniques for characterization of chemoporomechancial shale–fluid interactions is important for the design of drilling fluids that maximize shale stability. In this context, testing of millimeter-scale specimens is promising because small specimens require shorter test durations and are more readily available from offcuts of preserved core or potentially from drill cuttings or wellbore cave-in material than larger core plugs that are required for more conventional experimentation. Here we present experiments wherein we measure the axial displacement of 4mm long by 4mm diameter cylindrical shale specimens that are subjected firstly to a mechanical axial loading and then to an osmotic loading associated with a sudden increase in the salinity of the surrounding fluid. The response to both stages of loading is consistent with theoretical, chemoporoelastic predictions. In particular, the model predicts two types of behavior depending on the ratio between the reflection coefficient and the so-called chemomechanical coupling coefficient that quantifies the volumetric strain as a result of a change in ion content. Consistent with predictions, both monotonic shrinkage and initial shrinkage followed by partial recovery are observed in our testing campaign which includes 20 shales from a variety of geological settings. Quantitative characterization is also carried out by selecting chemoporoelastic parameter values that minimize the mismatch between the data and the model. The results show that the reflection coefficient and the chemomechanical coupling parameter are correlated with each other and with both the Cation Exchange Capacity (CEC) and the Specific Surface Area (SSA). Based on the consistency of the data from test to test and with the model, together with the fact that the key chemoporoelastic coefficients are sensibly correlated with CEC and SSA, we conclude that these millimeter-scale experiments are able to provide useful characterization for better understanding and predicting shale–fluid interactions. [Copyright &y& Elsevier]