Search

The contraction or expansion of a cylindrical cavity in an elastoplastic medium is usually analyzed from a continuum based approach with a plasticity constitutive model. However, localized deformations, which are rooted in the post‐failure softening response of geomaterials, are observed in the form of spiral‐shaped fractures in laboratory tests. An alternative approach based on dislocation theory is introduced in this paper for modeling cavity contraction or expansion. In this model, several equally spaced spiral‐shaped shear fractures initiate and propagate away from the cavity within the linearly elastic medium. The Mohr‐Coulomb criterion and a dilatancy rule are imposed on the shear fractures to constrain the stresses and the displacement jumps. The direction of fracture propagation is determined by minimizing plastic dissipation. The displacement discontinuity method is used to discretize the shear and normal displacement jumps along the fracture and solve the problem numerically. The calculated crack path follows a logarithmic‐like spiral, similar to the slip lines predicted by plasticity theory. The relationship between the pressure and radial displacement at the cavity boundary converge towards the classical elastoplastic solution as the number of fracture branches increases. [ABSTRACT FROM AUTHOR]

Fluid injection‐induced deformation around a cylindrical cavity is of particular interest in the area of subsurface energy extraction. In this study, a model is proposed to analyze the time‐dependent expansion of a cavity caused by fluid injection in an elastoplastic dry porous medium. This problem is characterized by the existence of two moving boundaries, a permeation front and an elastoplastic interface, which leads to distinct time‐dependent zones governed by different sets of equations. The interplay between these two boundaries leads to three phases of solution. The a priori unknown partitioning of the injection rate into the rate of change of cavity volume and infiltration in the porous medium necessitates the introduction of a time‐dependent permeation coefficient as one of the primary variables. The method of solution takes advantage of the quasi‐static and quasi‐stationary nature of the problem, which makes it possible to treat time as a parameter rather than a variable. It follows that the problem can be solved in two steps. In a first step, closed‐form expressions for the pore pressure, displacement, and stress fields in each zone are derived, with parameters in these expressions depending explicitly on four time‐dependent variables, namely the positions of the two interfaces, the cavity radius, and the permeation coefficient. In a second step, the rate equations governing the evolution of these variables during different phases are derived and solved numerically. The paper concludes with a parametric analysis of the influence of the stiffness and strength of the material on the solution. [ABSTRACT FROM AUTHOR]

This paper describes a KGD‐type model of a hydraulic fracture created by injecting fluid in weak, poorly consolidated rocks. The model is based on the key assumption that the hydraulic fracture is propagating within a domain where the hydraulic fields are quasi‐stationary. By further assuming a negligible toughness, the fracture is shown to grow as a square root of time. The asymptotic fracture propagation regimes at small and large time are constructed and the transient solution is computed by solving a nonlinear system of algebraic equations formulated in terms of the fracture aperture. At early time, the fracture is hydraulically invisible and the injection pressure increases with time t$t$ as logt$\log t$, while at late time, leak‐off from the borehole is negligible and the injection pressure decreases as t−1/4$t^{-1/4}$. According to this model, the peak injection pressure observed when injecting fluid in weak, poorly consolidated rocks should not be interpreted as indicating a breakdown of the formation, but rather as marking the transition between two asymptotic flow regimes. The timescale that legislates the transition between the small and large time asymptotic regimes is shown to be a strongly nonlinear function of a dimensionless injection rate. [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]

This paper presents a novel dynamical model to analyze the long-term response of a percussive drilling system. This departs from existing approaches that usually consider a single activation and bit/rock interaction cycle for the analysis of the process performance. The proposed model integrates the axial dynamics of an elastic piston and an elastic drill bit, a motion-dependent pressure law to drive the piston, and a generalized bit/rock interaction law representative of the dynamic indentation taking place at the bit/rock interface. It applies to down-the-hole percussive drilling as well as top-hole, with minor modifications. The model does not account for the angular motion or the hole cleaning, however. The model is first formulated mathematically; then, a finite-dimensional approximation is proposed for computations. Numerical analyses of the model response, for a low-size down-the-hole percussive system, follow. The period-1 stationary response for the reference configuration is studied in detail, and parametric analyses assessing the influence on the rate of penetration of the bit/rock interaction parameters, the feed force, and the percussive activation parameters are conducted. These analyses reveal that the multiscale nature of the process is well captured by the model and recover expected trends for the influence of the parameters. They also suggest that a significant increase of the penetration rate can be achieved by increasing the percussive frequency. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper proposes an energy-based measure for the evaluation of the local truncation error of two-level one-step integration schemes. The measure applies to multiple degree of freedom systems and does not necessarily require modal reduction to a scalar model; it naturally handles the structural damping and external forcing terms that are generally and mistakenly neglected in error analyses, and it segregates the error associated with the free and forced response components of the problem. To illustrate the approach, two examples associated with the application of the trapezoidal scheme and of a high-order scheme proposed in the literature are analyzed. The latter reveals the shortcomings of the standard approach that is based on the undamped/unforced linear oscillator and therefore highlights the need for the proposed framework. Indeed, the scheme order of accuracy is below expectation when structural damping or external forcing is considered, in the numerically dissipative setting. Developments on the basis of the time discontinuous Galerkin (TDG) method are then proposed to recover the scheme high-order accuracy. Additionally, they show the similarity that exists between schemes related to the TDG method and the ones obtained by integration by parts of the equation of motion. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The failure mechanisms induced by a wedge-shaped tool indenting normally against a rock surface are investigated using the discrete element method (DEM). The main focus of this study is to explore the conditions controlling the transition from a ductile to a brittle mode of failure. The development of a damage zone and the initiation and propagation of a brittle fracture is well captured by the DEM simulations. The numerical results support the conjecture that initiation of brittle fractures is governed by a scaled flaw length Λ, a ratio between the flaw size λ and the characteristic length [ABSTRACT FROM AUTHOR]

The coupled equations for a propagating hydraulic fracture (HF) exhibit a multi-scale structure for which resolution on all length scales becomes computationally prohibitive. Asymptotic analysis is able to identify the dominant physical process active at the computational length scale. This paper describes a novel algorithm that uses weak-form tip asymptotics on a rectangular Eulerian mesh to solve the problem of a propagating HF. The location of the fracture front is determined within each tip element by matching the volume associated with the known asymptotic solution to the flux of fluid into the given element. Even if the fracture front is curved, the algorithm is able to capture the solution on a relatively coarse rectangular mesh by implementing a weak form of the tip asymptotic solution, based on averaging the volume over a tip element to determine the fracture widths at tip element centers. The fracture is divided into a ‘channel’ region made up of elements that are filled with fluid and a ‘tip’ region comprising partially filled elements. An iterative procedure is used to determine the fracture widths and fluid pressures in the channel region and the fracture font locations in the tip regions. The algorithm is tested by analyzing an HF propagating in a viscosity-dominated regime within an impermeable homogeneous elastic material for which a similarity solution is available. The numerical results show close agreement with the exact solution even though a relatively coarse mesh is used. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]