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Sand production is a complex physical process that depends on the external stress and flow rate conditions as well as on the state of the material. Models developed for the prediction of sand production are usually solved numerically because of the complexity of the governing equations. Testing of new sand production models can very well be performed through calibration with laboratory experiments, which by construction possess geometric symmetry facilitating explicit mathematical analysis. We introduce an erosion model that is built upon the physics (poro-mechanical coupling of the fluid-solid system) usually incorporated in erosion models for the prediction of sand production. Around this model, we set up a mathematical framework in which sand production models because of erosion can be tested and calibrated without having to resort to complex numerical work or specialised software. The model is validated by data of volumetric sand production from a hollow cylinder test on synthetic sandstone. Generalisations of the model, which are naturally incorporated in the same framework and have useful phenomenological features, are discussed. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper studies the importance of the cohesive zone in the modelling of a fluid driven fracture under plain strain conditions. The fracture is driven by pumping of an incompressible viscous fluid at the fracture inlet. Rock deformation is modeled for linear elastic and poroelastic solids. Fluid flow in the fracture is modeled by lubrication theory. The cohesive zone approach is used as the fracture propagation criterion. Finite element analysis was used to compute the solution for the crack length, the fracture opening and propagation pressure as a function of the time and distance from the wellbore. It is demonstrated that the crack profiles and the propagation pressures are larger in the case of elastic-softening cohesive model compared to the results of the rigid-softening cohesive model for both elastic and poroelastic cohesive solids. It is found that the results are affected by the slope of the loading branch of the cohesive model and they are nearly unaffected from the exact form of the softening branch. Furthermore, the size of the process zone, the fracture geometry and the propagation pressure increase with increasing confining stresses. These results may explain partially the discrepancies in net-pressures between field measurements and conventional model predictions. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a decoupled Arbitrary Lagrangian–Eulerian (ALE) approach for the large deformation analysis of plane-strain elastoplastic problems. In this decoupled approach, the Eulerian step consists of first remeshing the deformed continuum and then remapping the state variables at the new quadrature points. Remeshing is performed without altering the element topology of the original mesh with the aid of the Spring Analogy Method enhanced with torsional springs. Before remeshing, nodes at free boundaries are relocated using an analytical approach, in order to preserve a good node distribution throughout the analysis. State variable remapping is achieved through the Radial Basis Point Interpolation Functions scheme. Large deformation elastoplastic analyses of two plane strain example problems are conducted using the presented ALE approach to test its robustness and effectiveness. The continuum is modeled as a Tresca or Mohr–Coulomb elastic–perfectly plastic material, while the meshes consist of second-order finite elements. The numerical results demonstrate that the present methodology is capable of predicting with adequate accuracy the load–displacement response even in analyses involving very large translations of the loaded boundary. [Copyright &y& Elsevier]