Summary We present a micromechanical approach based on zero‐thickness interface elements for modelling advanced localization and cracking states of cemented granular materials, such as reservoir sandstones. The proposed methodology is capable of reproducing the complex behaviour of intergranular and intragranular localization, cracking, and fracturing of rock formation that leads to sanding in hydrocarbon production. The model is calibrated at the macroscale, using only a few physical parameters, by reproducing the typical behaviour of compression element tests. The model exhibits clear transition behaviour from brittle dilatant to ductile compactant behaviour with increasing confining stress. The methodology is implemented for sand production prediction analysis based on the simulation of 2D micromechanical models of hollow cylinder cross sections. The obtained results are compared well with published experimental data from hollow cylinder tests characterized by strong scale effect in the range of small perforations.

SUMMARYRock sanding in oil wells is an erosion process in which grains are disaggregated due to a combination of stress and fluid flow. This process is studied here using the finite element method with interface elements and explicit representation of the material microstructure. A cross-section of a small-diameter side perforation of the main well is considered. Within a circular region around the hole, the individual rock grains are discretized, while the space between the ring perimeter and the square domain limits is filled with standard triangular elements. The space within each grain is discretized using elastic finite elements, while the intergranular contact is represented with zero-thickness interface elements equipped with a fracture-based constitutive law. Numerical analyses start from the in situ stress state and contemplate the perforation process and drawdown pressure. Preliminary results obtained in this on-going study suggest that the evolution of cracking and fracture around the hole can be represented quite realistically with this approach. Also, the correct trend that seems to emerge is the dominant effects of the initial stress value and the size of the perforation diameter.Brought to you by | Purdue University Libraries Authenticated Download Date | 5/29/15 2:25 AM Vol. 16, Nos. 1-2, 2005 Micromechanical Analysis of the Rock Sanding Problem investigations, particularly those realized in cylindrical samples /1 /, 121, and 13/ and second, numerical modelling carried out by FEM or DEM calculations 13/, /4/, 76/ and /5/.Brought to you by | Purdue University Libraries Authenticated Download Date | 5/29/15 2:25 AM Vol. 16, Nos. 1-2. 2005 Micromechanical Analysis of the Rock Sanding ProblemThis study is in a preliminary stage and on-going efforts are directed at continuing the reduction of the hole inner pressure to complete the perforation stage. We also consider cases with non-isotropic initial stress state, K 0 * 1. A next stage of the study will involve a coupled analysis required to simulate reduction of the transient downhole fluid pressure, and the parametric study to finally reach quantitative predictions of sand production in oil wells.

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Summary This paper describes a particular formulation of the extended finite element method (XFEM) specifically conceived for application to existing discontinuities of fixed location, for instance, in geological media. The formulation is based on two nonstandard assumptions: (1) the use of sub‐interpolation functions for each subdomain and (2) the use of fictitious displacement variables on the nodes across the discontinuity (instead of the more traditional jump variables). Thanks to the first of those assumptions, the proposed XFEM formulation may be shown to be equivalent to the standard finite element method with zero‐thickness interface elements for the discontinuities (FEM+z). The said equivalence is theoretically proven for the case of quadrangular elements cut in two quadrangles by the discontinuity, and only approximate for other types of intersections of quadrangular or triangular elements, in which the XFEM formulation corresponds to a kinematically restricted version of the corresponding interface plus continuum scheme. The proposed XFEM formulation with sub‐interpolation, also helps improving spurious oscillations of the results obtained with natural interpolation functions when the discontinuity runs skew to the mesh. A possible explanation for these oscillations is provided, which also explains the improvement observed with sub‐interpolation. The paper also discusses the oscillations observed in the numerical results when some nodes are too close to the discontinuity and proposes the remedy of moving those nodes onto the discontinuity itself. All the aspects discussed are illustrated with some examples of application, the results of which are compared with closed‐form analytical solutions or to existing XFEM results from the literature.