Abstract

Sand production mechanisms were numerically studied by means of a displacement discontinuity boundary-element method. The method allows an explicit modelling of fracture growth in rocks in 2D. Rock fracture in hollow cylinder sand production tests was simulated. Different types of fracture growth typically observed in hollow cylinder tests were investigated, i.e. breakout formation, slit propagation and uniform collapse of the cavity. Changing the mechanical behavior of the rock, represented by the properties and constitutive behavior of the displacement discontinuity elements, from brittle to ductile resulted in a change of the failure pattern from breakouts to uniform collapse, reproducing thusthe laboratory tests. A clear effect of the specimen size (external diameter) on the results was demonstrated numerically. The increase of the external diameter of the hollow cylinder results in a virtually linear increase of the hollow cylinder strength, at least in the range of diameter values investigated.

Introduction

Hollow cylinder tests with increasing confining stress and radial fluid flow are a standard means for modelling sand production in laboratory conditions. The strength value of the specimen obtained in such tests enters sand production/sand prediction models currently in use[1–3]. Therefore understanding the sandstone failure mechanisms and post-failure behaviour in hollow cylinder tests is important.

Three types of failure have been observed in sandstone hollow cylinder tests:

  • uniform failure of the drillhole,

  • formation of breakouts, and

  • formation of narrow slits (Fig.1)[4]. The first type, i.e. uniform failure of the hole, is usually attributed to ductile failure of a compacting material.

The other two types are attributed to shear and brittle tensile failure of the material, respectively. Breakouts are attributed to shear failure, while elongated slits are associated with tensile failure at the tip of the slit.

The failure of the sandstone in hollow cylinder tests was modeled here with the displacement discontinuity boundary element method, as described in the next section. The resulting failure type is shown to be a function of the post-failure stiffness modulus of the displacement discontinuity elements. Furthermore, numerical modeling was used to study the effect of specimen size (external diameter) on hollow cylinder ultimate strength (i.e. at specimen collapse), which is important for hollow cylinder test optimization and validation. This is because the hollow cylinder tests are considered as representative of the rock behavior in situ. In the latter case, however, the external diameter is effectively infinite and thus the stresses for both hole failure and specimen collapse are larger and of interest to quantify.

Displacement discontinuity modeling of sandstone fracture in hollow cylinder tests

The two-dimensional code DIGS (developed by Miningtek, South Africa), which is based on the displacement discontinuity method, was used for the simulations. The displacement discontinuity method is a boundary element method and enables an explicit simulation of fracture development[5,6]. The bulk material is assumed to be linear elastic. All inelasticity and/or elastic nonlinearity are due to internal displacement discontinuities, which may grow along a pre-defined mesh, usually resulting from a Delaunay triangulation. Our experience with different meshes suggests that a Delaunay triangulation mesh gives more realistic failure patterns than a Voronoi polygonization mesh. Therefore the Delaunay mesh was used in most simulations in the following.

At the beginning of the simulation, the geometry is determined (for instance, a ring representing a hollow cylinder in 2D) and the mesh of potential displacement discontinuity elements is generated. Failure criteria for the displacement discontinuities are then defined. We used the Mohr-Coulomb failure criterion for all elements. The parameters entering the failure criterion are tensile strength, friction angle (pre- and post-failure), cohesion (pre- and post-failure), dilatancy angle, softening moduli (cohesion and tensile strength). The displacement discontinuity elements are usually divided into several groups with the same values of parameters.

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