ABSTRACT: A common approach to predicting the onset of sand production is based on laboratory tests of thick-walled cylinders (TWC tests). In order to apply this to the field, one generally needs to correct the TWC results for a size effect and for anisotropic loading conditions (for example, horizontal hole). Contrary to the size effect, extrapolation to anisotropic loading conditions is still hampered by lack of comprehensive laboratory datasets and theoretical analyses.
This paper presents the results of a theoretical study into the impact of anisotropic loading conditions on the onset of sand production. The theoretical analysis is based on bifurcation theory in combination with a Cosserat continuum, which accounts for effects of grain size. Previously, this approach was successfully used to reproduce the experimentally observed size effect of TWC strength. Our results show that the correct stress-anisotropy factor by which TWC strength should be corrected depends very much on the size of the cavity (borehole, perforation). For larger cavities (e.g. boreholes), a factor based on the elastic Kirsch solution appears adequate, but for smaller cavities (e.g. perforations) a higher factor is required in order to realistically predict the onset of sand production. These results appear to be in line with laboratory data from the literature.
A common approach to predicting the onset of sand production is based on laboratory tests of thick-walled cylinders (TWC tests) [1]. These tests are generally conducted on small samples (typically . 1 cm hole diameter) under isotropic radial loading conditions. For perforations, such small test samples can be generally considered adequate, but for open hole completions, one needs to correct the results for a so-called size effect. The latter has been measured on different rocks, and published results (e.g., [2-6]) can be used to estimate the impact of size effect.
Apart from the small size, another disadvantage of the TWC test is that it measures the onset of sand production under isotropic (radial) loading conditions. Extrapolation of these results to anisotropic loading conditions (for example, horizontal hole) is still hampered by lack of comprehensive laboratory datasets and theoretical analyses.
The mechanical stability of a cavity (perforation, open hole) under anisotropic loading conditions is most commonly assessed based on linear elasticity, together with a strength criterion, such as the Mohr-Coulomb criterion [7-11]. Although attractive for its simplicity, such an approach is generally considered conservative and calibration is required [12-14]. The calibration is conducted usually based on observations of certain types of failure, such as borehole breakout, onset of sand production, or TWC collapse. The calibrated model is then assumed to be applicable to predictions of stability of cavities oriented in all other directions under 3D in-situ stress conditions. Alternatively, elasto-plastic
