Conventional theories of sand production prediction distinguish between compressive (shear) cavity (perforation, borehole) failure, induced by a combination of in-situ stress and drawdown, and tensile cavity failure, induced by the near-cavity pore pressure gradient. This paper shows, using bifurcation theory, that the preference for either compressive or tensile cavity failure only depends on cavity size and on the constitutive properties of the rock, and not on effective near-cavity stress or pore pressure gradient. It is shown that larger cavities (e.g. boreholes) always fail in compression rather than in tension. Only for sufficiently small cavities (e.g. perforations) in weak, moist sandstones, compressive failure is supressed, and tensile failure is possible. The above results deviate significantly from previous sand production prediction concepts, and are more in line with laboratory observations. One implication is that the primary role of fluid flow in sand production appears to be the removal of sand (debris) resulting from compressive failure, rather than failure of the intact sandstone itself.
Both the effective stress near the wellbore and flow rate into the wellbore have long been identified as the main formation destabilising factors influencing sand production. Several sand production prediction methods have been proposed based on these parameters. The Drucker-Prager model proposed by Antheunis et al. (1976) and Mohr-Coulomb model proposed by Coates and Denoo (1981) are examples of such methods based on consideration of the intact rock compressive strength, drawdown and in-situ stress. Alternatively, models such as Bratli and Risnes (1981) and Perkins and Weingarten (1988) compare the flow-induced pressure gradient with the residual strength of disaggregated material surrounding the cavity (perforation, borehole). A well-accepted conceptual model for sand production has been proposed by Morita et al (1989 a,b). Within this model, sand production can either be triggered by compressive (shear) failure, induced by a combination of in-situ stress and drawdown, or by 'tensile' failure, induced by the near-cavity pore pressure gradient. Compressive failure around a cylindrical cavity leads to the formation of breakouts adjacent to the cavity. Whether compressive failure or tensile failure prevails will depend on the precise values of in-situ stress, drawdown and flow rate in relation to the rock strength. This paper presents a theoretical analysis, based on bifurcation theory, of cylindrical cavities in weak sandstones under in-situ stress and flow conditions. The analysis employs a Cosserat-Mohr-Coulomb flow theory of elastoplasticity with hardening and softening which is calibrated on conventional triaxial compression test data. Previously, this theory was successfully applied to explain the experimentally observed size dependency of hollow cylinder strength in the absence of fluid flow (Papamichos and van den Hoek, 1995). In the present study, both in-situ stress and flow rate (i.e. near-cavity pore pressure gradient) have been varied over a large range of values in order to induce either compressive failure, defined by the bifurcation point, or tensile failure, defined by a tensile near-cavity radial effective stress (see, for example, Bratli and Risnes,1981). In addition, the cavity diameter has been varied.
