A New Concept of Sand Production Prediction: Theory and Laboratory Experiments
Authors: van den Hoek P.J. , Hertogh G.M.M. , Kooijman A.P. , de Bree Ph. , Kenter C.J. , Papamichos E. 
Published: December 2007

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 'large' 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. They are further supported by laboratory sand production experiments with 'large' cavities, where sand failure was only observed for near-cavity effective stresses above a certain threshold, independent of applied drawdown (i.e. flow rate). The experiments exhibited no correlation between the (non-) occurrence of sand production and drawdown.

From these results, it may be concluded that the primary role of fluid flow in sand production is the transport of loose sand (debris) resulting from compressive failure, rather than failure of the intact sandstone itself.

Introduction

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., and Mohr-Coulomb model proposed by Coates and Denoo are examples of such methods based on consideration of the intact rock compressive strength, drawdown and in-situ stress. Alternatively, models such as Bratli et al. and Perkins and Weingarten 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. 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. The extreme condition of compressive failure at zero flow rate is analogous to the problem of hollow cylinder collapse. The other extreme, tensile failure at zero (or very low) near-cavity effective stress would be similar to the unconsolidated sand failure experiments as performed by Hall and Harrisburger or Bratli and Risnes.

This paper presents the results of theoretical and experimental studies into the prediction of sand failure around cylindrical and hemispherical cavities in weak sandstones under a variety of in-situ stress and flow conditions. The theoretical analysis is based on bifurcation theory in combination with a Cosserat continuum, which accounts for effects of grain size. The constitutive model used in this analysis was calibrated to conventional triaxial compression test data. Previously, this approach was successfully used to reproduce the experimentally observed size dependency of hollow cylinder strength in the absence of fluid flow, see Fig. 1. In the present theoretical and experimental studies, 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 or tensile sand failure. The theoretical study also addressed the influence of cavity size on compressive versus tensile failure.

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