The paper presents a sand production model for a deforming oil sand matrix. The deformability of the oil sand matrix is an important issue given that in-situ and well pumping induced stresses impact on the susceptibility of the oil sand to produce sand. The sand production model is formulated in a consistent manner within the framework of mixture theory with the porosity as one of the main field state variables. The latter is split into two parts: one related to volume changes as a result of erosion in the oil sand matrix, and the other one due to deformations in the matrix subjected to a stress field. The coupling of the erosion model to a stress model is made through bulk volumetric strains. Also the erosion constitutive law is intimately tied with material strengths that enter the stress model. Finally, some numerical examples of sand production restricted to a rigid matrix are given in the interim to illustrate the proposed framework, pending completion of the finite element implementation of coupled stress-erosional model
Sand production during hydrocarbon production in oil wells is both a costly and prevalent phenomenon that is not well understood. Consequently, sand production and control has been a research topic for more than five decades. From a mechanistic viewpoint, sand production emanates from the progressive disaggregation of the poorly consolidated formation due to, many factors-notably, stresses, fluid flow, thermal, solution gas drive and reservoir heterogeneity in porosity. Once initiated, sand production can be progressive and may strike at varying degrees of severity ranging from erosion and plugging of pumps, valves and pipes, to the development of large cavities or wormhole-like structures in the formation resulting into damage and casing collapse.
A review of sand production issues together with the development of a model describing the erosion of sand grains in a rigid oil sand matrix were recently presented in Wan and Wang (2000). In this paper, the model is further developed with the constraint of rigid matrix removed so that both stress and strength characteristics enter formally into the formulation. It is well recognized that in-situ stresses as well as those induced during drilling impact on sand production. In this paper, a framework that considers the rigorous coupling between stress/deformations and erosion is proposed within the continuum theory of mixtures. Such consistent coupling is scare in the current literature, except for the work of Stavropoulou et. al. (1998)  in which the coupling between skeleton deformations and fluid transport was formulated in a not consistent manner.
Fig. 1 illustrates the mechanics of sand production around a wellbore with sand grains being dislodged from the oil sand matrix. From a mechanistic point of view, sand production emerges as a result of an instability occurring in a viscous fluid saturated porous medium that undergoes mechanical deformation in the presence of fluid fluxes. This condition can be described within a three-phase system in which solid (s), fluid (f), and fluidized fluid (ff) interact.