Analysis of Sand Production in Unconsolidated Oil Sand Using a Coupled Erosional-Stress-Deformation Model
Authors: Wan R.G. , Wang J. 
Published: March 2010

Abstract
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 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 to illustrate the theory, pending the completion of the finite element implementation of a coupled stress-erosional model.

Introduction
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 in 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 presented in Wan and Wang(1). In this paper, the model is further developed with the constraint of the 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, have an 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(2). Such rigorous coupling is scarce in the current literature, except for the work of Stavropoulou et al.(3) in which the coupling between skeleton deformations and fluid transport was formulated, but was not done in a consistent manner

Model Description
Figure 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.