Prediction of Volumetric Sand Production Using a Coupled Geomechanics-Hydrodynamic Erosion Model
Authors: Wan R.G. , Liu Y. , Wang J. 
Published: March 2010

Abstract
The production of sand grains from an unconsolidated porous solid matrix under viscous fluid flow is inevitable. While sand production has been found to effectively increase well productivity in both heavy oil and conventional light oil reservoirs, it can also lead to geomechanical problems such as sand failure and cavity (wormhole) formation. The paper investigates the phenomenon of sand production in a thick wall cylinder test that mimics both axial and radial flow near an oil well perforation. Then, an actual well section with perforations is analyzed with respect to sand production, failure, and cavity formation in the form of a wormhole. The numerical analysis is based on a reservoir-geomechanics model developed by the authors over the past several years. The model considers oil, fluidized sand, and sand phases interacting together through mechanical stresses and hydrodynamics within the framework of mixture theory. Interesting sand production mechanisms emerge from the interaction between geomechanics and an erosion process by which sand grains are detached from the solid matrix due to both fluid and stress gradients, once a certain level of material failure is reached.

Introduction
Sand production is a costly and inevitable phenomenon that occurs whenever drag forces on sand particles, induced by fluid flow and/or solution-gas drive, exceed the inter-granular forces (related to macroscopic strength of formation) so as to lead to the loss of mechanical integrity. This pre-supposes that the material has to undergo yielding and reach incipient failure from a geomechanical viewpoint before sand production may occur. There could also be another mechanism by which the sand grains crush under extreme stresses and fragment into smaller particles that become mobile. In any of the above cases, the material collapses locally, and the sand fragments are carried into the wellbore where they can block the flow, damage pumps and pipes, and contaminate the produced oil. Sand production creates cavities in the formation that continually increase in size and eventually become unstable, leading to the collapse of the wellbore. Each year, sanding problems cost the oil industry hundreds of millions of dollars. Hence, it is pertinent to study the mechanics of sand failure and its interaction with hydrodynamics with the view of developing an efficient computational model that can be used to predict sand production during field operations.
Vardoulakis et al.(1) were probably among the first to tackle the sand production problem as an erosion phenomenon, proposing a hydro-erosion model based on rigid porous media within a continuum mechanics framework in which mass balance is applied to a three-phase system comprised of solid, fluid, and fluidized solid using mixture theory(2). Subsequently, Wan and Wang(3–6) extended this pure erosion model to include the effect of the deformation of porous media, and more explicitly, material failure aspects. This approach results in solving a set of coupled non-linear time-dependent equations with fluidized solid concentration, fluid pressure, porosity, and deformation as main variables.