The production of sand grains from an unconsolidated porous solid matrix under viscous fluid flow is inevitable. While sand production has been found to increase effectively well productivity in both heavy oil and conventional light oil reservoir, it can also lead to geomechanical problems. This paper presents a simplified reservoir-geomechanics model in which, oil, fluidized sand and sand phases interact together through mechanical stresses and hydrodynamics within the framework of mixture theory. Sand production mechanisms are reflected 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. More precisely, the plastic shear deformation of a sand matrix around a well during drilling and pressure drawdown increases the erosion potential. In return, the erosion process also weakens the sand matrix through degradation of its mechanical strength. The self-adjusted mechanism enables the proposed model to predict the volumetric sand production. Both axial and radial viscous flow in a thick wall cylindrical sandstone specimen is computed using the developed model.
Sand production is a costly and inevitable phenomenon that occurs whenever the forces on sand particles, induced by fluid flow and/or solution-gas drive, are greater than the strength of the formation so as to lead to the loss of its mechanical integrity. The formation 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 fluidization and develop an efficient computational model that can be used to predict sand production during field operations.
Vardoulakis et al.(1) proposed 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 homogenization mixture theory. Subsequently, Wan &Wang(2)(3)(4)extended this pure erosion model to include the effect of the deformation of porous media. 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(3). However, within the context of an initial boundary value setting for solving realistic problems, numerical instabilities arise using standard numerical schemes since the governing equations contain high convection terms. Consequently, Wan &Wang(5) proposed an Optimized Local Mean Technique (OLMT) to modify local field variables such as density, flux, and stress found in the governing equations by expanding them into a Taylor series over a finite size domain in order to eliminate the associated node-to-node oscillations encountered in standard numerical schemes. On the side, this technique also lead to a framework which establishes a physical explanation for ad-hoc terms used in traditional stabilized numerical methods(6).
