This paper presents a fully coupled reservoir-geomechanics model with erosion mechanics to address wellbore instability phenomena associated with sand production within the framework of mixture theory. A Representative Elementary Volume (REV) is chosen to comprise of five phases, namely solid grains (s), fluidized solids (fs), oil fluid (f), water (w) and gas (g). The particle transport and balance equations are written to reflect the interactions among phases in terms of mechanical stresses and hydrodynamics. Constitutive laws (mass generation law, Darcy's law, and stress-strain relationships) are written to describe the fundamental behaviour of sand erosion, fluid flow, and deformation of the solid skeleton respectively. Subsequently, the resulting governing equations are solved numerically using Galerkin's method with a generic nonlinear Newton-Raphson iteration scheme. Numerical examples in a typical light oil reservoir are presented to illustrate the capabilities of the proposed model in the absence of the gas phase. It is found that there is an intimate interaction between sand erosion activity and deformation of the solid matrix. As erosion activity progresses, porosity increases and in turn degrades the material strength. Strength degradation leads to an increased propensity for plastic shear failure that further magnifies the erosion activity. An escalation of plastic shear deformations will inevitably lead to instability with the complete erosion of the sand matrix. The self-adjusted mechanism enables the model to predict both the volumetric sand production and the propagation of wormholes, and hence instability phenomena in the wellbore.
The production of formation sand has plagued the oil and gas industry for decades because of its adverse effects on wellbore stability and equipment, while it has also been proven to be a most effective way to increase well productivity. When hydrocarbon production occurs from shallow and geologically young (or so-called unconsolidated / weakly consolidated) formations that have little or no cementation to hold the sand particles together, the interaction of fluid pressure and stresses within the porous granular material can lead to the mechanical failure of the formation and unwanted mobilization of sand. It has been reported that 10%- 40% sand cuts normally stabilize in time to levels less than 5% in heavy oil reservoirs , while an average of 40% productivity increase was achieved through sand management in light oil reservoirs . When sand is produced from reservoir formations, it can cause a number of problems. These include the instability of wellbores, the erosion of pipes, the plugging of production liners, the subsidence of surface ground, and the need for disposal of sand in an environmentally acceptable manner. Each year, these issues cost the oil industry hundreds of millions of dollars. Furthermore, sand production and control becomes extremely crucial in offshore operations where a very low tolerance to sand production is allowed. Hence, it is imperative to find an efficient computational model that has the predictive capability to assist field operators to understand this unique process. The ultimate goal is to design an economical well-production strategy in which sand production and operating costs may be reduced to some extent with maximum hydrocarbon productivity.