Sand particles are frequently produced when fluid production occurs from underground porous media. An example of such a process is in the production of oil and gas. The interaction of fluid pressure and stresses within the porous granular material can lead to its mechanical falilure and the unwanted mobilization of sand. This may result in “wormholes” in the formation and “sand production” as described by the Petroleum Geomechanics jargon. When sand is produced from reservoir formations, it can cause a number of problems. These include instability of wellbores, erosion of pipes and pumps, plugging of production liners, subsidence of surface ground, and the disposal of sand in an environmentally acceptable manner. Each year, these issues cost the oil industry hundreds of millions of dollars.

Hence, it is imperative to find an efficient computational model which has the predictive capability to assist the field operator to understand this unique process. The ultimate goal is to design a proper production strategy so that sand production and operating costs may be reduced. Modelling such a complex problem is a challenging task since it needs multidisciplinary knowledge to capture the whole range of material response from sand initiation to fluidization.

A fully coupled reservoir-geomechanics model with erosion is proposed to address the instability phenomena associated with sand production within the framework of mixture and high gradient theories. A Representative Elementary Volume (REV), comprised of three phases: namely fluid (oil, water), fluidized solid, and solid, is chosen upon which the particle transport and balance equations are written to reflect the interactions among these phases through mechanical stresses and hydrodynamics.

When turning to realistic engineering problems, computational challenges are encountered while solving the governing equations numerically. An innovative numerical stabilized scheme, namely the Optimized Local Mean Technique (OLMT) method has been developed based on high gradient theory, through which the local field variables are enriched with high gradients to account for the effects of the local sharp changes. As such, the associated node-to-node oscillations encountered in standard numerical schemes are eliminated. It is interesting to note that the developed technique also leads to a framework that establishes a physical explanation for the ad-hoc terms used in traditional stabilized numerical methods.

Numerical results of sand production afforded by the proposed model are in good agreement with the lab test data. 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 strength of the solid matrix. Strength degradation leads to an increased propensity for plastic shear failure that further magnifies the erosion activity. An escalation of plastic shear deformation will inevitably lead to collapse 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 the wormhole formation.

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