Sand particles are frequently produced when solids are mobilized from a fluid-saturated porous granular material as a result of sharp fluid pressure and stress gradients, leaving behind mechanically damaged zones. These are commonly called “sand production” and “wormholes” respectively in 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. Hence, it is imperative to fluid an efficient computational model which has the predictive capability to assist the field operator to understand this unique process.; In this thesis, both the mathematical and numerical descriptions of sand production are explored within the realms of continuum mechanics and finite elements. Attention is given to the physics of sand production and its relation to the interaction between hydrodynamics and geomechanics.; When turning to realistic engineering problems, computational challenges are encountered while solving the governing equations as an initial boundary value problem. For instance, numerical instabilities arise since the governing equations contain high convection terms, and field variables also vary drastically with strong gradients in both space and time. A method is developed whereby local field variables such as density, flux, and stress found in the governing equations are enriched with high gradients to account for the effects of the local sharp changes by introducing an Optimized Local Mean Technique (OLMT). As such, the associated node-to-node oscillations encountered in standard numerical schemes are eliminated.; Numerical results of sand production afforded by the proposed model are in good agreement with available 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 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 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 wormholes.* (Abstract shortened by UMI.); *This dissertation is a compound document (contains both a paper copy and a CD as part of the dissertation). The CD requires the following system requirements: Adobe Acrobat.
展开▼
