A predictive model for sand production in poorly consolidated sands
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This thesis presents a model for the process of sand production that allows us to predict the stability of wellbores and perforation tunnels as well as mass of sand produced. Past analytical, numerical, and empirical models on material failure and erosion mechanisms were analyzed. The sand production model incorporates shear and tensile failure mechanisms. A criterion for sand erosion in failed sand was proposed based on a force balance calculation on the sand face. It is shown that failure, post failure sand mechanics and flow-dominated erosion mechanisms are important in the sand production process. The model has a small number of required input parameters that can be directly measured in the lab and does not require the use of empirical correlations for determining sand erosion. The model was implemented in a numerical simulator. Three different experiments using different materials were simulated and the results were compared to test the model. The model-generated results successfully matched the sand production profiles in experiments. When the post-failure behavior of materials was well-known, the match between the simulation and experiment was excellent. Sensitivity studies on the effect of mechanical stresses, flow rates, cohesion, and permeability show qualitative agreement with experimental observations. In addition, the effect of two-phase flow was presented to emphasize the importance of the water-weakening of the sand. These results show that catastrophic sand production can occur following water breakthrough. Finally the impact of increasing sand cohesion by the use of sand consolidation chemicals was shown to be an effective strategy for preventing sand production.