This doctoral research establishes a predictive framework for volumetric sand production by investigating the coupled hydro-mechanical processes of plastic yielding, material degradation, and hydrodynamic erosion in weakly consolidated formations. The investigation integrates two complementary approaches. First, a fully coupled, poro-elasto-plastic finite element model utilizing an Arbitrary Lagrangian-Eulerian (ALE) formulation to analyze stress evolution and material failure in hollow cylinder tests and secondly, a novel semi-analytical framework that reduces the erosion dynamics to a system of coupled ordinary differential equations governed by mean porosity and plastic zone depth. The primary contribution of this work is the quantitative demonstration that the sand production coefficient (λ), a key parameter in hydrodynamic erosion models, exhibits a strong power-law dependence on the applied far-field stress. This relationship, first identified through numerical simulations, is incorporated into the semi-analytical model as a constitutive law for material degradation. The resulting kinematic formulation accurately predicts cumulative sand production, plastic zone evolution, and porosity changes, showing excellent agreement with experimental data from multiple hollow cylinder tests under variable stress and intermittent flow conditions. Collectively, this research advances the state-of-the-art by providing a mechanistically grounded and computationally efficient methodology for calibrating erosion parameters and predicting sand production. The validated models provide a robust foundation for enhancing proactive sand control strategies and optimizing well completion designs in challenging geomechanical environments.
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