A hydro-mechanical erosion analytical model for sand prediction

Sand production is one of the major research subjects in petroleum industry. The physical processes that dominate the problem depend on the in-situ stress field and the hydro-mechanical conditions (i.e. the state of the material). The problem is usually dealt with either experimentally or numerically due to the complexity of the governing equations. In our previous work, we introduced an erosion model which is built upon the physics (fluid-solid poro-mechanical coupling) usually incorporated in erosion models for the prediction of sand production. In this work we briefly outline the mathematical framework upon which our sand production model works due to erosion. The focus of this analysis is the parametric investigation of the material parameters that dominate the poro-elastoplastic constitutive model (cohesion and friction angle) for weak unconsolidated formations. Typically such formations are dominated by plastic compaction upon loading and are characterized by low cohesive strength (low cohesion) but significant frictional stress dependent strength (high friction angle).