On the stress dependency of sand production coefficient in hydro-dynamical sanding criteria

Solids production is a complex physical process which is controlled by several factors including mechanical failure from in-situ stresses and hydrodynamic erosion from fluid flow. Hydrodynamic models for the prediction of sand production involve sanding criteria based on filtration theories. Such models contain a constitutive model parameter, the coefficient λ, with dimensions of inverse length which is calibrated by sand erosion tests, but its nature and its dependencies have not been clarified to date. The aim of this work is an attempt to refine the hydrodynamic models by investigating the dependence of the sand production coefficient λ on the external stress conditions and on the plastic zone Λ that is developed on hollow cylinders tests and propose an expression describing its importance in the sand production prediction modelling. The aim of the work is obtained through simulations with finite elements by utilizing the well-established Arbitrary Lagrangian-Eulerian (ALE) analysis considering the poro-mechanical coupling of the fluid-solid system for simulating hollow cylinder tests. Best fitting experimental data estimated values for the sand production coefficient for various values of external stress are obtained through back analysis. The dependence of λ on the external stress turns out to be fairly smooth and a three-parameter model is proposed to describe that dependence: a scale parameter, an exponent, and a stress parameter defining the magnitude of stress at which erosion onset is predicted. It turns out that the stress parameter is associated with the minimum stress required for plastic yielding to occur, which was also estimated theoretically. This finding is in agreement with the physical assumption underlying the simulations that erosion onsets and progresses after the material reaches a critical plastic strain as a consequence of material plastic yielding. A power law model describing the dependence of λ on the plastic zone depth is also proposed and discussed.