A hydro-mechanical semi-analytical framework for hollow cylinder sanding tests

Abstract

In this work we propose a novel semi-analytical hydro-mechanical framework for modeling sand production in the context of the hollow cylinder test, based on a kinematic formulation of the hydro-mechanical models of Vardoulakis et al. (1996) and Papamichos et al. (2001). We aim at the construction of a simple and useful tool which allows for quick estimates of the relevant quantities and can be efficiently used to study different forms of the postulated laws regarding the mechanics, hydrodynamics and degradation of the rock. In particular, this framework can be used to systematically calibrate the sand production coefficient λ as a function of the external conditions of the experiment, such as the external stress, which still is a major unknown in the hydro-mechanical modeling of the erosion process. As a first approximation we restrict ourselves to the case where pressure drawdown is small compared to the external stress, which is applicable in certain laboratory experiments. We illustrate the application of the framework by studying the effect of different forms of the hydrodynamic law, modified in the low porosity regime and the degradation law with respect to the non-linear dependence of cohesion and friction angle on the porosity. We use this framework to calibrate the dependence of λ on the external stress using the data of the experiment of Papamichos at al. (2001). We find that the sand production coefficient exhibits a power law modified by a decreasing exponential dependence as has been suggested in a recent work by the authors. The model is also applied in a different sanding experiment with varying external stress and flow rate exhibiting good agreement with the laboratory dataset.