A hydro-mechanical semi-analytical framework for hollow cylinder sanding tests
Journal
Geomechanics for Energy and the Environment
Date Issued
July 13, 2023
DOI
10.1016/j.gete.2023.100487
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.
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.
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