Abstract
A mathematical model of sand erosion in axial flow conditions is presented. The basic mass balance equations and sand erosion constitutive equation were given in Vardoulakis et al. (1996). As opposed to reference Vardoulakis et al. (1996), we consider here the extreme case where convection is null and hydrodynamic dispersion dominates. In addition, Brinkman's extension of Darcy's law is adopted to account for a smooth transition between channel flow and Darcian flow. The set of governing PDE's is presented in dimensionless form and is solved numerically. In concordance with the basic constitutive equation for erosion kinetics, the analysis shows that erosion progresses in time as a ‘front’ of high transport concentration. This result is justified by the highly non-linear character of the erosion source term which dominates in the diffusion-like governing equation.
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References
Bear J.: Dynamics of Fluids in Porous Media, Dover, New York, 1972.
Brinkman, H. C.: A calculation of the viscous force exterted by a flowing fluid on a dense swarm of particles, Appl. Sci. Res Al. 27-34 (1947).
Cook J. M., Bradford I. D. R and Plumb R. A.: A study of the physical mechanisms of sanding and application to sand production prediction, European Petrol. Conf., London, SPE 28852, 1994, pp.473-480.
Einstein, H. A.: Der Geschiebetrieb als wahrschein-lichkeits Problem, Mitt. d. Versuchsanstalt f. Wasserbau, Eidg. T. H., Zurich, 1937.
Neale, G. and Nader W.: Practical significance of Brinkman's extension of Darcy's Law: coupled parallel flows within a channel and a bounding porous medium, Canadian J. Chem. Eng. 52 (1974).
Papamichos, E., Vardoulakis. I. and Ouadfel, H.: Permeability reduction due to grain crushing around a perforation, J. Rock. Mech. Min. Sci. 30 (1993), 1223-1229.
Stavropoulou, M., Papanastasiou, P. and Vardoulakis, I.: Coupled wellbore erosion and stability analysis, Int. J. Num. Anal. Meth. Geomech. 22 (1998), 749-769.
Scheurmann, A., Vardoulakis, I., Papanastasiou, P. and Stavropoulou, M.: A sand erosion problem in axial flow conditions on the example of contact erosion due to horizontal groundwater flow, IUTAM Symp. on porous materials,Stuttgart, Elsevier (in print), 1999.
Sakthivadivel, R. and Irmay S.: A Review of Filtration Theories, HEL 15-4, University of California, Berkeley, 1966.
Tronvoll, J., Skjaerstein, A. and Papamichos, E.: Sand production: mechanical failure or hydrodynamic erosion, Int. J. Rock Mech. Min. Sci. 34(3/4) (1997), 465.
Vardoulakis, I., Stavropoulou, M. and Papanastasiou, P.: Hydro-mechanical aspects of the sand production problem, Transport in Porous Media 22 (1996), 225-244.
Walton, I. C.: Optimum underbalance for the removal of perforation damage, SPE Ann. Tech. Conf. Exhib., Dallas, TX, SPE 63108, 2000.
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Vardoulakis, I., Papanastasiou, P. & Stavropoulou, M. Sand Erosion in Axial Flow Conditions. Transport in Porous Media 45, 267–280 (2001). https://doi.org/10.1023/A:1012035031463
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DOI: https://doi.org/10.1023/A:1012035031463