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Analytical and Experimental Modeling of Internal Erosion in Porous Media Open Access


Other title
Internal Erosion
Analytical Modeling
Experimental Modeling
Type of item
Degree grantor
University of Alberta
Author or creator
Azadbakht, Saman
Supervisor and department
Dr. Alireza Nouri (Department of Civil and Environmental Engineering)
Dr. Dave Chan (Department of Civil and Environmental Engineering)
Examining committee member and department
Dr. Douglas Schmitt (Department of Physics)
Dr. Lijun Deng (Department of Civil and Environmental Engineering)
Dr. Huazhou Li (Department of Civil and Environmental Engineering)
Dr. Farshid Torabi (Department of Petroleum System Engineering, University of Regina)
Department of Civil and Environmental Engineering
Petroleum Engineering
Date accepted
Graduation date
Doctor of Philosophy
Degree level
Constitutive law is a key component in the development of numerical models to simulate erosion of solid particles in a porous medium. In combination with the principle of conservation of mass, these models allow the estimation of internal erosion rate as a function of various parameters such as fluid velocity and time. This research aims at enhancing the existing constitutive laws describing the internal erosion phenomenon. Using the principles of dimensional analysis, we developed a mathematical relation between the internal erosion rate, fluid velocity and a proportionality constant called erosion coefficient. An equation is derived which indicates that the erosion coefficient is a function of grain density, particle Reynolds number and porosity variation during the erosion. Results of a series of erosion experiments were used to calibrate and validate the proposed constitutive law. The model is able to explain decreasing erosion rate over time. Further, the comparison between experimental data and analytical predictions show that the proposed model is able to predict the experimental results with reasonable accuracy. An experimental apparatus was designed and set up to perform a series of internal erosion tests on unconsolidated sand packs with different grain size distributions (GSD). The tests were conducted at different hydraulic gradients. During the testing, inflow pressure, fluid flow rate and turbidity of outflow stream were monitored and recorded. In this way, the mass of eroded particles was estimated as a function of time for different GSD’s. Based on the observations from the experimental results, we developed another constitutive law to model internal erosion as an exponential decay process. This model is an enhancement to the model that we developed using dimensional analysis technique. The proposed constitutive law was calibrated using the test results we gathered in our experimental program and some experimental data that we obtained from the literature. The results of this analysis show that internal erosion is, indeed, an exponential decay phenomenon. This erosion constitutive model has two calibration parameters, namely, final value of porosity, φ_f, and decay coefficient, λ. We developed, using dimensional analysis technique, relationships to predict φ_f and λ using material and test parameters. The proposed relationships were calibrated and validated using experimental data and the validation results show that the proposed relationships can predict final porosity and decay coefficient with reasonable accuracy.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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