Solution of Liquid–Gas–Solid Coupled Equations for Porous Media Considering Dynamics and Hysteretic Retention Behavior
Publication: Journal of Engineering Mechanics
Volume 143, Issue 6
Abstract
This paper presents a solution procedure based on the finite element method for the three-constituent coupled problem representing the behavior of unsaturated porous media. A formulation is derived from the theory of porous media considering the dynamic behavior, the balance of momenta of porous liquid, porous gas, and solid porous matrix. The hysteresis of the liquid retention behavior is also modeled. A retention model able to smoothly represent the transition from maximum saturation to partially saturated states, and vice versa, is considered. With these features, the resulting system of equations is fairly complex; however an efficient, stable, and accurate numerical method is developed for its solution. The derivation of consistent tangent operators of first and second order to obtain quadratic convergence is presented in addition to all details to properly implement the numerical solver, e.g., consistent treatment of initial conditions. Finally, a number of numerical experiments are studied in order to illustrate the model capabilities in particular with regard to the influence of gas pressure on the unsaturated porous media behavior.
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Acknowledgments
The support of the Australian Research Council under grant DE120100163 is gratefully appreciated. The anonymous reviewers are also thanked for their suggestions.
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 6 • June 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jan 3, 2016
Accepted: Oct 4, 2016
Published online: Feb 14, 2017
Published in print: Jun 1, 2017
Discussion open until: Jul 14, 2017
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