Numerical Analysis Of Multiphase Flows In Porous Media On Non Rectangular Geometry
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Numerical Analysis of Multiphase Flows in Porous Media on Non-rectangular Geometry
Fluid flow through porous media is a subject of common interest in many branches of engineering as well as applied natural science. In this work, we investigate the behavior and numerical treatment of multiphase flow in porous media. To be more specific, we take the sequestration of CO2 in geological media as an example. Mathematical modeling and numerical study of carbon sequestration helps to predict both short and long-term behavior of CO2 storage in geological media, which can be a benefit in many ways. This work aims at developing accurate and efficient numerical treatment for problems in porous media on non-rectangular geometries. Numerical treatment of Darcy flow and transport have been developed for many years on rectangular and simplical meshes. However, extra effort is required to extend them to general non-rectangular meshes. In this dissertation work, for flow simulation, we develop new H(div)- conforming mixed finite elements (AT and AT [superscript red] ) which are accurate on cuboidal hexahedra. We also develop the new direct serendipity finite element (DS [subscript r] ), which is H1 -conforming and accurate on quadrilaterals and a special family of hexahedra called truncated cubes. The use of the direct serendipity finite element reduces the number of degrees of freedom significantly and therefore accelerates numerical simulations. For transport, we use the newly developed direct serendipity elements in an enriched Galerkin method (EG), which is locally conservative. The entropy viscosity stabilization is applied to eliminate spurious oscillations. We test the EG-DS [subscript r] method on problems with diffusion, transport, and coupled flow and transport. Finally, we study two-phase flow in heterogeneous porous media with capillary pressure. We work on a new formulation of the problem and force the continuity of the capillary flux with a modification to conquer the degeneracy. The numerical simulation of two-phase flow is conducted on non-rectangular grids and uses the new elements.
Computational Methods in Multiphase Flow V
Together with turbulence, multiphase flow remains one of the most challenging areas of computational mechanics and experimental methods and numerous problems remain unsolved to date. Multiphase flows are found in all areas of technology, at all length scales and flow regimes. The fluids involved can be compressible or incompressible, linear or nonlinear. Because of the complexity of the problems, it is often essential to utilize advanced computational and experimental methods to solve the complex equations that describe them. Challenges in these simulations include modelling and tracking interfaces, dealing with multiple length scales, modelling nonlinear fluids, treating drop breakup and coalescence, characterizing phase structures, and many others. Experimental techniques, although expensive and difficult to perform, are essential to validate models. This book contains papers presented at the Fifth International Conference on Computational Methods in Multiphase Flow, which are grouped into the following topics: Multiphase Flow Simulation; Interaction of Gas, Liquids and Solids; Turbulent Flow; Environmental Multiphase Flow; Bubble and Drop Dynamics; Flow in Porous Media; Heat Transfer; Image Processing; Interfacial Behaviour.
Mathematical Modelling Of Flow Through Porous Media - Proceedings Of The Conference
This proceedings volume contains contributions from leading scientists working on modelling and numerical simulation of flows through porous media and on mathematical analysis of the equations associated to the modelling. There is a number of contributions on rigorous results for stochastic media and for applications to numerical simulations. Modelling and simulation of environment and pollution are also subject of several papers. The published material herein gives an insight to the state of the art in the field with special attention for rigorous discussions and results.