0 Solute Transport With Chemical Reaction in Single-and Multi-Phase Flow in Porous Media

Transport phenomena in porous media describe the motion of fluids in media of porous structure which may be accompanied by heat/mass transfer and/or chemical reactions. While transport phenomena in fluid continua have been, to a large extent, very much comprehended, the subject matters in porous media are still under careful investigation and extensive research. Several reasons may be invoked to explain the difficulties associated with the study of transport phenomena in porous media. Probably the most obvious one is the fact that fluids move in porous media in complex, tortuous, and random passages that are even unknown a priori. Consequently, the governing laws may not be solved in any sense for the apparent difficulties in defining flow boundaries. Further complexities may be added should there exists heat transfer mechanisms associated with the flow and the interactions of heat transfer between the moving fluid and the solid matrix. Moreover, chemical reactions describe essential feature of transport in porous media. It is hardly to find transport processes in porous media without chemical reaction of some sort or another. Chemical reactions in porous media can occur naturally as a result of the interactions between the moving fluid and the surface of the solid matrix. These kinds of chemical reactions, which are usually slow, are pertinent to groundwater geochemistry, or it can be made to occur by utilizing the porous media surfaces to catalyze chemical reactions between reacting fluids. The study of these complex processes in porous media necessitate complete information about the internal structure of the porous media, which is far beyond the reach of our nowadays capacities. A fundamental question, thus, arises, in what framework do we need to cast the study of transport in porous media? In other words, do we really need to get such complete, comprehensive information about a given porous medium in order to gain useful information that could help us in our engineering applications? Do we really need to know the field variables distribution at each single point in the porous medium in order to be able to predict the evolution of this system with time, for example? Is it possible to make precise measurements within the porous media for field variables? And, even if we might be able to gain such detailed information, are we going to use them in their primitive forms for further analysis and development? The answer to these kind of questions may be that, for the sake of engineering applications, we do not need such a complete, comprehensive details, neither will we be able to obtain them nor will they 2

[1]  Abbas Firoozabadi,et al.  Control-Volume Model for Simulation of Water Injection in Fractured Media: Incorporating Matrix Heterogeneity and Reservoir Wettability Effects , 2007 .

[2]  M. Wheeler,et al.  Discontinuous Galerkin methods for coupled flow and reactive transport problems , 2005 .

[3]  P. Cheng,et al.  Heat Transfer in Geothermal Systems , 1979 .

[4]  P. Cheng,et al.  Thermal dispersion effects in non-Darcian convective flows in a saturated porous medium , 1981 .

[5]  H. L. Stone.  Estimation of Three-Phase Relative Permeability And Residual Oil Data , 1973 .

[6]  E. C. Childs.  Dynamics of fluids in Porous Media , 1973 .

[7]  Hussein Hoteit,et al.  Compositional Modeling by the Combined Discontinuous Galerkin and Mixed Methods , 2004 .

[8]  Hussein Hoteit,et al.  Multicomponent fluid flow by discontinuous Galerkin and mixed methods in unfractured and fractured media , 2005 .

[9]  B. Rivière,et al.  A Combined Mixed Finite Element and Discontinuous Galerkin Method for Miscible Displacement Problem in Porous Media , 2002 .

[10]  L. Young,et al.  A Generalized Compositional Approach for Reservoir Simulation , 1983 .

[11]  V. Starikovicius,et al.  The multiphase flow and heat transfer in porous media , 2003 .

[12]  Mary F. Wheeler,et al.  Symmetric and Nonsymmetric Discontinuous Galerkin Methods for Reactive Transport in Porous Media , 2005, SIAM J. Numer. Anal..

[13]  R. H. Brooks,et al.  Hydraulic properties of porous media , 1963 .

[14]  A. Salama,et al.  Effects of Chemical Reaction and Double Dispersion on Non-Darcy Free Convection Heat and Mass Transfer , 2008 .

[15]  P. S. Datti,et al.  Diffusion of chemically reactive species of a non-Newtonian fluid immersed in a porous medium over a stretching sheet , 2003 .

[16]  J. S. Nolen,et al.  Numerical Simulation Of Compositional Phenomena In Petroleum Reservoirs , 1973 .

[17]  William G. Gray,et al.  General conservation equations for multi-phase systems: 3. Constitutive theory for porous media flow. , 1980 .

[18]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[19]  Amgad Salama,et al.  Flow and Solute Transport in Saturated Porous Media: 1. The Continuum Hypothesis , 2008 .

[20]  Mohamed Fathy El-Amin,et al.  Double dispersion effects on natural convection heat and mass transfer in non-Darcy porous medium , 2004, Appl. Math. Comput..

[21]  C. L. Tien,et al.  Analysis of thermal dispersion effect on vertical-plate natural convection in porous media , 1987 .

[22]  M. Rahman,et al.  SIMILARITY ANALYSIS FOR NATURAL CONVECTION FROM A VERTICAL PLATE WITH DISTRIBUTED WALL CONCENTRATION , 2000 .

[23]  Kent S. Udell,et al.  Heat transfer in porous media considering phase change and capillarity—the heat pipe effect , 1985 .

[24]  E. Elbashbeshy.  Heat and mass transfer along a vertical plate with variable surface tension and concentration in the presence of the magnetic field , 1997 .

[25]  H. L. Stone.  Probability Model for Estimating Three-Phase Relative Permeability , 1970 .

[26]  Amgad Salama,et al.  Flow and solute transport in saturated porous media: 2. Violating the continuum hypothesis , 2008 .

[27]  Karsten Pruess,et al.  A semianalytical solution for heat-pipe effects near high-level nuclear waste packages buried in partially saturated geological media , 1988 .

[28]  William G. Gray,et al.  General conservation equations for multi-phase systems: 2. Mass, momenta, energy, and entropy equations , 1979 .

[29]  S. Matthäi.  Reservoir Simulation: Mathematical Techniques in Oil Recovery , 2008 .

[30]  O. V. Trevisan,et al.  Dispersion in heat and mass transfer natural convection along vertical boundaries in porous media , 1993 .

[31]  S. Whitaker.  Diffusion and dispersion in porous media , 1967 .

[32]  Abbas Firoozabadi,et al.  Implementation of higher-order methods for robust and efficient compositional simulation , 2010, J. Comput. Phys..

[33]  D. Dhir,et al.  BOILING AND TWO-PHASE FLOW IN POROUS MEDIA , 1994 .

[34]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[35]  M. Wheeler.  An Elliptic Collocation-Finite Element Method with Interior Penalties , 1978 .

[36]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[37]  Mary F. Wheeler,et al.  Analysis of Discontinuous Galerkin Methods for Multicomponent Reactive Transport Problems , 2006, Comput. Math. Appl..

[38]  William G. Gray,et al.  General conservation equations for multi-phase systems: 1. Averaging procedure , 1979 .

[39]  D. Peng,et al.  A New Two-Constant Equation of State , 1976 .

[40]  S. Whitaker.  Simultaneous Heat, Mass, and Momentum Transfer in Porous Media: A Theory of Drying , 1977 .