Some Mathematical and Computational Problems in Reactive Flow

We present an overview of several applications of reactive flow and transport in which interesting mathematical issues and computational challenges arise. The topics include front propagation through porous media in the presence of dispersion; numerical simulation of large-scale reactive transport problems; the reliability of processes that involve in-situ generation of viscosifying agents; methods for describing pore-scale geometry in granular media; and the information content of reactive tracer experiments. The intent of this survey is to heighten awareness of underlying mathmetical aspects and, it is hoped, to stimulate new contributions in these areas.

[1]  Bryant,et al.  Prediction of relative permeability in simple porous media. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[2]  S. Bryant,et al.  Quantification of Spatial Correlation in Porous Media and Its Effect on Mercury Porosimetry. , 1996, Journal of colloid and interface science.

[3]  Predicting formation factor and resistivity index in simple sandstones , 1996 .

[4]  Mary F. Wheeler,et al.  Efficient Parallel Computation Of SpatiallyHeterogeneous Geochemical Reactive Transport , 1998 .

[5]  J. A. Kittrick,et al.  Retention of neptunium, americium, and curium by diffusible soil particles , 1979 .

[6]  Sujoy B. Roy,et al.  Chemical factors influencing colloid-facilitated transport of contaminants in porous media , 1997 .

[7]  A. Page,et al.  Mobilization of colloids in groundwater due to infiltration of water at a coal ash disposal site. , 1990 .

[8]  J. S. Tang.  Partitioning tracers and in-situ fluid-saturation measurements , 1995 .

[9]  Richard Courant,et al.  Supersonic Flow And Shock Waves , 1948 .

[10]  P. Lax.  Hyperbolic systems of conservation laws II , 1957 .

[11]  Stig Bakke,et al.  Extending Predictive Capabilities to Network Models , 1998 .

[12]  S. Bryant,et al.  Prediction of elastic-wave velocities in sandstones using structural models , 1995 .

[13]  D. McKinney,et al.  Difluoromethane as Partitioning Tracer to Estimate Vadose Water Saturations , 1999 .

[14]  H. Scott Fogler,et al.  Influence of Transport and Reaction on Wormhole Formation in Porous Media , 1998 .

[15]  G. Whitham,et al.  Linear and Nonlinear Waves , 1976 .

[16]  G. Pope,et al.  Characterization of a TCE DNAPL Zone in Alluvium by Partitioning Tracers , 1999 .

[17]  M. Corapcioglu,et al.  The role of silica colloids on facilitated cesium transport through glass bead columns and modeling , 1998 .

[18]  D. McKinney,et al.  Contaminated Vadose Zone Characterization Using Partitioning Gas Tracers , 1999 .

[19]  G. Daccord,et al.  Fractal patterns from chemical dissolution , 1987, Nature.

[20]  P. Gschwend,et al.  Monodisperse ferrous phosphate colloids in an anoxic groundwater plume , 1987 .

[21]  S. Bakke,et al.  3-D Pore-Scale Modelling of Sandstones and Flow Simulations in the Pore Networks , 1997 .

[22]  M. Borkovec,et al.  Convective transport of acids and bases in porous media , 1994 .

[23]  J. Saunders,et al.  Modeling of radionuclide and heavy metal sorption around low- and high- pH waste disposal sites at Oak Ridge, Tennessee , 1995 .

[24]  Gary A. Pope,et al.  Analysis of Partitioning Interwell Tracer Tests , 1999 .

[25]  D. Mellor,et al.  Analysis of the Percolation properties of a Real Porous Material , 1991 .

[26]  Akhil Datta-Gupta,et al.  On the Sensitivity and Spatial Resolution of Transient Pressure and Tracer Data For Heterogeneity Characterization , 1997 .

[27]  Gary A. Pope,et al.  Anionic surfactant remediation of soil columns contaminated by nonaqueous phase liquids , 1999 .

[28]  David Mautner Himmelblau,et al.  Process Analysis and Simulation. Deterministic Systems , 1968 .

[29]  Gérard Daccord.  Chemical dissolution of a porous medium by a reactive fluid. , 1987 .

[30]  A. Suzuki,et al.  Fast Transport of Colloidal Particles through Quartz-Packed Columns , 1993 .

[31]  N. Amundson,et al.  A study of the shock layer in nonequilibrium exchange systems , 1971 .

[32]  D. K. Smith,et al.  Migration of plutonium in ground water at the Nevada Test Site , 1999, Nature.

[33]  J. L. Finney,et al.  Random packings and the structure of simple liquids. I. The geometry of random close packing , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[34]  M. Wheeler,et al.  A Two‐Tiered Approach to Reactive Transport: Application to Sr Mobility Under Variable pH , 1998 .

[35]  James Glimm,et al.  The interaction of nonlinear hyperbolic waves , 1988 .

[36]  Andrea Saltelli,et al.  Americium Filtration in Glauconitic Sand Columns , 1984 .

[37]  L. Filippov.  Coherent and incoherent frontal patterns for multicomponent adsorption dynamics—II. Non-uniqueness of frontal patterns in the isothermal case for convex isotherms of two-component mixtures , 1992 .

[38]  D. Devault.  The Theory of Chromatography , 1943 .

[39]  J. Glimm.  Solutions in the large for nonlinear hyperbolic systems of equations , 1965 .

[40]  Kamy Sepehrnoori,et al.  Analysis of field tracers for reservoir description , 1991 .

[41]  James R. Hunt,et al.  Transport of colloidal contaminants in groundwater : radionuclide migration at the Nevada Test Site , 1988 .

[42]  J. McCarthy.  Colloid-facilitated transport of contaminants in groundwater: mobilization of transuranic radionuclides from disposal trenches by natural organic matter , 1998 .

[43]  N. Amundson,et al.  On the theory of multicomponent chromatography , 1970, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[44]  M. Brusseau,et al.  Solubilization and removal of residual trichloroethene from porous media: comparison of several solubilization agents , 2000 .

[45]  Gary A. Pope,et al.  Laboratory characterization of non-aqueous phase liquid/tracer interaction in support of a vadose zone partitioning interwell tracer test , 2000 .

[46]  Gary A. Pope,et al.  New Approach for Estimating Alcohol Partition Coefficients between Nonaqueous Phase Liquids and Water , 1998 .

[47]  B. Logan,et al.  Facilitation of bacterial transport through porous media by changes in solution and surface properties , 1996 .

[48]  G. Eichholz,et al.  The movement of radioactive sodium and ruthenium through a simulated aquifer , 1968 .

[49]  Mary F. Wheeler,et al.  Simulation of miscible viscous fingering using a modified method of characteristics: effects of gravity and heterogeneity , 1989 .

[50]  L. Lake,et al.  Enhanced Oil Recovery , 2017 .

[51]  P. Lax.  Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves , 1987 .

[52]  William R. Penrose,et al.  Mobility of plutonium and americium through a shallow aquifer in a semiarid region , 1990 .

[53]  A. Hill,et al.  A mechanistic model of wormhole growth in carbonate matrix acidizing and acid fracturing , 1989 .

[54]  Gary A. Pope,et al.  Development of Partitioning Tracer Tests for Characterization of Nonaqueous-Phase Liquid-Contaminated Aquifers , 1997 .

[55]  Theory of multicomponent chromatography a state-of-the-art report , 1986 .

[56]  Matthias Kohler,et al.  Experimental Investigation and Modeling of Uranium (VI) Transport Under Variable Chemical Conditions , 1996 .

[57]  Fredrik Edvard Saaf.  A study of reactive transport phenomena in porous media , 1997 .

[58]  Tai-Ping Liu,et al.  Nonlinear Stability of Shock Waves for Viscous Conservation Laws , 1985 .

[59]  A. Hill,et al.  Modeling of the Acidizing Process in Naturally Fractured Carbonates , 2002 .

[60]  Steven L. Bryant,et al.  Physically representative network models of transport in porous media , 1993 .

[61]  H. S. Fogler,et al.  Pore evolution and channel formation during flow and reaction in porous media , 1988 .

[62]  Kamy Sepehrnoori,et al.  Partitioning Tracer Test for Detection, Estimation, and Remediation Performance Assessment of Subsurface Nonaqueous Phase Liquids , 1995 .

[63]  B. Kueper,et al.  Manipulation of density and viscosity for the optimization of DNAPL recovery by alcohol flooding , 1999 .

[64]  Craig Taylor,et al.  A Controlled Field Test of Surfactant‐Enhanced Aquifer Remediation , 1996 .

[65]  Dispersion-Induced Chromatographic Waves , 2000 .

[66]  Zhouping Xin,et al.  Nonlinear stability of viscous shock waves , 1993 .

[67]  F. Helfferich.  MULTICOMPONENT WAVE PROPAGATION: ATTAINMENT OF COHERENCE FROM ARBITRARY STARTING CONDITIONS† , 1986 .

[68]  R. S. Schechter,et al.  The change in pore size distribution from surface reactions in porous media , 1969 .