Statistical and continuum models of fluid-solid reactions in porous media

In this review, we discuss past theoretical works on fluid-solid reactions in a porous medium. Such reactions are often accompanied by a continuous alteration of the pore structure of the medium, and at high conversions they exhibit percolation-type behavior, i.e. the solid matrix of the medium and/or the fluid phase lose their macroscopic connectivity. These phenomena are, therefore, characterized by a percolation threshold which is the volume or area fraction of a phase (solid or fluid) below which that phase exists only in isolated clusters or islands. Important classes of such processes are acid dissolution of a porous medium and gas—solid reactions with pore volume growth, e.g. coal gasification, and with pore closure, e.g. lime sulfation, and catalyst deactivation. These processes are characterized by continuous changes in the pore space as a result of a chemical reaction. We also consider here other processes such as the flow of fines, stable emulsions and solid particles in a porous medium which also alter the structure of the pore space, but by physical interaction of the particles and the solid surface of the pores. In this review we compare two different modelling approaches to reactions accompanied by structural changes. First we review the continuum approach, which is based on the classical equations of transport and reaction supplemented with constitutive equations describing the effect of structural changes on reaction and transport parameters. We then outline the relevant concepts, ideas and techniques of percolation theory and the statistical physics of disordered media, and review their application to the phenomena mentioned above. In particular, we emphasize the fundamental role of connectivity of the porous medium in such phenomena. Since in both approaches one needs to estimate the effective transport properties of the porous medium that is undergoing continuous change, we also review continuum and statistical methods of estimating the effective transport properties of disordered porous media.

[1]  W. Brandt.  Use of percolation theory to estimate effective diffusion coefficients of particles migrating on various ordered lattices and in a random network structure , 1975 .

[2]  N. Amundson,et al.  Modelling of the Combustion of Single Char Particles , 1984 .

[3]  D. Nicholson,et al.  Capillary models for porous media. VII. Study of gaseous flow in the transition from the Knudsen to the counter-diffusion regimes , 1977 .

[4]  Neal R. Amundson,et al.  Studies on the gasification of a single char particle , 1982 .

[5]  M. Sahimi,et al.  Transport and conduction in random systems , 1984 .

[6]  Kyriacos Zygourakis,et al.  Evolution of pore structure during gas-solid reactions: Discrete models , 1986 .

[7]  Harold L. Weissberg,et al.  Effective Diffusion Coefficient in Porous Media , 1963 .

[8]  N. Mungan.  Permeability Reduction Due to Salinity Changes , 1968 .

[9]  C. Anderson,et al.  Critical Behavior of the Two-Dimensional Sticks System , 1983 .

[10]  Alan R. Kerstein,et al.  Critical Properties of the Void Percolation Problem for Spheres , 1984 .

[11]  W. Strieder,et al.  Effective-medium theory of the conductivity for a random-site honeycomb lattice , 1979 .

[12]  A. F. Sarofim,et al.  Fragmentation behavior of single coal particles in a fluidized bed , 1985 .

[13]  Touboul,et al.  Three-dimensional fractals: Experimental measurements using capillary effects. , 1987, Physical review. A, General physics.

[14]  H. S. Fogler,et al.  On the movement of multiple reaction zones in porous media , 1980 .

[15]  C. Satterfield,et al.  Gaseous Diffusion and Flow in Commercial Catalysts at Pressure Levels above Atmospheric , 1968 .

[16]  D. Harrison,et al.  The grain model applied to porous solids with varying structural properties , 1979 .

[17]  Julio M. Ottino,et al.  Effective transport properties of disordered, multi-phase composites: Application of real-space renormalization group theory , 1986 .

[18]  M. Sahimi.  Diffusion-controlled reactions in disordered porous media—I. Uniform distribution of reactants , 1988 .

[19]  M. Sahimi,et al.  Statistical modeling of gas-solid reaction with pore volume growth: kinetic regime , 1988 .

[20]  R. Stinchcombe.  Conductivity and spin-wave stiffness in disordered systems-an exactly soluble model , 1974 .

[21]  Stephen Whitaker,et al.  Dispersion in pulsed systems—II: Theoretical developments for passive dispersion in porous media , 1983 .

[22]  M. Thorpe,et al.  Elastic moduli of two‐dimensional composite continua with elliptical inclusions , 1985 .

[23]  R. Mann,et al.  Fouling and deactivation of a FCC catalyst.: I. A wedge-layering analysis of the influence of catalyst particle size, LHSV and temperature , 1982 .

[24]  P. L. Silveston,et al.  Gasification: Part I. Isothermal, kinetic control model for a solid with a pore size distribution , 1973 .

[25]  Schwartz,et al.  Transport properties of disordered continuum systems. , 1989, Physical review. B, Condensed matter.

[26]  Thorpe,et al.  Percolation properties of random ellipses. , 1988, Physical review. A, General physics.

[27]  L. L. Handy,et al.  Flow of Clay Suspensions Through Porous Media , 1989 .

[28]  Tomihisa Iwasaki,et al.  Some Notes on Sand Filtration , 1937 .

[29]  G. Froment,et al.  Rigorous kinetic models for catalyst deactivation by coke deposition: Application to butene dehydrogenation , 1986 .

[30]  Julio M. Ottino,et al.  Reaction and transport in disordered composite media: Introduction of percolation concepts , 1982 .

[31]  Peter Pfeifer,et al.  Surface geometric irregularity of particulate materials: the fractal approach , 1985 .

[32]  W. Ranz,et al.  A lamellar model for analysis of liquid-liquid mixing , 1979 .

[33]  R. E. Collins,et al.  Entrainment and Deposition of Fine Particles in Porous Media , 1982 .

[34]  M. Abbasi,et al.  A Monte Carlo simulation of the diffusion of gases in porous solids , 1980 .

[35]  Feng,et al.  Differences between lattice and continuum percolation transport exponents. , 1985, Physical review letters.

[36]  E. Cussler,et al.  Dissolution and reprecipitation in model systems of porous hydroxyapatite , 1987 .

[37]  P. M. Richards.  Theory of one-dimensional hopping conductivity and diffusion , 1977 .

[38]  A. Katz,et al.  Prediction of rock electrical conductivity from mercury injection measurements , 1987 .

[39]  H. S. Fogler,et al.  Acidization—V: The prediction of the movement of acid and permeability fronts in sandstone , 1976 .

[40]  E. Cussler,et al.  The effect of pore diffusion on the dissolution of porous mixtures , 1983 .

[41]  J. Straley,et al.  Distribution-induced non-universality of the percolation conductivity exponents , 1979 .

[42]  Gilbert F. Froment,et al.  Dehydrogenation of 1-Butene into Butadiene. Kinetics, Catalyst Coking, and Reactor Design , 1976 .

[43]  J. Sherwood.  Stability of a plane reaction front in a porous medium , 1987 .

[44]  Marvin F. L. Johnson.  Pore structure and gaseous diffusion in solid catalysts , 1965 .

[45]  J. G. Zabolitzky.  Monte Carlo evidence against the Alexander-Orbach conjecture for percolation conductivity , 1984 .

[46]  L. Paterson,et al.  Diffusion-Limited Aggregation and Two-Fluid Displacements in Porous Media , 1984 .

[47]  Larry W. Lake,et al.  Diffusion and solid dissolution/precipitation in permeable media , 1989 .

[48]  G. A. Gabriel,et al.  An experimental investigation of fines migration in porous media , 1983 .

[49]  G. Gavalas,et al.  Periodic capillary models of diffusion in porous solids , 1981 .

[50]  A. Kerstein,et al.  Fragmentation during carbon conversion: Predictions and measurements , 1985 .

[51]  J. G. Zabolitzky,et al.  Re-examination of 3D percolation threshold estimates , 1986 .

[52]  Hsueh-Chia Chang,et al.  Effective diffusion in bi-disperse media—an effective medium approach , 1984 .

[53]  Walter H. Stockmayer,et al.  Theory of Molecular Size Distribution and Gel Formation in Branched‐Chain Polymers , 1943 .

[54]  H. Damme,et al.  A fractal analysis of adsorption processes by pillared swelling clays , 1985 .

[55]  M. Rink,et al.  COMPUTATIONS OF NETWORK MODELS OF POROUS MEDIA , 1968 .

[56]  A. Levi,et al.  Percolation theoretical treatment of two-dimensional fragmentation in solids , 1984 .

[57]  N. Amundson,et al.  Diffusion and reaction in a char particle and in the surrounding gas phase. Two limiting models , 1984 .

[58]  J. Smith,et al.  Tortuosity factors for diffusion in catalyst pellets , 1983 .

[59]  J. W. Essam,et al.  Some Cluster Size and Percolation Problems , 1961 .

[60]  R. Zwanzig,et al.  Series expansions in a continuum percolation problem , 1977 .

[61]  S. V. Sotirchos,et al.  Analysis of multicomponent diffusion in pore networks , 1988 .

[62]  Rolf Landauer,et al.  The Electrical Resistance of Binary Metallic Mixtures , 1952 .

[63]  Scott Kirkpatrick,et al.  Classical Transport in Disordered Media: Scaling and Effective-Medium Theories , 1971 .

[64]  D. Stroud.  Generalized effective-medium approach to the conductivity of an inhomogeneous material , 1975 .

[65]  L. E. Scriven,et al.  Percolation and conduction on the 3D Voronoi and regular networks: a second case study in topological disorder , 1984 .

[66]  T. Edgar,et al.  Identification of the combustion behaviour of lignite char between 350 and 900 °C , 1984 .

[67]  M. Fixman.  Absorption by static traps: Initial‐value and steady‐state problems , 1984 .

[68]  I. Fatt.  The Network Model of Porous Media , 1956 .

[69]  A Rigorous Formulation of the Effect of Coke Formation on Catalyst Activity , 1982 .

[70]  P. Sharratt,et al.  Deactivation of a supported zeolitic catalyst: diffusion, reaction and coke deposition in stochastic pore networks , 1986 .

[71]  C. H. Seager,et al.  Percolation and conductivity: A computer study. II , 1974 .

[72]  R. Lenormand,et al.  Particle accumulation at the surface of a filter , 1986 .

[73]  J. Bernasconi.  Real-space renormalization of bond-disordered conductance lattices , 1978 .

[74]  J. Ottino,et al.  Transport and reaction in evolving, disordered composites. II: Coke deposition in a catalytic pellet , 1987 .

[75]  G. M. Watson,et al.  Interdiffusion of Helium and Argon in a Large-Pore Graphite. , 1961 .

[76]  M. Hartman,et al.  Reaction of Sulfur Dioxide with Limestone and the Influence of Pore Structure , 1974 .

[77]  R. S. Schechter,et al.  Matrix Acidization with Highly Reactive Acids , 1971 .

[78]  Ludwig C. Nitsche,et al.  Eulerian kinematics of flow through spatially periodic models of porous media , 1989 .

[79]  G. Simons,et al.  The Structure of Coal Char: Part I—Pore Branching , 1979 .

[80]  Tamás Vicsek,et al.  Dynamic Scaling for Aggregation of Clusters , 1984 .

[81]  A. Maroudas,et al.  Clarification of suspensions: a study of particle deposition in granular media: Part I—Some observations on particle deposition , 1965 .

[82]  CORRIGENDUM: Effective medium theory of site percolation in a random simple triangular conductance network , 1978 .

[83]  Y. Yortsos,et al.  Fines migration in porous media , 1987 .

[84]  Muhammad Sahimi,et al.  Real-space renormalization and effective-medium approximation to the percolation conduction problem , 1983 .

[85]  G. Froment,et al.  Stochastic Modeling of Catalyst Deactivation by Site Coverage. , 1987 .

[86]  T. Edgar,et al.  Distributed pore‐size model for sulfation of limestone , 1983 .

[87]  Y. Yortsos,et al.  A network model for deep bed filtration processes , 1987 .

[88]  L. E. Scriven,et al.  Percolation theory of residual phases in porous media , 1977, Nature.

[89]  L. E. Scriven,et al.  Percolation and conductivity of random two-dimensional composites , 1981 .

[90]  C. Wen,et al.  Reactivity of Coal and Char. 2. In Oxygen-Nitrogen Atmosphere , 1977 .

[91]  M. Sahimi,et al.  Stochastic transport in disordered systems , 1983 .

[92]  Muhammad Sahimi,et al.  The effect of morphological disorder on hydrodynamic dispersion in flow through porous media , 1988 .

[93]  M. Hori,et al.  Theoretical approaches to inhomogeneous transport in disordered media , 1977 .

[94]  G. Froment,et al.  Catalyst deactivation by site coverage and pore blockage: Finite rate of growth of the carbonaceous deposit , 1980 .

[95]  Reaction with mole changes in porous catalysts in the molecular, transition, and Knudsen regimes , 1973 .

[96]  Warren E. Stewart,et al.  Collocation analysis of multicomponent diffusion and reactions in porous catalysts , 1982 .

[97]  S. Prager,et al.  Statistical thermodynamics of phase equilibria in microemulsions , 1978 .

[98]  Sahimi,et al.  Dynamic scaling for the fragmentation of reactive porous media. , 1987, Physical review letters.

[99]  Andreas Acrivos,et al.  The effective conductivity of a periodic array of spheres , 1983, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[100]  J. Blackman,et al.  On theories of transport in disordered media , 1979 .

[101]  J. Ottino,et al.  Transport and reaction in evolving, disordered composites-I. Gasification of porous solids , 1987 .

[102]  Muhammad Sahimi,et al.  Dispersion in flow through porous media—I. One-phase flow , 1986 .

[103]  P. Libby,et al.  Theoretical study of burning carbon particles , 1979 .

[104]  D. Nicholson,et al.  Capillary models for porous media. V. Flow properties of random networks with various radius distributions , 1975 .

[105]  J. Szekely,et al.  A changing grain size model for gas—solid reactions , 1979 .

[106]  Fractal dimension in a percolation model of fluid displacement. , 1985, Physical review letters.

[107]  Evaluation of Monte Carlo Methods in Studying Fluid–Fluid Displacements and Wettability in Porous Rocks , 1959 .

[108]  A. Kerstein,et al.  Numerical simulation of particle size distribution evolution during pulverized coal combustion , 1987 .

[109]  Mukul M. Sharma,et al.  Transport of particulate suspensions in porous media: Model formulation , 1987 .

[110]  Theoretical and experimental aspects of surface diffusion in porous catalysts: I. Nonreactive conditions , 1986 .

[111]  S. Bhatia.  Combined surface and pore volume diffusion in porous media , 1988 .

[112]  Schwartz,et al.  New pore-size parameter characterizing transport in porous media. , 1986, Physical review letters.

[113]  N. Amundson,et al.  Dynamic behavior of a porous char particle burning in an oxygen‐containing environment: Part I: Constant particle radius , 1984 .

[114]  Girard A. Simons,et al.  The Structure of Coal Char: Part II.— Pore Combination , 1979 .

[115]  S. V. Sotirchos,et al.  Mathematical modelling of gas-solid reactions with solid product , 1985 .

[116]  J. Szekely,et al.  A structural model for gas-solid reactions with a moving boundary-II: The effect of grain size, porosity and temperature on the reaction of porous pellets , 1971 .

[117]  Adrian E. Scheidegger,et al.  Statistical Hydrodynamics in Porous Media , 1954 .

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

[119]  John C. Wierman,et al.  Bond percolation on honeycomb and triangular lattices , 1981 .

[120]  Diffusive motion on a fractal; Gnm(t). , 1985, Physical review. A, General physics.

[121]  H. T. Davis,et al.  Transport Processes in Composite Media , 1975 .

[122]  Raoul Kopelman,et al.  Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm , 1976 .

[123]  David R. McKenzie,et al.  Transport properties of regular arrays of cylinders , 1979, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[124]  K. Zygourakis,et al.  Evolution of pore surface area during noncatalytic gas-solid reactions. 2. Experimental results and model validation , 1987 .

[125]  S. V. Sotirchos,et al.  Intraparticle diffusion and char combustion , 1986 .

[126]  A. Maroudas,et al.  CLARIFICATION OF SUSPENSIONS: A STUDY OF PARTICLE DEPOSITION IN GRANULAR MEDIA, PART 2: A THEORY OF CLARIFICATION , 1965 .

[127]  E. T. Gawlinski,et al.  Continuum percolation in two dimensions: Monte Carlo tests of scaling and universality for non-interacting discs , 1981 .

[128]  C. Radke,et al.  Flow mechanism of dilute, stable emulsions in porous media , 1984 .

[129]  A. Deb.  Theory of Sand Filtration , 1969 .

[130]  D. D. Perlmutter,et al.  The effect of pore structure on fluid‐solid reactions: Application to the SO2‐lime reaction , 1981 .

[131]  Muhammad Sahimi,et al.  DISPERSION IN DISORDERED POROUS MEDIA , 1983 .

[132]  E. Petersen.  Reaction of porous solids , 1957 .

[133]  Effective-medium approximation for density of states and the spectral dimension of percolation networks , 1984 .

[134]  Joel Koplik,et al.  Theory of dynamic permeability and tortuosity in fluid-saturated porous media , 1987, Journal of Fluid Mechanics.

[135]  S. V. Sotirchos.  On a class of random pore and grain models for gas-solid reactions , 1987 .

[136]  M. Loewenberg,et al.  A Simplified Description of Char Combustion , 1987 .

[137]  M. Sadakata,et al.  Formation of submicron unburnt carbon and NOx from pulverized coal combustion system , 1985 .

[138]  H. Kesten.  The critical probability of bond percolation on the square lattice equals 1/2 , 1980 .

[139]  G. M. Watson,et al.  Gaseous Diffusion in Porous Media at Uniform Pressure , 1961 .

[140]  D. Stauffer.  Scaling Theory of Percolation Clusters , 1979, Complex Media and Percolation Theory.

[141]  Peter C. Lichtner,et al.  Exact and numerical solutions to the moving boundary problem resulting from reversible heterogeneous reactions and aqueous diffusion in a porous medium , 1986 .

[142]  R. Mann,et al.  Deactivation of a supported zeolite catalyst: simulation of diffusion, reaction and coke deposition in a parallel bundle , 1987 .

[143]  D. D. Perlmutter,et al.  A random pore model for fluid‐solid reactions: II. Diffusion and transport effects , 1981 .

[144]  J. W. Essam,et al.  Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions , 1964 .

[145]  V. Weekman,et al.  Kinetics of catalytic cracking selectivity in fixed, moving, and fluid bed reactors , 1970 .

[146]  H. S. Fogler,et al.  The existence of a critical salt concentration for particle release , 1984 .

[147]  R. Mann,et al.  Catalyst deactivation by fouling: a wedge-layering analysis of the consecutive reaction , 1985 .

[148]  Tiİmur Doǧu.  The Importance of Pore Structure and Diffusion in the Kinetics of Gas-Solid Non-catalytic Reactions: Reaction of Calcined Limestone with SO2 , 1981 .

[149]  K. Ives,et al.  Removal mechanisms in deep bed filtration , 1969 .

[150]  N. Amundson,et al.  Diffusion and reaction in a char particle and in the surrounding gas phase. A continuous model , 1984 .

[151]  S. Torquato.  Thermal Conductivity of Disordered Heterogeneous Media from the Microstructure , 1987 .

[152]  B. Payandeh.  A block cluster approach to percolation , 1980 .

[153]  M. Sahimi.  ON THE DETERMINATION OF TRANSPORT PROPERTIES OF DISORDERED SYSTEMS , 1988 .

[154]  C. Y. Wen,et al.  Reactivity of Coal and Char. 1. In Carbon Dioxide Atmosphere , 1977 .

[155]  P. Saffman,et al.  A theory of dispersion in a porous medium , 1959, Journal of Fluid Mechanics.

[156]  A. Aharony.  Anomalous Diffusion on Percolating Clusters , 1983 .

[157]  G. Simons.  Char Gasification: Part I. Transport Model , 1979 .

[158]  R. Mann,et al.  Predicted influence of pore structure modifications for catalyst pellets deactivated by fouling , 1981 .

[159]  C. H. Bartholomew,et al.  Sulfur Poisoning of Metals , 1982 .

[160]  S. V. Sotirchos,et al.  A generalized pore model for gas‐solid reactions exhibiting pore closure , 1987 .

[161]  James W. Evans,et al.  A structural model for gas—solid reactions with a moving boundary , 1970 .

[162]  Peter Pfeifer,et al.  Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces , 1983 .

[163]  Muhammad Sahimi,et al.  On the improvement of the effective-medium approximation to the percolation conductivity problem , 1984 .

[164]  D. D. Perlmutter,et al.  A random pore model for fluid‐solid reactions: I. Isothermal, kinetic control , 1980 .

[165]  H. Brenner,et al.  Dispersion resulting from flow through spatially periodic porous media , 1980, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[166]  D. D. Perlmutter,et al.  Effect of the product layer on the kinetics of the CO2‐lime reaction , 1983 .

[167]  Morrel H. Cohen,et al.  Quantitative methods for microgeometric modeling , 1982 .

[168]  Chi Tien,et al.  Application of porous media models to the study of deep bed filtration , 1974 .

[169]  K. Jensen,et al.  Percolation concepts in modelling of gas-solid reactions-III. Application to sulphation of calcined limestone , 1987 .

[170]  Charles R. O'Melia,et al.  Water and waste water filtration. Concepts and applications , 1971 .

[171]  Deactivation of porous catalysts by coke formation , 1978 .

[172]  Vinay Ambegaokar,et al.  Hopping Conductivity in Disordered Systems , 1971 .

[173]  G. Simons,et al.  Char Gasification: Part II. Oxidation Results , 1979 .

[174]  M. Muthukumar.  Concentration dependence of diffusion controlled processes among static traps , 1982 .

[175]  Muhammad Sahimi,et al.  Dynamic percolation and diffusion in disordered systems , 1986 .

[176]  K. Zygourakis,et al.  Discrete structural models and their application to gas‐solid reacting systems , 1988 .

[177]  P. Doyen,et al.  Permeability, conductivity, and pore geometry of sandstone , 1988 .

[178]  Clayton J. Radke,et al.  A filtration model for the flow of dilute, stable emulsions in porous media. II: Parameter evaluation and estimation , 1986 .

[179]  E. Touboul,et al.  Carbonate acidizing toward a quantitative model of the wormholing phenomenon , 1989 .

[180]  Charles W. Tobias,et al.  Resistance to Potential Flow through a Cubical Array of Spheres , 1959 .

[181]  W. E. Stewart,et al.  Multicomponent Diffusion of Gases in Porous Solids. Models and Experiments , 1974 .

[182]  P. Leath.  Cluster size and boundary distribution near percolation threshold , 1976 .

[183]  R. Mann,et al.  On the inevitability of non-uniform foulant deposition within a catalyst pellet , 1978 .

[184]  A. P. Malinauskas,et al.  Flow and Diffusion of Gases in Porous Media , 1967 .

[185]  R. Mann,et al.  Fouling and deactivation of a FCC catalyst: II. A wedge-layering analysis of the influence of changes in non-zeolitic pore size distribution , 1982 .

[186]  W. E. Stewart,et al.  Practical Models for Isothermal Diffusion and Flow of Gases in Porous Solids , 1973 .

[187]  M. Sahimi.  Scaling relation for the critical exponents of the backbone of percolation clusters , 1984 .

[188]  D. Nicholson,et al.  Capillary Models for Porous Media: III. Two-phase flow in a three-dimensional network with Gaussian radius distribution. , 1971 .

[189]  G. Froment,et al.  Deactivation of catalysts by coke formation in the presence of internal diffusional limitation , 1982 .

[190]  M. Sahimi,et al.  A percolation model of catalyst deactivation by site coverage and pore blockage , 1985 .

[191]  J. Szekely,et al.  A structural model for gas solid reactions with a moving boundary—VI: The effect of grain size distribution on the conversion of porous solids , 1975 .

[192]  Muhammad Sahimi,et al.  Percolation theory of two-phase relative permeability , 1992 .

[193]  B. P. Watson,et al.  Renormalization group approach for percolation conductivity , 1976 .

[194]  T. E. Harris.  Diffusion with “collisions” between particles , 1965, Journal of Applied Probability.

[195]  G. De Josselin De Jong,et al.  Longitudinal and transverse diffusion in granular deposits , 1958 .

[196]  I. Abramson,et al.  Diffusion of gases in porous solids: Monte Carlo simulations in the Knudsen and ordinary diffusion regimes , 1983 .

[197]  M. Hoefner,et al.  REACTION RATE VS. TRANSPORT LIMITED DISSOLUTION DURING CARBONATE ACIDIZING: APPLICATION OF NETWORK MODEL. , 1986 .

[198]  M. Avrami.  Kinetics of Phase Change. II Transformation‐Time Relations for Random Distribution of Nuclei , 1940 .

[199]  D. Wilkinson,et al.  Percolation with trapping , 1986 .

[200]  G. Froment,et al.  Catalyst deactivation by site coverage through multi-site reaction mechanisms , 1987 .

[201]  H. Davis.  The Effective Medium Theory of Diffusion in Composite Media , 1977 .

[202]  Robert W. Coughlin,et al.  Reaction of sulfur dioxide with limestone and the grain model , 1976 .

[203]  D. D. Perlmutter,et al.  Unified treatment of structural effects in fluid‐solid reactions , 1983 .

[204]  Paul J. Flory,et al.  Molecular Size Distribution in Three Dimensional Polymers. I. Gelation1 , 1941 .

[205]  L. E. Scriven,et al.  Percolation theory of two phase flow in porous media , 1981 .

[206]  B. Beshty.  A mathematical model for the combustion of a porous carbon particle , 1978 .

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

[208]  A. Scheidegger.  General Theory of Dispersion in Porous Media , 1961 .

[209]  S. Shtrikman,et al.  A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials , 1962 .

[210]  K. Jensen,et al.  Models for catalytic pore plugging: application to hydrodemetallation , 1989 .

[211]  A theory of conductivity in disordered resistor networks , 1976 .

[212]  L. Fan,et al.  Experimental study of deep bed filtration: A stochastic treatment , 1984 .

[213]  G. Froment,et al.  Catalyst Deactivation by Active Site Coverage and Pore Blockage , 1979 .

[214]  Z. Alexandrowicz,et al.  Critically branched chains and percolation clusters , 1980 .

[215]  John C. Slattery,et al.  Flow of viscoelastic fluids through porous media , 1967 .

[216]  Y. Nakano,et al.  Monte Carlo simulation of diffusion of gases in a porous solid: Calculations for a new class of solids , 1983 .

[217]  H. S. Fogler,et al.  A network model for deep bed filtration of solid particles and emulsion drops , 1988 .

[218]  K. Jensen,et al.  Estimation of effective transport coefficients in porous solids based on percolation concepts , 1985 .

[219]  K. Jensen,et al.  Percolation concepts in modelling of gas-solid reactions—II. Application to char gasification in the diffusion regime , 1986 .

[220]  I. Abramson,et al.  Effective transport coefficients in heterogeneous media , 1987 .

[221]  Robert M. Ziff,et al.  Kinetics of polymer degradation , 1986 .

[222]  Mukul M. Sharma,et al.  Application of percolation theory to noncatalytic gas‐solid reactions , 1984 .

[223]  D. Simonsson,et al.  Comparison of structural models for gas-solid reactions in porous solids undergoing structural changes , 1981 .

[224]  Y. Yortsos,et al.  Asymptotic analysis of single pore gas-solid reactions , 1983 .

[225]  Dietrich Stauffer,et al.  Gelation and critical phenomena , 1982 .

[226]  Boyd F. Edwards,et al.  Percolation model for simulation of char oxidation and fragmentation time-histories , 1987 .

[227]  Sen,et al.  Effective conductivity of anisotropic two-phase composite media. , 1989, Physical review. B, Condensed matter.

[228]  Chi Tien,et al.  Advances in deep bed filtration , 1979 .

[229]  G. E. Archie.  The electrical resistivity log as an aid in determining some reservoir characteristics , 1942 .

[230]  Dietrich Stauffer,et al.  Diffusion on random systems above, below, and at their percolation threshold in two and three dimensions , 1984 .

[231]  C. Radke,et al.  Flow of dilute, stable liquid and solid dispersions in underground porous media , 1985 .

[232]  J. Ottino,et al.  Monte Carlo calculations of cluster statistics in continuum models of composite morphology , 1988 .

[233]  Vasilis N. Burganos,et al.  Diffusion in pore networks: Effective medium theory and smooth field approximation , 1987 .

[234]  J. Garnett,et al.  Colours in Metal Glasses and in Metallic Films , 1904 .

[235]  G. Batchelor,et al.  Thermal or electrical conduction through a granular material , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[236]  Alan R. Kerstein,et al.  Equivalence of the void percolation problem for overlapping spheres and a network problem , 1983 .

[237]  Moshe Matalon,et al.  Steady burning of a solid particle , 1982 .

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

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

[240]  J. Hammersley,et al.  Percolation processes , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[241]  M. Sahimi,et al.  Computer simulations of miscible displacement processes in disordered porous media , 1990 .

[242]  W. V. Swaaij,et al.  39 Gasification of char particles with CO2 AND H2O , 1980 .

[243]  G. Milton.  Correlation of the electromagnetic and elastic properties of composites and microgeometries corresponding with effective medium approximations , 1984 .

[244]  H. S. Fogler,et al.  Network model for straining dominated particle entrapment in porous media , 1987 .

[245]  Edwards,et al.  Rate equation and scaling for fragmentation with mass loss. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[246]  D. A. G. Bruggeman.  Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen , 1935 .

[247]  Muhammad Sahimi.  Hydrodynamic dispersion near the percolation threshold: scaling and probability densities , 1987 .

[248]  M. Sahimi,et al.  Critical exponent of percolation conductivity by finite-size scaling , 1983 .

[249]  E. T. Gawlinski,et al.  Monte-Carlo renormalisation group for continuum percolation with excluded-volume interactions , 1983 .

[250]  L. Sander,et al.  Diffusion-limited aggregation, a kinetic critical phenomenon , 1981 .

[251]  Robert Ian Mackie,et al.  Dynamic modeling of deep‐bed filtration , 1987 .

[252]  B. Derrida,et al.  Transfer matrix calculation of conductivity in three-dimensional random resistor networks at percolation threshold , 1983 .

[253]  S. Bhatia.  Stochastic theory of transport in inhomogeneous media , 1986 .

[254]  H. Scott Fogler,et al.  Competition Among Flow, Dissolution, and Precipitation in Porous Media , 1989 .

[255]  George R. Gavalas,et al.  Analysis of Char Combustion Including the Effect of Pore Enlargement , 1980 .

[256]  R. Carbonell,et al.  Effective diffusivities for catalyst pellets under reactive conditions , 1980 .

[257]  J. Smith,et al.  Effect of sintering and porosity changes on rates of gas—solid reactions , 1977 .

[258]  Hong Yong Sohn,et al.  A structural model for gas-solid reactions with a moving boundary—III: A general dimensionless representation of the irreversible reaction between a porous solid and a reactant gas , 1972 .

[259]  R. Cukier,et al.  Diffusion controlled processes among stationary reactive sinks: Effective medium approach , 1983 .

[260]  Sahimi,et al.  Transport of large particles in flow through porous media. , 1987, Physical review. A, General physics.

[261]  Werner Stumm,et al.  Theory of Water Filtration , 1967 .

[262]  J. Smith,et al.  Diffusion in catalyst pellets , 1962 .

[263]  Clayton J. Radke,et al.  A filtration model for the flow of dilute, stable emulsions in porous media. I: Theory , 1986 .

[264]  K. Bruce,et al.  Effect of specific surface area on the reactivity of CaO with SO2 , 1986 .

[265]  A generalization of random walk models to correlations over two jumps , 1978 .

[266]  J. Straley.  Non-universal threshold behaviour of random resistor networks with anomalous distributions of conductances , 1982 .

[267]  J. R. Schopper,et al.  A THEORETICAL INVESTIGATION ON THE FORMATION FACTOR/PERMEABILITY/POROSITY RELATIONSHIP USING A NETWORK MODEL* , 1966 .

[268]  V. Shante.  Hopping conduction in quasi-one-dimensional disordered compounds , 1977 .

[269]  S. Kirkpatrick.  Percolation and Conduction , 1973 .

[270]  J. Koplik,et al.  Conductivity and permeability from microgeometry , 1984 .

[271]  W. Bell.  Effect of Micellar Behavior on Adsorption Characteristics of TWO Surfactants. , 1959 .

[272]  J. Koplik.  On the effective medium theory of random linear networks , 1981 .