Linear equilibrium adsorbing solute transport in physically and chemically heterogeneous porous formations: 2. Numerical results

Numerical Monte Carlo simulations were conducted to assess dispersion of reactive solutes in two-dimensional physically and chemically heterogeneous porous media, using random fields with assigned correlation structure for hydraulic conductivity and linear adsorption coefficient. Conditions under which linearization of adsorption is valid are discussed. Lognormal distributions of hydraulic conductivity and adsorption coefficient were assumed. Calculations have been performed for positive and negative correlation between hydraulic conductivity and adsorption coefficient, and for uncorrelated cases. Effects of varying different properties including mean and average sorption coefficient, physical and chemical integral scale, and variance of hydraulic conductivity on dispersive behavior are shown. A larger mean sorption coefficient enhances plume spreading in uncorrelated and in negatively correlated cases. In positively correlated cases, counteracting effects of physical and chemical heterogeneity play an important role. The outcome of these counteracting effects depends on the mean, variance, and integral scales of the spatially variable properties. The analytical solutions, derived in paper 1 (Bellin et al., this issue), reveal a good agreement with the numerical results in a significant range of heterogeneiti es. The generally surprisingly good agreement of the analytical solutions with the numerically obtained results can possibly be attributed to opposing effects of nonlinearities neglected in the derivation of the analytical solutions. In the case of strong physical heterogeneity the analytical solutions perform slightly better than in the case of strong chemical heterogeneity.

[1]  Sjoerd E. A. T. M. van der Zee,et al.  Analytical traveling wave solutions for transport with nonlinear and nonequilibrium adsorption , 1990 .

[2]  David L. Freyberg,et al.  Stochastic modeling of vertically averaged concentration uncertainty in a perfectly stratified aquifer , 1987 .

[3]  Andrew F. B. Tompson,et al.  Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media , 1990 .

[4]  D. Russo.  Field‐scale transport of interacting solutes through the unsaturated zone: 1. Analysis of the spatial variability of the transport properties , 1989 .

[5]  J.J.T.I. Boesten,et al.  Behaviour of herbicides in soil: simulation and experimental assessment. , 1986 .

[6]  Peter K. Kitanidis,et al.  Analysis of one‐dimensional solute transport through porous media with spatially variable retardation factor , 1990 .

[7]  Z. J. Kabala,et al.  A stochastic model of reactive solute transport with time‐varying velocity in a heterogeneous aquifer , 1991 .

[8]  Gedeon Dagan,et al.  Solute Dispersion in Unsaturated Heterogeneous Soil at Field Scale: II. Applications1 , 1979 .

[9]  Sjoerd E. A. T. M. van der Zee,et al.  Analysis of solute redistribution in a heterogeneous field , 1990 .

[10]  D. Freyberg,et al.  A natural gradient experiment on solute transport in a sand aquifer: 1. Approach and overview of plume movement , 1986 .

[11]  Gedeon Dagan,et al.  Unsaturated flow in spatially variable fields: 2. Application of water flow models to various fields , 1983 .

[12]  R. Ababou,et al.  Numerical simulation of three-dimensional saturated flow in randomly heterogeneous porous media , 1989 .

[13]  S. Zee,et al.  Influence of electrolyte composition and pH on cadmium sorption by an acid sandy soil , 1993 .

[14]  R. Freeze.  A stochastic‐conceptual analysis of one‐dimensional groundwater flow in nonuniform homogeneous media , 1975 .

[15]  Gedeon Dagan,et al.  Unsaturated flow in spatially variable fields: 3. Solute transport models and their application to two fields , 1983 .

[16]  Yoram Rubin,et al.  Linear equilibrium adsorbing solute transport in physically and chemically heterogeneous porous formations. 1. Analytical solutions , 1993 .

[17]  G. Dagan,et al.  A note on head and velocity covariances in three‐dimensional flow through heterogeneous anisotropic porous media , 1992 .

[18]  D. Russo.  Field‐scale transport of interacting solutes through the unsaturated zone: 2. Analysis of the spatial variability of the field response , 1989 .

[19]  Dennis McLaughlin,et al.  Stochastic analysis of nonstationary subsurface solute transport: 1. Unconditional moments , 1989 .

[20]  F. D. Haan,et al.  Spatial patterns of cadmium contents related to soil heterogeneity , 1991 .

[21]  J. Boesten,et al.  Effects of Soil Heterogeneity on Pesticide Leaching to Groundwater , 1991 .

[22]  William P. Ball,et al.  Variability of aquifer sorption properties in a field experiment on groundwater transport of organic solutes: Methods and preliminary results , 1986 .

[23]  Yoram Rubin,et al.  Prediction of tracer plume migration in disordered porous media by the method of conditional probabilities , 1991 .

[24]  V. Cvetkovic,et al.  Modeling solute advection coupled with sorption kinetics in heterogeneous formations , 1992 .

[25]  J. W. Biggar,et al.  Spatial variability of the leaching characteristics of a field soil , 1976 .

[26]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

[27]  V. Cvetkovic,et al.  Solute advection in stratified formations , 1989 .

[28]  G. Dagan.  Time‐dependent macrodispersion for solute transport in anisotropic heterogeneous aquifers , 1988 .

[29]  S. Goldberg,et al.  Use of surface complexation models in soil chemical systems , 1992 .

[30]  Vladimir Cvetkovic,et al.  Stochastic analysis of solute arrival time in heterogeneous porous media , 1988 .

[31]  Vladimir Cvetkovic,et al.  Field scale mass arrival of sorptive solute into the groundwater , 1991 .

[32]  Mark N. Goltz,et al.  Interpreting organic solute transport data from a field experiment using physical nonequilibrium models , 1986 .

[33]  G. Dagan,et al.  Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers: 1. Constant head boundary , 1988 .

[34]  G. Dagan.  Statistical Theory of Groundwater Flow and Transport: Pore to Laboratory, Laboratory to Formation, and Formation to Regional Scale , 1986 .

[35]  S. Zee,et al.  Significance of soil chemical heterogeneity for spatial behavior of cadmium in field soils. , 1992 .

[36]  Y. Rubin.  Stochastic modeling of macrodispersion in heterogeneous porous media , 1990 .

[37]  Michael A. Celia,et al.  Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts: 3. Hydraulic c , 1992 .

[38]  P. Knabner,et al.  Travelling waves in the transport of reactive solutes through porous media: Adsorption and binary ion exchange — Part 1 , 1992 .

[39]  Gedeon Dagan,et al.  Transport in heterogeneous porous formations: Spatial moments, ergodicity, and effective dispersion , 1990 .

[40]  G. Dagan.  Flow and transport in porous formations , 1989 .

[41]  W. Chardon.  Mobiliteit van cadmium in de bodem , 1984 .

[42]  Y. Rubin.  Transport in heterogeneous porous media: Prediction and uncertainty , 1991 .

[43]  G. Dagan.  Solute transport in heterogeneous porous formations , 1984, Journal of Fluid Mechanics.

[44]  Albert J. Valocchi,et al.  Spatial moment analysis of the transport of kinetically adsorbing solutes through stratified aquifers , 1989 .

[45]  David L. Freyberg,et al.  A natural gradient experiment on solute transport in a sand aquifer: 2. Spatial moments and the advection and dispersion of nonreactive tracers , 1986 .

[46]  C. Axness,et al.  Three‐dimensional stochastic analysis of macrodispersion in aquifers , 1983 .

[47]  Yoram Rubin,et al.  Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers: 2. Impervious boundary , 1989 .

[48]  A. Rinaldo,et al.  Simulation of dispersion in heterogeneous porous formations: Statistics, first‐order theories, convergence of computations , 1992 .

[49]  Allan L. Gutjahr,et al.  Stochastic models of subsurface flow: infinite versus finite domains and stationarity , 1981 .

[50]  S. P. Garabedian,et al.  Large-scale dispersive transport in aquifers : field experiments and reactive transport theory , 1987 .

[51]  D. R. Nielsen,et al.  Scaling Field-Measured Soil Hydraulic Properties Using a Similar Media Concept , 1977 .

[52]  E. Sudicky.  A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process , 1986 .

[53]  S.E.A.T.M. van der Zee,et al.  Transport of reactive solute in spatially variable soil systems , 1987 .

[54]  Peter K. Kitanidis,et al.  Generalized Taylor-Aris moment analysis of the transport of sorbing solutes through porous media with spatially-periodic retardation factor , 1992 .

[55]  Sjoerd E. A. T. M. van der Zee,et al.  Transport of reacting solute in a one-dimensional, chemically heterogeneous porous medium. , 1993 .

[56]  A. Rinaldo,et al.  Numerical experiments on dispersion in heterogeneous porous media , 1990 .

[57]  E. Sudicky,et al.  Spatial Variability of Strontium Distribution Coefficients and Their Correlation With Hydraulic Conductivity in the Canadian Forces Base Borden Aquifer , 1991 .

[58]  V. Cvetkovic,et al.  Mass arrival of sorptive solute in heterogeneous porous media. , 1990 .

[59]  S. P. Neuman,et al.  Stochastic theory of field‐scale fickian dispersion in anisotropic porous media , 1987 .

[60]  W. W. Wood,et al.  Large-Scale Natural Gradient Tracer Test in Sand and Gravel, , 1991 .