Skip to main content

Non-fickian Solute Transport

  • Chapter
  • First Online:
Non-fickian Solute Transport in Porous Media
  • 1185 Accesses

Abstract

This research monograph presents the modelling of solute transport in the saturated porous media using novel stochastic and computational approaches. Our previous book published in the North-Holland series of Applied Mathematics and Mechanics (Kulasiri and Verwoerd 2002) covers some of our research in an introductory manner; this book can be considered as a sequel to it, but we include most of the basic concepts succinctly here, suitably placed in the main body so that the reader who does not have the access to the previous book is not disadvantaged to follow the material presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

References

  • Aly AH, Peralta RC (1999) Optimal design of aquifer cleanup systems under uncertainty using a neural network and a genetic algorithm. Water Resour Res 35(8):2523–2532

    Article  Google Scholar 

  • Anderson MP, Woessner WW (1992) Applied groundwater modelling–simulation of flow and advective transport. Academic Press, New York

    Google Scholar 

  • ASCE Task Committee on Application of Artificial Neural Networks in Hydrology (2000a) Artificial neural networks in hydrology. I: preliminary concepts. J Hydrol Eng ASCE 5(2):115–123

    Google Scholar 

  • ASCE Task Committee on Application of Artificial Neural Networks in Hydrology (2000b) Artificial neural networks in hydrology. II: hydrologic applications. J Hydrol Eng ASCE 5(2):124–137

    Google Scholar 

  • Balkhair KS (2002) Aquifer parameters determination for large diameter wells using neural network approach. J Hydrol 265(1–4):118–128

    Article  Google Scholar 

  • Basawa IV, Prakasa Rao BLS (1980) Statistical inference for stochastic processes. Academic Press, New York

    Google Scholar 

  • Batu Vedat (2006) Applied Flow and Solute Transport Modelling in Aquifers. Taylor & Francis Group, Boca Raton

    Google Scholar 

  • Bear J (1972) Dynamics of fluids in porous media. American Elsevier Publishing Company, New York

    Google Scholar 

  • Bear J (1979) Hydraulics of groundwater. McGraw-Hill Inc., Israel

    Google Scholar 

  • Bear J, Zaslavsky D, Irmay S (1968) Physical principles of water percolation and seepage. Unesco Press, France

    Google Scholar 

  • Beaudeau P, Leboulanger T, Lacroix M, Hanneton S, Wang HQ (2001) Forecasting of turbid floods in a coastal, chalk karstic drain using an artificial neural network. Ground Water 39(1):109–118

    Article  Google Scholar 

  • Bibby R, Sunada DK (1971) Statistical error analysis of a numerical model of confined groundwater flow, in stochastic hydraulics. In: Chiu, CL (ed) Proceedings first international symposium on stochastic hydraulics, pp 591–612

    Google Scholar 

  • Carrera J (1987) State of the art of the inverse problem applied to the flow and solute transport problems. In: Proceedings of the groundwater flow and quality modelling. NATO ASI Series, pp 549–585

    Google Scholar 

  • Carrera J (1988) State of the art of the inverse problem applied to the flow and solute transport equations. In: Proceedings of the groundwater flow and quality modelling. NATO ASI serial, vol 224. Kulwer, Norwell, pp 549–585

    Google Scholar 

  • Carrera J, Glorioso L (1991) On geostatistical formulation of the groundwater inverse problem. Adv Water Resour 14(5):273–283

    Article  Google Scholar 

  • Carrera J, Neuman SP (1986) Estimation of aquifer parameters under transient and steady state conditions, 2, uniqueness, stability and solution algorithms. Water Resour Res 22(2):211–227

    Article  Google Scholar 

  • Chapman BM (1979) Dispersion of soluble pollutions in nonuniform rivers, I theory. J Hydrol 40(1/2):139–152

    Article  Google Scholar 

  • Coulibaly P, Anctil F, Aravena R, Bobee B (2001) Artificial neural network modeling of water table depth fluctuations. Water Resour Res 37(4):885–896

    Article  Google Scholar 

  • Cressie N (1993) Geostatistics: a tool for environmental modelers. In: Goodchild MF, Parks BO, Stegert LT (eds) Environmenatal modelling with GIS. Oxford Press, N.Y

    Google Scholar 

  • Cvetkovic V, Shapiro A, Dagan G (1992) A solute flux approach to transport in heterogeneous formations 2. Uncertainty analysis. Water Resour Res 28(5):1377–1388

    Article  Google Scholar 

  • Dagan G (1984) Solute transport in heterogeneous porous formations. J Fluid Mech 145:151–177

    Article  Google Scholar 

  • Dagan G (1986) Statistical theory of groundwater flow and transport: pore to laboratory, laboratory to formation, and formation to regional scale. Water Resour Res 22(9):120S–134S

    Article  Google Scholar 

  • Dagan G (1988) Time dependent macrodispersion for solute transport in anisotropic heterogeneous aquifers. Water Resour Res 24(9):1491–1500

    Article  Google Scholar 

  • Dagan G, Cvetkovic V, Shapiro A (1992) A solute flux approach to transport in heterogeneous formations 1. The general framework. Water Resour Res 28(5):1369–1376

    Article  Google Scholar 

  • Farrell BF (1999) Perturbation growth and structure in time-dependent flows. J Atmos Sci 56(21):3622–3639

    Article  Google Scholar 

  • Farrell BF (2002a) Perturbation growth and structure in uncertain flows. Part I. J Atmos Sci 59(18):2629–2646

    Article  Google Scholar 

  • Farrell BF (2002b) Perturbation growth and structure in uncertain flows. Part II. J Atmos Sci Boston 59(18):2647–2664

    Article  Google Scholar 

  • Fetter CW (1999) Contaminant hydrogeology. Prentice-Hall, New Jersey

    Google Scholar 

  • Fetter CW (2001) Applied hydrogeology. Prentice-Hall, New Jersey

    Google Scholar 

  • Foussereau X, Graham WD, Rao PSC (2000) Stochastic analysis of transient flow in unsaturated heterogeneous soils. Water Resour Res 36(4):891–910

    Article  Google Scholar 

  • Foussereau X, Graham WD, Akpoji GA, Destouni G, Rao PSC (2001) Solute transport through a heterogeneous coupled vadose zone system with temporal random rainfall. Water Resour Res 37(6):1577–1588

    Article  Google Scholar 

  • Freeze RA (1972) Regionalization of hydrologic parameters for use in mathematical models of groundwater flow. In: Gill JE (ed) Hydrogeology. Harpell, Gardenvale, Quebec

    Google Scholar 

  • Freeze RA (1975) A stochastic-conceptual analysis of one dimensional groundwater flow in a non-uniform homogeneous media. Water Resour Res 11(5):725–741

    Article  Google Scholar 

  • Freeze RA, Cherry JA (1979) Groundwater. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Freeze RA, Gorelick SM (2000) Convergence of stochastic optimization and decision analysis in the engineering design of aquifer remediation. Ground Water 38(3):328–339

    Article  Google Scholar 

  • Fried JJ (1972) Miscible pollution of ground water: a study of methodology. In: Biswas, AK (ed) Proceedings of the international symposium on modelling techniques in water resources systems, vol 2. Ottawa, Canada, pp 362–371

    Google Scholar 

  • Fried JJ (1975) Groundwater pollution. Elsevier Scientific Publishing Company, Amsterdam

    Google Scholar 

  • Frind EO, Pinder SF (1973) Galerkin solution to the inverse problem for aquifer transmissivity. Water Resour Res 9(4):1397–1410

    Article  Google Scholar 

  • Gelhar LW (1986) Stochastic subsurface hydrology from theory to applications. Water Resour Res 22(9):135S–145S

    Article  Google Scholar 

  • Gelhar LW, Axness CL (1983) Three dimensional stochastic of macro dispersion aquifers. Water Resour Res 19(1):161–180

    Article  Google Scholar 

  • Gelhar LW, Gutjahr AL, Naff RL (1979) Stochastic analysis of microdispersion in a stratified aquifer. Water Resour Res 15(6):1387–1391

    Article  Google Scholar 

  • Gill WN, Sankarasubramanian R (1970) Exact analysis of unsteady convective diffusion. Proc Roy Soc Lond A 316:341–350

    Article  Google Scholar 

  • Ginn TR, Cushman JH (1990) Inverse methods for subsurface flow: a critical review of stochastic techniques. Stoch Hydrol Hydraul 4:1–26

    Article  Google Scholar 

  • Gomez-Hernandez JJ, Sahuquillo A, Capilla JE (1997) Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data, 1, theory. J Hydrol 203:162–174

    Article  Google Scholar 

  • Gutjahr AL, Wilson JR (1989) Co-kriging for stochastic flow models. Transp Porous Media 4(6):585–598

    Article  Google Scholar 

  • Harleman, D.R.F.; and R.R. Rumer. 1963. The analytical solution for injection of a tracer slug in a plane. Fluid Mechanics, p 16

    Google Scholar 

  • Harter T, Yeh TCJ (1996) Stochastic analysis of solute transport in heterogeneous, variably saturated soils. Water Resour Res 32(6):1585–1596

    Article  Google Scholar 

  • Hassan AE, Hamed KH (2001) Prediction of plume migration in heterogeneous media using artificial neural networks. Water Resour Res 37(3):605–625

    Article  Google Scholar 

  • Hassoun MH (1995) Fundamentals of artificial neural networks. MIT Press, Cambridge

    Google Scholar 

  • Haykin S (1994) Neural networks: a comprehensive foundation. McMillan, New York

    Google Scholar 

  • Hegazy T, Fazio P, Moselhi O (1994) Developing practical neural network applications using back-propagation. Microcomput Civil Eng 9:145–459

    Article  Google Scholar 

  • Hertz JA, Krogh A, Palmer RG (1991) Introduction to the theory of neural computation. Addison-Wesley Publishing, Redwood City

    Google Scholar 

  • Hoeksema R, Kitanidis PK (1984) An application of the geostatistical approach to the inverse problem in two-dimensional groundwater modeling. Water Resour Res 20(7):1003–1020

    Article  Google Scholar 

  • Holden H, Øksendal B, Uboe J, Zhang T (1996) Stochastic partial differential equations. Birkhauser, Boston

    Book  Google Scholar 

  • Hong Y-S, Rosen MR (2001) Intelligent characterisation and diagnosis of the groundwater quality in an urban fractured-rock aquifer using an artificial neural network. Urban Water 3(3):193–204

    Article  Google Scholar 

  • Huang K, Van Genuchten MT, Zhang R (1996a) Exact solution for one-dimensional transport with asymptotic scale dependent dispersion. Appl Math Model 20(4):298–308

    Article  Google Scholar 

  • Huang K, Toride N, Van Genuchten MT (1996b) Experimental investigation of solute transport in large, homogeneous heterogeneous, saturated soil columns. Int J Rock Mech Min Sci 33(6):249A

    Google Scholar 

  • Jazwinski AH (1970) Stochastic processes and filtering theory. Academic Press, New York

    Google Scholar 

  • Johnson VM, Rogers LL (2000) Accuracy of neural network approximators in simulation-optimization. J Water Resour Plan Manage 126(2):48–56

    Article  Google Scholar 

  • Kaski S, Kangas J, Kohonen T (1998) Bibliography of self-organizing map (SOM) papers: 1981–1997. Neural Comput Surv 1:102–350

    Google Scholar 

  • Keidser A, Rosbjerg D (1991) A comparison of four inverse approaches to groundwater flow and transport parameter identification. Water Resour Res 27(9):2219–2232

    Article  Google Scholar 

  • Keizer J (1987) Statistical thermodynamics of nonequilibrium processes. Springer-Verlag, New York

    Book  Google Scholar 

  • Kitanidis PK (1985) Prior information in the geostatistical approach. In: Harry, CT (ed) Proceedings of the special conference on computer application in water resources. ASCE, Buffalo, 10–12 June 1985

    Google Scholar 

  • Kitanidis PK (1997) Introduction to geostatistics—application in hydrogeology. University press, Cambridge

    Google Scholar 

  • Kitanidis P, Vomvoris EG (1983) A geostatistical approach to the problem of groundwater modelling (steady state) and one-dimensional simulation. Water Resour Res 19(3):677–690

    Article  Google Scholar 

  • Klebaner FC (1998) Introduction to stochastic calculus with applications. Springer-Verlag, New York

    Google Scholar 

  • Klenk ID, Grathwohl P (2002) Transverse vertical dispersion in groundwater and the capillary fringe. J Contam Hydrol 58(1–2):111–128

    Article  Google Scholar 

  • Klotz D, Seiler K-P, Moser H, Neumaier F (1980) Dispersivity and velocity relationship from laboratory and field experiments. J Hydrol 45(1/2):169–184

    Article  Google Scholar 

  • Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43:59–69

    Article  Google Scholar 

  • Kohonen T (1990) The Self-organizing map. In Proceedings of the IEEE 78(9):1464–1480

    Article  Google Scholar 

  • Koutsoyiannis D (1999) Optimal decomposition of covariance matrices for multivariate stochastic models in hydrology. Water Resour Res 35(4):1219–1229

    Article  Google Scholar 

  • Koutsoyiannis D (2000) A generalized mathematical framework for stochastic simulation and forecast of hydrologic time series. Water Resour Res 36(6):1519–1533

    Article  Google Scholar 

  • Kruseman GP, De Ridder NA (1970) Analysis and evaluation of pumping test data. Int Inst Land Reclam Improv Bull 11:200–206

    Google Scholar 

  • Kuiper LK (1986) A comparison of several methods for the solution of the inverse problem in two-dimensional steady state groundwater flow modelling. Water Resour Res 22(5):705–714

    Article  Google Scholar 

  • Kulasiri D (1997) Computational modelling of solute transport using stochastic partial differential equations—a report to Lincoln Environment Ltd. Lincoln University, New Zealand, Centre for Computing and Biometrics

    Google Scholar 

  • Kulasiri D, Verwoerd W (1999) A stochastic model for solute transport in porous media: mathematical basis and computational solution. In: Proceedings of the International Congress on Modelling and Simulation. MODSIM 1999, vol 1, pp 31–36

    Google Scholar 

  • Kulasiri D, Verwoerd W (2002) Stochastic dynamics: modeling solute transport in porous media, North-Holland series in applied mathematics and mechanics, vol 44. Elsevier Science Ltd., Amsterdam

    Google Scholar 

  • Kutoyants YA (1984) Parameter estimation for stochastic processes. Herderman Verlag, Berlin

    Google Scholar 

  • Lee DR, Cherry JA, Pickens JF (1980) Groundwater transport of a salt tracer through a sandy lakebed. Limonol Oceanogr 25(1):45–61

    Article  Google Scholar 

  • Leeuwen MV, Butler AP, Te Stroet BM, Tompkins JA (2000) Stochastic determination of well capture zones conditioned on regular grids of transmissivity. Water Resour Res 36(4):949–958

    Article  Google Scholar 

  • Lindsay JB, Shang JQ, Rowe RK (2002) Using complex permittivity and artificial neural networks for contaminant prediction. J Environ Eng 128(8):740–747

    Article  Google Scholar 

  • Lipster RS, Shirayev AN (1977) Statistics of random processes: part I general theory. Springer, New York

    Google Scholar 

  • Lischeid G (2001) Investigating short-term dynamics and long-term trends of SO4 in the runoff of a forested catchment using artificial neural networks. J Hydrol 243(1–2):31–42

    Article  Google Scholar 

  • Loll P, Moldrup P (2000) Stochastic analysis of field-scale pesticide leaching risk as influenced by spatial variability in physical and biochemical parameters. Water Resour Res 36(4):959–970

    Article  Google Scholar 

  • Maier HR, Dandy GC (2000) Neural networks for the prediction and forecasting of water resources variables: a review of modelling issues and applications. Environ Modell Softw 15:101–124

    Article  Google Scholar 

  • Maren A, Harston C, Pap R (1990) Handbook of neural computing applications. Academic Press, California

    Google Scholar 

  • McLaughlin D, Townley LR (1996) A reassessment of the groundwater inverse problem. Water Resour Res 32(5):1161–1311

    Article  Google Scholar 

  • McMillan WD (1966) Theoretical analysis of groundwater basin operations. Water resources center contribution, vol 114. University of California, Berkerly, p 167

    Google Scholar 

  • Merritt WF, Pickens JF, Allison GB (1979) Study of transport in unsaturated sands using radioactive tracers. In Barry PJ (ed) Second report on hydrological and geo-chemical studies in the Perch Lake Basin, pp 155–164

    Google Scholar 

  • Miralles-Wilhelm F, Gelhar LW (1996) Stochastic analysis of sorption macrokinetics in heterogeneous aquifers. Water Resour Res 32(6):1541–1550

    Article  Google Scholar 

  • Morshed J, Kaluarachchi JJ (1998) Application of artificial neural network and generic algorithm in flow and transport simulations. Adv Water Resour 22(2):145–158

    Article  Google Scholar 

  • Mukhopadhyay A (1999) Spatial estimation of transmissivity using artificial neural network. Ground Water 37(3):458–464

    Article  Google Scholar 

  • Neuman SP (1973) Calibration of distributed parameter groundwater flow models viewed as a multiple-objective decision process under uncertainty. Water Resour Res 9(4):1006–1021

    Article  Google Scholar 

  • Neuman SP, Winter CL, Neuman CN (1987) Stochastic theory of field scale Fickian dispersion in anisotropic porous media. Water Resour Res 23(3):453–466

    Article  Google Scholar 

  • Neural Ware (1998) Neural computing: a technology handbook for NeuralWorks Professional II/PLUS and neuralworks explorer. Aspen Technology Inc., USA, p 324

    Google Scholar 

  • Oakes DB, Edworthy DJ (1977) Field measurements of dispersion coefficients in the United Kingdom. In: Proceedings of the groundwater quality, measurement, prediction and protection. Water Research Centre, England, pp 327–340

    Google Scholar 

  • Ogata A (1970) Theory of dispersion in granular medium. U.S. Geological survey professional paper, 411-I

    Google Scholar 

  • Ogata A, Bank RB (1961) A solution of the differential equation of longitudinal dispersion in porous media. USGS, Professional paper, No 411–A

    Google Scholar 

  • Øksendal B (1998) Stochastic differential equations. Springer Verlag, Berlin

    Book  Google Scholar 

  • Painter S (1996) Stochastic interpolation of aquifer properties using fractional Levy motion. Water Resour Res 32(5):1323–1332

    Article  Google Scholar 

  • Painter S, Cvetkovic V (2001) Stochastic analysis of early tracer arrival in a segmented fracture pathway. Water Resour Res 37(6):1669–1680

    Article  Google Scholar 

  • Peaudecef P, Sauty JP (1978) Application of a mathematical model to the characterization of dispersion effects of groundwater quality. Prog Water Technol 10(5/6):443–454

    Google Scholar 

  • Pickens JF, Grisak GE (1981) Scale-dependent dispersion in a stratified granular aquifer. Water Resour Res 17(4):1191–1211

    Article  Google Scholar 

  • Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C, the art of scientific computing, 2nd edn. University Press, Cambridge

    Google Scholar 

  • Ranjithan S, Eheart JW, Garrett JH Jr (1993) Neural network-based screening for groundwater reclamation under uncertainty. Water Resour Res 29(3):563–574

    Article  Google Scholar 

  • Rashidi M, Peurrung L, Thompson AFB, Kulp TJ (1996) Experimental analysis of pore-scale flow and transport in porous media. Adv Water Resour 19(3):160–180

    Google Scholar 

  • Rogers LL, Dowla FU (1994) Optimization of groundwater remediation using artificial neural networks with parallel solute transport modeling. Water Resour Res 30(2):457–481

    Article  Google Scholar 

  • Rogers LL, Dowla FU, Johnson VM (1995) Optimal field-scale groundwater remediation using neural networks and the genetic algorithm. Environ Sci Technol 29(5):1145–1155

    Article  Google Scholar 

  • Rojas R (1996) Neural networks: a systematic introduction. Springer-Verlag, Berlin

    Google Scholar 

  • Rubin Y, Dagan G (1992) A note on head and velocity covariances in three-dimensioanl flow through heterogeneous anisotropic porous media. Water Resour Res 28(5):1463–1470

    Article  Google Scholar 

  • Rudnitskaya A, Ehlert A, Legin A, Vlasov Y, Büttgenbach S (2001) Multisensor system on the basis of an array of non-specific chemical sensors and artificial neural networks for determination of inorganic pollutants in a model groundwater. Talanta 55(2):425–431

    Article  Google Scholar 

  • Rumelhart DE, McClelland JL, PDP Research Group (1986) Parallel distributed processing: explorations in the microstructure of cognition, vol 1. MIT Press, Cambridge

    Google Scholar 

  • Sagar B, Kisiel CC (1972) Limits of deterministic predictability of saturated flow equations. In: Proceedings of the second symposium on fundamentals of transport phenomena in porous media, international association of hydraulic research, 1972, vol 1. Guelph, Canada, pp 194–205

    Google Scholar 

  • Samarasinghe S (2006) Neural networks for applied sciences and engineering: from fundamentals to complex pattern recognition. Taylor & Franscis Group, USA

    Book  Google Scholar 

  • Scarlatos PD (2001) Computer modeling of fecal coliform contamination of an urban estuarine system. Water Sci Technol J Int Assoc Water Pollut Res 44(7):9–16

    Google Scholar 

  • Scheibe T, Yabusaki S (1998) Scaling of flow and transport behavior in heterogeneous groundwater systems. Adv Water Resour 22(3):223–238

    Article  Google Scholar 

  • Spitz K, Moreno J (1996) A practical guide to groundwater and solute transport modelling. Wiley-Interscience, New Jersey

    Google Scholar 

  • Sudicky EA, Cherry JA (1979) Field observations of tracer dispersion under natural flow conditions in an unconfined sandy aquifer. Water Qual Res J Can 14:1–17

    Google Scholar 

  • Sun NZ (1994) Inverse problems in groundwater modelling. Kluwer Academic Publishers, London

    Google Scholar 

  • Taylor G (1953) Dispersion of soluble matter in solvent flowing through a tube. Proc Roy Soc Lond A 219:186–203

    Article  Google Scholar 

  • Theis CV (1962) Notes on dispersion I fluid flow by geologic features. In Morgan JM, Kamison DK, Stevenson JD (eds) Proceedings of conference on ground disposal of radioactive wastes. Chalk River, Ontario

    Google Scholar 

  • Theis, CV (1963) Hydrologic phenomena affecting the use of tracers in timing ground water flow. Radioisotopes in Hydrology, pp 193–206

    Google Scholar 

  • Thompson AFB, Gray WG (1986) A second-order approach for the modelling of dispersive transport in porous media, 1. Theor Dev Water Resour Res 22(5):591–600

    Article  Google Scholar 

  • Unny TE (1989) Stochastic partial differential equations in ground water hydrology—part 1. J Hydrol Hydraul 3:135–153

    Article  Google Scholar 

  • Vanderborght J, Vereecken H (2002) Estimation of local scale dispersion from local breakthrough curves during a tracer test in a heterogeneous aquifer: the Lagrangian approach. J Contam Hydrol 54(1–2):141–171

    Article  Google Scholar 

  • Walton WC (1979) Progress in analytical groundwater modelling. J Hydrol 43:149–159

    Article  Google Scholar 

  • Wang HF, Anderson MP (1982) Introduction to groundwater modelling. W.H. Freeman, USA

    Google Scholar 

  • Warren JE, Price HS (1961) Flow in heterogeneous porous media. Soc Petrol Eng J 1:153–169

    Google Scholar 

  • Welty C, Gelhar LW (1992) Simulation of large-scale transport of variable density and viscosity fluids using a stochastic mean model. Water Resour Res 28(3):815–827

    Article  Google Scholar 

  • Yang J, Zhang R, Wu J, Allen MB (1996) Stochastic analysis of adsorbing solute transport in two dimensional unsaturated soils. Water Resour Res 32(9):2747–2756

    Article  Google Scholar 

  • Yeh WW-G (1986) Review of parameter identification procedures in groundwater hydrology: the inverse problem. Water Resour Res 22(2):95–108

    Article  Google Scholar 

  • Young N (1988) An introduction to Hilbert space. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Zhang D, Sun AY (2000) Stochastic analysis of transient saturated flow through heterogeneous fractured porous media: a double-permeability approach. Water Resour Res 36(4):865–874

    Article  Google Scholar 

  • Zheng C, Bennett GD (1995) Applied contaminant transport modelling. Van Nostrand Reinhold, New York

    Google Scholar 

  • Zhu AX (2000) Mapping soil landscape as spatial continua: the neural network approach. Water Resour Res 36(3):663–677

    Article  Google Scholar 

  • Zimmerman DA, de Marsily G, Gotway CA, Marietta MG, Axness CL, Beauheim RL et al (1998) A comparison of seven geostatistical based inverse approaches to estimate transmissivities for modelling advective transport by groundwater flow. Water Resour Res 34(6):1373–1413

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Don Kulasiri .

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kulasiri, D. (2013). Non-fickian Solute Transport. In: Non-fickian Solute Transport in Porous Media. Advances in Geophysical and Environmental Mechanics and Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34985-0_1

Download citation

Publish with us

Policies and ethics