Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-04-30T12:13:38.978Z Has data issue: false hasContentIssue false

4 - Groundwater flow and transport

Published online by Cambridge University Press:  06 December 2010

By
J. Carrera  and
S. A. Mathias
Edited by
Howard S. Wheater ,
Simon A. Mathias  and
Xin Li
Howard S. Wheater
Affiliation:
Imperial College of Science, Technology and Medicine, London
Simon A. Mathias
Affiliation:
University of Durham
Xin Li
Affiliation:
Chinese Academy of Sciences, Lanzhou, China
Get access

Summary

INTRODUCTION

A model is an entity built to reproduce some aspect of the behaviour of a natural system. In the context of groundwater, aspects to be reproduced may include: groundwater flow (heads, water velocities, etc.); solute transport (concentrations, solute fluxes, etc.); reactive transport (concentrations of chemical species reacting among themselves and with the solid matrix, minerals dissolving or precipitating, etc.); multiphase flow (fractions of water, air, non-aqueous phase liquids, etc.); energy (soil temperature, surface radiation, etc.); and so forth.

Depending on the type of description of reality that one is seeking (qualitative or quantitative), models can be classified as conceptual or mathematical. A conceptual model is a qualitative description of ‘some aspect of the behaviour of a natural system’. This description is usually verbal, but may also be accompanied by figures and graphs. In the groundwater flow context, a conceptual model involves defining the origin of water (areas and processes of recharge) and the way it flows through and exits the aquifer. In contrast, a mathematical model is an abstract description (abstract in the sense that it is based on variables, equations and the like) of ‘some aspect of the behaviour of a natural system’. However, the motivation of mathematical models is not abstract, but to aid quantification. For example, a mathematical model of groundwater flow should yield the time evolution of heads and fluxes (water movements) at every point in the aquifer.

Type
Chapter
Information
Groundwater Modelling in Arid and Semi-Arid Areas , pp. 39 - 62
Publisher: Cambridge University Press
Print publication year: 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, M. P. and Woessner, W. W. (1992) Applied Groundwater Modeling. Academic Press.Google Scholar
Ang, A. H. S. and Tang, W. H. (1975) Probability Concepts in Engineering Planning and Design, Vol. 1, Basic Principles. Wiley.Google Scholar
Ayora, C., Tabener, C., Saaltink, M. W. and Carrera, J. (1998) The genesis of dedolomites: a discussion based on reactive transport modeling. J. Hydrol. 209, 346–365.CrossRefGoogle Scholar
Bastidas, L. A., Gupta, H. V. and Sorooshian, S. (2002) Emerging paradigms in the calibration of hydrologic models. In Mathematical Models of Large Watershed Hydrology, ed. Singh, V. P. and Frevert, D. K., 23–87. Water Resources Publications.Google Scholar
Bear, J. (1979) Hydraulics of Groundwater. McGraw-Hill.Google Scholar
Beven, K. J. (2006) A manifesto for the equifinality thesis. J. Hydrol. 320, 18–36.CrossRefGoogle Scholar
Beven, K. J. and Binley, A. M. (1992) The future of distributed models: model calibration and uncertainty prediction. Hydrological Processes 6, 279–298.CrossRefGoogle Scholar
Carle, S. F. and Fogg, G. E. (1996) Transition probability-based indicator geostatistics. Math. Geol. 28(4), 453–476.CrossRefGoogle Scholar
Carrera, J. (1988) State of the art of the inverse problem applied to the flow and solute transport equations. In Groundwater Flow and Quality Modelling, 549–583. D. Reidel.CrossRefGoogle Scholar
Carrera, J. (1993) An overview of uncertainties in modeling groundwater solute transport. J. Contam. Hydrol. 13, 23–48.CrossRefGoogle Scholar
Carrera, J. and Neuman, S. P. (1986a) Estimation of aquifer parameters under transient and steady-state conditions. 1. Maximum likelihood method incorporating prior information. Water. Resour. Res. 22(2), 199–210.CrossRefGoogle Scholar
Carrera, J. and Neuman, S. P. (1986b) Estimation of aquifer parameters under transient and steady-state conditions. 2. Uniqueness, stability and solution algorithms. Water. Resour. Res. 22(2), 211–227.CrossRefGoogle Scholar
Carrera, J. and Neuman, S. P. (1986c) Estimation of aquifer parameters under transient and steady-state conditions. 3. Application to Synthetic and Field Data. Water. Resour. Res. 22(2), 228–242.CrossRefGoogle Scholar
Carrera, J., Mousavi, S. F., Usunoff, E., Sanchez-Vila, X. and Galarza, G. (1993) A discussion on validation of hydrogeological models. Reliability Engineering and System Safety 42, 201–216.CrossRefGoogle Scholar
Carrera, J., Sànchez-Vila, X., Benet, I.et al. (1998) On matrix diffusion: formulations, solution methods and qualitative effects. Hydrogeol. J. 6, 178–190.CrossRefGoogle Scholar
Carrera, J., Alcolea, A., Medina, A., Hidalgo, J. and Slooten, L. J. (2005) Inverse problem in hydrogeology. Hydrogeol. J. 13, 206–222.CrossRefGoogle Scholar
Castro, A., Vazquez-Sune, E., Carrera, J., Jaen, M. and Salvany, J. M. (1999) Calibracion del modelo regional de flujo subterraneo en la zona de Aznalcollar, Espana: ajuste de las extracciones [Calibration of the groundwater flow regional model in the Aznalcollar site, Spain: extractions fit]. In Hidrologa Subterranea. II, 13. ed Tineo, A.. Congreso Argentino de Hidrogeologia y IV Seminario Hispano Argentino sobre temas actuales de la hidrogeologia.Google Scholar
Celia, M. A., Russell, T. F., Herrera, I. and Ewing, R. E. (1990) An Eulerian–Lagrangian localized adjoin method for the advection–diffusion equation. Adv. Water Resour. 13, 187–206.CrossRefGoogle Scholar
Dagan, G. (1982) Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 1. Conditional simulation and the direct problem. Water Resources. Res. 18(4), 813–833.CrossRefGoogle Scholar
Dagan, G. (1984) Solute transport in heterogeneous porous formations. J. Fluid Mech. 145, 151–177.CrossRefGoogle Scholar
Dagan, G. (1989) Flow and Transport in Porous Formations. Springer, New York.CrossRefGoogle Scholar
Marsily, G., Delay, F., Gonçalvès, J.et al. (2005) Dealing with spatial heterogeneity, Hydrogeol. J. 13(1), 161–183.CrossRefGoogle Scholar
Desbarats, A. J. (1987) Numerical estimation of effective permeability in sand-shale formation. Water Resour. Res. 23(2), 273–286.CrossRefGoogle Scholar
Diersch, H. J. G. (2005) FEFLOW Reference Manual, WASY GmbH, Institute for Water Resources Planning and Systems Research, Berlin.Google Scholar
Duan, Q., Gupta, V. K. and Sorooshian, S. (1993) A shuffled complex evolution approach for effective and efficient global minimization. J. Optim. Theory Appl. 76(3), 501–521.CrossRefGoogle Scholar
Duan, Q. (2003) Global optimization for watershed model calibration. In Calibration of Watershed Models, ed. Duan, Q., Gupta, H. V., Sorooshian, S., Rousseau, A. N. and Turcotte, R.. Water Science and Application 6, 89–104. Am. Geophys. Union.CrossRefGoogle Scholar
Durlofsky, L. J. (2003) Upscaling of geocellular models for reservoir flow simulation: a review of recent progress. Proceedings of the 7th International Forum on Reservoir Simulation, Bühl/Baden-Baden, Germany, 23–27 June 2003.Google Scholar
Edwards, A. (1972) Likelihood. Cambridge Univ. Press.Google Scholar
Farmer, C. L. (2002) Upscaling: a review. Int. J. Numer. Meth. Fluids. 40, 63–78.CrossRefGoogle Scholar
Fogg, G. E., Noyes, C. D. and Carle, S. F. (1998) Geologically based model of heterogeneous hydraulic conductivity in an alluvial setting. Hydrogeol. J. 6, 131–143.CrossRefGoogle Scholar
Freeze, R. A. and Cherry, J. A. (1979) Groundwater. Prentice-Hall.Google Scholar
Freeze, R. A. and Witherspoon, P. A. (1966) Theoretical analysis of regional groundwater flow. II. Effect of water table configuration and subsurface permeability variations. Water Resour. Res. 3, 623–634.CrossRefGoogle Scholar
Galli, A., Beucher, H., Loch, G. and Doligez, B. (1994) The pros and cons of the truncated Gaussian method. In Geostatistical Simulations, ed. Armstrong, M. and Dowd, P. A., 217–233. Kluwer.CrossRefGoogle Scholar
Garven, G., and Freeze, R. A. (1984) Theoretical analysis of the role of groundwater flow in the genesis of stratabound ore deposits. II. Quantitative results. Amer. J. Sci. 284, 1125–1174.CrossRefGoogle Scholar
Gelhar, L. W., Gutjahr, A. L. and Naff, R. L. (1979) Stochastic analysis of macrodispersion in a stratified aquifer. Water Resour. Res. 15, 1387–1397.CrossRefGoogle Scholar
Gelhar, L. W. and Axness, C. L. (1983) Three Dimensional Stochastic Analysis of Macrodispersion in Aquifers. Water Resour. Res. 19, 161–180.CrossRefGoogle Scholar
Gelhar, L. W. (1986) Stochastic subsurface hydrology from theory to applications. Water Resour. Res. 22(9), 135s–145s.CrossRefGoogle Scholar
Gomez-Hernandez, J. J. and Journel, A. (1993) Joint sequential simulation of multigaussian fields. Geostat Troia. 1, 85–94.Google Scholar
Gorelick, S. (1983) A review of distributed parameter groundwater management modeling methods. Water Resour. Res. 19, 305–319.CrossRefGoogle Scholar
Gueguen, Y., Ravalec, M. and Ricard, L. (2006) Upscaling: effective medium theory, numerical methods and the fractal dream. Pure Appl. Geophys. 163, 1175–1192.CrossRefGoogle Scholar
Gutjahr, A., Gelhar, L., Bakr, A. and MacMillan, J. (1978) Stochastic analysis of spatial variability in subsurface flows. 2. Evaluation and application, Water Resour. Res. 14(5), 953–959.CrossRefGoogle Scholar
Haldorsen, H. H. and Chang, D. M. (1986) Notes on stochastic shales from outcrop to simulation models. In Reservoir characterization. ed. Lake, L. W. and Carol, H. B., 152–167. Academic.Google Scholar
Heinrich, J. C., Huyakorn, P. S., Mitchell, A. R. and Zienkiewicz, O. C. (1977) An upwind finite element scheme for two-dimensional transport equation. Int. J. Num. Meth. Eng. 11, 131–143.CrossRefGoogle Scholar
Hill, M. C. (1992) A computer program (MODFLOWP) for estimating parameters of a transient, three dimensional, groundwater flow model using nonlinear regression. USGS open-file report 91–484.
Holland, J. H. (1975) Genetic Algorithms, computer programs that ‘evolve’ in way that resemble even their creators do not fully understand. Scientific American, July 1975, 66–72.Google Scholar
Indelman, P. and Dagan, G. (1993a) Upscaling of permeability of anisotropic heterogeneous formations. 1. The general framework. Water Resour. Res. 29(4), 917–923.CrossRefGoogle Scholar
Indelman, P. and Dagan, G. (1993b) Upscaling of permeability of anisotropic heterogeneous formations. 2. General structure and small perturbation analysis. Water Resour. Res. 29(4), 925–933.CrossRefGoogle Scholar
King, P. R. (1989) The use of renormalization for calculating effective permeability. Transport in Porous Media 4, 37–58.CrossRefGoogle Scholar
Kipp, K. L. (1987) HST3D: a computer code for simulation of heat and solute transport in three dimensional groundwater flow systems. USGS Water Recourses Inv. Rep. 86–4095.
Knudby, C. and Carrera, J. (2005) On the relationship between indicators of geostatistical, flow and transport connectivity. Adv. Water. Resour. 28, 405–421.CrossRefGoogle Scholar
Kolterman, C. E. and Gorelick, S. M. (1992) Paleoclimatic signature in terrestrial flood deposits. Science 256, 1775–1782.CrossRefGoogle Scholar
Koltermann, C. E. and Gorelick, S. M. (1996) Heterogeneity in sedimentary deposits: a review of structure-imitating, process-imitating, and descriptive approaches. Water Resour. Res. 32, 2617–2658.CrossRefGoogle Scholar
Konikow, L. F. and Bredehoeft, J. D. (1978) Computer model of two-dimensional solute transport and dispersion in ground water. Techniques of Water Resources Investigations of the USGS, Book 7, Chapter C2.
Liu, Y. and Gupta, H. V. (2007) Uncertainty in hydrologic modeling: Toward an integrated data assimilation framework. Water Resour. Res. 43, W07401.CrossRefGoogle Scholar
Liu, Y. H, and Journel, A. (2004) Improving sequential simulation with a structured path guided by information content. Math. Geol. 36(8), 945–964.CrossRefGoogle Scholar
Loaiciga, H. and Marino, M. (1987) The inverse problem for confined aquifer flow: identification and estimation with extensions. Water Resour. Res. 23(1), 92–104.CrossRefGoogle Scholar
Long, J., Remer, J., Wilson, C. and Witherspoon, P. (1982) Porous media equivalents for networks of discontinuous fractures. Water Resour. Res. 18(3), 645–658.CrossRefGoogle Scholar
Long, J., Gilmour, P. and Witherspoon, P. (1985) A model for steady fluid flow in random three-dimensional networks of disc-shaped fractures. Water Resour. Res. 21(8), 1105–1115.CrossRefGoogle Scholar
Martinez-Landa, L. and Carrera, J. (2005) An analysis of hydraulic conductivity scale effects in granite (Full-scale Engineered Barrier Experiment (FEBEX), Grimsel, Switzerland). Water Resour. Res. 41, W03006, doi:10.1029/2004WR003458.Google Scholar
Mathias, S. A., Butler, A. P. and Zhan, H. (2008) Approximate solutions for Forchheimer flow to a well. J. Hydraul. Eng. 134(9), 1318–1325.CrossRefGoogle Scholar
Matheron, G. (1971) The Theory of Regionalized Variables and Its Applications. Les Cahiers du CMM, Fasc. No 5, ENSMP, Paris.Google Scholar
Matheron, G. and Marsily, G. (1980) Is transport in porous media always diffusive? A counterexample. Water Resour. Res. 16, 901–917.CrossRefGoogle Scholar
McDonald, M. G. and Harbaugh, A. W. (1988) A modular three-dimensional finite difference groundwater flow model. Techniques of Water Resources Investigations of the USGS, Book 6, Chapter A1.
McIntyre, N., Wheater, H. S. and Lees, M. J. (2002) Estimation and propagation of parametric uncertainty in environmental models. J. Hydroinform. 4(3), 177–198.CrossRefGoogle Scholar
Meier, P., Carrera, J. and Sanchez-Vila, X. (1998) An evaluation of Jacob's method work for the interpretation of pumping tests in heterogeneous formations. Water Resour. Res. 34(5), 1011–1025.CrossRefGoogle Scholar
,NEA-SKI (1990) The International HYDROCOIN Project, Level 2: Model Validation. OECD.
Neuman, S. P. (1981) A Eulerian-Lagrangian numerical scheme for the dispersion-convection equation using conjugate space-time grids. J. Comput. Phys. 41, 270–294.CrossRefGoogle Scholar
Neuman, S. P. (1990) Universal scaling of hydraulic conductivities and dispersivities in geologic media. Water Resour. Res. 26(8), 1749–1758.CrossRefGoogle Scholar
Neuman, S. P. (2003) Maximum likelihood Bayesian averaging of uncertain model predictions. Stochastic Environ. Res. Risk Assess. 17, 291–305.CrossRefGoogle Scholar
Neuman, S. P., Winter, C. L. and Newman, C. M. (1987) Stochastic theory of field-scale fickian dispersion in anisotropic porous-media. Water Resour. Res. 23(3), 453–466.CrossRefGoogle Scholar
Noetinger, B., Artus, V. and Zargar, G. (2005) The future of stochastic and upscaling methods in hydrogeology. Hydrogeol J. 13(1), 184–201.CrossRefGoogle Scholar
Olea, R. A. (1999) Geostatistics for Engineers and Earth Scientists. Kluwer Academic.CrossRefGoogle Scholar
Pruess, K., Oldenburg, C. M. and Moridis, G. (1999) TOUGH2 user's guide, version 2.0. Report LBNL-43134, Lawrence Berkeley National Laboratory.CrossRefGoogle Scholar
Renard, Ph. and Marsily, G. (1997) Calculating equivalent permeability: a review. Adv. Water Resour. 20(5–6), 253–278.CrossRefGoogle Scholar
Richtmyer, R. D. and Morton, K. W. (1957) Difference Methods for Initial Value Problems. Interscience.Google Scholar
Rubin, Y. and Gomez-Hernandez, J. J. (1990) A stochastic approach to the problem of upscaling of conductivity in disordered media: theory and unconditional numerical simulations. Water Resour. Res. 26(4), 691–701.CrossRefGoogle Scholar
Sanchez-Vila, X., Girardi, J. and Carrera, J. (1995) A synthesis of approaches to upscaling of hydraulic conductivities. Water Resour. Res. 31(4), 867–882.CrossRefGoogle Scholar
Sanchez-Vila, X., Guadagnini, A. and Carrera, J. (2006) Representative hydraulic conductivities in saturated groundwater flow. Rev. Geophys. 44, RG3002.CrossRefGoogle Scholar
Stallman, R. W. (1956) Numerical analysis of regional water levels to define aquifer hydrology. Transactions American Geophysical Union. 37(4), 451–460.CrossRefGoogle Scholar
Sorooshian, S. and Gupta, V. K. (1995) Model calibration. In Computer Models of Watershed Hydrology, ed. Singh, V. P., 23–68. Water Resources Publications.Google Scholar
Steefel, C. I., DePaolo, D. J. and Lichtner, P. C. (2005) Reactive transport modeling: An essential tool and a new research approach for the Earth sciences. Earth and Planetary Science Letters 240(3–4), 539–558.CrossRefGoogle Scholar
Strebelle, S. (2002) Conditional simulation of complex geological structures using multiple point statistics. Math. Geol. 34(1), 1–22.CrossRefGoogle Scholar
Sumner, N. R., Flemming, P. M. and Bates, B. C. (1997) Calibration of a modified SFB model for twenty-five Australian catchments using simulated annealing. J. Hydrol. 197, 166–188.CrossRefGoogle Scholar
Thiemann, T., Trosset, M., Gupta, H. and Sorooshian, S. (2001) Bayesian recursive parameter estimation for hydrologic models. Water Resour. Res. 37(10), 2521–2535.CrossRefGoogle Scholar
Thyer, M., Kuczera, G. and Bates, B. C. (1999) Probabilistic optimization for conceptual rainfall–runoff models: a comparison of shuffled complex evolution and simulated annealing algorithms. Water Resour. Res. 35(3), 767–773.CrossRefGoogle Scholar
Vrugt, J. A., Gupta, H. V., Bouten, W. and Sorooshian, S. (2003) A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters. Water Resour. Res. 39(8), 1201.CrossRefGoogle Scholar
Vrugt, J. A., Diks, C. G. H., Gupta, H. V., Bouten, W. and Verstraten, J. M. (2005) Improved treatment of uncertainty in hydrologic modeling: combining the strengths of global optimization and data assimilation. Water Resour. Res. 41, W01017.CrossRefGoogle Scholar
Wen, X.-H. and Gomez-Hernandez, J. J. (1996) Upscaling hydraulic conductivities in heterogeneous media: an overview. J. Hydrol. 183, ix–4ii.CrossRefGoogle Scholar
Wood, B. D. (2000) Review of Upscaling Methods for Describing Unsaturated Flow. Pacific Northwest National Lab., Richland, WA (US) PNNL-13325.CrossRefGoogle Scholar
Wu, Y. S. (2002) Numerical simulation of single-phase and multiphase non-Darcy flow in porous and fractured reservoirs. Transp. Porous Media 49(2), 1573–1634.CrossRefGoogle Scholar
Yapo, P. O., Gupta, H. V. and Sorooshian, S. (1998) Multi-objective global optimization for hydrologic models. J. Hydrol. 204, 83–97.CrossRefGoogle Scholar
Yeh, W. W.-G. (1986) Review of parameter identification procedures in groundwater hydrology: the inverse problem. Water Resour. Res. 22(2), 95–108.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×