Groundwater Flow

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 36)


Beginning with Darcy’s law, the basics of groundwater flow are covered. Unsaturated soils and the Richards equation are analysed, as well as immiscible two-phase flows and the Buckley–Leverett equation. There are sections on dual porosity models, contaminant transport, environmental bioremediation, precipitation and dissolution, consolidation, and compaction.


Porous Medium Hydraulic Conductivity Groundwater Flow Sedimentary Basin Nonlinear Diffusion Equation 


  1. Aagaard P, Helgeson H (1983) Activity/composition relations among silicates and aqueous solutions: II. Chemical and thermodynamic consequences of ideal mixing of atoms on homological sites in montmorillonites, illites, and mixed-layer clays. Clays Clay Miner 31:207–217 CrossRefGoogle Scholar
  2. Angevine CL, Turcotte DL (1983) Porosity reduction by pressure solution: a theoretical model for quartz arenites. Geol Soc Amer Bull 94:1129–1134 CrossRefGoogle Scholar
  3. Aris R (1956) On the dispersion of a solute in a fluid flowing through a tube. Proc R Soc A 235:67–78 CrossRefGoogle Scholar
  4. Athy LF (1930) Density, porosity, and compaction of sedimentary rocks. Am Assoc Pet Geol Bull 14:1–22 Google Scholar
  5. Audet DM, Fowler AC (1992) A mathematical model for compaction in sedimentary basins. Geophys J Int 110:577–590 CrossRefGoogle Scholar
  6. Bader FG (1978) Analysis of double-substrate limited growth. Biotechnol Bioeng 20:183–202 CrossRefGoogle Scholar
  7. Baú D, Gambolati G, Teatini P (2000) Residual land subsidence near abandoned gas fields raises concern over Northern Adriatic coastland. Eos 81(22):245–249 CrossRefGoogle Scholar
  8. Bear J (1972) Dynamics of fluids in porous media. Elsevier, Amsterdam (Dover reprint, 1988) MATHGoogle Scholar
  9. Bear J, Bachmat Y (1990) Introduction to modelling of transport phenomena in porous media. Kluwer, Dordrecht MATHGoogle Scholar
  10. Bear J, Verruijt A (1987) Modelling groundwater flow and pollution. Reidel, Dordrecht Google Scholar
  11. Beeftink HH, van der Heijden RTJM, Heijnen JJ (1990) Maintenance requirements: energy supply from simultaneous endogenous respiration and substrate consumption. FEMS Microbiol Lett 73:203–209 CrossRefGoogle Scholar
  12. Bensoussan A, Lions JL, Papanicolaou G (1978) Asymptotic analysis for periodic structures. North-Holland, Amsterdam MATHGoogle Scholar
  13. Birchwood RA, Turcotte DL (1994) A unified approach to geopressuring, low-permeability zone formation, and secondary porosity generation in sedimentary basins. J Geophys Res 99:20051–20058 CrossRefGoogle Scholar
  14. Brenner H (1980) A general theory of Taylor dispersion phenomena. Phys Chem Hydrodyn 1:91–123 Google Scholar
  15. Buckmaster JD, Ludford GSS (1982) Theory of laminar flames. Cambridge University Press, Cambridge MATHCrossRefGoogle Scholar
  16. Cogan NG, Keener JP (2004) The role of the biofilm matrix in structural development. Math Med Biol 21:147–166 MATHCrossRefGoogle Scholar
  17. Cushman JH (ed) (1990) Dynamics of fluids in hierarchical porous media. Academic Press, London Google Scholar
  18. Dewynne JN, Fowler AC, Hagan PS (1993) Multiple reaction fronts in the oxidation-reduction of iron-rich uranium ores. SIAM J Appl Math 53:971–989 MATHCrossRefMathSciNetGoogle Scholar
  19. Dockery J, Klapper I (2001) Finger formation in biofilm layers. SIAM J Appl Math 62:853–869 MATHMathSciNetGoogle Scholar
  20. Dullien FAL (1979) Porous media: fluid transport and pore structure. Academic Press, New York Google Scholar
  21. Eberl D, Hower J (1976) Kinetics of illite formation. Geol Soc Amer Bull 87:1326–1330 CrossRefGoogle Scholar
  22. Eberl HJ, Parker DF, Van Loosdrecht MCM (2001) A new deterministic spatio-temporal continuum model for biofilm development. Comput Math Methods Med 3:161–175 MATHGoogle Scholar
  23. Fowler AC (1997) Mathematical models in the applied sciences. Cambridge University Press, Cambridge Google Scholar
  24. Fowler AC, Yang X-S (1998) Fast and slow compaction in sedimentary basins. SIAM J Appl Math 59:365–385 CrossRefMathSciNetGoogle Scholar
  25. Fowler AC, Yang X-S (1999) Pressure solution and viscous compaction in sedimentary basins. J Geophys Res 104:12989–12997 CrossRefGoogle Scholar
  26. Fowler AC, Yang X-S (2003) Dissolution/precipitation mechanisms for diagenesis in sedimentary basins. J Geophys Res 108(B10):2509. doi: 10.1029/2002JB002269 CrossRefGoogle Scholar
  27. Freed RL, Peacor DR (1989) Geopressured shale and sealing effect of smectite to illite transition. Am Assoc Pet Geol Bull 73:1223–1232 Google Scholar
  28. Freeze RA, Cherry JA (1979) Groundwater. Prentice-Hall, London Google Scholar
  29. Hagan PS, Polizzotti RS, Luckman G (1986) Internal oxidation of binary alloys. SIAM J Appl Math 45:956–971 CrossRefMathSciNetGoogle Scholar
  30. Hunt JM (1990) Generation and migration of petroleum from abnormally pressured fluid compartments. Am Assoc Pet Geol Bull 74:1–12 Google Scholar
  31. Hüttmann A, Wilson RD, Thornton SF, Lerner DN (2003) Natural attenuation of ammonium at a former coal carbonisation plant (Mansfield, UK): conceptual model for biodegradation processes. In: Consoil 2003, Gent, Conference Proceedings CD, pp 1542–1547 Google Scholar
  32. Jeffrey A (2004) Handbook of mathematical formulas and integrals, 3rd edn. Elsevier, Amsterdam MATHGoogle Scholar
  33. Jeffreys H, Jeffreys B (1953) Methods of mathematical physics. Cambridge University Press, Cambridge Google Scholar
  34. Jones M (1994) Mechanical principles of sediment deformation. In: Maltman A (ed) The geological deformation of sediments. Chapman and Hall, London, pp 37–71 CrossRefGoogle Scholar
  35. Lambe TW, Whitman RV (1979) Soil mechanics, SI version. Wiley, New York Google Scholar
  36. Mayer KU, Benner SG, Frind EO, Thornton SF, Lerner DN (2001) Reactive transport modeling of processes controlling the distribution and natural attenuation of phenolic compounds in a deep sandstone aquifer. J Contam Hydrol 53:341–368 CrossRefGoogle Scholar
  37. Monod J (1949) The growth of bacterial cultures. Annu Rev Microbiol 3:371–394 CrossRefGoogle Scholar
  38. Ortoleva P (1994) Geochemical self-organisation. Oxford University Press, Oxford Google Scholar
  39. Picioreanu C, van Loosdrecht MCM, Heijnen JJ (1998) Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach. Biotechnol Bioeng 58:101–116 CrossRefGoogle Scholar
  40. Polubarinova-Kochina PYa (1962) Theory of ground water movement. Princeton University Press, Princeton MATHGoogle Scholar
  41. Price M (1985) Introducing groundwater. George Allen and Unwin, London Google Scholar
  42. Rittmann BE, McCarty PL (1980) Model of steady-state-biofilm kinetics. Biotechnol Bioeng 22:2343–2357 CrossRefGoogle Scholar
  43. Rubinstein J, Mauri R (1986) Dispersion and convection in periodic porous media. SIAM J Appl Math 46:1018–1023 MATHCrossRefMathSciNetGoogle Scholar
  44. Saffman PG (1959) A theory of dispersion in a porous medium. J Fluid Mech 6:321–349 CrossRefMathSciNetGoogle Scholar
  45. Sahimi M (1995) Flow and transport in porous media and fractured rock. VCH, Weinheim MATHGoogle Scholar
  46. Sanchez-Palencia E (1983) Homogenization method for the study of composite media. Springer, Berlin Google Scholar
  47. Sass BM, Rosenberg PE, Kittrick JA (1987) The stability of illite/smectite during diagenesis: an experimental study. Geochim Cosmochim Acta 51:2103–2115 CrossRefGoogle Scholar
  48. Sellmeijer JB, Koenders MA (1991) A mathematical model for piping. Appl Math Model 15:646–651 MATHCrossRefGoogle Scholar
  49. Smith JE (1971) The dynamics of shale compaction and evolution in pore-fluid pressures. Math Geol 3:239–263 CrossRefGoogle Scholar
  50. Taylor GI (1953) Dispersion of soluble matter in a solvent flowing slowly through a tube. Proc R Soc Lond A 219:186–203 CrossRefGoogle Scholar
  51. Wanner O, Eberl H, Morgenroth E, Noguera DR, Picioreanu C, Rittmann BE, van Loosdrecht MCM (2006) Mathematical modeling of biofilms. Report of the IWA Biofilm Modeling Task Group, Scientific and Technical Report No 18, IWA Publishing, London Google Scholar
  52. Wealthall GP, Thornton SF, Lerner DN (2001) Natural attenuation of MTBE in a dual porosity aquifer. In: 6th international conference on in situ and on site bioremediation, San Diego, pp 59–66 Google Scholar
  53. Yang X-S (2000) Nonlinear viscoelastic compaction in sedimentary basins. Nonlinear Process Geophys 7:1–7 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.MACSI, Department of Mathematics & StatisticsUniversity of LimerickLimerickIreland

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