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Analytical Solutions and Simulation Approaches for Double Permeability Aquifers

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Abstract

In this paper we develop analytical solutions for 1D unsteady flow in an infinite double permeability aquifer. Two asymptotic cases are considered: the near-hydraulic-equilibrium-state and the far-hydraulic-equilibrium-state. It is demonstrated that for both cases the equation for the piezometric head can be expressed in leading order, as the classical solution of the simple permeability medium, to which correction terms are added. On the basis of these findings the accuracy of the simulations using conventional approaches (i.e. MODFLOW, MT3D codes) is discussed, while decision tools for the choice of the adequate double continuum model are also provided.

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References

  • Abbo H, Shavit U, Markel D, Rimmel A (2003) A numerical study of the influence of fractured regions on lake/groundwater interactions; the Lake Kinneret (Sea of Galilee) case. J Hydrol 283:225–243

    Article  Google Scholar 

  • Ahmadi A, Quintard M, Whitaker S (1998) Transport in chemically and mechanically heterogeneous porous media V: two-equation model for solute transport with adsorption. Adv Water Resour 22:59–86

    Article  Google Scholar 

  • Aifantis EC (1977) Introducing a multi-porous medium. Dev Mech 8:209–211

    Google Scholar 

  • Aifantis EC (1979) A new interpetation of diffusion in high diffusivity paths – a continuum approach. Acta Metall 27:638–691

    Google Scholar 

  • Aifantis EC (1984) Application of mixture theory to fluid saturated and other geological media. In: Saxena SK (ed) Proceedings of the engineering foundation international conference on compressibility phenomena in subsidence, Henniker, New Hampshire. Engineering Foundation, New York, pp 65–78

    Google Scholar 

  • Andersson J, Thunvik R (1986) Predicting mass transport in discrete fracture networks with the aid of geometrical field data. Water Resour Res 22(13):1941–1950

    Article  Google Scholar 

  • Andersson JA, Shapiro AM, Bear J (1984) A stochastic model of a fractured rock conditioned by measured information. Water Resour Res 20(1):79–88

    Article  Google Scholar 

  • Bai MD, Elsworth D, Roegiers JC (1993) Multiporosity/multipermeability approach to the simulation of naturally fractured reservoirs. Water Resour Res 29(6):1621–1633

    Article  Google Scholar 

  • Barenblatt GI, Zheltov IP, Kochina N (1960) Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. J Appl Math Mech 24:1286–1303

    Article  Google Scholar 

  • Bear J, Tsang CF, de Marsily G (1993) Flow and contaminant transport in fractured rock. Academic, New York

    Google Scholar 

  • Bertin H, Panfilov M, Quintard M (2000) Two types of transient phenomena and full relaxation macroscale model for single phase flow through double porosity media. Transp Porous Media 39:73–96

    Article  Google Scholar 

  • Bibby R (1981) Mass transport of solutes in dual porosity media. Water Resour Res 17(4):1075–1081

    Article  Google Scholar 

  • Charlaix E, Guyon E, Roux S (1987) Permeability of a random array of fractures of widely varying apertures. Transp Porous Media 2:31–43

    Article  Google Scholar 

  • Cherblanc F, Ahmadi A, Quintard M (2003) Two-medium description of dispersion in heterogeneous porous media: calculation of macroscopic properties. Water Resour Res 39:1154–1173

    Article  Google Scholar 

  • Cherblanc F, Ahmadi A, Quintard M (2007) Two-domain description of solute transport in heterogeneous porous media: comparison between theoretical predictions and numerical experiments. Adv Water Resour 30:1127–1143

    Article  Google Scholar 

  • Fillion E, Noyer M-L (1996) Flow modelling in a dual porosity domain with automatic mesh generation and parameter calibration: application to the Aspoe site. J Hydrol 180:1–19

    Article  Google Scholar 

  • Froukh LJ (2002) Groundwater modelling in aquifers with highly Karstic and heterogeneous characteristics (KHC) in Palestine. Water Resour Manag 16:369–379

    Article  Google Scholar 

  • Gerke HH, van Genuchten MT (1993a) Evaluation of a 1st order water transfer term for variably saturated dual porosity flow models. Water Resour Res 29(4):1225–1238

    Article  Google Scholar 

  • Gerke HH, van Genuchten MT (1993b) A dual-porosity model for simulating the preferential movement of water and solutes in structured media. Water Resour Res 29:305–319

    Article  Google Scholar 

  • Gerke HH, Van Genuchten MT (1996) Macroscopic representation of structural geometry for simulating water and solute movement in dual-porosity media. Adv Water Resour 19:343–357

    Article  Google Scholar 

  • Hu BX, Huang H (2002) Stochastic analysis of solute transport in heterogeneous dual-permeability media. Transp Porous Media 48(1):1–39

    Article  Google Scholar 

  • Jha MK, Namgial D, Kamii Y, Pfeiffer S (2008) Hydraulic parameters of coastal aquifer systems by direct methods and an extended tide–aquifer interaction technique. Water Res Manag. doi:10.1007/s11269-008-9259-3 (in press)

  • Kalbacher T, Wang WQ, McDermott C, Kolditz O, Taniguchi T (2005) Development and application of a CAD interface for fractured rock. Environ Geol 47(7):1017–1027

    Article  Google Scholar 

  • Landereau P, Noetinger B, Quintard M (2001) Quasisteady two-equation models for diffusive transport in fractured porous media: large-scale properties for densely fractured systems. Adv Water Resour 24:863–876

    Article  Google Scholar 

  • Lang U, Keim B (1998) Modelling flow and transport processes in fractured or karstified media with a double continuum model. In: Abstracts of conference modflow ’98, Golden, CO, October 4–8, pp 329–336

  • Lee C-H, Yu J-L, Hwung H-H (1993) Fluid flow and connectivity in fractured rock. Water Res Manag 7:169–184

    Article  Google Scholar 

  • Lin B-S, Lee C-W (1998) Percolation and dispersion of mass transport in saturated fracture networks. Water Res Manag 12:409–432

    Article  Google Scholar 

  • Long J, Remer J, Wilson C, Witherspoon P (1982) Porous media equivalents for networks of discontinuous fractures. Water Resour Res 18(3):645–658

    Article  Google Scholar 

  • McWhorter DB, Sunada DK (1977) Groundwater hydrology and hydraulics. Water Resources, Fort Collins, CO

    Google Scholar 

  • McDonald M, Harbaugh AW (1988) A modular three-dimensional finite difference groundwater flow model, book 6. USGS, Washington, DC

    Google Scholar 

  • Meladiotis I, Moutsopoulos K (2002) Hydrogeological conditions and hydraulic behaviour of the fractured aquifer of Mavropigi (Prefecture of Kozani, Greece). Metalleiol Metall Chron 12(1–2):27–38 (in Greek)

    Google Scholar 

  • Moench A (1984) Double-porosity for a fissured groundwater reservoir with fracture skin. Water Resour Res 20(7):831–846

    Article  Google Scholar 

  • Moench AF, Barlow PM (2000) Aquifer response to streamstage and recharge variation. I. Analytical step-response functions. J Hydrol 230:192–210

    Article  Google Scholar 

  • Moutsopoulos KN, Tsihrintzis VA (2005) Approximate analytical solutions of the Forchheimer equation. J Hydrol 309(1–4):93–103

    Article  Google Scholar 

  • Moutsopoulos KN, Elefteriadis IE, Aifantis EC (1996) Numerical simulation of transport phenomena by using the double porosity/diffusivity continuum model. Mech Res Commun 23(6):577–582

    Article  Google Scholar 

  • Moutsopoulos KN, Konstantinidis AA, Meladiotis ID, Tzimopoulos CD, Aifantis EC (2001) On the numerical solution and qualitative behaviour of double porosity aquifers. Transp Porous Media 42:265–292

    Article  Google Scholar 

  • Noetinger B, Estebenet T, Quintard M (2001) Up-scaling flow in fractured media: equivalence between the large scale averaging theory and the continuous time random walk method. Transp Porous Media 43(3):581–596

    Article  Google Scholar 

  • Onder H (1998) One-dimensional transient flow in a finite fractured aquifer system. Hydrol Sci J 43(2):243–265

    Article  Google Scholar 

  • Osman YZ, Bruen MP (2002) Modelling stream-aquifer seepage: an improved loosing-stream package for MODFLOW. J Hydrol 264:69–86

    Article  Google Scholar 

  • Park E, Zhan H (2003) Hydraulics of horizontal wells in fractured shallow aquifer systems. J Hydrol 281:147–158

    Article  Google Scholar 

  • Pride SR, Berryman JG (2003) Linear dynamics of doubleporosity dual-permeability materials. I. Governing equations and acoustic attenuation. Phys Rev E 68(36603):1–10

    Google Scholar 

  • Quintard M, Cherblanc F, Whitaker S (2001) Dispersion in heterogeneous porous media: one-equation non-equilibrium model. Transp Porous Media 44:181–203

    Article  Google Scholar 

  • Scanlon BR, Mace RE, Barrett ME, Smith B (2003) Can we simulate regional groundwater flow in a karst system using equivalent porous media models? Case study, Barton Springs Edwards aquifer, USA. J Hydrol 276(1–4):137–158

    Article  Google Scholar 

  • Warren JE, Root PJ (1963) The behaviour of naturally fractured reservoirs. SPE J 3:245–255

    Google Scholar 

  • Wilson RK, Aifantis EC (1982) On the theory of consolidation with double porosity. Int J Eng Sci 20(9):1009–1035

    Article  Google Scholar 

  • Xu J, Hu BX (2004) Reactive solute transport in a nonstationary, fractured porous medium: a dual-porosity approach. Transp Porous Media 57(2):181–202

    Article  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 36:865–874

    Article  Google Scholar 

  • Zheng C, Wang PP (1999) A modular three-dimensional multispecies transport mode. US Army Corps of Engineers, Washington, DC

    Google Scholar 

  • Zielke W, Helmig R, Kröhn K-P, Shao H, Wollrath J (1991) Discrete modelling of transport processes in fractured porous rock. In: Proceedings of the international congress on rock mechanics, Aachen

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Correspondence to Konstantinos N. Moutsopoulos.

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Moutsopoulos, K.N., Tsihrintzis, V.A. Analytical Solutions and Simulation Approaches for Double Permeability Aquifers. Water Resour Manage 23, 395–415 (2009). https://doi.org/10.1007/s11269-008-9280-6

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  • DOI: https://doi.org/10.1007/s11269-008-9280-6

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