Radial Flow in a Bounded Randomly Heterogeneous Aquifer with Recharge

  • M. Riva
  • C. Tei
Conference paper
Part of the Quantitative Geology and Geostatistics book series (QGAG, volume 11)


We present analytical expressions for leading statistical moments of vertically averaged hydraulic head under steady state flow to a well that pumps water from a bounded, randomly heterogeneous aquifer, in the presence of a random recharge. The natural logarithm Y = In T of aquifer transmissivity T is modelled as a statistically homogeneous random field with a Gaussian spatial correlation function. Our solution is based on exact nonlocal moment equations for multidimensional steady state flow in bounded, randomly heterogeneous porous media. In contrast to most stochastic analyses of flow, which require that log transmissivity be multivariate Gaussian, our solution is free of any distributional assumptions. The two-dimensional nature of our solution renders it useful for relatively thin aquifers in which vertical heterogeneity tends to be of minor concern relative to that in the horizontal plane. It also applies to thicker aquifers when information about their vertical heterogeneity is lacking, as is commonly the case when measurements of head and flow rate are done in wells that penetrate much of the aquifer thickness.


Hydraulic Head Steady State Flow Radial Flow Moment Equation Conditional Moment 
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  1. G. Dagan, Flow and Transport in Porous Formations. Springer, 1989.Google Scholar
  2. G. Dagan, Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 1. Conditional simulation and the direct problem, Water Resour. Res., 18(4), 813–833, 1982.CrossRefGoogle Scholar
  3. G. Dagan, and SP. Neuman editors, Subsurface Flow and Transport: A Stochastic Approach, 241 pp., Cambridge University Press, 1997.Google Scholar
  4. A. Guadagnini, and S.P. Neuman, Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly nonuniform domains, 1, theory and computational approach, Water Resour. Res., 35(10), 2999–3018, 1999.CrossRefGoogle Scholar
  5. A. Guadagnini, and S. P Neuman, Recursive conditional moment equations for advective transport in randomly heterogeneous velocity fields. Transport in Porous Media, in press, 2000.Google Scholar
  6. G. Matheron, Elements Pour Une Theoriex des Milieux Poreux, Masson et Cie, 1967.Google Scholar
  7. Neuman, S. P., Eulerian-Lagrangian theory of transport in space-time nonstationary velocity fields: exact nonlocal formalism by conditional moments and weak approximation. Water Resour. Res. 29, 633–645, 1993.CrossRefGoogle Scholar
  8. S. P. Neuman, and S. Orr, Prediction of Steady State Flow in Nonuniform Geologic Media by Conditional Moments: Exact Nonlocal Formalism, Effective Conductivities, and Weak Approximation, Water Resour. Res., 29(2), 341–364, 1993.CrossRefGoogle Scholar
  9. S. P. Neuman, D. Tartakovsky, T.C. Wallstrom, and C.L. Winter, Correction to “Prediction of Steady State Flow in Nonuniform Geologic Media by Conditional Moments: Exact Nonlocal Formalism, Effective Conductivities, and Weak Approximation”, Water Resour. Res., 32(5), 1479–1480, 1996.CrossRefGoogle Scholar
  10. M. Riva, A. Guadagnini, S.P. Neuman and S. Franzetti, Radial Flow In a Bounded Randomly Heterogeneous Aquifer, Transport in porous media, submitted, 2000.Google Scholar
  11. Shvidler, M. I., Filtration Flows in heterogeneous Media (A Statistical Approach), Authorized Translation from the Russian, Consultants Bureau Enterprises, Inc., New York, 1964.Google Scholar
  12. C. Tei, Flussi Convergenti in Acquiferi ad Eterogeneità Aleatoria Multiscala, Graduation Thesis (in Italian), Politecnico di Milano, 2000.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • M. Riva
    • 1
  • C. Tei
    • 1
  1. 1.D.I.I.A.R.Politecnico di MilanoMilanoItaly

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