### Abstract

We develop analytical expressions for the effective hydraulic conductivity K(e) of a three-dimensional, heterogeneous porous medium in the presence of randomly prescribed head and flux boundaries. The log hydraulic conductivity Y forms a Gaussian, statistically homogeneous and anisotropic random field with an exponential autocovariance. By effective hydraulic conductivity of a finite volume in such a field, we mean the ensemble mean (expected value) of all random equivalent conductivities that one could associate with a similar volume under uniform mean flow. We start by deriving a first-order approximation of an exact expression developed in 1993 by Neuman and Orr. We then generalize this to strongly heterogeneous media by invoking the Landau-Lifshitz conjecture. Upon evaluating our expressions, we find that K(e) decreases rapidly from the arithmetic mean K(A) toward an asymptotic value as distance between the prescribed head boundaries increases from zero to about eight integral scales of Y. The more heterogeneous is the medium, the larger is K(e) relative to its asymptote at any given separation distance. Our theory compares well with published results of spatially power-averaged expressions and with a first- order expression developed intuitively by Kitanidis in 1990.

Original language | English (US) |
---|---|

Pages (from-to) | 1333-1341 |

Number of pages | 9 |

Journal | Water Resources Research |

Volume | 32 |

Issue number | 5 |

DOIs | |

State | Published - May 1996 |

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### ASJC Scopus subject areas

- Aquatic Science
- Environmental Science(all)
- Environmental Chemistry
- Water Science and Technology

### Cite this

*Water Resources Research*,

*32*(5), 1333-1341. https://doi.org/10.1029/95WR02712

**Effective hydraulic conductivity of bounded, strongly heterogeneous porous media.** / Paleologos, Evangelos K.; Neuman, Shlomo P; Tartakovsky, Daniel.

Research output: Contribution to journal › Article

*Water Resources Research*, vol. 32, no. 5, pp. 1333-1341. https://doi.org/10.1029/95WR02712

}

TY - JOUR

T1 - Effective hydraulic conductivity of bounded, strongly heterogeneous porous media

AU - Paleologos, Evangelos K.

AU - Neuman, Shlomo P

AU - Tartakovsky, Daniel

PY - 1996/5

Y1 - 1996/5

N2 - We develop analytical expressions for the effective hydraulic conductivity K(e) of a three-dimensional, heterogeneous porous medium in the presence of randomly prescribed head and flux boundaries. The log hydraulic conductivity Y forms a Gaussian, statistically homogeneous and anisotropic random field with an exponential autocovariance. By effective hydraulic conductivity of a finite volume in such a field, we mean the ensemble mean (expected value) of all random equivalent conductivities that one could associate with a similar volume under uniform mean flow. We start by deriving a first-order approximation of an exact expression developed in 1993 by Neuman and Orr. We then generalize this to strongly heterogeneous media by invoking the Landau-Lifshitz conjecture. Upon evaluating our expressions, we find that K(e) decreases rapidly from the arithmetic mean K(A) toward an asymptotic value as distance between the prescribed head boundaries increases from zero to about eight integral scales of Y. The more heterogeneous is the medium, the larger is K(e) relative to its asymptote at any given separation distance. Our theory compares well with published results of spatially power-averaged expressions and with a first- order expression developed intuitively by Kitanidis in 1990.

AB - We develop analytical expressions for the effective hydraulic conductivity K(e) of a three-dimensional, heterogeneous porous medium in the presence of randomly prescribed head and flux boundaries. The log hydraulic conductivity Y forms a Gaussian, statistically homogeneous and anisotropic random field with an exponential autocovariance. By effective hydraulic conductivity of a finite volume in such a field, we mean the ensemble mean (expected value) of all random equivalent conductivities that one could associate with a similar volume under uniform mean flow. We start by deriving a first-order approximation of an exact expression developed in 1993 by Neuman and Orr. We then generalize this to strongly heterogeneous media by invoking the Landau-Lifshitz conjecture. Upon evaluating our expressions, we find that K(e) decreases rapidly from the arithmetic mean K(A) toward an asymptotic value as distance between the prescribed head boundaries increases from zero to about eight integral scales of Y. The more heterogeneous is the medium, the larger is K(e) relative to its asymptote at any given separation distance. Our theory compares well with published results of spatially power-averaged expressions and with a first- order expression developed intuitively by Kitanidis in 1990.

UR - http://www.scopus.com/inward/record.url?scp=0029667849&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029667849&partnerID=8YFLogxK

U2 - 10.1029/95WR02712

DO - 10.1029/95WR02712

M3 - Article

AN - SCOPUS:0029667849

VL - 32

SP - 1333

EP - 1341

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 5

ER -