TY - JOUR

T1 - Time-dependent transport in heterogeneous formations of bimodal structures

T2 - 1. The model

AU - Dagan, G.

AU - Fiori, A.

PY - 2003/5

Y1 - 2003/5

N2 - Flow of uniform mean velocity U takes place in a heterogeneous medium made up from a matrix of conductivity K0 and inclusions of a different conductivity K. The inclusions of given shape are implanted at random and independently in the medium, without overlapping. The aim of the study is to derive simple, approximate solutions of advective transport of solutes in such heterogeneous formations for arbitrary permeability ratio k = K/K0 and inclusions volume fraction n. Transport is characterized by the spatial moments, which in turn are equal to the one particle trajectory statistical moments for ergodic plumes. The flow and transport problems are solved for isotropic media, for circular (2D) and spherical (3D) inclusions by using the model of composite inclusions of Hashin and Shtrikman [1962]. The results tend to the dilute limit analyzed in the past by Eames and Bush [1999] for n = o(1). Asymptotic, analytical results are derived for weak heterogeneity (k ≃ 1); they coincide with those of Rubin [1995] for a similar structure. Similarly, simple asymptotic expressions of the macrodispersivity are derived for low-permeability inclusions, k = o(1). The theoretical developments are applied to effectively computing trajectories moments in part 2 [Fiori and Dagan, 2003].

AB - Flow of uniform mean velocity U takes place in a heterogeneous medium made up from a matrix of conductivity K0 and inclusions of a different conductivity K. The inclusions of given shape are implanted at random and independently in the medium, without overlapping. The aim of the study is to derive simple, approximate solutions of advective transport of solutes in such heterogeneous formations for arbitrary permeability ratio k = K/K0 and inclusions volume fraction n. Transport is characterized by the spatial moments, which in turn are equal to the one particle trajectory statistical moments for ergodic plumes. The flow and transport problems are solved for isotropic media, for circular (2D) and spherical (3D) inclusions by using the model of composite inclusions of Hashin and Shtrikman [1962]. The results tend to the dilute limit analyzed in the past by Eames and Bush [1999] for n = o(1). Asymptotic, analytical results are derived for weak heterogeneity (k ≃ 1); they coincide with those of Rubin [1995] for a similar structure. Similarly, simple asymptotic expressions of the macrodispersivity are derived for low-permeability inclusions, k = o(1). The theoretical developments are applied to effectively computing trajectories moments in part 2 [Fiori and Dagan, 2003].

KW - Composite media

KW - Dilute suspensions

KW - Groundwater hydrology

KW - Heterogeneous aquifers

KW - Solute transport

UR - http://www.scopus.com/inward/record.url?scp=0842292536&partnerID=8YFLogxK

U2 - 10.1029/2002WR001396

DO - 10.1029/2002WR001396

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AN - SCOPUS:0842292536

SN - 0043-1397

VL - 39

SP - SBH21-SBH28

JO - Water Resources Research

JF - Water Resources Research

IS - 5

ER -