Flow and transport are solved for a heterogeneous medium modeled as an ensemble of spherical inclusions of uniform radius R and of conductivities K, drawn from a pdff(K) (Fig. 1). This can be regarded as a particular discretization scheme, allowing for accurate numerical and semi-analytical solutions, for any given univariate f (Y) (Y = In K) and integral scale I(y). The transport is quantified by the longitudinal equivalent macrodispersivity alpha(Leq), for uniform mean flow of velocity U and for a large (ergodic) plume of a conservative solute injected in a vertical plane (x = 0) and moving past a control plane at x >> I(y). In the past we have solved transport for advection solely for highly heterogeneous media of sigma(2)(Y) <= 8. We have found that alpha(Leq) increases in a strong nonlinear fashion with sigma(2)(Y) and transport becomes anomalous for the subordinate model. This effect is explained by the large residence time of solute particles in inclusions of low K. In the present work we examine the impact of local diffusion as quantified by the Peclet number Pe = UI(y)/D(0), where D(0) is the coefficient of molecular diffusion. Transport with diffusion is solved by accurate numerical simulations for flow past spheres of low K and for high Pe = O(10(2) - 10(4)). It was found that finite Pe reduces significantly alpha(Leq) as compared to advection, for sigma(2)(Y) greater than or similar to 3 (Pe = 1000) and for sigma(2)(Y) greater than or similar to 1.4 (Pe = 100), justifying neglection of the effect of diffusion for weak to moderately heterogeneous aquifers (e.g. sigma(2)(Y) <= 1). In contrast, diffusion impacts considerably alpha(Leq) for large sigma(2)(Y) due to the removal of solute from low K inclusions. Furthermore, anomalous behavior is eliminated, though alpha(Leq) may be still large for Pe >> 1. (C) 2008 Elsevier Ltd. All rights reserved.
Jankovic, I., Fiori, A., Dagan, G. (2009). The impact of local diffusion on longitudinal macrodispersivity and its major effect upon anomalous transport in highly heterogeneous aquifers RID A-2321-2010. ADVANCES IN WATER RESOURCES, 32(5), 659-669 [10.1016/j.advwatres.2008.08.012].
The impact of local diffusion on longitudinal macrodispersivity and its major effect upon anomalous transport in highly heterogeneous aquifers RID A-2321-2010
FIORI, ALDO;
2009-01-01
Abstract
Flow and transport are solved for a heterogeneous medium modeled as an ensemble of spherical inclusions of uniform radius R and of conductivities K, drawn from a pdff(K) (Fig. 1). This can be regarded as a particular discretization scheme, allowing for accurate numerical and semi-analytical solutions, for any given univariate f (Y) (Y = In K) and integral scale I(y). The transport is quantified by the longitudinal equivalent macrodispersivity alpha(Leq), for uniform mean flow of velocity U and for a large (ergodic) plume of a conservative solute injected in a vertical plane (x = 0) and moving past a control plane at x >> I(y). In the past we have solved transport for advection solely for highly heterogeneous media of sigma(2)(Y) <= 8. We have found that alpha(Leq) increases in a strong nonlinear fashion with sigma(2)(Y) and transport becomes anomalous for the subordinate model. This effect is explained by the large residence time of solute particles in inclusions of low K. In the present work we examine the impact of local diffusion as quantified by the Peclet number Pe = UI(y)/D(0), where D(0) is the coefficient of molecular diffusion. Transport with diffusion is solved by accurate numerical simulations for flow past spheres of low K and for high Pe = O(10(2) - 10(4)). It was found that finite Pe reduces significantly alpha(Leq) as compared to advection, for sigma(2)(Y) greater than or similar to 3 (Pe = 1000) and for sigma(2)(Y) greater than or similar to 1.4 (Pe = 100), justifying neglection of the effect of diffusion for weak to moderately heterogeneous aquifers (e.g. sigma(2)(Y) <= 1). In contrast, diffusion impacts considerably alpha(Leq) for large sigma(2)(Y) due to the removal of solute from low K inclusions. Furthermore, anomalous behavior is eliminated, though alpha(Leq) may be still large for Pe >> 1. (C) 2008 Elsevier Ltd. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
