1,721,165 research outputs found
An asymptotic analysis for determining concentration uncertainty in aquifer transport
No full textTransport of a conservative solute takes place by advection and by pore-scale dispersion in a formation of spatially variable logconductivity Y(x) = In K(x). The latter is modeled as a normal stationary random space function, characterized by a few statistical parameters, like the mean , the variance sigma(Y)(2), the horizontal and vertical integral scales I-h and I-v. The local solute concentration C(x, t), a random function of space and time, is characterized by its statistical moments, like, e.g. the mean and the standard deviation sigma(C). A simplified analysis for determining the concentration uncertainty is proposed. The proposed methodology, valid for nonreactive solutes, is based on a few simplifications, the most important being: (i) large transverse dimensions of the injected plume compared to the logconductivity correlation lengths, (ii) mild heterogeneity of the hydraulic properties, which allows for the use of the first-order analysis, (iii) highly anisotropic formations, and (iv) mean uniform flow. The concentration uncertainty is represented through the coefficient of variation CVC = sigma(C)/ at the plume center, where the expected concentration is maximum. Results for CVC are illustrated as function of time and on two dimensionless parameters: Omega = I-v(2)/(I(h)alpha(dT)) and Lambda = L-1/rootA(11)I(h), where L-1 is the longitudinal dimension of the initial plume, A(11) is the longitudinal macro dispersivity, and alpha(dT) is the local transverse dispersivity. Summary graphs lead to a quick and simple estimate of the time-dependent concentration uncertainty, as well as its peak and its setting time (i.e. the time needed to reach the peak coefficient of variation). The methodology and its results can be used to assess the concentration uncertainty at the plume center. The problem is quite important when dealing with contaminant prediction and risk analysis. (C) 2003 Elsevier B.V. All rights reserved
On the influence of pore-scale dispersion in nonergodic transport in heterogeneous formations RID A-2321-2010
No full textFlow of an inert solute in an heterogeneous aquifer is usually considered as dominated by large-scale advection. As a consequence, the pore-scale dispersion, i.e. the pore scale mechanism acting at scales lower than that characteristic of the heterogeneous field, is usually neglected in the computation of global quantities like the solute plume spatial moments. Here the effect of pore-scale dispersion is taken into account in order to find its influence on the longitudinal asymptotic dispersivity D-11; we examine both the two-dimensional and the three-dimensional flow cases. In the calculations, we consider the finite size of the solute initial plume, i.e. we analyze both the ergodic and the nonergodic cases. With Pe the Peclet number, defined as Pe = U lambda/D, where U, lambda, D are the mean fluid velocity, the heterogeneity characteristic length and the pore-scale dispersion coefficient respectively, we show that the infinite Peclet approximation is in most cases quite adequate, at least in the range of Peclet number usually encountered in practice (Pe > 10(2)). A noteworthy exception is when the formation log-conductivity field is highly anisotropic. In this case, pore-scale may have a significant impact on D-11,especially when the solute plume initial dimensions an not much larger than the heterogeneities' lengthscale. In all cases, D-11 appears to be more sensitive to the pore-scale dispersive mechanisms under nonergodic conditions, i.e. for plume initial size less than about 10 log-conductivity integral scales
The relative dispersion and mixing of passive solutes in transport in geologic media
No full textThe spreading of a contaminant in a heterogeneous aquifer depends on the scales of variability effectively explored by the plume. In particular, we observe two major contributions of the fluctuating velocity field in the contaminant movement: (i) the spreading caused by velocity variations of scales lesser than that of the plume size, which we will call "relative' spreading, and (ii) the meander-like movement of the plume as a whole caused by velocity variations of scale larger than that of the plume size. The aim of this work is to consider the effects of the finite size of the contaminant plume on the local concentration moments and sigma (C). In particular a "relative' concentration, which depends on the scales of variability effectively explored by the plume, is defined. First, the mathematical formulation of the problem is developed along the Lagrangian framework. In particular, the expressions for the relative mean concentration and its variance are presented. Then, the methodology is applied to the regional transport problem, where the influence of the size of the plume and the pore-scale dispersion are quantitatively assessed
Finite Peclet extensions of Dagan's solutions to transport in anisotropic heterogeneous formations RID A-2321-2010
No full textDagan's [1984] landmark solution for transport in heterogeneous porous formations is extended to the case of finite Peclet numbers. It is suggested that pore-scale dispersion matters only with reference to transverse spreading, and that Dagan's solution, valid for Pe = infinity, is an adequate approximation in a wide range of finite Peclet numbers
Features of solute transport in heterogeneous aquifers: preferential flow, tailing and the impact of local diffusion
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On the influence of local dispersion in solute transport through formations with evolving scales of heterogeneity RID A-2321-2010
No full textThe aim of the present study is to determine the longitudinal dispersion coefficient D-L for transport in formations of long-range permeability fields by considering both large-scale advection and local-scale dispersion; the nonergodicity of the plume will be considered throughout the work. The scope is twofold: (1) to analyze the mutual role played by both the "macroscale" and the local scales of heterogeneity in determining the overall transport properties and (2) to check the validity of the results obtained in the past, in particular concerning the occurrence of anomalous transport. The results are obtained through the Lagrangean formulation of transport, by the means of a few simplifying assumptions. Two models of permeability K variations are considered: (1) a stationary Y = In K with unbounded integral scale and (2) a formation of Y of stationary increments. For both cases, the longitudinal macrodispersion coefficient D-L always grows with time when local-scale dispersion is present, indicating that transport is always anomalous for the random fields examined. The results are in variance with those obtained in the past by considering nonergodic transport but neglecting the local-scale dispersion [e.g., Dagan, 1994; Bellin et al., 1996] and in qualitative agreement to those obtained by adopting the ergodic assumption [e.g., Neuman, 1990; Glimm and Sharp, 1991], which, however, predicted higher rates of growth of D, with time. We conclude that the interplay between large-scale, advective displacement and local-scale dispersion has a fundamental impact on the occurrence of anomalous transport in long-range correlated permeability random fields
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