1,721,037 research outputs found
Can we determine the transverse macrodispersivity by using the method of moments? RID A-2321-2010
No full textOne of the main assumptions that renders the stochastic theories applicable to real aquifers is the ergodic hypothesis, i.e. the possibility to exchange ensemble and spatial averages of a variable of interest. The principal aim of this paper is to elucidate the conditions that allow for an exchange between ensemble and spatially averaged second moments of concentration field (S-ij); the fulfillment of the ergodic condition underlies the applicability of the dispersion coefficients or other related quantities obtained by the stochastic theories to actual aquifers. The fulfillment of the ergodic hypothesis is assessed here by analyzing the diminishing of the variance of S-ij as the initial size of the plume V-0 grows, i.e. the tendency of S-ij toward its expected value (S-ij). It is shown that it is not always possible to assume ergodicity for solute plumes in heterogeneous aquifers. For the typical plume configurations encountered in applications, transverse and vertical spreading are the most problematic in this respect. In particular, satisfying the ergodic hypothesis depends largely on the initial plume configuration and size, on one hand, and the direction of the moment of interest, on the other. Numerical simulations based on the analytic element method elucidate the results. The relevance of the results is mostly felt for the inference of macrodispersive parameters, which are often derived through S-ij. The work indicates that S-ij may be a distorted and inadequate measure of the plume spread. This should serve as a warning against application of results based on ensemble averages to real-life plumes, particularly when estimating macrodispersion coefficient from field experiment. © 2005 Elsevier Ltd. All rights reserved
Analysis of the impact of injection mode in transport through strongly heterogeneous aquifers
No full textLarge-scale advective transport through highly heterogeneous 3D formations is investigated using highly resolved numerical simulations and simple analytic models. Investigations are focused on impacts of two types of contaminant injection on transport through isotropic formations where flow conditions are uniform in the average. Transport is quantified by analyzing breakthrough curves for control planes at various distances from the injection zone. In flux-proportional injection mode local mass in injection zone is proportional to local groundwater flux; this setup models many practical cases such as contaminant injection through wells. In resident concentration mode local concentration in injection zone is constant. Results show that impacts of injection mode on breakthrough curves and their moments are strong and they persist for hundreds of correlation scales. The resident concentration mode leads to a fatter tails of the breakthrough curves, while the peaks are generally underpredicted. For a synthetic porous medium with logconductivity variance of 8, dispersivity computed using resident concentration mode at control plane 100 integral scales away from the injection zone was about 10 times larger than corresponding one for flux-proportional mode. Hence, injection mode impacts on transport through highly heterogeneous formations are strong and they persist for large distances from the injection zone. (C) 2010 Elsevier Ltd. All rights reserved
Effective conductivity of 2D isotropic formation: performance of the effective medium approximation
No full textAnalysis of the longitudinal macrodispersivity of highly heterogeneous aquifers in presence of local diffusion
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Comment on ‘‘Comparison of Fickian and temporally nonlocal 2 transport theories over many scales in an exhaustively sampled 3 sandstone slab’’ by Elizabeth Major et al.
No full textFlow and transport in highly heterogeneous aquifers: Fickianity, Gaussianity and anomalous transport
No full textFlow and transport in highly heterogeneous formations: 3. Numerical simulations and comparison with theoretical results
No full text[1] In parts 1 [Dagan et al., 2003] and 2 [Fiori et al., 2003] a multi-indicator model of heterogeneous formations is devised in order to solve flow and transport in highly heterogeneous formations. The isotropic medium is made up from circular (2-D) or spherical (3-D) inclusions of different conductivities K, submerged in a matrix of effective conductivity. This structure is different from the multi-Gaussian one, even for equal log conductivity distribution and integral scale. A snapshot of a two-dimensional plume in a highly heterogeneous medium of lognormal conductivity distribution shows that the model leads to a complex transport picture. The present study was limited, however, to investigating the statistical moments of ergodic plumes. Two approximate semianalytical solutions, based on a self-consistent model (SC) and on a first-order perturbation in the log conductivity variance (FO), are used in parts 1 and 2 in order to compute the statistical moments of flow and transport variables for a lognormal conductivity pdf. In this paper an efficient and accurate numerical procedure, based on the analytic-element method [Strack, 1989], is used in order to validate the approximate results. The solution satisfies exactly the continuity equation and at high-accuracy the continuity of heads at inclusion boundaries. The dimensionless dependent variables depend on two parameters: the volume fraction n of inclusions in the medium and the log conductivity variance sigma(Y)(2). For inclusions of uniform radius, the largest n was 0.9 (2-D) and 0.7 (3-D), whereas the largest sigma(Y)(2) was equal to 10. The SC approximation underestimates the longitudinal Eulerian velocity variance for increasing n and increasing sigma(Y)(2) in 2-D and, to a lesser extent, in 3-D, as compared to numerical results. The FO approximation overestimates these variances, and these effects are larger in the transverse direction. The longitudinal velocity pdf is highly skewed and negative velocities are present at high sigma(Y)(2), especially in 2-D. The main results are in the comparison of the macrodispersivities, computed with the aid of the Lagrangian velocity covariances, as functions of travel time. For the longitudinal macrodispersivity, the SC approximation yields results close to the numerical ones in 2-D for n = 0.4 but underestimates them for n = 0.9. The asymptotic, large travel time values of macrodispersivities in the SC and FO approximations are close for low to moderate sigma(Y)(2), as shown and explained in part 1. However, while the slow tendency to Fickian behavior is well reproduced by SC, it is much quicker in the FO approximation. In 3-D the SC approximation is closer to numerical one for the highest n = 0.7 and the different sigma(Y)(2) = 2, 4, 8, and the comparison improves if molecular diffusion is taken into account. Transverse macrodispersivity for small travel times is underestimated by SC in 2-D and is closer to numerical results in 3-D, whereas FO overestimates them. Transverse macrodispersivity asymptotically tends to zero in 2-D for large travel times. In 3-D the numerical simulations lead to a small but persistent transverse macrodispersivity for large travel times, whereas it tends to zero in the approximate solutions. The results suggest that the self-consistent semianalytical approximation provides a valuable tool to model transport in highly heterogeneous isotropic formations of a 3-D structure in terms of trajectories statistical moments. It captures effects like slow transition to Fickian behavior and to Gaussian trajectory distribution, which are neglected by the first-order approximation
Statistical analisys of head and transmissivity in natural acquifers: application to structure identification and transport prediction
No full textFlow and transport through two-dimensional isotropic media of binary conductivity distribution. Part 1: NUMERICAL methodology and semi-analytical solutions RID A-2321-2010
No full textFlow and transport take place in a heterogeneous medium made up from inclusions of conductivity K submerged in a matrix of conductivity K-0. We consider two-dimensional isotropic media, with circular inclusions of uniform radii, that are placed at random and without overlap in the matrix. The system is completely characterized by the conductivity contrast kappa=K/K-0 and by the volume fraction n. The flow is uniform in the mean, of velocity U=const. The derivation of the velocity field is achieved by a numerical method of high accuracy, based on analytical elements. Approximate analytical solutions are derived by a few methods: composite elements, effective medium, dilute systems and first-order approximation in logconductivity variance. The latter was employed by Rubin (1995), while the dilute system approximation was used by Eames and Bush (1999) and Dagan and Lessoff (2001). Transport is solved in a Lagrangean framework, with trajectories determined numerically from the velocity field, by particle tracking. Results for the velocity variance and for the longitudinal macrodispersivity, for a few values of kappa and n, are presented in Part 2
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