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Characteristics and controlling factors of dispersion in bounded heterogeneous porous media
Author(s) -
Lu Zhiming,
Wolfsberg Andrew V.,
Dai Zhenxue,
Zheng Chunmiao
Publication year - 2010
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2009wr008392
Subject(s) - bounded function , dimensionless quantity , domain (mathematical analysis) , mathematics , mathematical analysis , boundary (topology) , monte carlo method , porous medium , physics , porosity , thermodynamics , statistics , materials science , composite material
In this study, we present first‐order (in terms of the log conductivity variance) analytical solutions to displacement covariances X ij and macrodispersion coefficients D ij for transport of conservative solutes in two‐dimensional, bounded heterogeneous porous media. These solutions are presented as infinity series and are explicit functions of the statistics of the log hydraulic conductivity. Using numerical examples, the convergence of these solutions in terms of the number of terms in truncated finite summations is first investigated, and the accuracy of these solutions is examined by comparing them with results from Monte Carlo simulations and the semianalytical solutions of Osnes (1998). Through several examples, the general features of time‐dependent X ij and D ij are discussed. Unlike in unbounded domains, the longitudinal macrodispersivity D 11 for bounded domains does not approach an asymptotic value at large dimensionless time but instead increases quickly near the downstream constant head boundary. In addition, D 11 for bounded domains is always larger than that in unbounded domains, and accordingly, the transverse macrodispersivity D 22 in bounded domains is smaller than that in unbounded domains. These differences stem from the lateral no‐flow boundaries in our bounded domain models. We also investigated the effect of domain sizes on X ij and D ij . Our study shows that both X ij and D ij depend not only on the dimensionless size of the domain but also on its aspect ratio. The dependence of X ij and D ij on the particles' initial location has also been investigated at detail. Our results indicate that while this dependence is very small for X 11 and D 11 , the release location has a significant impact on both X 22 and D 22 . Our solutions to both displacement covariances and macrodispersivity are compared against those derived from tracer test data at the Borden site. The comparison shows that our solutions are quite close to observed data, indicating that they may be applicable to predict solute transport at the field scale.