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WATER RESOURCES RESEARCH, VOL. 40, W05103, doi:10.1029/2003WR002871, 2004

Stochastic analyses and Monte Carlo simulations of nonergodic solute transport in three-dimensional heterogeneous and statistically anisotropic aquifers

You-Kuan Zhang

Department of Geoscience, IIHR Hydrosciences and Engineering, University of Iowa, Iowa City, Iowa, USA


Byong-min Seo

Department of Geoscience, IIHR Hydrosciences and Engineering, University of Iowa, Iowa City, Iowa, USA


Abstract

Stochastic analyses and Monte Carlo simulations were conducted for nonergodic transport of a nonreactive solute plume in three-dimensional heterogeneous and statistically anisotropic aquifers under uniform mean flow along the x axis. The hydraulic conductivity, K(x), is modeled as a random field which is assumed to be lognormally distributed with an anisotropic exponential covariance. The simulation model is validated with good comparison of the simulated and theoretical variogram model of the log K field, small mass balance errors, and a large number of Monte Carlo (MC) runs. The ensemble averages of the second spatial moments of a solute plume about its center of mass, Z ii , and the plume centroid variances, R ii , (i = 1, 2, 3) of 1600 MC runs were simulated for three degrees of heterogeneity and a line source of three different lengths along the y or z axis. At least 800 MC runs are needed to stabilize the simulated moments even for the mildly heterogeneous aquifers of σ Y 2 ≤ 0.5, and the ergodic condition is far from reaching for a line source with the initial dimension of several integral scales of log K field. The first-order theories predict well the longitudinal Z 11 and R 11 (thus the one-particle displacement variance, X 11 = Z11 + R11), significantly overestimate the horizontal transverse Z 22 and R 22 (thus X22), and overestimate the vertical transverse Z 33 but underestimate R 33.

Received 7 November 2003; accepted 20 February 2004; published 7 May 2004.

Index Terms: 1829 Hydrology: Groundwater hydrology; 1832 Hydrology: Groundwater transport; 1869 Hydrology: Stochastic processes.

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Citation: Zhang, Y.-K., and B. Seo (2004), Stochastic analyses and Monte Carlo simulations of nonergodic solute transport in three-dimensional heterogeneous and statistically anisotropic aquifers, Water Resour. Res., 40, W05103, doi:10.1029/2003WR002871.