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Title: Method of model reduction and multifidelity models for solute transport in random layered porous media

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 96; Journal Issue: 3; Related Information: CHORUS Timestamp: 2017-09-28 10:59:48; Journal ID: ISSN 2470-0045
American Physical Society
Country of Publication:
United States

Citation Formats

Xu, Zhijie, and Tartakovsky, Alexandre M. Method of model reduction and multifidelity models for solute transport in random layered porous media. United States: N. p., 2017. Web. doi:10.1103/PhysRevE.96.033314.
Xu, Zhijie, & Tartakovsky, Alexandre M. Method of model reduction and multifidelity models for solute transport in random layered porous media. United States. doi:10.1103/PhysRevE.96.033314.
Xu, Zhijie, and Tartakovsky, Alexandre M. Thu . "Method of model reduction and multifidelity models for solute transport in random layered porous media". United States. doi:10.1103/PhysRevE.96.033314.
title = {Method of model reduction and multifidelity models for solute transport in random layered porous media},
author = {Xu, Zhijie and Tartakovsky, Alexandre M.},
abstractNote = {},
doi = {10.1103/PhysRevE.96.033314},
journal = {Physical Review E},
number = 3,
volume = 96,
place = {United States},
year = {Thu Sep 28 00:00:00 EDT 2017},
month = {Thu Sep 28 00:00:00 EDT 2017}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on September 28, 2018
Publisher's Accepted Manuscript

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  • This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a known velocity covariance function. In the hierarchical model, we represent (random) concentration in terms of its cross-sectional average and a variation function. We derive a one-dimensional stochastic advection-dispersion-type equation for the average concentration and a stochastic Poisson equation for the variation function, as well as expressions for the effective velocity and dispersion coefficient. We observe that velocity fluctuations enhance dispersion in a non-monotonic fashion: the dispersionmore » initially increases with correlation length ╬╗, reaches a maximum, and decreases to zero at infinity. Maximum enhancement can be obtained at the correlation length about 0.25 the size of the porous media perpendicular to flow.« less
  • Solute transport in fractured porous media is typically 'non-Fickian'; that is, it is characterized by early breakthrough and long tailing and by nonlinear growth of the Green function-centered second moment. This behavior is due to the effects of (1) multirate diffusion occurring between the highly permeable fracture network and the low-permeability rock matrix, (2) a wide range of advection rates in the fractures and, possibly, the matrix as well, and (3) a range of path lengths. As a consequence, prediction of solute transport processes at the macroscale represents a formidable challenge. Classical dual-porosity (or mobile-immobile) approaches in conjunction with anmore » advection-dispersion equation and macroscopic dispersivity commonly fail to predict breakthrough of fractured porous media accurately. It was recently demonstrated that the continuous time random walk (CTRW) method can be used as a generalized upscaling approach. Here we extend this work and use results from high-resolution finite element-finite volume-based simulations of solute transport in an outcrop analogue of a naturally fractured reservoir to calibrate the CTRW method by extracting a distribution of retention times. This procedure allows us to predict breakthrough at other model locations accurately and to gain significant insight into the nature of the fracture-matrix interaction in naturally fractured porous reservoirs with geologically realistic fracture geometries.« less
  • Lattice Boltzmann models simulate solute transport in porous media traversed by conduits. Resulting solute breakthrough curves are fitted with Continuous Time Random Walk models. Porous media are simulated by damping flow inertia and, when the damping is large enough, a Darcy's Law solution instead of the Navier-Stokes solution normally provided by the lattice Boltzmann model is obtained. Anisotropic dispersion is incorporated using a direction-dependent relaxation time. Our particular interest is to simulate transport processes outside the applicability of the standard Advection-Dispersion Equation (ADE) including eddy mixing in conduits. The ADE fails to adequately fit any of these breakthrough curves.
  • A field experiment is reported which monitored the three-dimensional movement of cubic solute plumes through an unsaturated, loamy sand soil. The plumes were created with one of two methods, a two-dimensional flux application and an initial resident distribution. Soil coring was used to sample resident concentrations for the three solutes studied. The data were analyzed using the method of moments. In addition to the solute transport experiments, a detailed set of physical properties of the field was obtained by excavating three pits to a depth of 5.0 m and also by taking soil cores throughout the study area. This papermore » explains the experimental methodology, summarizes the relevant site characteristics. Mass balance varied between 78 and 138%. The field-averaged gravimetric water content and dry bulk density were used to accurately predict the mean vertical plume displacements. The plumes spread relatively little in the horizontal direction.« less
  • Solute plumes were created in an unsaturated field soil with either flux application or by leaching an initial resident distribution. The spatial variance of the plumes initially increased with time between the soil surface and a depth of 2.5 m, within which the soil was a nearly structureless loamy sand. Below this depth, the plumes were observed to compress in the vertical direction as they moved into, and through, a region of subangular blocky structure and loam texture (between 2.5 and 4.0 m depth). As the solute moved below the layer of fine texture, the plume variance again increased withmore » time. Using a transformed advection-dispersion equation description, two constant, field-averaged transport coefficients, V* and D*{sub zz}, were determined in a scaled coordinate system from the moment equations. These two constant parameters were then used to predict the observed local, or plot scale, transport. Results indicate that the two constant parameters describe transport reasonably well as each plot site and over all sampling depths.« less