Streamline-based simulation of advective–dispersive solute transport

Obi, Eguono-Oghene; Blunt, Martin J.

doi:10.1016/j.advwatres.2004.06.003

Cited by 33 publications

(24 citation statements)

References 34 publications

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“…We used the value λ = 1 obtained previously in equation 7.12 to predict the transit distributions for flow rates of 11 ml/min and 74 ml/min. The quality of the prediction, figure 7.16, is as good as obtained using streamline based simulation solving an ADE with a dispersion coefficient chosen to match the homogeneous results (Obi and Blunt, 2004) or…”

Section: Heterogeneous Porous Mediamentioning

confidence: 87%

“…A very good reproduction of similar experiments by Levy and Berkowitz (2003) was numerically simulated by Obi and Blunt (2004), figures 3.5(a) and 3.5(b). They simulated Figure 3.4: Plot of relative concentration of tracer vs. time for experiment 4 using Gaussian scaled axes by Silliman and Simpson (1987).…”

Section: Pore-scale Dispersionmentioning

confidence: 99%

“…We then divided the domain computationally into 86 × 10 × 45 grid blocks with a uniform permeability of 1500 mD and a porosity of 0.38. The porosity was assumed to be a reasonable value for a well sorted sand (Bear , 1972) and is the value used in the prediction work of Obi and Blunt (2004). We next ran our simulator for a flow rate of 36 ml/min.…”

Section: Homogeneous Sand Packmentioning

confidence: 99%

“…They performed field-scale experiments on a highly heterogeneous alluvial aquifer in Columbus, Mississippi which is subject to a Levy and Berkowitz (2003) in a homogeneous (a) and heterogeneous (b) sand pack to the simulations performed by Obi and Blunt (2004) in a 2D grid system in which the heterogeneity is explicitly modelled.…”

Section: Field-scale Anomalous Dispersion In Fractured and Homogeneoumentioning

confidence: 99%

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Transport in Heterogeneous Porous Media

Civan

2011

Porous Media Transport Phenomena

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We present a new algorithm for modelling single phase transport of a tracer in porous media which demonstrates that structure on all scales affects macroscopic transport behaviour. We marry the robustness of the continuous time random walk (CTRW) framework with the simplicity of a Monte Carlo approach to reservoir simulation. We simulate transport as a series of particles transitioning between nodes with probability ψ(t).dt that a particle will first arrive at a nearest neighbor in a time t to t + dt. To this end we first determine the mixing rules and transition probability ψ ADE (t) for transport governed by the advection-dispersion equation (ADE) (Rhodes and Blunt, 2006).We validate our algorithm by simulating advective transport in bond percolation clusters at the critical point. We compute the histogram of flow speeds using the velocities from the bonds on the backbone and find the multifractal spectrum for two-dimensional lattices with linear dimension L ≤ 2000 and in three dimensions for L ≤ 250. We demonstrate that in the limit of large systems all the negative moments of the velocity distribution become ill-defined. However, to model transport, the velocity histogram should be weighted by the flux to obtain a well-defined mean travel time. Finally, we use CTRW theory to demonstrate that anomalous transport is observed whose characteristics can be related to the multifractal properties of the system.We next demonstrate a pore-to-reservoir simulation methodology which is consistent across all scales of interest. At the micron scale, we fit a truncated power law ψ(t) for the distribution of particle transition times from pore to pore simulations. To do this we use our transport algorithm on a geologically representative network model of Berea sandstone and compare the results to the explicit modelling of advection and molecular

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Section: Heterogeneous Porous Mediamentioning

confidence: 87%

Section: Pore-scale Dispersionmentioning

confidence: 99%

Section: Homogeneous Sand Packmentioning

confidence: 99%

Section: Field-scale Anomalous Dispersion In Fractured and Homogeneoumentioning

confidence: 99%

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Transport in Heterogeneous Porous Media

Civan

2011

Porous Media Transport Phenomena

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“…However, in contrast to the traveltime methods discussed above, the streamline method aims to simulate the actual spatial distribution of concentration and thus requires determining the distribution of streamlines and computing the traveltime distribution along each of them. Obi and Blunt [2004] also extended the streamline-method to model diffusion and dispersion in solute transport problems using an operator splitting technique where dispersive transport is solved on an underlying spatial grid. Spatial aquifer characterizations may be associated with traveltimes to estimate spatial distributions of traveltimes [e.g., Datta-Gupta et al, 2002].…”

Section: Introductionmentioning

confidence: 99%

Traveltime‐based descriptions of transport and mixing in heterogeneous domains

Luo

Cirpka

2008

Water Resources Research

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[1] Modeling mixing-controlled reactive transport using traditional spatial discretization of the domain requires identifying the spatial distributions of hydraulic and reactive parameters including mixing-related quantities such as dispersivities and kinetic mass transfer coefficients. In most applications, breakthrough curves (BTCs) of conservative and reactive compounds are measured at only a few locations and spatially explicit models are calibrated by matching these BTCs. A common difficulty in such applications is that the individual BTCs differ too strongly to justify the assumption of spatial homogeneity, whereas the number of observation points is too small to identify the spatial distribution of the decisive parameters. The key objective of the current study is to characterize physical transport by the analysis of conservative tracer BTCs and predict the macroscopic BTCs of compounds that react upon mixing from the interpretation of conservative tracer BTCs and reactive parameters determined in the laboratory. We do this in the framework of traveltime-based transport models which do not require spatially explicit, costly aquifer characterization. By considering BTCs of a conservative tracer measured on different scales, one can distinguish between mixing, which is a prerequisite for reactions, and spreading, which per se does not foster reactions. In the traveltime-based framework, the BTC of a solute crossing an observation plane, or ending in a well, is interpreted as the weighted average of concentrations in an ensemble of non-interacting streamtubes, each of which is characterized by a distinct traveltime value. Mixing is described by longitudinal dispersion and/or kinetic mass transfer along individual streamtubes, whereas spreading is characterized by the distribution of traveltimes, which also determines the weights associated with each stream tube. Key issues in using the traveltime-based framework include the description of mixing mechanisms and the estimation of the traveltime distribution. In this work, we account for both apparent longitudinal dispersion and kinetic mass transfer as mixing mechanisms, thus generalizing the stochastic-convective model with or without inter-phase mass transfer and the advective-dispersive streamtube model. We present a nonparametric approach of determining the traveltime distribution, given a BTC integrated over an observation plane and estimated mixing parameters. The latter approach is superior to fitting parametric models in cases wherein the true traveltime distribution exhibits multiple peaks or long tails. It is demonstrated that there is freedom for the combinations of mixing parameters and traveltime distributions to fit conservative BTCs and describe the tailing. A reactive transport case of a dual Michaelis-Menten problem demonstrates that the reactive mixing introduced by local dispersion and mass transfer may be described by apparent mean mass transfer with coefficients evaluated by local BTCs.

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Vectorized simulation of groundwater flow and contaminant transport using analytic element method and random walk particle tracking

Majumder

Eldho

2017

Hydrological Processes

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Groundwater contaminant transport processes are usually simulated by the finite difference (FDM) or finite element methods (FEM). However, they are susceptible to numerical dispersion for advection‐dominated transport. In this study, a numerical dispersion‐free coupled flow and transport model is developed by combining the analytic element method (AEM) with random walk particle tracking (RWPT). As AEM produces continuous velocity distribution over the entire aquifer domain, it is more suitable for RWPT than FDM/finite element methods. Using the AEM solutions, RWPT tracks all the particles in a vectorized manner, thereby improving the computational efficiency. The present model performs a convolution integral of the response of an impulse contaminant injection to generate concentration distributions due to a permanent contaminant source. The RWPT model is validated with an available analytical solution and compared to an FDM solution, the RWPT model more accurately replicates the analytical solution. Further, the coupled AEM‐RWPT model has been applied to simulate the flow and transport in hypothetical and field aquifer problems. The results are compared with the FDM solutions and found to be satisfactory. The results demonstrate the efficacy of the proposed method.

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Streamline-based simulation of advective–dispersive solute transport

Cited by 33 publications

References 34 publications

Transport in Heterogeneous Porous Media

Transport in Heterogeneous Porous Media

Traveltime‐based descriptions of transport and mixing in heterogeneous domains

Vectorized simulation of groundwater flow and contaminant transport using analytic element method and random walk particle tracking

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