Anomalous transport in heterogeneous media demonstrated by streamline‐based simulation

Donato, Ginevra Di; Obi, Eguono-Oghene; Blunt, Martin J.

doi:10.1029/2003gl017196

Cited by 52 publications

(49 citation statements)

References 26 publications

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“…Several tracer tests in heterogeneous aquifers [Adams and Gelhar, 1992;Sidle et al, 1998;Becker and Shapiro 2000;Haggerty et al, 2001] have indicated behavior that cannot be predicted assuming Gaussian spreading of the plume. Di Donato et al [2003] demonstrated using streamline-based simulation that advective movement with particles experiencing a wide range of velocities could be the physical origin of anomalous transport at the large scale, confirming the theoretical and numerical studies of Berkowitz and Scher [1995, 1998, 2001]. We will pursue this concept further by including rate-limited sorption in the model.…”

Section: Introductionmentioning

confidence: 97%

“…It is possible to include dispersion and diffusion (both longitudinal and transverse) in a streamline model using an operator splitting technique, where the dispersive portion of the conservation equation is solved on the underlying grid using conventional techniques [Di Donato et al, 2003]. The effects of ignoring dispersion on the results presented in this paper will be discussed later.…”

Section: Passive Tracer Transport Modelmentioning

confidence: 99%

“…Since a source of tracer is initially present in the porous medium occupying a region with both high and low permeabilities, the tracer flows with highly variable velocities once water injection begins [Di Donato et al, 2003]. The first arrivals of the tracer depend on how high the permeability values are, while the behavior of the breakthrough curves at late time is controlled by the presence of the tracer in the low-permeability regions.…”

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confidence: 99%

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Streamline‐based dual‐porosity simulation of reactive transport and flow in fractured reservoirs

Donato

Blunt

2004

Water Resources Research

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[1] We present a streamline-based formulation to model two processes: transport of a tracer undergoing rate-limited sorption and two-phase (water/oil or air/water) transport in fractured systems, using a dual-porosity approach. We show that these two processes can be simulated using mathematically equivalent formulations. In both cases the system conceptually has two components: a flowing fraction connected to stagnant regions with transfer between the two domains. Streamlines capture movement through the flowing fraction. Fluid transfer between flowing and stagnant regions enters as a source/sink term in the one-dimensional transport equations along a streamline. To model flow and transport in fractured systems, we develop a new formulation for the transfer function that matches experimental imbibition data. Then we illustrate the streamline approach with synthetic reservoir problems. We use a finely gridded (over one million grid blocks) threedimensional domain with a highly heterogeneous permeability field to study both fracture flow and tracer transport. We find breakthrough curves that are consistent with anomalous transport described by an exponent that characterizes the longtime tail of the transit time distribution. For fracture flow we demonstrate that the speed of fluid advance in the fractures is controlled by the imbibition rate. The run times for the simulations scale approximately linearly with system size, making the method appropriate for the simulation of large numerical models.

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Section: Introductionmentioning

confidence: 97%

Section: Passive Tracer Transport Modelmentioning

confidence: 99%

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confidence: 99%

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Streamline‐based dual‐porosity simulation of reactive transport and flow in fractured reservoirs

Donato

Blunt

2004

Water Resources Research

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“…(b) The breakthrough curves for simulated field studies of varying heterogeneity by Di Donato et al (2003) Figure 3.1: The theoretical concentration plumes for Gaussian and anomalous transport and the breakthrough curves for simulated field-scale experiments demonstrating anomalous transport.…”

Section: Anomalous Transportmentioning

confidence: 99%

“…This will not be true in real systems where the injection conditions would force most of the fluid into the high flux regions surrounding the injector. Instead, the histogram of particle velocities must be weighted by the flux (velocity) to represent realistic initial conditions (Di Donato et al, 2003). If on the other hand we launch particles uniformly across the boundary this would not be the case and the standard f (α) curve would have to be used to model transport.…”

Section: Motivationmentioning

confidence: 99%

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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Solute transport in low‐heterogeneity sandboxes: The role of correlation length and permeability variance

Heidari

2014

Water Resources Research

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This work examines how heterogeneity structure, in particular correlation length, controls flow and solute transport. We used two-dimensional (2D) sandboxes (21.9 cm 3 20.6 cm) and four modeling approaches, including 2D Advection-Dispersion Equation (ADE) with explicit heterogeneity structure, 1D ADE with average properties, and nonlocal Continuous Time Random Walk (CTRW) and fractional ADE (fADE). The goal is to answer two questions: (1) how and to what extent does correlation length control effective permeability and breakthrough curves (BTC)? (2) Which model can best reproduce data under what conditions? Sandboxes were packed with the same 20% (v/v) fine and 80% (v/v) coarse sands in three patterns that differ in correlation length. The Mixed cases contain uniformly distributed fine and coarse grains. The Four-zone and One-zone cases have four and one square fine zones, respectively. A total of seven experiments were carried out with permeability variance of 0.10 (LC), 0.22 (MC), and 0.43 (HC). Experimental data show that the BTC curves depend strongly on correlation length, especially in the HC cases. The HC One-zone (HCO) case shows distinct breakthrough steps arising from fast advection in the coarse zone, slow advection in the fine zone, and slow diffusion, while the LCO and MCO BTCs do not exhibit such behavior. With explicit representation of heterogeneity structure, 2D ADE reproduces BTCs well in all cases. CTRW reproduces temporal moments with smaller deviation from data than fADE in all cases except HCO, where fADE has the lowest deviation.

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Anomalous transport in heterogeneous media demonstrated by streamline‐based simulation

Cited by 52 publications

References 26 publications

Streamline‐based dual‐porosity simulation of reactive transport and flow in fractured reservoirs

Streamline‐based dual‐porosity simulation of reactive transport and flow in fractured reservoirs

Transport in Heterogeneous Porous Media

Solute transport in low‐heterogeneity sandboxes: The role of correlation length and permeability variance

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