Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes

We investigate large‐scale particle motion and solute breakthrough in sparse three‐dimensional discrete fracture networks characterized by power law distributed fracture lengths. The three networks we consider have the same fracture intensity values but exhibit different percolation densities, geometric properties, and topological structures. We considered two different average transport models to predict solute breakthrough, a streamtube model and a Bernoulli continuous time random walk model, both of which provide insights into the flow fields within the networks. The streamtube model provides acceptable predictions at short distances in two of the networks but fails in all cases to predict breakthrough times at the outlet plane, which indicates that particle motion in such fracture networks cannot be characterized by a constant velocity between the inlet and control plane at which the breakthrough curve is detected. Rather, the structure of the network requires that frequent velocity transitions be made as particles move through the system. Despite the relatively broad distribution of fracture radii and relatively small number of independent velocity transitions, the continuous time random walk approach conditioned on the initial velocity distribution provides reasonable predictions for the breakthrough curves at different distances from the inlet. The application of these averaged transport models provides a richer understanding of the link from the fracture network structure to flow and transport properties.

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“…Under ergodic conditions, this means for a sufficiently large injection volume and flow domain, the steady space Lagrangian PDF

p_{ℓ} false(v false) = \lim_{ℓ \to \infty} {\overset{p}{true}}_{ℓ} false(v, ℓ false)

and the Eulerian velocity PDFs are related through flux‐weighting as shown in (Comolli & Dentz, ; Dentz et al, ; Kang et al, ):

p_{ℓ} false(v false) = \frac{v p_{e} false(v false)}{⟨ v_{e} ⟩} .

…”

Section: Flow and Transport Behaviormentioning

confidence: 99%

Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks

et al. 2019

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“…The difference between the two simulations is the initial positions of particles, flux weighted (left) and resident (right). More particles sample low-velocity regions under resident injection, which leads to a broader distribution of travel times and slower decay rate (Frampton and Cvetkovic, 2009;Kang et al, 2017). The simplest probability distribution that can describe this power law tail behavior is a Pareto distribution where t ,min denotes the minimum advective travel time across the population of streamlines.…”

Section: Discrete Fracture Network Simulations: Particle Travel Time mentioning

confidence: 99%

Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves

Hyman

Rajaram

Srinivasan

et al. 2019

Geophysical Research Letters

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We develop a theoretical model for power law tailing behavior of transport in fractured rock based on the relative dominance of the decay rate of the advective travel time distribution, modeled using a Pareto distribution (with tail decaying as ∼ time −(1+ ) ), versus matrix diffusion, modeled using a Lévy distribution. The theory predicts that when the advective travel time distribution decays sufficiently slowly ( < 1), the late-time decay rate of the breakthrough curve is −(1 + ∕2) rather than the classical −3/2. However, if > 1, the −3/2 decay rate is recovered. For weak matrix diffusion or short advective first breakthrough times, we identify an early-time regime where the breakthrough curve follows the Pareto distribution, before transitioning to the late-time decay rate. The theoretical predictions are validated against particle tracking simulations in the three-dimensional discrete fracture network simulator dfnWorks, where matrix diffusion is incorporated using a time domain random walk.

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“…Detailed investigations of the relationship between injection modes and heterogeneity in the dispersion of solute particles in fracture networks able to store parts of solute mass were recently conducted by [20][21][22]. Based on the results in [20,21], the type of injection mode has a significant persistent impact on dispersion in a fracture network; more so for larger heterogeneity.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the results in [20,21], the type of injection mode has a significant persistent impact on dispersion in a fracture network; more so for larger heterogeneity. The late arrivals for resident injection are several orders of magnitude larger than those related to flux injection, indicating that dispersion along the macroscopic flow direction is significantly enhanced by resident injection.…”

Section: Introductionmentioning

confidence: 99%

“…The main result of the study can be synthesized in the detection of strong Lagrangian correlation and anomalous dispersion for velocity distributions that are tailed toward low values, as well as in pronounced differences depending on the initial conditions. Note that all mentioned studies ( [20][21][22][23][24]) investigate the relationship between injection modes and advective heterogeneity on solute dispersion without discussing the effect of local dispersion magnitude. This effect is expected to be definitely more pronounced for transport in porous media, which is the focus of the present study.…”

Section: Introductionmentioning

confidence: 99%

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An Analytical Model of Fickian and Non-Fickian Dispersion in Evolving-Scale Log-Conductivity Distributions

Pannone

2017

Water

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Abstract:The characteristics of solute transport within log-conductivity fields represented by power-law semi-variograms are investigated by an analytical Lagrangian approach that accounts for the automatic frequency cut-off induced by the initial contaminant plume size. The transport process anomaly is critically controlled by the magnitude of the Péclet number. Interestingly enough, unlike the case of fast-decaying correlation functions (i.e., exponential or Gaussian), the presence of intensive transverse diffusion acts as an antagonist mechanism in the process of Fickian regime achievement. On the other hand, for markedly advective conditions and finite initial plume size, even the ergodic longitudinal dispersion coefficient turns out to be asymptotically constant, and the corresponding expected concentration distribution can therefore be obtained by conventional mathematical methods.

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Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes

Cited by 67 publications

References 98 publications

Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks

Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks

Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves

An Analytical Model of Fickian and Non-Fickian Dispersion in Evolving-Scale Log-Conductivity Distributions

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