## Impact of velocity correlation and distribution on transport in fractured media: Field evidence and theoretical model

## Abstract

Flow and transport through fractured geologic media often leads to anomalous (non-Fickian) transport behavior, the origin of which remains a matter of debate: whether it arises from variability in fracture permeability (velocity distribution), connectedness in the flow paths through fractures (velocity correlation), or interaction between fractures and matrix. Here we show that this uncertainty of distribution- versus correlation-controlled transport can be resolved by combining convergent and push-pull tracer tests because flow reversibility is strongly dependent on velocity correlation, whereas late-time scaling of breakthrough curves is mainly controlled by velocity distribution. We build on this insight, and propose a Lagrangian statistical model that takes the form of a continuous time random walk (CTRW) with correlated particle velocities. In this framework, velocity distribution and velocity correlation are quantified by a Markov process of particle transition times that is characterized by a distribution function and a transition probability. Our transport model accurately captures the anomalous behavior in the breakthrough curves for both push-pull and convergent flow geometries, with the same set of parameters. Thus, the proposed correlated CTRW modeling approach provides a simple yet powerful framework for characterizing the impact of velocity distribution and correlation on transport in fractured media.

- Authors:

- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Univ. de Rennes (France)
- Spanish National Research Council (CSIC), Barcelona (Spain). Inst. of Environmental Assessment and Water Research

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1557838

- Grant/Contract Number:
- SC0003907

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Water Resources Research

- Additional Journal Information:
- Journal Volume: 51; Journal Issue: 2; Journal ID: ISSN 0043-1397

- Publisher:
- American Geophysical Union (AGU)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 58 GEOSCIENCES

### Citation Formats

```
Kang, Peter K., Le Borgne, Tanguy, Dentz, Marco, Bour, Olivier, and Juanes, Ruben. Impact of velocity correlation and distribution on transport in fractured media: Field evidence and theoretical model. United States: N. p., 2014.
Web. doi:10.1002/2014WR015799.
```

```
Kang, Peter K., Le Borgne, Tanguy, Dentz, Marco, Bour, Olivier, & Juanes, Ruben. Impact of velocity correlation and distribution on transport in fractured media: Field evidence and theoretical model. United States. doi:10.1002/2014WR015799.
```

```
Kang, Peter K., Le Borgne, Tanguy, Dentz, Marco, Bour, Olivier, and Juanes, Ruben. Mon .
"Impact of velocity correlation and distribution on transport in fractured media: Field evidence and theoretical model". United States. doi:10.1002/2014WR015799. https://www.osti.gov/servlets/purl/1557838.
```

```
@article{osti_1557838,
```

title = {Impact of velocity correlation and distribution on transport in fractured media: Field evidence and theoretical model},

author = {Kang, Peter K. and Le Borgne, Tanguy and Dentz, Marco and Bour, Olivier and Juanes, Ruben},

abstractNote = {Flow and transport through fractured geologic media often leads to anomalous (non-Fickian) transport behavior, the origin of which remains a matter of debate: whether it arises from variability in fracture permeability (velocity distribution), connectedness in the flow paths through fractures (velocity correlation), or interaction between fractures and matrix. Here we show that this uncertainty of distribution- versus correlation-controlled transport can be resolved by combining convergent and push-pull tracer tests because flow reversibility is strongly dependent on velocity correlation, whereas late-time scaling of breakthrough curves is mainly controlled by velocity distribution. We build on this insight, and propose a Lagrangian statistical model that takes the form of a continuous time random walk (CTRW) with correlated particle velocities. In this framework, velocity distribution and velocity correlation are quantified by a Markov process of particle transition times that is characterized by a distribution function and a transition probability. Our transport model accurately captures the anomalous behavior in the breakthrough curves for both push-pull and convergent flow geometries, with the same set of parameters. Thus, the proposed correlated CTRW modeling approach provides a simple yet powerful framework for characterizing the impact of velocity distribution and correlation on transport in fractured media.},

doi = {10.1002/2014WR015799},

journal = {Water Resources Research},

number = 2,

volume = 51,

place = {United States},

year = {2014},

month = {12}

}

Works referenced in this record:

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- Pruess, Karsten
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