Fluid velocity and path length in fractured media

Parney, Robert; Smith, Leslie

doi:10.1029/95gl01494

Cited by 17 publications

(11 citation statements)

References 3 publications

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“…For a given flow rate, the lines of flux are arranged so that the potential drop is the smallest possible, and in any pore space there is only one solution to the flow equations, which is always the most efficient. Parney & Smith (1995) demonstrate this in simulations of fluid flow in discrete fracture networks. As the interconnections become more restricted, flow occurs along a path which is more geometrically tortuous on the average, but which makes the best use of the wider channels so that the velocity in the direction of the overall flow gradient is still the maximum possible.…”

Section: (84)mentioning

confidence: 90%

“…This is evident from flow simulations in networks (e.g. Ruth & Suman 1992;David 1993;Bernab6 1995) and in representational flow models (e.g., Parney & Smith 1995). Nevertheless, flow efficiency can still be expressed in this way providing that the 'paths' are correctly weighted for the flux that they carry.…”

Section: Tortuosity and Path Length Revisited" How Long Is A Piece Omentioning

confidence: 92%

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Tortuosity: a guide through the maze

Clennell

1997

361

241

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Despite its widespread use in petrophysics, tortuosity remains a poorly understood concept. Tortuosity can have various meanings when used by physicists, engineers or geologists to describe different transport processes taking place in a porous material. Values for geometrical, electrical, diffusional and hydraulic tortuosity are in general different from one another. Electrical tortuosity is defined in terms of conductivity whereas hydraulic tortuosity is usually defined geometrically, and diffusional tortuosity is typically computed from temporal changes in concentration. A better approach may be to define tortuosity in terms of the underlying flux of material or electrical current with respect to the forces which drive this flow. Unsteady transport processes, including diffusion, can be described only by a population of tortuosities corresponding to the different flow paths taken by particles traversing the medium. In measurements of steady flow (e.g., those normally used to obtain resistivity or permeability), information about particle travel times is lost, and so the multiple values of tortuosity are homogenised. It can be shown that the maximum amount of information about pore structure is embedded in transport processes that combine advective and diffusive elements. Most existing formulations of tortuosity are model-dependent, and cannot be correlated with independently measurable pore-structure properties. Nevertheless, tortuosity underpins the rigorous relationships between transport processes in rocks, and ties them with the underlying geometry and topology of their pore spaces. Tortuosity can be redefined in terms of the energetic efficiency of a flow process. The efficiency is related to the rate of entropy dissipation (or isothermally, energy dissipation) with respect to a simple, non-tortuous model medium using the postulates of non-equilibrium thermodynamics. Through Onsager’s reciprocity relation for coupled flows it is possible to inter-relate efficiency for pairs of transport processes, and so go some way towards unifying tortuosity measures. In this way we can approach the goal of predicting the value of one transport parameter from measurements of another.

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Section: (84)mentioning

confidence: 90%

Section: Tortuosity and Path Length Revisited" How Long Is A Piece Omentioning

confidence: 92%

Tortuosity: a guide through the maze

Clennell

1997

361

241

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“…If one considers that in order for multiple fractures to be hydraulically connected, channels must “link up” at fracture junctures, it may be that channeling can have a more profound effect over larger transport distances [ Abelin et al , 1991; Tsang et al , 1991]. Parney and Smith [1995] have suggested that transport paths in fractured media tend to lengthen as velocity increases. This implies that forced‐gradient tracer experiments may produce more channeled flow than would exist under natural gradients.…”

Section: Introductionmentioning

confidence: 99%

Interpreting tracer breakthrough tailing from different forced‐gradient tracer experiment configurations in fractured bedrock

Becker

Shapiro

2003

Water Resources Research

143

183

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[1] Conceptual and mathematical models are presented that explain tracer breakthrough tailing in the absence of significant matrix diffusion. Model predictions are compared to field results from radially convergent, weak-dipole, and push-pull tracer experiments conducted in a saturated crystalline bedrock. The models are based upon the assumption that flow is highly channelized, that the mass of tracer in a channel is proportional to the cube of the mean channel aperture, and the mean transport time in the channel is related to the square of the mean channel aperture. These models predict the consistent À2 straight line power law slope observed in breakthrough from radially convergent and weak-dipole tracer experiments and the variable straight line power law slope observed in push-pull tracer experiments with varying injection volumes. The power law breakthrough slope is predicted in the absence of matrix diffusion. A comparison of tracer experiments in which the flow field was reversed to those in which it was not indicates that the apparent dispersion in the breakthrough curve is partially reversible. We hypothesize that the observed breakthrough tailing is due to a combination of local hydrodynamic dispersion, which always increases in the direction of fluid velocity, and heterogeneous advection, which is partially reversed when the flow field is reversed. In spite of our attempt to account for heterogeneous advection using a multipath approach, a much smaller estimate of hydrodynamic dispersivity was obtained from push-pull experiments than from radially convergent or weak dipole experiments. These results suggest that although we can explain breakthrough tailing as an advective phenomenon, we cannot ignore the relationship between hydrodynamic dispersion and flow field geometry at this site. The design of the tracer experiment can severely impact the estimation of hydrodynamic dispersion and matrix diffusion in highly heterogeneous geologic media. INDEX TERMS:1829 Hydrology: Groundwater hydrology; 1832 Hydrology: Groundwater transport; 5104 Physical Properties of Rocks: Fracture and flow; KEYWORDS: fractured rock, matrix diffusion, tracer tests, contaminant transport, advection dispersion, channeling Citation: Becker, M. W., and A. M. Shapiro, Interpreting tracer breakthrough tailing from different forced-gradient tracer experiment configurations in fractured bedrock, Water Resour.

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“…Assuming statistical homogeneity, fitted particle‐motion distributions are then sampled in a random walk through a regional‐scale head field, which is solved by deterministic continuum modeling. This approach was later improved by accounting for preferential flow [ Parney and Smith , 1995], by including correlation between particle velocity and path length that is also determined from the “subdomain.” Recently, the linear Boltzmann transport equation was used in a rather similar hybrid approach to describe particle motion in fractured media [ Benke and Painter , 2003]. Fracture intersections are represented by “molecule collisions” in a fluid, in the sense that they may cause abrupt changes in the direction and velocity of a particle during a random walk.…”

Section: Introductionmentioning

confidence: 99%

A regional‐scale particle‐tracking method for nonstationary fractured media

Öhman

Niemi

Tsang

2005

Water Resources Research

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[1] A regional-scale transport model is introduced that is applicable to nonstationary and statistically inhomogeneous fractured media, provided that hydraulic flow, but not necessarily solute transport, can be approximated by equivalent continuum properties at some block scale. Upscaled flow and transport block properties are transferred from multiple fracture network realizations to a regional model with grid elements of size equal to that found valid for continuum approximation of flow. In the regional-scale model, flow is solved in a stochastic continuum framework, whereas the transport calculations employ a random walk procedure. Block-wise transit times are sampled from distributions linked to each block based on its underlying fracture network. To account for channeled transport larger than the block scale, several alternative sampling algorithms are introduced and compared. The most reasonable alternative incorporates a spatial persistence length in sampling the particle transit times; this tracer transport persistence length is related to interblock channeling, and is quantified by the number N of blocks. The approach is demonstrated for a set of field data, and the obtained regional-scale particle breakthroughs are analyzed. These are fitted to the one-dimensional advectivedispersive equation to determine an effective macroscale dispersion coefficient for the regional scale. An interesting finding is that this macroscale dispersion coefficient is found to be a linear function of the transport persistence, N, with a slope equal to a representative mean block-scale dispersion coefficient and a constant that incorporates background dispersion arising from the regional heterogeneous conductivity field.Citation: Ö hman, J., A. Niemi, and C.-F. Tsang (2005), A regional-scale particle-tracking method for nonstationary fractured media, Water Resour. Res., 41, W03016,

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Fluid velocity and path length in fractured media

Cited by 17 publications

References 3 publications

Tortuosity: a guide through the maze

Tortuosity: a guide through the maze

Interpreting tracer breakthrough tailing from different forced‐gradient tracer experiment configurations in fractured bedrock

A regional‐scale particle‐tracking method for nonstationary fractured media

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