Random Walk Methods for Modeling Hydrodynamic Transport in Porous and Fractured Media from Pore to Reservoir Scale

Nœtinger, B.; Roubinet, Delphine; Russian, Anna; Borgne, Tanguy Le; Delay, Frédérick; Dentz, Marco; Dreuzy, Jean‐Raynald de; Gouze, Philippe

doi:10.1007/s11242-016-0693-z

Cited by 110 publications

(98 citation statements)

References 207 publications

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“…The particle trajectory x ( s , a ) is obtained numerically from

x_{n + 1} = \frac{boldq false[x_{n} false] normalΔ s}{false| boldq false(x_{n} false) false|}, t_{n + 1} = t_{n} + \frac{normalΔ s}{boldq false[x_{n} false]},

where we set x n = x ( n Δ s , a ) and t n = t ( n Δ s , a ). This method can be considered a TDRW (Noetinger et al, ). It is of advantage in scenarios, which are characterized by the presence of regions of very low velocities as it the case in this study because the number of steps does not depend on the local velocity value as in time‐stepping methods.…”

Section: Flow and Transport In Heterogeneous Porous Mediamentioning

confidence: 99%

Upscaling and Prediction of Lagrangian Velocity Dynamics in Heterogeneous Porous Media

Hakoun

Comolli

Dentz

2019

Water Resources Research

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The understanding of the dynamics of Lagrangian velocities is key for the understanding and upscaling of solute transport in heterogeneous porous media. The prediction of large‐scale particle motion in a stochastic framework implies identifying the relation between the Lagrangian velocity statistics and the statistical characteristics of the Eulerian flow field and the hydraulic medium properties. In this paper, we approach both challenges from numerical and theoretical points of view. Direct numerical simulations of Darcy‐scale flow and particle motion give detailed information on the evolution of the statistics of particle velocities both as a function of travel time and distance along streamlines. Both statistics evolve from a given initial distribution to different steady‐state distributions, which are related to the Eulerian velocity probability density function. Furthermore, we find that Lagrangian velocities measured isochronally as a function of travel time show intermittency dominated by low velocities, which is removed when measured equidistantly as a function of travel distance. This observation gives insight into the stochastic dynamics of the particle velocity series. As the equidistant particle velocities show a regular random pattern that fluctuates on a characteristic length scale, it is represented by two stationary Markov processes, which are parametrized by the distribution of flow velocities and a correlation distance. The velocity Markov models capture the evolution of the Lagrangian velocity statistics in terms of the Eulerian flow properties and a characteristics length scale and shed light on the role of the initial conditions and flow statistics on large‐scale particle motion.

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“…The particle trajectory x ( s , a ) is obtained numerically from

x_{n + 1} = \frac{boldq false[x_{n} false] normalΔ s}{false| boldq false(x_{n} false) false|}, t_{n + 1} = t_{n} + \frac{normalΔ s}{boldq false[x_{n} false]},

Section: Flow and Transport In Heterogeneous Porous Mediamentioning

confidence: 99%

Upscaling and Prediction of Lagrangian Velocity Dynamics in Heterogeneous Porous Media

Hakoun

Comolli

Dentz

2019

Water Resources Research

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“…We consider here purely advective transport and represent the spreading of a nonreactive conservative solute in the DFN by a cloud of passive tracer particles, that is, using a Lagrangian approach. For the use of particle tracking to solve transport in fracture networks, see also Berkowitz and Scher () and Huseby et al () and the review by Noetinger et al (). The imposed pressure gradient is aligned with the x axis, and thus, the primary direction of flow is also in this direction.…”

Section: Flow and Transport Simulationsmentioning

confidence: 99%

Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks

et al. 2019

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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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“…To illustrate this point, we start with a simple fracture and matrix geometry. There are additional complications in the definition of shape factor when the matrix blocks are irregularly shaped and non-uniform in size [17][18][19][20][21][22][23][24][25][26][27]. As a start, we focus on the issue of non-uniform flow in the fractures, and choose a simple geometry to highlight this aspect.…”

Section: Tablementioning

confidence: 99%

Characteristic Fracture Spacing in Primary and Secondary Recovery for Naturally Fractured Reservoirs

Gong

Rossen

2017

Proceedings

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. Characteristic fracture spacing in primary and secondary recovery for naturally fractured reservoirs. Fuel: the science and technology of fuel and energy, 223, 470-485. https://doi.org/10.1016/j.fuel.2018.02.046 Important noteTo cite this publication, please use the final published version (if applicable). Please check the document version above. CopyrightOther than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policyPlease contact us and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim. A B S T R A C TIf the aperture distribution is broad enough in a naturally fractured reservoir, even one where the fracture network is highly inter-connected, most fractures can be eliminated without significantly affecting the flow through the fracture network. During a waterflood or enhanced-oil-recovery (EOR) process, the production of oil depends on the supply of injected water or EOR agent. This suggests that the characteristic fracture spacing (or shape factor) for the dual-porosity/dual-permeability simulation of waterflood or EOR in a naturally fractured reservoir should account not for all fractures but only the relatively small number of fractures carrying almost all the injected water or EOR agent ("primary," as opposed to "secondary," fractures). In contrast, in primary production even a relatively small fracture represents an effective path for oil to flow to a production well. This distinction suggests that the "shape factor" in dual-permeability reservoir simulations and the repeating unit in homogenization should depend on the process involved: specifically, it should be different for primary and secondary or tertiary recovery. We test this hypothesis in a simple representation of a fractured region with a non-uniform distribution of fracture flow conductivities. We compare oil production, flow patterns in the matrix, and the pattern of oil recovery with and without the "secondary" fractures that carry only a small portion of injected fluid. The role of secondary fractures depends on a dimensionless ratio of characteristic times for matrix and fracture flow (Peclet number), and the ratio of flow carried by the different fractures. In primary production, for a large Peclet number, treating all the fractures equally is a better approximation of the original model, than excluding the secondary fractures; the shape factor should reflect both the primary and the secondary fractures. For a sufficiently small Peclet number, it is more accurate to exclude the secondary fractures in calculation of the shape factor in the dual-porosity/dual-permeability models than to include them and, in effect, assume they play an equally important role in transport to and from the matrix. For waterflood or EOR, in most cases examined, the a...

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Random Walk Methods for Modeling Hydrodynamic Transport in Porous and Fractured Media from Pore to Reservoir Scale

Cited by 110 publications

References 207 publications

Upscaling and Prediction of Lagrangian Velocity Dynamics in Heterogeneous Porous Media

Upscaling and Prediction of Lagrangian Velocity Dynamics in Heterogeneous Porous Media

Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks

Characteristic Fracture Spacing in Primary and Secondary Recovery for Naturally Fractured Reservoirs

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