An Efficient Boundary Integral Formulation for Flow Through Fractured Porous Media

Lough, M.F.; Lee, S.H.; Kamath, Jairam

doi:10.1006/jcph.1998.5858

Cited by 82 publications

(60 citation statements)

References 8 publications

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“…The hydrofractures are extremely permeable with respect to other structural features and define the domain from which shale gas will be produced. In general, the aperture size of fractures is much smaller than the length scale of matrix block fractures, and the hydrofractures can be modelled as two-dimensional planes in an asymptotic approximation (Lough, Lee & Kamath 1998). …”

Section: Hydraulic Fracturesmentioning

confidence: 99%

A dual-tube model for gas dynamics in fractured nanoporous shale formations

Lunati

Lee

2014

J. Fluid Mech.

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Gas flow through fractured nanoporous shale formations is complicated by a hierarchy of structural features (ranging from nanopores to microseismic and hydraulic fractures) and by several transport mechanisms that differ from the standard viscous flow used in reservoir modelling. In small pores, self-diffusion becomes more important than advection; also, slippage effects and Knudsen diffusion might become relevant at low densities. We derive a nonlinear effective diffusion coefficient that describes the main transport mechanisms in shale-gas production. In dimensionless form, this coefficient depends only on a geometric factor (or dimensionless permeability) and on the kinetic model that describes the gas. To simplify the description of the complex structure of fractured shales, we observe that the production rate is controlled by the flow from the shale matrix (which has the smallest diffusivity) into the fracture network, which is assumed to produce instantaneously. Therefore, we propose to model the flow in the shale matrix and estimate the production rate with a simple bundle-of-dual-tubes model (BoDTM), in which each tube is characterized by two diameters (one for transport and the other for storage). The solution of a single tube is approximately self-similar at early time, but not at late time, when the gas flux decays exponentially owing to the finite length of the tube. To construct a BoDTM, a reliable estimate of the joint statistics of the matrix-porosity parameters is required. This can be either inferred from core measurements or postulated on the basis of some a priori assumptions when information from laboratory and field measurements is scarce. By comparison with field production data from the Barnett shale-gas field, we demonstrate that BoDTM can be calibrated to estimate structural parameters of the shale formation and to predict the cumulative production of shale gas. Our framework has enough flexibility to construct models of increasing complexity that can be employed in the presence of a complex dataset or when more information is available.

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Section: Hydraulic Fracturesmentioning

confidence: 99%

A dual-tube model for gas dynamics in fractured nanoporous shale formations

Lunati

Lee

2014

J. Fluid Mech.

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“…In order to homogenize small-scale fractures, Oda (1985) derived a simple analytical expression for enhanced matrix permeability for gridblocks that contain very short fractures. Likewise, Lough et al (1997Lough et al ( , 1998 developed a boundary element method (with uniform pressure and periodic boundary conditions) to calculate effective conductivity for gridblocks containing multiple fractures.…”

Section: Overview Of Edfmmentioning

confidence: 99%

Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs

et al. 2013

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Summary Many naturally fractured reservoirs around the world have depleted significantly, and improved-oil-recovery (IOR) processes are necessary for further development. Hence, the modeling of fractured reservoirs has received increased attention recently. Accurate modeling and simulation of naturally fractured reservoirs (NFRs) is still challenging because of permeability anisotropies and contrasts. Nonphysical abstractions inherent in conventional dual-porosity and dual-permeability models make them inadequate for solving different fluid-flow problems in fractured reservoirs. Also, recent technologies for discrete fracture modeling may suffer from large simulation run times, and the industry has not used such approaches widely, even though they give more-accurate representations of fractured reservoirs than dual-continuum models. We developed an embedded discrete fracture model (DFM) for an in-house compositional reservoir simulator that borrows the dual-medium concept from conventional dual-continuum models and also incorporates the effect of each fracture explicitly. The model is compatible with existing finite-difference reservoir simulators. In contrast to dual-continuum models, fractures have arbitrary orientations and can be oblique or vertical, honoring the complexity of a typical NFR. The accuracy of the embedded DFM is confirmed by comparing the results with the fine-grid, explicit-fracture simulations for a case study including orthogonal fractures and a case with a nonaligned fracture. We also perform a grid-sensitivity study to show the convergence of the method as the grid is refined. Our simulations indicate that to achieve accurate results, the embedded discrete fracture model may only require moderate mesh refinement around the fractures and hence offers a computationally efficient approach. Furthermore, examples of waterflooding, gas injection, and primary depletion are presented to demonstrate the performance and applicability of the developed method for simulating fluid flow in NFRs.

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“…The previous cell was used as a means to study porous media or fractures, in the same way as a Hele-Shaw cell can be used for such a study (e.g., Lough et al 1998;Oltean et al 2004). As the macroscopic flow is globally directed along x 1 , we can define both macroscopic 1D-pressure P and 1D-velocity V as follows: (1) where S(x 1 ) is the vertical cross-section, |S(x 1 )| is the cross-section area and e 1 is the unit vector along x 1 .…”

Section: Macroscopic Flow Equationmentioning

confidence: 99%

The impact of instability appearance on the quadratic law for flow through porous media

Lucas¹,

Panfilov²,

Buès³

2007

Transp Porous Med

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In the present paper, we attempt to explain the macroscopic flow law evolution in porous media according to the Reynolds number. A crenellated channel, considered as an element of such a medium, is used to perform numerical simulations in stationary and non-stationary cases. In the case of non-stationary laminar flows, we point out flow instabilities occurring in the channel at high Reynolds numbers and we focus on their influence on the macroscopic law. We qualitatively prove that they generate an additional quadratic contribution to Forchheimer's law. We use two methods to study this contribution: first, a periodic disturbance, for which the instabilities appearing at the beginning of disturbance become regular oscillations; then a pulse disturbance of the entry velocity field which enables us to link the additional quadratic contribution to the existence of an accumulation of fluid at low velocity in the channel.

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An Efficient Boundary Integral Formulation for Flow Through Fractured Porous Media

Cited by 82 publications

References 8 publications

A dual-tube model for gas dynamics in fractured nanoporous shale formations

A dual-tube model for gas dynamics in fractured nanoporous shale formations

Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs

The impact of instability appearance on the quadratic law for flow through porous media

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