One- And Two-Phase Flow in Network Models of Porous Media

Koplik, Joel; Lasseter, Thomas J.

doi:10.1080/00986448408940216

Cited by 44 publications

(11 citation statements)

References 4 publications

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“…There are two basic approaches to the simulation of multiphase flow in a porous medium. The first approach is to make some simplifying assumptions about the flow, such as a linear force-flux law, and also about the porous medium, such as its geometric properties [Chandler et al, 1982;Koplik and Lasseter, 1985;Dias and Payatakes, 1986]. This approach we generically call "network modeling" since the porous medium is typically modeled as a network of pores and throats.…”

Section: Methodsmentioning

confidence: 99%

Lattice‐Boltzmann studies of immiscible two‐phase flow through porous media

Gunstensen¹,

Rothman²

1993

J. Geophys. Res.

148

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Using a recently introduced numerical technique known as a lattice-Boltzmann method, we numerically investigate immiscible two-phase flow in a three-dimensional microscopic model of a porous medium and attempt to establish the form of the macroscopic flow law. We observe that the conventional linear description of the flow is applicable for high levels of forcing when the relative effects of capillary forces are small. However, at low levels of forcing capillary effects become important and the flow law becomes nonlinear. By constructing a two-dimensional phase diagram in the parameter space of nonwetting saturation and dimensionless forcing, we delineate the various regions of linearity and nonlinearity and attempt to explain the underlying physical mechanisms that create these regions. In particular, we show that the appearance of percolated, throughgoing flow paths depends not only on the relative concentrations of the two fluids but also on a dimensionless number that represents the ratio of the applied force to the force necessary for nonwetting fluid to fully penetrate through the porous medium. Finally, we fit a linear model to our simulation data in the high-forcing regions of the system and observe that an Onsager reciprocity holds for the viscous coupling of the two fluids. ß e ß e c ß ß ß ß ß ß e %, ß E ? Macmillan, New York, 1960. Wolfram, S., Cellular automaton fluids, 1, Basic theory, J. Stat. Phys., 45,471-526, 1986. Zanetti, G., The hydrodynamics of lattice gas automata, Phys. Rev A,

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Section: Methodsmentioning

confidence: 99%

Lattice‐Boltzmann studies of immiscible two‐phase flow through porous media

Gunstensen¹,

Rothman²

1993

J. Geophys. Res.

148

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“…The idea of modelling a porous medium by a network of randomly sized pores joined by randomly sized throats has been used by several authors (for instance Koplik & Lasseter 1985;Dias & Payatakes 1986a and references therein). If the fluids are Newtonian and if the capillary effects are neglected this approach leads to a linear system of equations in which the unknowns are the fluid pressures at the nodes.…”

Section: Principle Of the Network Simdatormentioning

confidence: 99%

“…The method of Koplik & Lasseter (1985) in this simple case, would consist in first making the hypothesis that the fluid flows only into tube 1, computing the corresponding pressure, checking if P < P,, and, if not, recomputing the pressure assuming that the fluid flows into both tubes. Dias & Payatakes ( 1 9 8 6~) would replace the cylindrical tubes by conical throats and compute step by step the menisci displacements.…”

Section: R Lenormand E Touboul and C Zarconementioning

confidence: 99%

Numerical models and experiments on immiscible displacements in porous media

1988

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Immiscible displacements in porous media with both capillary and viscous effects can be characterized by two dimensionless numbers, the capillary number C, which is the ratio of viscous forces to capillary forces, and the ratio M of the two viscosities. For certain values of these numbers, either viscous or capillary forces dominate and displacement takes one of the basic forms: (a) viscous fingering, ( b ) capillary fingering or (c) stable displacement. We present a study in the simple case of injection of a non-wetting fluid into a two-dimensional porous medium made of interconnected capillaries. The first part of this paper presents the results of network simulators (100 x 100 and 25 x 25 pores) based on the physical rules of the displacement a t the pore scale. The second part describes a series of experiments performed in transparent etched networks. Both the computer simulations and the experiments cover a range of several decades in C and M . They clearly show the existence of the three basic domains (capillary fingering, viscous fingering and stable displacement) within which the patterns remain unchanged. The domains of validity of the three different basic mechanisms are mapped onto the plane with axes C and M , and this mapping represents the 'phase-diagram ' for drainage. In the final section we present three statistical models (percolation, diffusion-limited aggregation (DLA) and anti-DLA) which can be used for describing the three 'basic' domains of the phase-diagram.

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“…The crossed-square lattice, or square lattice with nearest-and next-nearestneighbour bonds shown in Figure 2a, has proved popular as a model for pore-network structure (Singhal and Somerton 1977;Koplik and Lasseter, 1984). This is because its quasi-two-dimensional structure renders it computationally tractable, while allowing for the presence of bicontinuous fluid distributions.…”

Section: Application To the Crossed-square Latticementioning

confidence: 99%

Application of generalised effective-medium theory to transport in porous media

Harris

1990

Transp Porous Med

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Abstract. The use of effective-medium treatments to estimate bulk properties pertaining to transport (of, for example, fluids, heat, particles or electricity) through random composite media (such as reservoir rocks), is widespread. This is because they are relatively simple, often reasonably accurate (on occasion, remarkably so) and in many cases yield closed-form expressions for the properties concerned. However, the single-bond effective-medium treatment (EMT) of random resistor networks that has been used to determine transport coefficients for various transport problems in pore networks is limited to some special isotropic networks with nearest-neighbour connections. We demonstrate here that transport through two different fracture system models, with stress-induced anisotropy, can be treated using an EMT originally applied to anisotropic resistor networks. The main purpose of the present contribution, however, is to present a new, more general effective medium formalism applicable to networks of arbitrary topology. This new generalised EMT is used to obtain a new criterion for percolation of an arbitrary conducting network under random dilution. A specific application to unsaturated flow through a pore network with nearest-and next-nearest-neighbour connections is also given.

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One- And Two-Phase Flow in Network Models of Porous Media

Cited by 44 publications

References 4 publications

Lattice‐Boltzmann studies of immiscible two‐phase flow through porous media

Lattice‐Boltzmann studies of immiscible two‐phase flow through porous media

Numerical models and experiments on immiscible displacements in porous media

Application of generalised effective-medium theory to transport in porous media

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