Ensemble phase averaged equations for multiphase flows in porous media. Part 1: The bundle-of-tubes model

Yang, Dali; Currier, Robert P.; Zhang, Duan Z.

doi:10.1016/j.ijmultiphaseflow.2009.03.002

Cited by 20 publications

(10 citation statements)

References 42 publications

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“…(15) of [3], where P is an auxiliary pressure in the system, and I is the identity tensor. Except for flows in porous media [7,8], the choice of the auxiliary stress r Ak = ÀPI provides many conveniences in modeling multiphase flows, especially disperse multiphase flows. Although the pressure effect in the first and the second terms on the right hand side can be simplified as Prh k , the momentum equation in form (1) is especially convenient for its numerical implementation in the material point method, as shown in Section 6.2.…”

Section: Materials Point Methods For Multiphase Systemsmentioning

confidence: 99%

Distribution coefficient algorithm for small mass nodes in material point method

Giguere

Jayaraman

et al. 2010

Journal of Computational Physics

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Section: Materials Point Methods For Multiphase Systemsmentioning

confidence: 99%

Distribution coefficient algorithm for small mass nodes in material point method

Giguere

Jayaraman

et al. 2010

Journal of Computational Physics

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“…In the literature, there are extensive experimental, theoretical, and computational investigations of different properties of multiphase systems, which are directly related to the topology and property of fluid‐fluid interfaces and capillary forces acting on them. Of these studies, we can refer to calculation of effective viscosity in viscous fingering regime [ Koval , 1963; Sorbie et al , 1995], averaging the phase pressures [ Zhang et al , 2007; Nordbotten et al , 2007; Yang et al , 2009; Korteland et al , 2009], scaling of the fingering with dynamic properties of a system [ Tallakstad et al , 2009], crossover behavior from viscous fingering to compact flow or from capillary fingering to viscous fingering [e.g., Wilkinson , 1986; Fernández et al , 1991; Ferer et al , 1993], nonequilibrium relative permeability curves [e.g., Goode and Ramakrishnan , 1993; Tsakiroglou et al , 2003; Theodoropoulou et al , 2005], relaxation time in fluid distribution [e.g., Buyevich , 1995], etc. Many of these issues cannot be explained by classical Darcy's law for multiphase flow.…”

Section: Introductionmentioning

confidence: 99%

Specific interfacial area: The missing state variable in two‐phase flow equations?

Niasar

Hassanizadeh

2011

Water Resources Research

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[1] Classical Darcy's equation for multiphase flow assumes that gravity and the gradient in fluid pressure are the only driving forces and resistance to the flow is parameterized by (relative) permeability as a function of saturation. It is conceivable that, in multiphase flow, other driving forces may also exist. This would mean that such nonequilibrium effects are lumped into a permeability coefficient. Indeed, many studies have shown that the relative permeability coefficient generally depends not only on saturation but also on dynamics of the system. Through the application of rational thermodynamics, a theory of two-phase flow had been developed in which interfacial areas were introduced as separate thermodynamic entities and their macroscale effects were explicitly included. This theory includes new driving forces whose significance needs still to be established. To study new terms in the theory, we employ a dynamic pore network model called DYPOSIT. A long pore network (several representative elementary volumes connected in series) is generated, which represents as a one-dimensional porous medium column. This model provides pore scale distribution of local phase pressures, capillary pressure, interfacial area, saturation, and flow rate, which are averaged to obtain the macroscale distributions of these variables. Our analysis shows that there are discrepancies between the simulation results and the classical equations to describe the transient behavior, especially for the nonwetting phase transient permeability. The coefficients in the extended equations are quantified and parameterized. Although under the applied Dirichlet boundary conditions, flow varies significantly, there is a clear trend illustrating dependency of coefficients on saturation, independent of dynamic conditions. Furthermore, using the new coefficients, it is possible to explain either transient or steady state flow regimes, which is a new achievement.

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“…The concept of eluting the liquid using another liquid in many arranged in parallel capillary tubes, with different diameters, was also presented by Yang . The author assumed that capillary flow could be described by the Hagen‐Poiseulle equation, which also considers the influence of phase boundary curvature on the flow conditions.…”

Section: Introductionmentioning

confidence: 99%

Modelling and experimental study of pressure elution of high‐viscosity substances with a low‐viscosity liquid from granular bed

2016

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The pressurized elution of oily substances with high viscosities from porous granular media is of primary importance from the point of view of enhanced oil recovery techniques and technologies. Accurate prediction of such processes can lead to their technical and financial optimization. Modelling considerations existing in the literature neglect many factors affecting elution phenomena. Additionally, extensive experimental data are not available. Other description methods are needed to enable more precise descriptions of the process. This paper develops a theoretical model which considers the dependence of oily substance elution on many parameters characterizing porous granular beds and flowing liquids. The influence of grain size distribution in the bed was considered, as well as the finite dimensions of the real bed. The bed saturation at the beginning of the process was also included in the modelling work together with eluent flow rate and media viscosity. Theoretical considerations were verified and supported with extensive experimental measurements.

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Ensemble phase averaged equations for multiphase flows in porous media. Part 1: The bundle-of-tubes model

Cited by 20 publications

References 42 publications

Distribution coefficient algorithm for small mass nodes in material point method

Distribution coefficient algorithm for small mass nodes in material point method

Specific interfacial area: The missing state variable in two‐phase flow equations?

Modelling and experimental study of pressure elution of high‐viscosity substances with a low‐viscosity liquid from granular bed

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