Description of non-Darcy flows in porous medium systems

Dye, A. L.; McClure, James E.; Miller, Cass T.; Gray, William G.

doi:10.1103/physreve.87.033012

Cited by 19 publications

(15 citation statements)

References 47 publications

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“…A three‐dimensional, 19‐velocity‐vector (D3Q19), MRT LBM [ McClure et al ., ] was used to analyze the active fraction of the computational domain as a function of time for an equilibrium state simulation. A three‐dimensional, synthetic porous medium system was generated using a sphere packing algorithm [ Dye et al ., ]. The isotropic sphere pack consisted of 1,500 uniform size spheres arranged in a nonoverlapping fashion with a porosity of 0.42 and periodic boundaries.…”

Section: Discussionmentioning

confidence: 99%

An adaptive lattice Boltzmann scheme for modeling two‐fluid‐phase flow in porous medium systems

Dye

McClure

Adalsteinsson

et al. 2016

Water Resources Research

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We formulate a multiple-relaxation-time (MRT) lattice-Boltzmann method (LBM) to simulate two-fluid-phase flow in porous medium systems. The MRT LBM is applied to simulate the displacement of a wetting fluid by a nonwetting fluid in a system corresponding to a microfluidic cell. Analysis of the simulation shows widely varying time scales for the dynamics of fluid pressures, fluid saturations, and interfacial curvatures that are typical characteristics of such systems. Displacement phenomena include Haines jumps, which are relatively short duration isolated events of rapid fluid displacement driven by capillary instability. An adaptive algorithm is advanced using a level-set method to locate interfaces and estimate their rate of advancement. Because the displacement dynamics are confined to the interfacial regions for a majority of the relaxation time, the computational effort is focused on these regions. The proposed algorithm is shown to reduce computational effort by an order of magnitude, while yielding essentially identical solutions to a conventional fully coupled approach. The challenges posed by Haines jumps are also resolved by the adaptive algorithm. Possible extensions to the advanced method are discussed.

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Section: Discussionmentioning

confidence: 99%

An adaptive lattice Boltzmann scheme for modeling two‐fluid‐phase flow in porous medium systems

Dye

McClure

Adalsteinsson

et al. 2016

Water Resources Research

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“…where the column vectors of Q w are the eigenvectors of the resistance tensor, and Λ w is a diagonal tensor with the corresponding eigenvalues [74]. Assuming that the principal axes have been selected such that they correspond to the principal directions of the resistance tensor, making Rw = Λ w , Eqn (61) becomes…”

Section: E Momentum Transfer Analysismentioning

confidence: 99%

“…which in the classical literature is assumed to be symmetric positive semi-definite second-order tensor that is only dependent upon the pore morphology and topology, where the restriction of Darcy flow to the creeping flow regime is commonplace [69,74,75]. Some observations can be made regarding Eqn (68).…”

Section: E Momentum Transfer Analysismentioning

confidence: 99%

Non-Newtonian fluid flow in porous media

Bowers,

Miller

2019

Preprint

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Single-fluid-phase porous medium systems are typically modeled at an averaged length scale termed the macroscale, and Darcy's law is typically relied upon as an approximation of the momentum equation under laminar flow conditions. Standard approaches for modeling macroscale single-fluid-phase flow of non-Newtonian fluids extend the standard Newtonian model based upon Darcy's law using an effective viscosity and assuming that the intrinsic permeability is invariant with respect to fluid properties. This approach results in a need to determine the effective viscosity for every fluid composition and flow rate. We use the thermodynamically constrained averaging theory (TCAT) to examine the formulation and closure of a macroscale model for non-Netwonian flow that is consistent with microscale conservation principles and the second law of thermodynamics. A direct connection between microscale and macroscale quantities is used to formulate an expression for interphase momentum transfer for non-Newtonian flow in porous medium systems. Darcy's law is shown to approximate momentum transfer from the fluid phase to the solid phase. This momentum transfer is found to depend on the viscosity at the solid surface, which is only invariant for Newtonian flow. As a consequence of the derived equation for momentum transfer, the commonly called intrinsic permeability is not invariant for non-Newtonian flow, which is an assumption that underlies standard effective viscosity approaches for modeling non-Newtonian flow. TCAT is used to derive a macroscale equation relating the flow rate and the pressure gradient and dependent upon fluid properties. Non-Newtonian flow can be modeled using this equation along with characterization of the fluid properties and medium characterization under a single flow condition, breaking the need to investigate all flow and composition conditions that are hallmarks of extant approaches. This new approach is validated for model systems and used to interpret results from the literature, including an evaluation of conditions under which a transition occurs away from strictly laminar flow conditions. The results from this work form a basis for more rigorous and realistic modeling of non-Newtonian flow in porous medium systems.

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“…(4) and (5) may be presented in an adimensionalized form, that may be useful to generalize the results. As suggested by several authors ( Dye et al, 2013;Nemec and Levec, 2005 ), they can be re-written in terms of the Reynolds numbers for the liquid phase and the gas phase:…”

Section: Adimensionized Equationsmentioning

confidence: 99%

Modeling of inertial multi-phase flows through high permeability porous media: Friction closure laws

Clavier

Chikhi

Fichot

et al. 2017

International Journal of Multiphase Flow

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During a severe accident in a nuclear reactor, the core may be fragmented in a debris bed made of millimetric particles. The main safety procedure consists in injecting water into the core leading to a steamwater flow through a hot porous medium. To assess the coolability of debris bed, there is a need for an accurate two-phase flow model including closure laws for the pressure drop. In this article, a new model for calculating pressure losses in two-phase, incompressible, Newtonian fluid flows through homogeneous porous media is proposed. It has been obtained following recent developments in theoretical averaging of momentum equations in porous media. The pressure drops in the momentum equations are determined by eight terms corresponding to the viscous and inertial friction in liquid and gas phases, and interfacial friction between the phases. Analytical correlations with the void fraction have been formulated for each term using an original experimental database containing measurements of pressure drops, average velocities and void fractions from the IRSN CALIDE experiment. The new model has then been validated against the experimental data for various liquid and gas Reynolds numbers up to several hundreds. Finally, it has been compared to the models, usually used in the "severe accident" codes, which are based on a generalization of the Ergun law for multi-phase flows. The results show that the new model gives a better prediction both for the pressure drop and for the void fraction.

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Description of non-Darcy flows in porous medium systems

Cited by 19 publications

References 47 publications

An adaptive lattice Boltzmann scheme for modeling two‐fluid‐phase flow in porous medium systems

An adaptive lattice Boltzmann scheme for modeling two‐fluid‐phase flow in porous medium systems

Non-Newtonian fluid flow in porous media

Modeling of inertial multi-phase flows through high permeability porous media: Friction closure laws

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