Fluid flow through Apollonian packings

Oliveira, Rafael Soares de; Andrade, José S.; Andrade, Roberto F. S.

doi:10.1103/physreve.81.047302

Cited by 9 publications

(12 citation statements)

References 12 publications

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“…In fact, this type of techniques has been considered for different hierarchical structures to study critical phenomena [10][11][12][13][14]. This important property has also motivated using AN, as a first approximation, to study problems from several different areas, such as physiology, geology, communication, energy, and fluid transport [15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

q-state Potts model on the Apollonian network

2010

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The q-state Potts model is studied on the Apollonian network with Monte Carlo simulations and the Transfer Matrix method. The spontaneous magnetization, correlation length, entropy, and specific heat are analyzed as a function of temperature for different number of states, q. Different scaling functions in temperature and q are proposed. A quantitative agreement is found between results from both methods. No critical behavior is observed in the thermodynamic limit for any number of states.

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Section: Introductionmentioning

confidence: 99%

q-state Potts model on the Apollonian network

2010

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“…Under the action of drag forces, the disks are allowed to rotate around the respective centers. Eliminating the rotational degree of freedom restores the usual fixed disk condition [18].…”

Section: Modelmentioning

confidence: 95%

“…We perform CFD investigations in a two-dimensional channel of height H and length L = 32H [18]. The origin of the coordinate system lies at the center of the channel and the fluid flows from left to right due to an imposed constant pressure difference P 0 between channel inlet and outlet.…”

Section: Modelmentioning

confidence: 99%

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Fluid flow through packings of rotating obstacles

Oliveira

Andrade

2015

Phys. Rev. E

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We investigate through numerical simulation the nonstationary flow of a Newtonian fluid through a two-dimensional channel filled with an array of circular obstacles of distinct sizes. The disks may rotate around their respective centers, modeling a nonstationary, inhomogeneous porous medium. Obstacle sizes and positions are defined by the geometry of an Apollonian packing (AP). To allow for fluid flow, the radii of the disks are uniformly reduced by a factor 0.6≤s≤0.8 for assemblies corresponding to the four first AP generations. The investigation is targeted to elucidate the main features of the rotating regime as compared to the fixed disk condition. It comprises the evaluation of the region of validity of Darcy's law as well as the study of the nonlinear hydraulic resistance as a function of the channel Reynolds number, the reduction factor s, and the AP generation. Depending on a combination of these factors, the resistance of rotating disks may be larger or smaller than that of the corresponding static case. We also analyze the flow redistribution in the interdisk channels as a result of the rotation pattern and characterize the angular velocity of the disks. Here, the striking feature is the emergence of a stable oscillatory behavior of the angular velocity for almost all disks that are inserted into the assemblies after the second generation.

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“…Pfahler et al [31] and Gad el Hak [32] showed that there was a significant divergence of the Navier-Stokes forecasts in the smallest of the channels. In other words, it was no longer suitable for the original linear percolation theory [33,34]. Therefore, the interfacial effects between fluid and pore throat wall cannot be ignored in reservoirs at the micro/nano-scale.…”

Section: Introductionmentioning

confidence: 99%

Solid-Liquid Interfacial Effects on Residual Oil Distribution Utilizing Three-Dimensional Micro Network Models

Zhu

Liu

et al. 2017

Energies

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A number of experiments on fluid flow at the micro/nano-scale have demonstrated that flow velocity obviously deviates from the classical Poiseuille's law due to the micro forces between the wall and the fluid. Based on an oil-water two-phase network simulation model, a three-dimensional pore-scale micro network model with solid-liquid interfacial effects was established. The influences of solid-liquid interface effects including van der Waals force and wettability on the residual oil distribution and relative permeability were investigated through microscopic simulation. The effects of pore radius, pore-throat size ratio, shaping factor, and coordination number on the residual oil distribution were analyzed at the same time. The results showed that the oil recovery would be overestimated by about 4% without van der Waals force in a water-wet reservoir. The impact of van der Waals force on water-wet reservoirs was significantly obvious in contrast with oil-wet reservoirs. In addition, the residual oil distribution was significantly influenced by pore radius in water-wet reservoir, comparatively influenced by pore-throat size ratio in oil-wet reservoir. The present study illustrates the successful application of three-dimensional micro network models considering solid-liquid interfacial effects, and provides new insights for oil recovery enhancement.

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Fluid flow through Apollonian packings

Cited by 9 publications

References 12 publications

q-state Potts model on the Apollonian network

q-state Potts model on the Apollonian network

Fluid flow through packings of rotating obstacles

Solid-Liquid Interfacial Effects on Residual Oil Distribution Utilizing Three-Dimensional Micro Network Models

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