Mathematical Model for Flow of Pseudoplastic Fluids in Porous Media

Hemeida, Adel M.

doi:10.1016/s1018-3639(18)30621-4

Cited by 3 publications

(4 citation statements)

References 19 publications

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“…By viewing the internal properties and the practical usage several important relations exist in the literature. Pseudo-plastic material 1 – 6 is an important model. Several important works have been reported with different physical effects in different geometries with different techniques.…”

Section: Introductionmentioning

confidence: 99%

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Finite element analysis for ternary hybrid nanoparticles on thermal enhancement in pseudo-plastic liquid through porous stretching sheet

Sohail

El‐Zahar

Mousa

et al. 2022

Sci Rep

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Thermal performance can be enhanced due to the mixing of nanoparticles in base fluid. This research discusses the involvement of ternary hybrid nanoparticles in the mixture of pseudo-plastic fluid model past over a two dimensional porous stretching sheet. Modelling of energy equation is carried out in the presence of external heat source or sink and viscous dissipation. The flow presenting equations and derived in Cartesian coordinate system under usual boundary layer theory in the form of complex coupled partial differential equations (PDEs). The derived PDEs have been converted into corresponding ordinary differential equations (ODEs) with the engagement of suitable transformation. The engineers, scientists and mathematicians have great interest in the solution of differential equations because to understand the real physics of the problem. Here, finite element scheme has been used to approximate the solution of the converted problem. The contribution of several emerging parameters on solution have been displayed through graphs and discussed. It is recommended that the finite element method can be engaged to approximate the solution of nonlinear problems arising in modelling the problem in mathematical physics.

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Section: Introductionmentioning

confidence: 99%

“…Several important works have been reported with different physical effects in different geometries with different techniques. For instance, Hemeida 1 studied pseudo-plastic behaviour in porous medium and presented the analytic solution for developed modelled problem. Contribution of gravity effects are ignored during his work.…”

Section: Introductionmentioning

confidence: 99%

Finite element analysis for ternary hybrid nanoparticles on thermal enhancement in pseudo-plastic liquid through porous stretching sheet

Sohail

El‐Zahar

Mousa

et al. 2022

Sci Rep

View full text Add to dashboard Cite

show abstract

“…[8]). There is a considerable number of papers in the existing literature treating this problem from different points of view, theoretical, numerical or experimental [9,7,8,17,15,13,18].…”

Section: Introductionmentioning

confidence: 99%

Low-volume-fraction limit for polymer fluids

Fratrović

Marušić–Paloka

2011

Journal of Mathematical Analysis and Applications

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We study a stationary, purely viscous polymer flow through a porous medium modelled as a periodic array of cells consisted of a fluid part and a solid one. Solid parts of the domain present impermeable obstacles, whose impact on fluid flow may be seen as a slowing factor through averaged quantities such as the permeability function, obtained by the homogenization process. In that way, the influence of the microstructure is implemented in the homogenized equations through a kind of nonlinear Darcy's law. Our goal is to find more explicitly the dependence of the permeability function on the size η of the obstacle in the unit cell and the so-called low-volume-fraction limit. Main difficulties arise from the nonlinear character of the power-law viscosity and the apparent weak convergence of the solutions involved.

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“…Agora é preciso correlacionar a reologia dos fluidos com as características macroscópicas do escoamento levando em conta as propriedades petrofísicas do meio poroso. Nos trabalhos de Hirasaki e Pope (1974) [10] e Hemeida (1993) [9] verifica-se a relação dos modelos de Blake-Kozeny com a equação constitutiva ( 7) chegando-se a seguinte expressão para o gradiente de pressão no meio poroso:…”

Section: Fundamentosunclassified

Simulação De Escoamento De Soluções Poliméricas Em Meios Porosos Usando Modelo De Redes

GODOY¹

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Flow simulation of polymeric solutions in porous media using pore network modeling Polymeric solutions are widely used in Improved Oil Recovery (IOR) applications to increase sweep efficiency in oil reservoirs. Due to its rheological characteristics, polymeric solutions modify the mobility of the injected aqueous phase and make oil displacement more efficient. The viscosity of polymeric solutions typically changes with the deformation rate.The flow of these solutions through porous media can be described using Darcy equation and a characteristic viscosity of flow. In this work, the apparent rheology of these solutions was investigated in three samples of digitally reconstructed rocks by means of images obtained from micro CTscans. Macroscopic flow simulations were applied through network modeling methods (Pore Network Modeling, PNM), rather than direct numerical simulation (e.g.: Finite Element Method) because of the high computational cost of the last approach. The non-Newtonian behavior of polymer solutions was described with power-law viscosity model and were compared to apparent rheology models from literature such as modified Blake-Kozeny. The effect of viscosity on percolation was evaluated by checking the ratio of pores and throats that participated in the flow. The equivalent viscosity based on Darcy's Law was compared to curves obtained by rheometry and, at the end, the adjustable factor , which predicts the fluid apparent rheology, was calculated.

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Mathematical Model for Flow of Pseudoplastic Fluids in Porous Media

Cited by 3 publications

References 19 publications

Finite element analysis for ternary hybrid nanoparticles on thermal enhancement in pseudo-plastic liquid through porous stretching sheet

Finite element analysis for ternary hybrid nanoparticles on thermal enhancement in pseudo-plastic liquid through porous stretching sheet

Low-volume-fraction limit for polymer fluids

Simulação De Escoamento De Soluções Poliméricas Em Meios Porosos Usando Modelo De Redes

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