Evaluation of Darcy–Brinkman equation for simulations of oil flows in rocks

“…When a viscous fluid is considered in the porous model, Brinkman's equation is used as the governing equation rather than Darcy's since Darcy's equation is unable to account for the effects of the fluid's viscosity on a porous material. The Brinkman equation has involvement in several useful and interesting applications including the construction of caissons, operation of submarines, and oil extraction problems which are the conclusions of solving

2{\mathrm{D}}

lift‐up problems consisting of rigid porous beds [5–7].…”

Section: Introductionmentioning

confidence: 99%

Effect of magnetic field on viscous flow through porous wavy channel using boundary element method

Chhabra,

Nishad,

Sahni

2024

Z Angew Math Mech

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The study aims to investigate the effect of uniform inclined magnetic field on two‐dimensional flow of a steady, viscous incompressible fluid at low Reynolds number through a porous wavy channel. We consider a channel having sinusoidal walls filled with a fully saturated porous medium. The porous regime is assumed to be homogenous and isotropic. The viscous flow through a porous regime is governed by Brinkman equation, where the viscous forces are dominant. This allows us to assume the no‐slip boundary conditions at the walls of the wavy channel. Boundary element method (BEM) based on non‐primitive variables namely, stream function‐vorticity variables is used to solve the Brinkman equation. Further, we consider a very small magnetic Reynolds number to eliminate the magnetic‐induced equation. We analyzed that an increase in Hartman number, porosity, and reduction in inclination angle of magnetic field, wave amplitude, and Darcy number led to a reduction in horizontal velocity, whereas an increase in Hartman number, porosity, wave amplitude, and decrease in Darcy number and angle of inclination of magnetic field led to an increase in vertical velocity. Moreover, the flow reversal phenomena occur in the vicinity of the crest regime of the porous wavy channel for high wave amplitude and low Hartman number. The proposed investigation has widespread applications, such as drug delivery systems to target the drug precisely, magneto‐hydrodynamic pumps to regulate the blood flow in artificial hearts to reduce the risk of blood clotting, and so forth.

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“…Double-diffusive convection is a mechanism, in which the fluid motion occurs due to buoyancy arising from the combination of temperature and concentration gradients. It is related with an increasing number of fields such as, metallurgy, oceanography, contaminant transport, petroleum drilling etc., [5,40,35,39]. The accurate and efficient numerical solutions of these flows are known to be the core of many applications.…”

Section: Introductionmentioning

confidence: 99%

Continuous Data Assimilation for the Double-Diffusive Natural Convection

Akbas

Çıbık

2020

Preprint

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In this study, we analyzed a continuous data assimilation scheme applied on a double-diffusive natural convection model. The algorithm is introduced with a first order backward Euler time scheme along with a finite element discretization in space. The long time stability and convergence results are presented for different options of nudging parameters. Two elaborative numerical test are given in order to confirm the theory and prove the promise of the algorithm.

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Evaluation of Darcy–Brinkman equation for simulations of oil flows in rocks

Cited by 13 publications

References 18 publications

Frequency Characteristics of Dynamic Seepage Flow in a Porous Medium Including a Cavity

Frequency Characteristics of Dynamic Seepage Flow in a Porous Medium Including a Cavity

Effect of magnetic field on viscous flow through porous wavy channel using boundary element method

Continuous Data Assimilation for the Double-Diffusive Natural Convection

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