Comparison between Darcy and Brinkman laws in a fracture

On the non‐stationary non‐Newtonian flow through a thin porous medium

“…with the same constant C as in (18). Summing the inequalities (20) for every k ∈ T ε , which cover the domain ε , gives the desired result (17).…”

“…That motivated H. Brinkmann in 1947 to modify the Darcy law in order to be able to impose the no-slip boundary condition on an obstacle submerged in porous medium. Recently, in [20] Marušic-Paloka et al focus on Brinkman and Darcy laws. They derive them from microscopic equations by upscaling, compare them and estimate the error made by their application.…”

“…They derive them from microscopic equations by upscaling, compare them and estimate the error made by their application. About the comparison between Darcy and Brinkman law in the context of classical newtonian flow through a porous medium, see the cited references in the paper [20].…”

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

“…Many recent works can be found that adopt the Brinkman equation in substitution to the traditional Darcy's law for modeling flows through porous media (Auriault, 2009). These works do not only present physical applications of the equation (Pantokratoras, 2014;Rtibi et al, 2014;Bell et al, 2014;Yu and Wang, 2013;Jogie and Bhatt, 2013), but are also dedicated to the mathematical formalism of analytical and numerical solutions (Daozhi and Wang 2014;Evans and Hughes 2013;Cibik and Kaya 2013;Marusic-Paloka, et al, 2012). Nevertheless, it is not common to find in these articles a discussion about the limits of validity of the model.…”

Asymptotic Approach to the Generalized Brinkman’s Equation with Pressure-Dependent Viscosity and Drag Coefficient

“…For the flow through porous media, as governed by the Brinkman equation and its various generalizations, analytical treatments can be found only in the constant viscosity case (ˆ0 k  ). We refer the reader to Durlofsky and Brady (1987), Kuznetsov (1998), Malashetty et al (2001), Merabet et al (2008), Marušić-Paloka et al (2012), Khan et al (2014)). In the variable viscosity case (ˆ0 k  ), the numerical approach has been developed and we refer the reader to Naskhatrala and Rajagopal (2009), Srinivasan et al (2013).…”