Influence of fluid viscosity and flow transition over non-linear filtration through porous media

Abstract

The present study investigates two important though relatively unexplored aspects of non-linear Bltration through porous media. The Brst aspect is the inCuence of viscosity variation over the coefBcients of the governing equations used for modelling non-linear Bltration through porous media. Velocity and hydraulic gradient data obtained for a wide range of Cuid viscosities (8.03E-07 to 3.72E-05 N/m 2 ) were studied. An increase in Cuid viscosity resulted in an increased pressure loss through packing which can be quantiBed using the coefBcients of the governing equations. CoefBcients of Forchheimer equation represent linearly increasing trend with the kinematic viscosity. On the other hand, coefBcient of Wilkins equation represents similar values for different Cuid viscosities and remained unaffected by the variation in packing properties. Obtained data were utilized to understand the nature of Cow transition in porous media. Behaviour of polynomial and Power-law coefBcient with variation in Cow velocity were also examined. Critical Reynolds number corresponding to the deviation of Cow from Darcy regime varies with the porous packing and was observed to be in the range of 0-100. CoefBcients of polynomial (Forchheimer) model were observed to be independent of the range of Cow velocity, whereas the Power law coefBcients are extremely sensitive to the data.

Resistance and Regime Relationship In Flow Through Porous Media Considering the Effects of Porosity, Wall and Tortuosity

“…Ashes Banerjee et.al [22] developed a mathematical model which can be used to predict velocities corresponding to the specific hydraulic gradients for predefined media sizes and porosities. Ashes Banerjee et.al [26] found Coefficients of polynomial model were observed to be independent of the range of flow velocity, whereas the Power law coefficients are extremely sensitive to the data. Ashes Banerjee et.al [27] created a working model that can be used to predict flow in porous media under a variety of packing, fluid, and flow conditions.…”

Influence of relaxation on filtering microflows under harmonic action on the layer

“…It should be noted that the studies on this topic known in the literature were conducted mainly on the basis of the classi cal Darcy filtration law without taking relaxation processes into account. However, to date, a considerable amount of ex perimental evidence of deviations from Darcy's linear law has been collected [16], especially in relation to nonequilibrium highintensity processes, when the strengthening of nonlocal effects is observed [17].…”

“…But the condition ε > 1 can be eliminated if we choose an other form of representation (16). In particular, let us multiply equation ( 15) by a number (-λ) (here λ is positive), add y to both parts and finally obtain y -λ(ln y + 2yr c j -ln M) = y.…”