Porous media superficial velocity

In the equation, k=k rj denotes the permeability of the porous media, t] the fluid viscosity, p is the pressure and u represents the superficial flow velocity of the fluid. The permeability, k, taken as a constant, is an intrinsic property of the porous medium. The velocity in Darcy s law, m, is actually a mean velocity over the cross-section. Hence, the velocity profile of Darcy flow in a porous medirnn has a flat shape in the flow direction, indicating a constant velocity. 

Porous Media Packed beds of granular solids are one type of the general class referred to as porous media, which include geological formations such as petroleum reservoirs and aquifers, manufactured materials such as sintered metals and porous catalysts, burning coal or char particles, and textile fabrics, to name a few. Pressure drop for incompressible flow across a porous medium has the same quahtative behavior as that given by Leva s correlation in the preceding. At low Reynolds numbers, viscous forces dominate and pressure drop is proportional to fluid viscosity and superficial velocity, and at high Reynolds numbers, pressure drop is proportional to fluid density and to the square of superficial velocity. 

The expressions for the hydraulic diameter and the superficial velocity can be incorporated into the definition of the friction factor to give an equivalent expression for the porous medium friction factor ... 

In many problems of mass transfer in a solid porous medium with a large specific surface area (as with catalysts), with or without a chemical reaction, the solutes are considered to be carried only by diffusion (molecular, superficial or Knudsen diffusion), the molecular barycentric velocity being... 

A porous medium consists of a packed bed of solid particles in which the fluid in the pores between particles is free to move. The superficial fluid velocity V is defined as the volumetric flow rate of the fluid per unit of cross-sectional area normal to the motion. It is the imbalance between the pressure gradient (VP) and the hydrostatic pressure gradient (pg) that drives the fluid motion. The relation that includes both viscous and inertial effects is the Forscheimer equation [47]... 

The characteristic interstitial velocity ue can be related to the superficial velocity by equating the time required for a fluid element to travel with the superficial velocity q for a fixed apparent length L within the porous medium and the time for a fluid element to travel with the characteristic interstitial velocity ue in the pore for a fixed passage length of L/t. Hence, we obtain... 

The effluent concentration can be predicted by solving the mass conservation equation. The conservation equations of particulate matter consider the change in concentration of particulate and change of porosity with time. The amount of fines retained in the porous medium is represented by a, while u signifies the superficial velocity of the incompressible transport fluid. For constant volumetric, incompressible flow, neglecting dispersion and gravitational effects, the one dimensional conservation equation follows. 

Superficial velocity in porous medium equal to uniform velocity upstream of medium, Eq. (4.7.7)... 

If Eq. (6.6.1) is applied to a porous medium by a simple capillary model, then the superficial velocity is given by U = eu, where e is the porosity and is the convection velocity in Eq. (6.6.1). Locally, the interstitial convection velocity is made up of hydraulic and electroosmotic contributions and is given by... 

Generalized contravariant velocity component in configuration space (336) Generalized vector gradient in configuration space (337) Superficial velocity vector in a porous medium (171) heat-flux vector (307)-(308)... 

Superficial velocity of fluid flowing in a porous medium is less than the interstitial velocity according to the Dupuit relation ... 

Felicelli et al. [54] used a fixed finite element algorithm to calculate macrosegregation and the formation of channels and freckles in Pb-Sn alloys. They assumed that the mushy zone is a porous medium with an isotropic permeability and considered superficial velocity components for the fluid velocities in the mushy region. The superflcial velocities are... 

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