Pressure fluid flow through porous media

Flow of fluid through porous medium" (Darcy s Law, see Eq. 25-5) n i 8 = q (m s 1) h (m) Kq (m s 1) Discharge per area Hydraulic head (pressure change along flowpath x) Hydraulic conductivity of medium... 

When the fluid flows through a porous medium, the -.olid particles exert a force on the fluid equal and opposite to the drag force on the solid particles. This force must be balanced by the pressure gradient in the flow. i.e for flow through a control volume for any chosen direction ... 

Sometimes, fluids flow through a restriction, such as an orifice, a valve, or a porous medium, and a pressure drop occurs adiabatically. If the changes in kinetic and potential energies are negligible, the flow process is a throtding process, which causes no change in enthalpy at the inlet and outlet, and we have AH = 0. Some properties of throtding processes are ... 

For flow through porous media studies, the sandpacks used as porous media were flushed vertically with carbon dioxide for an hour to replace interstitial air. Distilled water was pumped and the pore volume (PV) of the porous medium was determined. By this procedure, the trapped gas bubbles in the porous media can be easily eliminated because carbon dioxide is soluble in water. For determining the absolute permeability of the porous medium, the water was pumped at various flow rates and the pressure drop across the sandpack as a function of flow rate was recorded. After the porous medium was characterized, the mixed surfactant solutions of known surface properties were injected. This was followed by air injection to determine the effect of chain length compatibility on fluid displacement efficiency, breakthrough time and air mobility in porous media. 

Permeability is the rate of flow of fluid through the rock. It is expressed by Darcy s Law. This states that the rate of flow of a homogeneous fluid in a porous medium is proportional to the pressure gradient and inversely proportional to the fluid viscosity. This is generally expressed mathematically thus ... 

Permeametry, the measurement of the rate of flow of a fluid through a porous medium under a known pressure gradient, is a technique by means of which a mean particle size (but not a particle size distribution) can be determined. The equation for the rate of fluid flow through a packed bed of uniform spheres is the semiempirical Ergun equation... 

The permeability of a porous medium (K) is defined as the proportionality constant that relates the flow rate through the medium to the pressure drop, the cross-sectional area, the fluid viscosity, and net flow length through the medium ... 

DARCY (D). A unit of permeability of a porous medium. One darcy equals 1 cF (cm/s)(cm/atm) equals 0.986923 square micrometers. (A permeability of 1 daicy will allow the flow of 1 cubic centimeter per second of fluid of 1 centipoise viscosity through an area of 1 square centimeter under a pressure gradient of 1 atmosphere per centimeter.)... 

The ease with which a fluid can flow through a porous medium, permeability, can be determined through the measurement of pressure drop (Ap) across the porous medium under steady flow. The intrinsic permeability (k) is defined by Darcy s law and is given by k=(Q/A)( /L/Ap) where Q is the discharge flow rate, A is the... 

The basic law governing viscous flow of pure fluid through a porous medium with pores much larger than the mean free path is that of Darcy [13]. This law states that the rate of flow is directly proportional to the pressure gradient causing the flow. In terms of mole flow rate Darcy s law can be written as... 

If the foam phase is thought of as a pseudo continuous fluid with an apparent viscosity Vapp = it follows that Papp is greater than that of the aqueous liquid phase. (For the tests here, values of Uapp were on the order of 1 to 50 times that of water). Because of this, when foam and liquid move through a porous medium under an applied pressure drop, the foam, being the most viscous phase, must occupy a larger region of the pore space. Consequently, as observed, the gas saturation is increased over that of non-dispersed phase flow and the liquid permeability is correspondingly decreased. 

In the integration of equation 12 to give equation 13 it was assumed that Q was not a function of pressure. However, when a compressible fluid such as a gas is flowing this assumption is not valid. As the gas flows through the porous medium from a high pressure to a low pressure it expands as the pressure decreases. Consequently for a compressible fluid Q must be measured at the mean pressure of the system, that is, at a pressure equal to (Pi -f- P2) /2. If Boyle s Law applies to the gas it is evident that... 

Permeability. The permeability of a porous medium is a measure of the ease with which a fluid can flow through it. In other words, it is a measure of the fluid conductivity of the medium that determines the flow rate of a given fluid for a given pressure gradient. 

Permeability A measure of the ease with which a fluid can flow (fluid conductivity) through a porous medium. Permeability is defined by Darcy s law. For linear, horizontal, isothermal flow, permeability is the constant of proportionality between flow rate times viscosity and the product of cross-sectional area of the medium and pressure gradient along the medium. 

Permeability is a parameter defined to measure the physical influence of a porous structure on fluid flow, and for a CVI process it is an important physical parameter for fibre preforms. Another important parameter for porous structure is the porosity, which is the most important geometrical property. According to Darcy s law, the volumetric flow rate Q of a fluid through a porous medium is proportional to the hydrostatic pressure difference (AP) across the structure (see Figure 2.16), the permeability and the cross-section area, and is also inversely proportional to the length of the structure and the viscosity of the fluid, as given by [26]... 

An inverse phenomenon streaming potential), generation of an electric field inside the membrane, takes place if the solution passes through this porous medium due to an imposed hydrostatic pressure. This time it is the flow of the fluid inside the pores that induces the displacement of the mobile part of the EDL at the surface of capillaries, with respect to the charges attached to the surface. These dipoles create an electric field, which, under stationary conditions, prevents the farther displacement of the mobile charges. The resulting potential difference across the membrane, A(p, is proportional to the excessive hydrostatic pressure, AP ... 

On the other hand, when a macroscopic pressure gradient VP is applied to the porous medium, the fluid percolates through it with a Darcy velocity U. Additionally, the electrolyte flowing in the interstices affects the equilibrium ion distribution within the Debye layer, so that these ions are also set into motion. This results in a macroscopic electric current density I flowing through the porous medium in the absence of any external electric field. 

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