Permeability flow velocity

The factors to consider in the selection of cross-flow filtration include the cross-flow velocity, the driving pressure, the separation characteristics of the membrane (permeability and pore size), size of particulates relative to the membrane pore dimensions, and the hydrodynamic conditions within the flow module. Again, since particle-particle and particle-membrane interactions are key, broth conditioning (ionic strength, pH, etc.) may be necessary to optimize performance. 

The flow velocity, pressure and dynamic viscosity are denoted u, p and fj and the symbol (...) represents an average over the fluid phase. Kim et al. used an extended Darcy equation to model the flow distribution in a micro channel cooling device [118]. In general, the permeability K has to be regarded as a tensor quantity accounting for the anisotropy of the medium. Furthermore, the description can be generalized to include heat transfer effects in porous media. More details on transport processes in porous media will be presented in Section 2.9. 

Flow Flux, Permeability, Conversion The productivity of a membrane module is described by its flux J = volumetric permeate flow rate/membrane area with units of volume per area per time. Relatively high flux rates imply that relatively small membrane areas are required. The permeate volume is usually greater than the feed volume for a given process. Flux is also the magnitude of the normal flow velocity with units of distance per time. 

Pumping during well development performs two important functions. First, pumping removes the materials from the borehole left behind by drilling. Second, as the water in the well is removed, groundwater flow velocity from the surrounding formation increases when it reaches the higher permeability filter pack around the well... 

Conventionally, the sample is initially saturated with one fluid phase, perhaps including the other phase at the irreducible saturation. The second fluid phase is injected at a constant flow rate. The pressure drop and cumulative production are measured. A relatively high flow velocity is used to try to negate capillary pressure effects, so as to simplify the associated estimation problem. However, as relative permeability functions depend on capillary number, these functions should be determined under the conditions characteristic of reservoir or aquifer conditions [33]. Under these conditions, capillary pressure effects are important, and should be included within the mathematical model of the experiment used to obtain property estimates. 

We presented a novel method to determine spatially resolved permeability distributions. We used MRI to measure spatially resolved flow velocities, and estimated the permeability from the solution of an associated system and parameter identification problem. 

Fines production from untreated test sands and permeability damage observed in untreated cores indicated that the laboratory test flow rates were above the critical flow velocity required to initiate fines migration. 

Be that as it may, Eq. (10) allows the calculation of the pressure necessary to achieve a given flow velocity in a column of known permeability. As we shall see in the next section, the choice of the velocity of the solvent is determined by the characteristics of the column as well as the desired efficiency or speed of analysis 18-21, 26).. . . 

An important measure concerning column characterization in LC is the column permeability, which represents the capacity of the support to transport the mobile phase as consequence of a pressure drop occurring over the column. In other words, the permeability of a column determines the required pressure to achieve the desired flow rate. The linear flow velocity (u) across an empty cylindrical column is given by... 

The flow resistance behavior of the reconstructed medium can now be examined by performing 3D flow simulations with the Lattice Boltzmann method (Chen and Doolen, 1998), and obtaining the permeability of the material (Konstandopoulos, 2003). Figure 8(a) depicts a visualization of 3D flow tubes and flow velocity distributions at different cross sections in a reconstructed filter material. Figure 8(b) shows the comparison of computer simulated and experimental permeabilities obtained with the experimental protocol described in Konstandopoulos (2003). 

Flow and diffusion transport dissolved and mobile particulate arsenic in groundwater. The flow velocity (speed and direction) of groundwater is largely controlled by changes in the elevation of the water table with lateral distance, water pressure and density, and the permeability and other properties of the aquifer. In some circumstances, temperature gradients may also affect groundwater flow (Freeze and Cherry, 1979), 25. 

When the packed segment is much less permeable than the open segment, the flow velocity in the packed segment is not significantly influenced by the pressure gradient. Then the actual velocity in the packed segment turns out to be identical to the virtual velocity as given by Eq. 1.38, and we obtain that... 

For soil systems contaminated with Na+, kinematic viscosity is not significantly affected, thus the components controlling water flow velocity are the hydraulic gradient (A< >/AX) and soil permeability (k). The latter component (k) is influenced by clay dispersion, migration, and clay swelling. These processes may cause considerable alteration to such soil matrix characteristics as porosity, pore-size distribution, tortuosity, and void shape. 

An important feature of an energy storage aquifer is the time required for charging and emptying. This time is determined by the permeability of the aquifer. The permeability is basically the proportionality factor between the flow velocity of a fluid or gas through the sediment and the pressure gradient causing the flow. The linear relationship assumed may be written... 

A comprehensive review of the important factors that affect the flow of emulsions in porous media is presented with particular emphasis on petroleum emulsions. The nature, characteristics, and properties of porous media are discussed. Darcy s law for the flow of a single fluid through a homogeneous porous medium is introduced and then extended for multiphase flow. The concepts of relative permeability and wettability and their influence on fluid flow are discussed. The flow of oil-in-water (OfW) and water-in-oil (W/O) emulsions in porous media and the mechanisms involved are presented. The effects of emulsion characteristics, porous medium characteristics, and the flow velocity are examined. Finally, the mathematical models of emulsion flow in porous media are also reviewed. 

The snowpack is a porous medium through which air flows if pressure differences exist within the snowpack. Such pressure gradients may be generated by the action of wind on sastrugi. Under most conditions relevant to snowpacks, the flow velocity v is proportional to the pressure gradient and the proportionality factor is the snow permeability Kp... 

This method is also referred to as the miscible-displacement or continuous-flow method. In this method a thin disk of dispersed solid phase is deposited on a porous membrane and placed in a holder. A pump is used to maintain a constant flow velocity of solution through the thin disk and a fraction collector is used to collect effluent aliquots. A diagram of the basic experimental setup is shown in Fig. 2-6. A thin disk is used in an attempt to minimize diffusion resistances in the solid phase. Disk thickness, disk hydraulic conductivity, and membrane permeability determine the range of flow velocities that are achievable. Dispersion of the solid phase is necessary so that the transit time for a solute molecule is the same at all points in the disk. However, the presence of varying particle sizes and hence pore sizes may produce nonuniform solute transit times (Skopp and McCallister, 1986). This is more likely to occur with whole soils than with clay-sized particles of soil constituents. Typically, 1- or 2-g samples are used in kinetic studies on soils with the thin disk method, but disk thicknesses have not been measured. In their study of the kinetics of phosphate and silicate retention by goethite, Miller et al. (1989) estimated the thickness of the goethite disk to be 80 /xm. 

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