Velocity superficial

For a single fluid flowing through a section of reservoir rock, Darcy showed that the superficial velocity of the fluid (u) is proportional to the pressure drop applied (the hydrodynamic pressure gradient), and inversely proportional to the viscosity of the fluid. The constant of proportionality is called the absolute permeability which is a rock property, and is dependent upon the pore size distribution. The superficial velocity is the average flowrate... 

Numbers on lines represent G values = gas flow in kg/(m -s) = nominal packing size = superficial velocity. To convert kg/(m -s) to lb/(h-ft )... 

Chaiacteiistics of tfie pads vaiy slighdy witfi mesh density, but void space is typically 97—99% of total volume. Collection is by inertial impaction and direct impingement thus efficiency will be low at low superficial velocities (usually below 2.3 m/s) and for fine particles. The desireable operating velocity is given... 

A differential countercurrent contactor operating with a dilute solution of the consolute component C and immiscible components A and B is shown in Figure 8. Under these conditions, the superficial velocities of the A-rich and B-rich streams can be assumed not to vary significantly with position in the contactor, and are taken to be and Ug, respectively. The concentration of C in the A-rich stream is and that in the B-rich stream is C-. ... 

However, in a countercurrent column contactor as sketched in Figure 8, the holdup of the dispersed phase is considerably less than this, because the dispersed drops travel quite fast through the continuous phase and therefore have a relatively short residence time in the equipment. The holdup is related to the superficial velocities U of each phase, defined as the flow rate per unit cross section of the contactor, and to a sHp velocity U (71,72) ... 

As the throughput in a contactor represented by the superficial velocities and is increased, the holdup / increases in a nonlinear fashion. A flooding point is reached at which the countercurrent flow of the two Hquid phases cannot be maintained. The flow rates at which flooding occurs depend on system properties, in particular density difference and interfacial tension, and on the equipment design and the amount of agitation suppHed (40,65). 

The basic concepts of a gas-fluidized bed are illustrated in Figure 1. Gas velocity in fluidized beds is normally expressed as a superficial velocity, U, the gas velocity through the vessel assuming that the vessel is empty. At a low gas velocity, the soHds do not move. This constitutes a packed bed. As the gas velocity is increased, the pressure drop increases until the drag plus the buoyancy forces on the particle overcome its weight and any interparticle forces. At this point, the bed is said to be minimally fluidized, and this gas velocity is termed the minimum fluidization velocity, The bed expands slightly at this condition, and the particles are free to move about (Fig. lb). As the velocity is increased further, bubbles can form. The soHds movement is more turbulent, and the bed expands to accommodate the volume of the bubbles. 

Particle Regimes. In 1973, particles were classified with respect to how they fluidize in air at ambient conditions into Geldart groups (6) (Fig. 4). Particles that formed bubbles immediately after the gas superficial velocity exceeded were designated as Group B particles. For these particles, the... 

Fundamental models correctly predict that for Group A particles, the conductive heat transfer is much greater than the convective heat transfer. For Group B and D particles, the gas convective heat transfer predominates as the particle surface area decreases. Figure 11 demonstrates how heat transfer varies with pressure and velocity for the different types of particles (23). As superficial velocity increases, there is a sudden jump in the heat-transfer coefficient as gas velocity exceeds and the bed becomes fluidized. 

In comparison, units that are designed with turbulent beds have a lower superficial velocity limit because of soflds entrainment and are unable to independently control the entrained soflds recycle. The soflds loading in the turbulent-bed regenerator configuration are equal to the reactor—regenerator circulation plus the entrained soflds via the cyclone diplegs. 

Asahi also reports an undivided cell process employing a lead alloy cathode, a nickel—steel anode, and an electrolyte composed of an emulsion of 20 wt % of an oil phase and 80 wt % of an aqueous phase (125). The aqueous phase is 10 wt % K HPO, 3 wt % K B O, and 2 wt % (C2H (C4H )2N)2HP04. The oil phase is about 28 wt % acrylonitrile and 50 wt % adiponitrile. The balance of the oil phase consists of by-products and water. The cell operates at a current density of 20 A/dm at 50°C. Circulated across the cathode surface at a superficial velocity of 1.5 m/s is the electrolyte. A 91% selectivity to adiponitrile is claimed at a current efficiency of 90%. The respective anode and cathode corrosion rates are about mg/(Ah). Asahi s improved EHD process is reported to have been commercialized in 1987. 

V = superficial velocity based upon the gross area of the screen K = velocity head loss... 

The volume fraction, sometimes called holdup, of each phase in two-phase flow is generally not equal to its volumetric flow rate fraction, because of velocity differences, or slip, between the phases. For each phase, denoted by subscript i, the relations among superficial velocity V, in situ velocity Vj, volume fraclion Rj, total volumetric flow rate Qj, and pipe area A are... 

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. 

For estimating purposes for direct-heat drying applications, it can be assumed that the average exit-gas temperature leaving the sohds bed wih approach the final solids discharge temperature on an ordi-naiy unit carrying a 5- to 15-cm-deep bed. Calculation of the heat load and selec tion of an inlet-air temperature and superficial velocity (Table 12-32) will then permit approximate sizing, provided an approximation of the minimum required retention time can be made. 

Table 14-2 illustrates the observed variations in values for different packing types and sizes for the COg-NaOH system at a 25 percent reactant-conversion level for two different liquid flow rates. The lower rate of 2.7 kg/(s-m ) or 2000 lb/(h-ft ) is equivalent to 4 (U.S. gal/min)/ft and is typical of the liquid rates employed in fume scrubbers. The higher rate of 13.6 kg/(s-m ) or 10,000 lb/(h-fU) is equivalent to 20 (U.S. gal/min)/ft and is more typical of absorption towers such as are used in CO9 removal systems. For example. We note also that two different gas velocities are represented in the table, corresponding to superficial velocities of 0.59 and 1.05 m/s (1.94 and 3.44 ft/s). 

Pinczewski and Fell [Trans. Inst. Chem E/ig., 55, 46 (1977)] show that the velocity at which vapor jets onto the tray sets the droplet size, rather than the superficial tray velocity. A maximum superficial velocity formulation that incorporates ( ), the fractional open area, is logical since the fractional open area sets the jet velocity. Stichlmair and Mers-mauu [Int. Chem. Eng., 18(2), 223 (1978)] give such a correlation ... 

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