Flow rate fractionation

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... 

Feed concentration Active zone concentration Deadzone concentration Effluent concentration Ideal tank concentration Total flow rate Fractional by-pass flow By-pass flow rate Dead volume fraction Deadzone exchange flow Rate constant Fractional conversion Fractional deadzone flow... 

Outlet molal flow rate Fraction conversion of limiting reagent at outlet Outlet concentration of limiting reagent FAfiU-fA out)... 

Since the velocity of a given phase in the bubble column usually differs from the other phases, the volumetric flow rate fraction of that phase is not equal to its corresponding holdup, and hence the slip velocity is introduced to account for this difference ... 

Total Liquid Hold-up Assuming a similar film thickness for bubble and slug and ignoring the velocity of the film, the length fraction of slugs can be equated to the flow rate fraction by... 

The variable that describes composition in Eqn. (3-5) is Nu the total moles of species i . It sometimes is more convenient to work problems in terms of either the extent of reaction or the fractional conversion of a reactant, usually the limiting reactant. Extent of reaction is very convenient for problems where more than one reaction takes place. Fractional conversion is convenient for single-reaction problems, hut can he a source of confusion in problems that involve multiple reactions. The use of all three compositional variables, moles (or molar flow rates), fractional conversion, and extent of reaction, wiU be illustrated in this chapter, and in Chapter 4. 

An improvement in the performance of the radiant premixed burners could be obtained by adopting perovskite-based catalysts, attractive because of their low cost, thermo-chemical stabihty at comparatively high temperature (900-1100 C) and catalytic activity [19] such catalysts increase the fuel flow rate fraction burnt within or just downstream the burner deck, thus maximizing the heat fraction transferred by radiation, cooling the flame temperature and improving the combustion completeness with lower CO, unbumed HC and NOx levels. 

V = vapor flow rate from the separator L = liquid flow rate from the separator Zi = mole fraction of component i in the feed y = mole fraction of component i in the vapor Xi = mole fraction of component i in the liquid... 

Figure 4.9 shows a plot of Eq. (4.12). As the purge fraction a is increased, the flow rate of purge increases, but the concentration of methane in the purge and recycle decreases. This variation (along with reactor conversion) is an important degree of freedom in the optimization of reaction and separation systems, as we shall see later. 

Holdup and Flooding. The volume fraction of the dispersed phase, commonly known as the holdup can be adjusted in a batch extractor by means of the relative volumes of each Hquid phase added. In a continuously operated weU-mixed tank, the holdup is also in proportion to the volume flow rates because the phases become intimately dispersed as soon as they enter the tank. 

Referring to Figure 2, by considering solute mass balances over n, (n — 1),. .. 2, 1 units in turn and eliminating intermediate solute mass fractions and flow rates, the amount of solute associated with the leached sohd may be calculated in terms of the composition of the sohd and solvent streams fed to the system. The resulting equation is (2)... 

These design fundamentals result in the requirement that space velocity, effective space—time, fraction of bubble gas exchanged with the emulsion gas, bubble residence time, bed expansion relative to settled bed height, and length-to-diameter ratio be held constant. Effective space—time, the product of bubble residence time and fraction of bubble gas exchanged, accounts for the reduction in gas residence time because of the rapid ascent of bubbles, and thereby for the lower conversions compared with a fixed bed with equal gas flow rates and catalyst weights. 

A sharp separation results in two high purity, high recovery product streams. No restrictions ate placed on the mole fractions of the components to be separated. A separation is considered to be sharp if the ratio of flow rates of a key component in the two products is >10. The separation methods that can potentially obtain a sharp separation in a single step ate physical absorption, molecular sieve adsorption, equiHbrium adsorption, and cryogenic distillation. Chemical absorption is often used to achieve sharp separations, but is generally limited to situations in which the components to be removed ate present in low concentrations. 

In any gas burner some mechanism or device (flame holder or pilot) must be provided to stabilize the flame against the flow of the unbumed mixture. This device should fix the position of the flame at the burner port. Although gas burners vary greatly in form and complexity, the distribution mechanisms in most cases are fundamentally the same. By keeping the linear velocity of a small fraction of the mixture flow equal to or less than the burning velocity, a steady flame is formed. From this pilot flame, the main flame spreads to consume the main gas flow at a much higher velocity. The area of the steady flame is related to the volumetric flow rate of the mixture by equation 18 (81,82)... 

For theJth. component, my = m iDy is the component mass flow rate in stream i is the mass fraction of component j in stream i and q is the net reaction rate (mass generation minus consumption) per unit volume V that contains mass M. If it is inconvenient to measure mass flow rates, the product of density and volumetric flow rate is used instead. 

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