Volumetric transfer coefficient

The matrix of volumetric transfer coefficients [K], averaged over the entire equilibration process is... 

Relations between slip velocity, holdup, and drop diameter, from the data of Letan and Kehat (L5) for a 3-in. column (kerosene-water system), are illustrated in Fig. 13. The increase in drop diameter with increasing holdup and decreasing slip velocity has some effect on the transfer area per unit volume, which nevertheless increases with decreasing Volumetric transfer coefficients increase correspondingly. 

The overall volumetric transfer coefficient is apparently independent of the continuous-phase flow rate over the range investigated. The ratio GJGc =2.87 is recommended (T2) for maximum efficiency of this system. 

Similar experiments were reported by Wilke et al. (WIO) who studied water injected into Aroclor in a 15-ft 3-in. pipe. Wilke s data also do not indicate any effect of temperature and physical properties on the volumetric transfer coefficients, and can be correlated in terms of the total mass flow rate, namely,... 

For comparison with other evaporation studies, it is noteworthy that the data presented in Fig. 21 was obtained with a temperature approach of 1.7°C at the continuous-phase outlet, and that the pentane feed entered the nozzles subcooled by some 1.5°C. A reduction in the free-rising stream line zone is feasible with superheated dispersed-phase feeds and closer approach temperatures. This would greatly increase the volumetric transfer coefficient which is inversely proportional to the temperature driving-force and the optimal column height. 

Harriott and Wiegandt (HlOa) studied an upflow cocurrent flash evaporator in which pentane or methylene chloride was mixed with the water before entering the 2-in. column. A sieve plate with or -in. holes was placed 1 ft upstream to facilitate dispersion. The volumetric transfer coefficients were estimated to be about 17 x 10 Btu/hr/ft /°F, based on an approach exit temperature of 0.5°C and a 1-ft length of pipe. This result is similar to that reported by Wilke et al. (WIO) for a cocurrent pipe evaporator, and is about one order of magnitude larger than that reported for the countercurrent spray... 

For condensation of methylene chloride in water, in cocurrent downflow 4-in. and 6-in. diam columns packed with i-in. Intalox saddles, the volumetric transfer coefficients reported (HlOa) were less than half those obtained with the sieve-plate column. The difference may be due partially to the different definition of the temperature driving-force applied for these two columns. (The log-mean AT was used for the packed bed, and a 2-in. transfer height was assumed.) The volumetric heat transfer coefficients increased with the 0.4-0.6 power of the liquid rate from 65,000 to 150,000 Btu/hr/ft /°F with the liquid rate increasing from 1 to 4 x 10" Ib/hr/ft. Contrary to the sieve-plate and spray-column studies, no effects of the vapor flow rate (from 1100 to 2500 Ib/hr/ft ) on the heat-transfer coefficient were noted in the packed bed study. 

As already mentioned, the viscosity of the dispersed phase affects the maximum obtainable transfer coefficients in spray-column operation lower viscosities allow higher coefficients at lower operating temperature level. For the hot-top spray column, a linear dependence of the transfer coefficients and the fluidity of the dispersed phase was found (T2). This phenomenon may also be associated with reduction in surface tension. A decrease in drop diameter and increase in transfer area per unit volume of column may then be expected to increase the volumetric transfer coefficients. 

The latter is obviously obtained independently (and for all M) from the definition of the over-all volumetric transfer coefficient, based on apparent exterior temperatures. The obvious and common technique of studying column performance is to keep G, and T (in) constant and vary G until the desired minimum approach temperature is obtained, corresponding to (Gc)min> Fig- 25(a). Now, since T 2 (out) ideally approaches T, only asymptotic-... 

With an aerobic bioprocess it is evident that, in addition to substrate, O2 can be rate limiting. The curve for biomass concentration increasing with time in a batch run is significantly influenced by the oxygen transfer rate quantified by the volumetric transfer coefficient This situation of an external... 

In through circulation fixed bed dryers and in moving or suspended bed dryers (spouted beds, fluidized beds, rotary dryers, and so on), the actual interfacial area participating in heat and mass transfer is unknown. For such cases it is appropriate to define volumetric transfer coefficients for heat and mass transfer, hy and K, respectively, as follows ... 

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