Mass transfer rate average value

Experimental work was undertaken (G8) to provide the information necessary to permit a test of this theoretical model. The system used bore complete geometrical and chemical similarity to that used by Cooper et al. (C9) so that their mass-transfer rate measurements, along with the average residence-time and power-consumption results determined in the experimental work (see Section II,D), were used to compare the experimental values with the model. 

In the early 1990s, Bakker and Van den Akker (1991, 1994) introduced an approximate but effective Euler Euler approach (see also A. Bakker s PhD Thesis, 1992) on the basis of a single-phase RANS flow field calculated by FLUENT, a code named GHOST calculated local and averaged values of bubble size db, gas hold-up a, and specific mass transfer rate kfl. 

Mass transfer rates from drops are obtained by measuring the concentration change in either or both of the phases after passage of one or more drops through a reservoir of the continuous phase. This method yields the average transfer rate over the time of drop rise or fall, but not instantaneous values. For measurements of the resistance external to the drop this is no drawback, because this resistance is nearly constant, but the resistance within the drop frequently varies with time. The fractional approach to equilibrium, F, is calculated from the compositions and is then related to the product of the overall mass transfer coefficient and the surface area ... 

The set of differential Eq. 2 and 3 can be solved analytically by means of Laplace transform in the cases of a zero- and first-order chemical reactions. The time-average value of the mass transfer rate, j, can be obtained by Eq. 5 [47] ... 

The Hatta-number represents the ratio of maximal possible reaction and mass transfer rates and helps to specify different absorption regimes. Depending on the Hatta-number value, it is possible to discriminate between very fast, fast, average and slow chemical reactions, in respect to physical mass transport [19, 20]. 

The internal mass transfer rate coefficient, kg is difficult to evaluate. It can be approximated as the time-averaged value proposed by Glueckauf [42]. 

The effect of slug flow on corrosion occurs in two ways. First, there is a dramatic increase in the turbulent intensity within the flow which causes an increase in the mass transfer rates of corrosive species to the corroding surface of up to 1000 times the average value. Second, there is extensive damage to the corrosion product layer which could otherwise have protected the surface from further corrosion. 

Figure 11.8 shows typical results, obtained as the dependence of the initial deposition probability (expressed in terms of the reduced mass transfer rate kc/fec) negatively charged polystyrene latex particles (averaged diameter 0.9 Jim) on the coverage of spherically shaped sites (positively charged polystyrene latex particles 0.45 (tm in diameter, deposited on abate mica surface) [72]. As can be seen, the deposition probability (reduced initial transfer rate) increased abmptly with the site coverage and attained maximum values pertinent to quasi-continuous surfaces... 

Oxygen transfer rate (OTR) The product of volumetric oxygen transfer rate kj a and the oxygen concentration driving force (C - Cl), (ML T ), where Tl is the mass transfer coefficient based on liquid phase resistance to mass transfer (LT ), a is the air bubble surface area per unit volume (L ), and C and Cl are oxygen solubility and dissolved oxygen concentration, respectively. All the terms of OTR refer to the time average values of a dynamic situation. 

Table 3.1 shows the kinetic parameters for cell growth, rate models with or without inhibition and mass transfer coefficient calculation at various acetate concentrations in the culture media. The Monod constant value, KM, in the liquid phase depends on some parameters such as temperature, initial concentration of the carbon source, presence of trace metals, vitamin B solution, light intensity and agitation speeds. The initial acetate concentrations in the liquid phase reflected the value of the Monod constants, Kp and Kp. The average value for maximum specific growth rate (/xm) was 0.01 h. The value... 

The rate parameters of importance in the multicomponent rate model are the mass transfer coefficients and surface diffusion coefficients for each solute species. For accurate description of the multicomponent rate kinetics, it is necessary that accurate values are used for these parameters. It was shown by Mathews and Weber (14), that a deviation of 20% in mass transfer coefficients can have significant effects on the predicted adsorption rate profiles. Several mass transfer correlation studies were examined for estimating the mass transfer coefficients (15, jL6,17,18,19). The correlation of Calderbank and Moo-Young (16) based on Kolmogaroff s theory of local isotropic turbulence has a standard deviation of 66%. The slip velocity method of Harriott (17) provides correlation with an average deviation of 39%. Brian and Hales (15) could not obtain super-imposable curves from heat and mass transfer studies, and the mass transfer data was not in agreement with that of Harriott for high Schmidt number values. 

Gas-side mass transfer in rotating packed beds does not show the same level of enhanced performance as liquid-side mass transfer. Average volumetric gas mass transfer values for a wire screen packing increased with gas flow rate but decreased with increased rotor speed. Compared to a packed tower, the RPB... 

Residence time distribution measurements, together with a theoretical model, provide a method to calculate the rate of mass transfer between the liquid flowing through the column, the dynamic holdup, and the stagnant pockets of liquid in between the particles. We have chosen the cross flow model (10). It has to be noted that the model starts from the assumption that the flow pattern has a steady-state character, which is in conflict with reality. Nevertheless, average values of the number of mass transfer units can be calculated as well as the part of the liquid being in the stagnant situation. 

In Figure 7 the effects of carbon feed rate and bubble size on the steady-state average carbon concentration are shown. The existence of critical bubble size for a fixed carbon feed rate can clearly be observed in this figure. It can also be observed that a critical carbon feed rate exists above which concentration runaway occurs, and a stable or steady-state condition can not be reached for a given bubble size. The value of the critical feed rate increases with a decrease in the bubble size. Under the critical condition, the maximum attainable rate of oxygen transfer from the bubble phase to the emulsion phase is reached, and it becomes the rate determining step for combustion as explained previously. To increase the carbon feed rate to a fluidized bed combustor, either the oxygen concentration in the air (gas) stream or the rate of mass transfer between the bubble and emulsion phase needs to be increased. ... 

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