Transport coefficient, overall

Reactions carried in aqueous multiphase catalysis are accompanied by mass transport steps at the L/L- as well as at the G/L-interface followed by chemical reaction, presumably within the bulk of the catalyst phase. Therefore an evaluation of mass transport rates in relation to the reaction rate is an essential task in order to gain a realistic mathematic expression for the overall reaction rate. Since the volume hold-ups of the liquid phases are the same and water exhibits a higher surface tension, it is obvious that the organic and gas phases are dispersed in the aqueous phase. In terms of the film model there are laminar boundary layers on both sides of an interphase where transport of the substrates takes place due to concentration gradients by diffusion. The overall transport coefficient /cl can then be calculated based on the resistances on both sides of the interphase (Eq. 1) ... 

The resulting values are shown in Table 4. As expected, the diffusion coefficients of prenal and citral are smaller in water than in n-hexane. Since the mass transport coefficients in each boundary layer directly correlate with the diffusion coefficient (Eq. 3), this result confirms the assumption that the overall mass transport resistance can be predominantly referred to the aqueous catalyst phase ... 

The overall mass transport coefficient for mass transport from the dispersed organic phase into the continuous aqueous phase was then calculated according to the Calderbank equation (Eq. 4) ... 

Table 5 Overall mass transport coefficients kn and kna values for the mass transport of prenal and citral in the Diphasic system n-hexane/water...

As expected, the overall reaction rate increases with increasing catalyst volume rate. The effect can be explained in terms of the dependency of the mass transport coefficient ll on the Re munber (Eq. 12). Due to the increase of the volume hold-up of the aqueous phase, the residence time of the organic phase decreases, so that the observed conversion degrees do not change within the limits of the investigated regime. 

Average body weight of the treated rats in the critical study (Paulet and Desbrousses 1972) was 0.225 kg. Since the overall mass transport coefficient (Kg) is not available, the value has been assumed to equal 1. 

Figure 9 Comparison of previously reported values of kSA for reduction by Fe° with external mass transport coefficients estimated for batch, column, and rotating disk electrode reactors. References for the overall rate coefficients are given in Fig. 1 of Ref. 101. Mass transport coefficients were estimated for the batch and column reactors based on empirical correlations discussed in Refs. 125 and 101. Mass transport coefficients for the RDE were calculated using the Levich equation [178].

One notes that the surface concentrations of A and B, and Cb, appear in the denominator of the overall transport coefficients and k i. Consequently, Equations (12-101), (12-102), and (12-103) must be solved simultaneously. In some cases analytical solutions are available, but for complex rate laws, one resorts to numerical solutions. However, we shall consider some limiting situations on the CD-ROM along with an example problem. 

The resistances to the mass transport that a species encounters when is transferred from the gas to the hquid phase are reported in Figure 38.3. Gas and liquid phases contribute to the overall resistance because of the formation of boundary layers close to the membrane surface. This imphes that the concentration of a generic species i in the bulk of the two phases is different from its concentration at the membrane surfaces. The resistance offered by the membrane with gas-filled pores will be different (generally lower) than that with liquid-filled pores, due to the different effective diffusion coefficients. The overall mass-transport coefficient is given by... 

Individual mass-transfer coefEcients are determined experimentally for every metal species in the processing time intervals between sampling (ti—t ), (tj—tj), (tf—tj), and so on. Then, for every metal transported, the overall mass-transfer coefficients on the feed side, Kp/p(t), and strip side, 1 e/r(V, the total overall mass-transfer coefEcients of the BAHLM system, were calculated, using Eqs (8), (9), and (47), respectively, for every samphng time interval. Separation factors of two metal species,... 

The possibility of the deactivation at the reactor walls of vibrationally excited molecules was not considered. This contribution to the overall loss of excitation is determined by the accomodation coefficient for vibrational energy of the wall material and by the transport coefficients of the molecules to the walls. An example will serve for illustration The first order rate constant kw which accounts for the losses of vibrational excitation of an excited species at the reactor walls can be expressed as... 

The various resistances for mass transfer and the concentration driving force for the transport of the reactants can be seen in Figure CSll.la. Based on these concentrations and the volumetric transport coefficients, the overall rate of reaction can be written as... 

Eq. (9.42) shows that the film transport resistances can be added to each other and an overall transport coefficient can be defined as... 

The model discussed here uses the effective transport concept, this time to formulate the fiux of heat or mass in the radial direction. This flux is superposed on the transport by overall convection, which is of the plug flow type. Since the effective diffusivity is mainly determined by the flow characteristics, packed beds are not isotropic for effective diffusion, so that the radial component is different from the axial mentioned in Sec. 11.6.b. Experimental results concerning D are shown in Fig. 11.7.a-l [61, 62,63]. For practical purposes Pe may be considered to lie between 8 and 10. When the effective conductivity, X , is determined from heat transfer experiments in packed beds, it is observed that X decreases strongly in the vicinity of the wall. It is as if a supplementary resistance is experienced near the wall, which is probably due to variations in the packing density and flow velocity. Two alternatives are possible either use a mean X or consider X to be constant in the central core and introduce a new coefficient accounting for the heat transfer near the wall, a , defined by ... 

Overall heat transport coefficient between the external and reaction bed Overall heat transfer coefficient between reaction and permeation zone Gas superficial velocity... 

Since the particle Reynolds numbers in laboratory PBRs are very low, as stated in Section 2.2.2.2, the range of flow rates to be covered for producing adequate increases in transport coefficients has to be rather wide. It is important to determine the minimum gas flow rate after which the exit conversions Xa or the global rates ( Ra)p remain constant (Figure 2.6). All subsequent kinetic experiments must be conducted at flow rates equal to or above this minimum. When the overall process is surface reaction controlled, that is, if intrinsic kinetics is being observed, neither Xa nor -Ra)p will change with increasing linear velocity of the fluid. 

Here, Nq2 designates the oxygen flux at the surface and Co2,b the oxygen concentration in the bulk. The overall mass transport coefficient, contains two terms the coefficient km which characterizes the convective transport and the coefficient kf. 

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