External resistance mass transfer

1 and 2 are the external mass-transfer resistance. Step 3 is the intraparticle mass-transfer resistance. 

If an enzyme is immobilized on the surface of an insoluble particle, the path is only composed of the first and second steps, external mass-transfer resistance. The rate of mass transfer is proportional to the driving force, the concentration difference, as 

During the enzymatic reaction of an immobilized enzyme, the rate of substrate transfer is equal to that of substrate consumption. Therefore, if the enzyme reaction can be described by the Michaelis-Menten equation, 

JVDa is known as Damkohler number, which is the ratio of the maximum reaction rate over the maximum mass-transfer rate. Dependingupon the magnitude of NDa, Eq. (3.2) can be simplified, as follows  

If NDa 1, the mass-transfer rate is much greater than the reaction rate and the overall reaction is controlled by the enzyme reaction, 

A modified Carbeny mixer was used by Ma and Lee to measure uptake rates for C4 hydrocarbons in 13X molecular sieve pellets using a helium carrier. Adsorption rates were slow and they concluded that the ratecontrolling mass transfer process was intracrystalline diffusion with a diffusiv-ity of order 10 cm s at 35°C. An independent study by Doelle and Riekert using large crystals of 13X zeolite ( 100 ftm) showed that the diffusivity of butane is, under comparable conditions, very much higher ( 10 -10 cm s ). The discrepancy appears to have arisen from the intrusion of external mass transfer resistance in the Carberry mixer. 

A very similar experimental system was used by Taylor who showed that the uptake rate in such systems could be correlated directly with the molecular diffusivity of the gas phase, strongly suggesting that external resistance was dominant. This conclusion was confirmed by detailed analysis of the experimental results which revealed that the measured mass transfer rates were consistent with established mass transfer correlations. The effect of 

FIGURE 6.20. Test of the spinning basket adsorber. Overall rate coefficients for adsorption of propane on Linde 5A at 54 C were measured at several speeds of rotation in the presence of 500 Torr of either iQH,) or SFj. These species are both too large to penetrate the sieve. The uptake rate correlates with the gas phase molecular diffusivity indicating external mass transfer control. (Data of Taylor. ° ) 

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Correlations of heat and mass-transfer rates are fairly well developed and can be incorporated in models of a reaction process, but the chemical rate data must be determined individually. The most useful rate data are at constant temperature, under conditions where external mass transfer resistance has been avoided, and with small particles... 

When there is an external mass transfer resistance, the value of C i (the concentration at the surface of the particle) is less than that in the bulk of the fluid (Cao) and will not be known. However, if the value of the external mass transfer coefficient is known, the mass transfer rate from the bulk of the fluid to the particle may be expressed as ... 

External mass transfer resistance for particle 644 Extruders 306... 

A final, obvious but important, caution about catalyst film preparation Its thickness and surface area Ac must be low enough, so that the catalytic reaction under study is not subject to external or internal mass transfer limitations within the desired operating temperature range. Direct impingement of the reactant stream on the catalyst surface1,19 is advisable in order to diminish the external mass transfer resistance. 

Figure 8.9 External mass transfer resistance—xylose hydrogenation and isomerization to xylitol and by-products on sponge Ni (based on the results of Mikkola et al. [22]).

External mass transfer resistance was neglected, as reported by [63] in biofilm reactors with granular particles (fluidized bed, airlift) the Biot number was generally larger than 100. 

Here, as in Section 8.5.4, we treat the isothermal case for ijo, and relate tj0 to 17. may then be interpreted as the ratio of the (observed) rate of reaction with pore diffusion and external mass transfer resistance to the rate with neither of these present. 

A kinetics or reaction model must take into account the various individual processes involved in the overall process. We picture the reaction itself taking place on solid B surface somewhere within the particle, but to arrive at the surface, reactant A must make its way from the bulk-gas phase to the interior of the particle. This suggests the possibility of gas-phase resistances similar to those in a catalyst particle (Figure 8.9) external mass-transfer resistance in the vicinity of the exterior surface of the particle, and interior diffusion resistance through pores of both product formed and unreacted reactant. The situation is illustrated in Figure 9.1 for an isothermal spherical particle of radius A at a particular instant of time, in terms of the general case and two extreme cases. These extreme cases form the bases for relatively simple models, with corresponding concentration profiles for A and B. 

Dimensionless numbers in mixing, 16 685 used in convection heat-transfer analysis, 73 246-247 Dimensionless parameter, external mass transfer resistance and, 25 290-292 Dimensionless reactor design formulation, 21 350... 

External humidification, 12 213 External interface management, in technology transfer, 24 366 External loop airlift bioreactors, 1 741, 742 Externally manifolded fuel cells, 12 200 External magnetic field, 23 835 External mass transfer, 15 728-729 External mass transfer resistance dimensionless parameter and,... 

Packed-bed reactors, 21 333, 352, 354 Packed beds, 25 718 Packed catalytic tubular reactor design with external mass transfer resistance, 25 293-298 nonideal, 25 295... 

The expression for the effectiveness factor q in the case of zero-order kinetics, described by the Michaelis-Menten equation (Eq. 8) at high substrate concentration, can also be analytically solved. Two solutions were combined by Kobayashi et al. to give an approximate empirical expression for the effectiveness factor q [9]. A more detailed discussion on the effects of internal and external mass transfer resistance on the enzyme kinetics of a Michaelis-Menten type can be found elsewhere [10,11]. 

As can be concluded from this short description of the factors influencing the overall reaction rate in liquid-solid or gas-solid reactions, the structure of the stationary phase is of significant importance. In order to minimize the transport limitations, different types of supports were developed, which will be discussed in the next section. In addition, the amount of enzyme (operative ligand on the surface of solid phase) as well as its activity determine the reaction rate of an enzyme-catalyzed process. Thus, in the following sections we shall briefly describe different types of chromatographic supports, suited to provide both the high surface area required for high enzyme capacity and the lowest possible internal and external mass transfer resistances. 

The results reviewed above suggest that gas-phase diffusion can contribute significantly to polarization as O2 concentrations as high as a few percent and are not necessarily identifiable as a separate feature in the impedance. Workers studying the P02 -dependence of the electrode kinetics are therefore urged to eliminate as much external mass-transfer resistance in their experiments as possible and verify experimentally (using variations in balance gas or total pressure) that gas-phase effects are not obscuring their results. 

Acrivos, A., On the combined effect of longitudinal diffusion and external mass transfer resistance in fixed bed operations. Chem. Eng. Sci. 13, 1 (1960). 

There are no solutions for transfer with the generality of the Hadamard-Rybczynski solution for fluid motion. If resistance within the particle is important, solute accumulation makes mass transfer a transient process. Only approximate solutions are available for this situation with internal and external mass transfer resistances included. The following sections consider the resistance in each phase separately, beginning with steady-state transfer in the continuous phase. Section B contains a brief discussion of unsteady mass transfer in the continuous phase under conditions of steady fluid motion. The resistance within the particle is then considered and methods for approximating the overall resistance are presented. Finally, the effect of surface-active agents on external and internal resistance is discussed. 

In trickle beds, the gas-to-liquid, kigaGL, and liquid-to-particle, kfaLS, coefficients are used to represent the effect of the external mass transfer resistances. The interfacial areas aGl and <2ls refer to the effective mass transfer surface per unit volume of empty reactor. Due to the fact that the coefficients kig and klL cannot be easily estimated independently from the corresponding interfacial areas aGL and aLS respectively, by simple experimental techniques, correlations are normally reported for the products kigaGL and k,a]S (Smith, 1981). 

Then, assume that the reaction takes place in a fixed bed of 1.61 m diameter and 16.1 m height, under contact time of 5 min, and the inlet temperature of gas being 50 °C, for different CO inlet concentration (several runs). Estimate the conversion of CO in an isothermal and adiabatic fixed-bed reactor and under the following assumptions isobaric process, negligible external mass transfer resistance, and approximately constant heat capacity of air (cp = 1 kJ/kg K) and heat of reaction (AH = -67,636 cal/mol). The inlet temperature of the reaction mixture is 50 °C and its composition is 79% N2 and approximately 21% 02, while the inlet CO concentration varies from 180-4000 ppm (mg/kgair) (for each individual ran). 

There are three distinct mass-transfer resistances (1) the external resistance of the fluid film surrounding the pellet, (2) the diffusional resistance of the macropores of the pellet, and (3) the diffusional resistance of the zeolite crystals. The external mass-transfer resistance may be estimated from well-established correlations (4, 5) and is generally negligible for molecular sieve adsorbers so that, under practical operating conditions, the rate of mass transfer is controlled by either macropore diffusion or zeolitic diffusion. In the present analysis we consider only systems in which one or other of these resistances is dominant. If both resistances are of comparable importance the analysis becomes more difficult. 

If we have an external mass transfer resistance at the surface, we need two parameters, v = n(0) and w = (1), 0 < v w < 1, and then there are various limiting cases according the path that (w, v) takes to the boundary of its triangular domain. The relevant equations are... 

An enzyme is immobilized on solid surface. Assume that the external mass-transfer resistance for substrate is not negligible and that the Michaelis-Menten equation describes the intrinsic kinetics of enzyme reaction. 

When the external mass transfer resistance is negligible and kgA is large, leading to Sha —> oo, then the boundary condition at w = 1.0 can be written as... 

Besides, if SHa — oo, then xa w=i.o = xAb This also corresponds to a negligible external mass transfer resistance. In both cases, that of a finite Sherwood number SHa or for SHa — oo, we get a two-point boundary value differential equation. For the nonlinear case this has to be solved numerically. However, as for the axial dispersion model, we will start out with the linear case that can be solved analytically. 

Calculate the isothermal effectiveness factor rj for the porous catalyst pellet in problem 1 as a function of the Thiele modulus d> for the first reaction A —> B utilizing the fact that the rate constant of the second reaction B —> C is half the rate constant of A —> B, the pellet is isothermal, and the external mass transfer resistance is negligible. 

The external mass-transfer resistance is to be taken into account. 

In general case, as was mentioned, the diffusion coefficient and/or convective velocity can depend on the space coordinate, thus D=D(y), u(y), [or on the concentration, D = D(c) or both of them, D = D(c, y)]. In the boundary conditions the external mass-transfer resistance is also taken into account. 

For the case, where there is an external mass transfer resistance, the reaction rate... 

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