External transport control

Figure 9-15 Schematic illustration of diagnostic experiments for external transport control/influence in a fixed-bed reactor. The linear velocity through the catalyst bed can be varied, without changing the space time, by changing the weight of catalyst in the reactor and the volumetric flow rate to the reactor in direct proportion, leaving the itmer diameter of the reactor unchanged.

Engineer A claims that there is a second way to test for the presence or absence of external mass transfer. Engineer A proposes to operate the reactor at constant space velocity and constant linear velocity, but to change the catalyst particle size. The mass-transfer coefficient and the external surface area per unit weight of catalyst both depend on particle size. Therefore, if the outlet conversion changes as the particle size is varied, it is safe to conclude that external transport controls or influences the reaction rate. Engineer B disagrees. 

Zogorski et al. [125] indicate that external transport is the rate-limiting step in systems having poor mixing, dilute concentration of adsorbate, small particle sizes of adsorbent, and a high affinity of adsorbate for adsorbent. Some experiments conducted at low concentrations have shown that film diffusion solely controls the adsorption kinetics of low molecular weight substances [81,85]. 

One of the exciting new directions is the control of activated rate processes using external fields. Addition of an external field opens the way for a wide variety of new phenomena such as stochastic resonance, resonance activation, directed transport, control of the hopping distribution in surface diffusion and more. Even the addition of a constant force to the problem leads to interesting additional phenomena such as the locked to running transition, which remains a topic of ongoing research. " Quantum mechanics in the presence of external fields may differ significantly from the classical. 

Convective diffusion — The electrochemical - mass transport controlled by both -> convection and - diffusion is called a process by convective diffusion [i]. Convection is caused by externally controlled force or spontaneous force. Convective diffusion has been conventionally used in a strict sense for well-controlled flow such as for -> rotating disk electrodes [ii], - channel elec-... 

The observed rate will depend on the molecular weight of the inert gas if it is influenced by the first step. External transport can also influence or control the rate of sorption/desorption if the sorbent consists of agglomerates of zeolite crystals such as pellets or layers. The rate of sorption or desorption will then depend on the size or shape of the agglomerates if it is influenced by the transport in the macropores between the crystals. 

Figure 6 provides a comparison between measured spectra and theoretical spectra calculated under the assumption that the adsorption/desorption process is controlled by either intracrystalline diffusion (Fig. 6a) or external transport resistances such as surface barriers (Fig. 6b). For simplicity in the calculations, the crystallites have been assumed to be of nearly spherical shape with a concentration-independent transport diffusivity Dj or surface permeability a, respectively. Values of the intracrystalline mean lifetime are therefore given by...

It is always best to operate an experimental reactor under conditions where all diffusional disguises are lifted (by using the criteria listed in the previous section). A less acceptable alternative is to account for them through appropriate effectiveness factors and external transport coefficients. A number of highly sophisticated computer-controlled reactor systems such as the Berty recycle reactor are commercially available. Many of them are available with software and appropriate interfacing that can set and implement the experiments for each of a series of sequential runs (see Mandler et al., 1983), resulting in the emergence of the most acceptable model at the end of the exercise. 

Further deviations are the result of transport influences represented in Fig. 5.5 by an Arrhenius-type plot for a case with strong internal and external diffusion control (Dialer and Lowe, 1975). One can see that only for the lowest temperatures is the value of E calculated from the linear slope a true value. 

A unique benefit of biofilm reactors for research purposes is the fact that due to the distinct separation between the L and the S phase (difference in density — Pl) high relative velocities can be realized. As a result, external transport limitation can be excluded or easily studied simultaneously with internal transport limitations in the case of uniform and controlled biofilm thickness. In this respect, biofilm reactors are superior to the conventional... 

Heat and mass transfer coefficients can be used to interrogate the importance of external transport phenomena and how to choose reactor size. The latter controls (i) pressure drop, (ii) residence time and thus reactant conversion or flow rate and thus power generated, (iri) the effective reaction rate and thus the process efficiency, (iv) the temperature and (v) whether a system is kinetically controlled and thus ideal for extraction of catalytic kinetics. Another application of Nu and Sh is that a 2D or 3D problem can be reduced to a computationally tractable problem by approximating the transverse transport phenomena using overall transport correlations. Such pseudo-2 D models (also called heterogeneous ID models for catalytic systems) have been used to explore the stability and performance of microbumers with a significantly lower computational effort than CFD models (e.g. [23-25]). 

ACID will immediately begin playback and will generate the MTC at the same time, using the output device or port specified in the Preferences dialog box. ACID s transport controls (Play and Stop) will be used to control the external devices. 

When T]kylc/kc 1 and the effectiveness factor is close to imity rj 1), the rate of reaction in the catalyst particle is Ra,p = VgCa - The concentration profile of reactant A is shown in Figure 9-12. Neither the internal nor the external transport resistance has any influence on the rate of reaction, and no transport coefficients ( c or DAfifd appear in the expression for the reaction rate. In this case, the reaction is said to be controlled by intrinsic kinetics. Stated differently, intrinsic kinetics is the controlling resistance. 

If a heterogeneous catalytic reaction is influenced or controlled by external transport, the actual rate of reaction will depend on the transport coefficients, h and kc. These coefficients depend on the velocity of the fluid relative to the catalyst particle, which will be represented... 

Diagnostic experiments can be carried out to determine whether a heterogeneous catalytic reaction is being affected by external transport. These experiments are based on a very simple concept. If a heterogeneous catalytic reaction is controlled by intrinsic kinetics. 

We know that the rate —rp, will depend on temperature and concentration. If the reaction is controlled or influenced by external transport, —rp also will depend on v. 

Suppose that we carry out two experiments in an ideal PFR at exactly the same value of To, at exactly the same inlet conditions, and at exactly the same temperature conditions, but at different values of v. If the outlet conversions are different for these two experiments, external transport must either control or influence the reaction rate. 

Diagnostic experiments can be designed to determine whether a heterogeneous catalytic reaction is controlled or influenced by external transport, based on the above idea. Consider a tubular reactor with an inner diameter A loaded with a weight of catalyst W. The height of catalyst in the reactor is L. An experiment is carried out with a volumetric inlet flow rate of Mb-The concentrations of the components of the feed stream are Cg), the inlet temperature is To, and the reactor is operated either isothermally or adiabatically. The conversion of A leaving the reactor xa is measured. This situation is shown schematically in Figure 9-15... 

In many cases, it is necessary to estimate the rate at which a heterogeneous catalytic reaction wfll proceed, if it is controlled by external mass transfer. Alternatively, it may be necessary to estimate the concentration difference (Ca,b — Ca ) and the temperature difference (7b — T ) that are required to sustain a known or measured rate of reaction. Calculations of Ca3 — Ca,s and Tb — Tg are the only way to evaluate the influence of external transport when definitive diagnostic experiments are not feasible. Calculations such as these can be performed using Eqns. (9-38) and (9-40), provided that the transport coefficients kc and h are known, or can be obtained from correlations. 

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