Gradientless differential reactors

In this paper the new results are given. They widen the classes of catalytic reactions mechanisms having some NCL under isothermal conditions of a gradientless differential reactor. Quasistationarity via basic substances is supposed to be. In table 1 the mechanisms in which X are intermediate substances on the catalyst surface are given. 

Gradientless differential reactors allow evaluation of kinetic data practically free of distortion by heat/temperature effects. Depending on the flow, a distinction is made between reactors with outer and inner circulation (recycle reactor, continuous stirred tank reactor. Figure 4.11.1). Evaluation of kinetic measurements by means of the differential method is straightforward as the algebraic balance equation for a stirred tank reactor can be applied (prerequisite high recycle ratio R). In practice it is found that recycle ratios of more than 10 are sufficient to achieve practically ideal... 

For the following calculations it is assumed that experiments are conducted in a good recycle reactor that is close to truly gradientless. Conceptually the same type of experiment could be conducted in a differential reactor but measurement errors make this practically impossible (see later discussion.) The close to gradientless conditions is a reasonable assumption in a good recycle reactor, yet it would be helpful to know just how close the conditions come to the ideal. 

In general, if heterogeneous catalytic reactions are to be conducted isothermally, the reactor design must provide for heat flow to or from the particles of catalyst so as to keep the thermal gradients small. Otherwise, temperatures within the catalyst bed will be non-uniform. The differential reactor and the various forms of the gradientless reactors are advantageous in this regard. 

In essence, a differential reactor is a tubular reactor operated in such a way that the difference in composition between the entering and exiting fluids is minimal (very small reactor size or very high flow rate). Since the reactor is, in effect, gradientless, its behavior equally resembles that of a continuous stirred-tank reactor at minimal conversion no difference between tube and CSTR at infinitesimal conversion ... 

A guideline for choosing a suitable method is to avoid approximations as much as possible. Thus, plots of concentration, or a function of concentrations, versus time or reactor space time are preferred for evaluation of experiments with batch, tubular, and differential recycle reactors, in which concentrations are directly measured and rates can only be obtained by a finite-difference approximation (see eqns 3.1, 3.2, 3.5, 3.6, and 3.8). On the other hand, plots of the rate, or a function of the rate, versus concentration or a function of concentrations serve equally well for evaluation of results from CSTRs or differential reactors without recycle (gradientless reactors), where concentrations and rate are related to one another by algebraic equations that involve no approximations (see eqns 3.3, 3.4, or 3.7). 

Suppression of the mutual correlation between parameters will be illustrated by a case study. Rates of catalytic reactions are very frequently measured in gradientless and differential reactors, and the rate expressions of the Langmuir-Hinshelwood type are frequently used in the interpretation of experimental data. The rate expression has the general form... 

In principle, r, is directly obtained by means of a measurement of the molar flow difference, hi — hoi. Mathematically, the differential reactor model coincides with the model of a gradientless test reactor presented in the next section. 

The limitation to low conversion is the major disadvantage of differential operation. This is not critical if the influence of the catalyst properties on deactivation is studied. If, on the other hand, one is interested in the mechanism and the kinetics of coke formation and in the deactivation of the main reactions, it is necessary to reach higher conversions. A solution to this problem is to combine the electrobalance with a recycle reactor. The recycle reactor is operated under complete mixing, so that the reactor is gradientless. Since in a completely mixed reactor the reactions occur at effluent conditions and not at feed conditions, a specific experimental procedure is necessary to obtain the deactivation effect of coke. 

The distinction between instantaneous and cumulative yield ratios or selectivities becomes immaterial in gradientless reactors (continuous stirred-tank at steady state or differential once-through reactors) or if the instantaneous values do not vary with conversion. 

It has become customary to classify evaluation methods as "differential" or "integral." These terms stem from a time when practically all experiments were conducted in batch reactors, so that rates had to be found by differentiation of concentration-versus-time data, and the calculation of concentrations from postulated rate equations required integration. The terms do not fit the work-up of data from gradientless reactors such as CSTRs, in which rates and concentrations are related to one another by algebraic equations requiring no calculus, and are therefore avoided here. 

Historically, the use of microreactors dates back to the 1940s when they were developed to measure kinetics of catalytic reactions.One of the key early findings was Denbigh s 1965 observation that if a reactor were made small enough, temperature and concentration gradients with the reactor would be negligible, so that differential (i.e., gradientless) behavior would be observed. This allowed much more accurate kinetic... 

To study the kinetics of immobilized enzymes a recirculation reactor may be used. This reactor allows one to perform kinetic measurements with defined external mass transfer effects, reached by establishing a high flow rate near the catalyst, minimizing mass transfer resistance. The reactor behaves as a differential gradientless reactor allowing initial-rate kinetic measurements to be made. 

The experiment must be isothermal and uniform in chemical composition (i.e., present perfect mixing). Temperature gradients may be minimized by intensive heat exchange, dilution of the active material, or rapid recirculation of fluid phase. The reaction zone may be minimized in order to render the reactor gradientless, such as in the cases of differential plug flow reactor (Section 10.4.1.1) or thin-zone TAP reactor (TZTR) (Section 10.6.1.2). 

However, be careful as far as the differential mode of operation is concerned, for the differential expression dc/dr (batch reacton dc/dt) has to be replaced by the ratio of the differences Ac/At, since arbitrarily small differences cannot be determined analytically. Consequently, the reaction rate can no longer be attributed precisely to a specific concentration. Also for this reason, more accurate gradientless reactors are frequently used. 

Different laboratory reactors are used for kinetic studies. For studies of liquid-liquid reactions and homogeneously catalyzed reactions, a batchwise operated stirred tank reactor is frequently used. Tubular reactors loaded with catalyst (fixed bed) are more common for studies of heterogeneously catalyzed gas reactions. The tubular reactor displays a simple design and is easy to operate. A simultaneous integral and differential mode of operation can be achieved by a tap reactor for measuring concentration and temperatures at defined axial positions. Gradientless operation with respect to temperature and concentration can be obtained by an external or internal recycle. 

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