Equivalent reactor volume

The equivalent reactor volume concept, introduced by Hougen and Watson [1] allows for a second way of dealing with nonisothermal data it first reduces the data to isothermality and determines the temperature dependence of the rate parameters in the second stage only. The equivalent reactor volume has been defined as that volume, which, at the reference temperature T, and the reference total pressure p,i, would give the same conversion as the actual reactor, with its temperature and pressure profiles. It follows that... 

In a kinetic study the activation energy is generally not known a priori, or only with insufficient accuracy. The use of the equivalent reactor volume concept therefore leads to a trial-and-error procedure a value of is guessed and with this value and the measured temperature profile Vp is calculated by graphical or numerical integration. Then, for the rate model chosen, the kinetic constant is derived. This procedure is carried out at several temperature levels and from the temperature dependence of the rate coefficient, expressed by Arrhenius formula, a value of is obtained. If this value is not in accordance with that used in the calculation of Vp the whole procedure has to be repeated with a better approximation for . 

We see how the curves do not extrapolate through the origin. This results from the fact that not all of the volume accounted for is at the reference temperature considered. The equivalent reactor volume concept will be used to reduce the data to isothermal conditions. 

With this value of and the temperature profiles the equivalent reactor volumes may be obtained as shown in Fig. 3. The curve x versus is shown in Fig. 4. The curves now extrapolate through the origin. With such a diagram the derivation of a rate equation may now be undertaken. 

Figure 3 Acetone cracking. Calculation of equivalent reactor volume from Froment, et al. [5, 6]).

Acetone cracking. Temperature profiles for calculation of equivalent reactor volume. From Froment et al. [1961a, b]. 

These reactors can be modelled in three ways (i) by direct experimental simulation, (ii) by equivalent reactor volume concept, and (iii) by conservation equations. Since the flow rates used in... 

If the temperature variations as a function of axial location can be predicted, the "equivalent reactor volume" concept (Hougen and Watson, 1947 Froment et al., 1961) can be applied to convert the data to a pseudo-isothermal basis. According to Hougen and Watson (1947), the equivalent reactor volume is defined as that volume which, at a constant reference temperature, would give the same conversion as the actual non-isothermal tubular reactor. The reference temperature has frequently been taken as the arithmetic mean of the process gas temperatures in the last 40% of the reactor (Van Damme et al., 1975). 

For example, if the reactor volume is 0.2 and the inlet volumetric flow rate is 0.01 mVs, it would take the upstream equivalent reactor volume (V = 0.2 m ) shown by the da.shed lines a lime t equal to... 

Figure 6.16 HCR rate constant versus equivalent reactor volume.

The supramolecular guest—Pd—dendrimer complex was found to have a retention of 99.4% in a CFMR and was investigated as a catalyst for the allylic ami-nation reaction. A solution of crotyl acetate and piperidine in dichloromethane was pumped through the reactor. The conversion reached its maximum ca. 80%) after approximately 1.5 h (which is equivalent to 2—3 reactor volumes of substrate solution pumped through the reactor). The conversion remained fairly constant during the course of the experiment (Fig. 8). A small decrease in conversion was observed, which was attributed to the slow deactivation of the catalyst. This experiment, however, clearly demonstrated that the non-covalently functionalized dendrimers are suitable as soluble and recyclable supports for catalysts. 

A 15 1 (11 1 working volume) Applikon stirred tank, or equivalent, reactor is used as a medium reservoir. 

We have been working up to now with an expression for the rate of reaction per unit reactor volume. Now we have to recognize that the reactor volume may be packed with a stationary bed of porous catalyst particles within which the reaction is taking place and that something more than a mere chemical reaction throughout a uniform homogeneous phase is involved. In spite of this, we would like to use an equivalent reaction rate per unit... 

If an absorption phenomenon is occurring, changing the materials of construction of the wetted surfaces could impact the results. The best reactor results (in which the reactor volume based on the tracer analysis most closely matches the geometrically calculated reactor volume) were attained with stainless steel materials of constmction. The injector loops, tubing from the injectors to the mixing tee, and the reactor were all changed to stainless steel materials of construction of equivalent volumes. The flat top experiments were repeated for this configuration Fig. 13.10 shows the results. 

From the slope of the curve for addition of sodium carbonate to the rumen fermentation of starch, one can estimate tht the net rate of acid formation is equivalent to 36 millimoles of acetic acid per liter per hour. If a level of no more than 0.2% acid must be maintained in the rumen fermentor, then the exchange rate across the membrane must be at least one liter per hour or half of the total reactor volume each hour. This is well below the observed exchange rate of 20 liters per hour. 

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