Equivalent reactor volume concept

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. 

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). 

When we consider the same two cases as they appear in flow reactors the concepts of reaction time become less clear. In the case of a constant-volume homogeneous phase reaction taking place in a PFR, an increment of feed has a transit time, or space time t, during which it traverses the length of the constant temperature plug flow reactor. Both these times are equivalent in this case. Assuming that the reactants were preheated in a relatively small volume and are cooled in a similarly small volume, the main course of the reaction takes place in the reactive volume of the reactor proper. The time spent in this volume can be calculated as the volume of the reactor divided by the volumetric feed rate of the reactants. 

Analysis This example gives an important industrial concept. These space times are (he times for each of (he reactors to take the volume of fluid equivalent to one reactor volume and pul it into the reactor. 

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