Tracers CSTR parameter modeling

Here we use a single parameter to account for the nonideality of our reactor. This parameter is most always evaluated by analyzing the RTD determined from a tracer test. Examples of one-parameter models for a nonideal CSTR include the reactor dead volume V, where no reaction takes place, or the fraction / of fluid bypassing the reactor, thereby exiting unreacted. Examples of one-parameter models for tubular reactors include the tanks-in-series model and the dispersion model. For the tanks-in-series model, the parameter is the number of tanks, n, and for the dispersion model, it is the dispersion coefficient D,. Knowing the parameter values, we then proceed to determine the conversion and/or effluent concentrations for the reactor. 

Real reactors deviate more or less from these ideal behaviors. Deviations may be detected with re.sidence time distributions (RTD) obtained with the aid of tracer tests. In other cases a mechanism may be postulated and its parameters checked against test data. The commonest models are combinations of CSTRs and PFRs in series and/or parallel. Thus, a stirred tank may be assumed completely mixed in the vicinity of the impeller and in plug flow near the outlet. 

B Using a Tracer to Determine the Model Parameters in a CSTR with an Exchange Volume 900... 

A real CSTR is believed to be modeled as a combination of an ideal CSTR of volume Vj, a dead zone of volume V. and a bypass with a volumetric flow rate (Figure 14-15). We have used a tracer experiment to evaluate the parameters of the model R, and V, Because the total volume and volumetric flow rate are known, once V, and are found, and V, can readily be calculated. 

In this equation, the numbers of ideal CSTRs, N is the parameter of the tanks in series model. This parameter N is estimated using the E-curve, obtained from the tracer experiment conducted on the reaction vessel. As a special case, consider a first-order reaction (n = 1). Substituting n = 1 in Equation 3.311 and solving the equation recursively for i = 1, 2,3,..., n, we get... 

It can be seen that the plot of E(9) versus 9 shifts away from the ideal CSTR plot and moves towards the ideal PFR plot as Pe increases. Given a plot of E(9) versus 9 obtained from the tracer experiment, the value of the parameter Pe is estimated as the value for which the experimental plot fits well with the theoretical plot of E(9) versus 9 shown in Figure 3.62. But one cannot derive a theoretical expression for E(9) as it is not possible to obtain an analytical solution to the model Equation 3.329 with Danckwarts boundary conditions (3.331) and (3.334). Flowever, an explicit equation relating the variance and mean 9 of the RTD to the Peclet number Pe has been derived using the method of moments without actually solving the model equation. This equation... 

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