Flow rates CSTR parameter modeling

The CRE approach for modeling chemical reactors is based on mole and energy balances, chemical rate laws, and idealized flow models.2 The latter are usually constructed (Wen and Fan 1975) using some combination of plug-flow reactors (PFRs) and continuous-stirred-tank reactors (CSTRs). (We review both types of reactors below.) The CRE approach thus avoids solving a detailed flow model based on the momentum balance equation. However, this simplification comes at the cost of introducing unknown model parameters to describe the flow rates between various sub-regions inside the reactor. The choice of a particular model is far from unique,3 but can result in very different predictions for product yields with complex chemistry. 

The main variable of design for a CSTR is the hydraulic retention time (HRT), which represents the ratio between volume and flow rate, and it is a measure of the average length of time that a soluble compound remains in the reactor. Capital costs are related to HRT, as this variable directly influences reactor volume [83]. HRT can be calculated by means of a mass balance of the system in that case, kinetic parameters are required. Some authors obtained kinetic models from batch assays operating at the same reaction conditions, and applied them to obtain the HRT in continuous operation [10, 83, 84]. When no kinetic parameters are available, HRT can be estimated from the time required to complete the reaction in a discontinuous process. One must take into account that the reaction rate in a continuous operation is slower than in batch systems, due to the low substrate concentration in the reactor. Therefore, HRT is usually longer than the total time needed in batch operation [76]. 

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. 

Figure 14-18(a) describes a real PFR or PER with channeling that is modeled as two PFRs/PBRs in parallel. The two parameters are the fraction of flow 10 the reactors [i.e., (3 and (1 - p)] and the fractional volume [i.e.. a and (1 - Qf] of each reactor. Figure 14-18(b) describes a real PFR/PBR that has a backmix region and is modeled as a PFR/PBR in parallel with a CSTR. Figures H-19(a) and (b) show a real CSTR modeled as two CSTRs with interchange. In one case, the fluid exits from the top CSTR (a) and in the other case the fluid exits from the bottom CSTR. The parameter p represents the interchange volumetric flow rate and a the fractional volume of the top reactor, where the fluid exits the reaction system. We note that the reactor in model 14-19(b) was found to describe extremely well a real reactor used in the production of terephthalic acid. A number of other combinations of ideal reactions can be found in Levenspiel. ... 

The arrangement that is chosen is largely based on intuition. The parameters in the model are the relative volumes of the CSTR s and PFR s that ms e up the model (minus one), and the circulation flow rates, divided by the reactor feed. The parameters are estimated by fitting of RTD-measurements. Then the conversion of a given chemical reaction in the simulated reactor is calculated. Since all elements are ideal reactors, the calculation methods of Chapter 3 may be applied, and so the entire reactor system can be described by relatively simple calculations. The calculated conversion is compared to the measured conversion, and when there are deviations, the model is adjusted. By trial and error one may arrive at a model that describes the real reactor satisfactorily. 

It is given in TSR notation , which is rather self explanatory. The CSTR statement declares that the reaction is taking place in a open flow reactor, with flow rate KO, and input species Br-, Br03-, ArOH, H20 and H+. This model contains 13 intermediate species, 33 processes, including the input and output flow processes, and 21 control parameters. 

The CIS model and the Dispersion model are referred to as one-parameter models, since only a single parameter, D/uLot N, is used to characterize mixing. When there is very little mixing in the direction of flow, i.e., when A is large otD/uL is small, the physical basis of the Dispersion model is stronger than that of the CIS model. Moreover, when the number of CSTRs in series is large, it can be tedious to calculate the performance of the series of reactors. On the other hand, it is relatively straightforward to use even the most complex rate equations in the CIS model. It is not necessary to restrict the analyses to first-order rate equations. 

In the previous section we indicated how various mathematical models may be used to simulate the performance of a reactor in which the flow patterns do not fit the ideal CSTR or PFR conditions. The models treated represent only a small fraction of the large number that have been proposed by various authors. However, they are among the simplest and most widely used models, and they permit one to bracket the expected performance of an isothermal reactor. However, small variations in temperature can lead to much more significant changes in the reactor performance than do reasonably large deviations inflow patterns from idealized conditions. Because the rate constant depends exponentially on temperature, uncertainties in this parameter can lead to design uncertainties that will make any quantitative analysis of performance in terms of the residence time distribution function little more than an academic exercise. Nonetheless, there are many situations where such analyses are useful. 

By and large we can describe the results of the analysis of distributed parameter systems (i.e., flow reactors other than CSTRs) in terms of the gradients or profiles of concentration and temperature they generate. To a large extent, the analysis we shall pursue for the rest of this chapter is based on the one-dimensional axial dispersion model as used to describe both concentration and temperature fields within the nonideal reactor. The mass and energy conservation equations are coupled to each other through their mutual concern about the rate of reaction and, in fact, we can use this to simplify the mathematical formulation somewhat. Consider the adiabatic axial dispersion model in the steady state. 

In [101], a cylindrical CSTR with an inner Pyrex liner was used (Fig. 3.56). Experiments in this reactor showed that the reaction has a thermal hysteresis, the parameters of which are in qualitative agreement with estimates obtained in [104] within the framework of a nonisother-mal kinetic model of the process. It was demonstrated that the residence time of the mixture in the CSTR after complete oxygen conversion does not affect the selectivity and yield of methanol. As in flow reactors, at a constant rate of reagents consumption, the selectivity and yield of methanol increase with the pressure, in agreement with the simulation results. Generally, the results obtained in CSTRs are consistent with the results obtained in flow reactors. 

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