Residence Time Space

Figure 5.21 Geometric interpretation of mixing in residence time space. Mixtures also lie on a straight line when residence time is used since residence time also obeys a linear mixing law.

Consequently, when rate vectors are to be defined for an AR in residence time space, the corresponding entry for t is assigned a scalar value of 1 ... 

Although residence time shares similar geometric traits to concentration, AR constructions in residence time space are inherently different to constructions solely in concentration space. Since there is no limitation on the value of residence time used (we are allowed to make the system residence time as large as desired), the corresponding AR boundaries may then also be arbitrarily large. 

Candidate ARs in residence time space are necessarily unbounded on the t axis, owing to the fact that a state achieved at a particular residence time is also achievable for all later residence times. 

In this scenario, an adiabatic system with a reactor type constraint is investigated. Specifically, the construction of the AR shall be carried out using PFRs only. The techniques developed in this section will be utilized in later examples, when interstage and cold-shot cooling in an adiabatic system is employed. The AR will be constructed in residence time space to find a reactor configuration that minimizes the total reactor volume for a given output concentration. 

For simplicity, it is assumed that the same reaction and kinetics are available as in Section 7.3.2 so that each reactor obeys Equations 7.14 and 7.15. The characteristic shape of each PFR trajectory is then uniquely defined when an inlet temperature Tj is specified. Identifying the reactor structure with minimum residence time is then found by generating a candidate AR in concentration-residence time space. In Figure 7.24, three PFR trajectories from the feed are plotted corresponding to inlet temperatures of 300,320, and 350 K, respectively. 

The algorithms described in this chapter deal mostly with candidate regions in concentration space alone. At present, some of the methods discussed are able to handle nonisothermal problems, such as those given in Chapter 7. Other methods possess the ability to compute candidate regions in residence time space (unbounded problems). As further research into AR construction methods continues, a broader range of techniques for the determination of the AR may be developed. 

It is also possible to include residence time in the state vector C and build ARs in residence time space. This is included in the usual manner, with the corresponding r component in r(C) given as unity (dr/dr = 1). 

An additional benefit of computing candidate ARs in this manner is that there is no need to assume that the feasible region be bounded. Candidate ARs in residence time space may therefore be determined with this method, such as that shown in Figure 8.26(a). 

In order to compute ARs in mass fraction residence time space, we must also be able to express o as a component in the rate vector. From the definition of reaction rate, we know... 

Here, Wr(C) is the equivalent rate vector in mass fraction space. Assuming that we are working in residence time space,... 

Calculate the average residence time, space time, and reactor volume for a final conversion of 75% by carrying out the reaction in a PFR and CSTR separately. What is the ratio between their volumes ... 

Other variations in the different zones of cascade reactors, which have not been reported, include residence time (space velocity), acid/hydrocarbon ratio, and character of the dispersions. The decreases in RON for alkylates in the latter zones are also partly due to degradation reactions. It has been shown (16,17) that TMPs degrade in the presence of sulfuric acid. It has also been indicated (14) that both the quality and quantity of allgrlates are reduced by such degradations the quality was estimated to reduce by perhaps 0.11 RON in cascade units. In Stratco units, the decrease was perhaps 0.07 RON this lower value is because of lower residence times. Degradation reactions of TMPs are also thought to be more pronounced in cascade reactors because of increased amounts of mixing of TMPs with olefins. 

A tube reactor is fed with a solution containing 2mol/dm diethyl adipate (A) and 3 mol/dm sodium hydroxide (B). The reactor is assumed to operate adiabatically. Determine the residence time (space time) by numerical simulations, which gives the maximum yield of the intermediate product, R. 

Therefore, for a good approximation to plug flow, the diffusion time needs to be only about 1/4 of the mean residence time (space time). The probability density function for various Bo and Po numbers for a system with open system boundaries is shown in Figure 12.2. For a satisfactory approximation to plug flow in a microreactor, the criteria Bo > 200 and Fo > 4 are necessary. 

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