Chemical Reaction Engineering (Homogeneous Reactions in Ideal Reactors) - Chapter 4. Design for Single Reactions - Mai Thanh Phong, Ph.D

Nội dung text: Chemical Reaction Engineering (Homogeneous Reactions in Ideal Reactors) - Chapter 4. Design for Single Reactions - Mai Thanh Phong, Ph.D

1. Chapter 4. Design for Single Reactions For mixed flow, Eq. 3.9 gives (4.2) whereas for plug flow, Eq. 3.14 gives (4.3) Dividing Eq. 4.2 by Eq. 4.3 gives (4.4) 2
2. Chapter 4. Design for Single Reactions Figure 4.1 Comparison of performance of single mixed flow and plug flow reactors for the nth- order reactions 4
3. Chapter 4. Design for Single Reactions 1.2 Variation of Reactant Ratio for Second-Order Reactions Second-order reactions of two components: behaves as second-order reactions of one component when the reactant ratio is unity. Thus When a large excess of reactant B is used then its concentration does not change appreciably (CB ~ CBO) and the reaction approaches first-order behavior with respect to the limiting component A, or Thus in Fig. 4.1, and in terms of the limiting component A, the size ratio of mixed to plug flow reactors is represented by the region between the first-order and the second-order curves. 6
4. Chapter 4. Design for Single Reactions Hence, N plug flow reactors in series with a total volume V gives the same conversion as a single plug flow reactor of volume V. 2.2. Equal-size mixed flow reactors in series In plug flow, the concentration of reactant decreases progressively through the system; in mixed flow, the concentration drops immediately to a low value. Consider a system of N mixed flow reactors connected in series: • The concentration is uniform in each reactor, • The concentration changes as fluid moves from reactor to reactor. This stepwise drop in concentration, illustrated in Fig. 4.2, suggests that the larger the number of units in series, the closer should the behavior of the system approach plug flow. 8
5. Chapter 4. Design for Single Reactions Evaluate the behavior of a series of N equal-size mixed flow reactors. Density changes will be assumed to be negligible; hence ε = 0 and t = τ. Figure 4.3 Notation for a system of N equal-size mixed reactors in series. First-Order Reactions: For component A about vessel i, it can be written: (4.8) 10
6. Chapter 4. Design for Single Reactions For N → ∞, this equation reduces to the plug flow equation (4.13) With Eqs. 4.12 and 4.13 we can compare performance of N reactors in series with a plug flow reactor or with a single mixed flow reactor. This comparison is shown in Fig. 4.4 for first-order reactions in which density variations are negligible. 12
7. Chapter 4. Design for Single Reactions Second-Order Reactions Consider reaction: N reactors in series: (4.14) Whereas for plug flow: (4.15) A comparison of the performance of these reactors is shown in Fig. 4.5. 14
8. Example 1. At present 90% of reactant A is converted into product by a second-order reaction in a single mixed flow reactor. We plan to place a second reactor similar to the one being used in series with it. (a) For the same treatment rate as that used at present, how will this addition affect the conversion of reactant? (b) For the same 90% conversion, by how much can the treatment rate be increased? 2. The following liquid-phase hydration reaction occurs in a 10,000 L CSTR: A+H2O → B with a first-order rate constant of 2.5 x 10-3 min-1. a) What is the steady-state fractional conversion of A if the feed rate is 0.3 L/sec and the feed concentration CAo = 0.12 mol/L? b) If the feed rate suddenly drops to 70% of its original value and is maintained there, what is the fractional conversion of A after 60 minutes, and what is the new steady state fractional conversion? 16
9. Chapter 4. Design for Single Reactions Noting that ε = 0, it can be written for component A in the first reactor: (4.16) or (4.17) Similarly, for the ith reactor we may write: (4.18) 18
10. Chapter 4. Design for Single Reactions 2.3.2 Determining the Best System for a Given Conversion Suppose we want to find the minimum size of two mixed flow reactors in series to achieve a specified conversion of feed which reacts with arbitrary but known kinetics. It can be written for component A in the first and second reactor: and (4.19) These relationships are displayed in Fig. 4.8 for two alternative reactor arrangements, both giving the same final conversion X2. Figure 4.8 shows that the total reactor volume is as small as possible (total shaded area is minimized) when the rectangle KLMN is as large as possible. 20