chemical and biochemical reaction

The paper contain three similar question with different data. I need to solve question with steps , formula, calculation, and graphs. 08/12/2015 1 University of Huddersfield Department of Chemistry. School of Applied Sciences CHAPTER 4: Design and selection of reactors for one simple reactions. Chemical Engineering 3 (SHC4012) Chemical and Biochemical Reaction Engineering (SIC2023) SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 CHAPTER 4 • One reactor performing the entire process • Combinations of reactors performing the entire process • Recycling reactor Perfect mix Plug flow ?????? = ????. ?? ???? ?????? = ????. ?? ???? 90% of conversion Page 7 08/12/2015 2 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 4.2.2. Stirred tank reactors working in series. Although the concentration is uniform in each reactor, there is a change in concentration as fluid moves from reactor to reactor. If we represent graphically the conversion obtained for one, three, and ten reactors in series, using the same total volume, we see the following, CHAPTER 4 Page 10 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 4.2.2. Stirred tank reactors working in series. CHAPTER 4 This suggests that when we increase the number of well mixed reactors keeping the total volume constant, the behaviour is closer to _____________________________ PLUG FLOW REACTOR . Page 10 08/12/2015 3 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 4.2.2.1. Series of perfect mix continuous reactors of EQUAL size. When all the reactors have the same volume, the performance equation for this system is ?? ???? = ?? ???? ???? = ?? ??? -???? ???? ???????????????? = ?????? When we work with a series of tanks of equal size, the 3 aims of design are: • XA at the end of a certain number of reactors of the same volume. • Number of reactors of fixed volume to achieve a certain conversion. • Volume of the reactors required when the conversion and the number of reactors is fixed (less common). CHAPTER 4 Page 11 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 Example 4.4. In the autocatalytic reaction of example 4.2, the best option for 90% of conversion was the plug flow pattern. Compare the continuous perfectly mixed reactor and the plug flow of example 4.2 at 90% of conversion, with the total volume of two tanks of equal size in series. What conversion do we obtain after the first tank? We approach the well mixed tanks to a perfectly mixed contact pattern. Hence, we need to solve the following equation: ????+??????????,?? = ????????????,?? + ???? ????????,?? = ????,?? - ????,?? ?? - ????,?? ????,?? + ?? + ????,?? - ????,?? ?? - ????,?? ????,?? + ?? As we have reactors of equal size: ????????????,?? = ???? ????????,?? ????,?? - ????,?? ?? - ????,?? ????,?? + ?? = ????,?? - ????,?? ?? - ????,?? ????,?? + ?? CHAPTER 4 Page 11 08/12/2015 4 What value of t1 /t2 I need to find in the graph is if both reactors have the same volume? _____ What value of XA,1 we have? SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 ????,1 = 0.65 ????+??????????,?? = 0.65 - 0 1 - 0.65 0.65 + 0.01 + 0.9- 0.65 1 - 0.9 0.9 + 0.01 = 5.57 ?????????????? ???? ???? = ??. ???????? ????????,?? = ??. ???? × ???? ??. ???? × ?????? = ????. ?? ???? CHAPTER 4 ?? Two PM of equal size in series ?????????????? ???? ???? = ????. ?? ???? Page 11-12 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 CHAPTER 4 Comparing the tanks in series with the other two configurations, the two tanks in series are BETTER THAN SINGLE REACTORS Page 12 08/12/2015 5 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 4.2.2.2. Series of perfect mix continuous reactors of DIFFERENT size. When the volumes are different: ?? ???? = ??=1 ?? ???? ???? = ??=1 ?? ???? - ????-1 -???? ???? ???????????????? = ??=1 ?? ???? When we need to design a series of tanks of different sizes we must consider: ? Conversion for a given reactor system. ? Best reactor system to achieve a given conversion. CHAPTER 4 ... Page 12 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 Example 4.5. In the same autocatalytic reaction conditions of Example 4.2 and 4.4, if we use two tanks in series of different size, what is the best configuration to obtain 90% of conversion? (CA,0 = 200 mol m–3 , CP,0 = 2 mol m–3 , q0 = 30 m3 h –1 , kA = 0.02 m3 mol–1 h –1 ). ????+??????????,?? ?????? = ????,?? - ????,?? ?? - ????,?? ????,?? + ?? + ????,?? - ????,?? ?? - ????,?? ????,?? + ?? ????+??????????,?? ?????? = ????,?? ?? - ????,?? ????,?? + ??. ???? + ??. ?? - ????,?? ??. ?????? CHAPTER 4 XA,0 and XA,2 are fixed (0 and 0.90) We can only optimise the system changing ????,?? Page 13 08/12/2015 6 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 ????+??????????,?? ?????? = ????,?? ?? - ????,?? ????,?? + ??. ???? + ??. ?? - ????,?? ??. ?????? CHAPTER 4 What conversion at the outlet of the first reactor does it show minimum volume or space time of the configuration? ????,?? = ??. ???? Page 13 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 ???????? = ???? ????,?????? - ????,???? ????????,?? ?? - ????,?????? ????,?????? + ?? ?????????? ?? = ???? × (??. ???? - ??) ??. ???? × ?????? ?? - ??. ???? ??. ???? + ??. ???? = ????. ???? ???? ?????????? ?? = ???? × (??. ?? - ??. ????) ??. ???? × ?????? ?? - ??. ?? ??. ?? + ??. ???? = ????. ???? ???? ?????????????? ???? ???? = ????. ???? + ????. ???? = ????. ?? ???? Two PM of different size in series ?????????????? ???? ???? = ????. ?? ???? CHAPTER 4 Page 13-14 08/12/2015 7 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 Do you think that we have an important improvement with tanks of different sizes? CHAPTER 4 Comparing the four configurations, the best option is 2 different size CSTR NO Page 14 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 4.2.3. Reactors of different type working in series. If reactors of different types are put in series, such as a mixed flow reactor followed by a plug flow reactor, which in turn is followed by another mixed flow reactor, we may write for the three reactors ??1 ???? = ??1 - ??0 -??1 ??2 ???? = ???? -?? ??2 ??1 = ???? -?? - ???? -?? ??1 ??0 ??2 ??0 ??3 ???? = ??3 - ??2 -??3 CHAPTER 4 If reactors of different types are put in series, such as a well-mixed flow reactor followed by a tubular reactor, which in turn is followed by another well-mixed flow reactor, we may write for the three reactors: Page 14 ??1 ???? = ??1 - ??0 -??1 ??2 ???? = ??1 ??2 ???? -?? ??3 ???? = ??3 - ??2 -??3 08/12/2015 8 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 CHAPTER 4 Example 4.6. Following the previous examples of autocatalytic reaction, find the best combination of one tubular reactor with one continuous stirred tank reactor to obtain at conversion at 90%. Approach the reactors to ideal contact patterns. (CA,0 = 200 mol m–3 , CP,0 = 2 mol m–3 , q0 = 30 m3 h –1 , kA = 0.02 m3 mol–1 h –1 ). In this case we have two options: Page 15 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 In the option A: ??????+????????????,?? ?????? = ????,?? - ????,?? ?? - ????,?? ????,?? + ?? + ?? ?? + ?? ???? ????,?? + ?? ?? - ????,?? ????,?? + ?? ?? - ????,?? In the option B: ??????+????????????,?? ?????? = ?? ?? + ?? ???? ????,?? + ?? ?? ?? - ????,?? + ????,?? - ????,?? ?? - ????,?? ????,?? + ?? CHAPTER 4 ??????+???? = ?????? + ?????? ??????+???? = ?????? + ?????? Page 15 08/12/2015 9 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 Let’s check option A: What conversion does it show minimum volume? ??????+????????????,?? ?????? = ????,?? ??- ????,?? ????,?? + ??. ???? + ??. ???? ???? ??. ???? ?? - ????,?? ??. ?? ????,?? + ??. ???? ?????? = 30 × 0.5 0.02 × 200 1 - 0.5 0.5 + 0.01 = 14.7 ??3 ?????? = 30 × 0.99 0.02 × 200 ???? 0.91 1 - 0.5 0.1 0.5 + 0.01 = 16.2 ??3 ?????????????? ???? ????+???? = ?????? + ?????? = ????. ?? + ????. ?? = ????. ?? ???? CHAPTER 4 ????,?? = ??. ?? Pages 15-16 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 Let’s check option B: What conversion does it show minimum volume? ??????+????????????,?? ?????? = ????,?? ??- ????,?? ????,?? + ??. ???? + ??. ???? ???? ??. ???? ?? - ????,?? ??. ?? ????,?? + ??. ???? What does it mean? It means than there is no configuration of plug flow + perfect mix that can improve the performance of only one plug flow reactor CHAPTER 4 ????,?? = ??. ?? Page 16 08/12/2015 10 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 PM + PF in series ?????????????? ???? ????+???? = ????. ?? ???? PF + PM in series ??????+???? = ?????? = ????. ?? ???? OPTION A OPTION B CHAPTER 4 1 Tubular 1 CSTR 2 CSTR =Size 2 CSTR ?Size CSTR + Tubular Tubular + CSTR 50.6 74.2 41.8 41.1 30.9 50.6 Page 16 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 4.3. RECYCLE REACTOR 4.3.1. Performance equation In certain situations it is advantageous to divide the product stream from a tubular reactor and return a portion of it to the entrance of the reactor. With this configuration it is possible that a tubular reactor acquires characteristics of a well mixed continuous reactor. This situation is frequently considered in the design of catalytic reactors. Page 17 CHAPTER 4 08/12/2015 11 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 CHAPTER 4 Page 17 This recycle ratio can be made to vary from zero to infinity. This means that as the recycle ratio is raised the behaviour shifts from plug flow (R = 0) to perfectly mixed flow (R = 8). Thus, recycling provides an alternative to obtain various degrees of backmixing in a tubular reactor. We need to define a new parameter, ????,?? ' , that will be the feed rate of A if the stream entering the reactor (fresh feed + recycle) were unconverted. Imagine that instead of the point Q of Figure 4.6 we had the following configuration: Figure 4.7 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 To obtain the performance equation for our reactor the reaction system Page 18 can be treated as it is shown in Figure 4.8: And our reference inlet will now be F’A,0, defined as, ????,0 ' = ?? ??h????h ?????????? ?????????? ???? ???? ?????????????????????? ?????????????? ???????????? + ?? ???????????????? ???? ????????h ???????? ????,0 ' = ????,0 + ??????,0 = (1 + ??)????,0 (4.3.2) CHAPTER 4 08/12/2015 12 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 As we need to know the performance equation of our plug reactor with recirculation we need to integrate the general performance equation between XA,1 and XA,2 According to our scheme of Figure 4.8 it is like to integrate between X’A,1 and X’A,2. Hence, ?? = -????,0 ' ????,1 ' ????,2 ' ?????? ???? Page 18 CHAPTER 4 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 ?? = -????,0 ' ????,1 ' ????,2 ' ?????? ???? ?? = -????,0 ?? + 1 ?? ??+1 ????,4 ????,4 ?????? ???? ????,0 ' = ????,0 + ??????,0 = (1 + ??)????,0 ????,2 ' = ????,0 ' - ????,2 ????,0 ' = ????,0 ' - ????,4 + ????,3 ????,0 ' = ????,0 ' - ????,4 + ??????,4 ????,0 ' = ????,0 ' - ????,4 1 + ?? ????,0 ' If we use the equation 4.3.2 to relate the Figure 4.7 with Figure 4.5: ????,2 ' = ????,0 ' - ????,4 1 + ?? ????,0 ' = (1 + ??)????,0 - ????,4 1 + ?? (1 + ??)????,0 = ????,0 - ????,4 ????,0 = ????,4 ????,2 ' = ????,4 ????,1 ' = ????,0 ' - ????,1 ????,0 ' = ????,0 ' - ????,0 + ????,3 ????,0 ' = 1 + ?? ????,0 - ????,0 - ??????,4 (1 + ??)????,0 ????,1 ' = ????,0 + ??????,0 - ????,0 - ??????,4 (1 + ??)????,0 = ?? ????,0 - ????,4 (1 + ??)????,0 = ??????,0????,4 (1 + ??)????,0 = ??????,4 1 + ?? ????,1 ' = ?? 1 + ?? ????,4 (4.3.3) Page 18 (4.3.4) CHAPTER 4 08/12/2015 13 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 The area of this integral is ?? ??+1 ????,4 ????,4 ?????? ???? = ????,4 - ?? ?? + 1 ????,4 1 -?? ?? In with the value of ?? ?? is the average value of reaction rate in the range XA,1 and XA,2. Then ?????? ????,0 = ?? + 1 ????,4 - ?? ?? + 1 ????,4 1 -?? ?? = ????,4 1 -?? ?? ?????? = ?? + 1 ????,4 - ?? ?? + 1 ????,4 ????,0 -?? ?? = ????,4 ????,0 -?? ?? (4.3.5) (4.3.6) CHAPTER 4 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 So the graphical representation of this reactor is The area in grey is the value of the integral times FA,0 of the equation 4.3.4. The rectangle is the volume of the recycling reactor. CHAPTER 4 08/12/2015 14 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 CHAPTER 4 SIC2023: Chemical and Biochemical Reaction Engineering SHC4012: Chemical Engineering 3 4.3.2. Optimal value of R When we observe graphically how R influences the volume, it can be inferred that there will be an optimum recycling ratio for minimum volume. • In the case of kinetics in which the curve FA,0/(-rA ) vs XA always increases, the best Ratio is R=0 (Plug flow) • When the kinetic shows a minimum in the curve FA,0/(-rA ) vs XA the recycling can be optimised. R will be optimum when: ????,0 -????,1 = ????,0 -?? ?? If we represent graphically CHAPTER 4