# (a) LEP Table 12-2: Exothermic Reaction with Heat Exchange Download the Polymath, MATLAB, Python, or Wolfram codes...

## Question:

(a) LEP Table 12-2: Exothermic Reaction with Heat Exchange Download the Polymath, MATLAB, Python, or Wolfram codes for the algorithm and data given in Table T12-2 for the exothermic gas phase reversible reaction A + B ⇄ C given on the Web in the Living Example Problems (LEPs). Vary the following parameters in the ranges shown in parts (i) through (xi). Write a paragraph describing the trends you find for each parameter variation and why they look the way they do. Use the base case for parameters not varied. The feedback from students on this problem is that one should use Wolfram on the Web in the LEP T12-2 as much as possible to carry out the parameter variations. For each part, write two or more sentences describing the trends.

**Table 12-2**

Wolfram and Python

(i) This is a Stop and Smell the Roses Simulation. View the base case X, X_{e}, and T profiles and explain why the conversion (X and X_{e}) and temperature profiles look the way they do.

(ii) The slider parameters Ua/rho, Θ_{I}, F_{A0}, and ΔH_{Rx} all can be moved to make the X and Xe profiles to come together and to separate. What is the reason these sliders affect the profiles similarly?

(iii) Starting with the base case, determine which parameters when changed only a small amount most dramatically affects the conversion and temperature profiles.

(iv) What parameters separate X and Xe the most?

(v) Finally, write at least three conclusions about what you found in your experiments (i) through (iv).

Polymath

(vi) Vary T_{0}: 310 K ≤ T0 ≤ 350 K and write a conclusion.

(vii) Vary T_{a}: 300 K ≤ Ta ≤ 340 K and write a conclusion.

Repeat (i) for countercurrent coolant flow.

(viii) Repeat this problem for the case of constant Ta and adiabatic operation, and describe the most dramatic affect you find.

(b) Example 12-1: Butane Isomerization

Wolfram and Python Co-Current

This is another Stop and Smell the Roses Simulation.

(i) Describe the differences of the X, X(ii) Explain why the temperature (T and T_{a}) and conversion (X and X_{e}) look the way they do, and explain what happens to the X, X_{e}, T, and Ta profiles as you move slider y_{A0}.

(iii) What parameter value brings T and Ta profiles close together?

(iv) What parameter when varied separates X and X_{e} the most?

(v) What parameter keeps the X and X_{e} profiles the closest together?

(vi) Write at least three conclusions about what you found in your experiments (i) through (v).

Polymath Co-Current

(vii) What is the entering value of the temperature Ta0 of the heat exchanger fluid below which the reaction will never “ignite”?

(viii) Vary some of the other parameters and see whether you can find unsafe operating conditions.

(ix) Plot Q_{r} and Ta as a function of V necessary to maintain isothermal operation.

Wolfram and Python Countercurrent

(x) Explain why T, T_{a}, X, and X_{e} profiles look the way they do for the base case.

(xi) Vary U_{a} and T_{a0} and describe what you find.

(xii) Vary yA0 and then one of the other parameters and describe what you find.

(xiii) Describe how Q_{r} and Q_{g} and their intersection change when you vary the molar flow rates of coolant, inert and y_{A0}.

(xiv) Write at least three conclusions about what you found in your experiments (x) through (xiii).

Polymath Countercurrent

(xv) Describe and explain what happens to the X and X_{e} profiles as you vary ΔH_{Rx}.

(xvi) Describe what happens to the temperature profile T and Ta as you vary F_{A0}.

(xvii) Compare the variations in the profiles for X, X_{e}, T, and Ta when you change the parameter values for all four cases: adiabatic, countercurrent exchange, co-current exchange, and constant Ta. What parameters when changed only a small amount dramatically change the profiles?

(xviii) The heat exchanger is designed for a maximum temperature of 370 K. Which parameter will you vary so that at least 75% conversion is still achieved while maintaining temperature under a safe limit?

Wolfram and Python Constant T_{a}

(xix) Vary y_{A0} and one other parameter of your choice, and describe how the X, X_{e}, and T profiles change.

(xx) Vary U_{a} and Ta and describe what you find.

(xxi) Vary ΔHRx° and then one of the other parameters (e.g., y_{A0}) and describe what you find.

(xxii) Write at least three conclusions about what you found in your experiments (xix)–(xxi).

Wolfram and Python Adiabatic Operation

(xxiii) Why do the shape of the profiles change in the way they do as you change y_{A0}?

(xxiv) Write a set of three conclusions, one of which compares adiabatic operation with the other three modes of heat transfer (e.g., co-current)., and T profiles between the four cases of heat exchange, co-current, counter current, constant T_{a}, and adiabatic.

**Example 12-1**

(c) Example 12-2: Production of Acetic Anhydride-Endothermic Reaction Wolfram and Python

Co-Current

(i) Explain why the temperatures (T and T_{a}) and conversions (X and X_{e}) look the way they do for the base case slider values.

(ii) What parameter value when increased or decreased causes the reaction to die out the most quickly near the reactor entrance?

(iii) Which parameter, when varied most, drastically changes the profiles?

Adiabatic

(iv) How does the conversion change as heat capacity of A is increased?

Constant Ta

(v) You find that conversion has decreased after 6 months of operation. You checked the flow rate and material properties and found that these values have not

changed. Which parameter would have changed?

Countercurrent

(vi) Explain why the temperatures (T and T_{a}) and conversions (X and X_{e}) look the way they do for the base case slider values.

(vii) Discuss the most profound differences between the four heat exchange modes (e.g., co-current, adiabatic) for this endothermic reaction.

(viii) Write two conclusions of what you learned from your experiments (i) through (vii).

Polymath

(ix) Let Q_{g} = rAΔ_{HRx} and Q_{r} = Ua (T – T_{a}), and then plot Q_{g} and Q_{r} on the same figure as a function of V.

(x) Repeat (vi) for V = 5 m^{3}.

(xi) Plot Q_{g}, Q_{r}, and –r_{A} versus V for all four cases on the same figure and describe what you find.

(xii) For each of the four heat exchanger cases, investigate the addition of an inert I with a heat capacity of 50 J/mol · K, keeping F_{A0} constant and letting the other inlet conditions adjust accordingly (e.g., ε).

(xiii) Vary the inert molar flow rate (i.e., Θ_{I}, 0.0 I.

(xiv) Finally, vary the heat-exchange fluid temperature Ta0 (1000 K

**Example 12-2**

Jeffreys, in a treatment of the design of an acetic anhydride manufacturing facility, states that one of the key steps is the endothermic vapor-phase cracking of acetone to ketene and methane is G. V. Jeffreys, A Problem in Chemical Engineering Design: The Manufacture of Acetic Anhydride, 2nd ed. London: Institution of Chemical Engineers.

CH_{3}COCH_{3} → CH_{2}CO + CH_{4}

The article further states that this reaction is first-order with respect to acetone and that the specific reaction rate is given by

ln k=34.34−34222T(E12-2.1)

where k is in reciprocal seconds and T is in Kelvin. It is desired to feed 7850 kg of acetone per hour to a tubular reactor. The reactor consists of a bank of 1000 oneinch,

schedule-40 tubes. We shall consider four cases of heat-exchanger operation. The inlet temperature and pressure are the same for all cases at 1035 K and 162 kPa (1.6 atm) and the entering heating-fluid temperature available is 1250 K. The heat-exchange fluid has a flow rate, m.c, of 0.111 mol/s, with a heat capacity of 34.5 J/mol·K. A bank of 1000 one-inch, schedule-40 tubes, 1.79 m in length corresponds to 1.0 m3 (0.001 m3/tube = 1.0 dm3/tube) and gives 20% conversion. Ketene is unstable and tends to explode, which is a good reason to keep the conversion low. However, the pipe material and schedule size should be checked to learn whether they are suitable for these temperatures and pressures. In addition, the final design and operating conditions need to be cleared by the safety committee before operation can

begin. Also check the Web site, Process Safety Across the Chemical Engineering Curriculum (http://umich.edu/~safeche/index.html).

(d) Example 12-3: Production of Propylene Glycol in a CSTR

Wolfram and Python

(i) Vary activation energy (E) and find the values of E for which there are at least two solutions.

(ii) Vary the flow rate of FB0 to find the temperature at which the conversion is 0.8.

(iii) What is the operating range of inlet temperatures such that at least one steady state solution exists while maintaining the reactor temperature below 640°R?

Describe how your answers would change if the molar flow rate of methanol were increased by a factor of 4.

(iv) Vary V and find the points of (1) tangency and (2) intersection of XEB and XMB.

(v) Write a set of conclusions based on your experiments (i) through (iv).

**Example 12-3**

Propylene glycol is produced by the hydrolysis of propylene oxide:

Ethylene oxide (C3H6O) is a 3-carbon compound with an Oxygen group connecting the first 2 carbons. This ethylene oxide and water react in the presence of sulfuric acid (H2SO4). The H plus and OH minus ions of the water molecule combine with the first and the second carbons of the oxide to form propylene glycol (C3H8O2). Over 900 million pounds of propylene glycol were produced in 2010 and the selling price was approximately $0.80 per pound. Propylene glycol makes up about 25% of the major derivatives of propylene oxide. The reaction takes place readily at room temperature when catalyzed by sulfuric acid. You are the engineer in charge of an adiabatic CSTR producing propylene glycol by this method. Unfortunately, the reactor is beginning to leak, and you must replace it. (You told your boss several times that sulfuric acid was corrosive and that mild steel was a poor material for construction. He wouldn’t listen.) There is a nice-looking,

bright, shiny overflow CSTR of 300-gal capacity standing idle in Professor Köttlov’s storage shed at his mountain vacation home. It is glass-lined, and you would like to use it.

We are going to work this problem in lb_{m}, s, ft^{3}, and lb-moles rather than g, mol, and m^{3} in order to give the reader more practice in working in both the English and metric systems. Why?? Many plants still use the English system of units.

You are feeding 2500 lbm/h (43.04 lb-mol/h) of propylene oxide (P.O.) to the reactor. The feed stream consists of

(1) an equivolumetric mixture of propylene oxide (46.62 ft^{3}/h) and methanol (46.62 ft^{3}/h),

(2) water containing 0.1 wt % H_{2}SO_{4}. The volumetric flow rate of water is 233.1 ft^{3}/h, which is 2.5 times the methanol–P.O. volumetric flow rate. The corresponding molar feed rates of methanol and water are 71.87 and 802.8 lb-mol/h, respectively. The water–propylene oxide–methanol mixture undergoes a slight decrease in volume upon mixing (approximately 3%), but you neglect this decrease in your calculations. The temperature of both feed streams is 58°F prior to mixing, but there is an immediate 17°F temperature rise upon mixing of the two feed streams caused by the heat of mixing. The entering temperature of all feed streams is thus taken to be 7°F (Figure E12-3.1).

A CSTR is shown in which the following are marked: The input, here is propylene oxide (F subscript A0) and methanol (F subscript M0), belonging to the first feed stream. Water (F subscript B0), belongs to the second feed streams at 58 degrees Fahrenheit. The temperature, T subscript 0 increases to 75 degrees Fahrenheit when it enters the tank reactor, on mixing. The temperature of the coolant is approximately 85 degrees Fahrenheit. The volume of the fluid inside the reactor is 300 gallons. The output values of T and X are to be found. The Furusawa Engineering Team in Japan state that under conditions similar to those at which you are operating, the reaction is apparent first-order in propylene oxide concentration and apparent zero-order in excess of water with the specific reaction rate

(e) Example 12-4: CSTR with a Cooling Coil

Wolfram and Python

(i) Explore how variations in the activation energy (E) and in the heat of reaction, at reference temperature (ΔHRx∘), affect the conversions X_{EB} and X_{MB}.

(ii) What variables most affect the intersection of and the points of tangency of X_{EB} and X_{MB}?

(iii) Find a value of E and of ΔHRx∘ that increase conversion to more than 80% while maintaining the constraint of 125°F maximum temperature.

(iv) Write two conclusions about what you found in your experiments (i) through (iii).

Polymath

(v) The space time was calculated to be 0.01 minutes. Is this realistic? Decrease ν_{0} and both reaction rate constants by a factor of 100 and describe what you find.

(vi) Use Figure E12-3.2 and to plot X versus T to find the new exit conversion and temperature.

(vii) Other data on the Jofostan chemical engineering Web site show ΔHRx∘=−38700 Btu/lb-mol and ΔC_{P }= 29 Btu/lb-mol/°F. How would these values change your results?

(viii) Make a plot of conversion as a function of heat exchanger area. [0 2] and write a conclusion.

**Example 12-4**

Fantastic! Max has located a cooling coil in an equipment storage shed in the small, mountainous village of Ölofasis, Jofostan, for use in the hydrolysis of propylene oxide discussed in Example 12-3. The cooling coil has 40 ft2 of cooling surface and the cooling-water flow rate inside the coil is sufficiently large that a constant coolant temperature of 85°F can be maintained. A typical overall heat-transfer coefficient for such a coil is 100 Btu/h·ft^{2}·°F. Will the reactor satisfy the previous constraint of 125°F maximum temperature if the cooling coil is used?

(f) Example 12-5: Parallel Reactions in a PFR with Heat Effects

Wolfram and Python

(i) Vary the sliders for the rate constants k_{1A0} and k_{2A0} and describe what you find.

(ii) What should be the initial concentration of A so that the company can produce equal flow rates of B and C?

(iii) Describe how the profiles for T, F_{A}, F_{B}, and F_{C} change as you move the sliders. Comment specifically on the drastic changes that occur when you change the

overall heat transfer coefficient.

(iv) What set of conditions give you the greatest selectivity, S˜B/C at the exit and what is the corresponding conversion.

(v) Write at least three conclusions about what you found in your experiments (i) through (iv).

Polymath

(vi) Why is there a maximum in temperature? How would your results change if there is a -pressure drop with α = 1.05 dm^{–3}?

(vii) What if the reaction is reversible with K_{C}= 10 at 450 K?

(viii) How would the selectivity change if Ua is increased? Decreased?

**Example 12-5**

The following gas-phase reactions occur in a PFR:

Reaction: 1A→k1B−r1A=k1ACA(E12-5.1)

Reaction: 22A→k2C−r2A=k2ACA2(E12-5.2)

(g) Example 12-7: Complex Reactions with Heat Effects in a PFR—Safety

Wolfram and Python

(i) Co-current: Explore the effect of the coolant flow rate m˙c on the reactant temperature and coolant temperature profiles, and describe what you find.

(ii) Co-current: Explore the effect of Ua on the selectivity and describe what you find.

(iii) Constant T_{a}: How does the overall heat transfer coefficient affect the product flow rate distribution? Should it be kept minimum or maximum? Explain.

(iv) Constant T_{a}: Which are the variables that have virtually no effect on the profiles? Explain the reason.

(v) Adiabatic: You want to save capital cost by using a smaller volume reactor, that is, 5 dm^{3} instead of 10 dm^{3}. Which parameters will you vary to achieve exit reactant and product flow rates same as base case?

(vi) Describe how the selectivity, S˜C/D changes as you change the parameters and operating conditions. What two variable slider(s) affect S˜C/D the most?

(vii) Write a set of conclusions of what you learned in experiments (i) through (vi).

Polymath

(viii) Plot Q_{g} and Q_{r} as a function of V. How can you keep the maximum temperature below 700 K? Would adding inerts help, and if so what should the flow rate be if CPI = 10 cal/mol/K?

(ix) Look at the figures. What happened to species D? What conditions would you suggest to make more species D?

(x) Make a table of the temperature (e.g., maximum T, T_{a}) and molar flow rates at two or three volumes, comparing the different heat-exchanger operations.

(xi) Why do you think the molar flow rate of C does not go through a maximum? Vary some of the parameters to learn whether there are conditions where it goes through a maximum. Start by increasing F_{A0} by a factor of 5.

(xii) Include pressure in this problem. Vary the pressure-drop parameter (0 –3) and describe what you find and write a conclusion.

(h) Review the steps and procedure by which we derived Equation (12-5).

**Equation (12-5)**(i) CRE Web site SO^{2} Example PRS-R12.4-1. Download the SO_{2} oxidation LEP R12-1. How would your results change if

(1) the catalyst particle diameter were cut in half?

(2) The pressure were doubled? At what particle size does pressure drop become important for the same catalyst weight, assuming the porosity doesn’t change?

(3) You vary the initial temperature and the coolant temperature? Write a paragraph with at least two conclusions describing what you find.

(j) SAChE. Go to the SAChE Web site, www.sache.org. Your instructor or department chair should have the username and password to enter the SAChE Web site in order to obtain the modules with the problems. On the left-hand menu, select “SAChE Products.” Select the “All” tab and go to the module titled, “Safety, Health and the Environment” (S, H & E). The problems are for KINETICS (i.e., CRE). There are some example problems marked “K” and explanations in each of the above S, H & E selections. Solutions to the problems are in a different section of the site. Specifically look at: Loss of Cooling Water (K-1), Runaway Reactions (HT-1), Design of Relief Values (D-2), Temperature Control and Runaway (K-4) and (K-5), and Runaway and the Critical Temperature Region (K-7). Go through the K problems and

write a paragraph on what you have learned.

**Example 12-7**

We will use the reactions that we discussed in Chapter 8 that were coded with dummy names, A, B, C, and D for reasons of national security.

The following complex gas-phase reactions follow elementary rate laws

(1)A+2B→C−r1A=k1ACACB2ΔHRx1B=−15000 cal/mol B(2)2A+3C→D−r2C=k2CCA2CC2ΔHRx2A=−10000 cal/mol A

and take place in a PFR. The feed is stoichiometric for reaction (1) in A and B with F_{A0} = 5 mol/min. The reactor volume is 10 dm^{3} and the total entering concentration is C_{T0} = 0.2 mol/dm^{3}. The entering pressure is 100 atm and the entering temperature is 300 K. The coolant flow rate is 50 mol/min and the entering coolant fluid has a heat capacity of CP_{C0} = 10 cal/mol · K and enters at a temperature of 325 K.

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