Class 21

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Non-Isothermal, Steady-State PFR Analysis

to be added

Learning Outcomes

After completing Class 21 you should…

  • Know the definition and/or defining equation for plug flow, PFR mole balance and PFR energy balance
  • Understand
    • the PFR model assumptions
  • Be able to
    • select, modify, and simplify the mole, energy, and momentum balance equations needed for modeling a given PFR using either the axial position or the cumulative volume as the independent variable
    • use the PFR design equations, together with any other necessary equations, to complete a reaction engineering assignment including assignments involving
      • changing the independent variable
      • calculation of the exchange fluid temperature
    • use qualitative analysis to assess and explain results from a quantitative analysis

Prepare

  • Read Chapter 9 and Examples 9.6.1 and 9.6.2 from REB, The Book.
  • Watch …
  • Write a concise summary of the learning activity assignment below to use in class.

Participate

  • Attend Class 21 virtually using the Class 21 Video, and engage in completing the following Learning Activity.

Class 21 Learning Activity A gas mixture at 140 ºC and 1.0 atm and containing 30% A and 70% B is fed to a steady-state PFR at a flow rate of 0.45 L min−1. The PFR diameter is 4 cm and there is no pressure drop along its length. An external fluid, also at a temperature of 140 ºC, is fed at a rate of 20 g min−1 to a perfectly mixed shell surrounding the reactor tube. The heat capacity of that fluid is 1.4 J g–1 K–1, and the heat transfer coefficient is 1.3 x 10–6 kJ min−1 cm−2 K−1.

Reactions (1) and (2) occur within the reactor at a space time of 20 min. The rate expressions for the reactions are given in equations (3) and (4). The pre-exponential factors for reactions (1) and (2) are equal to 1.65 × 104 mol min−1 cm−3 atm−2 and 3.24 × 104 mol min−1 cm−3 atm−2, respectively. The activation energies for reactions (1) and (2) are equal to 78 kJ mol−1 and 86 kJ mol−1, respectively. The standard heats of reactions (1) and (2) are −35.1 kJ mol−1 and −32.6 kJ mol−1, respectively. The heat capacities of the reagents, in J mol−1 K−1, are A: 78.3, B: 81.1, D: 75.4, Z: 68.3 and U: 76.3.

\[ A + B \rightarrow D + Z \tag{1} \]

\[ D + B \rightarrow U + Z \tag{2} \]

\[ r_1 = k_1 P_A P_B \tag{3} \]

\[ r_2 = k_2 P_D P_B \tag{4} \]

What are the conversion of A, the selectivity for D over U, the outlet temperature, and the outlet exchange fluid temperature?

Learning Activity 21 Solution

Learning Activity 21 Calculations

Practice

  1. Attempt to complete the assignment below using only the REB Equation Summary, and if you get stuck, each time
    1. note whether you didn’t know what to do or you knew what to do, but not how to do it
    2. refer to just enough of the provided solution to get un-stuck
  2. Check your solution against the provided one and if you find mistakes note whether they were due to
    1. a conceptual misunderstanding
    2. improper simplification of a design equation or substitution into it
    3. computational errors
  3. Make sure you have corrected knowledge gaps and misunderstanding revealed in steps 1 and 2, and think about how you might modify your study methods to avoid similar issues in the future.

Class 21 Practice Assignment A perfectly insulated PFR is being considered for producing Y and Z according to reaction (1). It would be fed a total of 100 mol s–1 of a mixture containing 20% inerts (I), 60% A and 20% B at a temperature of 150 °C and 2 atm. The gas phase reaction, equation (1), is first order in A and one–half order in B. The pre–exponential factor is equal to 2 x 1015 L0.5 mol–0.5 s–1 and the activation energy is 25,100 cal mol–1. The heat capacities in cal mol–1 K–1 are given in Table 1. The reaction can be assumed to be irreversible with a constant heat of –10 kcal mol–1. If 95% of the limiting reagent must be converted, how large must the reactor be, assuming there is no pressure drop in the reactor, and what would the final temperature equal?

\[ A + B \rightarrow Y + Z \tag{1} \]

Table 1: Heat capacities of the reagents.
Reagent Heat Capacity (cal mol⁻¹ K⁻¹)
\(A\) \(5\)
\(B\) \(7\)
\(Y\) \(6.5\)
\(Z\) \(5.5\)
\(I\) \(4.2\)

Class 21 Practice Assignment Solution

Class 21 Practice Assignment Calculations

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