Class 23

Reaction Engineering Basics Logo

Steady-State Packed Bed PFRs

to be added

Learning Outcomes

After completing Class 23 you should…

  • Know the definition/defining equation for boundary layer, internal and external gradients, porosity, tortuosity, Thiele modulus, and effectiveness factor
  • Understand that
    • when using the pseudo-homogeneous approximation, the rate must be normalized per bed volume
    • when solid catalyst particles are present in a packed-bed PFR, temperature and concentration gradients exist between the bulk fluid and the particle surface, and within the solid packing if it is porous
  • 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 involving packed bed PFRs and concentration gradients
    • use qualitative analysis to assess and explain results from a quantitative analysis

Prepare

  • Review Section 9.5, and read Examples 9.6.5 and 9.6.6 from REB, The Book.
  • Watch …
  • Write a concise summary of the learning activity assignment below to use in class.

Participate

  • Attend Class 23 virtually using the Class 23 Video, and engage in completing the following Learning Activity.

Class 23 Learning Activity On a molar basis, a gas phase mixture contains 20% reagent A, 45% reagent B, 25% reagent C, and 10% reagent I at 220 °C and 3 atm. The mixture is fed at a rate of 1000 L min–1 to a PFR with a diameter of 5 cm and a length of 1 m. A fluid at a constant temperature of 185 °C surrounds the reactor tube which has a heat transfer coefficient of 850 cal m–2 min–1 K–1. The heat capacities of A, B, C, X, Y, ,Z and I are constant and equal to 12.7, 8.6, 11.3, 6.3, 14.4, 10.8, and 15.6 cal mol–1 K–1, respectively.

Heterogeneous catalytic reactions (1) and (2) take place within the PFR with no pressure drop. The bed density is 2.3 g cm–3. The rate expressions are given in equations (3) and (4). The pre-exponential factors for reactions (3) and (4) are 4.35 x 105 mol g–1 atm–2 min–1 and 2.17 x 106 mol g–1 atm–2 min–1, respectively, and the activation energies are 19.7 and 21.3 kcal mol–1, respectively. The heat of reaction 1 is 28.3 kcal mol–1 and the heat of reaction (2) is 29.8 kcal mol–1.

What are the conversion of B, the selectivity in moles of Y per mole of Z, and the temperature at the reactor outlet?

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

\[ B + C \rightarrow X + Z \tag{2} \]

\[ r_1 = k_1P_AP_B \tag{3} \]

\[ r_2 = k_2P_BP_C \tag{4} \]

Learning Activity 23 Solution

Learning Activity 23 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 23 Practice Assignment Suppose reaction (1) is taking place in an isothermal, steady-state PFR. The reaction is catalyzed by porous spherical catalyst particles wherein the effective diffusion coefficient is 2.7 x 10–7 cm2 s–1. The rate, normalized with respect to the bed volume, is first order in A, and the rate coefficient is 0.019 s–1. The flow rate of the feed is 1 L min–1, and there are no external concentration gradients and no pressure drop in the reactor. Calculate the catalyst bed volume necessary to achieve 90% conversion of a 1 M feed of A for pellet diameters of 0.04, 0.27, 0.55, and 0.77 mm.

\[ A \rightarrow Z \tag{1} \]

Class 23 Practice Assignment Solution

Class 23 Practice Assignment Calculations

This website is licensed under the Creative Commons Attribution-Non-Commercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0).