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User-Friendly Energy Balance Derivations for Adiabatic CSTR and PFR Operations

Solve reactor volume, temperature, and conversion problems for adiabatic CSTR and PFR operations with inerts and species A. Utilize Levenspiel Plot and equilibrium conversion analysis. Apply energy balance principles effectively.

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User-Friendly Energy Balance Derivations for Adiabatic CSTR and PFR Operations

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  1. Lecture18 Thursday 3/13/08Solution to Tuesdays In-class Problem .User Friendly Energy Balance DerivationsAdiabatic (Tuesday’s lecture) .Heat Exchange Constant Ta .Heat Exchange Variable Ta Co-current .Heat Exchange Variable Ta Counter Current

  2. Adiabatic Operation Elementary liquid phase reaction carried out in a CSTR The feed consists of both inerts I and Species A with the ratio of inerts to the species A being 2 to 1. (a) Assuming the reaction is irreversible, A  B, (KC = 0) what reactor volume is necessary to achieve 80% conversion? (b) If the exiting temperature to the reactor is 360K, what is the corresponding reactor volume? (c) Make a Levenspiel Plot and then determine the PFR reactor volume for 60% conversion and 95% conversion. Compare with the CSTR volumes at these conversions (d) Now assume the reaction is reversible, make a plot of the equilibrium conversion as a function of temperature between 290K and 400K.

  3. CSTR Adiabatic Mole Balance Rate Law Stoichiometry

  4. Energy Balance – Adiabatic, DCP = 0

  5. Irreversible for Parts (a) through (c) (a) Given X = 0.8, find T and V

  6. (b)

  7. (c)  Levenspiel Plot

  8. CSTR     X = 0.6     T = 360 CSTR     X = 0.95     T = 395

  9. PFR     X = 0.6 PFR     X = 0.95

  10. Summary

  11. (d) At Equilibrium

  12. (e) Te = 358 Xe = 0.59

  13. User Friendly Equations Relate T and X or Fi

  14. User Friendly Equations Relate T and X or Fi

  15. Heat Exchange Elementary liquid phase reaction carried out in a PFR The feed consists of both inerts I and Species A with the ratio of inerts to the species A being 2 to 1.

  16. Mole Balance (1) Rate Law (2) (3) (4) Stoichiometry (5) (6) Parameters (7) – (15)

  17. Energy Balance Adiabatic and (16A) Additional Parameters (17A)&(17B) Heat Exchange (16B)

  18. A. Constant Ta (17B) Ta = 300K Additional Parameters (18B – (20B): B. Variable Ta Co-Current (17C) C. Variable Ta Counter Current (18C) Guess Ta at V = 0 to match Ta = Tao at exit, i.e., V = Vf

  19. More heat effects mc HC Ta Ta T Fi Fi T FA, Fi V V+ΔV V V+ΔV In - Out + Heat Added = 0

  20. Heat generated Heat removed

  21. Example: Constant Ta Find conversion, Xeq and T as a function of reactor volume Xeq X T rate X V V V • Mole balance • Rates • Stoich • Heat effects Parameters

  22. Example: Variable Ta CoCurrent Coolant balance: In - Out + Heat Added = 0 All equations can be used from before except Ta parameter, use differential Ta instead, adding mC and CPC Example: Variable Ta Counter - Current In - Out + Heat Added = 0 All equations can be used from before except dTa/dV which must be changed to a negative to arrive at the correct integration we must guess the Ta value at V=0, integrate and see if Ta0 matches; if not, reguess the value for Ta at V=0

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