1 - 12/09/2015 Department of Chemical Engineering Lecture 6 Kjemisk reaksjonsteknikk Chemical Reaction Engineering  Review of previous lectures  Pressure drop in fixed bed reactor  PFR reactor design with pressure drop (ε=0)

2 - 12/09/2015 Department of Chemical Engineering These topics build upon one another Mole BalanceRate LawsStoichiometry Reaction Engineering 2 Isothermal reactor design

3 - 12/09/2015 Department of Chemical Engineering Reactor Mole Balances in terms of conversion ReactorDifferentialAlgebraicIntegral CSTR PFR Batch X t PBR X W 3

4 - 12/09/2015 Department of Chemical Engineering Gas Phase Flow System: Concentration Flow System: 4

5 - 12/09/2015 Department of Chemical Engineering Note: Pressure drop does NOT affect liquid phase reactions Sample Question: Analyze the following second order gas phase reaction that occurs isothermally in a PBR: 2A  B Mole Balance: Must use the differential form of the mole balance to separate variables: Second order in A and irreversible: Rate Law: Pressure Drop in Packed Bed Reactors 5

6 - 12/09/2015 Department of Chemical Engineering Stoichiometry: Isothermal, T=T 0 Combine: Need to find (P/P 0 ) as a function of W (or V if you have a PFR) Pressure Drop in Packed Bed Reactors 6

7 - 12/09/2015 Department of Chemical Engineering Ergun Equation: Pressure Drop in Packed Bed Reactors 7 P pressure, kPa Φ porosity (volume of void/total bed volume) 1- Φ (volume of solid/total bed volume) g c conversion factor. 1.0 for metric system D p diameter of particle in bed m μ viscosity of gas passing through the bed kg/m.s Z length down the packed bed m u, superficial velocity m/s ρ gas density kg/m 3 G= ρu superficial mass velocity kg/m 2,s

8 - 12/09/2015 Department of Chemical Engineering Ergun Equation: Pressure Drop in Packed Bed Reactors 8 Constant mass flow:

9 - 12/09/2015 Department of Chemical Engineering Variable Density Let Pressure Drop in Packed Bed Reactors 9

/09/2015 Department of Chemical Engineering Catalyst Weight Let Pressure Drop in Packed Bed Reactors 10 Where A c, cross section area

/09/2015 Department of Chemical Engineering We will use this form for single reactions: Isothermal case Pressure Drop in Packed Bed Reactors 11

/09/2015 Department of Chemical Engineering The two expressions are coupled ordinary differential equations. We can only solve them simultaneously using an ODE solver such as Polymath. For the special case of isothermal operation and epsilon = 0, we can obtain an analytical solution. Polymath will combine the mole balance, rate law and stoichiometry. and or Pressure Drop in Packed Bed Reactors 12

/09/2015 Department of Chemical Engineering PBR 1) Mole Balance: 2) Rate Law: ABAB 13

/09/2015 Department of Chemical Engineering PBR 14 Initial condition

/09/2015 Department of Chemical Engineering W P 1 15

/09/2015 Department of Chemical Engineering CACA 2 W 16

/09/2015 Department of Chemical Engineering -r A 3 W 17

/09/2015 Department of Chemical Engineering X 4 W 18

/09/2015 Department of Chemical Engineering 19

/09/2015 Department of Chemical Engineering 5 W

/09/2015 Department of Chemical Engineering Example 1: Gas Phase Reaction in PBR for δ = 0 Gas Phase Reaction in PBR with δ = 0 (Polymath Solution) A + B  2C Repeat the previous one with equil molar feed of A and B and k A = 1.5dm 9 /mol 2 /kg/min α = kg -1 Find X at 100 kg 21

/09/2015 Department of Chemical Engineering A + B  2C Case 2: Example 1: Gas Phase Reaction in PBR for δ = 0 22 Case 1:

/09/2015 Department of Chemical Engineering 1) Mole Balance: 2) Rate Law: 3) 4) Example 1: Gas Phase Reaction in PBR for δ = 0 23

/09/2015 Department of Chemical Engineering 5) Example 1: Gas Phase Reaction in PBR for δ = 0 24

/09/2015 Department of Chemical Engineering Example 1: Gas Phase Reaction in PBR for δ = 0 25

/09/2015 Department of Chemical Engineering 26 Example A + B → 2C

/09/2015 Department of Chemical Engineering 27 Example A + B → 2C