Chemical Reaction Engineering

Transcription

1 Lecture 8 Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place.

2 oday s lecture Block 1: Mole Balances on Rs and BR Must Use the Differential orm Block : Rate Laws Block 3: Stoichiometry ressure Drop: Liquid hase Reactions: ressure Drop does not affect the concentrations in liquid phase rx. Gas hase Reactions: Epsilon not Equal to Zero d()/d(w).. olymath will combine with d()/f(w)..for you Epsilon and Isothermal f(w) Combine then Separate Variables (,W) and Integrate

3 Reactor Mole Balances in terms of conversion Reactor Differential lgebraic Integral Batch CSR N d dt r V V r t N d r V t 3 R BR d dv d d r V r W r r d W

4 Gas hase low System: Concentration low System: ( ) ( ) ( ) ( ) 1 1 C 1 1 C + ε + ε υ υ υ C ( ) 1 ε + υ υ ( ) ( ) B B B B 1 a b C 1 a b C + ε Θ + ε υ Θ υ 4

5 ressure Drop in acked Bed Reactors Note: ressure drop does NO affect liquid phase reactions Sample Question: 5 nalyze the following second order gas phase reaction that occurs isothermally in a BR: à B Mole Balance: Must use the differential form of the mole balance to separate variables: Rate Law: Second order in and irreversible: d r r kc

6 ressure Drop in acked Bed Reactors Stoichiometry: C υ C ( 1 ) 1 +ε ( ) Isothermal, C C ( 1 ) 1 +ε ( ) Combine: d kc ( 1 ) ( 1+ ε) 6 Need to find (/ ) as a function of W (or V if you have a R)

7 7 ressure Drop in acked Bed Reactors Ergun Equation: Constant mass flow: d dz υ υ υ υ m G 1 φ 15( 1 φ) µ G 3 ρg φ cdp Dp LMINR ρ ρ m ρυ ρ υ υ υ ( 1+ ε) URBULEN

8 ( ) p 3 p c 1.75G D D g G dz d + φ µ φ φ ρ ρ ρ Variable Density ( ) + φ µ φ φ ρ β G 1.75 D D g G p 3 p c Let ressure Drop in acked Bed Reactors 8

9 ressure Drop in acked Bed Reactors Catalyst Weight W z c ρ b z 1 φ ρ c ( ) c Where ρ b bulk density ρ c solid catalyst density φ porosity (a.k.a., void fraction) d c β ( 1 φ) ρc 9 Let α c β 1 ( 1 φ) ρc

10 ressure Drop in acked Bed Reactors dy We will use this form for single reactions: d ( ) dy α y α 1 ( ) ( 1+ ) ε α y ( 1+ ε) y 1 dy α y ( 1+ ε) Isothermal case

11 ressure Drop in acked Bed Reactors d kc ( ) 1 ( 1+ ε) y 11 d f (,) d dy and f (, ) or f ( y, ) he two expressions are coupled ordinary differential equations. We can only solve them simultaneously using an ODE solver such as olymath. or the special case of isothermal operation and epsilon, we can obtain an analytical solution. olymath will combine the mole balance, rate law and stoichiometry.

12 BR à B 1 1) Mole Balance: d ( 1 ) ( 1+ ε) r ) Rate Law: ( 1 ) r kc ( 1+ ε) C C C ( 1 ) ( 1+ ε) y y

13 BR or ε dy α y When W y 1 dy α y (1 αw) y (1 αw) 1/ 13

14 1 y ( 1 αw) 1 14 W

15 C C C 1 ( ) No Δ Δ 15 W

16 3 -r r kc No Δ Δ 16 W

17 4 No Δ Δ 17 W

18 υ υ ( 1+ ε), y υ 1 υ (1 + ε)y f 18

19 υ 5 Δ 1. No Δ 19 W

20 Example 1: Gas hase Reaction in BR for δ Gas hase Reaction in BR with δ (olymath Solution) + B à C Repeat the previous one with equil molar feed of and B and k 1.5dm 9 /mol /kg/min α.99 kg -1 ind at 1 kg

21 Example 1: Gas hase Reaction in BR for δ + B à C k dm mol kg min α.99 kg 1 Case 1: Case : W 1 kg?? 1 D D 1 1?? 1

22 Example 1: Gas hase Reaction in BR for δ 1) Mole Balance: d r' ) Rate Law: r ' kccb 3) C ( 1 )y C 4) C ( 1 )y CB W y 1

23 Example 1: Gas hase Reaction in BR for δ 5) dy α ydy α y y 1 αw y ( 1 αw) 1 r kc ( ) ( ) 1 y kc 1 ( 1 αw) 3 d kc ( 1 ) ( 1 αw)

24 Example 1: Gas hase Reaction in BR for δ d ( 1 ) kc α ( 1 W) kc αw W 1 4 W,, W W,.6.75 ( with pressure drop) ( without pressure drop,i.e. α )

25 5 Example + B C

26 6 Example + B C

27 Example : Gas hase Reaction in BR for δ olymath Solution + B à C is carried out in a packed bed reactor in which there is pressure drop.he fed is stoichiometric in and B. lot the conversion and pressure ratio y / as a function of catalyst weight upto 1 kg. dditional Information k 6dm 9 /mol /kg/min α. kg -1 7

28 Example : Gas hase Reaction in BR for δ + B à C 1) Mole Balance: d r' ) Rate Law: r ' kc C 3) Stoichiometry: Gas, Isothermal B ( 1+ ) V V ε 8 C C ( 1 ) ( 1+ ε) y

29 9 Example : Gas hase Reaction in BR for δ ( ) ( ) y! 4) C B C B! 1+! dy α 5) ( 1+ ε) y ( ) 6) f! 1+ "! y 7) ε C k 6 α. 3 Initial values: W,, y1 à W1 Combine with olymath. If, polymath must be used to solve.

30 3 Example : Gas hase Reaction in BR for δ

31 31 Example : Gas hase Reaction in BR for δ

32 3

33 33 Engineering nalysis

34 34 Engineering nalysis

35 35 Engineering nalysis

36 ressure Change Molar low Rate 36 d dy dy β ρ 1 ϕ ρ β c ( ) c α β y c ( 1 ϕ) ρ ( ) C 1 ϕ ρ C c α y Use for heat effects, multiple rxns d ( 1+ ε) Isothermal: ( 1+ ε) α y

37 Heat Effects Isothermal Design Stoichiometry Rate Laws Mole Balance 37

38 Gas hase low System: Concentration low System: ( ) ( ) ( ) ( ) 1 1 C 1 1 C + ε + ε υ υ υ C ( ) 1 ε + υ υ ( ) ( ) B B B B 1 a b C 1 a b C + ε Θ + ε υ Θ υ 38 Gas hase Reaction with ressure Drop

39 Example : Gas hase Reaction in BR for δ + B à C 1) Mole Balance: d! " r ) Rate Law:! r " kc C B 39 3) Stoichiometry: Gas, Isothermal ( )!! 1+ " ( 1! ) C C 1 + " ( ) y

40 4 End of Lecture 8