Chemical Reaction Engineering. Lecture 2

Transcription

1 hemical Reaction Engineering Lecture 2

2 General algorithm of hemical Reaction Engineering Mole balance Rate laws Stoichiometry Energy balance ombine and Solve

3 lassification of reactions Phases involved: Homogeneous reaction reaction that occur in one phase Heterogeneous reaction reaction that involves more than one phase and usually occurs at the interface between the phases (e.g. heterogeneous catalysis) Equilibrium position Reversible reaction reaction that can proceed in either direction depending on the concentration of reagents and products Irreversible reaction reaction that at given conditions can be assumed to proceed in one direction only (i.e. reaction equilibrium involves much smaller concentration of the reagents)

4 Elementary reactions Kinetics of chemical reactions determined by the elementary reaction steps. Molecularity of an elementary reaction is the number of molecules coming together to react in one reaction step (e.g. uni-molecular, bimolecular, termolecular) Probability of meeting 3 molecules is very small, so uni-molecular and bimolecular reaction are the only two to consider

5 Elementary reactions Uni-molecular: first order in the reactant d [ ] P k[ ] dt Bimolecular: first order in the reactant d [ ] + B P k[ ][ B] dt H + Br HBr + Br 2 Proportional to collision rate! rate of disappearance of individual components can be calculated as: v 1 dni ν dt i dξ dt

6 Relative Rates of Reaction a + bb c + dd if we are interested in species we can use as the basis of calculation and define the reaction rate with respect to b c d + B + D a a a r a Reaction rate is not a constant, it depends - on concentration of the reagents - on the temperature - on the total pressure in the reactions involving gas phase - ionic strength and solvent in liquid state - presence of a catalyst r [ k ( T )][ fn(, B,...)] r b r c B r d D

7 Rates of Reaction r [ k ( T )][ fn(, B,...)] rrhenius law kt ( ) e E / RT algebraic function of concentrations α B β... reaction order: n α + β +... reaction rate is found experimentally, data on frequency factor (), activation energy (E) and the order of the reaction can be found in relevant handbooks. units of the reaction rate constant [ k] ( oncentration) time 1 n

8 on-elementary Reaction rates The reaction rate dependence on the concentration and temperature will become more complicated when a reaction comprising several elementary steps is considered (incl. catalytic and reversible reactions)

9 Reversible reaction Let s consider a reaction of diphenyl formation 2 k H H H k 1 B D rate of change for benzene dh [ ] 6 6 dt r 2k + 2k 2 B 1 B 1 D H 2

10 Equilibrium constant dh [ ] 6 6 dt r 2k + 2k 2 B 1 B 1 D H 2 noticing that the equilibrium constant: K k1 k 1 2 DH 2 r B 2k1 B Kc in terms of concentration reaction rates in terms of other reagents: r 2 rd B 2 D H 2 k1 B 1 Kc

11 Few more facts of K RT ln K ΔG From thermodynamics for gases, K can be defined in terms of pressures or concentrations r K p p p p p ca / da / D ba / B c d b K K ( ) ; 1 / p RT δ δ + a a a ca / da / D ba B temperature dependence: d ln K dt Δ HT r ( ) 2 RT d Δ H ( T ) +Δc ( T T ) ln r R p R 2 K dt RT ΔrH ( T) 1 1 Kp( T) Kp( T1 )exp 2 RT T1 T

12 Reaction rate Below, we will consider only the concentration and temperature dependence of the reaction rate Dependence on the concentration can be calculated knowing reaction mechanism, as before dh [ 6 6] dt 2 D rb 2k1 B + K H 2 Temperature dependence: rrhenius equation kt ( ) e E / RT

13 Reaction rate From the collision theory, only molecules with the energy higher than the activation energy can react: The usual rule of thumb that the reaction rate doubles with every 1º is not always true: kt ( ) kt ( ) e E/ R T 1 T 2

14 Summary of the Reactor design equations In the previous lecture we found design equations for various reactors: To solve them we need to find disappearence rate as a function of conversion: r g( )

15 Relative Rates of Reaction a + bb c + dd if we are interested in species we can define as the basis of calculation conversion: b c d + B + D a a a Moles of reacted Moles of fed Let s see how we can relate it to the reaction rate for various types of reactors.

16 conversion: Batch reactor b c d + B + D a a a Moles of reacted Moles of fed number of moles left after conversion: 1 ( ) number of moles B left after conversion: b B B a ( ) 1 ( b a ) ( ) Θ ( ) b a B B B B

17 Batch reactors For every component in the reactor we can write after conversion is achieved: δ - the total molar increase per mole of reacted δ T T + δ

18 Batch reactor ow, if we know the number of moles of every component we can calculate concentration as a function of conversion. ( ) ( ) ( ) ( ) ( ) ( ) ( ) a d a c a b a b D D D B B B B + Θ + Θ Θ 1 However, generally can be a function of as well... In a constant volume reactor (e.g. batch reactor, liquid reactor): ( ) ( ) ( ) etc., ; 1 a b B B Θ

19 Flow reactors Equations for flow reactors are the same with number of moles changed for flow rate F [mol/s].

20 Flow reactors Stoichiometric table for a flow system

21 Flow reactors For a flow system a concentration at any point can be obtained from molar flow rate F and volumetric flow rate F v For reaction in liquids, the volume change is negligible (if no phase change occurred): F b ( ) B ΘB v a 1 moles time liter time

22 Reactions involving volume change In a gas phase reaction a molar flow rate might change as the reaction progresses + 3H 2H moles 2 moles In a gas phase reaction a molar flow rate might change as the reaction progresses

23 Batch reactor with variable volume s such it would be a rare case (e.g. internal combustion engine), but a good model case: If we divide the gas equation at any moment in time by the one at moment zero: RT Z P T compressibility factor T T Z Z T T P P T T T ε δ ( ) T T P P ε + 1 function g()

24 Flow reactor with variable flow rate Using the gas equation we can derive the total concentration as: total concentration: T F v T P ZRT at the entrance: T F v P Z RT T total volume rate: F P Z T T v v F T P Z T Fj FT P Z T Fj P Z T j Fj v T v FT P Z T FT P Z T 1

25 Flow reactor with variable flow rate In a gas phase reaction a molar flow rate might change as the reaction progresses P T P T F P Z T v v ( ) ( ) 1+ yδ v 1+ ε P T P T T v v F T PZ T F F + F δ T T j F ( Θ + ν ) j j ( 1+ ε ) P T v P T

26 Example 3.6 (p.118) O 2O For reaction above calculate equilibrium conversion in a constant batch reactor; equilibrium conversion in a flow reactor; assuming the reaction is elementary, express the rate of the reaction plot Levenspil plot and determine STR volume for 8% conversion assume the feed is pure 2 O 4 at 34K and 22.6kPa. oncentration equilibrium constant: K.1mol/l; k.5 min -1.

27 Example 1. Batch reactor equilibrium conversion: K e Be e e ( ) e e e y P RT mol/dm.

28 2. Flow reactor B ( ) ( ε ) Example ( ) F F 1 1 v v ε 1 + ε K Be 4 e 4e ( 1 ) ( 1 )( 1+ ε ) e e e e y P RT 3.71mol/dm. e.51

29 Example 2 3. Rate laws r k K B K 2 2 ( 1 ) 4 r k 1+ ε K 1+ ε onstant volume r k ( ) Flow ( ) 2 Levenspiel plot

30 Example 4. STR volume for.4, feed of 3 mol/min r k ( ) 4 K onstant volume r F r dm 3 PFR in the next lecture

31 Problems lass: P3-15 Home: P3-7, P3-13