CHEMICAL REACTION ENGINEERING

Transcription

1 CHEMICL RECTION ENGINEERING Unit 5 nalysis of reactor DT

2 Collection and analysis of rate data Batch reactor for homogenous and heterogeneous reactions measurement during the unsteady-state operation Differential reactor for solid-fluid reactions measurement during steady state operation product concentration is usually monitored for different feed conditions.

3 nalysing methods Differential method Integral method Half-lives method Initial rate method Linear regression Non-linear regression Batch reactors Software packages

4 nalysing methods Differential method Integral method Half-lives method Initial rate method Linear regression Non-linear regression Batch reactors Software packages

5 Batch reactor Differential method of rate analysis When a reaction is irreversible, it is possible to obtain the specific rate constant by numerically differentiating concentration versus time data. concentration versus time data What we measured What we want to develop dc dt k C For example: decomposition reaction products ssuming the rate law as: What about + B products? r kc

6 Method of excess + B products ssuming the rate law as: r k C C β B Run in an excess of B, so that C B remains essentially unchanged during the course of the reaction k C r fter determing, the reaction is run in an excess of β k C B r

7 Constant-volume batch reactor r kc constant volume r dn Vdt dc dt k C ln (-dc /dt) Slope ln dc dt ln k + ln C Differential method ln C

8 Methods for the determination of the Graphical differentiation derivatives plotting C / t as a function of t using equal-area differentiation to obtain dc /dt Numerical differentiation when the data points in the independent variable are equally spaced weighted averaged C Differentiation of a polynomial fit to the data Excel, MatLaband other software can be used

9 Differential method example Gas-phase decomposition of di-tert-butyl peroxide: (CH 3 ) 3 COOC(CH 3 ) 3 C 2 H 6 + 2CH 3 CCH 3 O Time (min) Total ressure (mmhg)

10 Differential method example ostulate a rate law r kc Mole balance d dt dc dt kc 1 ( 2RT ) (3 For a constant volume batch reactor k C ) V V 3 C 2RT X (1 ε ) T T X

11 Differential method example ) ( 1 ) ( 1 ) ( 1 y X δ δ ε For isothermal operation and constant volume ) (1 ) (1 ) (1 X RT X V N X C C For the reaction y δ δ ε 1+2-1

12 d dt k 1 ( 2RT) (3 ) d dt k ( 3 ) ln (d/dt) d ln( ) lnk + ln(3 ) dt t ln (3 -)

13 nalysing methods Differential method Batch reactors Integral method Half-lives method Initial rate method Linear regression Non-linear regression Software packages

14 Integral Method trial-and-error procedure to find reaction order Guess the reaction order Integrate the differential equation This method is used most often when the reaction order is known and it is desired to evaluate the specific reaction rate constants at different temperatures to determine the activation energy. We are looking for the appropriate function of concentration corresponding to a particular rate law that is linear with time.

15 For the reaction products For a zero-order reaction -r -k C dc dt k For a first-order reaction -r -k C ln (C /C ) t C dc dt C kc kt C ln kt t C For a second-order reaction -r -k C 2 dc 2 kc dt 1/C t 1 C 1 C kt

16 Integral method example Gas-phase decomposition of di-tert-butyl peroxide: (CH 3 ) 3 COOC(CH 3 ) 3 C 2 H 6 + 2CH 3 CCH 3 O Time (min) Total ressure (mmhg)

17 d dt k 1 ( 2RT) (3 ) d dt k ( 3 ) Differential method Integral method ssuming 1 d dt k ( 3 ) 2 ln( 3 ) k t d ln( ) lnk + ln(3 ) dt ln [2 /(3 -)] Bingo! t

18 nalysing methods Differential method Integral method Batch reactors Half-lives method Initial rate method Linear regression Non-linear regression

19 Method of half-lives The half-life of a reaction, t 1/2, is defined as the time it takes for the concentration of the reactant to fall to half of its initial value. By determining the half-life of a reaction as a function of the initial concentration, the reaction order and specific reaction rate can be determined.

20 products dc dt kc t k( 1) C C 1 1 ln (t C C 1/2 ) C 2 Slope 1- t k( 1) C 1 ln C 2 1 ln( t1 ) ln + (1 ) lnc 2 k( 1)

21 nalysing methods Differential method Integral method Half-lives method Batch reactors Initial rate method Linear regression Non-linear regression

22 Method of initial rates When the reaction is reversible, the method of initial rates can be used to determine the reaction order and the specific rate constant. series of experiments is carried out at different initial concentrations and the initial rate of reactionis determined for eachrun. The initial rate can be found by differentiating the data and extrapolating to zero time. By various plotting or numerical analysis techniques relating -r to C, we can obtain the appropriate rate law: kc r

23 Initial rate method example The dissolution of dolomite using hydrochloric acid: 4HCl + CaMg(CO 3 ) 2 Mg 2+ + Ca Cl - +2CO 3 + 2H 2 O The concentration of HCl at various times was determined from atomic absorption spectrophtometer measurements of the calcium and magnesium ions C HCl 4N HCl 1N HCl t p. 24

24 Evaluating the mole balance on a constant-volume batch reactor at t : dc HCl ( rhcl ) kchcl, dchcl dt ln lnk lnc + HCl, dt C HCl, (N) Initial reaction rate r HCl, (mol/cm 2 s) x ln - r HCl, Slope ln C HCl

25 nalysing methods Differential method Integral method Half-lives method Initial rate method Differential reactor Linear regression Non-linear regression Batch reactors

26 Differential reactors The criterion for a reactor being differential is that the conversion of the reactants in the bed is extremely small, as is the change in reactant concentration through the bed. The reactant concentration through the reactor is essentially constant (i.e. the reactor is considered to be gradientless) The rate of reaction is determined for a specified number of pre-determined initial or entering reactant concentrations. Determine the rate of reaction as a function of either concentration or partial pressure. C C C e C ~ C ~ C e

27 Differential reactors The reactor is considered to be gradientless (considered as a CSTR). They operate essentially in an isothermal manner. (Limitation) If the catalyst under investigation decays rapidly, the differential reactor is not a good choice because the reaction rate parameters at the start of a run will be different from those at the end of the run.

28 Differential catalyst bed F C L W F e C p F p The rate of reaction per unit mass of catalyst, r flow rate in -flow rate out + rate of generation rate of accumulation F Fe + r W F Fe vc vc r W W When constant flow rate, v v : r v ( C C W e) v C p W The reaction rate can be determined by measuring the product concentration, C p e roduct concentration

29 Differential reactor example The formation of methane from carbon monoxide and hydrogen using a nickel catalyst at 5 F in a differential reactor: 3H 2 + CO CH 4 + 2H 2 O Run CO (atm) H2 (atm) C CH4 (g mol/dm 3 ) x x x x x x g catalyst exit volumetric flow rate: 3 roduct composition was monitored dm 3 /min

30 vcch 4 r r CH 4 W dm gmol/ dm 3 gmolch4 r min rch 1g cat. g cat. min We can then relate the rate of reaction to the exit methane concentration for each single run. For constant hydrogen concentration, the rate law: 1 r CH k ( 4 CO f H 2 ) r ln + CH k 4 CO ln( rch ) k 4 CO We observe: (1) at low H 2 concentration where r CH4 increases as H2 increases, the rate law may be of the form: r CH4 ~ H2 β1 (2) at high H 2 concentration where r CH4 decreases as H2 increases, the rate law may be of the form: r CH4 ~ H2 1/β2

31 We suggest that the rate law can be the form: r β 1 H 2 CH ~ 4 β β b 1 1/2 H 2 β 2 1 ctually, this is the typical form of the rate law for heterogeneous catalysis. This predicts that if the rate-limiting step in the overall reaction is the reactionbetweenatomic hydrogen absorbed on the nickel surface and CO in the gas phase.

32 r CH 4 ~ 1 + H 2 b 1 / 2 1 H 2 r CH k CO 4 CO r CH H / 2 r CH a 4 1 CO + H b 2 H 1 / 2 2 H 2 r CH CO H 2 H 2 1 / 2 CO r CH H 4 1 / a + b a H 2

33 Experimental planning Fogler, 1999

34 Features of representative laboratory reactors [Levenspiel, 1979].