Lecture 10 Kjemisk reaksjonsteknikk Chemical Reaction Engineering

Transcription

1 Lecture 10 Kjemisk reaksjonsteknikk hemical Reaction Engineering Review of previous lectures Procedure of RE data analysis Reactors for kinetic study Determining the Rate Law from Experimental Data Integral Method Differential (Graphical) Method Nonlinear Least Regression Homogeneous Heterogeneous 1-19/09/2012

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3 1) Mole balance 2) Rate law First-order r k t Batch reactor N ln k 1 x dx r 3) Stoichiometry: 1 X dx 0 V Second-order r k 2 2 4) ombine: k 1 X k 2 5. Evaluation x 1 exp( k1t) t x dx X X x k 2 0 (1 x) tk tk 2 0 t 3-19/09/2012

4 STR reactor 1) Mole balance V F 0 X r 2) Rate law First-order Second-order 3) Stoichiometry: 4) ombine: 5. Evaluation r k F V x F 1 0 k 1 k 0 X 0 x k (1 x) r k 2 2 F F 0 1 X 0 x V 1 k 2k 0 x 2 0 ( 1 x) 0 2k X 4k /09/2012

5 PFR reactor 1) Mole balance F 0 dx dv r 2) Rate law First-order Second-order 3) Stoichiometry: 4) ombine: r k F F dx k 1 X d ( V / ) X 5. Evaluation 1 k (1 ) ln 1 x X k 0 x 2 r k X 1 X dx k 2 d ( V / ) X 1 ln1 X 2 X X X /09/2012 X

6 RE Data nalysis 1) Developing an algebraic rate expression consistent with experimental observations 2) nalyzing the rate expression in a such manner that the rate expression parameters can readily be determined from experimental data 3) Find a mechanism and rate determining step consistent with the experimental data (for nonelementary reactions) 6-19/09/2012

7 7-Step Procedure for RE Data analyses (1) 1. Postulate a rate law. Power law models fro for homogeneous reactions r k B B. Langmuir-Hinshelwood models for heterogeneous reactions r kp PB ( 1 K P K BPB 2. Select reactor type and corresponding mole balance.if batch reactor, use mole balance on Reactant r d B.If differential PBR, use mole balance on product P ( P) F P P 0 r W W 2 ) 7-19/09/2012

8 7-Step Procedure for RE Data analyses (2) 3. Process your data in terms of the measured variables (e.g. N,, or P ). If necessary, rewrite your mole balance in terms of your measured variables 4. Look for simplification For example, if one of the reactants is in excess, assume its concentration is constant,. If the gas phase mole fraction of reactant is small, set ε=0 5. For a batch reactor, calculate r as a function of concentration to determine the reaction order:.differential analysis B.Integral method.nonlinear regression 8-19/09/2012

9 7-Step Procedure for RE Data analyses (3) 6. For differential PBR, calculate r as a function of or P FP P 0 r. alculate W W as a function of reactant concentration or partial pressure P B. hoose a model, e.g., r kp 1 K. Use nonlinear regression to find the best model and model parameters P 7. nalyze your rate law model for goodness of fit. alculate a correlation coefficient. 9-19/09/2012

10 Reactors for kinetic study 10-19/09/2012

11 Batch Reactor Batch dn r V Select the stirring speed to make well-mixing 2. Measure the concentration as a function of time 3. Determine the reaction rates at different initial concentrations ( 0 ) and temperatures 11-19/09/2012

12 STR STR 12 r F 0 V F Reaction rate can be directly measured as a function of outlet concentration and temperatures 12-19/09/2012

13 Differential reactor Inn - ut + formed = accumulated F 0 - F + r W = 0 -r =(F 0 -F ) / W= F 0 X / W In practice, the conversion is controlled to be low enough (X< 5-10 %) to make the concentration approximately gradientless 13-19/09/2012

14 Recycle-reactor o v o inn Mass balanse on the mixing point: W v R v o o + v R = (v o + v R ) inn -r = v o ( o - ) / W With increasing v R, inn is close to 14-19/09/2012

15 Mixed Flow Reactor It requires a uniform composition of fluid throughout. Examples arberry basket type mixed flow reactor. atalyst placed in a basket which rotates in the reaction gas Difficult to measure the temperature Should not be used for exothermic and endothermic reactions - r = Berty reactor F X W ' 0 out out Recycling of reaction gases 15-19/09/2012

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17 Guidelines for Selecting Reactors for Kinetic Study Liquid phase Batch reactor: must often used, simple, rich in kinetic data STR: simple for determining reaction rates Gas phase Homogenous: PFR, differential or integral Heterogamous: Differential: Easy determination of rate, easy to remove temperature gradients, different to study at high conversion level Integral: easy analysis of the products but not easy to eliminate the temperature gradients ycling reactors, combining the advantages of differential or integral reactors, easy determination of rate at different conversion degrees, easy to get concentration and temperature gradientless, but complex reactor configuration 17-19/09/2012

18 Methods of ER data analysis 18-19/09/2012

19 Integral Method onsider the following reaction that occurs in a constant volume Batch Reactor: (We will withdraw samples and record the concentration of as a function of time.) Products 19 Mole Balance: Rate Law: Stochiometry: ombine: dn r r V k V V 0 d k 19-19/09/2012

20 Finally we should also use the formula to plot reaction rate data in terms of conversion vs. time for 0, 1st and 2nd order reactions. Derivation Equations used to Plot 0, 1st and 2nd order reactions. These types of plots are usually used to determine the values k for runs at various temperatures and then used to determine the activation energy. Zero order First Order Second Order 20 d r k at t 0, 0 0 kt d r k at t 0, 0 ln 0 kt d r k 2 at t 0, kt 20-19/09/2012

21 Finding the Rate law (Integral Method) Guess and check for reaction order of α = 0, 1, 2 and check against experimental plot r 0 kt ln ln( 0 / ) t 0 kt t 1 1/ 1 0 kt t 21-19/09/2012

22 Differential Method Taking the natural log of d k 22 ln d ln k ln The reaction order can be found from a ln-ln plot of: d d P ln P Slope = α ln k d d p vs p 22-19/09/2012

23 Methods for finding the slope of log-log and semi-log graph papers may be found at However, we are usually given concentration as a function of time from batch reactor experiments: time (s) 0 t 1 t 2 t 3 23 concentration (moles/dm 3 ) /09/2012

24 Three Ways to determine (-d /) from oncentration- Time Data Graphical differentiation Numerical differentiation formulas Differentiation of a polynomial fit to the data 1. Graphical t 24 t 24-19/09/2012

25 t d 0 25 d d t 1 t 2 0 t t 1 2 The method accentuates measurement error! t 25-19/09/2012

26 Example - Finding Rate Law t(min) (mol/l) t t reas equal for both sides of the histogram t 26-19/09/2012

27 Example - Finding Rate Law Find the f(t) of t using equal area differentiation d / Plot d / as a function of 27 d / ln Slope = α ln k d p p 27-19/09/2012

28 Non-Linear Least-Square nalysis We want to find the parameter values (α, k, E) for which the sum of the squares of the differences, the measured rate (r m ), and the calculated rate (r c ) is a minimum. 2 n i1 r mi r 2 ci N K 28 That is we want 2 to be a minimum. N: Number of runs K: number of parameters to be determined 28-19/09/2012

29 Non-Linear Least-Square nalysis For concentration-time data, we can integrate the mole balance equation for r k to obtain d k 29 t kt /09/2012

30 Non-Linear Least-Square nalysis s 2 N mi 2 ci mi 0 i1 N i1 1 1 kt 11 2 i We find the values of alpha and k which minimize s /09/2012

31 Regression Method Guess values forα and k and solve for measured data points then sum squared differences: meas alc ( c - m ) ( c - m ) for α= 2, k = 1 S 2 = 0.07 for α = 2, k = 2 S 2 = 0.27 etc. until S 2 is a minimum 31-19/09/2012

32 Determining reaction order and activation energy based on data obtained from STR 32-19/09/2012