Lecture 10 Kjemisk reaksjonsteknikk Chemical …folk.ntnu.no/audunfor/5. semester/Rektek/Lecture...
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1 - 19/09/2012 Department of Chemical Engineering Lecture 10 Kjemisk reaksjonsteknikk Chemical Reaction Engineering Review of previous lectures Procedure of CRE data analysis Reactors for kinetic study Determining the Rate Law from Experimental Data Integral Method Differential (Graphical) Method Nonlinear Least Regression Homogeneous Heterogeneous
Transcript of Lecture 10 Kjemisk reaksjonsteknikk Chemical …folk.ntnu.no/audunfor/5. semester/Rektek/Lecture...
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Departm
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ical Engineering
Lecture 10Kjemisk reaksjonsteknikk
Chemical Reaction Engineering
Review of previous lectures Procedure of CRE data analysis Reactors for kinetic study Determining the Rate Law from Experimental Data Integral Method Differential (Graphical) Method Nonlinear Least Regression Homogeneous Heterogeneous
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Batch reactor
1) Mole balance
AA kCr
VrdtdXN A0A
1
1ln1xk
t
2) Rate law
X
tFirst-order Second-order2
2 AA Ckr
3) Stoichiometry: X1CC 0AA
4) Combine: Xkdtdx
1 202 1 XCkdtdx
A
5. Evaluation)1(02 xCk
xtA
)exp(1 1tkx 02
02
1 A
A
CtkCtkx
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CSTR reactor
1) Mole balance
AA kCr
2) Rate law First-order Second-order2
2 AA Ckr
3) Stoichiometry: XFF AA 10
4) Combine:
)1(0
0
xkCxCV
A
A
5. Evaluation
k
kx
1
A
0A
rXFV
X1CX1FFC 0A0
0AAA
20 )1( xkC
xV
A
0
00
24121
A
AA
kCkCkC
x
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PFR reactor
1) Mole balance
AA kCr
2) Rate law First-order Second-order2
2 AA Ckr
3) Stoichiometry: XFF AA 10
4) Combine:
5. Evaluation
xx
k
1
1ln)1(
A0A rdVdXF
X1
X1CC 0AA
2
202
11
)/( XXCk
Vddx A
X1
X1XX1ln12kC2
20A
X
XkVddx
11
)/(
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CRE Data Analysis
1) Developing an algebraic rate expression consistent with experimental observations
2) Analyzing 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 non-elementary reactions)
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7-Step Procedure for CRE Data analyses (1)
1. Postulate a rate law A. Power law models fro homogeneous reactions
B. Langmuir-Hinshelwood models for heterogeneous reactions
2. Select reactor type and corresponding mole balance A.If batch reactor, use mole balance on Reactant A
B.If differential PBR, use mole balance on product P (A →P)
BAA CkCr
2)1( BBAA
BAA PKPK
PkPr
dtdCr A
A
WC
WFr PP
A
0
dtdCr A
A
WC
WFr PP
A
0
1. Postulate a rate law A. Power law models for homogeneous reactions
B. Langmuir-Hinshelwood models for heterogeneous reactions
2. Select reactor type and corresponding mole balance A.If batch reactor, use mole balance on Reactant A
B.If differential PBR, use mole balance on product P (A →P)
WC
WFr PP
A
0
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7-Step Procedure for CRE Data analyses (2)
3. Process your data in terms of the measured variables (e.g. NA, CA, or PA). 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 A is small, set ε=0
5. For a batch reactor, calculate –rA as a function of concentration CA to determine the reaction order:A.Differential analysisB.Integral methodC.Nonlinear regression
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7-Step Procedure for CRE Data analyses (3)
6. For differential PBR, calculate –rA as a function of CA or PA
A. Calculate as a function of reactant concentration CA or partial pressure PA
B. Choose a model, e.g.,
C. Use nonlinear regression to find the best model and model parameters
7. Analyze your rate law model for “goodness of fit”. Calculate a correlation coefficient.
WC
WFr PP
A
0
AA
AA PK
kPr
1
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Reactors for kinetic study
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Batch Reactor
dN A
dt rAV
Batch
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1. 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 (CA0) and temperatures
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CSTR
CSTR
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VFFr AA
A 0
Reaction rate can be directly measured as a function of outlet concentration and temperatures
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Differential reactor
Inn - ut + formed = accumulated
FA0 - FA + rA W = 0
-rA = (FA0 - FA) / W= FA0X / W
In practice, the conversion is controlled to be low enough (X< 5-10 %) to make the concentration approximately gradientless
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Recycle-reactor
W
CA
vRCA
CoA
vo
CinnA
Mass balanse on the mixing point:
vo CoA + vR CA = (vo+ vR) CA
inn
-rA’ = vo (Co
A - CA) / W
With increasing vR , CinnA is close to CA
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Mixed Flow Reactor
Carberry basket type mixed flow reactor.
Catalyst placed in a basket which rotates in the reaction gas
Difficult to measure the temperature
Should not be used for exothermic and endothermic reactions
• It requires a uniform composition of fluid throughout.• Examples
Berty reactor
Recycling of reaction gases
' A 0 AoutAout
F XrW
- =
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Guidelines for Selecting Reactors for Kinetic Study
Liquid phase Batch reactor: must often used, simple, rich in kinetic data
CSTR: 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
Cycling 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
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Methods of CER data analysis
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Integral Method
Consider the following reaction that occurs in a constant volumeBatch Reactor: (We will withdraw samples and record the concentration of A as a function of time.)
A ProductsdN A
dt rAVMole Balance:
rA kC ARate Law:
V V0Stochiometry:
dC A
dt kCA
Combine:19
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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
dC A
dt rA k
at t 0, CA CA 0
CA CA 0 kt
dC A
dt rA kC A
at t 0, CA CA 0
lnCA 0
CA
kt
dC A
dt rA kC A
2
at t 0, CA CA 0
1
CA
1
CA 0
kt20
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Guess and check for reaction order of α = 0, 1, 2 and check against experimental plot
ktCC
ktCCktCr
AAA
AAA
0
00
11 ln
2 1 0
t
CA
t
ln(CA0/CA)
t
1/CA
Finding the Rate law (Integral Method)
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Differential Method
AA Clnkln
dtdCln
AA kC
dtdCTaking the natural log of
dC A
dt
vs CA
The reaction order can be found from a ln-ln plot of:
dtdC A
ACAPC
P
A
dtdC
Slope = α
ln
ln
Ap
p
A
Cdt
dC
k
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Methods for finding the slope of log-log and semi-log graph papers may be found at http://www.physics.uoguelph.ca/tutorials/GLP/.
However, we are usually given concentration as a function of time from batch reactor experiments:
time (s) 0 t1 t2 t3
concentration (moles/dm3) CA0 CA1 CA2 CA3
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Three Ways to determine (-dCA/dt) from Concentration-Time Data Graphical differentiationNumerical differentiation formulasDifferentiation of a polynomial fit to the data1. Graphical
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C A
t
t
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The method accentuates measurement error!
1t
A
dtdC
C A
t
0
A
dtdC
2t
A
dtdC
0 1t 2t t
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Example - Finding Rate Law
t(min) 0 1 2 3
CA(mol/L) 1 0.7 0.5 0.35
0.3 0.2 0.15t
C A
tC A
.1.2.3
t1 2 3
Areas equal for both sides of the histogram
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Example - Finding Rate Law
Find the f(t) of using equal area differentiation
tC A
CA 1 0.7 0.5 0.35
-dCA/dt 0.35 0.25 0.175 0.12
Plot –dCA/dt as a function of CA
Ap
p
A
Cdt
dC
k
ln
CA
Slope = αdCA/dt
ln27
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Non-Linear Least-Square Analysis
2 rmi rci 2
N Ki1
n
That is we want to be a minimum. 2
We want to find the parameter values (α, k, E) for which the sum of the squares of the differences, the measured rate (rm), and the calculated rate (rc) is a minimum.
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N: Number of runs
K: number of parameters to be determined
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Non-Linear Least-Square Analysis
For concentration-time data, we can integrate the mole balance equation for to obtainrA kC A
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dC A
dt kC A
t 0
CA CA 0
CA CA 01 1 kt 1
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Non-Linear Least-Square Analysis
s2 CAmi CAci 2
i1
N
CAmi CA 01 1 kt i 1 1 2
i1
N
We find the values of alpha and k which minimize s2
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Cmeas 1 0.7 0.5 0.35
CCalc 1 0.5 0.33 0.25
(Cc-Cm) 0 -0.2 -0.17 -0.10
(Cc-Cm)2 0 0.04 0.029 0.01 0.07
for α= 2, k = 1 → S2 = 0.07
for α = 2, k = 2 → S2 = 0.27
etc. until S2 is a minimum31
Regression MethodGuess values forα and k and solve for measured data points then sum squared differences:
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Determining reaction order and activation energy based on data obtained from
CSTR
