A First Course on Kinetics and Reaction Engineering

Class 17 on Unit 17

Where We’re Going

• Part I - Chemical Reactions• Part II - Chemical Reaction Kinetics• Part III - Chemical Reaction Engineering

‣ A. Ideal Reactors- 17. Reactor Models and Reaction Types

‣ B. Perfectly Mixed Batch Reactors‣ C. Continuous Flow Stirred Tank Reactors‣ D. Plug Flow Reactors‣ E. Matching Reactors to Reactions

• Part IV - Non-Ideal Reactions and Reactors

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Reaction Engineering

• Objectives‣ Construct accurate mathematical models of real world reactors‣ Use those models to perform some engineering task

• Tasks‣ Reaction engineering: studies involving an existing reactor‣ Reactor design: specifying a reactor that doesn’t yet exist along with its operating procedures

• Real world reaction engineering‣ Maximize the rate of profit realized by operating the overall process (not just the reactor)‣ Integration of the reactor into the overall process may place constraints upon the reactor

design and operating conditions

• Generally‣ generate the desired product as fast as possible‣ with the highest selectivity possible‣ using as little energy as possible‣ in as small a reactor volume as possible‣ while maintaining

- reliability - operability - environmental compatibility- safety

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Ideal Reactor Design Equations

Batch Reactor

dnidt

=V ν i, jrjj=all

reactions

∑

!Q − !W = dTdt

niCpi( )i=allspecies

∑ +V rjΔH j( )j=all

reactions

∑ − dPdtV − P dV

dt

CSTR

!ni!V

dVdt

+ V!V

d !ni

dt−!niV!V 2

d !Vdt

= !ni0 − !ni +V ν i, jrj

j=allreactions

∑

!Q − !W = !ni0 Cpi dTT 0

T

∫⎛

⎝⎜⎞

⎠⎟i=allspecies

∑ +V rjΔH j T( )j=all

reactions

∑ + V!V!niCpi( )

i=allspecies

∑ dTdt

⎛⎝⎜

⎞⎠⎟ −V

dPdt

⎛⎝⎜

⎞⎠⎟ + P

dVdt

⎛⎝⎜

⎞⎠⎟

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Ideal Reactor Design Equations

Steady State CSTR

0 = !ni0 − !ni +V ν i, jrj

j=allreactions

∑

!Q − !W = !ni0 Cpi dTT 0

T

∫⎛

⎝⎜⎞

⎠⎟i=allspecies

∑ +V rjΔH j T( )j=all

reactions

∑

PFR

∂ !ni∂z

= πD2

4ν i, jrj

j=allreactions

∑ − πD2

4 !V∂ !ni∂t

+ πD2 !ni4 !V 2

∂ !V∂t

πDU Te −T( ) = !niCpii=allspecies

∑⎛

⎝

⎜⎜

⎞

⎠

⎟⎟∂T∂z

+ πD2

4rjΔH j( )

j=allreactions

∑ + πD2

4 !V!niCpi( )

i=allspecies

∑ ∂T∂t

− πD2

4∂P∂t

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Ideal Reactor Design Equations

Steady State RFR

∂ !ni∂z

= πD2

4ν i, jrj

j=allreactions

∑

πDU Te −T( ) = !niCpii=allspecies

∑⎛

⎝

⎜⎜

⎞

⎠

⎟⎟∂T∂z

+ πD2

4rjΔH j( )

j=allreactions

∑

∂ P∂ z

= − Ggc

4πD2

⎛⎝⎜

⎞⎠⎟∂ !V∂ z

− 2 fG2

ρD

∂ P∂ z

= −1− εε 3

G2

ρΦsDpgc

150 1− ε( )µΦsDpG

+1.75⎡

⎣⎢⎢

⎤

⎦⎥⎥

(Unpacked Tube)

(Packed Bed)

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Typical Kinetics Behaviorand Reaction Classification

• Typical kinetics behavior‣ As T increases, the rate increases

- final conversion decreases for exothermic; increases for endothermic reactions‣ As concentration or partial pressure of reactants decreases, the rate decreases‣ As the concentration or partial pressure of products increases, the rate decreases for

reversible reactions; is not strongly affected for irreversible reactions

• Reaction Classification‣ Auto-thermal reactions: the (exothermic) heat of reaction is sufficiently large to heat the

reactants to reaction temperature‣ Auto-catalytic reactions: rate increases as the product concentration increases‣ Reactant Inhibited Reactions: rate decreases as the reactant concentration increases‣ Product Inhibited Reactions: rate decreases as the product concentration increases‣ Parallel Reactions

- A → B- A → C

‣ Series Reactions- A → B- B → C

‣ Series-Parallel Reactions- A + B → R + S- R + B → T + S

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Questions?

8

Exam Procedure

9

• When you arrive‣ Place coats, hats, backpacks, etc. along the front or side walls of the room‣ Take only pencil, eraser and/or pen to your seat‣ The exam will not begin until everyone is seated

• Once the exam starts, you may not leave the room‣ If you leave, you must turn in your exam before doing so, and you will not be permitted to

resume the exam‣ Therefore, use the restroom prior to the exam

• The exam will end at 10:50 AM

Solution to the Practice Exam

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1. Which of the following is the Arrhenius expression?a. ! b.

c. ! d.

e.

2. True or false? Every mechanism has a rate-determining step.3. A Lineweaver-Burke plot is (choose all that are true)

a. a plot of a linearized form of a Michaelis-Menten kinetic expression b. used to determine whether the kinetics of an enzyme-catalyzed reaction obey Michaelis-

Menten kineticsc. used to determine the values of the parameters appearing in a Michaelis-Menten kinetic

expression d. parabolic in shape with the concave side facing upe. parabolic in shape with the concave side facing down

K j = exp

−ΔGj

RT⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪ k j = exp

ΔS j

R⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪exp

−ΔH j

RT⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

K j = K0, j exp

−ΔH j

RT⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

kj = k0, jTa exp

−Ej

RT⎛⎝⎜

⎞⎠⎟

kj = k0, j exp−Ej

RT⎛⎝⎜

⎞⎠⎟

4. The age function is measured by applying a stimulus and measuring a response.a. The stimulus is applied at the inlet to the reactor and the response is measured at the inlet to

the reactor.b. The stimulus is applied at the outlet from the reactor and the response is measured at the

outlet from the reactor.c. The stimulus is applied at the outlet from the reactor and the response is measured at the inlet

to the reactor.d. The stimulus is applied at the inlet to the reactor and the response is measured at the outlet

from the reactor.e. The stimulus can be applied at either the inlet or the outlet of the reactor, and the response is

measured at the other location.

5. The limiting values of the age function area. F(0) = 1 and F(1) = ∞b. F(1) = 0 and F(∞) = ∞c. F(0) = 1 and F(1) = ∞d. F(0) = 0 and F(∞) = 1e. F(0) = -∞ and F(1) = ∞

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• Stable species: C7H8, Cl2, C7H7Cl and HCl• Reactive intermediates: Al2Cl6, HCl−AlCl3−AlCl3, HCl−AlCl3, Cl2−AlCl3 and

AlCl4−C7H8Cl• There is no rate determining step, therefore write rate with respect to a

reactant or product‣

• Not acceptable, eliminate concentrations of reactive intermediates

‣ Step 1 is equilibrated:

‣ Conservation of catalyst:

‣ Bodenstein steady state approximation on all but two of the reactive intermediates:

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Problem 1

rC7H8 = k3 f Cl2 − AlCl3[ ] C7H8[ ]− k3r AlCl4 −C7H8Cl[ ]

K1 =Al2Cl6[ ] HCl[ ]

HCl − AlCl3 − AlCl3[ ]C0 = Al2Cl6[ ]+ HCl − AlCl3 − AlCl3[ ]

+0.5 HCl − AlCl3[ ]+ 0.5 Cl2 − AlCl3[ ]+ 0.5 AlCl4C7H8Cl[ ]

0 = k3 f Cl2 − AlCl3[ ] C7H8[ ]− k4 f AlCl4 −C7H8Cl[ ]0 = k1 f Al2Cl6[ ] HCl[ ]− k1r HCl − AlCl3 − AlCl3[ ]0 = k2 f HCl − AlCl3 − AlCl3[ ] Cl2[ ]− k2r HCl − AlCl3[ ] Cl2 − AlCl3[ ]+k4 f AlCl4 −C7H8Cl[ ]− k5 f HCl − AlCl3[ ] Cl2[ ]+ k5r Cl2 − AlCl3[ ] HCl[ ]

(1)

(2)

(3)

(4)

(5)

(6)

• Solve equations (1) through (5) simultaneously to get expressions for [Al2Cl6], [HCl−AlCl3−AlCl3], [HCl−AlCl3], [Cl2−AlCl3] and [AlCl4−C7H8Cl]

• Substitute the resulting expressions for [Cl2−AlCl3] and [AlCl4−C7H8Cl] into equation (6)

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• Let A = C3H6, B = C6H6 and Z = C9H14 so A + B → Z• Given: V = 3.27 L, T = 500 K, P0 = 340 mm Hg, and a data set with values

of t and P• Mole balance design equation: • Eliminate PA and PB

• Separate variables and integrate

• Linearize the equation

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Problem 2

dnAdt

= −kVPAPB

PA =nARTV PB =

nBRTV

=nB0 − nA

0 + nA( )RTV

dnAdt

= −k RT( )2V

nA nB0 − nA

0 + nA( )

dnAnA nA

0 − nB0 − nA( )nA

0

nA

∫ =k RT( )2

Vdt

0

t

∫ ⇒ −1nA

0 − nB0 ln nB

0 − nA0 + nAnA

⎛⎝⎜

⎞⎠⎟nA

0

nB0

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥ =

k RT( )2

Vt

y = −1nA0 − nB

0 lnnB0 − nA

0 + nAnA

⎛⎝⎜

⎞⎠⎟nA0

nB0

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥ x = RT( )2

Vt y = kx

• Fit y = kx to the data by calculating x and y for each data point and then fitting numerically‣ To do so need values for nA0, nB0 and nA for each data point

• Fitting will yield r2, a model plot and the value of the slope, in this case k with its uncertainty‣ If r2 is close to 1.0 AND the data in the model plot scatter randomly from the line by a small

amount (no systematic deviations), the rate expression is acceptable.

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ntot0 = P

0VRT

nA0 = 2

3ntot0 nB

0 = 13ntot0

ntot =PVRT

ntot = ntot0 −ξ ⇒ ξ = ntot

0 − ntot nA = nA0 −ξ

• Given: V = 276 cm3, T = 505 K and a data set including values of P, ṅA0, ṅI0 ( = ṅI) and ṅS for each experiment

• Mole balance design equation: • Linearize the equation

‣ ‣ ‣

• Fit y = k1x to the experimental data by calculating x and y for each data point and then fitting numerically‣ To do so, need ṅA and PA for each data point

• Fitting will yield r2, a model plot and the value of the slope, in this case k with its uncertainty‣ If r2 is close to 1.0 AND the data in the model plot scatter randomly from the line by a small

amount (no systematic deviations), the rate expression is acceptable.

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Problem 3

!nA − !nA0 = −k1VPA

y = k1x

y = !nA − !nA0

x = −VPA

!nS = !nS0 + ξ = ξ

!nA = !nA0 −ξ

PA =

!nA!ntot

P =!nA0 −ξ

!nA0 + !nI

0 + 2ξP

Where We’re Going

• Part I - Chemical Reactions• Part II - Chemical Reaction Kinetics• Part III - Chemical Reaction Engineering

‣ A. Ideal Reactors- 17. Reactor Models and Reaction Types

‣ B. Perfectly Mixed Batch Reactors- 18. Reaction Engineering of Batch Reactors- 19. Analysis of Batch Reactors- 20. Optimization of Batch Reactor Processes

‣ C. Continuous Flow Stirred Tank Reactors‣ D. Plug Flow Reactors‣ E. Matching Reactors to Reactions

• Part IV - Non-Ideal Reactions and Reactors

17