[PPT] - A First Course on Kinetics and Reaction Engineering Class 17 on PowerPoint Presentation

SLIDE 1

A First Course on Kinetics and Reaction Engineering

Class 17 on Unit 17

SLIDE 2

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

2

SLIDE 3

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
perability
environmental compatibility
safety

3

SLIDE 4

Ideal Reactor Design Equations

Batch Reactor

dni dt = V νi, jrj

j=all reactions

∑

Q −

W = dT dt ni ˆ Cpi

( )

i=all species

∑

+V rjΔH j

( )

j=all reactions

∑

− dP dt V − P dV dt

CSTR

ni
V

dV dt + V

V

d ni dt − niV

V 2

d V dt = ni

0 −

ni +V νi, jrj

j=all reactions

∑

Q −

W =

ni

ˆ Cpi dT

T 0 T

∫

⎛ ⎝ ⎜ ⎞ ⎠ ⎟

i=all species

∑

+V rjΔ H j T

( )

j=all reactions

∑

+ V

V
ni ˆ

Cpi

( )

i=all species

∑

dT dt ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −V dP dt ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + P dV dt ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

4

SLIDE 5

Ideal Reactor Design Equations

Steady State CSTR

0 = ni

0 −

ni +V νi, jrj

j=all reactions

∑

Q −

W =

ni

ˆ Cpi dT

T 0 T

∫

⎛ ⎝ ⎜ ⎞ ⎠ ⎟

i=all species

∑

+V rjΔ H j T

( )

j=all reactions

∑

PFR

∂ ni ∂z = πD2 4 νi, jrj

j=all reactions

∑

− πD2 4 V ∂ ni ∂t + πD2 ni 4 V 2 ∂ V ∂t πDU Te −T

( ) =

ni ˆ

Cpi

i=all species

∑

⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ∂T ∂z + πD2 4 rjΔH j

( )

j=all reactions

∑

+ πD2 4 V

ni ˆ

Cpi

( )

i=all species

∑

∂T ∂t − πD2 4 ∂P ∂t

5

SLIDE 6

Ideal Reactor Design Equations

Steady State RFR

∂ ni ∂z = πD2 4 νi, jrj

j=all reactions

∑

πDU Te −T

( ) =

ni ˆ

Cpi

i=all species

∑

⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ∂T ∂z + πD2 4 rjΔH j

( )

j=all reactions

∑

∂ P ∂ z = − G gc 4 π D2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ∂ V ∂ z − 2 fG2 ρD ∂ P ∂ z = −1− ε ε 3 G2 ρΦsDpgc 150 1− ε

( )µ

ΦsDpG +1.75 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥

(Unpacked Tube) (Packed Bed)

6

SLIDE 7

Typical Kinetics Behavior and 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

7

SLIDE 8

Questions?

8

SLIDE 9

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

SLIDE 10

Solution to the Practice Exam

10

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 kinetics

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

expression

d. parabolic in shape with the concave side facing up
e. parabolic in shape with the concave side facing down

K j = exp −ΔG j RT ⎧ ⎨ ⎪ ⎩ ⎪ ⎫ ⎬ ⎪ ⎭ ⎪ k j = exp ΔS j R ⎧ ⎨ ⎪ ⎩ ⎪ ⎫ ⎬ ⎪ ⎭ ⎪ exp −ΔH j RT ⎧ ⎨ ⎪ ⎩ ⎪ ⎫ ⎬ ⎪ ⎭ ⎪ K j = K0, j exp −ΔH j RT ⎧ ⎨ ⎪ ⎩ ⎪ ⎫ ⎬ ⎪ ⎭ ⎪ k j = k0, jT a exp −E j RT ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ k j = k0, j exp −E j RT ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

SLIDE 11

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
utlet 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 are
a. 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(∞) = 1
e. F(0) = -∞ and F(1) = ∞

11

SLIDE 12

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:

12

Problem 1

r

C7H8 = 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)

SLIDE 13

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)

13

SLIDE 14

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
f t and P
Mole balance design equation:
Eliminate PA and PB
Separate variables and integrate
Linearize the equation

14

Problem 2

dnA dt = −kVP

AP B

P

A = nART

V P

B = nBRT

V = nB

0 − nA 0 + nA

( )RT

V dnA dt = − k RT

( )

2

V nA nB

0 − nA 0 + nA

( )

dnA nA nA

0 − nB 0 − nA

( )

nA nA

∫

= k RT

( )

2

V dt

t

∫

⇒ −1 nA

0 − nB 0 ln

nB

0 − nA 0 + nA

nA ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ nA nB ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = k RT

( )

2

V t y = −1 nA

0 − nB 0 ln

nB

0 − nA 0 + nA

nA ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ nA nB ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ x = RT

( )

2

V t y = kx

SLIDE 15

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. 15

ntot

0 = P0V

RT nA

0 = 2

3 ntot nB

0 = 1

3ntot ntot = PV RT ntot = ntot

0 −ξ ⇒ ξ = ntot 0 − ntot

nA = nA

0 −ξ

SLIDE 16

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. 16

Problem 3

nA −

nA

0 = −k1VP A

y = k1x y = nA − nA x = −VP

A

nS =

nS

0 +ξ = ξ

nA =

nA

0 −ξ

P

A =

nA

ntot

P =

nA

0 −ξ

nA

0 +

nI

0 + 2ξ P

SLIDE 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
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