1. Reactor Theory: kinetics
TVM 4145 Vannrenseprosesser / unit processes
Reactor Theory:
kinetics
Prof. TorOve Leiknes

2. Reactor kinetics: What makes a reaction take place?
How does a reaction start?
What affects / influences a reaction?
How fast does a reaction proceed?

3. Gibb’s free energy: Generally:
The energy which is available for a reaction is the free energy of the reactionen:
Δ G
Reaction dergee
1.0
Equilibrium
positive ΔG negative Δ G
All products
All reactants
Generally:
product
reactants

4. Activation energy? Reactants Products A B Energy catalyst effectDE B
Reaction progress

5. Temperature dependence:
Generally:
reaction rate
temperature
increase of 10° C gives ca. 2-3 times increase in rate
Arrhenius (1889) :
for constant Eact
Eact – activation energy
R – the universal gas constant
T – absolute temperature
A – integration constant (frequency factor)

6. NB ! Empiric form most often used: Where: T is temperature in oC
q is a process dependent constant
NB !
Arrhenius:
Enzyme reactions:
Oxidation:
Temperature oC
Reaction rate
Temperature oC
Reaction rate
Temperature oC
Reaction rate

7. Definitions and classification of reactions:
Generally:
Elementary reactions:
1. 0.-order reactions; A P
; independent of [A]
2. 1.-order reactions; A P
3. 2.-order reactions;
A+B P 2A P
Composite reactions :
1. Reversible reactions;
A+B
C+D 2C C
2. Consecutive reactions; A B
3. Chain reactions; 2A
A+B2
P+B
B+A2
P+A
A2+B2 2P

8. Reactions in water are often complex:
Example
Chlorination of phenol
consecutive kinetics
competing reactions
Reaction pathways;
Calculation results; P
2CP
4CP
24DCP
26DCP
246TCP X OH Cl
Phenol
PCP

9. 0. order reactions : enzyme kinetics and biological treatment
reactants absorbed on a surface
integrared
where:
CAo CA t tk k0
CA can not be negative

10. 1. order reactions : where: for non-reversible reactions CA CAo t lnCA
integrated or
where:
Half-life: CA
CAo t
lnCA
lnCAo t k1
Generally:

11. 2. order reactions : where: For: t k2 t k2(CAo- CBo)/2.3 Generally:
integrated
(where a+b=2)
where:
For: t k2
log CA/CB
log CAo/CBo t
k2(CAo- CBo)/2.3 2A P
A+B P
(and Ao=Bo)
Generally:

12. Other “cases”: Retardant: Autocatalytic:
change in rate over time as f(concentration)
where  is a characteristics constant
Autocatalytic:
spontaneous acceleration as time proceeds
A + P
P + P
When:
Rearranged:
Several empirical models exist depending on the system

13. Enzyme kinetics Michaelis-Menton
Biological reactions:
Degradation of substrate is an enzyme-catalytic reaction
Reactions follow thermodynamic principles
Historic developments:
Our understanding of mechanisms can be dated back to the 1800s
1892, 1902; do not follow a simple 2.order kinetics - Brown
1903; theory that enzymes form complexes with the substrate - Henri
ca.1913; Henri’s experiments improved by Michaelis og Menton
1925; Briggs og Haldane reached the same expressions/equations
Enzyme kinetics Michaelis-Menton

14. E + S ES E + P 1 2 3 Michaelis-Menton: Balance on ES;k1 k2 k3 k4 ES
E + P
Balance on ES; 1
Reaction rate is dependent on
product formation; 2
Mass balance maintained; 3
Formation of ES from product is insignificant;

15. ES cannot be measured – rewrite equations in measureable parameters:
Assume steady state: 1. 2. 3. 4.
Michaelis constant / saturation constant 5. 6.
Reaction rate 7. If
We have vmax
Substitute into 5.

16. So what…? Rewrite equation: Michaelis-Menton Assumptions:
Rate
[S]
vmax
Assumptions:
only one substrate
initial rate must be extrapolated
concentration of E is constant
[E] > [S]o for steady state conditions
temp., pH, IS, are constant

17. Microbial growth kinetics:
Growth of cell mass:
Monod found that growth of microorganisms followed enzyme reactions:
Growth of microorganisms = f(substrate used)

18. In summary To design a reactor we need to know…
What components are to be transformed?
How do they react?
what is needed to make a reaction happen?
how fast does a reaction occur?
what factors affect / impact the reaction?
How can we express / model the reaction?