Week 5.1 - Compact Notation Derivation for a simple Mechanism

Compact Notation derivation for a simple mechanism

Objective:

To derive a compact notation for the below mechanism;

Reaction rate:

The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit time.

Compact Notation:

Since mechanisms may involve many elementary steps and many species, a compact notation has been developed to represent both the mechanism, e.g., R.1–R.4 . . . , and the individual species production rates. This helps the computer to solve the mechanism in a more efficient manner.

Rates of change of species in reactions;

Let the reactions be represented by i ;

i	Reaction
1
2
3
4

Let the species present in the reactions be represented as follows;

j	species
1	CO
2	O2
3	CO2
4	O
5	H2O
6	OH
7	H

No.of moles of species j in reaction i on the reactants side;

here, rows represent j and columns represent i

No.of moles of species j in reaction i on the products side;

here, rows represent j and columns represent i

Difference between product and reactant side stoichiometric matrix,

Net reaction rate:

where, kfi, kri - the rate of forward and backward reaction of 'i' th reaction respectively

Xj - concentration of 'j' th species

Net reaction rates of the mechanism are as follows;

Net Production rate:

It is the summation of the product of the reaction rate and stoichiometric matrix.

Production rates of all species are as follows;

=

Now,

This provides the reaction rates of each and every species. Generally, it is a stiff ODE system where one of the species changes its concentration rapidly while others change at a much slower rate.