Week 5.1 - Compact Notation Derivation for a simple Mechanism

Assignment no. 04-Compact Notation Derivation for a simple Mechanism

Objective-Derive the reaction rate ODEs of simple reaction mechanism. To use the compact notation and find out the desired matrices

Reaction mechanism:

Where Kf= rate of forward reaction

Kr=rate of reversed reaction

The rate of change of concentration for O2:

The rate of change of concentration for CO:

The rate of change of concentration for CO2:

The rate of change of concentration for H2O:

The rate of change of concentration for O:

The rate of change of concentration for OH:

The rate of change of concentration for H:

Reaction are donated by i

Hence i from 1-4, reactions R1, R2, R3, R4

And species donated by j

j1=O2, j2=CO, j3=CO2, j4=H2O, j5=O, j6=OH, j7=H

compact notation matrix:

Stoichiometric coefficient, matrix for reactants side

Stoichiometric coefficient, matrix for product side

Difference of matrices

Net reaction for each reactions

Net production rate

Net production for each species

Final ODE system becomes:

This ODE system can be integrated by any integration package for example ODE45 of MATLAB and octave

note-please refer word file