An Illustration of Quasi Steady State

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BACKGROUND CONCEPTS

The text developed the mathematical formulas for the exact and QSSA solutions to the following set of simple elementary reactions.

(1)

We will be running a simulation program that changes the value of k₂ with the value of k₁ held fixed. This simulation will allow us to observe the concentrations of A, B and C that result from an exact solution to the set of design equations for a batch reactor (dc_j/dt = R_j, where c_A(0) = c_A0),

		(1)
		(2)
		(3)

compare the concentration of C predicted by the exact solution to that predicted by the QSSA solution,

(4)

and view the error between the exact and QSSA solutions for the concentration of C

(5)

as we change the value of k₂.

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THE SIMULATION

1. Run the simulation using the default setting of k₂ = 10 min^-1. Notice that you can see the concentration of B go through a maximum and then decrease to zero. You will also notice that you can observe distinctly different curves for the exact and steady state solutions for C. Finally the error is quite large (approximately 10 % after one time constant) for this relative ratio of rate constants.

2. Now increase the value of the rate constant k₂. You should notice that the curve for the concentration of B does not appear above zero for k₂ = 1000 min^-1, and that it is hard to distinguish between the exact and QSSA solution. Even though the concentrations look close there is a difference as revealed in the error plot. This error quickly decreases below 1%.

3. Keep increasing the value of k₂ and notice how the error gets smaller and smaller, and does so almost instantly. This should give you a feel for what you would look for in terms of relative rates to feel comfortable invoking the QSSA.