I have "tested" (i.e. simulated) the bubble column method for kinetic analysis using hydrogenation of 2,4,4-trimethyl-1-pentene (TMP1) and 2,4,4-trimethyl-2-pentene (TMP2) to 2,2,4-trimethyl-pentane (isooctane) in cyclohexane as the reaction system. The kinetics of this system was studied by M. Lylykangas at Helsinki Univ. of Technology. His PhD dissertation (2004) is available [ISBN 951-22-6912-0 (print), 951-22-6913-9 (pdf, available at http://lib.hut.fi/Diss/)]. Lylykangas used a cstr sytem with a fixed catalyst bed to obtain the kinetics for several catalysts. I used the Langmuir-Hinshelwood model that he obtained for the cobalt catalyst in my laboratory simulation. For the bubble column, I assumed that the catalyst particles would be small enough to eliminate internal diffusion resistance. The catalyst support screen in the cstr study required larger particles.
Lylykangas reported that the isomerization reaction for the pentenes was not a major reaction. I have ignored that reaction also in the present work, but I plan to study its effect later.
The Langmuir-Hinshelwood model used is shown below:
where the r's are for the two reactions and the C's are the liquid concentrations of TMP1, TMP2 (the i compounds) and hydrogen. Note that the adsorption terms are assumed to be the same for both reactions.
In order to separate the reactions, I conducted "experiments" with only one of the organic reactants at a time. For example, with TMP1 as a reactant, the k1 and K_TMP1 (TMP1 rate constant and TMP1 adsorption coefficient, respectively) were determined.
The hydrogen adsorption term reported by Lylykangas is insignificant compared to the other terms in the denominator. If it had been significant, it would not have been possible to determine its value in a single run because the hydrogen concentration is constant. Runs at several pressures could be used to determine the hydrogen inhibition effect by determining the effect on the overall rate constant. In my experiments at 10, 20, 30 and 40 bar, the estimated rate constant changes were minor when using the Lylykangas hydrogen adsorption term for the "experimental data" but ignoring the term in the estimation phase.
Once the parameters had been obtained from the two runs (at 20 bar, 65 C), a run with mixed feed was studied. The adsorption constants obtained from the previous runs were fixed and the reaction rate constants were re-estimated to see if they changed with the presence of the other pentene present on the catalyst. The results of these estimates are shown in the table below.
Lylykangas stated that the adsorption coefficients were independent of temperature. Therefore, the activation energies for k1 and k2 can be easily determined by two or more additional experiments at different temperatures.
In summary, seven experiments could be used to determine this system with the calorimetric method. However, preliminary experiments are also needed to insure that the gas adsorption is in the kinetic controlled region. Also, the temperature controller needs to be checked and the catalyst concentration needs to be adjusted to obtain the heat release needed for parameter estimation without exceeding the condenser capacity. Most of these concerns can be addressed in the experimental design, but verification runs are still needed.
Cyclohexane is not highly volatile and I was prepared to change the solvent, but it appears that it would work. Lower boiling solvents reduces the flow rate needed for the control gas (hydrogen), so a study of solvents may be in order.
The results of this study are very encouraging. The parameter estimates for a complex rate expression were extremely good and the system was otherwise very realistic. In this case, the model used in the estimation phase was exact. Next, I will look at alternative models, including power law models, of this same system.
I have no laboratory, so these simulation studies are my only means of developing this method. Please contact me if you would like to apply this method.