Figure 4. Experimental and simulated data of experiment number 2 for model validation.
In figure 4, the squares and circles indicate the measured concentrations of COH and CCI respectively. The continuous line shows the simulated values for COH concentration, surrounded by a shaded area which indicates concentration value ranges induced by the standard deviation ranges of the kinetic parameters. The dotted line indicates the simulated values for CCI, again surrounded by a value range induced by the standard deviations obtained in the kinetic parameters determination. The dashed line shows the overall molar balance equation which is unchanged during the course of a simulation due to the equimolar reactions, while the experimentally measured molar balances are indicated by the diamonds. The overall molar balance includes the components CAL and CAC.
As can be seen in figure 4, the intermediate concentration of COH increases for the first 65 h and then decreases after the organic cycle is connected and the lipase performs the esterification reaction, leading to a constant increase in CCI concentration. The mean deviations of the experimental values from the simulated values are 26.7 % and 20.8 % for COH and CCI respectively. CCI shows good agreements throughout the experiment, while COH concentrations vary towards the end of the experiment. Deviations of experimental and simulated COH values can also be observed during the first phase of the experiments at around 2000 min. In both cases, these deviations can be explained with the experimentally measured overall molar balance, which does not mathematically add up during those measurements. Especially in the last 800 min of the experiment, the experimentally determined molar balance varies: this can be due to dead volume in the organic cycle containing xylene, leading to a dilution of the samples or precipitation of the components CAL, COH, or CAC.
Throughout all six experiments we simulated for model validation, the mean deviation reached values of 26.0 % and 22.6 % for COH and CCI respectively. In literature, mathematical models for such complex multi-enzyme processes across phase boundaries in miniplant-scale and continuous operation cannot be found to the best of our knowledge. Examples of enzyme-based process modeling and simulation exist that do not validate the model with independent experimental data, or their validation is based on qualitative agreement between experimental and simulated values. Few examples exist for less complex and less time intensive reaction sequences that allow for a quantitative evaluation, giving deviations in the range of approximately 25 %, or of above 30 % for dynamic simulations. In the reactive zone filled with Novozym®435 of a technical-scale reactive dividing wall column operated with one reaction, Egger observed concentration deviations between experiments and simulations of up to 20 %. Therefore, it can be stated that the simulated values throughout all six experiments presented in this work lie in good agreement with the experimental results, proving the applicability of our model to the reactor setup. Using our validated model, process optimization can now thus be conducted without the need for further experimental runs.