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.