466670 Kinetic Parameter Estimation Including Uncertainty Under Mass Transfer Limited Conditions
Kinetic models are commonly used to describe chemical processes (1) to allow gaining insight in the underlying reactions, and (2) for process optimisation. In the former application, the model needs to be calibrated using experimental data. The main aim of such a calibration exercise is to obtain kinetic parameter values which are independent from process settings such as the mixing speed, the reactor geometry, etc. This can only be achieved if the reactor is not suffering from mass transfer limitations and, hence, no major spatial heterogeneities exist. This “homogeneous” reactor behaviour is aimed for by mixing. However, it is often not possible to have nonlimiting mass transfer, and thus it becomes impossible to use kinetic models to estimate the intrinsic parameter values using only a kinetic model and assuming a CSTR. However, by coupling computational fluid dynamics (CFD) with the kinetic model, it is possible to account for these spatial heterogeneities and calibrate the kinetic model.
Recently, Verbruggen et al. (2016) [1] coupled a Langmuir model with CFD, and stated that they were able to accurately retrieve the intrinsic kinetic parameter values. This approach proved to be very powerful, but requires the evaluation of the CFD model at multiple parameter values to find the minimum of the objective function, and thus is computationally very demanding. When overcoming the computational burden, however, it might seem that the problem of estimating the intrinsic parameter values has been solved. But this is not the case as one can only prove that the obtained parameter values really represent the intrinsic parameter values when the measurements are not noise corrupted and an unlimited amount of such data is available (the socalled theoretical identifiability). In reality, only a limited amount of noisecorrupted measurements is available, and thus the reliability of the estimated parameter value will depend on the measurement uncertainty and the experimental design (e.g. the sampling locations and the initial substrate concentrations). As a consequence, only parameters with a sufficiently important (and uncorrelated) impact on the model predictions will be estimated properly. Therefore, it is important to assess the uncertainty of the parameter estimates in such a calibration context. This is often referred to as practical identifiability analysis [2].
It is clear that even for parameter estimations performed with CFD, assessing the parameter uncertainty remains an important aspect, since uncertain parameter estimates will yield models with low predictive power. The application of uncertainty analysis for CFDbased kinetic model calibration has not yet been performed to our knowledge. A new methodology is developed, and is applied in silico to a secondorder reaction (Eq. (1)) for a microreactor where the enzyme is immobilised at the wall (Figure 1).
Figure 1: Microreactor (W=200 µm, L=0.10 m) with enzyme immobilised at the walls.

 (1)

The corresponding kinetic model is given in Eq. (2), and was implemented in OpenFOAM 2.2.2:

 (2)

The uncertainty of k_{cat} was estimated as a function of the “optimal” k_{cat }value, using the likelihood confidence region method [3]. Since the parameter uncertainty is affected by the mass transfer, the sampling locations, and measurement noise, a Monte Carlo strategy was used to determine the impact of these degrees of freedom on the parameter uncertainty. The use of the developed methodology showed that in this case k_{cat}, could be properly estimated when using the CFDbased model calibration, even when mass transfer limitations were high. Moreover, it allows estimating the uncertainty of the parameter values.
References
[1] Verbruggen, S.W., Keulemans, M., van Walsem, J., Tytgat, T., Lenaerts, S., Denys, S., (2016) CFD modeling of transient adsorption/desorption behavior in a gas phase photocatalytic fiber reactor, Chem Eng J, 292:4250
[2] Dochain, D., Vanrolleghem, P.A., (2001) Dynamical Modelling and Estimation in Wastewater Treatment Processes
[3] Seber G.A.F., Wild C.J., (1989) Nonlinear Regression
See more of this Group/Topical: Computing and Systems Technology Division