Parameter Identification in Reaction Systems Under Inlet Composition Uncertainty

Reaction systems are usually modeled using conservation laws described by mass and energy balance equations. These equations represent different phenomena acting on the system, namely reaction, and transport dynamics [1]. The particular structure in the balance equations has been exploited to decouple the process dynamics in variants and invariants of reaction by means of a diffeomorphic linear transformation. The resulting dynamics is described in terms of extents [2]. This decomposition approach has been extended to include a more general representation of the reaction systems, such as systems with multiple phases, mass transfer, non-isothermal dynamics (see [3,4,5,6]). There has also been substantial effort in using this decomposition for control, and state and parameter estimation purposes. In particular, the estimation of kinetic parameters has been addressed via the extent representation using via incremental estimation or graph-based techniques [7,8]. Extent-based incremental parameter estimation refers to a two-step estimation procedure. First, the concentration/mole measurement is transformed into extent-based variables to decouple the effects. Secondly, the parameters affecting each dynamics are computed separately, which can lead to better parameter identifiability conditions. However, the extent-based incremental identification has been applied mainly for batch reaction systems. This limits the applicability of the incremental identification approach for semi-batch or continuous operations. Additionally, a frequent problem in semi-batch and continuous process operations is the variability of the feedstock or raw material used. This poses a problem when applying the linear transformations to compute the extents for these two cases. Furthermore, the subsequent kinetic parameter estimation is not reliable due to the incorrect extent calculation as a consequence of the uncertainty in the inlet composition.

In this work, we consider the incremental identification approach for semi batch and continuous operations. We also analyze the effect of the inlet composition uncertainty in the construction of the extent linear transformations. This analysis allows us to quantify, under some metric, the deviation of the extents from the nominal ones. Furthermore, we propose an optimization problem to reconstruct the uncertainty based on concentration/mole data, and provide the conditions to guarantee a reliable estimation in terms of the number of measurements. Using the estimated uncertainty, the true extents are computed to estimate the kinetic parameters. Finally, the approach is illustrated in semi-batch, and CSTR reactors.

Acknowledgments: This work has been done within the INSPEC project with the support of the Institute for Sustainable Process Technology (ISPT).

References

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