Incremental model identification for homogeneous systems – A comparison

The identification of reaction kinetics involves the determination of a model structure (reaction stoichiometry, rate laws for all reactions) and its corresponding parameters from experimental data. An incremental identification approach for determining the kinetics of homogeneous reaction systems from transient concentration measurements has been developed in previous work [1, 2]. This approach decomposes the identification task into a sequence of sub-tasks that include the identification of the rate laws for every reaction and of the corresponding rate parameters. The approach is closely related to the “differential method”, because reaction rates are estimated through numerical differentiation of concentration measurements. An alternative incremental identification approach based on the “integral method” has been proposed recently [3]. It uses the concept of extent of reaction and proceeds in two steps: (i) the computation of extents from measured concentrations of all or a subset of the reacting species and, optionally, from the inlet and outlet flowrates, and (ii) for each reaction individually, the estimation of rate parameters from the corresponding extent using the integral method. The objective of this work is to compare the performance of the two types of incremental approaches with respect to their ability to discriminate between two or more competing rate laws and to estimate the rate parameters with high accuracy. In particular, we investigate the propagation of errors from the concentration measurements to the rates or extents and finally to the estimated kinetic parameters. The main features are illustrated via the startup of a continuous stirred-tank reactor. A well-known criterion is used to discriminate between competing rate laws [4]. It is shown that the (integral) extent-based methods is in many aspects (e.g. for low-frequency noisy concentration measurements) superior to the (differential) rate-based method, if the final, simultaneous correction step is avoided in the latter: it better discriminates between competing kinetic laws and it results in parameter estimates with tighter confidence intervals while less meta-parameters need to be adjusted. However, the rate-based method can be computationally advantageous for multiple-reaction systems when all kinetic laws are uncertain.