Search

In this work, a hybrid semi-parametric modelling framework implemented using mixed integer linear programming (MILP) is used to extract (coupled) nonlinear ordinary differential equations (ODEs) from process data. Applied to fed-batch (bio) chemical reaction systems, unknown (or partially known) system connectivity and/or reaction kinetics are represented using a multivariate rational function (MRF) superstructure. The MRF’s are embedded within an ODE framework which is used to incorporate known system model characteristics. Using derivative estimation, the ODEs are decoupled and a MILP algorithm is then used to identify appropriate constitutive model terms using sparse regression. Superstructure sparsity is promoted using a L 0 – pseudo norm penalty, i.e. the cardinality of the model parameter vector, enabling the simultaneous yet decoupled identification of the parameters and model structure discrimination. Using simulated data, two case studies demonstrate a principled approach to hybrid model development, distilling unknown elements of (bio) chemical model structures from process data. [ABSTRACT FROM AUTHOR]

The manual determination of chemical reaction networks (CRN) and reaction rate equations is cumbersome and becomes workload prohibitive for large systems. In this paper, a framework is developed that allows an almost entirely automated recovery of sets of reactions comprising a CRN using experimental data. A global CRN structure is used describing all feasible chemical reactions between chemical species, i.e. a superstructure. Network search within this superstructure using mixed integer linear programming (MILP) is designed to promote sparse connectivity and can integrate known structural properties using linear constraints. The identification procedure is successfully demonstrated using simulated noisy data for linear CRNs comprising two to seven species (modelling networks that can comprise up to forty two reactions) and for batch operation of the nonlinear Van de Vusse reaction. A further case study using real experimental data from a biodiesel reaction is also provided. [ABSTRACT FROM AUTHOR]

Abstract: This paper demonstrates how, in principle, a chemical reaction mechanism (reaction network) can be inferred using relatively simple systematic mathematical and statistical analyses of experimental data obtained from chemical reactors. This method involves specifying a global ordinary differential equation (ODE) model structure capable of representing an entire set of possible chemical reactions. Mathematical and statistical tests are then used to reduce the ODE model structure to a subset of reactions. Finally, a model rationalisation procedure, relying on exploiting the basic rules of reaction chemistry, is used to obtain a consistent set of reactions which are combined to give the overall reaction network. The identification procedure is demonstrated for pure batch operation with a worked example using simulated noisy data from an extended Van de Vusse reaction network consisting of five species and four elementary reactions [Van de Vusse, J.G., 1964. Plug-flow type reactor versus tank reactor. Chemical Engineering Science 19, 994–997]. A further case study of a semi-batch (fed batch) system using simulated data from a simplified biodiesel system, with six chemical species involved in three elementary reactions, is provided. It is shown that the method is able to correctly identify the underlying structure of the network of chemical reactions and provide accurate estimates of the network rate constants. [Copyright &y& Elsevier]

Abstract: The oxidative carbonylation of phenylacetylene was studied in order to determine the production distribution and reaction conditions which result in oscillatory versus non-oscillatory behaviour. Unambiguous identification of the products and their distribution was undertaken, after which, it was found that reaction conditions which result in oscillatory behaviour produce high conversions, and more selective product distribution. [Copyright &y& Elsevier]