Algebraic system identification for a homogeneous catalyzed reaction: application to the rhodium-catalyzed hydroformylation of alkenes using in situ FTIR spectroscopy

An algebraic system identification procedure has been developed and tested on a single semibatch homogeneous rhodium-catalyzed alkene hydroformylation. The goal of this study was to determine the primary algebraic structures which describe the catalytic system in terms of observables. The sole experimental input to the identification is a matrix of in situ spectroscopic data A and a matrix of initial moles N0. Subsequently, we determine (1) the number S of observable species and their characteristic pure-component spectra a, (2) the moles of all observable species N, (3) the number R of reactions present and their reaction stoichiometries υ, and finally (4) the extent of reactions ξ. Meaningful extraction of such algebraic system information (an inverse algebraic problem) is a prerequisite to subsequent detailed kinetic modeling (an inverse kinetics problem). The methodology is successfully applied to this homogeneous transition-metal-catalyzed hydroformylation reaction. The methodological development has clear implications for exploratory studies of new catalytic systems (so-called “gray” reaction systems), in which only in situ spectroscopic reaction data and knowledge of the initial amounts of reagents put into the reactor/system are available.