Nonlinear model reconstruction by frequency and amplitude response for a heterogeneous binary reaction in a chemostat

Here we present an analysis of a binary heterogeneous reaction in a chemostat for the particular case of reagents with unequal mass transfer coefficients. For fast irreversible kinetics, there are two potential steady states—the dispersed phase is preferentially populated by one reagent and essentially depleted of the other. The selection of which steady state occurs depends on the operating parameter which is the concentration ratio σσ of the slower (B) to the faster (A) transferring reagent in the feed stream. The demarcation between these operating regimes is the critical value of this ratio:σcrit=KA+KAKBKB+KAKB,where KiKi is the mass transfer coefficient of reagent ii. Although the concentrations of each species in each phase are piecewise linear in σσ, the fact of the crossover of operating regimes can be exploited for the inverse problem of kinetic parameter estimation by introducing an oscillation in the feed concentration with a protocol for frequency and amplitude response. The mass transfer coefficients can be estimated by operating conditions σσ on either side of σcritσcrit, permitting the estimate of σcritσcrit, which is shown to have the greatest sensitivity to the intrinsic chemical kinetics, even when fast and nearly irreversible. Assimilating data from a single experiment conducted at σ=σcritσ=σcrit, reliable estimates are made even with classically undersampled estimates of the Fourier coefficients for the fundamental and first harmonic frequencies according to the Nyquist–Shannon sampling theorem.