Instantaneous limits of reversible chemical reactions in presence of macroscopic convection

Chemically reacting systems frequently involve fast reversible reactions, additional slow reactions as well as mass transport due to macroscopic convection. In this situation, the passage to infinite reaction speed is a means to reduce the complexity of the reaction kinetics and to avoid the need for explicit values of the rate constants. Thereby the large stiffness of the original system of differential equations is also removed. In the present paper this instantaneous reaction limit is studied for systems with independent fast reversible reactions, where the rate functions are given by mass-action kinetics. Under realistic assumptions the limiting dynamical system is derived and convergence of the solutions is obtained as the rate constants tend to infinity. The proof is based on Lyapunov functions techniques and exploits the structure of rate functions that results from mass-action kinetics. This approach is complementary to the quasi-steady-state approximation which is often applied in chemical engineering. The differences are illustrated by means of a classical enzyme–substrate reaction scheme.