On the statistical sensitivity analysis of models for chemical kinetics

The differential equations governing the propagation in time of the sensitivity matrix for a mathematical model given by a system of ordinary differential equations are derived. These equations are used to perform a statistical sensitivity analysis of models for chemical reactors. The behavior of the sensitivities at equilibrium is analyzed. It is shown that the sensitivity equations for linear kinetics may be solved using an analytic representation. The numerical solution of these equations is discussed, and illustrative examples are presented. The lognormal distribution is presented as being representative of errors in rate constants.