Derived sensitivity densities in chemical kinetics: A new computational approach with applications

Partial differential equations for derived sensitivity densities corresponding to reaction/diffusion problems are developed. The elementary sensitivity densities do not appear explicitly in these equations thus showing that the derived sensitivity densities need not be "derived" from the elementary densities, but may be calculated directly. The derived sensitivities allow for studies of the interrelationship between chemical species concentrations at different locations in space and points in time. In a similar fashion the interactive role of system variables can be examined including the intriguing case of correlation between kinetic and transport effects for controlling the overall reaction. The method is demonstrated for a three-species linear reaction/diffusion problem for which an exact solution is available. The resulting sensitivity densities are found to have an enlightening physical interpretation which may be applied to more complicated reaction/diffusion problems.