Fast and accurate parameter sensitivities for the general rate model of column liquid chromatography

A fast and accurate solver for the general rate model is extended for computing sensitivities that describe the impact of small parameter changes on the simulated chromatograms. Parameter sensitivities are required by many optimization algorithms and are useful for understanding how chromatograms depend on specific system properties or operating conditions. They are efficiently computed with arbitrary precision by integrating a forward sensitivity DAE system that is derived from the original DAE system. The involved partial derivatives are either manually derived or computed by algorithmic differentiation. This approach is demonstrated to be more robust and faster for realistically sized problems, as compared to the traditional finite difference approach. Sensitivities are computed not only with respect to intrinsic model parameters, such as diffusion coefficients and isotherm parameters, but also with respect to parameters in the boundary concentrations, such as the slope of an elution salt gradient. The extended solver is part of the Chromatography Analysis and Design Toolkit (CADET).