Adjoint-based estimation and optimization for column liquid chromatography models

• Derivation of the adjoint method for computing parameter derivatives for a wide range of column liquid chromatography models.
• Assembly of the adjoint problem using the existing block-structure of the simulation.
• Application to SMA parameter determination of ternary model protein mixture achieved a speed-up of 8 over a finite difference approximation.

Simulation and optimization of chromatographic processes are continuously gaining practical importance, as they allow for faster and cheaper process development. Although a lot of effort has been put into developing numerical schemes for simulation, fast optimization and estimation algorithms also are of importance. To determine parameters for an a priori defined model, a suited approach is the inverse method that fits the measurement data to the model response.This paper presents an adjoint method to compute model parameter derivatives for a wide range of differentiable liquid chromatography models and provides practical information for the implementation in a generic simulation framework by the example of ion-exchange chromatography.The example shows that the approach is effective for parameter estimation of model proteins and superior to forward sensitivities in terms of computational effort. An optimization of peak separation in salt step elution demonstrates that the method is not restricted to inverse parameter estimation.