Optimal Control of Periodic Adsorption Processes

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Periodic adsorption processes are widely established in process engineering for the production of gases, fine chemicals or Pharmaceuticals, and novel uses involve the combination of adsorption and reaction processes. Characteristic for all these processes are traveling concentration fronts of different species in a solid fixed bed, and periodic switching between different types of operation. The dynamics of each phase can be modelled by instationary partial differential algebraic equations (PDAE) in one or two spatial dimensions, so that the overall system is described by periodically switched PDAE. Following start-up, a periodic attractor, or Cyclic Steady State (CSS), is finally reached and used for production. This CSS should ideally be optimal with respect to operational costs and product specifications, and recent years have seen the development of a variety of novel process operation variants to improve efficiency. Two of these are the processes to be investigated in Dortmund: the simulated moving bed (SMB) with variable inlet concentrations (ModiCon-SMB) studied in the group of Prof. Engell and the entirely novel fixed bed catalytic reactor with desorptive cooling (in the following called Desorptive cooling (DC)-Process ) in the group of Prof. Agar.Due to the large scale of the process models and due to their periodic nature, only few model based optimisation approaches exist and their use for large scale applications is limited by prohibitive computation times. Aim of the project is to develop efficient numerical methods for optimisation of periodic adsorption processes described by periodically switched large scale instationary PDAE. These methods shall combine novel reduced Newton type optimisation methods with a type of Picard iteration to cope efficiently with the periodicity constraints. The following features shall characterise our new methods:¿ a simultaneous optimisation framework is chosen in which the discretised model equations enter the optimisation problem as nonlinear constraints¿ only one cycle is simulated and optimised, and periodicity is imposed in form of additional constraints¿ a time-domain decomposition is used to handle the intermediate switching and the enormous amount of data¿ a novel reduced SQP framework being able to cope with inexact Jacobians is used to solve the nonlinear programming problem resulting after discretisation of model equations and controls¿ a mixed Newton-Picard scheme is used to treat the periodicity constraints efficientlyThe method development is driven by the requirements of the two processes in Dortmund. Final application aim of the project is the optimisation and experimental validation of the operating regime of the novel desorptive cooling (DC) process.