44300-G9
Dynamic Optimization of Process Systems Using Molecular Simulations
The research activities pursued by our group can be briefly described as focusing on the development of algorithms for the design of complex chemical processes. Our motivation comes from a wide variety of chemical processes for which available descriptions come be in the form of microscopic evolution rules. The use of such atomistic simulations pose significant challenges both from analysis and design point of view. These difficulties can be attributed in part to the unavailability of closed-form models to describe the microscopic process evolution. We are also interested in complex transport-reaction process systems that are characterized by events that take place at disparate time and length scales. These processes are modeled by either partial-differential or multiscale systems which consist of coupled continuum and discrete descriptions. The solution of such problems is challenging owing to large computational requirements of the multiscale process model.
In the proposed research we have laid the theoretical foundation for the development of approximate coarse timesteppers (ACTs) that can be specifically tailored for the solution of previously computationally intractable optimization problems. ACTs circumvent in part the problems of complexity and computational requirements that are associated with stochastic integration during optimization, by acting as a computational "intermediate" between the search algorithm and the stochastic simulation thus allowing us to formulate and efficiently solve complex optimization problems using standard algorithms. The developed solution methodologies were applied to a variety of processes, including thin film deposition processes, an example relevant to the microelectronics industry, and representative catalytic oxidation processes where optimal inlet concentration profiles are computed in order to guide the microscopic system to the desired objective.
The successful construction of the ACTs hinges on the properly chosen identification of macroscopic variables that accurately describe the microscopic process evolution. During the first year of this project, we developed a mathematically robust and consistent method that identifies a minimum set of ``coarse'' variables that accurately describe the dominant behavior of a deposition surface during thin-film growth under adsorption and surface diffusion. These parameters can be subsequently employed to develop the ACTs for optimization as well as low-order state-space models for controller synthesis as an alternative to computationally expensive kMC simulations.
During the second year of the project, the problem of dynamic optimization for multiscale systems comprising of coupled continuum and discrete descriptions was considered. As stated previously, the solution of such problems is challenging owing to large computational requirements of the multiscale process model. This problem was addressed by developing a multiscale ACT. This was achieved by combining order reduction techniques for dissipative partial-differential equations (PDEs) with adaptive tabulation of microscopic simulation data. The multiscale process optimization problem was subsequently solved using standard search algorithms. The proposed method was applied to two representative catalytic oxidation processes where optimal inlet concentration profiles were computed to guide the microscopic system from one stable stationary state to another stable stationary state.
Once these processes have been designed, a further requirement is the design of controllers to ensure seamless process operation. That implies the design of feedback controllers for controlling thin film microstructure, during thin film deposition for our first example and the reactivity of the catalytic surfaces in the second example. The objective was to develop a computationally tractable online process model identification which takes into account the change in the underlying process dynamics as process traverses different regions in the variable state space.
During the second year, we considered the problem of online system identification and nonlinear control of microscopic processes. The unavailability of closed-form models or accurate low-order models to describe the process evolution renders the standard model-based controller design methodologies inappropriate. Two distinct methodologies were developed for on-line system identification and feedback control of a) microscopic processes and b) processes described by nonlinear PDEs. We successfully illustrated the applicability of the proposed methodologies on catalytic reactor with a simplified surface reaction scheme that describes the dynamics of CO oxidation by O<sub>2</sub> on a Pt catalytic surface. In the former case a a Kinetic Monte Carlo (KMC) realization of the catalytic surface was employed, while in the later case an PDE model describing the energy conservation of the catalytic surface was used.
The project partially funded the research activities of three students and the PI. It was also used to finance the contributed presentations listed at the end of this report and the publication costs associated with the referenced journal and peer-reviewed conference proceedings papers. The funded research has so far led to one book, one PhD thesis, three journal publications, seven refereed conference proceedings papers, and numerous invited and contributed presentations. Furthermore, one journal manuscript and one conference proceeding manuscripts are currently in press.
