Motivated by the threat of climate change, engineers are developing new power system technologies with increased efficiencies and reduced CO2 emissions. Flowsheet optimization methods help reduce technology deployment times and carbon capture cost by systematically exploring different design configurations and manipulating operating conditions to improve one or more performance metrics (e.g., cost of electricity). However, applying traditional flowsheet optimization tools to power systems requires new methodologies for embedded multi-scale models of complex subsystems, such as reactors or boilers. In this paper, we present recent work on a trust region optimization algorithm and its application to oxycombustion system design, in which the fuel (e.g., coal, biomass, etc.) is combusted in a N2 lean environment, producing a flue gas rich in CO2(70 – 85%) for economical sequestration.
In contrast to previous systems analysis of the oxycombustion system, we are modeling the entire system in an equation-based framework. First and second derivative calculations from the algebraic model allow the use of efficient large-scale nonlinear programming algorithms. With these methods, sensitivity information is easily obtained from the multipliers at the optimum rather than having to perturb design parameters. In addition, the framework allows simultaneous optimization of the oxycombustion subsystems (e.g., air separation unit, steam cycle, CO2 processing unit and compression train, etc.) rather than analyzing the subsystems in isolation. We have demonstrated this approach by optimizing the sub-ambient separations and their accompanying multistream heat exchangers for oxycombustion power systems1,2.
Optimization of the steam cycle in an oxycombustion process requires special care. Flue gas recycle is used to replace N2 in air by mainly CO2 and H2O to regulate the flame temperature and the heat transfer profile. As a consequence, boiler performance correlations for air fired (N2 atmosphere) boilers are not applicable, and discretized partial differential equation based numerical models are preferred. This presents a challenge for optimization with state-of-the-art nonlinear programming algorithms, which assume that accurate derivative information is cheaply available. In this work, we use a hybrid zonal boiler model that considers detailed 3D radiation behavior3.
A common approach for including computationally expensive black box functions/simulations in nonlinear programming algorithms is through surrogate models. However, experience has shown that no matter how much care is placed into constructing these models, the optimizer is very good at exploiting the error to artificially improve the objective. We are developing a trust region algorithm4that is capable of adaptively managing surrogate model error, with provable convergence to critical points of the true problem (with the full, detailed model). The trust region filter algorithm has been applied to both air-fired and oxy-fired steam cycle case studies to integrate the boiler model as well as external function calls to obtain steam table based thermodynamics. The air fired results confirm that our methodology matches with expected designs from the literature, while the oxy-fired results provide insight on key oxycombustion design decisions.
- Dowling, A. W., & Biegler, L. T. (2015). A framework for efficient large scale equation-oriented flowsheet optimization. Computers & Chemical Engineering, 72, 3–20.
- Dowling, A. W., Balwani, C., Gao, Q., Biegler, L.T. (2015), Optimization of Sub-ambient Separation Systems with Embedded Cubic Equation of State Thermodynamic Models and Complementarity Constraints. Computers & Chemical Engineering(in press).
- Ma, J., Dowling, A., Eason, J., Biegler, L., & Miller, D. (2014). Development of First Principle Boiler Model and Its Reduced Order Model for the Optimization of Oxy-combustion Power Generation System. In 39th International Technical Conference on Clean Coal & Fuel Systems.
- Eason, J. P., and Biegler, L. T. 2015. Reduced model trust region methods for embedding complex simulations in optimization problems. In 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering.