Reduced Order Model Based on Principal Component Analysis for Process Simulation and Optimization † Yi-dong Lang, ‡,§ Adam Malacina, ‡,§ Lorenz T. Biegler,* ,‡,§ Sorin Munteanu, | Jens I. Madsen, ⊥ and Stephen E. Zitney § Department of Chemical Engineering, Carnegie Mellon UniVersity, Pittsburgh, PennsylVania 15213, Collaboratory for Process and Dynamic Systems Research, National Energy Technology Laboratory, Morgantown, West Virginia 26507, Ansys, Inc., Lebanon, New Hampshire 03766, and Ansys, Inc., Morgantown, West Virginia 26505 ReceiVed NoVember 11, 2008. ReVised Manuscript ReceiVed January 12, 2009 It is well-known that distributed parameter computational fluid dynamics (CFD) models provide more accurate results than conventional, lumped-parameter unit operation models used in process simulation. Consequently, the use of CFD models in process/equipment co-simulation offers the potential to optimize overall plant performance with respect to complex thermal and fluid flow phenomena. Because solving CFD models is time-consuming compared to the overall process simulation, we consider the development of fast reduced order models (ROMs) based on CFD results to closely approximate the high-fidelity equipment models in the co-simulation. By considering process equipment items with complicated geometries and detailed thermodynamic property models, this study proposes a strategy to develop ROMs based on principal component analysis (PCA). Taking advantage of commercial process simulation and CFD software (for example, Aspen Plus and FLUENT), we are able to develop systematic CFD-based ROMs for equipment models in an efficient manner. In particular, we show that the validity of the ROM is more robust within well-sampled input domain and the CPU time is significantly reduced. Typically, it takes at most several CPU seconds to evaluate the ROM compared to several CPU hours or more to solve the CFD model. Two case studies, involving two power plant equipment examples, are described and demonstrate the benefits of using our proposed ROM methodology for process simulation and optimization. 1. Introduction Steady-state process simulators typically solve systems of nonlinear equations consisting of mass and energy balances, thermodynamic relationships, and phase and chemical equilib- rium calculations. However, process simulations typically do not consider equipment geometry or fluid dynamics inside the equipment. For example, the unit operation model of a continu- ous stirred tank reactor (CSTR) ignores the influence of fluid dynamics and assumes that the contents of the reactor are perfectly mixed. Additionally, unit operation models in process simulators do not consider operating parameters related to mixing and fluid flow, such as the shaft speed in a CSTR. Instead, computational fluid dynamics (CFD) is required to focus on the microscale phenomena within process equipment items. In process design, analysis, and optimization, it is not uncommon that engineers are interested not only in process design but also in equipment design, because the equipment affects the overall process performance significantly and also has a potentially large impact on capital cost and therefore process economics. For example, shaft speed affects CSTR conversion and yield; overall chemical process performance, nozzle design, and dense mul- tiphase flow are critical for determining gasifier exit conditions and overall power plant performance; and multiphase flows are essential for spray dryers in food-processing applications. Moreover, striking an economic balance between mechanical equipment cost versus performance loss from poor fluid flow and heat and mass transfer is essential to explore at the design stage. For advanced process design, analysis, and optimization, we consider here the use of CFD models within a process/equipment “co-simulation”. 1,2 Since 2000, co-simulation technology has been developed by the Department of Energy’s (DOE) National Energy Technology Laboratory (NETL) and its research collaborators. 3,4 The team has developed the advanced process engineering co-simulator (APECS), a co-simulation software framework that integrates CFD-based equipment models with process simulators using the process industry CAPE-OPEN (CO) software standard. 1 With APECS, one can integrate CO- compliant equipment models based on CFD (e.g., FLUENT) † Disclaimer: Any opinions, findings, conclusions, or recommendations expressed herein are those of the author(s) and do not necessarily reflect the views of the Department of Energy (DOE). * To whom correspondence should be addressed. Fax: (412) 268-7139. E-mail: lb01@andrew.cmu.edu. ‡ Carnegie Mellon University. § National Energy Technology Laboratory. | Ansys, Inc., Lebanon, NH. ⊥ Ansys, Inc., Morgantown, WV. (1) Zitney, S. E. CAPE-OPEN integration for CFD and process co-simulation. Proceedings of the American Institute of Chemical Engineers (AIChE) 2006 Annual Meeting, 3rd Annual U.S. CAPE-OPEN Meeting, San Francisco, CA, Nov 12-17, 2006. (2) Zitney, S. E.; Syamlal, M. Integrated process simulation and CFD for improved process engineering. Proceedings of the European Symposium on Computer Aided Process Engineering-12 (ESCAPE-12); Grievink, J., van Schijndel, J., Eds.; The Hague, The Netherlands, May 26-29, 2002; pp 397-402. (3) Sloan, D. G.; Fiveland, W. A.; Osawe, M. O.; Zitney, S. E.; Syamlal, M. Demonstration of coupled cycle and CFD simulations over a LAN. Clearwater Coal Conference, 2005. (4) Sloan, D.; Fiveland, W.; Zitney, S. E.; Osawe, M. O. Plant design: Integrating plant and equipment models. Power Mag. 2007, 151,8. Energy & Fuels 2009, 23, 1695–1706 1695 10.1021/ef800984v CCC: $40.75  2009 American Chemical Society Published on Web 02/19/2009