(518c) Closed-Loop Control for Uncertainty Mitigation and Disturbance Rejection in Cryogenic Air Separation Unit Startup

Current market dynamics, such as increased variability in electricity pricing, incentivize the intermittent operation of cryogenic air separation units (ASUs), which consume large amounts of electricity. One of such intermittent operation policies is shutting down ASUs during extended periods of high electricity pricing, particularly if the plant startup is fast or economically optimal (Chen et al., 2010; Miller et al., 2008). Adoption of such a policy will result in an increased number of startups, beyond those following shutdowns due to maintenance and equipment failure. However, startup of ASUs as practiced in industry faces key challenges, in particular: (i) long startup time which can last several hours (Miller et al., 2008; Zhu, et al., 2011); (ii) limited revenue generation; and (iii) limited automation (Caspari et al., 2020). However, despite its economic and operational impact, studies on ASU startup in the literature are scant.

Simulation and optimization of ASU startup require dealing with challenges resulting from complex thermodynamics, discontinuous behavior, and process dynamics. Thus, most of the studies on ASU startup present modelling approaches for dynamic simulation of these rigorous models. Miller et al. (2008) consider a multiproduct ASU with four distillation columns, and present a nonsmooth formulation for modelling startup discontinuities. Dynamic simulation is used to demonstrate the time saving potential of inventorying select columns with liquid from shutdown. Kender et al. (2019, 2021) develop digital twins of different ASUs through utilization of a pressure-driven approach. Their high-fidelity model simulates the entire operation range from warm startup (i.e., startup from ambient conditions) through steady state to shutdown. The dynamic optimization studies on ASU startup handle startup discontinuities by applying smoothing approximations, such as a smoothed Fischer-Burmeister formulation (Caspari et al., 2020) and sigmoidal functions (Quarshie et al., 2023a & 2023b). These open-loop control studies use quadratic target-tracking objective functions (Caspari et al., 2020; Quarshie et al., 2023a) and time and profit related objective functions (Quarshie et al., 2023b).

Despite the fact that quantifiable improvements have been demonstrated using open-loop control strategies (Quarshie et al., 2023a & 2023b), these gains may be lost in the presence of model uncertainty and disturbances. This study sets out to evaluate the potential benefit of closed-loop control framework for ASU startups in response to model uncertainty and disturbances. An economic model predictive control (EMPC) strategy is developed using a dynamic startup model based on our earlier contribution (Quarshie et al., 2023a). The model uncertainty results in plant-model mismatch and is addressed through parameter estimation. As the closed-loop strategy being used solves dynamic optimization problems recursively, solution time is paramount. To that end, the following approaches are utilized toward efficient computation: (i) a PI control-based parameter estimation approach (van Lith et al., 2001; Hedengren et al., 2007); (ii) a shift initialization strategy (Diehl et al., 2009); (iii) a rolling horizon approach for a batch-like processes; and (iv) the collocation-based model reduction (Cao et al., 2016) technique. The dynamic optimization problem of the EMPC is converted into a large-scale nonlinear programming (NLP) problem (resulting in over 900,000 variables) using complete discretization, and the NLP is solved using IPOPT (Wächter and Biegler, 2006). We do our implementation using the Python-based CasADi package (Andersson et al., 2018). We demonstrate the profit recovery potential of the EMPC based formulation through two industrial relevant case studies: mitigation of a measured disturbance and addressing unmeasured parameter uncertainty. This paper will highlight the startup discontinuity modelling, present details on the EMPC framework including the shift initialization strategy, the rolling horizon approach for a batch-like processes and the PI control-based estimation approach, and show results from the case studies.

References

J. A. E. Andersson, J. Gillis, G. Horn, J. B. Rawlings, M. Diehl, CasADi – A software framework for nonlinear optimization and optimal control, Mathematical Programming Computation (2018).

Y. Cao, C. L. E. Swartz, J. Flores-Cerrillo, and J. Ma. “Dynamic modeling and collocation-based model reduction of cryogenic air separation units”. In: AIChE Journal 62.5 (2016), pp. 1602–1615

A. Caspari, S. R. Fahr, C. Offermanns, A. Mhamdi, L. T. Biegler, and A. Mitsos. “Optimal start-up of air separation processes using dynamic optimization with complementarity constraints”. In: Computer Aided Chemical Engineering 48 (2020), pp. 1–8

Z. Chen, M. A. Henson, P. Belanger, and L. Megan. “Nonlinear Model Predictive Control of High Purity Distillation Columns for Cryogenic Air Separation”. In: IEEE Transactions on Control Systems Technology 18.4 (2010), pp. 811–821

M. Diehl, H. J. Ferreau, and N. Haverbeke. “Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation”. In: Nonlinear Model Predictive Control: Towards New Challenging Applications. Ed. by L. Magni, D. M. Raimondo, and F. Allgöwer. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009, pp. 391–417

J. D. Hedengren, K. V. Allsford, and J. Ramlal. “Moving Horizon Estimation and Control for an Industrial Gas Phase Polymerization Reactor”. In: 2007 American Control Conference. 2007, pp. 1353–1358

R. Kender, B. Wunderlich, I. Thomas, A. Peschel, S. Rehfeldt, and H. Klein. “Pressure-driven dynamic simulation of startup and shutdown procedures of distillation columns in air separation units”. In: Chemical Engineering Research and Design 147 (2019), pp. 98–112

R. Kender, F. Kaufmann, F. Rößler, B.Wunderlich, D. Golubev, I. Thomas, A. M. Ecker, S. Rehfeldt, and H. Klein. “Development of a digital twin for a flexible air separation unit using a pressure-driven simulation approach”. In: Computers & Chemical Engineering 151 (2021), p. 107349

J. Miller,W. L. Luyben, and S. Blouin. “Economic incentive for intermittent operation of air separation plants with variable power costs”. In: Industrial & Engineering Chemistry Research 47.4 (2008), pp. 1132–1139

J. Miller, W. L. Luyben, P. Belanger, S. Blouin, and L. Megan. “Improving agility of cryogenic air separation plants”. In: Industrial & Engineering Chemistry Research 47.2 (2008), pp. 394–404

A. W. K. Quarshie, C. L. E. Swartz, P. B. Madabhushi, Y. Cao, Y. Wang, and J. Flores-Cerrillo. “Modeling, simulation, and optimization of multiproduct cryogenic air separation unit startup”. In: AIChE Journal 69.2 (2023), e17953

A. W. K. Quarshie, C. L. E. Swartz, Y. Cao, Y. Wang, and J. Flores-Cerrillo. “Dynamic Optimization of Multiproduct Cryogenic Air Separation Unit Startup”. In: Industrial & Engineering Chemistry Research (2023) 62(27), 10542–10558.

P. F. van Lith, H. Witteveen, B. H. L. Betlem, and B. Roffel. “Multiple nonlinear parameter estimation using pi feedback control”. In: Control Engineering Practice 9.5 (2001), pp. 517-531A. Wächter, L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Mathematical Programming 106 (2006) 25–57

Y. Zhu, S. Legg, and C. D. Laird. “A multiperiod nonlinear programming approach for operation of air separation plants with variable power pricing”. In: AIChE Journal 57.9 (2011), pp. 2421–2430