(246g) Dynamic Operability Analysis Employing Kriging-Based Surrogate Models

In recent years, steady-state operability analysis has been developed to optimize the process design while considering the controller’s ability to take the system from one steady state to another. Dynamic Operability then further extended the analysis to transient operations, being employed to solve minimum-time optimal control problems for setpoint tracking and disturbance rejection cases [1]. A new notion of Dynamic Operability could also be seen as a time-variant, discretized counterpart of steady-state operability, in which dynamic input-output mappings would be obtained as time progresses [2]. However, this dynamic mapping task can be computationally expensive due to the increase in number of variables and thus space dimensionality when each predictive time step is added to the calculation. In this work, Kriging-based models (also known as Gaussian Process Regression) [3] are proposed as surrogates to the first-principles or process simulation-based dynamic models for Dynamic Operability [1], [2], [4]. The use of such surrogate models has potential of reducing the computational effort of process operability calculations, while generating results that are accurate when compared to the first-principles dynamic models that are typically used.

To achieve this goal, Gaussian Process approximations with a Nonlinear Autoregressive Model with Exogenous Inputs (GP-NARX) [5] are investigated for dynamic operability calculations. The proposed framework using surrogate model responses is benchmarked against the current dynamic operability examples for operability mapping computations involving nonlinear models. In addition, the Kriging-based dynamic models are employed to measure the Dynamic Operability Index (dOI) online for the first time.

As a case study to illustrate the proposed approach, a membrane reactor for direct methane aromatization conversion is addressed [6]. This case study is modeled using spatial discretization of the partial differential equations needed to describe the process. The dynamic mapping employing a first-principles dynamic model is compared to the mapping of a Kriging-based model. The results show the accurate prediction capabilities of the GP-NARX structure when compared against the nonlinear first-principles model-based dynamic operability, which makes the proposed approach a feasible candidate for dynamic operability calculations. This approach can also be employed to enhance the design and intensification of complex dynamic chemical and energy systems, ultimately reducing operating costs and increasing process efficiency.

References

[1] D. Uztürk and C. Georgakis, “Inherent Dynamic Operability of Processes: General Definitions and Analysis of SISO Cases,” Industrial & Engineering Chemistry Research, vol. 41, pp. 421-432, 2002.

[2] W. R. d. Araujo, F. V. Lima and H. Bispo, “Dynamic and Statistical Operability of an Experimental Batch Process,” Processes, vol. 9, 2021.

[3] C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning, Cambridge, MA: MIT Press, 2006.

[4] C. Georgakis, D. Uztürk, S. Subramanian and D. R. Vinson, “On the operability of continuous processes,” Control Engineering Practice, vol. 11, pp. 859-869, 2003.

[5] K. Juš, Modelling and control of dynamic systems using Gaussian process models, 1 ed., Springer, 2016.

[6] J. C. Carrasco and F. V. Lima, “Novel operability-based approach for process design and intensification: Application to a membrane reactor for direct methane aromatization,” AIChE Journal, vol. 63, pp. 975-983, 2017.