(246h) Probabilistic Process Design Under Uncertainty Via Dynamic Optimization

Process flowsheet optimization involves finding design specifications and operating conditions that maximize the economic benefit and/or energy efficiency; it relies on mathematical process models. The parameters involved in such models are often subject to considerable uncertainty, owing to external factors such as fluctuating market conditions or internal factors such as variable equipment efficiency, and insufficiently characterized thermodynamic and kinetic properties [1]. It is therefore critical to ensure that these parameter uncertainties are taken into account during design optimization [2].

In its most general form, the problem of optimization under uncertainty involves uncertain parameters drawn from continuous probability distributions and is infinite-dimensional. Solution approaches generally rely on the discretization of the stochastic variables and the creation of multiple scenarios, to approximate the expected value of the objective function [3] [4]. In the case of many uncertain parameters or when a fine discretization is desired, scenario-based approaches can quickly grow computationally intractable. To some extent, this has been mitigated by reformulating scenario-based problems as dynamic optimization programs, whereby scenarios are arranged chronologically in a pseudo-time domain rather than solved simultaneously [3] [5]. These “sequential” methods have been shown to have significant memory usage benefits compared to “simultaneous” multi-scenario approaches, as well as to present practical benefits in terms of reducing the number of flowsheet initialization calculations.

In this work, we propose abandoning the scenario-based approach altogether, instead treating the uncertain parameters of a process flowsheet as time-varying disturbance variables acting on a (static or pseudo-transient [6]) process model over a pseudo-time domain. The parameter uncertainty space is then mapped using the intersections of continuous parameter trajectories, rather than via a finite set of discrete scenarios. We illustrate the significant computational benefits of the proposed strategy with two case studies: a dimethyl ether plant and the Williams-Otto process.

References

[1] M Baldea and P Daoutidis. Dynamics and nonlinear control of integrated process systems. Cambridge University Press, Cambridge, UK, 2012.

[2] LT Biegler and IE Grossmann. Retrospective on optimization. Comput. Chem. Eng., 28(8):1169-1192, 2004.

[3] S Wang and M Baldea. Identification-based optimization of dynamical systems under uncertainty. Comput. Chem. Eng., 64:138-152, 2014.

[4] Y Zhu, S Legg, and CD Laird. Optimal design of cryogenic air separation columns under uncertainty. Comput. Chem. Eng., 34(9):4104-4123, 2010.

[5] RF Gutierrez, CC Pantelides, and CS Adjiman. Risk analysis and robust design under technological uncertainty. Comput. Aided Chem. Eng., 21:191-196, 2006.

[6] RC Pattison and M Baldea. Equation‐oriented flowsheet simulation and optimization using pseudo‐transient models. AIChE Journal, 60(12):4104-4123, 2014.