(110g) Pseudo-Transient Flowsheet Optimization Using Inertial Manifolds

The computational optimization of process flowsheets (flowsheet optimization) remains challenging for many large-scale problems [1,2]. Pseudo-transient (PT) continuation was recently introduced as a framework for process simulation and optimization, and was shown to exhibit improved convergence properties compared the Newton-type methods currently in use in most software tools [2]. The PT concept involves converting a subset of the flowsheet equations to ordinary differential equations, resulting in a differential-algebraic equation (DAE) system. The resulting dynamics are not physically meaningful, but rather a numerical device that allows for computing the solution of the original algebraic model by simulating (integrating) the reformulated DAE system in pseudo-time to steady state. Due to the reliance on numerical integration techniques, the pseudo-transient approach is more computationally demanding than a Newton-type solver.

Recently, we introduced a new simulation approach for PT reformulations of process flowsheet models based on a hierarchical, multiply-singularly perturbed formulation of the PT dynamics [3]. The approach sequentially replaces subsets of differential equations with algebraic quasi-steady-state equations as the system approaches the inertial manifold defined by steady state of the respective dynamics. We demonstrated that this technique allows a seamless transition from PT integration to efficient, Newton-type algebraic solvers, and we proved that the method converges to the solution of the original algebraic system in a finite number of steps. Moreover, the time-scale decomposition of PT dynamics simplifies the definition of the PT model, as it does not require that the time constant for the dynamics in each time scale be specified explicitly.

In this work, we present a novel development whereby we apply the inertial-manifolds algorithm to flowsheet optimization of prototypical process flowsheets. We employ the feasible-path, time-relaxation-based optimization algorithm proposed for PT models [2]: a pseudo-transient model is used to initialize the process flowsheet model and relevant derivatives at each optimization iteration, while an optimization solver updates the decision variables between iterations. The bulk of the computation time required for process optimization is typically spent on initializing the flowsheet, with relatively little time required for steady-state algebraic solution and computation of gradients [4]. We demonstrate that PT simulation of the process flowsheet at each iteration can be substituted with a hybrid time integration/nonlinear algebraic solution using the inertial-manifolds approach, and investigate the computational benefits of accelerating PT simulation on flowsheet optimization.

References:

[1] Biegler, L. T., Grossmann, I. E., & Westerberg, A. W. (1997). Systematic methods for chemical process design.

[2] Pattison, R. C., & Baldea, M. (2014). Equation‐oriented flowsheet simulation and optimization using pseudo‐transient models. AIChE J., 60(12), 4104-4123.

[3] Tsay, C., & Baldea, M. (2019). Fast and efficient chemical process flowsheet simulation by pseudo-transient continuation on inertial manifolds. Comput. Methods Appl. Mech. and Eng., 348:935-953.

[4] Ma, Y., Luo, Y., Ma, X., Yang, T., Chen, D., & Yuan, X. (2018). Fast Algorithms for Equation-Oriented Flowsheet Simulation and Optimization Using Pseudo-Transient Models. Ind. Eng. Chem. Res., 57(42), 14124-14142.