(708d) Optimal Scheduling of Parallel Distillation Column System with Continuous-Time Formulation

Optimal scheduling of continuous processes with parallel units has been extensively investigated. According to how time is represented, the existing scheduling formulations can be classified into discrete time and continuous time formulations. Early attempts in modeling scheduling problems relied on the discrete-time approach that divides the time horizon into a known number of periods of equal duration.^1,2 However, the discrete-time representation has two inherent shortcomings, namely, formulation size and solution accuracy. ³ Therefore, some researchers resorted to the continuous-time approach, in which the time horizon is partitioned into time periods of variable durations that are determined by optimization. Although the continuous-time approach can reduce model size and improve solution accuracy, most previous studies were in favor of the discrete-time approach due to modeling and computational challenges in dealing with the continuous-time formulation.

In this work, we consider a distillation process that consists of parallel distillation columns, which can be operated in different modes with different yields and energy costs. The products may be delivered continuously, at predefined time points, or at any time points within given time windows. The goal is to minimize the operating cost while satisfying the demand and storage constraints. In a discrete time formulation, the transition between two operating modes can be readily modeled over the predefined time grid, but in a continuous time formulation, it is challenging because the time grid is also a decision that the optimization needs to determine. The other challenge in the problem is to guarantee demand satisfaction over the entire scheduling horizon. In a discrete time formulation, demand is only addressed at a finite number of time points (either on the predefined time grid or not⁴), and in a continuous time formulation, additional variables and constraints are needed to establish material balance equations for all time points over the scheduling horizon.

We propose a continuous time formulation that overcomes the two challenges. In this formulation, the sequence-dependent transition behavior of distillation columns is formulated in a new way such that it requires fewer binary variables than an approach in the literature.⁵ For computational efficiency, the MINLP formulation is transformed into a MILP formulation through exact linearization. We will show that the final MILP formulation is smaller in size and computationally more efficient than the discrete time formulation that we previously developed. ⁶

Reference:

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[5] Lei Shi, Yongheng Jiang, Ling Wang, Dexian Huang. A Continuous-time formulation for refinery production scheduling problems involving operational transitions in mode switching. Chinese Journal of Chemical Engineering 24 (2016) 1020–1031.

[6] Yingyan Luo, Qi Zhang, Lingyu Zhu, Xi Chen. Optimal operation of parallel distillation systems with multiple product grades: An industrial case study. Computers and Chemical Engineering 111 (2018) 210–224.