(61x) Generalised Optimisation Framework for Process Synthesis and Intensification in the Equation-Oriented Environment

Equation-oriented (EO) process simulations and optimisations are widely used and critical enablers in the process synthesis and intensification. They have distinct advantages over sequential modular approaches, including efficient large-scale solvers and low-cost sensitivity analysis. However, many commercial process simulators that use EO approaches suffer various drawbacks. Except for gPROMS, other commercial process simulators such as Aspen Custom Modeller, have limited model formulation flexibility for MINLP problems. Even when the models are reformulated as relaxed NLP problems, simulations may fail due to the appearance of zero flows in some streams which are prevalent in the process synthesis and intensification problems. If the equipment is not selected, the material flow through this equipment naturally becomes zero. For some simple units like splitters and valves, zero flows do not affect the units. But in other, more complex units such as distillation columns, "disappearing" flows dispatch errors, causing the failure of simulation. Setting the lower bound of the flowrate to a small value (e.g., 1 × 10-²⁰) is not always working. The best approach to circumvent the zero-flow effect is to deactivate the associated constraints for calculating the mass and energy balance and the physical and chemical equilibrium. Generalized Disjunctive Programming (GDP) proposed by Yeomans and Grossmann (2000) succeeds in this regard by using Boolean variables to enforce the selection of a certain set of constraints representing the units, which provides an alternative to MINLP modelling and avoids numerical singularities in the nonlinear equations that are due to the disappearance of columns, sections of columns, and streams. Only GAMS algebraic modelling language supports GDP model implementation. However, GAMS is a generic optimisation platform and does not have any unit operation models, physical property database and flow sheeting capabilities. The accuracy of thermodynamics calculations may be compromised. In the meanwhile, elusive good initial points are required due to the highly nonconvexities of rigorous distillation models to foster the simulation convergence.

To address the aforementioned zero flow impact and convergence difficulty issues, we propose a novel superstructure-based optimisation framework consisting of two components: a novel mathematical model constructed in the commercial modelling software - Aspen Custom Modeller (ACM) and the associated solution algorithm. The model makes use of the "IF structure" syntax to activate certain sets of equations and addresses the typical simulation failure issues when the flowrate of streams entering the units becomes zero. The formulated mixed integer nonlinear programming (MINLP) problem is optimised by our previously developed feasible path-based branch and bound (FPBB) method (Liu et al., 2022), in conjunction with an improved sequential quadratic programming (SQP) algorithm to solve the relaxed nonlinear programming (NLP) problem at each node. Our framework has been applied to solve three complex distillation column synthesis problems for ternary and quaternary hydrocarbon mixture separations using rigorous tray by tray model from random starting points. The optimal configurations can be selected from the superstructure using the State Task Network (STN) formalism (Caballero and Grossmann, 2004) which considers all the sequencing alternatives from conventional sequences to fully thermally coupled distillation sequences. The results validate the capability of handling the issue of zero flows entering distillation column sections. They also demonstrate the superiority that no tailor-made initialisation procedure is required to foster the convergence to optimum. In the future, this novel framework can also be extended to more complex process synthesis and intensification problems using superstructure coupled with reactors and separators.

Yeomans, H. and Grossmann, I.E. (2000). Optimal Design of Complex Distillation Columns Using Rigorous Tray-by-Tray Disjunctive Programming Models. Industrial & engineering chemistry research, 39(11), pp.4326–4335.

Caballero, J.A. and Grossmann, I.E. (2004). Design of distillation sequences: from conventional to fully thermally coupled distillation systems. Computers & chemical engineering, 28(11), pp.2307–2329.

Chao Liu et al. (2022). Feasible Path-Based Branch and Bound Algorithm for Highly Nonconvex Mixed-Integer Nonlinear Programming Problems. Chemical engineering transactions, 94.