Monotonic reformulation and bound tightening for global optimization of ideal multi-component distillation columns

Abstract

This paper addresses the problem of determining cost-minimal process designs for ideal multi-component distillation columns. The special case of binary distillation was considered in the former work [2]. Therein, a problemspecific bound-tightening strategy based on monotonic mole fraction profiles of single components was developed to solve the corresponding MINLPs (mixedinteger nonlinear problems) globally. In the multi-component setting, the mole fraction profiles of single components may not be monotonic. Therefore the bound-tightening strategy from the binary case cannot be applied directly. In this follow-up paper, a model reformulation for ideal multi-component distillation columns is presented. The reformulation is achieved by suitable aggregations of the involved components. Proofs are given showing that mole fraction profiles of aggregated components are monotonic. This property is then used to adapt the bound-tightening strategy from the binary case to the proposed model reformulation. Computational results are provided that indicate the usefulness of both the model reformulation and the adapted bound tighten

Relaxing the constant molar overflow assumption in distillation optimization

“…We analytically prove the aforementioned results by first repurposing the CMO proof of Mertens et al 36 to prove an ordering on stage-wise ratios of cumulative latent-heat fractions in the CHT framework (Theorem 1), which implies monotonicity of cumulative latent-heat fractions in the column (Remark 1). This then allows us to prove monotonicity of average latent heat (Proposition 1) and monotonicity of vapor and liquid molar flow rates in the column (Theorem 2).…”

On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments

“…Other well-documented examples of this approach are reported in [84]. Notably, similar design arguments can be easily applied to many systems, such as trays of binary distillation columns [94], where concentrations and temperatures profiles follow monotonic trends, and chains of chemical reactors, where masses, flow rates, and concentrations obey to mass conservation principle. iii.…”

Global optimization of distillation columns using explicit and implicit surrogate models

“…The row labeled by "reference" shows a reference solution obtained by rigorous global optimization of the corresponding ideal distillation column model. As shown in a previous work by Mertens et al (2018) these models can be solved to global optimality in a short amount of time using model reformulations and a problem specific bound tightening strategy. These methods are implemented in a SCIP 5.0 framework (Gleixner et al, 2017) and used to solve the rigorous column model to global optimality.…”

“…Exploiting problem-specific properties enables significant reductions of the computational effort, which was demonstrated in (Ballerstein et al, 2015) for binary ideal distillation and extended in (Mertens et al, 2018) to multicomponent mixtures. The monotonicity of concentration variables in distillation columns was exploited to systematically reduce the search space of the problem using specific model reformulations.…”

“…The first case study consists of two parts. In the first part, a globally optimal reference solution for an ideal multicom-ponent distillation process is calculated with the methods described by Mertens et al (2018). It is demonstrated that the new surrogate-based approach finds a solution close to a global optimum.…”