Synthesis of heat-integrated distillation sequences with mechanical vapor recompression by stochastic optimization

Highlights

• MVR-HIDSs are synthesized.

• Green electricity partially replaces the fossil fuel in MVR-HIDSs.

• MVR-HIDSs have obvious energy saving and lower cost.

• Our models can get the optimal MVR-HIDS with high probabilities.

Abstract

A method of synthesis of heat-integrated distillation sequences with mechanical vapor recompression (MVR-HIDSs) is proposed based on stochastic optimization in this study. The purpose is to introduce heat pump operation, which can be driven by green electricity, to distillation sequencing as a way of altering stream temperatures to increase the chance of heat integrations. Two types of MVR-HIDSs, namely the vapor recompression heat-integrated distillation sequences (VR-HIDSs) and bottom flashing heat-integrated distillation sequences (BF-HIDSs), are considered for the synthesis separately. To illustrate the proposed method, a case for separating five-component alcohol mixture is solved by the proposed method. The results show that the incorporation of the MVR can provide effectively higher economic efficiency compared with the traditional optimal heat-integrated and thermal coupled distillation sequences. The proposed method makes it possible to synthesize distillation sequences that use green electricity to partially replace the fossil fuel based thermal energy to reduce CO₂ emission.

Introduction

Distillation has been the most widely used industrial separation technic with energy consumption up to 40–60% in the process industries (Humphrey and Siebert, 1992; Sholl and Lively, 2016), while its thermodynamic efficiency is usually less than 10% (Jana, 2010; Kiss et al., 2012). The synthesis of distillation sequences is an important and effective method to improve the energy and economic efficiency for multicomponent separation processes due to the significant economic differences between different separation sequences. And various models and methods for synthesis of distillation sequences constitute one of major achievements in chemical process systems engineering.

The studies of synthesis of distillation sequences started with simple models of sharp-split sequence problems (Qian and Lien, 1995; Thompson and King, 1972; Stephanopoulos and Westerberg, 1976). And then, increasingly more comprehensive modeling methods were proposed to realize the synthesis of distillation sequences with sharp or nonsharp-splits (Yeomans and Grossmann, 2000; Zhang and Linninger, 2006; Wang et al., 2016), and heat integration and/or thermal coupling were taken into account to obtain more significant reduction in energy consumption for multicomponent distillation separation (Yeomans and Grossmann, 1999b; Caballero and Grossmann, 2004, 2011, 2013; Zhang et al., 2018).

In addition to considering possible heat integration and thermal coupling in optimal synthesis of distillation sequence, mechanical vapor recompression (MVR) is also a practical energy saving technology, which can realize the energy reutilization by consuming a certain amount of compression work to augment the energy level of the system (Jana, 2014). MVR is often used in distillation processes, mostly appearing as heat pump distillation (Díez et al., 2009; Luo et al., 2015; You et al., 2016), but rarely considered simultaneously in the synthesis of distillation sequences with the other options like heat integration and thermal coupling. One of the reasons underlying the exclusion of the MVR from synthesis of distillation sequences is that its economic benefit may not be necessarily significant when the use of traditional thermal energy is relatively cheaper than the use of electricity, which is often accompanied by additional capital cost for compressors as well. However, in the context of global warming and under the pressure of carbon emission reduction, it becomes quite attractive to use green electricity to partially or even totally replace thermal energy that is produced by fossil fuel for distillation separation. Therefore, it becomes important to include MVR in the structure alternatives in the synthesis of distillation sequences to increase the use of electricity and limit the use of the traditional thermal energy. Another reason of not considering the MVR in distillation sequencing is that the size of the search space of the synthesis problem would increase dramatically if the MVR option is included and result in a large scale mixed-integer nonlinear programming (MINLP) problem that is difficult to model and solve effectively. These are why the application of MVR has been studied only for existing distillation configurations to improve energy efficiency and most for binary mixture separations, and, as a result, the problem of synthesizing MVR distillation sequences still remains open and challenging. For solving large scale complex distillation sequencing problems, several methods have been developed.

Mathematical programming is one of the most widely used methods, the synthesis problem is usually formulated as a mixed-integer linear programming (MILP) or MINLP problems based on superstructure, and deterministic algorithms were often used to solve the optimization problem (Biegler and Grossmann, 2004). Leeson et al. (2017) proposed a method for preliminary design of sharp heat-integrated distillation sequences based on MILP model. Yeomans and Grossmann (1999a) introduced a nonlinear generalized disjunctive programming method to overcome the difficulty in formulating the synthesis of sharp heat-integrated distillation sequences into an MILP problem. Caballero and Grossmann (2014) presented a MILP a two-level superstructure to solve a complex problem of synthesis thermally coupled distillation sequences. As demonstrated by many authors, the MINLP model for distillation sequencing is combinatorial in nature and sometimes non-convex. Gooty et al. (2019) solved an MINLP problem they proposed for thermally coupled distillation sequences using a branch-and-bound algorithm and decomposition strategy (Novak et al., 1996; Floudas and Gounaris, 2008), in fact, however, large-scale combinatorial problem is inevitable and a real challenge for all the deterministic mathematical programing methods to find a global optimum, even with the most advanced solvers available today.

The matrix method is another effective approach for the synthesis of distillation sequences. Shah and Agrawal (2010) proposed a matrix method for representing all basic configurations (distillation sequence with N–1 columns) and feasible thermally coupled distillation sequences. Nallasivam et al. (2016) and Jiang et al. (2019) applied this method to generate all distillation sequences for a given mixture, and conducted the optimization using enumeration based approach. Hou and Luo (2019) expanded the matrix method for distillation from configurations with N–1 to those with less than N–1 columns to include more advanced sequence configurations. The advantage of both the original matrix method and the improved matrix method is that it is easy to generate sequences, however, they are a kind of enumeration-based approach and heat integration was not considered in the synthesis of distillation sequences.

Compared with the above methods, stochastic algorithms can overcome the computational difficulties of deterministic optimization algorithms, as they can search the optimal solution automatically based on the stochastic optimization strategy in an evolutionary process, which allows stochastic optimization algorithms to efficiently solve the mathematical model with considering the non-linearity and non-convexity. The stochastic optimization algorithms can avoid numerous local optima and obtain the global optimum with high probability (Wang et al., 2008). Stochastic optimization methods have been shown powerful for solving large scale complex optimization problems for distillation sequence synthesis (Wang and Li, 2008; Jain et al., 2012). In a recent attempt, made by Zhang et al. (2021), a novel stochastic optimization method based on simulated annealing (SA) and particle-swarm optimization (PSO), namely SA-PSO method, was developed for automatic synthesis of large-scale nonsharp-split distillation sequence considering heat integration and thermal coupling. An efficient coding method was proposed in this method and enabled effective representations for all the alternative sequences possibly containing simple and complex distillation columns, heat integrations, and thermal couplings. The SA was used in an outer circle to explore sequence configurations by varying the codes and the PSO was used in an inner loop to optimize a sequence identified by the SA in each circle. The most promising feature of the SA-PSO is that, due to its coding technology and stochastic optimization strategy, it can easily incorporate energy-saving technologies such as heat integration and thermal coupling into the optimization framework, so that the continuous operating variables of columns and the discrete variables corresponding to distillation sequences and thermally coupled structures can be optimized simultaneously.

In the present work, a method of the synthesis of heat-integrated distillation sequences with mechanical vapor recompression (MVR-HIDSs) is proposed based on stochastic optimization method. In order to optimize MVR structures, a potential compressor ratio for each distillation column is introduced as a continuous optimization variable. The synthesis problem is formulated as an implicit MINLP problem, and solved by the SA-PSO algorithm to minimize the total annual cost (TAC) of the system. An example case of synthesizing five-component MVR-HIDSs is presented to validate the proposed method and demonstrate the necessity of involving MVR in synthesis of distillation sequences. The result proved that the distillation sequences with MVR have better economic efficiency compared with those sequences with only heat integration or thermally coupling considered, and our models can get the optimal sequence with high probabilities in a reasonable computing time.