The synthesis and intensification of chemical processes have been widely researched, with distillation structures and their connectivity being given in advance using optimization algorithms based on mathematical programming or stochastic optimization. For example, heat integration in intensified distillation in order to separate multicomponent mixtures [1], reactive distillation ^[2][3][2,3], and membrane-assisted distillation [4], among other distillation-based intensified processes, have been considered. Previous works used superstructure representations comprising several unit operations such as distillation columns, heat exchangers, decanters, or membranes. A superstructure is a representation in which all possible interconnections among process units are included; this development has been a significant breakthrough in process synthesis, design, and optimization, because it has made it possible to depart from experience-based heuristics and thermodynamic approaches, and propose more systematic ways to assess any possible flowsheet alternatives simultaneously [5]. Nevertheless, there is an intrinsic limitation when superstructures are composed of unit operations [6]. Thus, one way to overcome this limitation is to depart from the idea of unit operations and synthesize processes based on phenomenological approaches.

Several process synthesis and intensification approaches based on phenomenological analysis have been proposed over the last few decades. This section summarizes the achievements of several research groups, and the next section addresses our PS+I framework in detail.

Gani and coworkers have proposed a phenomena-based process synthesis method consisting of phenomena building blocks (PBBs). This methodology presents systematic identification, generation, and screening of phenomena-based flowsheet options. It was applied for the reactive distillation process to produce isopropyl acetate from acetic acid and isopropanol, and the solution achieved a 99% conversion of isopropanol, with energy requirements 90% less than those of the conventional process [7]. This combined intensification–synthesis methodology was applied to produce methyl acetate through a membrane-assisted process [8]. Kongpanna et al. proposed a PBB framework for dimethyl carbonate production with CO₂ utilization consisting of three stages: synthesis, design, and innovation. The proposed processes included process intensification alternatives such as membrane-assisted and reactive distillation and membrane reactors [9]. Garg et al. generated innovative and sustainable designs of chemical and biochemical processes using the PBB framework in which intensified processes such as reactive distillation, divided-wall distillation, crystallization-membrane, distillation-membrane, etc. attained savings of more than 20% in economic and environmental contexts, compared to the conventional cases [10]. The PBBs were represented in a superstructure model for a reactor network comprising arbitrary combinations of non-isothermal reactor models. The transesterification of propylene carbonate with methanol was taken as a case study, and the results prove the benefits of the proposed method over predefined unit operations [11]. In a recent work, Garg et al. summarize the most relevant works using the PBB framework to generate novel and intensified processes [12].

Papalexandri and Pistikopoulos proposed the Generalized Modular Representation Framework (GMF) for process synthesis [13]. They proposed multipurpose mass and heat-transfer modules as the framework’s building blocks, as represented by a superstructure. This framework was applied for acetone recovery, benzene alkylation, ethylene glycol production, and heat integration. The GMF was applied for the separation of a benzene/toluene/o-xylene mixture based on aggregated physical models comprised by a superstructure, which then were reformulated as a mixed-integer nonlinear programming (MINLP) problem. The most energy-efficient distillation column sequence was the Petlyuk column, attaining 30% energy savings [14]. Later, the GMF was applied to synthesize a NOx reactive absorption process, obtaining the most economical design, meeting the design targets, and leading to economic and environmental benefits [15]. The GMF has also been applied to the water/ethanol extractive distillation process, in which the entrainer selection, synthesis, and intensification were considered in a single mixed-integer nonlinear optimization (MINLP). The optimal result from the synthesis problem was validated through process simulation in Aspen Plus [16]. Later, a multiperiod GMF was proposed to ensure that the designs could be operated under specified ranges of uncertain parameters to produce methyl tert-butyl ether. Also, risk assessment, accounting for equipment failure frequency and consequence severity, was incorporated into the synthesis problem to derive inherently safer designs, which were validated through process simulation [17].

Hasan and coworkers proposed a block-based superstructure of blocks arranged in a two-dimensional grid as an alternative method for synthesizing chemical processes. The synthesis problem was reformulated as an MINLP problem for the purposes of generating automated flowsheets and their optimization. Three reactor/separator systems were studied to validate the proposed method. The first case study investigates the hydrodealkylation of the toluene process used to produce benzene, and the second one involves four components: A and B are used as raw materials to produce C, which reacts further in a second reaction to obtain the final product, D. Thus, five separations and three reaction alternatives are available. The third case is the reaction of methane and CO₂ to produce value-added products, such as methanol. In all cases, the resulting processes were intensified and showed a better performance in terms of energy consumption and cost. Nevertheless, solving MILP problems and reducing the feasible region posed difficulties [18]. A later work proposed a Process Synthesis, Integration, and Intensification approach to produce ethylene glycol by reacting ethylene oxide and water, although a further reaction between the ethylene oxide and ethylene glycol produces diethylene glycol. The intensified solution was a reactive distillation producing mainly ethylene glycol and some diethylene glycol. However, these components were separated in a distillation column [19]. The same method was extended for synthesizing and intensifying membrane separations, such as separating nitrogen from methane to produce fuel-grade methane or in the methanol/water separation through vapor permeation. In both cases, membrane-based processes can offer significant benefits in terms of economics and sustainability, and they are potential alternatives which could replace conventional energy-intensive adsorption and distillation-based processes [20].

Manousiouthakis and coworkers proposed an Infinite Dimensional State-Space (IDEAS) framework for synthesizing chemical processes. The IDEAS process representation considers all possible connections among a network of unit operations, and it can solve a convex problem because it can be solved as a linear programming (LP) problem. Thus, due to their great network flexibility, the optimal solutions often include nonintuitive and counterintuitive process units [21]. This approach has been applied to synthesize multi-pressure distillation of homogeneous azeotropic mixtures [22] and to intensify reactive separator networks [23].

Hasebe and coworkers have extended the IDEAS framework to the separation of binary [24] and ternary [25] mixtures, including two important features: (1) relaxation of liquid compositions and (2) solution interpretation to obtain intensified and realistic distillation processes. This approach has been applied for synthesizing and intensifying reactive distillation processes [26] and separating heterogeneous azeotropes [27].

Our proposed Process Synthesis and Intensification (PS+I) framework is a further extension of the IDEAS framework and a continuation of the latest works from Hasebe and coworkers. The PS+I framework takes advantage of the following key novelties: (1) it departs from the unit operation concept, and instead, it connects “functional modules” as building blocks that represent physical and chemical phenomena resulting in intensified processes; (2) the synthesis problem is solved without any a priori knowledge or preset connectivity among equipment; and (3) although the synthesis problem solution will result in an unknown process structure, after interpretation, it is known and post-optimized. Thus, the resulting process is intensified.

In our approach, we have formulated the synthesis problems as LP problems and as mixed-integer linear programming (MILP) problems, while other approaches, such as the PPB and GMF, have used nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP). In our proposed framework, intensive properties (e.g., composition, and molar enthalpy) are input as parameters in the optimization problem, and the optimization variables are extensive properties (e.g., mass and energy flows).

The original aspect and main contribution of this entry is the description of the synthesis and intensification of distillation-based processes using preestablished information relating to the distillation process structure, which means that their connections are not needed. Thus, it does not consider any structural assumption, which is why the proposed approach can derive novel, counterintuitive distillation structures. For example, a combination of conventional distillation columns will never result in a Petlyuk column. In addition, the mathematical formulation is relatively simple and compact, yet powerful enough to solve even millions of equations. Also, the post-optimization step helps to refine the solution obtained from solving the synthesis problem.