The principal methods for reaching the maximum process efficiencies are classified into three extensive categories: thermodynamic methods, heuristic methods, and optimization methods [
9]. Thermodynamic methods provide means for analyzing systems, while heuristic and optimization methods provide means for improvements. However, a solution is the most constructive, when all three methods are used conjointly.
2.1.1. Thermodynamic Methods
Thermodynamic approaches consist of evaluating a process quality according to the laws of thermodynamics. Heat integration and exergy analysis are the most powerful and frequently used thermodynamic approaches for process improvement [
10].
Pinch analysis, is a method that aims to identify the possibilities of heat recovery in complex processes. This method was mainly developed in the early 1970s by Linnhoff and his colleagues [
11] who developed a graphical method that enabled the calculation of the minimum energy required of a process and the design of its heat exchanger network HEN. The main tool employed in the pinch analysis was the composite curve graph showing simultaneously the hot streams and cold streams processes, the heat transfer potential between them, and the heat recovery bottleneck, as well as the external minimum energy supply required for heating noted HMER (hot minimal energy required) and for cooling CMER (cold minimal energy required). The purpose of energy integration was to take advantage of the potential interactions among the process units to maximize heat recovery and thus minimize the energy consumption; the HEN synthesis manifests as the key step to implement the identified synergies for a given process. It ensures economically optimal design that enables reaching the minimum energy targets computed by the pinch analysis [
12].
Pinch analysis has been adopted by several researchers and engineers in different sectors. Beninca et al. [
13] have optimized an olefin plant following the traditional pinch analysis to evaluate the possibilities of reducing heat requirements and to identify the network of heat exchangers that makes it possible to achieve these possibilities. In refining, attempts have been made to improve the thermodynamic efficiency and energy integration of the distillation sequence. Linhoff and Dunford [
14] applied the principles of the Pinch method to find the most appropriate heat recovery devices for a distillation column in a process.
Therefore, the pinch method is simple, visual, powerful, systematic, general, and capable of minimizing the overall heat consumption of the process by optimally matching the needs and the availabilities in it. However, restricted to thermal flows and temperature parameters, this method presents a non-integrated approach between the HEN and the rest of the process (including pressures and compositions) [
15]. Moreover, pinch analysis satisfies the thermal energy demand of a process by finding corresponding internal availabilities but it is unable of doing the inverse. This means that having certain energy availabilities in a process, pinch analysis cannot search for ways to valorize them in order to possibly improve the process.
The second powerful process improvement method is exergy analysis. The exergy concept is defined as the maximum amount of work achieved when a material is brought to a state of thermodynamic equilibrium with its surrounding by means of reversible processes [
16]. Unlike the energy balance, based on the energy conservation law, the exergy balance is based on the energy quality degradation law stating that, even if there is a quantitative conservation, the quality between the various forms of energy varies [
17]. The fundamentals of exergy analysis can be found in Moran and Shapiro’s book [
18]. The exergy invested in entering the system is partially destroyed internally because of the systems’ irreversibility. The remaining available exergy is then split between the useful exergy and the lost, not valorized exergy.
The application of exergy analysis in energy systems and industrial processes has been widespread in recent decades because it provides the opportunity to reduce or eliminate sources of inefficiency. Among the works carried out, one quotes Khan et al. [
19] who used the exergy analysis to locate the irreversibilities taking place in the unit operations of the cycle of the propane pre-cooling in a system of liquefaction of natural gas. Having underlined the importance of the operating conditions of the various stages of evaporation, its exergy study made it possible to determine the best operating scenario. Tchanche et al. [
20] developed an approach to evaluate the performance of different organic Rankine cycle configurations using several exergy-based criteria. Tirandazi et al. [
21] and Mehrpooya et al. [
22] studied a multi-stage refrigeration cycle with propane as a refrigerant. They calculated the exergy efficiency and the losses in the main equipment of the cycle and showed that the heat exchanger and expansion produce the most losses. Similarly, Thengane et al. [
23] conducted an exergy-efficient study of a hydrogen production process to compare and determine whether saving in chemical exergy or thermal exergy reduces exergy destruction in the process. They demonstrated through a case study that the recovery of chemical exergy is more beneficial. The exergy analysis may indicate only the potential for improvement of a given process, but it cannot indicate if this improvement is practically feasible or the means to achieve it. Indeed, the exergy analysis compares the actual performance with the ideal one. In reality, some exergy losses are inevitable and no improvement can reduce them. Feng and Zhu [
24] proposed a new method that divides exergy losses into avoidable losses and unavoidable losses in order to identify practical and economic potentials for improvement.
This method is an auditing tool that analyzes industrial processes and evaluates them based on their exergy balance; it allows quantifying and tracking inefficiencies in order to improve them. In addition, this method takes into account all process variables, including temperatures, pressures, and compositions. On the other hand, the conventional exergetic analysis is criticized for serving only as an evaluation indicator and not as an improvement indicator. This approach lacks the systematic aspect and is dependent on the engineers reading and interpretation of exergy balance.
This limitation led to the development of an advanced exergy-based analysis by Tsatsaronis and his colleagues [
25,
26,
27,
28] in which the exergy destruction as well as the associated costs and environmental impacts are split into avoidable/unavoidable and endogenous/exogenous parts. Based on the avoidable parts and on the effect of parameter variations on component interactions, potential and strategies for improvement are revealed. The main role of an advanced exergy analysis is to provide engineers with accurate and additional information useful for improving the design and operation of energy conversion systems.
2.1.2. Heuristic Methods
By definition, a heuristic method is an approach that re-uses knowledge from previous experiences with comparable problems to find solutions. It is defined as an “aid to learning, discovery, or problem-solving by experimental and especially trial-and-error methods” [
29]. These methods improve the conceptual exploration and allow reducing the solution time and cost. However, being drawn from practice, there is a risk that the knowledge will not be of use in the future, because there is no effective or structured way to access it. A number of previous works have embarked in the task of offering a structured approach towards the incorporation of heuristics in the product design process. SCAMPER [
30] proposes a set of seven heuristics with the purpose of generating new alternatives from the reconfiguration of existing solutions. When it comes to using common sense guidelines based on the second law, Sama and his colleagues [
31,
32,
33,
34] introduced 21 rules reflecting a thermodynamicist’s perception to obtain the best structure of a process, minimizing the overall irreversibility. These rules are not replaced by a systematic methodology and it is left to the engineers’ knowledge to improve the structure.
More generally, the main inconvenience of using heuristic-based approach alone is that they may be restricted to typical and suboptimal solutions.
2.1.3. Optimization Methods
An optimization problem is the search for the minimum or maximum of a given function. Numerical optimization is used in energy and exergy efficiency process improvement methods in order to minimize the consumption or maximize the efficiency.
In the field of energy integration, and given the complexity of manually building the optimal network of heat exchangers for multiple process streams, numerical methods have been used to systematically solve the problem. Grossmann and his colleagues [
35] developed a mathematical programming framework for the design of the HEN. This technique solved using numerical models, involves the development of a superstructure that incorporates all the connections possibilities that form potential candidates of the optimal design. The mixed integer linear programming MILP [
36], allowed having the minimum number of heat exchangers assembly resulting in an optimal utility target. Zoughaib [
37] scanned different simultaneous, sequential, linearization, and heuristic approaches to systematize the design of the exchanger network. He also introduced the CERES platform [
38] used in this work and based on a MILP solver and a genetic algorithm optimizer, which optimizes heat recovery in industrial processes while implementing the pinch analysis.
Combined with exergy analysis, optimization-based researches are numerous. Lee et al. [
39] used nonlinear programming to find optimal values of mixed refrigerant composition in a natural gas liquefaction process; afterward they used judgment and heuristics to modify flow and pressures. Shirazi et al. [
40] constructed a MATLAB mathematical model of a peak-shaving production liquefaction plant and optimized it with a genetic algorithm using as variables the condensation, evaporation and intermediate pressures, flow and mixed refrigerant composition. Sanavandi et al. [
41] similarly optimized the operating parameters in order to maximize the exergy efficiency of the C3MR process, but what distinguishes their approach from the others is that this preselects the parameters having the most influence on the objective function by performing a sensitivity study. This study highlights the important effect of mixed refrigerant composition and optimizes it, first time numerically according to sequential quadratic programming and second time by proposing 20,000 mixed refrigerant compositions and comparing each time the correspondence with the ideal case.
Mathematical optimization methods are systematic and reduce the computational time and solution space. However, used alone, they lack the comprehensive, practical, and feasible approach. When it comes to optimizing an objective function by varying the operating parameters, this approach is non-deterministic. The optimization of all operating parameters consumes time and does not necessarily give the best solutions. That is why, a sensitivity study is necessary to be able to prioritize the parameters by their importance and the influence they have on the objective function.