A review on heat and mass integration techniques for energy and material minimization during CO_{2} capture
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Abstract
One major challenge confronting absorptive CO_{2} capture is its high energy requirement, especially during stripping and sorbent regeneration. To proffer solution to this challenge, heat and mass integration which has been identified as a propitious method to minimize energy and material consumption in many industrial applications has been proposed for application during CO_{2} capture. However, only a few review articles on this important field are available in open literature especially for carbon capture, storage and utilization studies. In this article, a review of recent progress on heat and mass integration for energy and material minimization during CO_{2} capture which brings to light what has been accomplished till date and the future outlook from an industrial point of view is presented. The review elucidates the potential of heat and mass exchanger networks for energy and resource minimization in CO_{2} capture tasks. Furthermore, recent developments in research on the use of heat and mass exchanger networks for energy and material minimization are highlighted. Finally, a critical assessment of the current status of research in this area is presented and future research topics are suggested. Information provided in this review could be beneficial to researchers and stakeholders working in the field of energy exploration and exploitation, environmental engineering and resource utilization processes as well as those doing a process synthesisinclined research.
Keywords
CO_{2} capture systems Energy minimization Energy penalty Heat and mass exchanger networks Mathematical programmingIntroduction
Carbon capture and storage (CCS) is a promising technology that aims at reducing CO_{2} emissions from large point sources such as power plants [1, 2, 3]. However, high energy demands and excessive material usage associated with CO_{2} compression and separation processes have been the main challenges currently facing the commercialization of most CO_{2} capture and storage technologies [4]. There is a need to save energy and minimize material usage during CO_{2} capture to ensure the economic advantage of the capture technology [5, 6]. This is because, the cost of energy and materials for CO_{2} capture has increased and this trend is expected to continue with an increase of about 13.4% by the year 2040 due to consistent high energy demand from many industrialized nations globally [7]. The challenge of energy and excessive use of materials in process industries can be tackled to a large extent by minimizing the consumption of energy and mass [8]. In the context of this review, energy refers to the heat required during sorbent regeneration, while material (mass) refers to the mass separating agents (sorbents) and external utilities such as cooling water and steam which ought to be minimized during CO_{2} capture.
Heat and mass exchanger network retrofitting is envisaged as a promising option for reducing energy and material consumption which could lead to enhanced economic and environmental sustainability. The main aim of heat exchanger networks (HENs) and mass exchanger networks (MENs) retrofitting is to decrease the external energy demand and extra material consumption by increasing heat and mass exchange simultaneously among process streams in an existing process plant [9, 10]. HENs and MENs retrofitting can be performed using pinch analysis and/or mathematical programming. Over the past decades, systematic methods based on simultaneous mathematical programming and sequential techniques have been applied to achieve improved energy and material minimization in chemical process industries [9].
Review of synthesis methods for heat and mass exchanger networks
Application of heat exchanger networks (HENS) and mass exchanger networks (MENS) in CO_{2} capture is an important strategy to minimize energy and utility targets of the capture process. Methodologies for the synthesis of HENS and MENS are broadly classified into two: (i) sequential and (ii) simultaneous synthesis methods. Section 2.1 briefly describes the sequential synthesis technique, while Sect. 2.2 discusses simultaneous synthesis technique.
The sequential synthesis method
Comparison of energy and material minimization techniques
Technique  What can be minimized?  

Energy consumption  Material usage  
Use of additives, e.g. piperazine  ✓  X 
Ammonia cycling  ✓  X 
Waste heat utilization  ✓  X 
Fluor Econamine process  ✓  X 
Heat and mass integration  ✓  ✓ 
The simultaneous synthesis method
Brief overview of process integration as an optimal process development strategy
Process integration has been widely embraced as an integral part of process intensification which can be used in describing specific systemoriented activities related to process design with applications exclusively focused on resource conservation, pollution prevention and energy management [24, 25]. Synthesis, analysis and optimization are the three basic components in any effective process integration methodology. Process integration has a significant effect on many chemical industries through heat exchanger network optimization.
The application of process integration in CO_{2} capture systems makes it possible to identify the optimal process development strategy for the capture networks as well as identifying the most costeffective way to complete the CO_{2} capture process [26, 27, 28]. Amongst the available process integration methodologies, pinch analysis is currently the most commonly used. This could be attributed to the simple nature of its underlying concepts and the spectacular results it has presented in numerous studies in the past. Hence, it forms a major point of discussion in this review.
Although pinch analysis has been reported for various energy and resource saving studies in the past, its application in energy and material minimization studies with respect to CO_{2} capture system is still new and cannot be traced to any current report in open literature. For example, Kemp [29] reported the application of pinch analysis for the efficient use and minimization in a dryer where a direct reduction of dryer heat duty was discussed. Despite the huge success of the pinch technique reported by the author for energy minimization, the principles have not been extended to designing a network for CO_{2} capture. In scenarios where CO_{2}producing plants are colocated within an industrial development zone or geographical area, it is imperative to design an optimal network for energy reduction and efficient resource usage using process network integration as this will offer immense opportunities for energy and resource sharing amongst the plants.
According to the literature reports reviewed so far, it is evident that researchers have made significant efforts to develop new strategies for energy minimization in many industrial applications on one hand. On the other hand, methodologies for material usage minimization have also been developed. However, most of the suggested strategies do not involve a concurrent minimization of both energy and mass. This review suggests that energy consumption and material usage can be minimized simultaneously during industrial processes like CO_{2} capture using a combined heat and mass integration approach.
State of the art in the application of heat integration techniques
Heat integration is mostly applied in energy systems when examining the potential of improving heat exchange between heat sources and heat sinks to reduce the amount of external heating and cooling utilities which is a way of ensuring energy minimization [28, 33, 34]. Heat integration during CO_{2} capture could be a reliable method for reducing the high energy penalty associated with most CO_{2} capture technologies. Researchers have developed new calculation methods for energy and material minimization as well as design of heat exchanger and coupling of utilities in many energyintensive processes with minimum temperature difference through heat integration using pinch concepts [35, 36, 37]. However, the application of pinch analysis alone cannot adequately achieve a simultaneous energy and material minimization in a process such as CO_{2} capture. This is because, heat transfer occurs in most of these systems with some inefficiency due to unavoidable stack losses. This makes the heat value of the burnt fuel always greater than that absorbed by the process. As a result, energy and material consumption cost may not be easily evaluated directly from the energy targets indicated in the pinch diagrams. It has also been pointed out in previous research [36, 37] that the loss of some important information can occur when process and utility streams are combined into the same grand composite curve (GCC). This loss of information has led to missed opportunities in designing an optimal network for energy and material minimization.
To provide solution to the aforementioned problem posed by the pinch technique, researchers have come up with different methodologies for a simultaneous energy and material minimization during CO_{2} capture. For instance, in the studies reported by Romeo et al. [38] and Berstad et al. [39], calcium looping was recommended as the most suitable CO_{2} capture technique for effective energy and material minimization. This is because the researchers envisaged that the waste CaO from CO_{2} capture in a cement plant can be combined with waste energy from the clinker cooling and CO_{2} capture system which can then be used to generate additional power without the utilization of coal. Furthermore, part of the power generated can be used for CO_{2} compression. The purge from the CO_{2} capture system can also be used as input to the cement plant, thus reducing the raw material consumption and fuel usage for the calcination of the saved limestone. By applying this method, the authors confirmed a lower CO_{2} avoidance cost with the integrated process than with any other combination method (either with power plants and CO_{2} capture system, or cement plants with CO_{2} capture systems). As such, the authors proposed that if these three processes are integrated, about 94% of CO_{2} that would have been emitted into the atmosphere can be avoided because of the energetic efficiency augmentation associated with the integrated processes. However, a major drawback of this integrated process is that both systems have to operate simultaneously and this requires a lot of energy consumption although material usage could be minimized. Furthermore, there could be some effects of sulphur and CaSO_{4} formed during the CO_{2} capture process on the cement characteristics and the deactivated CaO in the clinker during production, thus reducing the quality of cement produced from the integrated cement production plant.
Nemet et al. [40] reported a new methodology for heat integration with emphasis on optimization of heat exchanger networks’ cost over a long period. The authors developed a deterministic and stochastic multiperiod mixedinteger nonlinear programming (MINLP) model for synthesis of heat exchanger networks in which the utility cost coefficients were forecasted for the lifetime of the process. The stochastic approach was applied to the simultaneous consideration of future price projections of HENs, while the multiperiod approach with future price projections was applied for sustainable design of HENs with higher heat recovery and, consequently, with lower utility consumption. The study revealed that utility savings were 18.4% for hot and 32.6% for cold utility, yielding an increase in the net present value (NPV) by 7.8%. As much as this proposed methodology was useful for minimizing heat energy usage, it could not be conveniently applied in the case of CO_{2} capture due to the fact that CO_{2} capture is a simultaneous heat and mass exchange process, which involves the application of both heat and mass exchange networks. In view of this, the proposed methodology is not sufficient for energy and material minimization studies because it is limited to only heat exchanger networks.
MohdNawi et al. [41] suggested a new algebraic technique for total site carbon integration. This proposed technique is capable of minimizing energy requirement during carbon capture, utilization and storage. The method was applied to a hypothetical case study to determine potential CO_{2} exchange using CO_{2} headers at different percentage purity as well as a central pure CO_{2} generator. The authors reported a 43% reduction in CO_{2} emission with reduced energy consumption using this novel technique. The proposed targeting technique could be used by carbon planners to conduct further analysis and feasibility studies involving carbon capture storage and utilization. However, the technique did not include analysis of more carbon capture methods as well as a technoeconomic study to ascertain its applicability on a large scale. It is envisaged in this review that a combined application of the aforementioned techniques in integrated symbiotic systems might further minimize energy usage and also reduce energy penalty associated with most CO_{2} capture technologies.
Escudero et al. [42] applied a pinch analysis approach in combination with Aspen plus simulation to evaluate the heat recovery options and to design an optimized heat exchanger network for a specified power plant. The authors used an Aspen Plus simulation model to simulate the power plant (including all the subsystems and the new networks). At the end, the authors reported a net increase of about 32.5% in the net efficiency of the power plant. Energy penalty was also reduced from 10.54 to 7.28 efficiency points using this concept. However, CO_{2} capture is a simultaneous mass and heat exchange process, and the authors did not consider the synthesis of mass exchanger networks to take care of external mass separating agents or utilities in their study. Nevertheless, synthesis of a hybrid network that considers simultaneous heat and mass exchange for effective design of a CO_{2} capture network as proposed in this paper is capable of minimizing the external mass separating agents and utilities involved in the design.
Application of process synthesis techniques for HENs ans MENs in literature
Network type  Synthesis technique  Method  Application/focus  References 

HENs and MENs  Simultaneous  Mathematical programming  Pollution prevention  
MENs  Sequential  Carbon storage composite curves (CSCC)  Carbon capture and storage planning  [30] 
HENs  Sequential and simultaneous  Pinch analysis and mathematical programming  Process Integration  
HENs  Sequential  Pinch analysis  Heat exchanger network design  [51] 
HENs  Simultaneous  Mathematical programming  Environmental sustainability  [52] 
HENs and MENs  Simultaneous  Nonlinear programming  Chemical process optimization  [53] 
HENs  Simultaneous  Nonlinear and general disjunctive programming  Process systems engineering  [54] 
WENs  Simultaneous  Mathematical programming  Water integration  [55] 
WENs  Simultaneous  Mathematical programming  Water network design  [56] 
HENs  Sequential  Floating pinch method  Utility targeting  [57] 
HENs  Sequential  Graphical/pinch method  Energy saving and pollution reduction  
WENs  Simultaneous  Mathematical programming  Minimization of overall environmental impact and TAC  [60] 
HENs  Simultaneous  Mathematical programming  Heat exchanger network retrofit  [61] 
HENs  Sequential  Sequential LP, MILP and NLP models  Minimum utilities demand and pinch point  [62] 
HENs  Sequential  Pinch retrofit method  Methods for achieving costeffective HENs retrofit  
HENs  Simultaneous  Reassignment strategies and multiobjective optimization  HENs retrofit  [65] 
HENs and WNs  Simultaneous  Mathematical programming  Energy and water minimization  [66] 
HENs–WN  Simultaneous  Mathematical programming  Energy and water minimization  [67] 
MENs  Simultaneous  Mixedinteger linear programming  Industrial resource conservation  [68] 
HENs  Simultaneous  Mathematical programming  Carbon sequestration retrofits in the electricity sector  [69] 
MENs  Sequential  Multiobjective pinch analysis  Hydrogen and water conservation  [70] 
MENs  Sequential  Pinch technology  Reduction in pollutant emissions and use of MSAs  [10] 
MENs  Simultaneous  Mathematical programming  Waste minimization  [71] 
MENs  Simultaneous  Mathematical programming  Pollutant emissions reduction  [72] 
MENs  Simultaneous  Mathematical programming  Nonuniform exchanger specifications and MSA regeneration  [73] 
HENs  Sequential  Pinch technology  Utility targeting  [74] 
MENs  Simultaneous  Mathematical modelling  Determination of minimum energy targets  [75] 
MENs  Sequential  Gas cascade analysis technique, composition interval method  Minimum utility targeting  
Combined MENs and HENs  Sequential  Pinch analysis  Absorption of SO_{2} from gas streams  [78] 
CMAHENs  Sequential  Mass pinch and pseudoTH diagram  Minimization of the total annualized cost of CHAMEN  [45] 
MENs  Sequential and Simultaneous  CID and algorithmic programming  Material recovery/synthesis of costeffective MEN’s  [79] 
MENs  Sequential  Pinch analysis  Water minimization  [80] 
MENs  Simultaneous  Mathematical programming  Efficient separations and optimal use of MSAs  [81] 
Flexible HENs and MENs  Simultaneous  Mathematical programming  Minimizing total annualized cost (TAC)  [82] 
HENs  Simultaneous  Timesharing schemes  Minimization of utility consumption rate  [83] 
MENs  Simultaneous  Mixedinteger nonlinear programming  Minimizing the TAC (multicomponent)  [84] 
HENs  Sequential  Pinch point analysis  CO_{2} transport and Storage  [85] 
HENs  Simultaneous  Mathematical programing and heuristics  Minimization of TAC (area, pumping, and utility expenses)  [86] 
HENs  Simultaneous  Mathematical programming  Minimization of utility and piping cost  [87] 
HEN and UEN synthesis  Sequential and simultaneous  Pinch analysis and mathematical programming  Cost and exergy derivative analysis  [88] 
HENs  Simultaneous  Metaheuristic approach  Multiperiod optimization of HEN  [89] 
Recent trends in scientific publication for HENs and MENs synthesis methodologies
Figure 9 shows that in 77 contributions, the mathematical programming (MP) method was applied; pinch analysis (PA) technique was used in 244 contributions, while a combination of a combined pinch analysis and mathematical programming (PA–MP) was applied in 18 contributions. It is evident that the pinch analysis technique is well researched and has been used the most by researchers in the field of process integration. In addition, mathematical programming techniques in HENs and MENs synthesis was first introduced as early as 1977, but its application for energy and material minimization was not fully considered afterwards. According to the time frame considered in this review (1990–2018), full application of mathematical programming for environmental sustainability studies was reported only after 2002, while the combination of pinch analysis and mathematical programming started in 2003, and till date it has not been adequately researched compared to other methods. It is also worthy to note that there has been an increasing number of publications in the application of process synthesis techniques in the last 8 years (2010–2018). Figure 10 shows that 65% of the aforementioned contributions were used in heat exchanger network (HEN) synthesis, and 26% of the reported techniques were applied in mass exchanger network (MEN) synthesis, while a combined HEN and MENs synthesis accounted for only 9%. The trend observed in this section reveals that combined pinch–mathematical programming techniques for the synthesis of a combined heat and mass exchangers still need further research and development research and more concerted research efforts should be directed towards it. Hence, it forms a major recommendation from this review.
Application of pinch analysis and mathematical programming in CO_{2} capture systems
Recent studies in sustainable environmental engineering have highlighted the need to improve the efficiency, material and energysaving potential of most CO_{2} capture methodologies [90, 91, 92]. The amount of CO_{2} emitted from industrial processes need to be minimized using the CCS techniques with minimum energy expenditure and material usage. With the application of pinch analysis in CO_{2} capture systems, appropriate loads on various process streams can be identified and, as such, energy consumption and material usage during CO_{2} capture can also be minimized [93, 94, 95]. In addition, pinch analysis can provide a target for the minimum energy consumption of the entire CO_{2} capture process from the process data of a CO_{2} capture operation. The energysaving potential for the process is then obtained using composite curves. The minimum energysaving requirements set by composite curves depend on the energy and material balance of the CO_{2} capture process. Adjusting the energy and material balance of the capture system makes it possible to further reduce its energy requirement [95].
Pinch analysis, which is based on thermodynamic principles, provides a systematic approach for energy saving with a wide range of applications in many chemical processes [96, 97], in finance [98], supply chain management [87, 99] and power sector planning [63, 87, 100]. The use of pinch analysis in setting energy targets and mass separating agents targets in industrial processes has attracted a lot of attention in the past [101, 102, 103], though not directly applied to CO_{2} capture studies. In addition, it also has wide applications in both new and retrofit design situations. So far, the application of pinch technology in retrofit design is much higher than in new design applications [104, 105]. Pinch analysis approach was first reported by Tan and Foo [106] to address CCS planning problem, particularly for carbon capture planning. The basic concept of pinch analysis in heat integration is to match the available internal heat sources with the appropriate heat sinks to maximize energy recovery and to minimize the need for external utilities [107]. To maintain costeffective mass and heat exchange networks during the design and integration of individual network in CO_{2} capture systems resulting from the interaction which exists amongst the process parameters, it is essential to apply pinch analysis techniques during process integration and design [9, 108].
Apart from pinch technology, mathematical programming is another technique currently used to synthesize optimum heat and mass exchanger networks for effective energy and material minimization [45, 51, 79, 109], but it has not been adequately tested in CO_{2} capture systems. Design and synthesis of heat and mass exchanger networks give rise to discrete optimization problems, which if presented in algebraic form will result in mixedinteger optimization problems [110]. Mathematical programming through the use of computer programs in choosing a suitable alternative from a set of available options is a very good technique to solve the aforementioned problem [111]. There have been substantial advances in the application of mathematical programming methods for process synthesis in the past. The solutions of mixedinteger nonlinear programming problems as well as the rigorous global optimization of nonlinear programs have also become a reality in recent times. There have also been new trends towards logicbased formulations that can facilitate the modelling and solution of these problems.
In this review, it is recognized that availability of modelling strategies that can facilitate the formulation of optimization problems have recorded tremendous progress through mathematical programming, as well as the development of several solution strategies in process synthesis. This section further suggests that the idea of mathematical programming can be used in conjunction with pinch analysis and extended to different capture methods such as membrane separation, adsorptive and absorptive CO_{2} capture.
Energy penalty in CO_{2} capture systems
One important issue that needs to be considered in most CO_{2} capture methods is the high energy requirement, because energy availability is an important global issue. High energy penalty and excessive use of external utilities are another challenge confronting the capture of CO_{2} from power plants [112]. CO_{2} compression and sorbent regeneration during CO_{2} capture account for about 92% of the energy penalty associated with most carbon capture and storage technologies [113]. For instance, a typical CO_{2} capture system that is based on monoethanolamine (MEA) requires a significant amount of energy at about 3.0–4.5 GJ/t CO_{2} to regenerate the solvent in the stripper reboiler as well as energy for the stripper feed which is usually provided by cooling of the lean solvent [114]. According to a report by ZenzHouse et al. [115], energy penalty associated with retrofitting CO_{2} capture devices into existing power plants is estimated between 50 and 80%. A further analysis of the thermodynamic limit indicates that energy penalty during CO_{2} capture can be improved by harnessing the available waste heat and improving the secondlaw efficiency of temperatureswing adsorption systems [116]. ZenzHouse et al. [115] postulated that in reallife situation, it is difficult to attain an energy penalty reduction below 25% during postcombustion CO_{2} capture. The authors also indicated that to offset the energy penalty incurred during capture and storage, about 80% CO_{2} emissions will require either an additional 390–600 million tonnes of fuel, additional 69–92 gigawatts of CO_{2}freebaseload power, or a 15–20% reduction in overall electricity usage. CO_{2} capture units also require power to operate the gas compressors and other auxiliary equipment. Heat energy is also rejected from the stripper and compressor during CO_{2} capture and compression. Retrofitting CO_{2} capture devices in existing power plants will lead to a deficit of heat in the plant which has generally been proposed to be overcome by supplying heat and extracting steam from the turbine to the stripper reboiler [116]. This subsequently reduces energy expenditure, but drops the net efficiency of the power plant by approximately 30–40% [117].
Advances in energy penalty reduction during CO_{2} capture
Energy penalty can be reduced in a number of ways and this solely depends on the CO_{2} capture technology used [118]. According to Jassim and Rochelle [119], high energy penalty associated with chemical absorption systems during sorbent regeneration can be lowered by varying the solvents used. Yoro and Sekoai [1] suggested the use of additives such as piperazine in amine systems during CO_{2} capture by chemical absorption to reduce the high energy requirement during sorbent regeneration in absorption systems. Reddy et al. [120] suggested the application of the Fluor Econamine Plus process for energy minimization. This technology involves a combination of improved solvent formulation with an improved process design which includes absorber intercooling, split flow arrangements, integrated steam generation and stripping with flash steam to reduce total energy consumption. The authors claimed that about 20% reduction in energy penalty associated with CO_{2} capture was achieved in pilot studies with Fluor Econamine Plus process in original monoethanolamine plants. Conversely, the major drawback is that the methodology is limited to only absorption technique and does not provide a solution for minimization of extra utilities (mass) during the process.
Stankewitz et al. [121] recommended the use of ammonia cycle to generate energy from the available waste heat in a monoethanolaminebased CO_{2} capture system retrofitted to a power plant. By applying the ammonia cycle method, the authors observed that energy penalty reduced significantly from 28 to 22%. However, the major challenge associated with this method is that the ammonia condenser must be operated with continuous flow of cooling water at 15 °C. If the ammonia condenser is operated with cooling water at a warmer temperature above 15 °C, the said level of efficiency would not be achieved.
Selected CO_{2} capture methods in literature, their associated energy consumption and plant efficiencies
Type of system  Energy consumption (kJ/mol)  Plant efficiency (%)  References 

Absorption; MEA  1.03  21.39  [123] 
Absorption; MEA  2.32  14.93  [124] 
Absorption; MEA  7.76  14.52  [125] 
Absorption; K_{2}CO_{3}/PZ  7.44  20.29  [126] 
Absorption; NH_{3}  25.48  17.03  [127] 
Absorption; generic solvent  7.62  20.67  [128] 
Adsorption; zeolite 13X  22.57  16.11  [129] 
Membrane; onestage  98.56  8.88  [130] 
Membrane; twostage  12.76  4.54  [131] 
Cryogenic; Stirling coolers  169.84  3.90  [132] 
So far, several researchers have suggested the utilization of waste heat during CO_{2} capture to reduce energy penalty associated with retrofitting CCS devices onto a power plant [133, 134, 135, 136]. However, plant efficiency, optimum energy and material usage are usually compromised while attempting to capture CO_{2} by retrofitting CO_{2} capture devices on existing power plants. New methods to reduce energy penalty during CO_{2} capture while maintaining stable plant efficiency are highly sought for till date. Synthesis of a combined heat and mass exchange network for this purpose could proffer a lasting solution to the drop in plant efficiency, high energy and material consumption associated with retrofitting CCS devices in power plants. As far as could be ascertained from previous studies, no report in open literature has applied process integration visàvis pinch analysis together with mathematical programming in a combined manner to systemically integrate a CCS system within a power plant for energy penalty and material usage minimization during CO_{2} capture; as such, it can form a very interesting topic for future research.
Recent highlights on heat and mass exchanger network synthesis
Heat and mass exchanger network synthesis remains an area of continuous development in process engineering due to the current trend of increasing energy and material costs. Heat and mass exchanger networks use available heat in a process through the exchange that occurs between hot and cold process streams to decrease energy demands, utility costs and capital investment in most industrial processes. Integration of heat and mass exchanger networks for industrial applications can improve the economics of plant operation.
Several advances have been reported for the design of heat and mass exchanger networks using approaches which involve the pinch point and mathematical programming. Recently, simultaneous design and optimization methodologies have been proposed [137]. Due to the complex nature of most mathematical equations involved in the synthesis of heat and mass exchanger networks, the application of mathematical programming in process synthesis could be achieved by simplifying various superstructures and model equations through the use of simplified capital cost functions. Mathematical programming has also shown significant potentials in solving HENs and MENs problem with the recent advancement in computing technology. It deals mainly with heat integration, synthesis of heat and mass exchanger networks or synthesis of process schemes and process subsystems. It is remarkable to note that the final effect of the synchronized method is not only the expected reduction in energy consumption, but also the reduction in raw material consumption. The scope of process integration through mathematical programming has improved in recent times and it can be applied in process industries to optimize heat and mass exchanger networks for carbon emission reduction and water minimization [33, 36].
The foremost role of mathematical programming in synthesis of HENs and MENs is to improve concepts (and also create new ones) by expressing them in precise forms to obtain ideal and feasible solutions of complex problems [138]. Apposite tradeoffs between raw materials, operating and investment costs as well as product income can be established by applying mathematical programming in overall systems concurrently, thus attaining accurately integrated details. Mathematical programming techniques in the synthesis of HENs and MENs require postulation of a superstructure of alternatives (whether it involves a high level aggregated model or a detailed model). The main issues associated with postulating superstructures for HENs and MENs include the major type of representations that can be used, its modelling implications, and the feasible alternatives that must be included to guarantee that the global optimum is not ignored. To analytically generate superstructures that contain all the alternatives of interest in a process such as CO_{2} capture, a graphical–theoretical approach with polynomial complexities is proposed in this review to find all interconnections in process networks with nodes for processes and chemicals adequately specified. Apart from the selection of superstructures, the choice of a detailed optimization model is also necessary for an effective energy and material minimization. Postulation of superstructures and selection of optimization models will be a very reliable procedure in synthesizing process networks for waste minimization during CO_{2} capture.
Heat and mass exchanger networks for energy and material minimization
Heat exchanger network synthesis is the most commonly studied problem in process synthesis than mass exchanger network synthesis [139]. The major heat transfer unit between process industries in any chemical industry is the heat exchanger [71]. As such, synthesis of heat exchanger networks (HENs) can been intensively studied as a systematic way to effectively minimize energy consumption in most industrial processes [140]. A typical heat exchanger network represents an interaction between hot and cold process streams as well as utilities, while a mass exchanger network depicts an interaction between rich and lean streams in a process to meet optimum plant requirement.
In Fig. 14, Y^{s} is the supply composition of the rich stream, Y^{t} is the target composition of the rich stream, \(T_{\text{di}}^{\text{tm}}\) is the mass exchange temperature of the lean substream, X^{s} is the supply composition of the lean stream, X^{t} is the target composition of the lean stream, \(T_{\text{h}}^{\text{t}}\) is the target temperature of the lean stream, \(T_{\text{C}}^{\text{S}}\) is the supply temperature of the lean stream \(T_{\text{di}}^{\text{r}}\) is the regeneration temperature of the lean substream, \(Z_{\text{y}}^{\text{s}}\) is the supply composition of the regenerating stream and \(Z_{\text{y}}^{\text{t}}\) is the target composition of the regeneration stream.
Conclusions

High consumption of energy and materials associated with most CO_{2} capture methods has hindered its implementation and commercialization on a pilot scale in most developing countries. Implementation of inexpensive strategies such as heat and mass integration as suggested in this paper to check this limitation could boost its process development and largescale application.

Till date, the use of inhibitors and additives has been the common strategy used to minimize high energy requirement in energyintensive processes such as absorptive CO_{2} capture. However, the use of these additives is only suitable in gas–liquid absorption systems and cannot be fully extended to gas–solid adsorption or membrane systems during CO_{2} capture because it is limited in terms of solvent capacity.

Application of heat and mass integration techniques through the synthesis of heat and mass exchanger networks play a very crucial role in the improvement of system efficiency in industrial processes. It has proven to be a reliable strategy to minimize high energy and material consumption in both liquid and solid sorbents applications; hence, it is applicable in all CO_{2} capture methods.

Since a typical CO_{2} capture methodology involves both heat and mass exchange occurring simultaneously, a combined heat and mass integration network could be synthesized to concurrently minimize energy and material minimization in CO_{2} capture studies using the methodologies proposed in this review.
Future research outlook

Despite the tremendous potentials of heat and mass integration for utility minimization, limited investigations have been reported for synthesis of heat and mass exchanger networks for energy and material minimization in CO_{2} capture studies. This field constitutes an emerging area of research in the scientific community, and application of process synthesis techniques to solve problems in environmental studies will be one of the hot research topics in future.

Heat and mass integration techniques proposed in this review could be extended in future research to take into account a combined heat and mass exchanger network for CO_{2} capture, which can also be linked to a regeneration network to account for energy and material loss during sorbent regeneration. This has not been given adequate attention in the past and could constitute a potential research topic in this field.

Combination of pinch analysis with mathematical programming in a single methodology is still a more effective technique during heat and mass integration in CO_{2} capture systems compared to other methods previously reported in literature. A hybrid network optimization approach may also be tried for heat and mass exchanger applications in future studies.

Life cycle assessment (LCA) of heat and mass exchangers should be carried out in future studies to investigate its environmental impact using mixedinteger linear and nonlinear programming mathematical models.

To ensure effective utilization of CO_{2} with minimized material wastage using the strategies highlighted in this review, future R&D could consider a detailed design of a transport network to transport captured CO_{2} from different power plants to a central storage site or utilization point.
Notes
Acknowledgements
The financial support received from the National Research Foundation of South Africa (NRF—Grant Number 107867) and the University of the Witwatersrand through the postgraduate merit award (WITSPMA 2017–2019) is highly appreciated.
Compliance with ethical standards
Conflict of interest
The authors declare no conflict of interest regarding the publication of this manuscript.
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