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Prospects and challenges for chemical process synthesis with P-graph
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ScienceDirect Prospects and challenges for chemical process synthesis with P-graph Ferenc Friedler1, Kathleen B Aviso2, Botond Bertok3, Dominic CY Foo4 and Raymond R Tan2 The P-graph framework was developed to solve Process Network Synthesis (PNS) problems in plant design. It provides a powerful engineering toolbox based on the constituent Maximal Structure Generation (MSG), Solution Structure Generation (SSG) and Accelerated Branch-and-Bound (ABB) algorithms. During the four decades of its development, the P-graph framework has proven to be capable of solving various engineering applications framed as PNS problems. This review paper gives a survey of the development of the P-graph framework, with emphasis on its enhancements and the diversification of applications in process engineering. Research gaps and promising directions for P-graph research are then discussed. Addresses 1 Pa´zma´ny Pe´ter Catholic University, Szentkira´lyi utca 28, 1088 Budapest, Hungary 2 De La Salle University, 2401 Taft Avenue, 0922 Manila, Philippines 3 University of Pannonia, Egyetem u. 10, 8200 Veszpre´m, Hungary 4 The University of Nottingham Malaysia, Jalan Broga, 43500 Semenyih, Selangor, Malaysia Corresponding authors: Aviso, Kathleen B ([email protected]), Tan, Raymond R ([email protected])
Current Opinion in Chemical Engineering 2019, 26:58–64 This review comes from a themed issue on Energy, environment, and sustainability: sustainability modeling Edited by Heriberto Cabezas
https://doi.org/10.1016/j.coche.2019.08.007 2211-3398/ã 2019 Elsevier Ltd. All rights reserved.
configurations given process unit ‘building blocks’ is a particularly important feature which can be linked to other process systems engineering (PSE) tools such as mathematical programming (MP) models [6,7]. This is a capability still absent even in modern commercial flowsheet software, which are widely used as mainstream tools but which require network topology to be manually defined before simulations can be done [8]. Solutions derived in this manner may potentially be caught in a ‘topological trap’ and have subpar performance in comparison to superior designs that were missed during synthesis. This gap severely limits the capability of such software to optimize the integration of novel processes into industrial plants, which has led to intensified PSE research to develop the next generation of tools for computer-aided process design [9]. Conversely, the P-graph framework offers the potential for much-needed computeraided process innovation to develop more efficient and sustainable industrial plants [6]. The purpose of this paper is to give a critical survey of the P-graph literature, and then to map out promising directions for future research on chemical engineering applications. In this respect, it differs from previous review papers and mini-reviews focusing on its application for PNS and supply chains [10], the diversity of applications [11], future directions for research [12], and non-conventional problems which exhibit PNS-like structures [13]. The rest of the paper is organized as follows. The next section gives a brief overview of the basic P-graph framework. Subsequent sections then discuss important methodological extensions and different process engineering applications. The strategic outlook for future P-graph research is then discussed in the final section.
Fundamentals of P-graph and the P-graph Studio software Introduction The development of P-graph began in the late 1970s [1] as a methodology for automated computer-aided generation of process networks. The definition of formal axioms for process network synthesis (PNS) problems [2] led to the development in the 1990s of the main algorithms that comprise the P-graph framework [3,4,5]. Characterized by its rigorous mathematical foundations, computational efficiency, and versatility, P-graph was demonstrated to be a powerful tool for solving PNS and PNS-like problems. The capability to generate alternative process network Current Opinion in Chemical Engineering 2019, 26:58–64
A P-graph is a bipartite graph whose nodes are classified either as M-type (materials) or O-type (operations). In PNS problems, O-type nodes represent processes whose inputs and outputs are signified by arcs connecting them to M-type nodes. Numerical coefficients reflect the input–output ratios of streams associated with any process, for example as a result of stoichiometry or thermodynamics. The P-graph framework is based on five axioms [2] which provide rigorous mathematical basis for its three component algorithms, namely, Maximal Structure Generation (MSG), Solution Structure Generation (SSG), and Accelerated Branch-and-Bound (ABB). The MSG www.sciencedirect.com
Prospects and challenges for chemical process synthesis with P-graph Friedler et al. 59
algorithm applies a rigorous procedure to generate a complete superstructure (i.e. the maximal structure) which becomes the basis for subsequent optimization [4]; it eliminates the potential for human error that may occur when an ad hoc approach is applied to superstructure generation [14]. SSG generates all combinatorially feasible networks (i.e. subsets of the maximal structure) for a given PNS problem while automatically eliminating structurally infeasible ones [3]. Optimization can be performed locally within each of these network structures, and globally across all structures in the problem. This feature allows for optimal and near-optimal solutions to be automatically generated, which can facilitate identification of good solutions for implementation in real world problems [15]. Furthermore, the search for the global optimum is made more efficient by using implicit information common to all PNS problems to avoid redundant solutions. ABB is thus more computationally efficient than standard branch-and-bound which is used to solve generic mixed integer programming (MIP) models [5]. Software for the implementation of P-graph methodology has undergone multiple generations of upgrade. The Pgraph Studio version 5.2.3.1 is currently hosted by the University of Pannonia.5 The site includes a portal for accessing the software remotely, has links to the P-graph literature and provides on-line tutorials. Technical support is also available for users. A screenshot of the P-graph Studio interface is shown in Figure 1. After four decades of development, P-graph methodology has some visibility in professional chemical engineering literature, including a mainstream textbook [16]. From an educational standpoint, the capability to automatically generate multiple optimal and near-optimal solutions also encourages indepth problem analysis by students and simulates realworld problem-solving scenarios [17]. Note that P-graph Studio is not a commercial software package, and is still undergoing continuous improvement for features such as user interface, modularity, and file import/export.
P-graph applications and extensions P-graph has been applied for PNS and PNS-like design problems because of its ability to efficiently identify the maximal structure of the system being analyzed using the MSG algorithm and at the same time provide a systematic procedure for generating all combinatorially feasible solution structures using the SSG algorithm. These two issues (e.g. superstructure optimization and generation of alternatives) remain relevant considerations for process synthesis [18]. It was then used for separation network synthesis (SNS) [14] to illustrate its capability of generating a more complete superstructure through the inclusion of additional structure components, particularly 5
Center of Advanced Process Optimization, University of Pannonia, P-graph (http://p-graph.org). www.sciencedirect.com
those which facilitate recycling and improve redundancy of the system. Feng et al. [19] implemented the P-graphbased approach for the design and synthesis of azeotropic distillation. However, it was only in 2010 that a formal analogy between SNS and PNS was proposed providing a rigorous discussion on how various SNS types can be implemented using the P-graph methodology [20]. Xu et al. [21] recently proposed the integration of hierarchical decomposition with P-graph for more robust SNS. The first demonstration of the use of P-graph for establishing reaction network pathways was done for biochemical reactors [22] and the efficient identification of reaction pathways for ammonia synthesis [23]. More recently, it has been used to determine the feasible reaction pathways for the methanation of CO2 with the integration of available experimental data to further confirm the feasible pathways [24]. Lakner et al. [25], on the other hand, developed an algorithm for identifying only the startable reaction pathways. The algorithms in P-graph have been extended to accommodate the design for multi-period operations which occur when process variations are expected because of changes in raw material availability or product demands. The optimal design is thus selected and sized to remain feasible in all periods considered. Multi-period modelling with P-graphs was initially presented by Friedler et al. [26] for HENs, and a more detailed discussion on the technique was then presented by Heckl et al. [27] for general PNS. This was later extended to account for part-load operating limits of process units [28,29]. Bertok and Bartos [30] presented the most recent developments in P-graph Studio and demonstrated how the multi-period model is implemented together with waste management and storage options. For batch process scheduling without predefined time periods, time constrains were added to the P-graph formulation [31], and an algorithmic method has been developed to handle multiple storage policies by time constrained P-graphs [32]. It has also been proposed that the P-graph model be extended to accommodate variability in the inputs and outputs or process unit efficiencies [33]. Practical engineering problems are typically evaluated based on multiple criteria; thus, recent works using P-graph have not only focused on costs, but also considered the inclusion of reliability, safety, redundancy, and sustainability metrics into the network assessment. The integration of reliability aspects was initially proposed by Orosz et al. [34]. The concept was later extended to consider the inclusion of redundant process units for structural reliability [35] and the use of the minimal path set concept which identifies the minimum number of operating units to keep the entire system operational [36]. A more extensive discussion of evaluating structural reliability with P-graphs is presented in Kovacs et al. [37]. Sustainability metrics were considered by Fan et al. [38] using a segregated assessment of Current Opinion in Chemical Engineering 2019, 26:58–64
60 Energy, environment, and sustainability: sustainability modeling
Figure 1
Current Opinion in Chemical Engineering
User interface of software P-graph Studio.
pre-treatment and post-treatment for the anaerobic digestion of lignocellulosic waste using P-graph for economic assessment and the GaBi software for environmental assessment. Varbanov and Friedler [39] examined the tradeoff between cost and carbon emissions in the synthesis of fuel cell-based CHP systems. Bertok and Heckl [40] on the other hand discuss how the sustainability metric can be integrated into the P-graph framework by treating the environment as a limited resource with cost. A fuzzy P-graph model to consider potentially conflicting objectives of maximizing product demands and minimizing resource use was also developed [41]. For general multi-objective optimization problems, the use of P-graph with the classic e-constraint method for generating Pareto-optimal solutions has been demonstrated by Vance et al. [42]. Engineers can consider such solutions, as well as near-optimal solutions in the vicinity of the Pareto frontier, to facilitate the decision-making process Current Opinion in Chemical Engineering 2019, 26:58–64
[17,42]. Monte Carlo simulation can also be applied to gauge the robustness of the alternative network designs [43]. One of the earliest applications of P-graphs for process synthesis was for mass exchange networks (MENs) [44] which demonstrated its efficiency against conventional mathematical programming approaches in identifying feasible structures. Nagy et al. [45] then proposed the integration of process synthesis and heat exchange networks (HENs). Friedler et al. [26] later presented the extension of this for multi-period operations. Recently, Ong et al. [46] presented the possibility of performing simultaneous heat and mass integration in P-graphs. Some recent extensions of P-graph were reported for the synthesis of material-based resource conservation network (RCN) problems, which were traditionally the domain of Process Integration research. These include www.sciencedirect.com
Prospects and challenges for chemical process synthesis with P-graph Friedler et al. 61
water recovery and property integration problems with reuse and regeneration schemes [47,48]. Another recent extension was reported in a heat-integrated water recovery system [49]. A summary of the key papers in P-graph literature is shown in Table 1.
Research challenges and outlook By far the most important research challenge is to utilize the capability of P-graph to generate alternative configurations during process synthesis or flowsheeting. Even though various process design models have been proposed in the past decades to assist the creation of process flowsheet, the large number of design alternatives often prevents all alternatives from being assessed. In most cases, only several alternatives are chosen to undergo detailed analysis. The latter usually involves the calculation of mass and energy balances. Even with modern software, such calculations are done after the process flowsheet is created by the user [8]. The limitation of this approach is that, there is a risk that some potentially good alternatives may not be selected for detailed analysis. With the feature of MSG, P-graph can automatically and rigorously determine complete superstructures to prevent the occurrence of such ‘topological traps’ [14]. It is worth noting that the strength of commercial simulation software lies with their thermodynamic model databases. Hence, it is expected that the integration of P-graph and commercial simulation software will be a powerful tool for the automated generation of optimum and near-optimum processes that will be of great assistance to process designers. It has also been shown that P-graph (specifically SSG) can be used to generate networks which then provide basis for the formulation of MP models for PNS [6,7]. To overcome the limitations of the current generation of flowsheeting software, P-graph can also potentially feed them computer-generated network topologies which can be the basis for novel, innovative designs [9]. In such an integrated system, thermodynamic model databases embedded in commercial software can also feedback
updated numerical coefficients into the P-graph module. The proposed framework is illustrated in Figure 2. This research gap needs to be dealt with from both theoretical and practical (i.e. software implementation) perspectives. While the P-graph framework was originally intended for PNS problems in grassroots plant design, there is significant potential for it to be extended to other PNS-like chemical engineering problems. This potential has been illustrated in the past work for various cases of process synthesis problems normally handled through Process Integration techniques such as MP or Pinch Analysis. In each of these cases, the problem being solved was mapped to an equivalent PNS problem and solved with P-graph. The latter identifies other near-optimum solutions, apart from the optimum ones, which have good practical value from an industrial perspective. A similar approach is expected to solve other Process Integration problems, such as the synthesis of work exchange networks (WENs) [50] and combined work and heat exchange networks (WHENs) [51]. It is worth noting that some of the Process Integration tools, particularly those developed for HEN synthesis are now integrated with process simulation software (e.g. Aspen Engineering Suite). Hence, the integration of P-graph into commercial process simulation tools would be an added advantage in solving other process integration problems. Another prospective application for P-graph is in Process Intensification. Literature in this area focuses on modification of processes and equipment to achieve accelerated reaction and transport rates, which allows plants to be more compact, or alternatively allows plant capacity to be increased through retrofits [52]. In the case of retrofits, implementation of Process Intensification can result in cascading effects through an existing process network [53]. The concept of global Process Intensification can take advantage of such effects, as opposed to local Process Intensification that focuses only at the level of individual processes [54]. There is significant potential for P-graph methodology to be used to optimize the implementation
Table 1 Key papers in P-graph literature
Fundamentals Extended features
Applications
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Scope
References
Axioms and theorems of P-graph Algorithms in P-graph Multi-period optimization Scheduling Variable process yields or efficiencies Reliability Multi-objective optimization Process design and synthesis Separation network synthesis Process integration Reaction pathways Energy systems
[2] [3,4,5], [26,27,28–30] [31,32], [33] [34–36,37], [40,41,42], [6,15,16], [14,19,20], [26,43–45,46,47–49] [22–25] [7,26,27,28,29,38,39,41,42,45,46,49]
Current Opinion in Chemical Engineering 2019, 26:58–64
62 Energy, environment, and sustainability: sustainability modeling
Figure 2
ENGINEER Knowhow Market situation Experience
Alternative solution
Alternative flowsheet simulations Background knowledge Professional insights
Optimization knowhow
Products Raw materials
Market conditions Heuristics
Intermediates Byproducts
Thermodynamic
Alternative flowsheet configurations
data Capital cost data
FLOWSHEET SOFTWARE
Process units New technologies
P-GRAPH Current Opinion in Chemical Engineering
Roadmap for integration of the P-graph framework with flowsheeting software.
of Process Intensification retrofits, through the selection of appropriate techniques and final network topology.
can also be optimized subject to other engineering constraints such as cost, space, and so on.
There is a significant body of literature on the use of Pgraph for the analysis of complex chemical reactions. These prior works suggest that P-graph methodology can be applied at the scale of molecules, which suggests the potential to use the P-graph framework for product design as well. Molecular design problems that are now dealt with using MP models can be mapped into equivalent PNS form. The same principle can also be applied to a combined product and process design framework [55]. The computational capabilities of P-graph can provide a much-needed enhancement of currently available computer tools for integrated product and process design [9].
The growing interest in developing more sustainable and flexible chemical processes will also require that process synthesis and design approaches can generate process designs which are Pareto optimal in the context of multiple criteria (e.g. economic, environmental, social, reliability) [42]. The emerging trends of Industry 4.0 and Circular Economy will introduce new business models (e.g. personalized products) and require new performance indicators for chemical process industries. The impact of disruptive technologies on macro-scale industrial networks can be analyzed by taking advantage of the capability of P-graph to generate alternative topologies, in the same manner that this feature has been applied to networks at the scale of process plants.
Recent work on the use of P-graph framework for reliability engineering suggests important directions for future extensions, particularly in the area of process safety. Conventional approaches in this area make use of analytical and graphical approaches to analyze the confluence of events that can lead to major accidents. Such interrelated events can be visualized as networks that can be analyzed using P-graph, while effects of countermeasures, via redundancy or fail-safe modes, Current Opinion in Chemical Engineering 2019, 26:58–64
Conflict of interest statement Nothing declared.
Acknowledgement This work was supported by the Pa´zma´ny Pe´ter Catholic University Central Funds Program. The funding source has allowed for the conduct of meetings and discussions between the authors of this manuscript. www.sciencedirect.com
Prospects and challenges for chemical process synthesis with P-graph Friedler et al. 63
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ScienceDirect Prospects and challenges for chemical process synthesis with P-graph Ferenc Friedler1, Kathleen B Aviso2, Botond Bertok3, Dominic CY Foo4 and Raymond R Tan2 The P-graph framework was developed to solve Process Network Synthesis (PNS) problems in plant design. It provides a powerful engineering toolbox based on the constituent Maximal Structure Generation (MSG), Solution Structure Generation (SSG) and Accelerated Branch-and-Bound (ABB) algorithms. During the four decades of its development, the P-graph framework has proven to be capable of solving various engineering applications framed as PNS problems. This review paper gives a survey of the development of the P-graph framework, with emphasis on its enhancements and the diversification of applications in process engineering. Research gaps and promising directions for P-graph research are then discussed. Addresses 1 Pa´zma´ny Pe´ter Catholic University, Szentkira´lyi utca 28, 1088 Budapest, Hungary 2 De La Salle University, 2401 Taft Avenue, 0922 Manila, Philippines 3 University of Pannonia, Egyetem u. 10, 8200 Veszpre´m, Hungary 4 The University of Nottingham Malaysia, Jalan Broga, 43500 Semenyih, Selangor, Malaysia Corresponding authors: Aviso, Kathleen B ([email protected]), Tan, Raymond R ([email protected])
Current Opinion in Chemical Engineering 2019, 26:58–64 This review comes from a themed issue on Energy, environment, and sustainability: sustainability modeling Edited by Heriberto Cabezas
https://doi.org/10.1016/j.coche.2019.08.007 2211-3398/ã 2019 Elsevier Ltd. All rights reserved.
configurations given process unit ‘building blocks’ is a particularly important feature which can be linked to other process systems engineering (PSE) tools such as mathematical programming (MP) models [6,7]. This is a capability still absent even in modern commercial flowsheet software, which are widely used as mainstream tools but which require network topology to be manually defined before simulations can be done [8]. Solutions derived in this manner may potentially be caught in a ‘topological trap’ and have subpar performance in comparison to superior designs that were missed during synthesis. This gap severely limits the capability of such software to optimize the integration of novel processes into industrial plants, which has led to intensified PSE research to develop the next generation of tools for computer-aided process design [9]. Conversely, the P-graph framework offers the potential for much-needed computeraided process innovation to develop more efficient and sustainable industrial plants [6]. The purpose of this paper is to give a critical survey of the P-graph literature, and then to map out promising directions for future research on chemical engineering applications. In this respect, it differs from previous review papers and mini-reviews focusing on its application for PNS and supply chains [10], the diversity of applications [11], future directions for research [12], and non-conventional problems which exhibit PNS-like structures [13]. The rest of the paper is organized as follows. The next section gives a brief overview of the basic P-graph framework. Subsequent sections then discuss important methodological extensions and different process engineering applications. The strategic outlook for future P-graph research is then discussed in the final section.
Fundamentals of P-graph and the P-graph Studio software Introduction The development of P-graph began in the late 1970s [1] as a methodology for automated computer-aided generation of process networks. The definition of formal axioms for process network synthesis (PNS) problems [2] led to the development in the 1990s of the main algorithms that comprise the P-graph framework [3,4,5]. Characterized by its rigorous mathematical foundations, computational efficiency, and versatility, P-graph was demonstrated to be a powerful tool for solving PNS and PNS-like problems. The capability to generate alternative process network Current Opinion in Chemical Engineering 2019, 26:58–64
A P-graph is a bipartite graph whose nodes are classified either as M-type (materials) or O-type (operations). In PNS problems, O-type nodes represent processes whose inputs and outputs are signified by arcs connecting them to M-type nodes. Numerical coefficients reflect the input–output ratios of streams associated with any process, for example as a result of stoichiometry or thermodynamics. The P-graph framework is based on five axioms [2] which provide rigorous mathematical basis for its three component algorithms, namely, Maximal Structure Generation (MSG), Solution Structure Generation (SSG), and Accelerated Branch-and-Bound (ABB). The MSG www.sciencedirect.com
Prospects and challenges for chemical process synthesis with P-graph Friedler et al. 59
algorithm applies a rigorous procedure to generate a complete superstructure (i.e. the maximal structure) which becomes the basis for subsequent optimization [4]; it eliminates the potential for human error that may occur when an ad hoc approach is applied to superstructure generation [14]. SSG generates all combinatorially feasible networks (i.e. subsets of the maximal structure) for a given PNS problem while automatically eliminating structurally infeasible ones [3]. Optimization can be performed locally within each of these network structures, and globally across all structures in the problem. This feature allows for optimal and near-optimal solutions to be automatically generated, which can facilitate identification of good solutions for implementation in real world problems [15]. Furthermore, the search for the global optimum is made more efficient by using implicit information common to all PNS problems to avoid redundant solutions. ABB is thus more computationally efficient than standard branch-and-bound which is used to solve generic mixed integer programming (MIP) models [5]. Software for the implementation of P-graph methodology has undergone multiple generations of upgrade. The Pgraph Studio version 5.2.3.1 is currently hosted by the University of Pannonia.5 The site includes a portal for accessing the software remotely, has links to the P-graph literature and provides on-line tutorials. Technical support is also available for users. A screenshot of the P-graph Studio interface is shown in Figure 1. After four decades of development, P-graph methodology has some visibility in professional chemical engineering literature, including a mainstream textbook [16]. From an educational standpoint, the capability to automatically generate multiple optimal and near-optimal solutions also encourages indepth problem analysis by students and simulates realworld problem-solving scenarios [17]. Note that P-graph Studio is not a commercial software package, and is still undergoing continuous improvement for features such as user interface, modularity, and file import/export.
P-graph applications and extensions P-graph has been applied for PNS and PNS-like design problems because of its ability to efficiently identify the maximal structure of the system being analyzed using the MSG algorithm and at the same time provide a systematic procedure for generating all combinatorially feasible solution structures using the SSG algorithm. These two issues (e.g. superstructure optimization and generation of alternatives) remain relevant considerations for process synthesis [18]. It was then used for separation network synthesis (SNS) [14] to illustrate its capability of generating a more complete superstructure through the inclusion of additional structure components, particularly 5
Center of Advanced Process Optimization, University of Pannonia, P-graph (http://p-graph.org). www.sciencedirect.com
those which facilitate recycling and improve redundancy of the system. Feng et al. [19] implemented the P-graphbased approach for the design and synthesis of azeotropic distillation. However, it was only in 2010 that a formal analogy between SNS and PNS was proposed providing a rigorous discussion on how various SNS types can be implemented using the P-graph methodology [20]. Xu et al. [21] recently proposed the integration of hierarchical decomposition with P-graph for more robust SNS. The first demonstration of the use of P-graph for establishing reaction network pathways was done for biochemical reactors [22] and the efficient identification of reaction pathways for ammonia synthesis [23]. More recently, it has been used to determine the feasible reaction pathways for the methanation of CO2 with the integration of available experimental data to further confirm the feasible pathways [24]. Lakner et al. [25], on the other hand, developed an algorithm for identifying only the startable reaction pathways. The algorithms in P-graph have been extended to accommodate the design for multi-period operations which occur when process variations are expected because of changes in raw material availability or product demands. The optimal design is thus selected and sized to remain feasible in all periods considered. Multi-period modelling with P-graphs was initially presented by Friedler et al. [26] for HENs, and a more detailed discussion on the technique was then presented by Heckl et al. [27] for general PNS. This was later extended to account for part-load operating limits of process units [28,29]. Bertok and Bartos [30] presented the most recent developments in P-graph Studio and demonstrated how the multi-period model is implemented together with waste management and storage options. For batch process scheduling without predefined time periods, time constrains were added to the P-graph formulation [31], and an algorithmic method has been developed to handle multiple storage policies by time constrained P-graphs [32]. It has also been proposed that the P-graph model be extended to accommodate variability in the inputs and outputs or process unit efficiencies [33]. Practical engineering problems are typically evaluated based on multiple criteria; thus, recent works using P-graph have not only focused on costs, but also considered the inclusion of reliability, safety, redundancy, and sustainability metrics into the network assessment. The integration of reliability aspects was initially proposed by Orosz et al. [34]. The concept was later extended to consider the inclusion of redundant process units for structural reliability [35] and the use of the minimal path set concept which identifies the minimum number of operating units to keep the entire system operational [36]. A more extensive discussion of evaluating structural reliability with P-graphs is presented in Kovacs et al. [37]. Sustainability metrics were considered by Fan et al. [38] using a segregated assessment of Current Opinion in Chemical Engineering 2019, 26:58–64
60 Energy, environment, and sustainability: sustainability modeling
Figure 1
Current Opinion in Chemical Engineering
User interface of software P-graph Studio.
pre-treatment and post-treatment for the anaerobic digestion of lignocellulosic waste using P-graph for economic assessment and the GaBi software for environmental assessment. Varbanov and Friedler [39] examined the tradeoff between cost and carbon emissions in the synthesis of fuel cell-based CHP systems. Bertok and Heckl [40] on the other hand discuss how the sustainability metric can be integrated into the P-graph framework by treating the environment as a limited resource with cost. A fuzzy P-graph model to consider potentially conflicting objectives of maximizing product demands and minimizing resource use was also developed [41]. For general multi-objective optimization problems, the use of P-graph with the classic e-constraint method for generating Pareto-optimal solutions has been demonstrated by Vance et al. [42]. Engineers can consider such solutions, as well as near-optimal solutions in the vicinity of the Pareto frontier, to facilitate the decision-making process Current Opinion in Chemical Engineering 2019, 26:58–64
[17,42]. Monte Carlo simulation can also be applied to gauge the robustness of the alternative network designs [43]. One of the earliest applications of P-graphs for process synthesis was for mass exchange networks (MENs) [44] which demonstrated its efficiency against conventional mathematical programming approaches in identifying feasible structures. Nagy et al. [45] then proposed the integration of process synthesis and heat exchange networks (HENs). Friedler et al. [26] later presented the extension of this for multi-period operations. Recently, Ong et al. [46] presented the possibility of performing simultaneous heat and mass integration in P-graphs. Some recent extensions of P-graph were reported for the synthesis of material-based resource conservation network (RCN) problems, which were traditionally the domain of Process Integration research. These include www.sciencedirect.com
Prospects and challenges for chemical process synthesis with P-graph Friedler et al. 61
water recovery and property integration problems with reuse and regeneration schemes [47,48]. Another recent extension was reported in a heat-integrated water recovery system [49]. A summary of the key papers in P-graph literature is shown in Table 1.
Research challenges and outlook By far the most important research challenge is to utilize the capability of P-graph to generate alternative configurations during process synthesis or flowsheeting. Even though various process design models have been proposed in the past decades to assist the creation of process flowsheet, the large number of design alternatives often prevents all alternatives from being assessed. In most cases, only several alternatives are chosen to undergo detailed analysis. The latter usually involves the calculation of mass and energy balances. Even with modern software, such calculations are done after the process flowsheet is created by the user [8]. The limitation of this approach is that, there is a risk that some potentially good alternatives may not be selected for detailed analysis. With the feature of MSG, P-graph can automatically and rigorously determine complete superstructures to prevent the occurrence of such ‘topological traps’ [14]. It is worth noting that the strength of commercial simulation software lies with their thermodynamic model databases. Hence, it is expected that the integration of P-graph and commercial simulation software will be a powerful tool for the automated generation of optimum and near-optimum processes that will be of great assistance to process designers. It has also been shown that P-graph (specifically SSG) can be used to generate networks which then provide basis for the formulation of MP models for PNS [6,7]. To overcome the limitations of the current generation of flowsheeting software, P-graph can also potentially feed them computer-generated network topologies which can be the basis for novel, innovative designs [9]. In such an integrated system, thermodynamic model databases embedded in commercial software can also feedback
updated numerical coefficients into the P-graph module. The proposed framework is illustrated in Figure 2. This research gap needs to be dealt with from both theoretical and practical (i.e. software implementation) perspectives. While the P-graph framework was originally intended for PNS problems in grassroots plant design, there is significant potential for it to be extended to other PNS-like chemical engineering problems. This potential has been illustrated in the past work for various cases of process synthesis problems normally handled through Process Integration techniques such as MP or Pinch Analysis. In each of these cases, the problem being solved was mapped to an equivalent PNS problem and solved with P-graph. The latter identifies other near-optimum solutions, apart from the optimum ones, which have good practical value from an industrial perspective. A similar approach is expected to solve other Process Integration problems, such as the synthesis of work exchange networks (WENs) [50] and combined work and heat exchange networks (WHENs) [51]. It is worth noting that some of the Process Integration tools, particularly those developed for HEN synthesis are now integrated with process simulation software (e.g. Aspen Engineering Suite). Hence, the integration of P-graph into commercial process simulation tools would be an added advantage in solving other process integration problems. Another prospective application for P-graph is in Process Intensification. Literature in this area focuses on modification of processes and equipment to achieve accelerated reaction and transport rates, which allows plants to be more compact, or alternatively allows plant capacity to be increased through retrofits [52]. In the case of retrofits, implementation of Process Intensification can result in cascading effects through an existing process network [53]. The concept of global Process Intensification can take advantage of such effects, as opposed to local Process Intensification that focuses only at the level of individual processes [54]. There is significant potential for P-graph methodology to be used to optimize the implementation
Table 1 Key papers in P-graph literature
Fundamentals Extended features
Applications
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Scope
References
Axioms and theorems of P-graph Algorithms in P-graph Multi-period optimization Scheduling Variable process yields or efficiencies Reliability Multi-objective optimization Process design and synthesis Separation network synthesis Process integration Reaction pathways Energy systems
[2] [3,4,5], [26,27,28–30] [31,32], [33] [34–36,37], [40,41,42], [6,15,16], [14,19,20], [26,43–45,46,47–49] [22–25] [7,26,27,28,29,38,39,41,42,45,46,49]
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62 Energy, environment, and sustainability: sustainability modeling
Figure 2
ENGINEER Knowhow Market situation Experience
Alternative solution
Alternative flowsheet simulations Background knowledge Professional insights
Optimization knowhow
Products Raw materials
Market conditions Heuristics
Intermediates Byproducts
Thermodynamic
Alternative flowsheet configurations
data Capital cost data
FLOWSHEET SOFTWARE
Process units New technologies
P-GRAPH Current Opinion in Chemical Engineering
Roadmap for integration of the P-graph framework with flowsheeting software.
of Process Intensification retrofits, through the selection of appropriate techniques and final network topology.
can also be optimized subject to other engineering constraints such as cost, space, and so on.
There is a significant body of literature on the use of Pgraph for the analysis of complex chemical reactions. These prior works suggest that P-graph methodology can be applied at the scale of molecules, which suggests the potential to use the P-graph framework for product design as well. Molecular design problems that are now dealt with using MP models can be mapped into equivalent PNS form. The same principle can also be applied to a combined product and process design framework [55]. The computational capabilities of P-graph can provide a much-needed enhancement of currently available computer tools for integrated product and process design [9].
The growing interest in developing more sustainable and flexible chemical processes will also require that process synthesis and design approaches can generate process designs which are Pareto optimal in the context of multiple criteria (e.g. economic, environmental, social, reliability) [42]. The emerging trends of Industry 4.0 and Circular Economy will introduce new business models (e.g. personalized products) and require new performance indicators for chemical process industries. The impact of disruptive technologies on macro-scale industrial networks can be analyzed by taking advantage of the capability of P-graph to generate alternative topologies, in the same manner that this feature has been applied to networks at the scale of process plants.
Recent work on the use of P-graph framework for reliability engineering suggests important directions for future extensions, particularly in the area of process safety. Conventional approaches in this area make use of analytical and graphical approaches to analyze the confluence of events that can lead to major accidents. Such interrelated events can be visualized as networks that can be analyzed using P-graph, while effects of countermeasures, via redundancy or fail-safe modes, Current Opinion in Chemical Engineering 2019, 26:58–64
Conflict of interest statement Nothing declared.
Acknowledgement This work was supported by the Pa´zma´ny Pe´ter Catholic University Central Funds Program. The funding source has allowed for the conduct of meetings and discussions between the authors of this manuscript. www.sciencedirect.com
Prospects and challenges for chemical process synthesis with P-graph Friedler et al. 63
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