P-Graph Approach to Optimizing Crisis Operations in an Industrial

Article pubs.acs.org/IECR

P‑Graph Approach to Optimizing Crisis Operations in an Industrial Complex Raymond R. Tan,*,† Michael Francis D. Benjamin,‡ Christina D. Cayamanda,† Kathleen B. Aviso,† and Luis F. Razon† †

Chemical Engineering Department, De La Salle University, 2401 Taft Avenue, 0922 Manila, Philippines Research Center for the Natural and Applied Sciences, University of Santo Tomas, España Blvd., 1006 Manila, Philippines

‡

ABSTRACT: Industrial complexes allow for efficient and sustainable production of various goods, but at the same time they are also vulnerable to cascading failures caused by disruptions in process capacity or resource availability. Climate change in particular may cause significant perturbations in the supply of important process inputs such as water, energy, or feedstocks. Thus, for industrial complexes, proper risk management strategies must be developed as part of overall climate change adaptation and resilience measures. Rigorous modeling approaches are needed to ensure that economic losses resulting from a disruption are minimized. In this paper, a P-graph-based methodology is used to determine optimal adjustments to crisis conditions in order to minimize manufacturing losses; this graph theoretic methodology has traditionally been used for process network synthesis problems but has recently proven to be useful for structurally analogous problem domains. Two case studies on the reallocation of production capacities and product streams in an aluminum production complex and a biomass processing complex are used to illustrate the methodology. on the flow of a dimensionless risk metric called inoperability, which assumes intermediate values from 0 to 1 depending on the degree of failure of a system component. The I−O framework has similarly been extended to the analysis of industrial complexes (i.e., clusters of industrial plants linked by the flow of products and intermediates).8 Such I−O models have also been extended to allow for sustainability analysis in industrial systems through additional equations for natural resource inputs and waste or pollutant outputs.9 Enterprise I− O models have also been developed for such applications as debottlenecking10 and implementation of resource conservation measures.11 In all cases, the fundamental building block of I−O models is a scale invariant process (i.e., a physical process or an activity) for which fixed input−output coefficients denote the rate at which inflows are consumed to generate every unit of outflow. I−O models have also been developed for optimization problems in various contexts. Of particular interest here are those works that have used such models to determine optimal reallocation of streams and process capacities in response to various disruptions that cause parts of the system to become partially inoperable. For example, a multiple-objective optimization variant of IIM was proposed by Jiang and Haimes12 for planning crisis response. Kasivisvanathan et al.13 developed a mixed integer linear programming (MILP) model with a physical I−O structure for determining optimal operational adjustments in polygeneration plants. Fuzzy linear program-

1. INTRODUCTION Sustainability is now widely regarded as an increasingly important and fundamental dimension for decision-making in business and industry. In particular, interlinked sustainability issues such as climate change, land use and water stress are considered to be significant at both global and local scales; there have been attempts to develop quantitative indicators to allow sustainability thresholds to be identified for benchmarking purposes.1 Climate change is considered as particularly critical, given historically unprecedented atmospheric CO2 levels that now exceed 400 ppm, coupled with unabated growth in global greenhouse gas (GHG) emissions. These trends make it imperative for decision-makers in industry to consider climate change adaptation strategies to cope with climatic effects that are already occurring,2 in addition to pursuing mitigation efforts to reduce GHG emission levels. The problem is further compounded by interdependencies among different sustainability issues. For example, energy and water use are closely linked in a manner that requires an integrated approach for efficient use of these resources in industry.3 Process systems engineering (PSE) techniques are thus needed to ensure proper adaptation measures are taken in response to various climatic effects (such as droughts or extreme weather events) that threaten the continuity of industrial operations. Analysis of risks arising from climatic effects requires determining what can go wrong, finding out the likelihood of such adverse events, and finally assessing their consequences.4 It has been suggested that proper elucidation of risks in manmade systems should take into account interdependencies that exist in networks exhibiting high levels of connectivity; for example, inoperability input−output modeling (IIM) was introduced for the analysis of “ripple effects” in infrastructure5 and economic systems.6 The mathematical framework of IIM is based on Leontief’s input−output (I−O) model7 but focuses © XXXX American Chemical Society

Special Issue: Sustainable Manufacturing Received: August 31, 2015 Revised: November 5, 2015 Accepted: November 5, 2015

A

DOI: 10.1021/acs.iecr.5b03205 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

economic break-even point; this limit is assumed to be known a priori based on site-specific data. Each plant also has a maximum rated capacity, which may be greater than or equal to the previously specified baseline operating capacity. The input− output coefficients of each plant remain fixed throughout the entire feasible operating range from the lower bound (i.e., the minimum part-load capacity) to the upper bound (i.e., the maximum rated capacity). This is equivalent to the scale invariance assumption that leads to the linearity of I−O models. • It is assumed that a disturbance occurs which temporarily reduces the capacity of one or more plants that comprise the industrial complex. The degree of inoperability of the affected plants may be expressed in fractional form, such that a value of 0 corresponds to normal operation and a value of 1 corresponds to complete failure; intermediate values indicate partial inoperability. Because of the crisis, the industrial complex must operate for an extended period at a new steady state that accounts for this inoperability. • The objective is to determine the allocation of streams and adjustment of operating capacities of the plants in the industrial complex to maximize total economic value of the products for the duration of operations at the new steady state; in other words, the goal is to determine optimal “damage control” during the crisis phase.

ming (FLP) models were also proposed to plan optimal responses to loss of natural resource inputs in economic I−O systems14 and industrial complexes.15 These works used the scale invariance assumptions of the I−O models to ensure linearity, such that globally optimal solutions could be determined easily. More recently, an alternative approach to optimizing operations in I−O systems during a crisis has been proposed based on graph theory. This so-called process graph (P-graph) methodology was developed for process network synthesis (PNS) problems in a series of papers in the early 1990s16−18 and is described in greater detail in a later section. Tan et al.19 applied P-graph methodology for optimal operational adjustments in polygeneration plants as an alternative to an earlier MILP technique.13 Then, Aviso et al.20 proposed a similar approach to rationing electricity during a shortage across economic sectors in a city-scale I−O model. Despite the development of this P-graph approach for enterprise-level and economy-level I−O models, to date, no such application at the intermediate level of the industrial complex has been reported in PSE literature. In this work, a novel application of P-graph methodology is proposed for determining optimal and near-optimal operations in an industrial complex when a crisis is caused by a disturbance that reduces production capacity in one or more component plants. This method offers a significant, practical approach for guiding decision-makers in industry in the event of crises such as natural calamities, industrial accidents, or malicious attacks. This concept has previously been proposed for analogous problems at the enterprise level19 and at an economy-wide scale;20 this current work thus proposes a similar strategy at an intermediate (i.e., industrial complex) scale. The rest of this paper is organized as follows. Section 2 first gives a formal problem statement. Section 3 then briefly describes the P-graph framework. Then, sections 4 and 5 describe two illustrative case studies of industrial complexes operating under crisis conditions. Case study 1 deals with an aluminum production complex, while case study 2 deals with a bioenergy park. Finally, section 6 gives conclusions and prospects for future research.

3. P-GRAPH METHODOLOGY P-graph methodology is a framework for solving process network synthesis problems.16−18 PNS problems are inherently combinatorial in nature and thus present significant modeling and computational challenges. The P-graph framework allows for rigorous model-building and efficient identification of optimal and near-optimal solutions by taking advantage of unique information embedded in all PNS problems. A P-graph is a bipartite graph consisting of a set of processes or operating units (known as O-type vertices represented as horizontal bars) and a set of materials or streams (known as M-type vertices represented by dots). Streams are either consumed or produced by a processing unit; such relationships are denoted by a directed arc linking a stream to an operating unit. This convention eliminates ambiguities and enables P-graphs to be used for PNS problems. The set of materials are further classified into raw materials (RM), intermediates (I), and products (P). The distinctions among these material types are used as information to facilitate the rigorous and efficient generation of feasible solution structures. Note that despite the terminology which originated from PNS applications in chemical engineering, in principle, Otype vertices may be used to represent any generic activity (e.g., a chemical reactor, an economic sector, or an organizational unit) while M-type vertices can be used to represent any generic flow that needs to be accounted for (e.g., products, pollutants, money). Such analogs permit the use of P-graphs to a wide range of nonconventional applications. In addition, it can be seen that the basic process unit in the P-graph framework has similar properties as the fundamental process unit in I−O models, which again allows I−O systems to be represented as P-graphs.19,20 The P-graph framework is based on five axioms stated by Friedler et al. as follows:16 1. Every final product is represented in the graph. 2. A vertex of the M-type has no input if and only if it represents a raw material

2. PROBLEM STATEMENT The modeling problem addressed in this work is structurally similar to that proposed in Tan et al.19 and Aviso et al.,20 but, as previously noted, occurs at an intermediate scale. It may be stated formally as follows: • The industrial complex is assumed to have a total of M product streams and comprises a set of N component plants. The baseline state input−output linkages within the industrial complex are assumed to be known, and the unit price of each of the product streams is fixed. Alternatively, the relative economic values of these products may be specified in dimensionless form. • Each plant is assumed to be characterized by a fixed set of proportions of input and output streams (i.e., input−output coefficients). Such proportions reflect fixed ratios that arise from thermodynamic and stoichiometric principles, as well as the current state of technology. The baseline capacity of each of the plants is also assumed to have been previously determined during the design stage. • For each plant, a minimum part-load operating capacity is specified. Below this level, it is assumed that part-load operation is unstable or otherwise uneconomical; thus, it becomes necessary to shut the plant down entirely. In practice, this part-load limit coincides with the production level at the plant’s B


Article


Table 1. Selected P-Graph Applications Reported in the Literature

3. Every vertex of the O-type represents an operating unit defined in the synthesis problem. 4. Every vertex of the O-type has at least one path leading to a vertex of the M-type representing a final product. 5. If a vertex of the M-type belongs to the graph, it must be an input to or output from at least one vertex of the Otype in the graph. These axioms formalize information that is normally implicit in PNS, which allows for the subsequent development of efficient algorithms that take advantage of the specialized structure of such problems to achieve computational efficiency. P-graph methodology uses three main algorithms: • Maximal structure generation (MSG) identifies a network structure within which is embedded all possible solution structures of the problem. The maximal structure is generated in polynomial time using the information contained in the specification of the process units and materials via the five axioms. The maximal structure is, in effect, a rigorously generated superstructure. • Solution structure generation (SSG) generates all combinatorially feasible possible solution structures based on subsets of the maximal structure of the problem. Each solution structure represents a potential network configuration and can be determined before problem parameters are specified. • Accelerated branch-and-bound (ABB) identifies the optimal structure based on the solution structures, combined with additional information in the form of exogenously defined problem parameters (e.g., flow rates, costs). P-graph methodology implements a more efficient optimization by using available information from MSG and SSG to drastically reduce the size of the search space compared to the conventional branch-and-bound algorithm, in some cases by multiple orders of magnitude, thus allowing for rapid identification of solutions in large-scale problems. Furthermore, it is also possible to determine the n-best (near-optimal) solutions, thus providing decision-makers with richer information for real-life problems. A detailed, formal account of its mathematical foundations and implementation are discussed in the series of papers by Friedler et al.16−18 Tutorials are also available in a recent book21 and a dedicated Web site.22 The latter Web site also provides downloadable open access P-graph software (i.e., PNS Studio, PNS Draw, and the recently released integrated PGraph Studio) as well as links to additional sources of information. In addition, in the literature there have been numerous diverse applications of P-graph methodology to various problem domains.23 Many key developments are shown in Table 1. The problem posed in this work can be formulated as the MILP model shown in the Appendix, for which a global optimum can be found using the conventional branch-andbound algorithm available in commercial optimization software. However, use of P-graph methodology has specific advantages, particularly its computational efficiency17 and the aforementioned capability of identifying n-best optimal and near-optimal solutions. In the subsequent sections, two case studies are solved to illustrate this P-graph methodology for optimizing crisis operations in industrial complexes. These examples were both implemented using the P-graph software previously described.22

P-graph applications

authors Lee and Park24 Nagy et al.25

mass exchange networks synthesis synthesis of process and heat exchanger networks catalytic reaction pathway identification

Seo et al.;26 Fan et al.;27 Lin et al.;28 Lin et al.29 Halasz et al.30

optimal retrofit and operation of a steamsupply network waste minimization in chemical processes synthesis of distillation systems synthesis and retrofit of bioprocess systems identifying multiple cellular metabolic pathways estimating the sustainability potential of chemical processes price targeting for novel processing equipment designing cost-optimal fuel cell combined cycle plants sustainable energy supply chains separation-network synthesis transportation management synthesis of biomass and biofuel production networks planning building evacuation routes modeling of business processes planning and management of carbon capture storage systems design and evaluation of wastewater treatment plants as an energy source designing renewable optimal energy systems for smart cities process network synthesis with process scheduling multiperiod operations of bioenergy supply chains designing an organization-based multiagent system parallel implementation of ABB algorithm for synchronization and load distribution strategies allocation of inoperability in urban infrastructure

Halim and Srinivasan;31 Halim and Srinivasan32 Feng et al.33 Liu et al.;34 Liu et al.;35 Xu et al.36 Lee et al.37 Fan et al.38 Fan et al.39 Varbanov and Friedler40 Lam et al;41 Bertok et al.;42 Vance et al.;43 Vance et al.44 Heckl et al.45 Barany et al.;46 Adonyi et al.47 Lam et al.;48 Lam49 Garcia-Ojeda et al.50 Tick et al.51 Chong et al.52 Kollmann et al.53 Maier and Narodoslawsky54 Frits and Bertok55 Heckl et al.56 Garcia-Ojeda et al.57 Bartos and Bertok58 Tan et al.59

4. CASE STUDY 1: ALUMINUM COMPLEX The P-graph methodology is illustrated here with a case study of an aluminum industrial complex. Aluminum is used for various applications at a scale that exceeds all other metals except for iron. Typical uses include vehicle parts, packaging materials, and aircraft components. The global production of primary aluminum was 41.1 × 106 t in 2010.60 This industry is associated with high levels of CO2 emissions because of the high level of energy use. The energy-intensive nature of primary aluminum production can be attributed to the use of electrical power to reduce alumina (Al2O3) derived from bauxite ore into virgin aluminum via electrolysis. In addition to being a significant contributor to climate change, this high demand for electrical power also puts the aluminum industry squarely in the energy−water nexus, where climatic effects pose significant risks to stable, profitable operations. Specifically, severe drought due to climate change may affect electricity supply because of the water requirements of power plants; the ensuing power C


Article


Figure 1. Baseline state of aluminum complex in case study 1.

shortage may, in turn, cause dramatic reductions in the capacity to produce primary aluminum. This hypothetical but plausible scenario is illustrated with a numerical example based on a modified literature case.9,15 The industrial complex at the baseline state is shown schematically in Figure 1, which shows the input−output linkages among the component plants, as well as flows of major material and energy streams. Note that all flows are normalized to one ton of primary aluminum production per hour, for clarity. The bauxite mining and primary smelting operations serve to provide the bulk of the aluminum ingot production; however, there is an additional 0.203 t of aluminum ingot recycled from downstream process scrap for each ton of virgin aluminum from primary smelting. The combined output of primary and secondary aluminum in ingot form is then distributed as shown to downstream operations to manufacture various products: shape casting (e.g., vehicle engine blocks), extrusion (e.g., bars and tubes), and rolling (e.g., foil). Process scrap from these operations is collected and recycled in the secondary smelting operations into new ingots. All operations in the complex consume a total of 15 971 kWh per ton of primary aluminum produced. It can be seen that a large proportion of this total (15 875 kWh) is consumed in the primary smelting operations. The corresponding P-graph representation of the industrial complex is shown in Figure 2. Each plant is represented by a horizontal bar, while each commodity (i.e., raw material, product, or intermediate) is represented with a dot. The arcs in

Figure 2. P-graph of baseline state of aluminum complex in case study 1.

D


Article

Industrial & Engineering Chemistry Research the P-graph indicate the input−output linkages in the industrial complex labeled with the intensity associated with the material or energy flow. Next, it is assumed that there is an arbitrary 2% reduction in the availability of electricity due to a droughtinduced power shortage (in practice, the degree of reduction is highly context-specific). This deficit thus necessitates planning for optimal operations for the duration of the crisis. Table 2 Table 2. Characteristics of Operations Generating Final Aluminum Products operation shape casting extrusion rolling

baseline-state output (t/h)

minimum partial load (%)

relative value of product per unit mass

0.738

60

1.5

0.228 0.034

50 80

1.2 1.0

lists the characteristics of the shape casting, extrusion, and rolling operations in the industrial complex. The third column gives the minimum partial viable load for the plants; below these thresholds, the plants cannot operate economically and would thus need to be shut down completely. The fourth column gives the relative prices of the three final products; for example, the relative cost of 1.25 indicates that shape cast aluminum is 25% more expensive than rolled aluminum per unit mass. These prices are assumed to be fixed (in practice, the model can also be implemented using actual prices per unit mass). The resulting problem is to determine the optimal adjustment of operating capacities for the plants during the power shortage, and consequently to determine the adjusted allocation of streams in the industrial complex. This “damage control” plan may be determined by maximizing the total combined value of product output from the system using PGraph Studio, subject to a new upper limit on the availability of electricity supply. The resulting P-graph for the optimal state of the industrial complex during the crisis is shown in Figure 3. Note that the network topology remains the same as in Figure 2, indicating that a 2% reduction of power supply does not necessitate shutting down any of the component plants. Table 3 gives the relative reduction in capacities of the plants in the industrial complex. It can be seen that the optimal solution that maximizes total product value requires sacrificing the lowervalue products in favor of the higher-value products. In this case, the model solution prescribes no reduction in the output of shape cast aluminum, while the outputs of extruded aluminum and rolled aluminum are reduced by 5.5% and 20%, respectively. Outputs of the other component plants are adjusted accordingly based on material and energy balance considerations in the system. One of the advantages of P-graph methodology is the capability of identifying near-optimal solutions. At 2% perturbation, there are nine possible alternative solutions. Figure 4 then shows the levels of production in each of these nine solutions, arranged in descending order of optimality rank (i.e., the first-ranked production levels coincide with the results shown in Figure 3 and Table 3). Note that these are the optimal solutions for each of nine feasible network topologies identified within the P-graph framework. The eight nearoptimal solutions may then be considered by a decision-maker for implementation in addition to the optimal one, especially if intangible criteria need to be taken into account. It should be noted that enumerating such solutions is not readily

Figure 3. P-graph of optimal operating state under crisis of aluminum complex in case study 1.

Table 3. Optimal Reduction in Capacity under Crisis Conditions in Case Study 1 process

capacity reduction (%)

power generation mining primary smelting recycling shape casting extrusion cold rolling

2 1.9 1.9 5.5 0 5.5 20

accomplished via mathematical programming methods.15 In practice, it is also essential to assess the impact of different magnitudes of perturbation. Figure 5 shows the sensitivity of the optimal solution to the gravity of the power shortage beyond the 2% scenario previously analyzed. Shortage levels ranging from 5−30% are assessed at increments of 5%. Note that, in the optimal solution, the rolling operations are shut down completely at 5% shortage and above. On the other hand, the extrusion plant is also prescribed to be shut down once electricity availability drops by 30% below the normal state.

5. CASE STUDY 2: BIOMASS PROCESSING COMPLEX This case study is based on a biomass processing complex concept described by Martin and Eklund.61 Such systems are also known by various terms, such as “bioenergy parks” which is derived from similar terminology in industrial symbiosis (IS) literature (e.g., eco-industrial parks). While it has been argued that integration among plants in a biomass processing complex can yield significant gains in resource efficiency and emissions reduction,61 it has also been argued that such tightly integrated systems are vulnerable to cascading failures when subjected to disruptive events.62 Furthermore, in practice, such systems need E


Article


Figure 4. Optimal and near-optimal solutions in case study 1.

Figure 5. Sensitivity analysis for case study 1.

to be planned to be robust to multiple disruption scenarios63 and subsequently able to recover to normal production levels.64 Figure 6 shows the baseline state of the system with four major component plants. The main products are bioethanol (from wheat), biodiesel (from vegetable oil and ethanol), and biogas (from waste biomass), produced by the plants labeled as BEP, BDP, and BGP, respectively. The relevant data for these three plants are summarized in Table 4. Note that the gross output of the BEP and BGP exceed the final product rates that exit the industrial complex because some of the ethanol and biogas are consumed internally within the system. A centralized combined heat and power (CHP) plant is used to supply the electricity and steam requirements within the complex, using biogas and externally sourced biomass as fuel. The equivalent depiction of this industrial complex as a P-graph is shown in Figure 7.

It is then assumed that there is a 2% loss of capacity of the CHP plant, which manifests as proportionate reductions in both electricity and steam output. As in the previous case study, this level of inoperability is arbitrary, and in practice the extent of capacity loss may vary depending on the context. The problem is to determine the capacity adjustments in the other plants in order to achieve the highest total revenue from the product streams during the crisis. The optimal “damage control” strategy is shown as a P-graph in Figure 8. Table 5 summarizes the capacity adjustments necessary for the component plants. Note that the BEP and BDP need to reduce output at a scale similar to that of the CHP plant; however, the BGP is immediately adjusted to its lowest feasible output level, corresponding to 85% of its baseline state. This trend is attributable to the relatively low value of the biogas product. Unlike in the previous case study, only one feasible F


Article


Figure 6. Baseline state of bioenergy complex in case study 2.

its rated capacity but is never shut down entirely, because the biogas is needed as fuel for the CHP. On the other hand, at 25% loss of CHP capacity, it becomes necessary to temporarily shut down the BDP, which then allows the scarce power and heat to be prioritized for use by the BEP and BGP.

Table 4. Characteristics of Operations Generating Final Biomass-Based Products plant

baseline-state output

minimum partial load (%)

price of product

BEP BDP BGP

29 720 L/h 20 000 L/h 1 447 m3/h

75 80 85

US$0.56/L US$1.00/L US$0.42/m3

6. CONCLUSION A P-graph approach to optimizing crisis operations in an industrial complex has been developed in this work. This method enables optimal and near-optimal reallocation of production capacity and product streams to be determined to minimize losses during such crises that may be caused by

network topology exists, so that only one optimal solution is identified. Further sensitivity analysis with respect to reduction of the CHP output by 5−25% is shown in Figure 9. It is notable that, throughout this entire range, the BGP operates at 85% of

Figure 7. P-graph of baseline state of biomass complex in case study 2. G


Article


Figure 8. P-graph of optimal operating state under crisis of biomass complex in case study 2.

discretized linear operating states under different partial load conditions. Also, a multiperiod variant can also be developed based on this approach given a dynamic perturbation profile.56,65 In addition, the capability of P-graph methodology to generate a set of near-optimal solutions suggests that a detailed hybrid decision analysis approach can be developed to aid in practical decision-making industrial contexts.

Table 5. Optimal Reduction in Capacity in Case Study 2 under Crisis Conditions process

capacity reduction (%)

CHP BEP BDP BGP

2 1.1 0 15

■

APPENDIX The general PNS problem can also be formulated as an MILP model, as shown:

climatic effects, as well as disruptive events such as industrial accidents, intentional malicious attacks, and natural disasters. One key advantage of this approach is the ability to identify an array of near-optimal solutions, which is not readily possible using mathematical programming, but may be necessary in reallife decision-making that often involves intangible considerations. Two literature case studies on an aluminum complex and a biomass processing complex have been solved to illustrate this methodology. It is seen in both examples that the P-graph framework enables systematic planning of operations during the transient crisis. In addition to these problems, the P-graph framework lends itself to various potential extensions for industrial complex optimization. For example, future work can focus on extending this to a multiobjective framework by integrating economic and sustainability considerations. Nonlinearity in the process coefficients can be reflected via a set of

max c1Ty − (c 2 Tx + c3Tb)

subject to Ax = y

(A-1)

(A-2)

yL ≤ y ≤ yU

(A-3)

diag(b)xL ≤ x ≤ diag(b)xU

(A-4)

bi ∈ {0, 1} ∀ i

(A-5)

In general, the objective function maximizes annual profit (eq A-1), which comprises the net annual value of streams (c1Ty) minus the annualized capital cost of process units (c2Tx + c3Tb).

Figure 9. Sensitivity analysis for case study 2. H


Article


Contribution to AR5. Available at: http://www.ipcc-wg2.gov/AR5/ (accessed March 4, 2014). (3) Varbanov, P. S. Energy and water interactions: implications for industry. Curr. Opin. Chem. Eng. 2014, 5, 15−21. (4) Kaplan, S.; Garrick, B. On the quantitative definition of risk. Risk Anal. 1981, 1, 11−27. (5) Haimes, Y. Y.; Jiang, P. Leontief-Based Model of Risk in Complex Interconnected Infrastructures. Journal of Infrastructure Systems 2001, 7, 1−12. (6) Santos, J. R.; Haimes, Y. Y. Modeling the demand reduction input-output (I-O) inoperability due to terrorism of interconnected infrastructures. Risk Anal. 2004, 24, 1437−1451. (7) Leontief, W. Quantitative input and output relations in the economic system of the United States. Review of Economics and Statistics 1936, 18, 105−125. (8) Isard, W.; Vietorisz, T. Industrial complex analysis and regional development. Papers in Regional Science 1955, 1, 227−247. (9) Hendrickson, C. T.; Lave, L. B.; Matthews, H. S. Environmental Life Cycle Assessment of Goods and Services: An Input-Output Approach; Resources for the Future Press: Washington, DC, 2006. (10) Tan, R. R.; Lam, H. L.; Kasivisvanathan, H.; Ng, D. K. S.; Foo, D. C. Y.; Kamal, M.; Hallaler, N.; Klemes, J. J. An algebraic approach to identifying bottlenecks in linear process models of multi-functional energy systems. Theor. Found. Chem. Eng. 2012, 46, 642−650. (11) Jia, X. P.; Li, Z.; Wang, F.; Foo, D. C. Y.; Tan, R. R. Integrating input-output models with pinch technology for enterprise sustainability analysis. Clean Technol. Environ. Policy 2015, 17, 2255−2265. (12) Jiang, P.; Haimes, Y. Y. Risk management for Leontief-based interdependent systems. Risk Anal. 2004, 24, 1215−1229. (13) Kasivisvanathan, H.; Bareilea, I. D. U.; Ng, D. K. S.; Tan, R. R. Optimal operational adjustment in multi-functional energy systems in response to process inoperability. Appl. Energy 2013, 102, 492−500. (14) Tan, R. R.; Aviso, K. B.; Promentilla, M. A. B.; Yu, K. D. S.; Santos, J. R. A fuzzy linear programming model for allocation of inoperability in economic sectors due to loss of natural resource inputs. DLSU Business & Economics Review 2015, 24, 1−12. (15) Tan, R. R.; Aviso, K. B.; Cayamanda, C. D.; Chiu, A. S. F.; Promentilla, M. A. B.; Ubando, A. T.; Yu, K. D. S. A fuzzy linear programming enterprise input−output model for optimal crisis operations in industrial complexes. International Journal of Production Economics 2015, in press. DOI: 10.1016/j.ijpe.2015.10.012. (16) Friedler, F.; Tarjan, K.; Huang, Y. W.; Fan, L. T. Graphtheoretic approach to process synthesis: axioms and theorems. Chem. Eng. Sci. 1992, 47, 1973−1988. (17) Friedler, F.; Tarjan, K.; Huang, Y. W.; Fan, L. T. Combinatorial algorithms for process synthesis. Comput. Chem. Eng. 1992, 16, 313− 320. (18) Friedler, F.; Tarjan, K.; Huang, Y. W.; Fan, L. T. Graphtheoretic approach to process synthesis: polynomial algorithm for maximal structure generation. Comput. Chem. Eng. 1993, 17, 929−942. (19) Tan, R. R.; Cayamanda, C. D.; Aviso, K. B. P-graph approach to optimal operational adjustment in polygeneration plants under conditions of process inoperability. Appl. Energy 2014, 135, 402−406. (20) Aviso, K. B.; Cayamanda, C. D.; Solis, F. D. B.; Danga, A. M. R.; Promentilla, M. A. B.; Yu, K. D. S.; Santos, J. R.; Tan, R. R. P-Graph Approach for GDP-Optimal Allocation of Resources, Commodities and Capital in Economic Systems under Climate Change-Induced Crisis Conditions. J. Cleaner Prod. 2015, 92, 308−317. (21) Klemeš, J. J.; Friedler, F.; Bulatov, I.; Varbanov, P. Sustainability in the Process Industry: Integration and Optimization. McGraw-Hill: New York, 2011. (22) www.p-graph.com (accessed August 30, 2015). (23) Klemeš, J. J.; Varbanov, P. S. Spreading the Message: P-Graph Enhancements: Implementations and Applications. Chem. Eng. Trans. 2015, 45, 1333−1338. (24) Lee, S.; Park, S. Synthesis of mass exchange network using process graph theory. Comput. Chem. Eng. 1996, 20, S201−S205.

The material and energy balances of the system are signified by eq A-2. The rows and columns of the process matrix A correspond to streams and process units, respectively; sign convention is based on enterprise I−O models.9 Vector x denotes the non-negative capacities of process units. Vector y denotes the net flow rates of streams exiting the system, which are assumed here to be given on an annual basis. Note that the values of the elements of y are negative for inputs (e.g., raw materials), zero for intermediates, and positive for outputs (i.e., products). Limiting values for net flow rates are specified by eq A-3. Similarly, eq A-4 specifies limits for the capacities of the process units; the vector of binary variables b signifies the existence or nonexistence of process units (eq A-5). This generic MILP model for PNS problems can then be modified for the specific problem in this paper, as follows: • Only the first term of the objective function is considered; c2 and c3 are assumed to be equal to zero because the “process units” (i.e., plants) already exist, and capital investments are sunk costs. • The vector xL is used to specify the lower operating limit of the plants in absolute units; hence, the ratios of corresponding elements of xL and x give the fractional part-load operating limits, below which these plants are not economically viable to operate. • The vector b is used to denote whether plants continue to operate during the crisis or need to be temporarily shut down.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors are grateful for the financial support of the Philippine Commission on Higher Education (CHED) via the PHERNet Sustainability Studies Program.

■

NOMENCLATURE

Parameters

A = Process matrix c1 = Stream unit price vector c2 = Annualized variable capital cost coefficient vector c3 = Annualized fixed cost coefficient vector xL = Process unit capacity lower limit vector xU = Process unit capacity upper limit vector yL = Net output lower limit vector yU = Net output upper limit vector Variables

b = Process unit selection vector with binary elements x = Process unit capacity vector y = Net output vector

■

REFERENCES

(1) Steffen, W.; Richardson, K.; Rockstrom, J.; Cornell, S. E.; Fetzer, I.; Bennett, E. M.; Biggs, R.; Carpenter, S. R.; de Vries, W.; de Wit, C. A.; Folke, C.; Gerten, D.; Heinke, J.; Mace, G. M.; Persson, L. M.; Ramanathan, V.; Reyers, B.; Sorlin, S. Planetary boundaries: Guiding Human development on a changing planet. Science 2015, 347, 1259855. (2) Intergovernmental Panel on Climate Change. Climate change 2014: Impacts, adaptation and vulnerability, IPCC Working Group II I


Article

Industrial & Engineering Chemistry Research (25) Nagy, A. B.; Adonyi, R.; Halasz, L.; Friedler, F.; Fan, L. T. Integrated synthesis of process and heat exchanger networks: algorithmic approach. Appl. Therm. Eng. 2001, 21, 1407−1427. (26) Seo, H.; Lee, D. Y.; Park, S.; Fan, L. T.; Shafie, S.; Bertok, B.; Friedler, F. Graph-theoretical identification of pathways for biochemical reactors. Biotechnol. Lett. 2001, 23, 1551−1557. (27) Fan, L. T.; Bertok, B.; Friedler, F. A graph-theoretic method to identify candidate mechanisms for deriving the rate law of a catalytic reaction. Comput. Chem. 2002, 26, 265−292. (28) Lin, Y. C.; Fan, L. T.; Shafie, S.; Hohn, K. L.; Bertók, B.; Friedler, F. Catalytic pathways identification for partial oxidation of methanol on copper-zinc catalysts: CH3OH + 1/2O2 ↔ CO2 + 2H2. Ind. Eng. Chem. Res. 2008, 47, 2523−2527. (29) Lin, Y. C.; Fan, L. T.; Shafie, S.; Bertok, B.; Friedler, F. Graphtheoretic approach to the catalytic pathway identification of methanol decomposition. Comput. Chem. Eng. 2010, 34, 821−824. (30) Halasz, L.; Nagy, A. B.; Ivicz, T.; Friedler, F.; Fan, L. T. Optimal retrofit design and operation of the steam-supply system of a chemical complex. Appl. Therm. Eng. 2002, 22, 939−947. (31) Halim, I.; Srinivasan, R. Systematic waste minimization in chemical processes. 1. Methodology. Ind. Eng. Chem. Res. 2002, 41, 196−207. (32) Halim, I.; Srinivasan, R. Systematic waste minimization in chemical processes. 3. Batch operations. Ind. Eng. Chem. Res. 2006, 45, 4693−4705. (33) Feng, G.; Fan, L. T.; Seib, P. A.; Bertok, B.; Kalotai, L.; Friedler, F. Graph-theoretic method for the algorithmic synthesis of azeotropicdistillation systems. Ind. Eng. Chem. Res. 2003, 42, 3602−3611. (34) Liu, J.; Fan, L. T.; Seib, P.; Friedler, F.; Bertok, B. Downstream process synthesis for biochemical production of butanol, ethanol, and acetone from grains: generation of optimal and near-optimal flowsheets with conventional operating units. Biotechnol. Prog. 2004, 20, 1518−1527. (35) Liu, J.; Fan, L. T.; Seib, P.; Friedler, F.; Bertok, B. Holistic approach to process retrofitting: application to downstream process for biochemical production of organics. Ind. Eng. Chem. Res. 2006, 45, 4200−4207. (36) Xu, X.; Zhu, C.; Ma, Y.; Song, H. A robust combinatorial approach based on P-graph for superstructure generation in downstream bioprocesses. Braz. J. Chem. Eng. 2015, 32, 259−267. (37) Lee, D. Y.; Fan, L. T.; Park, S.; Lee, S. Y.; Shafie, S.; Bertok, B.; Friedler, F. Complementary identification of multiple flux distributions and multiple metabolic pathways. Metab. Eng. 2005, 7, 182−200. (38) Fan, L. T.; Zhang, T.; Liu, J.; Schlup, J. R.; Seib, P. A.; Friedler, F.; Bertok, B. Assessment of sustainability-potential: hierarchical approach. Ind. Eng. Chem. Res. 2007, 46, 4506−4516. (39) Fan, L. T.; Zhang, T.; Liu, J.; Seib, P.; Friedler, F.; Bertok, B. Price-targeting through iterative flowsheet syntheses in developing novel processing equipment: pervaporation. Ind. Eng. Chem. Res. 2008, 47, 1556−1561. (40) Varbanov, P.; Friedler, F. P-graph methodology for costeffective reduction of carbon emissions involving fuel cell combined cycles. Appl. Therm. Eng. 2008, 28, 2020−2029. (41) Lam, H. L.; Varbanov, P. S.; Klemes, J. J. Optimisation of regional energy supply chains utilising renewables: P-graph approach. Comput. Chem. Eng. 2010, 34, 782−792. (42) Bertok, B.; Kalauz, K.; Sule, Z.; Friedler, F. Combinatorial algorithm for synthesizing redundant structures to increase reliability of supply chains: application to biodiesel supply. Ind. Eng. Chem. Res. 2012, 52, 181−186. (43) Vance, L.; Cabezas, H.; Heckl, I.; Bertok, B.; Friedler, F. Synthesis of sustainable energy supply chain by the P-graph framework. Ind. Eng. Chem. Res. 2012, 52, 266−274. (44) Vance, L.; Heckl, I.; Bertok, B.; Cabezas, H.; Friedler, F. Designing sustainable energy supply chains by the P-graph method for minimal cost, environmental burden, energy resources input. J. Cleaner Prod. 2015, 94, 144−154.

(45) Heckl, I.; Friedler, F.; Fan, L. T. Solution of separation network synthesis problems by the P-graph methodology. Comput. Chem. Eng. 2010, 34, 700−706. (46) Barany, M.; Bertok, B.; Kovacs, Z.; Friedler, F.; Fan, L. T. Solving vehicle assignment problems by process-network synthesis to minimize cost and environmental impact of transportation. Clean Technol. Environ. Policy 2011, 13, 637−642. (47) Adonyi, R.; Heckl, I.; Olti, F. Scheduling of bus maintenance by the P-graph methodology. Optimization and Engineering 2013, 14, 565−574. (48) Lam, H. L.; Klemes, J. J.; Varbanov, P. S.; Kravanja, Z. P-graph synthesis of open-structure biomass networks. Ind. Eng. Chem. Res. 2012, 52, 172−180. (49) Lam, H. L. Extended P-graph applications in supply chain and process network synthesis. Curr. Opin. Chem. Eng. 2013, 2, 475−486. (50) Garcia-Ojeda, J. C.; Bertok, B.; Friedler, F. Planning evacuation routes with the P-graph framework. Chem. Eng. Trans. 2012, 29, 1531−1536. (51) Tick, J.; Imreh, C.; Kovacs, Z. Business process modeling and the robust PNS problem. Acta Poly. Hung. 2013, 10, 193−204. (52) Chong, F. K.; Lawrence, K. K.; Lim, P. P.; Poon, M. C. Y.; Foo, D. C. Y.; Lam, H. L.; Tan, R. R. Planning of carbon capture storage deployment using process graph approach. Energy 2014, 76, 641−651. (53) Kollmann, R.; Maier, S.; Shahzad, K.; Kretschmer, F.; Neugebauer, G.; Stoeglehner, G.; Ertl, T.; Narodoslawsky, M. Waste water treatment plants as regional energy cells − evaluation of economic and ecologic potentials in Austria. Chem. Eng. Trans. 2014, 39, 607−612. (54) Maier, S.; Narodoslawsky M. Optimal renewable energy systems for smart cities. Proceedings of the 24th European Symposium on Computer Aided Process Engineering − ESCAPE 24, June 15−18, 2014, Budapest, Hungary, pp 1849−1854. (55) Frits, M.; Bertok, B. Process scheduling by synthesizing time constrained process-networks. Proceedings of the 24th European Symposium on Computer Aided Process Engineering − ESCAPE 24, Budapest, Hungary, June 15−18, 2014; pp 1345−1350. (56) Heckl, I.; Halasz, L.; Szlama, A.; Cabezas, H.; Friedler, F. Process synthesis involving multi-period operations by the P-graph framework. Comput. Chem. Eng. 2015, 83, 157−164. (57) Garcia-Ojeda, J. C.; Bertok, B.; Friedler, F.; Argoti, A.; Fan, L. T. A Preliminary Study of the Application of the P-graph Methodology for Organization-based Multiagent System Designs: Assessment. Acta Poly. Hung. 2015, 12, 103−122. (58) Bartos, B.; Bertok, B. Synchronization and Load Distribution Strategies for Parallel Implementations of P-graph Optimizer. MACRo 2015 − 5th International Conference on Recent Achievements in Mechatronics, Automation, Computer Science and Robotics, Tirgu Mures, Romania, March 6−7, 2015; pp 303−313. (59) Tan, R. R.; Aviso, K. B.; Yu, K. D. S; Promentilla, M. A. B; Santos, J. R. P-Graph Approach to Allocation of Inoperability in Urban Infrastructure Systems. Chem. Eng. Trans. 2015, 45, 1339−1344. (60) Nappi, C. 2013. The Global Aluminum Industry 40 Years from 1972. www.world-aluminium.org (accessed April 30, 2015). (61) Martin, M.; Eklund, M. Improving the environmental performance of biofuels with industrial symbiosis. Biomass Bioenergy 2011, 35, 1747−1755. (62) Benjamin, M. F. D.; Tan, R. R.; Razon, L. F. A methodology for criticality analysis in integrated energy systems. Clean Technol. Environ. Policy 2015, 17, 935−946. (63) Benjamin, M. F. D; Tan, R. R.; Razon, L. F. Probabilistic multidisruption risk analysis in bioenergy parks via physical input-output modeling and analytic hierarchy process. Sustainable Production and Consumption 2015, 1, 22−33. (64) Benjamin, M. F. D.; Ubando, A. T.; Razon, L. F.; Tan, R. R. Analyzing the disruption resilience of bioenergy parks using dynamic inoperability input−output modeling. Environment Systems and Decisions 2015, 35, 351−362. J


Article

Industrial & Engineering Chemistry Research (65) Tan, R. R.; Aviso, K. B. An Extended P-Graph Approach to Process Network Synthesis for Multi-Period Operations. Comput. Chem. Eng. 2015, 85, 40−42.

K


P-Graph Approach to Optimizing Crisis Operations in an Industrial

Recommend Documents