P-Graph Synthesis of Open-Structure Biomass Networks - American

Article pubs.acs.org/IECR

P‑Graph Synthesis of Open-Structure Biomass Networks Hon Loong Lam,† Jiří Jaromír Klemeš,*,‡ Petar Sabev Varbanov,‡ and Zdravko Kravanja§ †

Department of Chemical and Environmental Engineering, University of Nottingham Malaysia Campus, Jalan Broga, 43500 Semenyih, Selangor, Malaysia ‡ Centre for Process Integration and Intensification - CPI2, Research Institute of Chemical and Process Engineering - MŰ KKI, Faculty of Information Technology, University of Pannonia, Egyetem u. 10, H-8200, Veszprém, Hungary § Faculty of Chemistry and Chemical Engineering, University of Maribor, Smetanova ul. 17, SI-2000, Maribor, Slovenia ABSTRACT: This paper presents an extended implementation of a P-graph for an open-structure biomass network synthesis. Biomass and biofuel production networks syntheses are generally complex tasks of a considerable scale and comprehensive interactions. The applications of information technology and computer software tools, in this case P-graph, are essential for providing fast and as accurate as possible solutions with a user-friendly interface. This work demonstrates the relationships of mathematical models with P-graph representations. A case study is included that demonstrates the implementation of a framework regarding a P-graph for an extension to biomass network synthesis. An assessment and evaluation of P-graph and Mathematical Programming as a method for biomass supply chain synthesis concludes this paper.

1. INTRODUCTION The P-graph framework was first introduced by Friedler et al.1 and further developed for systematic optimal design of industrial processes2,3 as generating candidate molecules with desired properties,4 developing a separation network system by Kovacs et. al.5 and later further developed by Heckl et al.,6 synthesizing alternative sequences for azeotropic distillation system,7 generating an integrated synthesis of heat exchanger network,8 indentifying the pathways for chemical9 and biochemical reaction,10 deriving the rate law of a catalytic reaction,11 synthesizing the sustainable process for renewable resources,12 cost-effective reduction of carbon emissions involving fuel cell combined cycles,13 generating regional renewable energy supply chain,14 developing a cell-based dynamic heat exchanger models,15 and also solving the supply chain problem such as minimizing the cost and environmental impact of transportation,16 with considering the uncertainties along the supply chain.17 These papers show how the synthesis of optimal solution can successfully be performed in a systematic way. The holistic biomass supply network synthesis is generally a complex task of considerable scale and comprehensive interactions. This is mainly due to (i) large land areas used to collect and process the incoming solar radiation before the energy can be harvested, (ii) the distributed nature of the biomass resources, and (iii) the usually low-energy density of the biomass. It should be noted that due to this complexity, the term used is “supplynetwork” rather than “supply-chain”. The methods for optimizing supply chains have traditionally relied on Mathematical Programming (MP). MP has also been used for renewable energy supply chain studies, such as modeling, optimization, and synthesis. There are several challenges concerning biomass utilization that have to be solved:18 (i) The bioenergy networks should as much as possible utilize raw materials. (ii) The choices of feedstock and products are mutually related and significantly affect the overall economic viability and emissions as well as each other. (iii) The modeling framework should provide evaluations of alternative options for locating and sequencing the © 2012 American Chemical Society

various processing and transportation operations within the supply networks. There are some works have been carried out to tackle the biomass supply chain issues. Lam et al.19,20 presented an application of the Pinch analysis analogy regarding biomass network synthesis, zone clustering, and regional resources management. Lam et al.21 also discussed the complexities of large-scale biomass networks and proposed the model-size reduction techniques accordingly for solving complex biomass network problems. Freppaz et al.22 demonstrated a decision support system, which aimed at optimizing forest biomass exploitation for energy supply at a regional level. Dunnett et al.23 presented a systems’ modeling framework for the simultaneous design and operations scheduling of a biomass to heat supply chain. Rentizelas et al.24 focused on the logistics issue of biomass utilization, especially storage and multibiomass supply chain optimization. An Integrated Biomass Supply and Logistics (IBSAL) Model was proposed and presented by Shahab et al.25 IBSAL consists of a series of equations that calculate the collectable fractions of biomass, while tracking biomass moisture during harvesting and storage, machinery performance, compositional changes, and dry matter losses. Iakovou et al.26 provided an overview of the generic system’s components and then the unique characteristics of waste biomass-to-energy supply chain management that differentiate them from traditional supply chains. Recently, the research on the biomass supply chains also focuses on the sustainable development such as the total footprints-based multicriteria optimization of regional biomass energy supply chains presented by Č uček et al.27 and supply chain management of agricultural Special Issue: L. T. Fan Festschrift Received: Revised: Accepted: Published: 172

May 7, August August August

2012 21, 2012 29, 2012 29, 2012

dx.doi.org/10.1021/ie301184e | Ind. Eng. Chem. Res. 2013, 52, 172−180

Industrial & Engineering Chemistry Research

Article

Figure 1. Open-structured regional biomass network (after Lam et al.21).

representation that describes the concept of the supply network. A case study is demonstrated in order to illustrate the advantages of applying a P-graph to the synthesis of a biomass supply network.

waste for biomass utilization and CO2 emission reduction by Thanarak.28 Biomass frameworks can be categorized as (i) open-structured networks and (ii) fix-structured networks. The open-structured biomass network gives rise to a generic model covering all possible connections within the system. These connections can be formed between all points or nodes from different layers, such as the harvesting, collection and prepreparation, core processing, and distribution of products, as shown in Figure 1. The fixstructured biomass network is modeled based on well predefined superstructural nodes (production plants and technologies) and their connections, for example the biomass network shown in Figure 2. The open-structured network is typically used for the synthesis of new biomass supply networks, while the fix-structured network is for the reconstruction of existing ones. In both cases, a solution network-structure will be selected from those feasible connections and technologies that are defined as alternatives within their superstructures. On the one hand in the open-structured network problems, there are many alternatives for selecting plants, technologies, and connections. As a result the synthesis task usually poses a highly combinatorial problem. On the other hand, the fix-structured network does not contain many alternatives, and, consequently, it features much simpler combinations. The applications of information technology and computer software tools, such as the PNS Editor29 which is a software package designed to solve problems in process network synthesis by P-graph methodology.1 Those tools are essential for providing fast and as far as possible accurate solutions with a user-friendly interface. This paper first presents a brief overview of the P-graph framework. It is followed by a section that presents the P-graph

2. P-GRAPH FRAMEWORK The P-graph is a directed bipartite graph, having two types of vertices − one for operating units and the other for those objects representing material or energy-flows’ quantities. The vertices are connected by directed arcs.1 Operating units and process streams are modeled by separate sets (O and M respectively), and the arcs are expressed as ordered pairs. E.g. if an operation o1 ∈ O consumes material m1 ∈ M, then the arc representing this relationship is (m1, o1). There are several combinatorial instruments associated with it. The first is the set of axioms ensuring representation unambiguity1 and the consistencies of the resulting superstructures and solution networks. The other instruments are the three main algorithms as follows: (i) superstructure construction − MSG,30 (ii) superstructure traversal and the generation of combinatorially feasible network structures − SSG,31 and (iii) superstructure optimization branch-and-bound algorithm ABB.32 The procedure for the supply network synthesis with P-graph approach follows the algorithm illustrated in Figure 3. 3. BIOMASS SUPPLY NETWORK MODEL WITH P-GRAPH REPRESENTATION An open-structure four-layer supply chain network has been developed Č uček et al.18 It includes the harvesting, collection and preprocessing, core processing, and distribution of products (see Figure 4). This considered system’s boundaries involve a region, 173



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Figure 2. Fix-structured biomass network (after Lam et al.14).

Figure 4. The open-structure of the networks for renewable energy production and consumption (after Č uček et al.18).

Some of the important mass-balance equations are summarized in the following equations; the environmental impact, cost functions, and the objective functions are fully presented in the paper of Č uček et al.18 The mass balance model follows the four-layer nature of the network’s superstructure Figure 4, starting from the harvesting and supply (L1) layer, collection and preprocessing (L2), main processing (L3), up to the use of the (L4) layer. Biomass pi produced at zone i, is transported from L1 to collection centers m at L2: Figure 3. P-graph biomass supply network synthesis procedure (after Lam et al.14).

qim, pi,L1 =

∑ m∈M

which is then divided into zones for optimizing conversion operations and transportation flows. This model has been formulated with profit maximization as the optimization criterion.

qim, m,L1,L2 ∀ pi ∈ PI , ∀ i ∈ I , pi

(1)

This equation is then represented in the P-graph approach in Figure 5. Constraint in eq 2 is used to determine the selection or rejection of the collection and intermediate process center m. 174



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Figure 5. P-graph representations of the relationships between L1-L2.

These centers have to operate within the minimal and maximal products’ mass flows: qm ,L2,LO·ymL2 ≤

∑ ∑

Figure 7. P-graph representation of the technology selection-scheme in the Plant n.

qim, m,L1,L2 ≤ qm ,L2,UP ·ymL2 ∀ m ∈ M , pi

i ∈ I pi ∈ PI

(2)

The produced products pp are finally collected from different technologies and plants and sent to customers:

The pretreated intermediate product pi can be transported from the collection and intermediate process center m at L2 to the process plant n at L3 or directly to customer j at L4, if the product pi is also a direct product pd(pi). Figure 6 shows the P-graph representation of these relationships.

∑

qnm, pi,T,L2,L3 = , pp , t

∑

(pi , t ) ∈ PT (pi , pp) ∈ PIP

∀ n ∈ N , pp ∈ PP ∑ qnm,j,L3,L4 , pp j∈J

(6)

The P-graph representation of the L3-L4 relationship is shown in Figure 8.

Figure 8. P-graph representation of the relationships between L3-L4.

Local demand for products p is the sum of the produced products from plants pp and the directly used products pd: Figure 6. P-graph representations of the relationships between L2-L3 and L2-L4.

Dem jo , p ≥

qnm, j,L3,L4 + o , pp

∑ ∑ n ∈ N pp ∈ PP ⊆ P

∑

qim, m,L1,L2 ·f piconv,L2 , pi

i∈I

∑

=

qmm,,L2,L3 n , pi

+

n∈N

∑ ∑

∑ m∈M

=

∑

qnm, pi,T,L2,L3 ,t

(7)

Objective Function. The objective function maximizes the profit before tax (PB):

(3)

PB =

∑∑ ∑ o

3, L 4 price qnm, j,oL, pp ·cpp

n ∈ N j ∈ J pp ∈ PP

∀ n ∈ N , ∀ pi ∈ PI

+

price qmm,,L2,L4 ·cpd j o , pd

∑ ∑ ∑ o

m ∈ M j ∈ J pd ∈ PD

(pi , t ) ∈ PT

(4)

+

where the intermediate product is converted into the endconv,L3 product pp using the corresponding conversion factor f pi,pp,t . Process conversion is handled as the amount of product flow-rate compared to the inlet flow-rate to the processing plant with technology t, f m,T,L2,L3 n,pi,pp,t (t/y) and is shown in eq 5 and Figure 7.

∑∑ ∑ e

price qnm, j,L3,L4 ·0.9·cpp e , pp

n ∈ N j ∈ J pp ∈ PP

+

∑ ∑ ∑ e

price qmm,,L2,L4 ·0.9·cpd j e , pd

m ∈ M j ∈ J pd ∈ PD

−

qnm, pi,T,L2,L3 ·f piconv,L3 = qnm, pi,T,L2,L3 , pp , t ,t , pp , t

∑ ∑ i ∈ I pi ∈ PI

qim, pi,L1·cpi − c tr − c op − c inv

(8)

The income represents the revenue from selling the products and from the tax imposed on the waste. The expenses represent the raw materials’ cost with price cpi, the transportation cost (ctr), the operating cost (cop), and annualized network investments (cinv).

∀ (n ∈ N , pi ∈ PI , pp ∈ PP , t ∈ T , (pi , pp) ∈ PIP)

qmm,,L2,L4 j o , pd

m ∈ M pd ∈ PD ⊆ P

∀ j ∈ J, ∀ p ∈ P

j ∈ J pd ∈ PD ⊆ PI

At plan n, the intermediate product pi is sent to the alternative technologies t: qmm,,L2,L3 n , pi

∑

o

qmm,,L2,L4 j , pd

∀ m ∈ M , ∀ pi ∈ PI

∑

(5) 175



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Figure 9. Regional plan for the demonstrated case study (after Č uček et al.18).

4. DEMONSTRATION CASE STUDY The data for this study were developed based on Central European conditions,. The structure of the bioenergy supply chain network is illustrated in Figure 9. The objective of superstructure optimization is to find an economically optimal strategy for coproducing bioethanol, heat, electricity, furniture boards, and corn for food. According to the above definition of ‘sets’, the demonstrated region was divided into ten zones (the rectangular box in Figure 9), each covering an area of 100 km2. The availability of resources is specified in Table 1 for each

intermediate materials. The latter can be regarded as the stepping stones on the paths from the system inputs to the products. As an example, materials/streams, identified for the considered system, are listed in Table 2. The demands for the products and their prices are shown in Table 3. In addition to the relevant material/ Table 2. Materials and Unit for P-Graph

Table 1. Regional Supply Data for the Case Study zone

available area for planting (km2)

forestry area (km2)

biomass waste (t/d)

MSW (kg/(capita·d))

1 2 3 4 5 6 7 8 9 10

20 20 65 30 40 25 65 45 10

15 60 10 15 100 30

4 4 2.75 1.25 2.75 2.75 3 2 2.5

1 1 -

zone. Several biomass were considered as the potential raw materials: corn grain (CG), corn stover (CS), wood chips (WC), municipal solid waste (MSW), manure (MN), and timber (TB). Various possible geographical features have been considered in the case study, for example, a hill and a lake, as illustrated in Figure 9. These features change the road conditions and the distances for biomass transportation within the considered case. In this case study, six collection centers (m), three plants (n), two locations of local customer demands (j1,2), and one export market (j3) are present. The transport conditions and distances between each layer are specified in Figure 9. Several technological options for raw material processing were considered during the synthesis. These are the dry-grind process for corn-based ethanol plants, anaerobic digestion of biomass waste, incineration of MSW, corn stover and wood-waste, and the sawing of timber for manufacturing boards. 4.1. Identification of Materials and Units in the PGraph Method. This step produces the specifications for the inputs to and outputs from the system, along with those for the

symbols

P-graph classification

CG CS TB WC MSW MN heat Elc BioE DDGS dig boards tl t2 t3 t4 t5 il,2,...,10

raw material raw material raw material raw material raw material raw material product/output product/output product/output product/output product/output product/output operating unit operating unit operating unit operating unit operating unit operating location

m1,2,...,6 nl,2,3 jl,2 j3

operating location operating location operating location operating location

description corn grain, produce from plantation area corn stover, produce from plantation area timber, produce from forestry area wood chips, residues from wood industry municipal solid waste, waste from resident area manure, residues from farming activity heat electricity bioethanol distillers dried grains with solubles digestates board for furniture bioethanol plant anaerobic digestion general incineration boards making MSW incineration 10 zones that supply the biomass to the network 6 collection centers 3 biomass conversion plants 2 local biomass product demands biomass products export market

Table 3. Demands for the Products and Their Prices heat electricity bioethanol corn-food DDGS digestate boards 176

demand

price

174,000 MWh/y 87,000 MWh/y 3,480 t/y 5,800 t/y -

61 €/MWh 100 €/MWh 550 €/t 121 €/t 120 €/t 24 €/t 250 €/t



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collection centers are illustrated in Figure 9. Once the raw materials are collected, they are sent to all feasible process plants (n1, n2, n3) for further biomass conversion. The location of the process plants is selected based on the optimum solution of the maximum profit which is subject to the transportation costs as well as the technologies (t) selected in the plant. Figure 10 shows an example that, once the corn stover is collected at m3, it is then sent to process plant n2 for further processing by an incinerator (t3). Finally the product of biomass conversion, electricity and heat are sent to local demand j2. The software tool Process Network Synthesis Editor29 is used to obtain the optimum solution for minimum production cost.

stream prices, other performance and economic data for the calculation are referred to in a previous paper:18 a) characteristics of the biomass, b) investment and operating cost of the preprocessing and process plants, c) product conversion rate, and d) parameters for environmental impact and transportation. 4.2. Identification of the Operating Candidate. This modeling step produces a set of candidate operating units, capable of transforming certain materials/streams into other ones so that the desired products can be produced from the specified raw materials through the defined intermediates.13 The candidate operating units such as the collection centers, process plants, and conversion technologies can be regarded as potential bridges between the intermediates. The hyperstructure is generated based on the P-graph representation as shown in Section 3. The hyperstructure is developed to find sufficient operating unit candidates so that there is at least one path connecting every product to at least one raw material. For illustration purposes, a part of the network from Zone −5 (i5) is shown in Figure 10. As defined in Table 1, Zone-5

5. RESULTS AND DISCUSSION The synthesis of biomass network has been performed based on the superstructure type involving 4 layers: supply, collection and pretreatment, processing, use. It has been implemented in a previous work as a Mixed-Integer Linear Programming (MILP) model33 and has been solved using GAMS (v. 23.6), CPLEX solver.34 In this the synthesis as been performed using a P-graph model. The optimum selection of technologies, plants location, and the annual amount of biomass product has been formulated with profit maximization as the optimization criterion as shown in Section 3. Both optimization results from the MILP and the Pgraph procedures are very similar regarding the optimum profit value around 34 M €/y, with only 4.3% difference, which was mainly because of the decimal point rounding. The optimum pathways/structures resulting from the P-graph are given in Table 4 and Figure 11, which include the following: input biomass quantities, type of energy carriers (input and intermediate materials), operating units, and final products for customers. Figure 11 shows an overall roadmap solution for the biomass supply chain problem discussed in the previous section. For example the corn stover stock from Zone 6, CS6, is transported to the collection point m1. Thereafter this corn stover is be sent to the conversion process complex n1 for further processing into other biomass products, such as distillers dried grains with solubles (DDGS), bioethanol, electricity, and heat. These specific final products are then distributed to the customers (j1, j2, and j3). For instance, those DDGSn1 produced from complex n1 are sent to customer j3 as DDGSj3. Combine the information and results presented in Table 3 and Figure 11, most of the raw materials are sent to the collection point m1 and continue the process at a biorefinery plant located within the same zone, n1. This is mainly because of the customer j1 requested huge demand for biomass products in this zone. It can be seen that for the biomass production within this relatively small-sized area, the central processing is economically more favorable than the distributed one (Table 4). The results also indicate that the reduction in cost of transportation has a significant effect on overall costing. It should also be noted that the amount of biomass satisfied the entire demand for electricity and biofuels in both cities j1 and j2.

Figure 10. An example of P-graph representation of the Zone i5 biomass supply chain network.

(i5) is suitable for a plantation which could produce corn grain (CG5) and corn stover (CS5) as the potential raw materials. Moreover, there is also some forestry area in Zone-5 which provides the raw materials of timber (TB5) and wood chips (WC5). The residence and farming activity in this zone also contributes municipal solid waste (MSW5) and manure (MN5). All these potential materials are then connected to all possible collection centers, namely m1, m2, ... m6. The locations of the Table 4. Location of the Plant and Yearly Amount of Bioenergy

products technologies

plant location

heat (MWh/y)

electricity (MWh/y)

ethanol (t/y)

DDGS (t/y)

digestate (t/y)

boards (t/y)

bioethanol plant (t1) anaerobic digestion (t2) general incineration (t3) boards making (t4) MSW incineration (t5)

n1 n3 n1 and n2 n1 n1, n2, and n3

36,469 27,097 329,360

25,462 19,053 229,779

63,300 -

48,995 -

6,571 -

9,182 -

177



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Figure 11. Graphical P-graph solution for optimum biomass supply chain.

The P-graph is easy for a user without a mathematical modeling background, as the user just needs to define the inputs and outputs for certain operating units. The P-graphs are powerful regarding the reduction of search space, which leads to faster solutions of extensive problems. The P-graph can be further supplemented by Mathematical Programming (MP), exhibiting useful and complementary advantages. Future development can be based on both further development of the P-graph framework and also on combining both the methods described.35 The possible research directions for combined P-graph and MP methods are as follows: 1. Multiple objective optimization for biomass supply networks that involve the economic, environmental, and social impacts, simultaneously. 2. A fast P-graph solution could provide mapping sets for the MP model in order to reduce superstructure and, hence, the model’s size. 3. Probably the most promising is the combination: The MP method could act as the external module for the P-graph, in order to provide external calculation/data such as nonlinear equations and experimental results for a further optimization system approach. With the use of the combined P-graph and MP framework, larger and more complex supply networks’ problems could be efficiently solved by exploiting the powerful complementary capabilities of both approaches.

Almost 95% of the ethanol and 70% of the electricity were exported via the market place indicated as j3.

6. ADVANTAGES OF THE P-GRAPH The P-graph shows its advantages as a powerful and flexible optimization tool for all concluded case studies. For the demonstrated biomass supply chain network synthesis it has been rather obvious. The P-graph is very efficient for effective examination of ‘what-if’ scenarios and conduction of the sensitivity analyses. The other advantages are summarized below: 1) Easy to implement. Most users, such as engineers and policy-makers, tend to favor algebraic and visualization tools such as the PNS Editor. The users of P-graph do not need special training with a modeling mathematical background, which is naturally appreciated by practicing engineers. The user just needs to define the relationships between the units and the respective input/output materials. P-graph models can be formulated in generic data-independent form; they are developed once only and can then be used for different applications by specifying only the related data inputs. 2) Flexibility during future extensions. Whenever new potential raw materials or technology are introduced, they can be defined under the P-graph framework, and the optimum solution will be recalculated using the new specifications. 3) Easily captures the synthetic and semantic contents of a process superstructure. It can be efficiently applied to model-size reduction by eliminating nonfeasible solutions within the network. P-graph is therefore especially powerful when optimizing open superstructures with many infeasible routes between all possible connections from each zone to each collection-node, from each collection to each process and technological node, and from there to each user node. 4) Fast solutions when generating all feasible solutions, especially for fixed-structured networks as demonstrated elsewhere.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The financial support from Grant Agreement No. 262205, the ́ Program Hungarian project Társadalmi Megújulás Operating (TÁ MOP-4.2.2/B-10/1-2010-0025), and Slovenian Program No. P2-0032 is gratefully acknowledged.

■

7. CONCLUSIONS This paper demonstrated the efficiency of applications of the P-graph method for the synthesis of an open-structure biomass production supply network. The relationships between the optimization equations and the related P-graph representations have been demonstrated on an open-structure biomass network.

NOMENCLATURE

Superscripts

UP LO L1 178

upper bound lower bound harvesting and supply layer dx.doi.org/10.1021/ie301184e | Ind. Eng. Chem. Res. 2013, 52, 172−180

Industrial & Engineering Chemistry Research L2 L3 L4 conv tr road yb op inv fix var.

Article

Variables

collection and preprocessing layer main processing layer customer layer conversion transport road conditions yearly basis operating costs investment costs cost coefficient for the fixed part of the annualized investment cost coefficient for the variable part of the annualized investment

qm,L1 ipi qm,La,Lb x,y,p qm,T,L2,L3 n,pi,t qm,T,L2,L3 n,pi,pp,t ctr cop cop,L2 pi cop,L3 pi,t

Sets

I M N T P J

set of supply zones set of collection and intermediate process centers set of process plants set of technological options set of products set of demand locations

cinv cpi PB

Binary Variables

yL2 m binary variable for existence of collection and intermediate process center m

Subsets

Jo Je PI PD PP

set of local demand locations jo (subset of J) set of demand locations je for export (subset of J) set of intermediate products pi (subset of P) set of directly used products pd (subset of P) set of produced products from plants pp (subset of P)

■

index for supply zones index for collection and intermediate process centers index for process plants index for technological options index for products index for demand locations index for demand locations at local level index for demand locations for export index for intermediate products index for directly used products index for produced products from plants

Scalars

f yb cost coefficient for yearly basis qm,L2 minimal or maximal flow-rate at collection center m, t/y Parameters

qm,L1,L2 pi Demjo,p f conv,L2 pi qm,L3 t f conv,L3 pi,pp,t ctr,La,Lb p cfix,inv,L2 cfix,inv,L3 t cvar.,inv,L3 t DLa,Lb x,y f road,La,Lb x,y cprice p

REFERENCES

(1) Friedler, F.; Tarjan, K.; Huang, Y. W.; Fan, L. T. Graph-Theoretical Approach to Process Synthesis: Axioms and Theorems. Chem. Eng. Sci. 1992, 47, 1972−1988. (2) Friedler, F. Process Integration, Modelling and Optimisation for Energy Saving and Pollution Reduction. Chem. Eng. Trans. 2009, 18, 1− 26. (3) Friedler, F. Process Integration, Modelling and Optimisation for Energy Saving and Pollution Reduction. Appl. Therm. Eng. 2010, 30 (16), 2270−2280. (4) Friedler, F.; Fan, L. T.; Kalotai, L.; Dallos, A. A Combinatorial Approach for Generating Candidate Molecules with Desired Properties Based on Group Contribution. Comput. Chem. Eng. 1998, 22, 809−817. (5) Kovacs, Z.; Ercsey, Z.; Friedler, F.; Fan, L. T. Exact Super-Structure for the Synthesis of Separation-Networks with Multiple Feed-Streams and Sharp Separators. Comput. Chem. Eng. 1999, 23, S1007−1010. (6) Heckl, I.; Kovacs, Z.; Friedler, F.; Fan, L. T. Super-structure Generation for Separation Network Synthesis Involving Different Separation Methods. Chem. Eng. Trans. 2003, 3, 1209−1214. (7) Bertok, B.; Friedler, F.; Feng, G.; Fan, L. T. Systematic Generation of the Optimal and Alternative Flowsheets for Azeotropic Distillation Systems. Comput.-Aided Chem. Eng. 2001, 9, 351−356. (8) 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 (13−14), 1407− 1427. (9) Fan, L. T.; Shafie, S.; Bertok, B.; Friedler, F.; Lee, D.-Y.; Seo, H.; Park, S.; Lee, S.-Y. Graph-Theoretic Approach for Identifying Catalitic or Metabolic Pathways. J. Chin. Inst. Eng. 2005, 28, 1021−1037. (10) Seo, H.; Lee, D.-Y.; Park, S.; Fan, L. T.; Shafie, S.; Bertok, B.; Friedler, F. Graph-Theoretical Identification of Pathways for Biochemical Reactions. Biotechnol. Lett. 2001, 23, 1551−1557. (11) Fan, L. T.; Bertok, B.; Friedler, F.; Shafie, S. Mechanisms of Ammonia-Synthesis Reaction Revisited with the Aid of a Novel GraphTheoretic Method for Determining Candidate Mechanisms in Deriving the Rate Law of a Catalytic Reaction. Hung. J. Ind. Chem. 2001, 29, 71− 80. (12) Halasz, L.; Povoden, G.; Narodoslawsky, M. Sustainable Processes Synthesis for Renewable Resources. Resour., Conserv. Recycl. 2005, 44, 293−307. (13) 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.

Indexes

i m n t p j jo je pi pd pp

production rate of intermediate product pi at supply zone i, t/y mass flow-rate of product p from object x in layer a to object y in layer b, t/y mass flow-rate of intermediate product pi to the selected technology t at the process plant n, t/y mass flow-rate of produced products pp from intermediate product pi with the selected technology t at the process plant n, t/y transportation costs, €/y operating costs, €/y operating costs by the preprocessing for product pi, €/y operating costs by the processing for product pi and technology t, €/y annual investment, €/y price for intermediate product pi, €/t profit before taxes, €/y

product’s mass flow-rate at collection center m, t/y regional demand at location jo for product p, t/y conversion factor of intermediate product pi by preprocessing inlet mass flow-rate to the selected technology, t/y conversion factor of intermediate product pi by processing transportation cost coefficient of product from layer a to layer b, €/y coefficient for the fixed part of the annualized investment by preprocessing, €/y coefficient for the fixed part of the annualized investment by processing, €/y coefficient for the variable part of the annualized investment by processing, €/y distance between object x in layer a and object y in layer b, km road condition factor between object x in layer a and object y in layer b price of the product, €/t or €/MWh or €/MJ 179



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P-Graph Synthesis of Open-Structure Biomass Networks - American

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