Water Sources Diagram in Multiple Contaminant Industrial Case Studies

Article pubs.acs.org/IECR

Water Sources Diagram in Multiple Contaminant Industrial Case Studies: Adoption of a Decomposition Approach Ewerton E. S. Calixto, Ana Carolina L. Quaresma, Eduardo M. Queiroz,* and Fernando L. P. Pessoa Programa de Tecnologia de Processos Químicos e Bioquímicos, Escola de Química, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brasil ABSTRACT: The use of water in industrial processes has become an important issue over the last 20 years, and then the optimization of water reuse considering multiple contaminants has gained great attention. This paper presents a new approach for the algorithmic procedure Water Sources Diagram (WSD), which is developed to be applied in large multiple contaminants water allocation problems (WAPs). In the WSD procedure, the reference contaminant definition is a key step and often leads to cumbersome calculations in following steps to get the final network from an intermediate structure, which is obtained based on the reference contaminant. The proposed new approach reduces the importance of the reference contaminant choice, simplifying the following calculations by adopting a decomposition strategy. It is applied in two large process plant examples, and the results show a good performance of the new approach.

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Some efforts have been recently made in the field of graphic approaches, in multiple contaminants problems, minimizing the consumption of fresh resources such as water and hydrogen. Zhao et al.6 proposed a multiple contaminant deficit method for the analysis of hydrogen distribution networks, which can also be applied to minimize the fresh water consumption in WAPs. In the same direction, Zhang et al.7 developed a graphical method to the simultaneous design of resource conservation networks and the targeting of minimum fresh resource demand involving multiples contaminants. They concluded that if a key contaminant is present, the method can determine the theoretical minimum demand. However, they did not propose a systematic method to determine the key contaminant. In the oil-refining field, some graphical approaches have also been applied to minimize the fresh water consumption and wastewater discharge. One of them is the work of Pombo et al.,8 applying Pinch Technique to reduce the withdrawal of water and its associated costs in three refining process units: distillation, hydrodesulphurization (HDS), and desalting. Pombo et al.8 recognize the necessity of defining a reference contaminant in the presence of multiple contaminants, in order to make the procedure feasible. They adopted as reference contaminant the H2S, based only on the fact that H2S is a major pollutant in the petroleum refinery. Therefore, they also did not propose a systematic way to define the reference contaminant. Hou et al.9 proposed an algorithmic procedure for the simultaneous synthesis of water and energy networks, involving single and multiple contaminants. To determine the precedence order of the process units, the authors used the concentration potential concepts10 regarding the demand (CPD) and source (CPS) streams. For the reference contaminant determination, they proposed the identification of the contaminant which

INTRODUCTION In recent years, the necessity of water conservation has become a common issue around the world. Environmental government agencies and private and state-owned companies are more attentive to the question of the rational and sustainable use of water. Despite its abundance in oceans, water is increasingly scarce in subsoil, rivers, and lake reservoirs.1 The water access is a matter of survival for all humanity.2 The new social organization around the world has been providing important changes in the resources use regulation. Chemical process industries represent a significant parcel in water consumption, with water being used in great quantities for various purposes, such as vapor generation, cooling water, washing, etc. Large industries require a considerable amount of water. A great part of it returns to the environment as wastewater, requiring previous treatment to meet the established limits dictated by environmental legislation agencies, such as EPA (USA), CONAMA (Brazil), EEA (Europe), etc.3 Some laws have as the main purpose to solve one of the most critical issues: the management of water and its distribution for the populations.4 In industries, water and wastewater treatment represent costs, and so wastewater reuse became an important option. There are many reasons to reuse water in refineries and petrochemical plants. Many of those are related to the fresh water cost and environmental issues. Notwithstanding, according to Jeżowski,5 this cost can be increased by the needed infrastructure (i.e., piping lines and pumping stations to remote locations). This is an important issue that companies, such as petrochemical industries and refineries, have to face. Although, the supply of fresh water (coming from an external source) is now economically viable in many companies and in the long term, it will certainly become a major issue in many regions of the world. In order to determine the optimum consumption rate of fresh water, an optimization analysis of water reuse is required. In this context, many strategies have been developed in the field of Process Integration, such as the use of mathematical programming, or the proposal of algorithmic or graphical approaches. © 2015 American Chemical Society

Received: Revised: Accepted: Published: 10040

May 12, 2015 September 1, 2015 September 29, 2015 September 29, 2015 DOI: 10.1021/acs.iecr.5b01749 Ind. Eng. Chem. Res. 2015, 54, 10040−10053

Article

Industrial & Engineering Chemistry Research concentration reaches a limiting value first. Hence, Hou et al.9 pointed out a direction for the reference contaminant determination, which should be more intensively investigated in other industrial situations to be considered a consolidated proposal. Fan et al.11 extended the concentration potential concept, proposed by Liu et al.,10 including recycles. The method was applied to a wider range of examples from the literature and achieved good results when compared to the corresponding ones obtained using mathematical programming. Using the same strategy, Li et al.12 developed a manual procedure for designing multicontaminant water using networks in batch processes, also getting good results. On the other hand, some insight-based approaches, presented by Foo13 in a recent review, have not achieved significant results for multiple contaminants processes. Some mathematical programming approaches follow the same previously presented conception, when defining the reference contaminant. For example, Deng et al.14 chose as major oil contaminants in a refinery process case study, H2S and salt. In an opposite way, Liu et al.15 claimed to overcome some limitations of previous research efforts, proposing a mathematical model for a WAP without the need of a key contaminant definition. The methodology was tested for just one simple case study, not proving therefore its efficacy in larger real problems. A procedure proposed by Castro et al.16 was the basis for Gomes et al.17 to develop an algorithmic strategy, known as Water Sources Diagram (WSD), which has been enhanced over the last years.18 Nevertheless, the last WSD proposed procedure18 leads to cumbersome calculations when dealing with many processes and contaminants in WAPs. These difficulties are directly linked to the choice of the reference contaminant, for which, until now, a consolidated criterion has not been defined. The decomposition concept in the Process Integration is not new. Amidpour and Polley19 presented a decomposition methodology, which is based on the idea of zoning or area of integrity20 and applied it to a heat exchanger network of an existing aromatic plant. It takes into account the regions in the process which are associated with practical considerations such as flexibility, safety, and plant layout. In terms of application, it can help plant operators to easily understand the “local” networks, which are less complex than the others generated by the traditional Pinch Analysis. Lee and Yoon21 developed a systematic approach to decompose a large-scale process into subprocesses and then diagnose them. They developed a diagnosis system for large-scale chemical processes. In adopting process decomposition, the following advantages can be highlighted: flexible diagnosis throughout operational condition changes; size reduction of the knowledge bases for process interactions; and consistent, reliable construction and maintenance of the knowledge base. The decomposition concept was also employed in the synthesis of water and wastewater networks. Hernández-Suárez et al.22 presented a superstructure decomposition and parametric optimization approach for the synthesis of distributed wastewater treatment networks with no stream recycles or recirculations. A typical complex network superstructure for simultaneous design was decomposed into a set of basic networks superstructures. They showed that the complexity of a design problem for a distributed wastewater treatment network, without recycles or recirculations, is increased by the number of available treatment units, but not by the number of contaminants or effluent streams. In the same way, Zheng et al.23 proposed a

decomposition approach using graph theory algorithms for the design of water distribution networks. A full water network was initially decomposed into different subnetworks based on the connectivity of the network’s components. The original network was simplified to a directed augmented tree, in which the subnetworks are substituted by augmented nodes and directed links are created to connect them. One of the major advantages pointed out by Zheng et al.23 is that, with multiples subnetworks, the optimization of the water distribution systems can be performed using parallel computing technology. All subnetworks can be optimized separately and simultaneously by parallel computing technology. In another work, Zheng et al.24 used Evolutionary Algorithms to optimize the subnetworks from the decomposition of a Water Distribution Network (WDN). To decompose the network, they also used graph theory. The next step was to employ a multidifferential evolution (MODE) algorithm to optimize the subnetworks separately. Zheng et al.24 highlight the possibility of using this decomposition strategy in other water resource optimization problems, such as design of integrated urban wastewater systems. This paper discusses a novel criterion to determine the reference contaminant and the reference operation in the context of the WSD procedure. Its major objective is to present a new systematic procedure, adopting a decomposition approach, that eliminates the cumbersome step in the original WSD,18 which was necessary to take out all the concentration violations in the intermediate structure generated based on the reference contaminant. In this way, the proposed methodology does not need initial guesses, a major problem in using mathematical programming approaches, and it also eliminates the evolution step of the WSD, which it was, until now, not a well-consolidated step. In many cases, this evolution is carried out by adopting an intuitive procedure. These preceding features bring to these regular methods, difficulties which are eliminated in the new approach. Furthermore, the new approach enables the engineer to use its process experience in each step, usually taking into account process constraints, like forbidden reuse among operations, without the complex knowledge needed when leading with mathematical programming algorithms. The proposed procedure is then applied in two industrial case studies taken from the literature, involving many operations and contaminants, in order to show its performance.

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REFERENCE CONTAMINANT AND OPERATION The rules of the algorithm are applied to the reference contaminant. Hence, it should represent the behavior of all other contaminants. With the network structure defined based on the reference contaminant, the concentrations of the other contaminants are calculated based on the corresponding mass balance. On the other hand, the reference operation is the unit which demands the use of the cleanest external fresh water available. Note that in a process more than one reference operation may be present. Choice of a Reference Contaminant. Gomes et al.18 proposed seven steps to apply the WSD in multicontaminant processes. One of these steps is related to the choices of the reference contaminant and of the reference operation. Despite not mentioned, this step is closely related to the last one, where the concentration violations in the structure obtained based only on the reference contaminant are eliminated, sometimes demanding cumbersome calculations. Therefore, a “scenario” avoiding these violations should be a goal in the way of turning WSD calculations more direct and easier. Hence, the definition 10041

DOI: 10.1021/acs.iecr.5b01749 Ind. Eng. Chem. Res. 2015, 54, 10040−10053

Industrial & Engineering Chemistry Research

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DECOMPOSITION APPROACH: PROBLEM DECOMPOSITION AND “BLOCKS” DEFINITION The original set of operations (superstructure) is decomposed in small regions called “blocks”. As a suggestion, the number of blocks is related to the number of all possible reference operations. A block can have one or more operations, and each block must contain one reference operation, which cannot migrate to another block. Only operations that are not a reference one can be present in more than one initial block as it migrates to other blocks. A sketch of the complete decomposition approach is shown in Figure 2, and the presentation of each step is made in the following sections. Reference Operations and Reference Contaminants Identification. Among all considered operations, the ones with the inlet concentration of some contaminant equal to zero will be taken as reference in the calculations. Thus, if the number of such operations is N, then, the minimum number of blocks should also be N. If in a set there is not such operation, the block division will be free and the reference operation in each block will be the one with the lowest inlet concentration. The flowsheet of this procedure can be seen in Figure 3. A generic process has (N + M) operations, where M operations do not have any inlet concentration equal to zero. Note that the generation of blocks among this specific set depends on the number of blocks dictated by the number of reference operations equal to N. The ideal block number related to a minimum decomposition degree is the one that guarantees the possibility of obtaining flowsheets with no concentration violations. After the blocks and respective reference operation definitions, the WSD algorithm is applied inside each block. Hence, the choice of a reference contaminant must be made in each block, and the G parameter is then used. The reference contaminant will be the one with the greatest value of Gwu,c. If there is more than one contaminant with inlet concentration equal to zero in the reference operation, Gwu,c should also be calculated based on it. The G parameter is similarly used in a block without inlet concentrations equal to zero. The corresponding algorithm is shown in Figure 4. Flowsheet Generation. A set of flowsheets is created per block, and the number of possible flowsheets inside each block (CC) is defined by a mathematical combination of the present operations (nb). Equation 2 represents this combination.

of the reference contaminant could be considered an important challenge in enhancing the WSD procedure. To minimize violation problems, Savelski and Bagajewicz25 proposed an optimality condition for multiple contaminants WAPs, which is incorporated by the WSD. The condition is related to a behavior of monotonicity used to define the reference contaminant, which can be analyzed using the following parameter: Guw, c =

Δm u,c max Cu,c,out

Article

(1)

where Δmu,c is the mass load of contaminant c and Cmax u,c,out is the maximum outlet concentration of contaminant c in unit u. The reference contaminant is the one with the greatest value of Gwu,c, where w indicates the fresh water source as the basis. In other words, this contaminant reaches first its maximum inlet concentration in a process unit when fresh water is used. This rule was also confirmed by others authors,26−29 and then is adopted in the present study, as will be seen in details in the following text. Choice of a Reference Operation. A simple reuse is not possible in the reference operation, and it must be the first one positioned in the sources diagram. Moreover, Savelski and Bagajewicz,25 in one of their proposed theorems, showed that the optimum solution is found when the outlet reference contaminant concentration in a partial provider head process (PPHP) is equal to its maximum. A PPHP is a specific operation in a set of operations, called head processes (H), which utilizes only clean external water. The head processes are the processes that receive only fresh water, while intermediate processes (I) receives also effluents from other processes (reuse). Following Savelski and Bagajewicz,25 Figure 1 illustrates the position of this kind of

Ckn = CC =

Figure 1. A schematic representation of a water network.

n! k ! (n − k )!

(2)

with,

operation in a water network. Operations at the end of the network are the terminal wastewater user processes (T). Faria and Bagajewicz30 presented the concept of a complete water network (CWN), which considers the influence of the pretreatment units subsystem in the water-using units and treatment subsystems and vice versa. The presence of pretreatment units, which provides fresh water with different qualities, depends on how much smaller fresh water usage can be achieved. The constraints at the inlet of pretreatment units and also their different outlet concentrations led to the need for considering different fresh water sources, in which there was a complete analysis of the water system. In the present algorithm, the presence of an inlet concentration equal to zero will define a reference operation. In a set of operations without this feature, the reference will be the one with the lowest inlet concentration.

k = nb − 1 n = Nop − Nb

(3)

where Nop is the total number of operations and Nb is the number of blocks used to decompose the process. Among each set of flowsheets (corresponding to each block), a subset with no concentration violation is arranged in terms of the lower fresh water consumption, generating a set of flowsheets which are candidates to be in the final flowsheet. After the analysis inside each block, a new set of “complete flowsheets” is generated. A “complete flowsheet” comes from the composition of candidate flowsheets coming from each block. This composition can generate flowsheets involving repeated operations, which are discarded in a permutation step. After that, the 10042


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Figure 3. Blocks generation algorithm.

introduced in Table 1, which shows the highest inlet (Cmax u,c,in) and outlet (Cmax ) concentration, and streamflow rates of a unit u,c,out operation u (f u). The corresponding mass loads (Δmu,c) of all contaminants are also shown. Step 1: Reference Operation Candidates. Operation 1 has all its contaminants with maximum inlet concentrations equal to zero, and then it is a candidate to be a reference operation and it will be inside one block. Among the other operations, there is not another one with this feature. The adoption of only one block is contrary to the decomposition proposal, and therefore, in this case, it has defined the use of a second block. As among operations 2, 3, and 4, the one with the lowest inlet concentration is operation 2, and then it is taken as a second reference operation candidate (see Figure 3). Step 2: Blocks’ Formation and Choice of the Respective Reference Contaminant. This second step is a strategic one where some options should be analyzed by carrying out various combinations inside each block, which may or may not lead to future concentration violations. From step one, operations 1 and 2 are the reference candidates. Hence, for each of them, there will be one block, and then the problem will be decomposed in two blocks. Therefore, there are three options to distribute the operations in each block: (i) two operations in each block; (ii) one operation in block 1 and three operations in block 2; and (iii) three operations in block 1 and one in block 2. Having all operations in one block is also possible, but as it was discussed previously, this option does not represent a decomposition strategy. The viable options adopting two blocks are then shown in Table 2. Step 3: Reference Contaminant Definition for Each Block. With all blocks and reference operations defined, it is necessary to determine the reference contaminant for each block, using the algorithm presented in Figure 4. The results of this algorithm are summarized in Table 3. As shown in Table 3, in operation 1, any contaminant can be the reference because all of them have the same value of Gwu,c. On the other hand, in operation 2, contaminant B is the reference due to its higher Gwu,c. Step 4: Application of WSD in Each Combination Inside Each Block. This step is related to flowsheets generation inside each block and the observation of the possible presence of concentration violations. In each block, there is the possibility of performing combinations among all no reference operations, with the number of possible combinations calculated by Equation 2. The results for all blocks in each option are shown in Table 4. The total number of possible flowsheets, where the WSD should be applied, is then eight.

Figure 2. Decomposition algorithm flowsheet.

remaining “complete flowsheet” with the lowest fresh water consumption is the final result of the procedure.

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METHODOLOGY STEP BY STEP For the presentation of the proposed algorithm, an example used by Doyle and Smith,31 containing three contaminants and four operations, is used. The contaminant limit data composition are 10043


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Figure 4. Reference contaminant identification algorithm.

Note that, from Table 4, option 1/block 1 presents two possible flowsheets: the first with operations 1 (the reference) and 3, and the second with operations 1 and 4. Operation 2 could not be present in option 1/block 1 because it is the reference in block 2. Applying the WSD in the four combinations of option 1, no violations are observed. The respective fresh water consumptions are also shown in Table 5, for blocks 1 and 2, respectively.

Table 1. Limiting Data for All Contaminants operation (u) f u (t/h) 1

34

2

75

3

20

4

contaminant c

Cmax u,c,in (ppm)

Cmax u,c,out (ppm)

Δmu,c (kg/h)

A B C A B C A B C A B C

0 0 0 200 100 500 600 850 390 300 460 400

160 450 30 300 270 740 1240 1400 1580 800 930 900

5.44 15.3 1.02 7.5 12.75 18 12.8 11 23.8 40 37.6 40

80

Table 5. Possible Flowsheets in Option 1

Table 2. Block Options Adopting Two Blocks number of operations in the process

block 1

block 2

1 2 3

4 4 4

2 1 3

2 3 1

Table 3. Parameter Gwu,c Values in the Reference Operations of Each Block reference operation

candidates to reference contaminant

Gwu,c

1

A B C A B C

34000 34000 34000 25000 47222 24324

2

reference contaminant A/B/C

B

Table 4. Flowsheet Combinations Per Option and Block option 1 2 3 total

blocks

Nop

Nb

nb

k

n

CC

block 1 block 2 block 1 block 2 block 1 block 2

4

2

4

2

4

2

2 2 1 3 3 1

1 1 0 2 2 0

2 2 2 2 2 2

2 2 1 1 1 1 8

operations

fresh water consumption (t/h)

violation?

flowsheet 1 flowsheet 2 block 2

1, 3 1, 4 operations

34.00 68.66 fresh water consumption (t/h)

no no violation?

flowsheet 1 flowsheet 2

2, 3 2, 4

65.59 75.00

no no

The flowsheets involving operations (1,3) in blocks 1, and (2,3) in block 2, have the lowest fresh water consumption; however, they have in common operation 3. Therefore, a complete flowsheet with these two flowsheets is not possible because operation 4 would be out of the structure. This issue will be addressed in the permutation step. As a reference, Figures 5 and 6 show the WSD, adopting contaminant A as the reference, and the correspondent flowsheet, respectively, for the combination involving operations 1 and 3, in option 1/block 1. Details in the WSD application, see the work of Gomes et al.18 In Figure 6 is adopted the criterion of mixing all wastewater streams to generate a unique block outlet stream. This procedure makes easier the composition of the block results in generating the complete flowsheets in a following step of the algorithm. In option 2, there are two blocks, but one of them has only one operation. Option 3 has a similar structure. Hence, the WSD is applied only in the blocks with more than one operation. Results for the fresh water consumption and presence of violations are shown in Tables 6 and 7, for options 2 and 3, respectively. Step 5: Set of Candidate Flowsheets. A candidate flowsheet, in an option, is a combination involving one flowsheet of each block of the option, all of them without violations. For example, as can be seen in Table 8, for option 1 the candidate flowsheets are those composed by the combinations of the flowsheets coming from block 1 [(1,3) and (1,4)] and block 2 [(2,3) and (2,4)], as all of them do not present a violation. The unique possible complete flowsheet in option 2 has a

operations per block option

block 1

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Figure 5. WSD for operations (1,3), option 1/block 1. A as the reference contaminant.

Figure 6. Flowsheet of the WSD of Figure 5. Operations (1,3), option 1/block 1.

Step 6: Permutation Analysis. In this step, all candidate flowsheets are put together and analyzed in order to define structures in accordance with the process specifications. In these structures, all operations must appear only one time. Therefore, as can be seen in Table 8, two of the candidates must be discharged [(1,2) and (1,4)]. Then the structure, which represents the final result, comes from this new set of complete flowsheets shown in Table 9.

Table 6. Possible Flowsheets in Option 2 block 1

operation


violation?

flowsheet 1 block 2

1 operation

34.00 fresh water consumption (t/h)

no violation?

flowsheet 1

2, 3, 4

75.78

yes

Table 7. Possible Flowsheets in Option 3 block 1

operation


violation?

flowsheet 1 block 2

1, 3, 4 operation

79.37 fresh water consumption (t/h)

no violation?

flowsheet 1

2

34.00

no

Table 9. Complete Flowsheets operations complete flowsheets (1,1) (1,3) (3,1)

Table 8. Candidate Flowsheets operations

option option 1

option 3

candidate flowsheet (1,1) (1,2) (1,3) (1,4) (3,1)

block 1 1 1 1 1 1

3

3 3 4 4 4

block 2 2 2 2 2 2

4 3 3 4


block 1 1 1 1

3

3 4 4

block 2 2 2 2

4 3

fresh water consumption (t/h) 109.00 134.25 135.86

Step 7: Final Flowsheet Proposal. In this step, an objective function should be used to define the best option among the available complete flowsheets in the adopted scenario. In the present example, the adopted objective function is the minimum fresh water consumption, hence the complete flowsheet (1,1) from Table 9 is the final result of the procedure. This flowsheet is shown in Figure 7. This final result presents a fresh water consumption 18% greater than the result of Doyle et al.31 Note that, in this example, the decomposition was performed only to illustrate the methodology, since following the rule to identify reference operations only operation 1 should be selected then the traditional WSD should be used. The restriction to the water reuse among blocks inerent to the decomposition procedure is the reason for this worst result. It is also worth noting that

109.00 99.59 134.25 143.66 135.86

violation and then is not present in this step. Option 3 offers more than one possibility. Note that the candidate flowsheet with the lowest fresh water consumption is not feasible because operation 3 appears two times and operation 4 is not present. Therefore, it is necessary for a new step, called permutation analysis, where this kind of problem is addressed. 10045


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Figure 7. Final Flowsheet.

applying only the traditional WSD to this example (see Gomes et al.18), we can get the same optimum result found by Doyle et al.31 but with the cumbersome step procedure to remove the violations found in the intermediate network obtained based on the reference contaminant.

Table 11. Continuation of Table 10 operation u

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CASE STUDY To test the robustness of the WSD decomposition approach algorithm, a real industry case study presented by Leewongtanawit and Kim32 is here analyzed. The process consists of a system with ten operations and four contaminants. To minimize the fresh water consumption, Leewongtanawit and Kim32 used a software called WATER, version 2.0, which was developed by the Centre for Process Integration at the University of Manchester. The mass loads of the contaminants and the limiting inlet and outlet concentration data are shown in Table 10. Two external fresh water sources are available, one at 0 ppm (ES1) and another at 10 ppm (ES2). Step 1: Reference Operation Candidates. Looking at Table 10, we can see that the operations 6, 7, and 10 have, at least, one of its contaminants with maximum inlet concentration equal to zero, and therefore they are candidates to be the reference operations. It is also an indication that we can decompose our problem in three blocks. Step 2: Blocks’ Formation and Choice of Respective Reference Contaminant. The problem was decomposed in Table 10. Limiting Data for All Contaminants operation u

f u (t/h)

contaminant c

Cmax u,c,in

Cmax u,c,out

Δmu,c (kg/h)

1

24.87

A B C D A B C D A B C D

200 500 100 1500 350 3000 500 400 350 450 150 500

25000 20000 28500 230000 8000 9000 24080 3000 3500 2500 1500 1500

616.78 484.97 706.31 5682.80 313.50 245.88 966.31 106.55 123.48 80.36 52.92 39.20

2

40.98

3

39.2

f u (t/h)

4

4

5

3.92

6

137.5

7

290.96

8

23.81

9

65.44

10

4

contaminant c

Cmax u,c,in

Cmax u,c,out

Δmu,c (kg/h)

A B C D A B C D A B C D A B C D A B C D A B C D A B C D

800 650 450 300 1300 2000 2000 4000 3000 2000 100 0 450 0 250 650 100 250 200 550 150 450 3000 100 0 0 0 0

15000 5000 700 1500 2000 7000 9000 10000 12000 10000 8000 200 2000 3000 1000 12000 3450 4000 700 7000 1000 1000 4000 100 100 100 100 100

56.80 17.40 1.00 4.80 2.74 19.60 27.44 23.52 1237.50 1100.00 1086.25 27.5 450.99 872.88 218.22 3302.40 79.76 89.29 11.91 153.57 55.62 35.99 65.44 0 0.40 0.40 0.40 0.40

three blocks. To determine the number of options (Nopt) (i.e., the number of possible combinations for the amount of operations we can have in each block), it can be used as an adaptation of the combinatorial theorem proposed by Feller33 called Star and Bars. It says that for any pairs of natural numbers n and k, the number of distinct k-tuples of non-negative integers whose sum is n is given by the binomial coefficient n + nk − 1 . In our case, n = Nop and k = Nb. It is not possible to consider in the combinations, the reference operations that are inside the blocks. As the number of reference operations is equal to the number of

(

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Industrial & Engineering Chemistry Research blocks, we can subtract Nop from Nb (Nop − Nb) and only take into account the combinations of the others operations. Thus, the binomial coefficient is now represented as follows. Nopt =

Table 13. Flowsheets Options block 1

⎛ Nop + Nb − Nb − 1⎞ ⎛ Nop − 1 ⎞ ⎟=⎜ ⎟ = ⎜⎜ ⎟ ⎜N − N ⎟ − N N op b op b ⎝ ⎠ ⎝ ⎠ (Nop − 1)! (Nop − Nb) ! [(Nop − 1) − (Nop − Nb)]!

(4)

In the case study, Nop = 10 operations and Nb = 3 blocks. Substituting these values in equation 4, the binomial coefficient is now: ⎛10 − 1⎞ ⎛ 9 ⎞ 9! ⎟=⎜ ⎟= ⎜ = 36 ⎝10 − 3⎠ ⎝ 7 ⎠ 7! (9 − 7)!

(5)

It means that there are 36 different options to be analyzed. It is really tiresome to perform all those combinations by hand. One way to avoid combinations which result in flowsheets with violations in the limit contaminant concentration is to verify the monotonicity criterion18 of all contaminants. The contaminants that do not obey this rule in a combination set of operations give an indication that this combination will produce a flowsheet with some contaminant violation. Therefore, we can now eliminate those options with this characteristic and then to apply the WSD in less options. Note that the higher the number of operations, the higher will also be the number of possible violations. Step 3: Reference Contaminant Definition for Each Block. The contaminants A, B, C, and D in operation 10, B in operation 7, and D in operation 6, have its maximum inlet concentration equal to zero and can be considered as reference contaminant for its respective block. For operation 10, any of the contaminants can be referenced. The candidates to be the reference contaminants and the reference contaminants of choice are listed in Table 12. Table 12. Candidates and Reference Contaminants of Choice for Each Reference Operation reference operation

candidates to reference contaminant

Gwu,c

10

A B C D A B C D A B C D

4000 4000 4000 4000 225494 290960 218220 275200 103125 110000 135781 137500

7

6

reference contaminant

block 2

block 3

option

nb

CC

nb

CC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 5 5 5 5 6 6 6 7 7 8

1 1 1 1 1 1 1 1 7 7 7 7 7 7 7 21 21 21 21 21 21 35 35 35 35 35 35 35 35 35 21 21 21 7 7 1

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 1 2 3 4 5 6 1 2 3 4 5 1 2 3 4 1 2 3 1 2 1

1 8 7 7 21 6 35 5 35 4 21 3 7 2 1 1 1 7 7 6 21 5 35 4 35 3 21 2 7 1 1 6 7 5 21 4 35 3 35 2 21 1 1 5 7 4 21 3 35 2 35 1 1 4 7 3 21 2 35 1 1 3 7 2 21 1 1 2 7 1 1 1 sum of total CC

nb

CC

total CC

1 7 21 35 35 21 7 1 7 21 35 35 21 7 1 21 35 35 21 7 1 35 35 21 7 1 35 21 7 1 21 7 1 7 1 1

3 15 43 71 71 43 15 3 15 35 63 77 63 35 15 43 63 77 77 63 43 71 77 77 77 71 71 63 63 71 43 35 43 15 15 3 1.728

A/B/C/D

Option 18, Block 1. The reference operations candidates are 6, 7 e 10, as seen in section 0. In this block, we used the operation 10 and thus the possible combinations will include necessarily operation 10 and optionally the others: 1, 2, 3, 4, 5, 8, and 9. The use of operation 10 in block 1 is related to the fact that in this operation all the maximum inlet concentrations are zero. In this option, as can be seen in Table 13, there are 3 operations and 21 possible flowsheets. Thus,

B

D

block 1 = (10, ? , ? )

(6)

The main features of these 21 flowsheets are shown in Table 14. Some of these flowsheets present violations while the minimum fresh water consumption occurs in the flowsheet 16, where 4 t/h come from the external fresh water source at 0 ppm and 3.12 t/h from the second external fresh water source at 10 ppm. As an example, Figures 8 and 9 show the WSD and the respective water network for this optimum combination. Note that all combinations have an equivalent network and not all of them are feasible. The complementary operations may also be present in more than one block, which also represents an

Step 4: Application of WSD in Each Combination Inside Each Block. The Table 13 shows all the options with its respective performed combinations per option per block. The combinations of flowsheets in each block were obtained using equation 2. As can be seen from Table 13, there are 1.728 combinations including all the 36 options. To illustrate how the procedure is done inside each option, and also to save space, we arbitrarily use option 18. 10047


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Industrial & Engineering Chemistry Research Table 14. Combinations for Block 1 flowsheet 1 flowsheet 2 flowsheet 3 flowsheet 4 flowsheet 5 flowsheet 6 flowsheet 7 flowsheet 8 flowsheet 9 flowsheet 10 flowsheet 11 flowsheet 12 flowsheet 13 flowsheet 14 flowsheet 15 flowsheet 16 flowsheet 17 flowsheet 18 flowsheet 19 flowsheet 20 flowsheet 21

operations

fresh water consumption (ES1) (t/h)


discharge (t/h)

violation?

1, 2 e 10 1, 3 e 10 1, 4 e 10 1, 5 e 10 1, 8 e 10 1, 9 e 10 2, 3 e 10 2, 4 e 10 2, 5 e 10 2, 8 e 10 2, 9 e 10 3, 4 e 10 3, 5 e 10 3, 8 e 10 3, 9 e 10 4, 5 e 10 4, 8 e 10 4, 9 e 10 5, 8 e 10 5, 9 e 10 8, 9 e 10

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

59.51 56.80 24.39 24.51 43.63 74.17 67.93 37.98 39.37 56.96 70.68 36.69 36.69 55.78 89.19 3.12 23.25 56.24 23.25 56.24 76.05

63.51 60.80 28.14 28.51 47.63 78.17 71.93 41.98 43.37 60.96 74.68 40.69 40.69 59.78 93.19 7.12 27.25 60.06 27.25 60.24 80.05

yes no yes yes yes yes yes yes no yes yes no no no no no no no no no no

Figure 8. WSD for option 18, flowsheet 16 in block 1.

Figure 9. Flowsheet corresponding to WSD of Figure 8 (option 18, flowsheet 16 in block 1).

unfeasible condition for the final network. These constraints show the importance of knowing the options of each block, as

shown in Table 13, where only the combinations without violations are candidates to be in the final network. 10048


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Industrial & Engineering Chemistry Research Table 15. Combinations for Block 2 flowsheet 1 flowsheet 2 flowsheet 3 flowsheet 4 flowsheet 5 flowsheet 6 flowsheet 7 flowsheet 8 flowsheet 9 flowsheet 10 flowsheet 11 flowsheet 12 flowsheet 13 flowsheet 14 flowsheet 15 flowsheet 16 flowsheet 17 flowsheet 18 flowsheet 19 flowsheet 20 flowsheet 21

operations



discharge (t/h)

violation?

1, 2 e 7 1, 3 e 7 1, 4 e 7 1, 5 e 7 1, 8 e 7 1, 9 e 7 2, 3 e 7 2, 4 e 7 2, 5 e 7 2, 8 e 7 2, 9 e 7 3, 4 e 7 3, 5 e 7 3, 8 e 7 3, 9 e 7 4, 5 e 7 4, 8 e 7 4, 9 e 7 5, 8 e 7 5, 9 e 7 8, 9 e 7

290.96 290.96 290.96 290.96 290.96 290.96 290.96 290.96 290.96 290.96 290.96 290.96 290.96 290.96 290.96 290.96 290.96 290.96 290.96 290.96 290.96

62.07 58.73 25.67 26.95 44.47 85.28 76.66 43.58 42.21 62.40 103.21 40.90 39.54 59.73 100.54 6.45 26.64 67.45 25.28 66.09 86.27

353.03 349.69 316.63 317.91 335.43 376.24 376.62 334.54 333.17 353.36 394.17 331.86 330.50 350.69 391.50 297.41 317.60 358.41 316.24 357.05 377.23

yes yes yes yes yes yes yes no no no no no no no no no no no no no no

Table 16. Combinations for Block 3 flowsheet 1 flowsheet 2 flowsheet 3 flowsheet 4 flowsheet 5 flowsheet 6 flowsheet 7 flowsheet 8 flowsheet 9 flowsheet 10 flowsheet 11 flowsheet 12 flowsheet 13 flowsheet 14 flowsheet 15 flowsheet 16 flowsheet 17 flowsheet 18 flowsheet 19 flowsheet 20 flowsheet 21 flowsheet 22 flowsheet 23 flowsheet 24 flowsheet 25 flowsheet 26 flowsheet 27 flowsheet 28 flowsheet 29 flowsheet 30 flowsheet 31 flowsheet 32 flowsheet 33 flowsheet 34 flowsheet 35

operations



discharge (t/h)

violation?

1, 2, 3 e 6 1, 2, 4 e 6 1, 2, 5 e 6 1, 2, 8 e 6 1, 2, 9 e 6 1, 3, 4 e 6 1, 3, 5 e 6 1, 3, 8 e 6 1, 3, 9 e 6 1, 4, 5 e 6 1, 4, 8 e 6 1, 4, 9 e 6 1, 5, 8 e 6 1, 5, 9 e 6 1, 8, 9 e 6 2, 3, 4 e 6 2, 3, 5 e 6 2, 3, 8 e 6 2, 3, 9 e 6 2, 4, 5 e 6 2, 4, 8 e 6 2, 4, 9 e 6 2, 5, 8 e 6 2, 5, 9 e 6 2, 8, 9 e 6 3, 4, 5 e 6 3, 4, 8 e 6 3, 4, 9 e 6 3, 5, 8 e 6 3, 5, 9 e 6 3, 8, 9 e 6 4, 5, 8 e 6 4, 5, 9 e 6 4, 8, 9 e 6 5, 8, 9 e 6

189.49 165.18 165.18 183.70 230.44 180.39 180.39 198.91 245.83 156.07 162.32 221.51 174.59 221.51 240.03 170.92 170.92 189.44 236.36 146.61 165.13 212.05 165.13 212.05 230.57 161.82 180.34 227.26 180.34 227.26 245.78 156.02 202.94 221.46 221.46

53.06 42.14 41.70 43.46 36.58 25.15 25.07 26.47 21.18 13.80 15.56 10.27 15.12 9.83 11.59 50.73 50.29 52.05 46.76 39.38 41.14 35.84 40.70 35.40 37.16 22.39 24.15 18.85 23.71 18.41 20.17 12.79 7.5 9.26 8.82

242.55 207.32 206.88 227.16 267.02 205.46 205.46 225.38 267.01 169.90 190.15 231.78 189.71 231.34 251.62 221.65 221.21 241.49 283.12 185.98 206.26 247.89 205.83 247.45 267.73 184.21 204.48 246.11 204.04 245.67 265.95 168.81 210.44 230.72 230.28

no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no no

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Industrial & Engineering Chemistry Research Option 18, Block 2. In this block, the reference operation is operation 7, and we have 3 operations. Then, to compose the block, the operations to be combined are 1, 2, 3, 4, 5, 8, and 9. Therefore, we have block 2 = (7, ? , ? )

Table 17. Best Flowsheets operations

(7)

This combination also produces 21 different flowsheets for the proposed number of operations in the block (see Table 15). Option 18, Block 3. This third block has operation 6 as a reference and also presents 4 operations and 35 flowsheet possibilities (Table 13). The main features of these combinations are presented in Table 16. Step 5: Candidates Flowsheets. The candidate flowsheets are those in Tables 14, 15, and 16 which present no violation in any contaminant concentrations. In block 1, the flowsheets from 1 to 6 presented violations and all other flowsheets are candidates. In blocks 2 and 3, all flowsheets are candidates because no violation was found in any of them. The set of combinations with the minimum fresh water consumption in each block are flowsheets 16 (4,5,10), 16 (4,5,7), and 32 (4,5,8,6) for the blocks 1, 2, and 3, respectively. We can note that operations 4 and 5 are common to the three blocks. For this reason, the next step is necessary. Step 6: Permutation Analysis. The final structure provided by option 18 is the composition of flowsheets generated in each block. Thus, any operation cannot be repeated in this final structure. Note that the superposition of the best networks of each block produces one network with repetition of operations 4 and 5. Therefore, it is necessary to carry out a combinatorial permutation to know which configuration represents the lowest fresh water consumption, without operation repetition, among the candidates generated in option 18. At this point, this elimination step is required because it is not possible to discard flowsheets with repeated operations without the previous knowledge of which operation(s) will be part of a block, using the star and bars combinatorial equation. Therefore, the best flowsheet pointed out by option 18 is block 1, operations 3, 9 and 10; block 2, operations 2, 8 and 7; and block 3, operations 1, 4, 5, and 6, with a fresh water consumption of 616.42 t/h. The same situation occurs for the other 35 options. Thus, it is necessary to perform the WSD for the combinations in all the blocks of each option and then to perform the same permutation analysis, as it was carried out in option 18. The results are in Table 17, where we can see that option 20 leads to the best result, with a fresh water consumption of 614.18 t/h. To have an idea of the computational effort necessary to this analysis, equation 8 calculates the total number of flowsheets (Ntotal CC ) which should be treated in a process with Nop operations, using Nb blocks. A relation among this total number and the number of operations and blocks is shown in Figure 10. =

∑∑ j=1 i=1

(Nop − Nb)! (n bi ,j − 1) ! [(Nop − Nb) − (n bi ,j − 1)]!

block 3


1 2 3 4 5 9 10 11 12 13 16 17 18 19 20 22 23 24 25

10 10 10 10 10 9 10 9 10 9 10 3 10 3 10 3 9 10 3 9 10 3 9 10 3 9 10 1 3 10 1 3 4 10 1 3 4 10 1 3 4 10 1 3 4 10

7 37 297 2597 24597 7 37 237 2597 24597 7 27 287 1257 24597 7 27 297 2597

12345689 1294586 134586 13486 1386 1234586 124586 14586 1486 186 124586 14586 1456 486 86 25896 5896 586 86

634.26 632.66 625.44 622.68 621.45 621.62 620.02 617.61 616.34 615.11 618.81 617.50 616.42 615.38 614.18 626.40 625.08 617.57 614.82

(

j=1 i=1

=

block 2

exceed the number of operations. Figure 10 shows a threedimensional graphic with (Ntotal CC ) as a function of Nop and Nb. As we can see from Figure 10, when the number of operations increases, the number of options also increases. As the number of blocks increases, the number of options decreases and so forth. This is a typical behavior of the binomial distribution n + nk − 1 . Moreover, note that the total number of combinations is not a function of the number of contaminants, which is a number that only has influence in the specific WSDs made in each combination. Step 7: Composition of Final Flowsheet. The final flowsheet proposed for the water system comes from option 20, consumes 614.18 t/h of fresh water, and has the structure showed in Figure 11. Leewongtanawit and Kim32 achieved a value of 432.46 t/h for the total fresh water consumption from ES1 and 179.54 t/h from ES2 and a total wastewater discharge of 611.99 t/h. The corresponding results obtained by the present proposed algorithm are 450.98 , 163.20, and 614.18 t/h, respectively. Comparing these results, the decomposition approach of the WSD indicates a consumption of 4.11% greater than the

∑ ∑ CCi ,j

Nopt Nb

block 1

Figure 10. Three-dimensional graphic of the number of options as a function of the number of blocks and operations in the process.

Nopt Nb total NCC

option

(8)

where i represents the blocks, going from 1 to Nb, and j the options, going from 1 to the number of options in the problem (Nopt: see equation 4). Note that the number of blocks must not 10050

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Figure 11. Final flowsheet.

■

CONCLUSIONS In this work a procedure is proposed adopting the strategy of decomposition of the original problem in order to facilitate the use of the WSD in large scale problems. This decomposition

ES1 source and 9.10% lower than the ES2 source. On the other hand, in terms of total wastewater discharge, the difference is 0.36% greater compared to results obtained by Leewongtanawit and Kim32 using WATER. 10051


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(4) Scarborough, B.; Watson, L. R. Encyclopedia of Energy, Natural Resource, and Environmental Economics; Elsevier: Amsterdam, 2013. (5) Jeżowski, J. Review of Water Network Design Methods with Literature Annotations. Ind. Eng. Chem. Res. 2010, 49, 4475. (6) Zhao, Z.; Liu, G.; Feng, X. The Integration of the Hydrogen Distribution System with Multiple Impurities. Chem. Eng. Res. Des. 2007, 85, 1295. (7) Zhang, Q.; Feng, X.; Chu, K. H. Evolutionary Graphical Approach for Simultaneous Targeting and Design of Resource Conservation Networks with Multiple Contaminants. Ind. Eng. Chem. Res. 2013, 52, 1309. (8) Pombo, F. R.; Magrini, A.; Szklo, A. An Analysis of Water Management in Brazilian Petroleum Refineries Using Rationalization Techniques. Resour. Conserv. Recycl. 2013, 73, 172. (9) Hou, Y.; Wang, J.; Chen, Z.; Li, X.; Zhang, J. Simultaneous Integration of Water and Energy on Conceptual Methodology for Both Single- and Multi-Contaminant Problems. Chem. Eng. Sci. 2014, 117, 436. (10) Liu, Z.-Y.; Yang, Y.; Wan, L.-Z.; Wang, X.; Hou, K.-H. A Heuristic Design Procedure for Water-Using Networks with Multiple Contaminants. AIChE J. 2009, 55, 374. (11) Fan, X.-Y.; Li, Y.-P.; Liu, Z.-Y.; Pan, C.-H. A New Design Method for Water-Using Networks of Multiple Contaminants with the Concentration Potential Concepts. Chem. Eng. Sci. 2012, 73, 345. (12) Li, B.-H.; Liang, Y.-K.; Chang, C.-T. Manual Design Strategies for Multicontaminant Water-Using Networks in Batch Processes. Ind. Eng. Chem. Res. 2013, 52, 1970. (13) Foo, D. C. Y. State-of-the-Art Review of Pinch Analysis Techniques for Water Network Synthesis. Ind. Eng. Chem. Res. 2009, 48, 5125. (14) Deng, C.; Feng, X.; Wen, Z. Optimization of Water Network Integrated with Process Models. Clean Technol. Environ. Policy 2013, 15, 473. (15) Liu, L.; Du, J.; El-Halwagi, M. M.; Ponce-Ortega, J. M.; Yao, P. Synthesis of Multi-Component Mass-Exchange Networks. Chin. J. Chem. Eng. 2013, 21, 376. (16) Castro, P.; Matos, H.; Fernandes, M. C.; Nunes, C. P. Improvements for Mass-Exchange Networks Design. Chem. Eng. Sci. 1999, 54, 1649. (17) Gomes, J. F. S.; Queiroz, E. M.; Pessoa, F. L. P. Design Procedure for Water/wastewater Minimization: Single Contaminant. J. Cleaner Prod. 2007, 15, 474. (18) Gomes, J. F. S.; Mirre, R. C.; Delgado, B. E. P. C.; Queiroz, E. M.; Pessoa, F. L. P. Water Sources Diagram in Multiple Contaminant Processes: Maximum Reuse. Ind. Eng. Chem. Res. 2013, 52, 1667. (19) Amidpour, M.; Polley, G. T. Aplication of Problem Decomposition in Process Integration. Chem. Eng. Res. Des. 1997, 75, 53. (20) Kemp, I. C.; Deakin, A. W. The Cascade Analysis for Energy and Process Integration of Batch Processes. I: Calculation of Energy Targets. Chem. Eng. Res. Des. 1989, 67, 495. (21) Lee, G.; Yoon, E. S. A Process Decomposition Strategy for Qualitative Fault Diagnosis of Large-Scale Processes. Ind. Eng. Chem. Res. 2001, 40, 2474. (22) Hernández-Suárez, R.; Castellanos-Fernández, J.; Zamora, J. M. J. M.; Hernandez-Suarez, R.; Castellanos-Fernandez, J.; Zamora, J. M. J. M. Superstructure Decomposition and Parametric Optimization Approach for the Synthesis of Distributed Wastewater Treatment Networks. Ind. Eng. Chem. Res. 2004, 43, 2175. (23) Zheng, F.; Simpson, A. R.; Zecchin, A. C.; Deuerlein, J. W. A Graph Decomposition-Based Approach for Water Distribution Network Optimization. Water Resour. Res. 2013, 49, 2093. (24) Zheng, F.; Simpson, A.; Zecchin, A. Improving the Efficiency of Multi-Objective Evolutionary Algorithms through Decomposition: An Application to Water Distribution Network Design. Environ. Model. Softw. 2015, 69, 240. (25) Savelski, M.; Bagajewicz, M. On the Necessary Conditions of Optimality of Water Utilization Systems in Process Plants with Multiple Contaminants. Chem. Eng. Sci. 2003, 58, 5349.

begins at the identification of the reference operations which defines the number of blocks in which the problem will be subdivided. Inside each block, an exhaustive search of the best structure is performed, without the need to eliminate violations, since in the traditional WSD, this step can involve complex calculations. Therefore, the analysis of largescale problems is simplified and can be performed without the need of proprietary software. The proposed decomposition strategy proved to be efficient in a problem involving ten operations and four contaminants, reaching a result close to the one obtained with the use of mathematical programming. Moreover, this approach does not require an initial guess to find a solution, and the process engineers do not need specific knowledge related to complex mathematical programming models. Considering the large number of intermediate flowsheets which must be generated, it is important to have a spreadsheet to automatically perform the WSD procedure without the cumbersome step of violation elimination. In both case studies, it was observed that the calculations may become significantly time-consuming if one decides to perform it by hand.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +55 21 2562-7603. Fax: +55 21 2562-7567. E-mail: mach@eq ufrj.br. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS Authors thank the ANP for financial support. NOTATIONS Gwu,c = parameter used to define the reference contaminant. Related to the contaminant c in the unit u f u = inlet and outlet flow rate of a unit u Δmu,c = Mass load of contaminant c in unit u Cu,c = Concentration of contaminant c of unit u Cmax u,c,in = maximum inlet concentration of contaminant c in unit u Cmax u,c,out = Maximum outlet concentration of contaminant c in unit u c = contaminant u = unit operation w = fresh water source Cnk = mathematical flowsheet combination nb = number of operations in the block Nb = number of blocks in the process Nop = number of all operations in the process Nopt = number of options Ntotal cc = number of all possible combinations of flowsheets k = nb − 1 n = Nop − Nb

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REFERENCES

(1) UNEP. Vital Water Graphics: An Overview of the State of the World’s Fresh and Marine Waters http://www.unep.org/dewa/vitalwater/ article32.html (accessed May 11, 2015). (2) Al Jayyousi, O.; Jayyousi, O. Al. Water as a Human Right: Towards Civil Society Globalization. Water Resour. Dev. 2007, 23, 329. (3) UNESCO. Managing Water under Uncertainty and Risk; The United Nations World Water Development Report 4; United Nations Educational, Scientific and Cultural Organization: Paris, 2012; Vol. 1. 10052


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Industrial & Engineering Chemistry Research (26) Poplewski, G.; Jeżowski, J. M.; Jeżowska, A. Water Network Design with Stochastic Optimization Approach. Chem. Eng. Res. Des. 2011, 9, 2085. (27) Yang, L.; Grossmann, I. E. Water Targeting Models for Simultaneous Flowsheet Optimization. Ind. Eng. Chem. Res. 2013, 52, 3209. (28) Khor, C. S.; Chachuat, B.; Shah, N. Optimization of Water Network Synthesis for Single-Site and Continuous Processes: Milestones, Challenges, and Future Directions. Ind. Eng. Chem. Res. 2014, 53, 10257. (29) Lira-Barragán, L. F.; Ponce-Ortega, J. M.; Nápoles-Rivera, F.; Serna-González, M.; El-Halwagi, M. M. Incorporating Property-Based Water Networks and Surrounding Watersheds in Site Selection of Industrial Facilities. Ind. Eng. Chem. Res. 2012, 52, 91. (30) Faria, D. C.; Bagajewicz, M. J. O. On the Appropriate Modeling of Process Plant Water Systems. AIChE J. 2010, 56, 668. (31) Doyle, S. J.; Smith, R. F. Targeting Water Reuse With Multiple Contaminants. Process Saf. Environ. Prot. 1997, 75, 181. (32) Leewongtanawit, B.; Kim, J.-K. Synthesis and Optimisation of Heat-Integrated Multiple-Contaminant Water Systems. Chem. Eng. Process. 2008, 47, 670. (33) Feller, W. Introduction to Probability Theory and Its Applications, 1 ed.; John Wiley & Sons: Hoboken, NJ, 1950.

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Water Sources Diagram in Multiple Contaminant Industrial Case Studies

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