Graphical Targeting Approach of Water Networks with Two-Stage

Article Cite This: Ind. Eng. Chem. Res. 2018, 57, 9591−9603

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Graphical Targeting Approach of Water Networks with Two-Stage Regeneration Recycling Haonan Ding and Xiao Feng*

Ind. Eng. Chem. Res. 2018.57:9591-9603. Downloaded from pubs.acs.org by UNIV OF SUSSEX on 08/07/18. For personal use only.

School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an 710049, P.R. China ABSTRACT: Water networks with regeneration recycling, an important part of water system integration, can minimize freshwater consumption and wastewater discharge to a maximum extent, and so its integration method has received extensive attention. However, relative works only involves the water network with one-stage regeneration recycling. The cost of wastewater regeneration can be obviously reduced via multistage regeneration recycling with the same freshwater consumption and wastewater discharge. In this paper, how to construct the optimal water supply line with two-stage regeneration recycling is proposed. A graphical approach to determine targets of such water network is established, including the optimal freshwater flow rate, the optimal first stage regenerated water flow rate, the optimal second stage regenerated water flow rate, and the optimal regeneration concentration. Formulas to calculate these targets are deduced, and accordingly the improved problem table is presented to obtain these targets accurately. Based on the determined targets, the associated water network can be designed. Compared with the water network with one-stage regeneration recycling, the water network with two-stage regeneration recycling has significant advantages in terms of regeneration cost and using water according to the quality.

1. INTRODUCTION With the global water shortage becoming more and more serious, the importance of water saving and recycling has gained much more attention. The industrial water usage accounts for a large proportion of the total water consumption, and the industrial wastewater discharge is the main source of water pollution. Water system integration can effectively reduce the industrial freshwater consumption and wastewater discharge. The water network with regeneration recycling is an important part of water system integration and can reduce freshwater consumption and wastewater discharge to the maximum extent. Methods to deal with water system integration may be classified into two main categories, graphical approach (pinch approach) and mathematical programming. The graphical approach that can show the insights of the system1 is an effective approach for water networks with a single contaminant. When faced with a new problem, the graphical approach can give a valuable enlightening solution. Kuo and Smith2 pioneered the subject of graphical optimization of water systems through regeneration reuse/ recycle. Dhole at el.3 proposed the mass load-flow rate diagram to determine the pinch. Mann and Liu4 pointed out that, when taking regeneration reuse into consideration, there is a point above the pinch to limit the water supply line of the system. Feng and Chu5 showed that the cost of wastewater regeneration rises exponentially with contaminant removal efficiency. Feng at el.6 established the graphical method for water networks with regeneration recycling and pointed out that in the water system with regeneration recycling, the optimal regeneration concen© 2018 American Chemical Society

tration can be higher than, lower than, or equal to the pinch concentration, depending on the shape of limiting composite curve. In addition, by analyzing the limiting composite curve of a single-contaminant water system, they deduced out the formulas to calculate the optimal regenerated water flow rate and the optimal regeneration concentration, and furthermore, the improved problem table is presented to determine these targets. Tan et al.7 improved the design method of water networks with regeneration recycling. Deng at el.8 found the necessary condition of zero discharge for regeneration recycling water networks with single contaminant. Ng at el.9 proposed a linear algebraic method to automatically target the minimum freshwater consumption of water networks with a single contaminant. Feng at el.10 investigated the effect of the limiting composite curve change on the pinch location and freshwater consumption based on the graphical approach. Wang at el.11 discussed the trade-off of freshwater flow rate and regenerated water flow rate in regeneration recycling water networks with a single contaminant. Deng at el.12 provided the process-based graphical approach for water network optimization. Deng and Feng extended the composite table algorithm as the improved problem table13 and proposed the generalized improved problem table, aiming at determining the flow rate targets of water networks with regeneration recycling.14 Xu at el.15 Received: Revised: Accepted: Published: 9591

March 22, 2018 June 25, 2018 June 26, 2018 June 26, 2018 DOI: 10.1021/acs.iecr.8b01264 Ind. Eng. Chem. Res. 2018, 57, 9591−9603

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Industrial & Engineering Chemistry Research

Figure 1. Composite water supply line of water network with one-stage regeneration recycling.

with the water network with one-stage regeneration recycling, it can reduce the regeneration cost effectively and so has great application prospect. In this paper, such a water network is defined as the water network with multistage regeneration recycling. A water network with two-stage regeneration recycling is a simple structure of a water network with multistage regeneration recycling. In this paper, the graphical method is used, for it can give the insight of a new problem, which will be helpful to further establish the mathematical programming model of such systems. A graphical approach and improved problem table are proposed to target the water network with two-stage regeneration recycling, based on the relationship between the limiting composite curve and composite water supply line. Methods given in this paper can be extended to water networks with multistage regeneration recycling.

predicted the effect of regeneration recycling on the pinch in water networks. Zhang at el.16 found that pinch location of water networks with regeneration recycling is influenced by the concave location and the concaving extent of the limiting composite curve. Shi at el.17 studied water networks with double outlets regeneration units and provided formulas for calculating the flow rate targets by graphical approach. Li at el.18 discussed the influence of the regeneration concentration on the regenerated water flow rate. Parand at el. pointed out with extension of the composite table algorithm19 that some of the water networks with regeneration recycling may reach zero discharge.20 Fan at el.21 presented new formulas for targeting regeneration recycling water networks with a single contaminant, based on the graphical approach. In all works for water networks with regeneration recycling, the regenerated water is considered to be recycled back after being regenerated to the postregeneration concentration, which means that there is one-stage regeneration recycling. In an actual industrial system, the wastewater regeneration/treatment unit is usually a combination of multiple processes which allow wastewater to be regenerated to the required postregeneration concentration. If meeting the requirement of some water-using units, the outlet streams from intermediate regeneration processes can be reused also. The concentrations of the regenerated water from the intermediate regeneration process are certainly higher than the final postregeneration concentration. Because the regeneration cost is normally increased nearly proportionally with flow rate and exponentially with the postregeneration concentration,5 for a certain regeneration process, if some water is taken out for recycled back to waterusing processes from intermediate regeneration processes with no capital cost of additional equipment, the total regeneration cost is lower.22 Such water network contains several regenerated water with different postgeneration concentrations. Compared

2. PROBLEM STATEMENT Given is a set of water-using processes including limiting inlet concentrations, limiting outlet concentrations, and contaminant mass loads. A water system with two-stage regeneration recycling is targeted. The two postregeneration concentrations are taken to be known. The graphical method, involved pinch, limiting composite curve and water supply line, is employed to analyze the system. An approach to construct the optimal water supply line for the system, based on the characteristic of the limiting composite curve and the two postregeneration concentrations, is presented. The targets would be determined including the freshwater flow rate, the first-stage regenerated water flow rate, the second-stage regenerated water flow rate and the regeneration concentration. Finally, the water network will be built based on the targets. 9592

DOI: 10.1021/acs.iecr.8b01264 Ind. Eng. Chem. Res. 2018, 57, 9591−9603

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Figure 2. Composite water supply line of water network with two-stage regeneration recycling.

Figure 3. Optimal composite water supply line of the water network with two-stage regeneration recycling.

3. COMPOSITE WATER SUPPLY LINE OF A WATER NETWORK WITH TWO-STAGE REGENERATION RECYCLING

line, and concentrations Cin and Cout are the regeneration concentration and the postregeneration concentration, respectively. The composite water supply line ABEF can be obtained by combining lines AC and DE between Cin and Cout. The water supply line of a water network with two-stage regeneration recycling can be constructed in the similar way. For a water network with two-stage regeneration recycling, the freshwater supply line AC and the wastewater discharge line EF

Feng at el.6 proposed a method to construct the composite water supply line of water network with one-stage regeneration recycling, when ignoring the water loss, as is shown in Figure 1. Lines AC, DE, and EF in sequence are the freshwater supply line, the regenerated water supply line, and the wastewater discharge 9593


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Figure 4. Determination of the flow rate targets.

4. TARGETING BY GRAPHICAL APPROACH

are the same as those of the water network with one-stage regeneration recycling, as shown in Figure 2. There are two regenerated water supply lines, line C1F1 and line C2F2 with Cout1 and Cout2 as the postregeneration concentrations, respectively. The composite water supply line ABDEF can be obtained by composing AC, C1F1, and C2F2, as shown in Figure 2. Concentration Cin is the regeneration concentration.

4.1. Targets to Be Determined. Compared to a water network with one-stage regeneration recycling, a water network with two-stage regeneration recycling has the following extra important parameters: the second stage regenerated water flow rate and the second stage postregeneration concentration. In the composite water supply line, line BE changes to curve BDE. 9594


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Figure 5. Composite water supply line of a water network with two-stage regeneration recycling.

beyond Cout2, the composite water supply line could not be directly determined due to the concentration of its upper end as one of the targets. Additionally, as for the discharged water line, it can only be known that the discharged water line has the same slope with the freshwater supply line. Therefore, in the construction steps, the straight line with a same slope of the freshwater supply line can first be determined, and then the third part of the composite water supply line could be drawn. The touching point of the two lines means the optimal regeneration concentration. From the composite water supply line of the water network with two-stage regeneration in Figure 2, it can be seen that line AB and line EF of the curve are determined by the freshwater supply line, line BD is combined by the freshwater supply line and the first stage regenerated water supply line, line DE is composited by the freshwater supply water, the first stage regenerated water supply line, and the second stage regenerated water supply line, and the regeneration concentration is determined by the location of point E. If the optimal composite water supply line is known, the targets can be determined in the sequence of the regeneration concentration, the freshwater flow rate, the first stage regenerated water flow rate, and the second stage regenerated water flow rate. Therefore, the key work to do for targeting the water network with two-stage regeneration recycling is to construct the optimal composite water supply line. The steps to construct the optimal composite water supply line are as follows, by using the limiting composite curve (dotted curve) in Figure 3 as an example. Step 1: In the concentration interval between 0 and Cout1, draw a straight line from point A and make it always below the limiting composite curve. Then, the line with the greatest slope is the line AB (point B is the touching point with the concentration line at Cout1).

Thus, the important parameters of the water network with two-stage regeneration recycling include the freshwater flow rate, the first stage regenerated water flow rate, the second stage regenerated water flow rate, the first stage postregeneration concentration, the second stage postregeneration concentration, and the regeneration concentration. Among the parameters mentioned above, the two postregeneration concentrations are determined by two factors: economic factors and water-using requirement. The location of the postregeneration concentration is required to bring economic benefits to the water network. Besides, the water network should have a certain water-using requirement for the regenerated water at the concentrations. Since the optimal postregeneration concentration should be determined by the economic factors, it cannot be targeted by the graphical approach. Therefore, the two postregeneration concentrations are taken to be known in this paper. In conclusion, the targets of the water network with two-stage regeneration recycling to be determined in this paper are as follows: the freshwater flow rate, the first stage regenerated water flow rate, the second stage regenerated water flow rate, and the regeneration concentration. 4.2. Optimal Composite Water Supply Line. For a certain water system, the limiting composite curve can be constructed. Based on the limiting composite curve and the two postregeneration concentrations, if the optimal composite water supply line can be obtained, all the targets can be determined accordingly. In each concentration interval from the bottom to the top, the line segment of the optimal composite water supply line must be always below and as close as possible to the limiting composite curve, with the upper end as the starting point of the composite water supply line of the next interval. It should be noted that in the concentration interval 9595


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Industrial & Engineering Chemistry Research Step 2: In the concentration interval between Cout1 and Cout2, draw a straight line from point B and make it always below the limiting composite curve. Then, the line with the greatest slope is the line BE (point E is the touching point with the concentration line at Cout2). Step 3: Draw a straight line MN with the slope same as line AB and the abscissa of point N is equal to that of point Q (the end point of the limiting composite curve). Move line MN to touch the limiting composite curve and make it always below or touched the limiting composite curve. Line MN is the wastewater discharge line. Step 4: Draw a straight line from point E. Make it always below the limiting composite curves with the maximum slope. The touching point of the line with line MN is point M. The curve ABEMN is the optimal composite water supply line. 4.3. Determine Targets. The method to determine the targets is shown in Figure 4. The optimal regeneration concentration is determined by the ordinate of point M. The freshwater flow rate is the reciprocal of the slope of line AB. The optimal freshwater supply line can be obtained by extending line AB as line AP, and point P is the intersection point of the extension line of AB with the horizontal line at Cin. The optimal first stage regenerated water flow rate will be determined by the optimal first stage regenerated water supply line CQ. The construction method for the optimal first stage regenerated water supply line is as follows. First, extend line BE as line BQ, and point Q is the intersection point of the extension line of BE with the horizontal line at Cin. Point C has the same ordinate with point P and the same abscissa with point B. Link point C and point Q to get line CQ, the optimal first stage regenerated water supply line. The optimal first stage regenerated water flow rate is the reciprocal of line CQ’s slope. The optimal second stage regenerated water flow rate will be determined by the optimal second stage regenerated water supply line GM. Point G has the same abscissa with point Q and the same ordinate with point M. Then link point G and point M to get line GM, the optimal second stage regenerated water supply line. The optimal second stage regenerated water flow rate is the reciprocal of line GM’s slope. The method to construct these water supply lines is shown in Figure 4a. These lines after moving the second regenerated water supply line to the regeneration line PC are shown in Figure 4b.

optimal composite water supply line. In each concentration interval of this water network, there is a limiting point of the composite water supply line. Formulas derived from Figure 5 are general for water networks with two-stage regeneration recycling. Considering all the points in Figure 5, formulas can be obtained to calculate the targets 5.1.1. Optimal Freshwater Flow Rate. The limiting point for the optimal freshwater flow rate is below the first stage postregeneration concentration Cout1. It is the point B for the water network in Figure 5. According to line AB in Figure 5, it can be obtained as follows: W MB = Fmin CB W Fmin =

∵ AN = AM + MN

l AN = MC o o o o o W o AM = MB = Fmin CB m o o o o W R1 o o MN = Fmin (CC − C B) + Fmin (CC − Cout1) n W W R1 ∴ MC = Fmin C B + Fmin (CC − C B) + Fmin (CC − Cout1) W R1 MC = Fmin CC + Fmin (CC − Cout1)

Therefore, the optimal first stage regenerated water flow rate is R1 Fmin =

Cout,max /ppm i

mass load/kg h−1

1 2 3 4

0 50 75 100

100 150 100 125

6 4 2.5 1.25

W MC − Fmin CC CC − Cout1

(2)

where MC and CC are the contaminant mass load and concentration at point C, respectively, and FR1 min is the optimal first stage regenerated water flow rate. 5.1.3. Optimal Second Stage Regenerated Water Flow Rate. The limiting point for the optimal second stage regenerated water flow rate is in the concentration interval between Cout2 and Cin. It is point D of the water network in Figure 5. According to line ABCD in Figure 5, it can be obtained as follows:

Table 1. Limiting Water Data for Example 1 Cin,max /ppm i

(1)

where MB and CB are the contaminant mass load and concentration at point B, respectively, and FW min is the optimal freshwater flow rate. 5.1.2. Optimal First Stage Regenerated Water Flow Rate. The limiting point for the optimal first stage regenerated water flow rate is in the concentration interval of Cout1 and Cout2. It is point C of the water network in Figure 5. According to line ABC in Figure 5, it can be obtained as follows:

5. IMPROVED PROBLEM TABLE TO DETERMINE TARGETS Following the way shown by Feng at el.,6 the limiting point of each target is determined by the graphical approach first. Then

process number

MB CB

∵ AO = AM + MN + NO

l AO = MD o o o o o W o o AM = Fmin CB o o o o o W R1 m MN = Fmin (CC − C B) + Fmin (CC − Cout1) o o o o o o W R1 o NO = (Fmin + Fmin )(Cout2 − CC) o o o o W R1 R2 o + ( F + F min min + Fmin)(C D − Cout2) n

based on geometric derivation, formulas for calculating the targets are obtained. Finally, the improved problem table can be established. 5.1. Limiting Point and Formula of Each Target. Figure 5 shows the limiting composite curve of a water system and its 9596


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Industrial & Engineering Chemistry Research Table 2. Improved Problem Table for Example 1

Figure 6. Optimal composite water supply line of example 1.

Table 3. Limiting Water Data for Example 2 process number

Cin,max /ppm i

Cout,max /ppm i

mass load/kg h−1

1 2 3 4 5

0 100 100 300 400

200 200 400 400 600

8000 5000 9000 6000 8000

R2 Fmin =

W R1 MD − Fmin C D − Fmin (C D − Cout1) C D − Cout2

(3)

where MD and CD are the contaminant mass load and concentration at point D, respectively, and FR2 min is the optimal second stage regenerated water flow rate. 5.1.4. Optimal Regeneration Concentration. The optimal regeneration concentration is determined by the optimal second stage regenerated water supply line and the optimal wastewater discharge line. The optimal second stage regenerated water flow rate is fixed according to the method mentioned above. The optimal wastewater discharge line is considered now. The limiting point for the optimal wastewater discharge line is above the second stage regeneration concentration Cout2. It is point F for the water network in Figure 5. According to line ABCDEF in Figure 5, it can be obtained as follows:

W W R1 MD = Fmin C B + Fmin (CC − C B) + Fmin (CC − Cout1) W R1 + (Fmin + Fmin )(Cout2 − CC) W R1 R2 + (Fmin + Fmin + Fmin )(C D − Cout2) W R1 R2 MD = Fmin C D + Fmin (C D − Cout1) + Fmin (C D − Cout2)

Therefore, the optimal second stage regenerated water flow rate

∵ AF = AM + MN + NO + OP + PQ

is 9597


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Figure 7. Optimal composite water supply line of example 2.

Table 4. Improved Problem Table for Example 2

l AF = MF o o o o o W o o AM = Fmin CB o o o o o W R1 o o MN = Fmin (CC − C B) + Fmin (CC − Cout1) o o o o o W R1 m NO = (Fmin )(Cout2 − CC) + Fmin o o o W R1 R2 o o )(C D − Cout2) + (Fmin + Fmin + Fmin o o o o o o W R1 R2 o o OP = (Fmin + Fmin + Fmin)(Cin − C D) o o o o o W o PQ = Fmin (C F − Cin) o n

W W R1 ∴ MF = Fmin C B + Fmin (CC − C B) + Fmin (CC − Cout1) W R1 + (Fmin + Fmin)(Cout2 − CC) W R1 R2 + (Fmin + Fmin + Fmin )(C D − Cout2) W R1 R2 + (Fmin + Fmin + Fmin )(Cin − C D) W + Fmin(C F − Cin) W R1 R2 MF = Fmin C F + Fmin (Cin − Cout1) + Fmin (Cin − Cout2)

Therefore, the optimal regeneration concentration: Cin =

W R1 R2 MF − Fmin C F + Fmin Cout1 + Fmin Cout2 R1 R2 Fmin + Fmin

(4)

where MF and CF are the contaminant mass load and concentration at point F, respectively. 9598


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Figure 8. Grid diagram of example 1.

For a water network with two-stage regeneration recycling, concentrations can be divided into four intervals: below Cout1, between Cout1 and Cout2, between Cout2 and Cin, and above Cin. In each concentration interval, there will be touching point(s) between the optimal composite water supply line and the limiting composite curve. The touching points in the four concentration intervals are the limiting points of the freshwater supply line, the first stage regenerated water supply line, the second stage regenerated water supply line, and the regeneration concentration, respectively. According to eqs 1−4 and the abscissa and the ordinate of the limiting points, the optimal targets can be obtained in sequence of the optimal freshwater flow rate, the optimal first stage regenerated water flow rate, the optimal second stage regenerated water flow rate, and the optimal regeneration concentration. 5.2. Improved Problem Table. The limiting point lies at the upper end or the middle of the limiting composite curve in each concentration interval. There are two methods to determine the limiting points, graphical method, and the improved problem table. In this section, we improve the problem table to determine all the targets without drawing a diagram. The method to construct the improved problem table is as follows. Step 1: All the concentrations are arranged in increasing order in the first column, including freshwater concentration, inlet and

Figure 9. Conventional flowsheet of example 1.

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Figure 10. Network structure of example 1.

Figure 11. Network structure of example 2.

outlet concentrations of all process, and the first and second stage postregeneration concentrations. Step 2: All process streams are represented by vertical arrows, starting from their inlet concentrations and end at the outlet concentrations. Step 3: Calculate the mass load of each concentration intervals and list them in the third column. Step 4: Calculate the cumulative mass load of each concentration intervals and list them in the fourth column. Step 5: In the fifth column, at each concentration less than or equal to the first stage postregeneration concentration, calculate the possible freshwater flow rates by eq 1. The maximum one is the target for freshwater flow rate. Step 6: In the sixth column, at each concentration, from the concentration just greater than the first stage postregeneration concentration to the second stage postregeneration concentration, calculate the possible first stage regenerated water flow rate at each point by eq 2. The maximum one is the optimal first stage regenerated water flow rate. Step 7: In the seventh column, at each concentration greater than the second stage postregeneration concentration, calculate the possible second stage regenerated water flow rate by eq 3. The maximum one is the target of the second stage regenerated water flow rate. Step 8: In the eighth column, at each concentration greater than the second stage postregeneration concentration, calculate the possible regeneration concentration by eq 4. The maximum one is the optimal regeneration concentration. 5.3. Case Study. Two examples are carried out to illustrate the graphical approach and the improved problem table proposed in this paper. Example 1. The limiting water data is from Feng at el.,6 as shown in Table 1. It is a single contaminant water system with four water-using units. It is assumed that two-stage regeneration recycling is used in this water-using system, with the first stage

postregeneration concentration at 40 mg/L and the second stage postregeneration concentration at 75 mg/L. Table 2 is the improved problem table for this example. It can be seen that the optimal freshwater flow rate is 60 t/h, the optimal first stage regenerated water flow rate is 28.57 t/h, the optimal second stage regenerated water flow rate is 111.43 t/h, and the optimal regeneration concentration is 105.36 mg/L. Figure 6 can be obtained by the proposed graphical approach. It can be found that the targets in Figure 6 are in good agreement those obtained by the improved problem table. Example 2. Example 2 is taken from Kuo and Smith.2 The water system has five water-using units, and Table 3 shows the limiting water data of each unit. In this paper, the improved problem table is used to solve the problem with an assumption that the two stage postregeneration concentration are 10 mg/L and 150 mg/L, respectively. By the proposed graphical method, Figure 7 can be obtained. Table 4 is the improved problem table for this example. It is shown in Table 4 that the optimal freshwater flow rate is 40 t/h, the optimal first stage regenerated water flow rate is 28.57 t/h, the optimal second stage regenerated water flow rate is 51.43 t/ h, and the optimal regeneration concentration is 250 mg/L. These targets are quite different from those in ref 2. The targets in ref 2 are as follows: the freshwater flow rate is 40t/h, the regenerated water flow rate is 42.1 t/h, and the inlet concentration of the regeneration system reaches 556 mg/L. The regeneration concentration is much higher than that in the two-stage regenerated water network, indicating a higher cost in regeneration. The comparison of regeneration cost will be given later. 5.4. Construction of Water Network. Based on the targets determined by the proposed method, the associated water network with two-stage regeneration recycling can be constructed. The water network can be constructed according to the method proposed by Wang and Smith,23 and the only difference is that there are two regenerated water lines. For 9600


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Figure 12. Comparison of water supply lines for systems with one and two stage regeneration.

two kinds of regeneration recycling have the same optimal freshwater flow rate, while the regeneration concentrations are different. In each of the two examples, the optimal regeneration concentration with two-stage regeneration recycling (Cin2) is less than that with one-stage regeneration recycling (Cin1). In addition, the optimal first stage regenerated water flow rate with two-stage regeneration recycling is less than the optimal regenerated water flow rate with one-stage regeneration recycling, while the total regenerated water with two-stage regeneration recycling is more than that with one-stage regeneration recycling. Besides, in the concentration interval from the first stage postregeneration concentration to the second stage postregeneration concentration, the optimal composite water supply line with two-stage regeneration recycling is closer to the limiting composite curve than that with one-stage regeneration recycling, revealing that it has the advantage in using water on the basis of quality.

example 1, Figure 8 is the grid diagram of the network. After removing loops, Figure 9 can be obtained. Therefore, the structure of water network with two-stage regeneration recycling of example 1 can be determined, as shown in Figure 10. The same method can be used to determine the water network structure of example 2, as shown in Figure 11.

6. COMPARISON WITH ONE-STAGE REGENERATION RECYCLING SYSTEM For the data shown in Tables 1 and 3, the optimal composite water supply lines with one-stage regeneration recycling can be obtained by the method proposed by Feng at el.,6 and those with two-stage regeneration recycling by the method proposed in this paper, as shown in Figure 12. Comparing those optimal composite water supply lines and the corresponding targets obtained in Figure 12, the following results can be obtained. For the same water using system, the 9601


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stage regeneration recycling at the same freshwater consumption and wastewater discharge. Although this paper only deals with the water network with two-stage regeneration recycling in series connection, the method can be easily extended to the water network with multistage regeneration recycling or with two independent regenerating devices. The method proposed in this paper can only deal with single contaminant water systems. Using the mathematical programming method to deal with multiplecontaminant systems will be our further work, and some insights found from the graphical analysis in this paper will be helpful to establish the mathematical programming model of such systems with multiple-contaminants.

Comparing with the water network with one-stage regeneration recycling, for the water network with two-stage regeneration recycling in example 1, the flow rate of the regenerated water required to recycle from Cin to Cout2 raises from 75 t/h to 140 t/h, but the flow rate of the regenerated water required to recycle from Cout2 to Cout1 decreases from 75 to 28.57 t/h. By the formula proposed by Feng at el.,6 cost of the wastewater regeneration can be calculated. The regeneration costs of the water network with one-stage regeneration recycling and two-stage regeneration recycling are 322.45 mu/h and 159.59 mu/h, respectively. Similarly, for example 2, the flow rate of the regenerated water required to recycle from Cin to Cout2 raises from 40 to 51.43 t/h, but the flow rate of the regenerated water required to recycle from Cout2 to Cout1 decreases from 40 to 28.57 t/h. The regeneration costs of the water network with one-stage regeneration recycling and two-stage regeneration recycling are 57332.60 mu/h and 13534.70 mu/h, respectively. It can be seen that the water network with two-stage regeneration recycling can effectively reduce the cost of wastewater regeneration.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +86 29 82664376. Fax: +86 29 82665836. E-mail: [email protected]. ORCID

Xiao Feng: 0000-0001-6539-634X Notes

The authors declare no competing financial interest.

7. CASE WITH TWO INDEPENDENT REGENERATING DEVICES In this paper, we consider that the outlet stream of the second stage regeneration is from intermediate regeneration processes, that is, the two stage regeneration units are serial. The consideration for such serial regeneration is because in an actual industrial system, the wastewater regeneration unit is usually a combination of multiple processes, if some intermediate water can be recycled to water-using processes, the regeneration cost can be reduced. If there is a need to use two independent regenerating devices, that is, the two regenerating devices are parallel, each regeneration process has its own inlet and outlet concentrations. Compared with the serial regeneration processes, the only difference is that there are two regeneration concentrations, named as Cin1 and Cin2. The method proposed in this paper can be extended to the water network with two independent regenerating devices. For constructing the optimal composite water supply line, the only difference is in the concentration interval of Cin1−Cin2. In the concentration interval of Cin1−Cin2, the optimal composite water supply line is composed of those of freshwater and a kind of regenerated water, causing the slope of the line in this interval larger than that in the interval of Cout2−Cin1 and less than that of the wastewater discharge line. After the optimal composite water supply line in the interval of Cout2−Cin1 is determined, all the targets can be obtained.

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ACKNOWLEDGMENTS Financial support from the National Key Research Program of China (Grant 2017YFF0206700) and the National Natural Science Foundation of China under Grant No. 21736008 is gratefully acknowledged.

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NOMENCLATURE Cin = regeneration concentration, ppm Cout = postregeneration concentration, ppm Cout1 = first postregeneration concentration, ppm Cout2 = second postregeneration concentration, ppm CB = concentration at point B, ppm CC = concentration at point C, ppm CD = concentration at point D, ppm CF = concentration at point F, ppm FW min = The optimal freshwater flow rate, t/h FR1 min = The first stage regenerated water flow rate, t/h FR2 min = The second stage regenerated water flow rate, t/h MB = contaminant mass load at point B, kg/h MC = contaminant mass load at point C, kg/h MD = contaminant mass load at point D, kg/h MF = contaminant mass load at point F, kg/h

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REFERENCES

(1) Foo, D. C. Y. A generalised guideline for process changes for resource conservation networks. Clean Technol. Environ. Policy 2013, 15 (1), 45−53. (2) Kuo, W. C. J.; Smith, R. Design of Water-Using Systems Involving Regeneration. Process Saf. Environ. Prot. 1998, 76 (2), 94−114. (3) Dhole, V. R.; Ramchandani, N.; Tainsh, R. A.; Wasilewski, M. Make your process water pay for itself. Chem. Eng. 1996, 103 (1), 100− 103. (4) Mann, J.; Liu, Y. A. Industrial Water Reuse and Wastewater Minimization; McGraw Hill: New York, 1999. (5) Feng, X.; Chu, K. H. Cost Optimization of Industrial Wastewater Reuse Systems. Process Saf. Environ. Prot. 2004, 82 (3), 249−255. (6) Feng, X.; Bai, J.; Zheng, X. On the use of graphical method to determine the targets of single-contaminant regeneration recycling water systems. Chem. Eng. Sci. 2007, 62 (8), 2127−2138.

8. CONCLUSION The single contaminant water system with two-stage regeneration recycling is studied in this paper. Based on the constructed optimal composite water supply line, a graphical approach to target the important parameters is established, which include the optimal freshwater flow rate, the optimal first stage regenerated water flow rate, the optimal second stage regenerated water flow rate, and the regeneration concentration. Furthermore, based on deduced formulas to calculate these targets, the improved problem table is presented to determine these targets. For much lower regeneration cost, the water network with two-stage regeneration recycling has a great advantage over that with one9602


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Graphical Targeting Approach of Water Networks with Two-Stage

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