- Email: [email protected]
Graphically Based Optimization of Single-Contaminant Regeneration Reuse Water Systems
GRAPHICALLY BASED OPTIMIZATION OF SINGLE-CONTAMINANT REGENERATION REUSE WATER SYSTEMS J. Bai, X. Feng and C. Deng Department of Chemical Engineering, Xi’an Jiaotong University, Xi’an, P.R. China.
Abstract: In this paper, graphical method is employed to optimize single-contaminant regeneration reuse water systems. On the concentration-mass load diagram, three categories of waterusing systems with regeneration reuse are analyzed in terms of the geometric features of limiting composite curve. Total regeneration and partial regeneration are identified first. Then based on sequential optimization and at a specified post-regeneration concentration, the optimal water supply lines for regeneration reuse systems can be constructed. The optimal water supply line corresponds to minimum freshwater consumption, minimum regenerated water flowrate and minimum contaminant regeneration load. Formulas for calculating these targets are summarized and interactions of these parameters are discussed. The concepts of limiting points for regeneration reuse, which are the counterpart of pinch for direct reuse, are proposed to indicate the bottlenecks of a water system with regeneration reuse. Different locations of the limiting points for different systems underlie that the optimal regeneration concentration can be greater than, equal to or smaller than the pinch concentration of the system. Keywords: integration; regeneration reuse; graphical method; mass problem table; water system.
INTRODUCTION
Correspondence to: Professor X. Feng, Department of Chemical Engineering, Xi’an Jiaotong University, Xi’an 710049, P.R. China. E-mail: [email protected]
DOI: 10.1205/cherd06252 0263–8762/07/ $30.00 þ 0.00 Chemical Engineering Research and Design Trans IChemE, Part A, August 2007 # 2007 Institution of Chemical Engineers
Graphical method was initiated by Wang and Smith (1994). They introduced several important concepts, such as limiting water profile, limiting composite curve and pinch. Then the water demand and supply of a system can be described on the concentration-mass load diagram, whether water reuse, regeneration reuse or regeneration recycling is considered. For regeneration reuse, at a given post-regeneration concentration, the optimal regeneration concentration is taken as the pinch concentration of the system in the paper. Later, Mann and Liu (1999) found that when considering water regeneration reuse, some systems had another pinch point, regeneration pinch, which is higher than the conventional pinch for freshwater targeting. Castro et al. (1999) introduced a multiple-pinch-points concept and proposed a novel re-use network targeting/design methodology for single contaminant systems. This method can be utilized to design and optimize regeneration reuse water systems. The above research on optimizing regeneration reuse systems all resorts to graphical method, thus only applies to single-contaminant systems. When mathematical programming is utilized, regeneration reuse, as one of the possibilities to reduce the freshwater consumption
Water system integration is one of the most efficient technologies for minimizing freshwater consumption and wastewater discharge simultaneously. Excluding the possibility of making process changes to reduce the inherent demand for water, there are three approaches for wastewater minimization: water reuse, regeneration reuse and regeneration recycling (Wang and Smith, 1994). A water system with regeneration options (regeneration reuse or/and regeneration recycling) can reduce more freshwater intake and wastewater discharge than that with mere water reuse, since the contaminant mass load of the system is partially removed by regeneration units. It is important to distinguish between regeneration reuse and regeneration recycling, for sometimes people do not favour recycling owing to the build-up of contaminants. For example, in some cases, traces of byproducts of corrosion in the recycle may contaminate catalysts. Therefore, it is worthy of studying the optimization of regeneration reuse water systems. In recent years, much research has been conducted on this topic mainly based on two traditional methods: graphical method and mathematical programming. 1178
Vol 85 (A8) 1178 –1187
OPTIMIZATION OF SINGLE-CONTAMINANT REGENERATION REUSE WATER SYSTEMS or total cost of a water system, is incorporated in the superstructure (Takama et al., 1980; Huang et al., 1999; Bagajewicz, 2001; Feng and Chu, 2004; Xu et al., 2004; Gunaratnam et al., 2005). The targeting and design of regeneration reuse systems are performed by solving the corresponding mathematical models. Based on a sequential three-step programming method, Xu et al. (2003) investigated the relationship between the freshwater flowrate required and regeneration concentration of a regeneration reuse system. Their study shows that the regeneration of water at pinch concentration does not always minimize the freshwater consumption and there are three possibilities for the minimum regeneration concentration: below, above or at the pinch. Owing to the limitations of the method they used, these conclusions are not analysed in details, which we will give a conceptual explanation on the concentrationmass load diagram in this paper. In our previous paper (Feng et al., 2007), based on sequential optimization, we proposed a handy method to construct the optimal water supply line for a regeneration recycling system, and introduced the improved mass problem table to target for freshwater, regenerated water and regeneration concentration. Here we will adopt the procedure of sequential optimization and extend the methodology to regeneration reuse systems. Before continuing this paper, it is recommended that the reader study the sequential optimization approach as introduced by Feng et al. (2007).
PROBLEM TO BE SOLVED Considering a water network with regeneration reuse, in which wastewater from several processes can be regenerated by partial or total treatment to remove the contaminants and then reused in other processes. Different from regeneration recycling, the water after regeneration can not re-enter processes in which it has previously been used. There are two kinds of regeneration reuse: total regeneration and partial regeneration. For total regeneration, all the water, the concentration of which reaches the regeneration concentration, is sent to regeneration system for treatment. Thus the flowrate of regenerated water is equal to that of freshwater, if water loss in processes is ignored. While for partial regeneration, only partial amount of contaminated water is regenerated, and the residual wastewater is directly re-used or discharged. That means the regenerated water flowrate is smaller than the freshwater consumption. If regenerating part of water can meet the demand of the system, partial regeneration is undoubtedly utilized instead of total regeneration to assure a lower regeneration cost. The approach to identify whether total or partial regeneration should be used will be developed later. Both total and partial regeneration can be depicted on the concentration-mass load diagram. Partial regeneration re-use systems are identical to regeneration recycling systems in terms of graphical representation, since the limiting freshwater supply line in both of the cases is determined by the limiting composite curve below the post-regeneration concentration. In addition to different network structure, on the concentration-mass load diagram the difference between them lies in the quantitative relationship of freshwater and regenerated water flowrate. For regeneration recycling, the flowrate of regenerated water can be greater than, equal to or smaller than that of freshwater. While in case of partial
1179
regeneration reuse, the regenerated water flowrate should be smaller than the freshwater consumption. In other words, only from the point of graphical representation, partial regeneration reuse systems can be taken as a special case of regeneration recycling systems when the flowrate of regenerated water is smaller than that of freshwater. Then the targeting procedure for partial regeneration reuse systems can be performed by the method for regeneration recycling systems. Since regeneration units are involved as in regeneration recycling systems, the optimization of total regeneration reuse systems can also be conducted on the basis of the method for regeneration recycling systems. Similar to regeneration recycling systems, a water-using network with regeneration reuse needs to determine the targets for freshwater comsumption, regenerated water flowrate, regeneration and post-regeneration concentration. In this paper, sequential optimization presented by Feng et al. (2007) is adopted to analyse the optimization of regeneration reuse systems. Since a partial regeneration system is similar to a regeneration recycling system on the concentrationmass load diagram, our discussion only confines to total regeneration systems. At a specified post-regeneration concentration, freshwater consumption (regenerated water flowrate) and regeneration concentration are minimized step by step to depict the optimal water supply line for total regeneration reuse systems. Formulas for calculating the targets for total regeneration reuse systems can be summarized by the geometrical relationships on the concentration-mass load diagram. Three representative water-using systems are employed to illustrate the methodology.
THREE REPRESENTATIVE WATER-USING SYSTEMS Before discussing pinch analysis for regeneration reuse systems, three representative water-using systems will be addressed. For each water system, the water supply line with minimum freshwater flowrate and pinch point under the condition of only considering water reuse are given, as shown in Figures 1–3. Obviously the three representative water-using systems have different characteristics. For water-using system 1 (Figure 1), the limiting composite curve touches the limiting water supply line only at the pinch, and the corresponding limiting water data is shown in Table 1. For water-using system 2 (Figure 2), besides pinch, one turning point (point E) of the limiting composite
Figure 1. Limiting composite curve of water-using system 1.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178–1187
1180
BAI et al. Table 1. Limiting water data of water-using system 1. Process number 1 2 3 4
Figure 2. Limiting composite curve of water-using system 2.
curve above the pinch approaches the limiting water supply line, and the limiting water data is shown in Table 2. For water-using system 3 (Figure 3), the approaching point (point G) appears below the pinch, and the limiting water data is shown in Table 3. The post-regeneration concentrations of these systems are assumed to be 14 ppm, 10 ppm and 18 ppm, respectively.
C In,Max ppm
C Out,Max ppm
Mass load g h21
0 20 80 60
80 80 150 80
4000 2250 2600 2750
the flowrate of freshwater is greater than that of regenerated water, partial regeneration is feasible. Contrarily, total regeneration must be implemented. From Figure 4, it can be seen that, the slope of line AG is larger than that of line HQ, that is, the flowrate of freshwater is smaller than that of regenerated water. Thus total regeneration must be chosen for waterusing system 2. In this way, whether partial or total regeneration should be utilized for a water system can be easily identified. For the three representative water-using systems, it can be concluded that partial regeneration can not meet the demand of these systems. Therefore, total regeneration is directly considered in the following.
OPTIMIZATION FOR THREE REPRESENTATIVE WATER-USING SYSTEMS Optimization for Water-Using System 1
TOTAL REGENERATION VERSUS PARTIAL REGENERATION Regenerated water flowrate is the major impact factor to regeneration cost. Therefore, when implementing regeneration reuse, partial regeneration reuse should be considered first for a lower regeneration cost. Total regeneration reuse is chosen under the condition that partial regeneration can not satisfy the requirement of the system. Here a handy method is presented to decide whether partial or total regeneration should be utilized. Take water-using system 2 for example. Firstly, suppose partial regeneration is utilized. As stated previously, partial regeneration systems are totally identical to regeneration recycling systems in terms of graphical representation. Thus the optimal water supply line for partial regeneration reuse systems can be constructed according to the methodology proposed by Feng et al. (2007). Figure 4 shows the optimal water supply line for water system 2 with regeneration recycling. Secondly, compare the flowrate of freshwater and regenerated water. If
At the given post-regeneration concentration, Figure 5 depicts the water supply line for water-using system 1 when total regeneration is utilized. The freshwater consumption, regenerated water flowrate and regeneration concentration at this time, are all arbitrarily taken, which will be optimized subsequently. Three basic parameters for specifying the regeneration reuse process in a water system, including post-regeneration concentration, regeneration concentration and regenerated water flowrate, are denoted as COutR, CInR and the reciprocal of line HJ’s slope in Figure 5, respectively. Similar to regeneration recycling systems, line AF and line HJ depict the use of freshwater and regenerated water, respectively. However, different from regeneration recycling, the flowrate of freshwater is equal to that of regenerated water when total regeneration is considered, thus these two lines have the same slope. In addition, the fact that the water intake to a system is equal to the effluent from the system (water loss is ignored) indicates that the slope of line JP is also equal to that of line AF. Then points H, J, P are actually on the same line. The composite water supply line of the system with total regeneration can be represented by line ASJP. Since line ASJP is always beneath the limiting composite curve, the water supply scheme is feasible, but not optimal. In order to optimize the water-using mode, the flowrate of freshwater and regenerated water are expected to be
Table 2. Limiting water data of water-using system 2. Process number 1 2 3 4
C In,Max ppm
C Out,Max ppm
Mass load g h21
0 50 60 100
60 60 100 140
1380 1550 1610 630
Figure 3. Limiting composite curve of water-using system 3. Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178– 1187
OPTIMIZATION OF SINGLE-CONTAMINANT REGENERATION REUSE WATER SYSTEMS
1181
Table 3. Limiting water data of water-using system 3. Process number
C In,Max ppm
C Out,Max ppm
Mass load g h21
0 20 35 60 85
35 35 85 85 130
805 1265 2760 920 1150
1 2 3 4 5
minimized, which means increasing the slope of line AF and line HP simultaneously. Then point F and point J move leftward along the horizontal line through CInR. When point F and point J reach point G and point Q in Figure 6, respectively, the composite water supply line ASQP touches the limiting composite curve at the pinch point D. At this time point F and point J cannot move further, otherwise some water-using processes in the system cannot be supplied with suitable quality water. Therefore, the flowrate of freshwater and regenerated water both reach the minimum. Figure 6 shows the water supply line of total regeneration at the minimum freshwater consumption. The minimum freshwater consumption can be identified as the reciprocal of line AG’s slope in Figure 6, which also corresponds to the minimum regenerated water flowrate owing to the total regeneration scheme. According to the geometrical relationships in Figure 6, the minimum freshwater consumption or minimum regenerated water flowrate can be calculated.
Figure 5. Total regeneration composite curve of water-using system 1.
where CPinch is the pinch concentration; C0 is the post-regeneration concentration; F W is the minimum freshwater consumption; F R is the minimum regenerated water flowrate; MPinch is the contaminant mass load at the pinch. At the minimum flowrate of freshwater and regenerated water, the contaminant regeneration load of the system can be further minimized to guarantee a lower regeneration cost. This can be realized by decreasing the regeneration concentration, which is arbitrarily chosen at first. Certainly,
there is a limit for the decrease of regeneration concentration, which corresponds to the minimum regeneration concentration. When the regeneration concentration is lower than the minimum one, some water-using processes in the system cannot be supplied with suitable quality water unless more freshwater is sent to the system. We defined this limit for regeneration concentration as the optimal regeneration concentration, and the water supply line at this time as the optimal water supply line. Optimal here means that the freshwater consumption, regenerated water flowrate and contaminant regeneration load all reach their minimum. For water-using system 1, the limit for regeneration concentration is just the pinch concentration, namely point D in Figure 6. That is to say, for water-using system 1, the optimal regeneration concentration is equal to the pinch concen tration of the system, namely CInR ¼ CPinch. Figure 7 describes the optimal water supply line for water-using system 1. The optimal water supply mode is determined above at the premise of a given post-regeneration concentration. If the post-regeneration concentration changed, the corresponding optimal water supply line would vary. For waterusing system 1, Figure 8 shows the total regeneration at different post-regeneration concentrations. It can be seen that, as the post-regeneration concentration decreases, the minimum freshwater consumption (minimum
Figure 4. Optimal water supply line for water-using system 2 with regeneration recycling.
Figure 6. Water-using system 1 with total regeneration reuse at the minimum freshwater consumption.
{ Mpinch ¼ F W C0 þ (F R þ F W ) (Cpinch C0 ) FW ¼ FR [ FW ¼ FR ¼
Mpinch 2 Cpinch C0
(1)
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178–1187
1182
BAI et al.
Figure 7. Water-using system 1 with total regeneration reuse at the optimal regeneration concentration.
regenerated water flowrate) decreases, the minimum regeneration load increases, while the optimal regeneration concentration remains to be the pinch concentration of the system.
Optimization for Water-Using System 2 Similarly, water-using system 2 with total regeneration can also be optimized. With the fixed post-regeneration concentration and an assumed regeneration concentration, Figure 9 shows the total regeneration at the minimum freshwater consumption (also the minimum regenerated water flowrate). For water-using system 2, one turning point (E) of the limiting composite curve above the pinch (D) approaches the limiting water supply line with water reuse. Therefore, when minimizing the flowrate of freshwater and regenerated water, the composite water supply line ASQP first touches the limiting composite curve at point E that is above the pinch, instead of the pinch, as is shown in Figure 9. Actually the assumed regeneration concentration in Figure 9 is lower than the optimal one. By increasing the regeneration concentration CInR, line ASQP is much closer to the limiting composite curve of the system, and the freshwater consumption (regenerated water flowrate)
Figure 8. Water-using system 1 with total regeneration reuse at different post-regeneration concentrations.
Figure 9. Water-using system 2 with total regeneration reuse at the minimum freshwater consumption.
can be further reduced. When line ASQP touches point D, increasing CInR further will have no effect on saving freshwater and only make line QP move rightwards. The regeneration concentration at this time (point Q in Figure 10) corresponds to the optimal regeneration concentration. Figure 10 shows water-using system 2 with total regeneration reuse at the optimal regeneration concentration. Obviously, different from water system 1, the optimal regeneration concentration for water system 2 is higher than the pinch concentration of the system. Formulas for calculating the primary targets for water-using system 2 can be deduced from the geometrical relationships in Figure 10.
{ Mpinch ¼ F W C0 þ (F W þ F R ) (Cpinch C0 ) [ FW ¼ FR ¼
Mpinch 2Cpinch C0
(2)
{ ME ¼ F W C0 þ (F W þ F R ) (CInR C0 ) þ F W (CE CInR )
Figure 10. Water-using system 2 with total regeneration reuse at the optimal regeneration concentration.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178– 1187
OPTIMIZATION OF SINGLE-CONTAMINANT REGENERATION REUSE WATER SYSTEMS
1183
Figure 13. Water-using system 3 with total regeneration reuse at the minimum freshwater consumption. Figure 11. Water-using system 2 with total regeneration reuse at a lower post-regeneration concentration.
Optimization for Water-Using System 3 that is ME ¼ F R C0 þ 2F R (CInR C0 ) þ F R (CE CInR ) [ CInR ¼
ME F R (CE C0 ) FR
(3)
where CInR is the optimal regeneration concentration; CE is the concentration at the limiting point above pinch (point E in Figure 10); ME is the contaminant mass load at the limiting point above pinch (point E in Figure 10). Post-regeneration concentration also has an effect on the optimization of water system 2 with total regeneration. Figures 11 and 12 show water-using system 2 with total regeneration reuse at a lower and a higher post-regeneration concentration, respectively. For water-using system 2, when total regeneration is implemented, with the increase of postregeneration concentration, the minimum freshwater consumption (minimum regenerated water flowrate) increases, while the optimal regeneration concentration and minimum contaminant regeneration load both decrease.
Figure 12. Water-using system 2 with total regeneration reuse at a higher post-regeneration concentration.
Water-using system 3 is similar to the example system analyzed by Feng et al. (2007), where it acts as a regeneration recycling system. The limiting composite curve of the system possesses some special features. One turning point (G) of the limiting composite curve below the pinch (D) closes to the limiting water supply line with water reuse, as is shown in Figure 13. This turning point G lies above line AD (the limiting water supply line with water reuse) and below line BD. With given regeneration and post-regeneration concentrations, Figure 13 shows the total regeneration at the minimum freshwater consumption for water-using system 3. From Figure 13, it can be seen that, when the flowrate of freshwater and regenerated water are minimized, the water supply line ASQP first touches the limiting composite curve at point G that is below the pinch, instead of the pinch point D. In Figure 13, the flowrate of freshwater and regenerated water both reaches the minimum, while the regeneration concentration is still higher than the optimal one. Thus we should further reduce the regeneration concentration to decrease the contaminant regeneration load of the system. Figure 14 gives the water supply line of total regeneration at the optimal regeneration concentration for water-using system 3. Obviously, the optimal regeneration concentration for waterusing system 3 is the concentration at point Q, which is lower than the pinch concentration of the system.
Figure 14. Water-using system 3 with total regeneration reuse at the optimal regeneration concentration.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178–1187
1184
BAI et al.
In Figure 14 { MG ¼ F W C0 þ (F W þ F R ) (CG C0 ) MG [ FW ¼ FR ¼ 2CG C0 { MPinch ¼ F W C0 þ (F W þ F R ) (CInR C0 )
(4)
þ F W (CPinch CInR ) [ CInR ¼
MPinch F R (CPinch C0 ) FR
(5)
where CG is the concentration at the limiting point below pinch ( point G in Figure 14). MG is the contaminant mass load at the limiting point below pinch (point G in Figure 14). The optimization of a regeneration reuse system is closely related to the post-regeneration concentration, which is especially prominent for water-using system 3. In the analysis above, the optimal regeneration concentration for waterusing system 3 is lower than the pinch concentration of the system. However, if the post-regeneration concentration is low enough, the optimal regeneration concentration can also be equal to the pinch concentration. As a matter of fact, unlike water-using system 1 and 2, there is an interim post-regeneration concentration for water-using system 3. The interim post-regeneration concentration is determined by the crossing point V of line DG and line AV. The slope of line AV is double of that of line DG, as is shown in Figure 15. The concentration at point V is just the interim post-regeneration concentration, which can be denoted as COutRc. Note that the interim post-regeneration concentration for total regeneration is different from that for regeneration recycling, which can be concluded from the methods by which they are determined. Total regenerations at different post-regeneration concentrations for water-using system 3 are shown in Figures 15– 17, respectively. When the post-regeneration concentration is equal to COutRc, the optimal water supply line touches the limiting composite curve at both point G and point D (Figure 15). When the post-regeneration concentration is higher than COutRc, the touching points are also point G and point D (Figure 16). When the post-regeneration concentration is lower than COutRc, the touching point only corresponds to the pinch point, point D (Figure 17). On the basis of the geometrical relationships in Figure 15, formulas for calculating the interim post-regeneration
where CoutRc is the interim post-regeneration concentration. Then the interim post-regeneration concentration for waterusing system 3 can be obtained by equation (6), that is 13.75 ppm. From Figures 15 –17, the effect of post-regeneration concentration on regeneration concentration for water-using system 3 can be seen. When the post-regeneration concentration is higher than COutRc, the optimal regeneration concentration is lower than the pinch concentration, and increases with the decrease of the post-regeneration concentration. When the post-regeneration concentration reduces to COutRc, the optimal regeneration concentration increases to the pinch concentration. If the post-regeneration concentration keeps on decreasing, the optimal regeneration concentration no longer changes, and is always equal to the pinch concentration. Moreover, as the post-regeneration
Figure 15. Water-using system 3 with total regeneration reuse at the interim post-regeneration concentration.
Figure 17. Water-using system 3 with total regeneration reuse at a lower post-regeneration concentration.
Figure 16. Water-using system 3 with total regeneration reuse at a higher post-regeneration concentration.
concentration can be concluded. According to equation(4), F W ¼ MG =(2CG CoutRc ) In Figure 15, the minimum freshwater consumption can be identified by the reciprocal of line AV’s slope, which is two times of line GD’s slope. That is, Fw ¼
[ CoutRc ¼ 2Cpinch
Mpinch Ma 2Cpinch CG
2MG (Cpinch CG ) Mpinch MG
(6)
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178– 1187
OPTIMIZATION OF SINGLE-CONTAMINANT REGENERATION REUSE WATER SYSTEMS concentration decreases, the minimum flowrate of freshwater and regenerated water both decrease, while the minimum contaminant regeneration load increases.
GENERAL TARGETING METHOD FOR REGENERATION REUSE SYSTEMS Obviously, the formulas above for calculating the minimum freshwater consumption (minimum regenerated water flowrate) and the optimal regeneration concentration are totally different for different water-using systems, which is not favourable for general use. Nevertheless, according to the relationships between the limiting composite curve and the water supply line for each specific system, the formulas for different systems can be unified. Now several concepts are introduced before presenting the general formulas for calculating the targets. On the concentration-mass load diagram, the composite water supply line for a total regeneration reuse system is composed of two parts: the part below the pinch concentration and the part above the pinch concentration. These two parts restrict the freshwater consumption (also the regenerated water flowrate) and regeneration load of the system, respectively. Therefore, two intersections arise between the limiting composite curve and the optimal water supply line, which we called limiting freshwater and regenerated water point, and limiting regeneration load point, respectively. The limiting freshwater and regenerated water point is defined as the touching point of the limiting composite water supply line and the limiting composite curve below the pinch. The limiting composite water supply line below the pinch is always beneath the limiting composite curve and possesses the maximum slope. The limiting regeneration load point is defined as the touching point of the limiting composite water supply line and the limiting composite curve above the pinch. These limiting points for total regeneration reuse systems are actually a transformation of those limiting points for regeneration recycling. Since for total regeneration, the flowrate of freshwater is equal to that of regenerated water, the limiting freshwater point and the limiting regenerated water point are unified as the limiting freshwater and regenerated water point. The two limiting points indicate the bottlenecks of a water system with total regeneration. They are virtually the counterparts of pinch for water reuse without regeneration. The optimal regeneration concentration of a water system with total regeneration actually depends on the limiting points of the system, without direct relationships with the pinch concentration of the system. As presented for the three representative water systems, it can be higher than, equal to or lower than the pinch concentration. Since each water-using system has distinctive limiting composite curve, different water systems have different limiting points for total regeneration. In terms of limiting composite curve, water-using systems can be mainly classified into three categories. For the first category, the limiting composite curve touches the limiting water supply line with direct reuse only at the pinch, such as water-using system 1 (Figure 7). The limiting freshwater and regenerated water point and the limiting regeneration load point of this category both correspond to the normal pinch. For the second category, take water-using system 2 (Figure 10) for example. Besides pinch, one turning point
1185
(point E in Figure 10) of the limiting composite curve above the pinch approaches the limiting water supply line with direct reuse. The limiting freshwater and regenerated water point of this category is the pinch of the system, while the limiting regeneration load point in this case corresponds to a certain point above the pinch, such as point E in Figure 10. For the third category, which water-using system 3 belongs to, an approaching point (point G in Figure 14) appears below the pinch. The limiting freshwater and regenerated water point corresponds to a certain point below the pinch, point G in Figure 14, and the limiting regeneration load point refers to the pinch of the system. These three categories of water-using systems can represent all the single-contaminant water systems. Resorting to the concept of limiting points, two general formulas for calculating the targets for total regeneration systems can be concluded. Minimum freshwater consumption (minimum regenerated water flowrate): FR ¼ FW ¼
MR 2CR C0
(7)
Optimal regeneration concentration: CInR ¼
MC F R (CC C0 ) FR
(8)
In equation (7), MR and CR are the contaminant mass load and the concentration at the limiting freshwater and regenerated water point, respectively. In equation (8), MC and CC are the contaminant mass load and the concentration at the limiting regeneration load point. Both total regeneration reuse and regeneration recycling involves regeneration units. Without considering the conceptual distinction between them, their difference only lies in the quantitative relationships between freshwater and regenerated water. Therefore, equations (7) and (8) can also be directly obtained by applying the restriction that the freshwater consumption is equal to the regenerated water flowrate to the general formulas for regeneration recycling systems. Only some simple mathematical transformation is needed. By using these formulas, the targets for any single-contaminant water systems with total regeneration reuse can be obtained. Equations (1) –(5) are actually a variety of specific applications of equations (7) and (8). For a total regeneration reuse water system with a certain post-regeneration concentration, after identifying the limiting freshwater and regenerated water point, and the limiting regeneration load point, the targets for the system can be calculated by using equations (7) and (8) in sequence. Graphical methods can be employed to determine the limiting points for total regeneration. However, it appears to be more complicated. Because for total regeneration reuse systems, the flowrate of freshwater and regenerated water are correlated, one should find those limiting points by trail and error. Here an improved mass problem table, which is easy to handle, is recommended to target for total regeneration reuse systems. It is similar to the mass problem table for regeneration recycling proposed by Feng et al. (2007). The regenerated water flowrate column and the regeneration concentration column are added to the improved mass problem table. The targeting procedure is as follows. Firstly, simple
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178–1187
1186
BAI et al. Table 4. Mass problem table for water-using system 3 with total regeneration reuse.
Concentration ppm
P1
P2
P3
P4
P5
Mass load kg h21
Accumulative mass load kg h21 0
0
Fresh water flowrate t h21 0
Regenerated water flowrate t h21 0
Regeneration concentration ppm —
0.46 20
0.46
23
20.91
—
2.07
59.14
39.81
—
3.45
57.5
33.82
—
5.75
67.65
37.83
77.44
6.9
53.08
—
61.32
1.61 35 1.38 60 2.3 85 1.15 130
calculations are carried out for the mass load, cumulative mass load and freshwater flowrate columns by using the traditional method. Then the pinch of the system can be determined. Secondly, in the regenerated water flowrate column, each concentration lower than the pinch concentration (including pinch concentration) is assumed to be the limiting freshwater and regenerated water point, and the corresponding regenerated water flowrate is calculated by equation (7). The concentration corresponding to the maximum regenerated water flowrate is taken as the actual limiting freshwater and regenerated water point. Thus the minimum freshwater consumption or minimum regenerated water flowrate can be obtained. Thirdly, in the regeneration concentration column, for each concentration higher than the pinch concentration (including pinch concentration) the corresponding regeneration concentration is calculated by equation (8), and the concentration corresponding to the maximum regeneration concentration is taken as the limiting regeneration load point. Then the optimal regeneration concentration can be identified. Take water-using system 3 for example. The post-regeneration concentration is taken to be 18 ppm. Table 4 shows the improved mass problem table for water system 3 with total regeneration reuse. The pinch of the system arises at 85 ppm. From the regenerated water flowrate column, one can see that the limiting freshwater and regenerated water point corresponds to the concentration of 35 ppm, and the minimum regenerated water flowrate (minimum freshwater consumption) of the system is 39.81 t h21. The optimal regeneration concentration is equal to 77.44 ppm, at the limiting regeneration load point of 85 ppm, as is shown in the regeneration concentration column. According to the previous graphical analysis, when the post-regeneration concentration is higher than the interim post-regeneration concentration (18 ppm . 13.75 ppm), the optimal regeneration concentration is lower than the pinch concentration (77.44 ppm , 85 ppm). The conclusion is also demonstrated by the calculation of mass problem table. In the same way, the targets for the other two water systems with total regeneration can be calculated by the improved mass problem table. The details are not stated here and only results are given. For water-using system 1, since the post-regeneration concentration is 14 ppm
(Figure 7), the minimum freshwater consumption (minimum regenerated water flowrate) is 61.64 t h21 and the optimal regeneration concentration is 80 ppm. For water-using system 2, since the post-regeneration concentration is 10 ppm (Figure 10), the minimum flowrate of freshwater and regenerated water both equal to 26.64 t h21 and the optimal regeneration concentration corresponds to 80.44 ppm.
CONCLUSIONS Three representative single-contaminant water systems with regeneration reuse are analysed in this paper. A handy method is proposed to determine whether partial or total regeneration should be utilized. The optimization of partial regeneration reuse systems is identical to that of regeneration recycling systems owing to their similarities in terms of graphical representation. Thus this paper mainly focuses on total regeneration reuse systems. By minimizing the freshwater consumption, which corresponds to the regenerated water flowrate, and regeneration concentration in sequence, the optimal water supply line for total regeneration reuse systems can be constructed and the targets can be obtained. Then general formulas for calculating the targets are developed on the basis of the concept of limiting points for total regeneration reuse systems. These limiting points indicate the bottlenecks of a water system with total regeneration reuse. Generally there are three categories of water-using systems. The introduction of the limiting freshwater and regeneration water point and the limiting regeneration load point assists the identification of different water-using systems. The optimal regeneration concentration, which is unrelated to the pinch concentration, actually depends on these limiting points besides the post-regeneration concentration. Furthermore, the improved mass problem table, which is recommended to target for regeneration reuse systems, excels in accuracy and efficiency.
NOMENCLATURE In,Max
C C Out,Max CInR C0, COutR COutRc
maximum inlet concentration, ppm maximum outlet concentration, ppm regeneration concentration, ppm post-regeneration concentration, ppm interim post-regeneration concentration, ppm
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178– 1187
OPTIMIZATION OF SINGLE-CONTAMINANT REGENERATION REUSE WATER SYSTEMS CPinch FR FW CInR MPinch CE ME CG MG MR CR MC CC
pinch concentration, ppm minimum regenerated water flowrate, t h21 minimum freshwater consumption, t h21 optimal regeneration concentration, ppm contaminant mass load at the pinch, g h21 concentration at the limiting point above pinch, ppm contaminant mass load at the limiting point above pinch, g h21 concentration at the limiting point below pinch, ppm contaminant mass load at the limiting point below pinch, g h21 contaminant mass load at the limiting freshwater and regenerated water point, g h21 concentration at the limiting freshwater and regenerated water point, ppm contaminant mass load at the limiting regeneration load point, g h21 concentration at the limiting regeneration load point, ppm
REFERENCES Bagajewicz, M., 2001, On the use of linear models for the design of water utilization systems in process plants with a single contaminant, Trans IChemE, 79(Part A): 600– 610. Castro, P., Matos, H., Fernandes, M.C. and Nunes, C.P., 1999, Improvements for mass-exchange networks design, Chem Eng Sci, 54, 1649– 1665.
1187
Feng, X. and Chu, K., 2004, Cost optimization of industrial wastewater reuse systems, Process Safety and Environmental Protection, 82(B3): 249–255. Feng, X., Bai, J. and Zheng, X.S., 2007, On the use of graphical method to determine the targets of single-contaminant regeneration recycling water systems, Chem Eng Sci, 62: 2127– 2138. Gunaratnam, M., Alva-Argaez, A., Kokossis, A., Kim, J.-K. and Smith, R., 2005, Automated design of total water systems, Ind Eng Chem Res, 44: 588–599. Huang, C.H., Chang, C.T., Ling, H.C. and Chang, C.C., 1999, A mathematical programming model for water usage and treatment network design, Ind Eng Chem Res, 38: 2666–2679. 1999. Mann, J.G. and Liu, Y.A., 1999, Industrial Water Reuse and Wastewater Minimization (McGraw-Hill, New York, USA). Takama, N., Kuriyama, T., Shiroko, K. and Umeda, T., 1980, Optimal water allocation in a petroleum refinery, Comp Chem Eng, 4: 251– 258. Wang, Y.P. and Smith, R., 1994, Wastewater minimization, Chem Eng Sci, 49(7): 981–1006. Xu, D.M., Hu, Y.D., Hua, B. and Wang, X.L., 2003, Minimization of the flowrate of fresh water and corresponding regenerated water in water-using system with regeneration reuse, Chinese J Chem Eng, 11(3): 257 –263. Xu, D.M., Hu, Y.D., Hua, B. and Wang, X.L., 2004, Optimum design of water-using network with regeneration reuse, Chinese J Chem Eng, 18(2): 202–207.
ACKNOWLEDGEMENTS Financial support provided by the National Natural Science Foundation of China under Grant No. 20436040 is gratefully acknowledged.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178–1187
Abstract: In this paper, graphical method is employed to optimize single-contaminant regeneration reuse water systems. On the concentration-mass load diagram, three categories of waterusing systems with regeneration reuse are analyzed in terms of the geometric features of limiting composite curve. Total regeneration and partial regeneration are identified first. Then based on sequential optimization and at a specified post-regeneration concentration, the optimal water supply lines for regeneration reuse systems can be constructed. The optimal water supply line corresponds to minimum freshwater consumption, minimum regenerated water flowrate and minimum contaminant regeneration load. Formulas for calculating these targets are summarized and interactions of these parameters are discussed. The concepts of limiting points for regeneration reuse, which are the counterpart of pinch for direct reuse, are proposed to indicate the bottlenecks of a water system with regeneration reuse. Different locations of the limiting points for different systems underlie that the optimal regeneration concentration can be greater than, equal to or smaller than the pinch concentration of the system. Keywords: integration; regeneration reuse; graphical method; mass problem table; water system.
INTRODUCTION
Correspondence to: Professor X. Feng, Department of Chemical Engineering, Xi’an Jiaotong University, Xi’an 710049, P.R. China. E-mail: [email protected]
DOI: 10.1205/cherd06252 0263–8762/07/ $30.00 þ 0.00 Chemical Engineering Research and Design Trans IChemE, Part A, August 2007 # 2007 Institution of Chemical Engineers
Graphical method was initiated by Wang and Smith (1994). They introduced several important concepts, such as limiting water profile, limiting composite curve and pinch. Then the water demand and supply of a system can be described on the concentration-mass load diagram, whether water reuse, regeneration reuse or regeneration recycling is considered. For regeneration reuse, at a given post-regeneration concentration, the optimal regeneration concentration is taken as the pinch concentration of the system in the paper. Later, Mann and Liu (1999) found that when considering water regeneration reuse, some systems had another pinch point, regeneration pinch, which is higher than the conventional pinch for freshwater targeting. Castro et al. (1999) introduced a multiple-pinch-points concept and proposed a novel re-use network targeting/design methodology for single contaminant systems. This method can be utilized to design and optimize regeneration reuse water systems. The above research on optimizing regeneration reuse systems all resorts to graphical method, thus only applies to single-contaminant systems. When mathematical programming is utilized, regeneration reuse, as one of the possibilities to reduce the freshwater consumption
Water system integration is one of the most efficient technologies for minimizing freshwater consumption and wastewater discharge simultaneously. Excluding the possibility of making process changes to reduce the inherent demand for water, there are three approaches for wastewater minimization: water reuse, regeneration reuse and regeneration recycling (Wang and Smith, 1994). A water system with regeneration options (regeneration reuse or/and regeneration recycling) can reduce more freshwater intake and wastewater discharge than that with mere water reuse, since the contaminant mass load of the system is partially removed by regeneration units. It is important to distinguish between regeneration reuse and regeneration recycling, for sometimes people do not favour recycling owing to the build-up of contaminants. For example, in some cases, traces of byproducts of corrosion in the recycle may contaminate catalysts. Therefore, it is worthy of studying the optimization of regeneration reuse water systems. In recent years, much research has been conducted on this topic mainly based on two traditional methods: graphical method and mathematical programming. 1178
Vol 85 (A8) 1178 –1187
OPTIMIZATION OF SINGLE-CONTAMINANT REGENERATION REUSE WATER SYSTEMS or total cost of a water system, is incorporated in the superstructure (Takama et al., 1980; Huang et al., 1999; Bagajewicz, 2001; Feng and Chu, 2004; Xu et al., 2004; Gunaratnam et al., 2005). The targeting and design of regeneration reuse systems are performed by solving the corresponding mathematical models. Based on a sequential three-step programming method, Xu et al. (2003) investigated the relationship between the freshwater flowrate required and regeneration concentration of a regeneration reuse system. Their study shows that the regeneration of water at pinch concentration does not always minimize the freshwater consumption and there are three possibilities for the minimum regeneration concentration: below, above or at the pinch. Owing to the limitations of the method they used, these conclusions are not analysed in details, which we will give a conceptual explanation on the concentrationmass load diagram in this paper. In our previous paper (Feng et al., 2007), based on sequential optimization, we proposed a handy method to construct the optimal water supply line for a regeneration recycling system, and introduced the improved mass problem table to target for freshwater, regenerated water and regeneration concentration. Here we will adopt the procedure of sequential optimization and extend the methodology to regeneration reuse systems. Before continuing this paper, it is recommended that the reader study the sequential optimization approach as introduced by Feng et al. (2007).
PROBLEM TO BE SOLVED Considering a water network with regeneration reuse, in which wastewater from several processes can be regenerated by partial or total treatment to remove the contaminants and then reused in other processes. Different from regeneration recycling, the water after regeneration can not re-enter processes in which it has previously been used. There are two kinds of regeneration reuse: total regeneration and partial regeneration. For total regeneration, all the water, the concentration of which reaches the regeneration concentration, is sent to regeneration system for treatment. Thus the flowrate of regenerated water is equal to that of freshwater, if water loss in processes is ignored. While for partial regeneration, only partial amount of contaminated water is regenerated, and the residual wastewater is directly re-used or discharged. That means the regenerated water flowrate is smaller than the freshwater consumption. If regenerating part of water can meet the demand of the system, partial regeneration is undoubtedly utilized instead of total regeneration to assure a lower regeneration cost. The approach to identify whether total or partial regeneration should be used will be developed later. Both total and partial regeneration can be depicted on the concentration-mass load diagram. Partial regeneration re-use systems are identical to regeneration recycling systems in terms of graphical representation, since the limiting freshwater supply line in both of the cases is determined by the limiting composite curve below the post-regeneration concentration. In addition to different network structure, on the concentration-mass load diagram the difference between them lies in the quantitative relationship of freshwater and regenerated water flowrate. For regeneration recycling, the flowrate of regenerated water can be greater than, equal to or smaller than that of freshwater. While in case of partial
1179
regeneration reuse, the regenerated water flowrate should be smaller than the freshwater consumption. In other words, only from the point of graphical representation, partial regeneration reuse systems can be taken as a special case of regeneration recycling systems when the flowrate of regenerated water is smaller than that of freshwater. Then the targeting procedure for partial regeneration reuse systems can be performed by the method for regeneration recycling systems. Since regeneration units are involved as in regeneration recycling systems, the optimization of total regeneration reuse systems can also be conducted on the basis of the method for regeneration recycling systems. Similar to regeneration recycling systems, a water-using network with regeneration reuse needs to determine the targets for freshwater comsumption, regenerated water flowrate, regeneration and post-regeneration concentration. In this paper, sequential optimization presented by Feng et al. (2007) is adopted to analyse the optimization of regeneration reuse systems. Since a partial regeneration system is similar to a regeneration recycling system on the concentrationmass load diagram, our discussion only confines to total regeneration systems. At a specified post-regeneration concentration, freshwater consumption (regenerated water flowrate) and regeneration concentration are minimized step by step to depict the optimal water supply line for total regeneration reuse systems. Formulas for calculating the targets for total regeneration reuse systems can be summarized by the geometrical relationships on the concentration-mass load diagram. Three representative water-using systems are employed to illustrate the methodology.
THREE REPRESENTATIVE WATER-USING SYSTEMS Before discussing pinch analysis for regeneration reuse systems, three representative water-using systems will be addressed. For each water system, the water supply line with minimum freshwater flowrate and pinch point under the condition of only considering water reuse are given, as shown in Figures 1–3. Obviously the three representative water-using systems have different characteristics. For water-using system 1 (Figure 1), the limiting composite curve touches the limiting water supply line only at the pinch, and the corresponding limiting water data is shown in Table 1. For water-using system 2 (Figure 2), besides pinch, one turning point (point E) of the limiting composite
Figure 1. Limiting composite curve of water-using system 1.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178–1187
1180
BAI et al. Table 1. Limiting water data of water-using system 1. Process number 1 2 3 4
Figure 2. Limiting composite curve of water-using system 2.
curve above the pinch approaches the limiting water supply line, and the limiting water data is shown in Table 2. For water-using system 3 (Figure 3), the approaching point (point G) appears below the pinch, and the limiting water data is shown in Table 3. The post-regeneration concentrations of these systems are assumed to be 14 ppm, 10 ppm and 18 ppm, respectively.
C In,Max ppm
C Out,Max ppm
Mass load g h21
0 20 80 60
80 80 150 80
4000 2250 2600 2750
the flowrate of freshwater is greater than that of regenerated water, partial regeneration is feasible. Contrarily, total regeneration must be implemented. From Figure 4, it can be seen that, the slope of line AG is larger than that of line HQ, that is, the flowrate of freshwater is smaller than that of regenerated water. Thus total regeneration must be chosen for waterusing system 2. In this way, whether partial or total regeneration should be utilized for a water system can be easily identified. For the three representative water-using systems, it can be concluded that partial regeneration can not meet the demand of these systems. Therefore, total regeneration is directly considered in the following.
OPTIMIZATION FOR THREE REPRESENTATIVE WATER-USING SYSTEMS Optimization for Water-Using System 1
TOTAL REGENERATION VERSUS PARTIAL REGENERATION Regenerated water flowrate is the major impact factor to regeneration cost. Therefore, when implementing regeneration reuse, partial regeneration reuse should be considered first for a lower regeneration cost. Total regeneration reuse is chosen under the condition that partial regeneration can not satisfy the requirement of the system. Here a handy method is presented to decide whether partial or total regeneration should be utilized. Take water-using system 2 for example. Firstly, suppose partial regeneration is utilized. As stated previously, partial regeneration systems are totally identical to regeneration recycling systems in terms of graphical representation. Thus the optimal water supply line for partial regeneration reuse systems can be constructed according to the methodology proposed by Feng et al. (2007). Figure 4 shows the optimal water supply line for water system 2 with regeneration recycling. Secondly, compare the flowrate of freshwater and regenerated water. If
At the given post-regeneration concentration, Figure 5 depicts the water supply line for water-using system 1 when total regeneration is utilized. The freshwater consumption, regenerated water flowrate and regeneration concentration at this time, are all arbitrarily taken, which will be optimized subsequently. Three basic parameters for specifying the regeneration reuse process in a water system, including post-regeneration concentration, regeneration concentration and regenerated water flowrate, are denoted as COutR, CInR and the reciprocal of line HJ’s slope in Figure 5, respectively. Similar to regeneration recycling systems, line AF and line HJ depict the use of freshwater and regenerated water, respectively. However, different from regeneration recycling, the flowrate of freshwater is equal to that of regenerated water when total regeneration is considered, thus these two lines have the same slope. In addition, the fact that the water intake to a system is equal to the effluent from the system (water loss is ignored) indicates that the slope of line JP is also equal to that of line AF. Then points H, J, P are actually on the same line. The composite water supply line of the system with total regeneration can be represented by line ASJP. Since line ASJP is always beneath the limiting composite curve, the water supply scheme is feasible, but not optimal. In order to optimize the water-using mode, the flowrate of freshwater and regenerated water are expected to be
Table 2. Limiting water data of water-using system 2. Process number 1 2 3 4
C In,Max ppm
C Out,Max ppm
Mass load g h21
0 50 60 100
60 60 100 140
1380 1550 1610 630
Figure 3. Limiting composite curve of water-using system 3. Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178– 1187
OPTIMIZATION OF SINGLE-CONTAMINANT REGENERATION REUSE WATER SYSTEMS
1181
Table 3. Limiting water data of water-using system 3. Process number
C In,Max ppm
C Out,Max ppm
Mass load g h21
0 20 35 60 85
35 35 85 85 130
805 1265 2760 920 1150
1 2 3 4 5
minimized, which means increasing the slope of line AF and line HP simultaneously. Then point F and point J move leftward along the horizontal line through CInR. When point F and point J reach point G and point Q in Figure 6, respectively, the composite water supply line ASQP touches the limiting composite curve at the pinch point D. At this time point F and point J cannot move further, otherwise some water-using processes in the system cannot be supplied with suitable quality water. Therefore, the flowrate of freshwater and regenerated water both reach the minimum. Figure 6 shows the water supply line of total regeneration at the minimum freshwater consumption. The minimum freshwater consumption can be identified as the reciprocal of line AG’s slope in Figure 6, which also corresponds to the minimum regenerated water flowrate owing to the total regeneration scheme. According to the geometrical relationships in Figure 6, the minimum freshwater consumption or minimum regenerated water flowrate can be calculated.
Figure 5. Total regeneration composite curve of water-using system 1.
where CPinch is the pinch concentration; C0 is the post-regeneration concentration; F W is the minimum freshwater consumption; F R is the minimum regenerated water flowrate; MPinch is the contaminant mass load at the pinch. At the minimum flowrate of freshwater and regenerated water, the contaminant regeneration load of the system can be further minimized to guarantee a lower regeneration cost. This can be realized by decreasing the regeneration concentration, which is arbitrarily chosen at first. Certainly,
there is a limit for the decrease of regeneration concentration, which corresponds to the minimum regeneration concentration. When the regeneration concentration is lower than the minimum one, some water-using processes in the system cannot be supplied with suitable quality water unless more freshwater is sent to the system. We defined this limit for regeneration concentration as the optimal regeneration concentration, and the water supply line at this time as the optimal water supply line. Optimal here means that the freshwater consumption, regenerated water flowrate and contaminant regeneration load all reach their minimum. For water-using system 1, the limit for regeneration concentration is just the pinch concentration, namely point D in Figure 6. That is to say, for water-using system 1, the optimal regeneration concentration is equal to the pinch concen tration of the system, namely CInR ¼ CPinch. Figure 7 describes the optimal water supply line for water-using system 1. The optimal water supply mode is determined above at the premise of a given post-regeneration concentration. If the post-regeneration concentration changed, the corresponding optimal water supply line would vary. For waterusing system 1, Figure 8 shows the total regeneration at different post-regeneration concentrations. It can be seen that, as the post-regeneration concentration decreases, the minimum freshwater consumption (minimum
Figure 4. Optimal water supply line for water-using system 2 with regeneration recycling.
Figure 6. Water-using system 1 with total regeneration reuse at the minimum freshwater consumption.
{ Mpinch ¼ F W C0 þ (F R þ F W ) (Cpinch C0 ) FW ¼ FR [ FW ¼ FR ¼
Mpinch 2 Cpinch C0
(1)
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178–1187
1182
BAI et al.
Figure 7. Water-using system 1 with total regeneration reuse at the optimal regeneration concentration.
regenerated water flowrate) decreases, the minimum regeneration load increases, while the optimal regeneration concentration remains to be the pinch concentration of the system.
Optimization for Water-Using System 2 Similarly, water-using system 2 with total regeneration can also be optimized. With the fixed post-regeneration concentration and an assumed regeneration concentration, Figure 9 shows the total regeneration at the minimum freshwater consumption (also the minimum regenerated water flowrate). For water-using system 2, one turning point (E) of the limiting composite curve above the pinch (D) approaches the limiting water supply line with water reuse. Therefore, when minimizing the flowrate of freshwater and regenerated water, the composite water supply line ASQP first touches the limiting composite curve at point E that is above the pinch, instead of the pinch, as is shown in Figure 9. Actually the assumed regeneration concentration in Figure 9 is lower than the optimal one. By increasing the regeneration concentration CInR, line ASQP is much closer to the limiting composite curve of the system, and the freshwater consumption (regenerated water flowrate)
Figure 8. Water-using system 1 with total regeneration reuse at different post-regeneration concentrations.
Figure 9. Water-using system 2 with total regeneration reuse at the minimum freshwater consumption.
can be further reduced. When line ASQP touches point D, increasing CInR further will have no effect on saving freshwater and only make line QP move rightwards. The regeneration concentration at this time (point Q in Figure 10) corresponds to the optimal regeneration concentration. Figure 10 shows water-using system 2 with total regeneration reuse at the optimal regeneration concentration. Obviously, different from water system 1, the optimal regeneration concentration for water system 2 is higher than the pinch concentration of the system. Formulas for calculating the primary targets for water-using system 2 can be deduced from the geometrical relationships in Figure 10.
{ Mpinch ¼ F W C0 þ (F W þ F R ) (Cpinch C0 ) [ FW ¼ FR ¼
Mpinch 2Cpinch C0
(2)
{ ME ¼ F W C0 þ (F W þ F R ) (CInR C0 ) þ F W (CE CInR )
Figure 10. Water-using system 2 with total regeneration reuse at the optimal regeneration concentration.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178– 1187
OPTIMIZATION OF SINGLE-CONTAMINANT REGENERATION REUSE WATER SYSTEMS
1183
Figure 13. Water-using system 3 with total regeneration reuse at the minimum freshwater consumption. Figure 11. Water-using system 2 with total regeneration reuse at a lower post-regeneration concentration.
Optimization for Water-Using System 3 that is ME ¼ F R C0 þ 2F R (CInR C0 ) þ F R (CE CInR ) [ CInR ¼
ME F R (CE C0 ) FR
(3)
where CInR is the optimal regeneration concentration; CE is the concentration at the limiting point above pinch (point E in Figure 10); ME is the contaminant mass load at the limiting point above pinch (point E in Figure 10). Post-regeneration concentration also has an effect on the optimization of water system 2 with total regeneration. Figures 11 and 12 show water-using system 2 with total regeneration reuse at a lower and a higher post-regeneration concentration, respectively. For water-using system 2, when total regeneration is implemented, with the increase of postregeneration concentration, the minimum freshwater consumption (minimum regenerated water flowrate) increases, while the optimal regeneration concentration and minimum contaminant regeneration load both decrease.
Figure 12. Water-using system 2 with total regeneration reuse at a higher post-regeneration concentration.
Water-using system 3 is similar to the example system analyzed by Feng et al. (2007), where it acts as a regeneration recycling system. The limiting composite curve of the system possesses some special features. One turning point (G) of the limiting composite curve below the pinch (D) closes to the limiting water supply line with water reuse, as is shown in Figure 13. This turning point G lies above line AD (the limiting water supply line with water reuse) and below line BD. With given regeneration and post-regeneration concentrations, Figure 13 shows the total regeneration at the minimum freshwater consumption for water-using system 3. From Figure 13, it can be seen that, when the flowrate of freshwater and regenerated water are minimized, the water supply line ASQP first touches the limiting composite curve at point G that is below the pinch, instead of the pinch point D. In Figure 13, the flowrate of freshwater and regenerated water both reaches the minimum, while the regeneration concentration is still higher than the optimal one. Thus we should further reduce the regeneration concentration to decrease the contaminant regeneration load of the system. Figure 14 gives the water supply line of total regeneration at the optimal regeneration concentration for water-using system 3. Obviously, the optimal regeneration concentration for waterusing system 3 is the concentration at point Q, which is lower than the pinch concentration of the system.
Figure 14. Water-using system 3 with total regeneration reuse at the optimal regeneration concentration.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178–1187
1184
BAI et al.
In Figure 14 { MG ¼ F W C0 þ (F W þ F R ) (CG C0 ) MG [ FW ¼ FR ¼ 2CG C0 { MPinch ¼ F W C0 þ (F W þ F R ) (CInR C0 )
(4)
þ F W (CPinch CInR ) [ CInR ¼
MPinch F R (CPinch C0 ) FR
(5)
where CG is the concentration at the limiting point below pinch ( point G in Figure 14). MG is the contaminant mass load at the limiting point below pinch (point G in Figure 14). The optimization of a regeneration reuse system is closely related to the post-regeneration concentration, which is especially prominent for water-using system 3. In the analysis above, the optimal regeneration concentration for waterusing system 3 is lower than the pinch concentration of the system. However, if the post-regeneration concentration is low enough, the optimal regeneration concentration can also be equal to the pinch concentration. As a matter of fact, unlike water-using system 1 and 2, there is an interim post-regeneration concentration for water-using system 3. The interim post-regeneration concentration is determined by the crossing point V of line DG and line AV. The slope of line AV is double of that of line DG, as is shown in Figure 15. The concentration at point V is just the interim post-regeneration concentration, which can be denoted as COutRc. Note that the interim post-regeneration concentration for total regeneration is different from that for regeneration recycling, which can be concluded from the methods by which they are determined. Total regenerations at different post-regeneration concentrations for water-using system 3 are shown in Figures 15– 17, respectively. When the post-regeneration concentration is equal to COutRc, the optimal water supply line touches the limiting composite curve at both point G and point D (Figure 15). When the post-regeneration concentration is higher than COutRc, the touching points are also point G and point D (Figure 16). When the post-regeneration concentration is lower than COutRc, the touching point only corresponds to the pinch point, point D (Figure 17). On the basis of the geometrical relationships in Figure 15, formulas for calculating the interim post-regeneration
where CoutRc is the interim post-regeneration concentration. Then the interim post-regeneration concentration for waterusing system 3 can be obtained by equation (6), that is 13.75 ppm. From Figures 15 –17, the effect of post-regeneration concentration on regeneration concentration for water-using system 3 can be seen. When the post-regeneration concentration is higher than COutRc, the optimal regeneration concentration is lower than the pinch concentration, and increases with the decrease of the post-regeneration concentration. When the post-regeneration concentration reduces to COutRc, the optimal regeneration concentration increases to the pinch concentration. If the post-regeneration concentration keeps on decreasing, the optimal regeneration concentration no longer changes, and is always equal to the pinch concentration. Moreover, as the post-regeneration
Figure 15. Water-using system 3 with total regeneration reuse at the interim post-regeneration concentration.
Figure 17. Water-using system 3 with total regeneration reuse at a lower post-regeneration concentration.
Figure 16. Water-using system 3 with total regeneration reuse at a higher post-regeneration concentration.
concentration can be concluded. According to equation(4), F W ¼ MG =(2CG CoutRc ) In Figure 15, the minimum freshwater consumption can be identified by the reciprocal of line AV’s slope, which is two times of line GD’s slope. That is, Fw ¼
[ CoutRc ¼ 2Cpinch
Mpinch Ma 2Cpinch CG
2MG (Cpinch CG ) Mpinch MG
(6)
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178– 1187
OPTIMIZATION OF SINGLE-CONTAMINANT REGENERATION REUSE WATER SYSTEMS concentration decreases, the minimum flowrate of freshwater and regenerated water both decrease, while the minimum contaminant regeneration load increases.
GENERAL TARGETING METHOD FOR REGENERATION REUSE SYSTEMS Obviously, the formulas above for calculating the minimum freshwater consumption (minimum regenerated water flowrate) and the optimal regeneration concentration are totally different for different water-using systems, which is not favourable for general use. Nevertheless, according to the relationships between the limiting composite curve and the water supply line for each specific system, the formulas for different systems can be unified. Now several concepts are introduced before presenting the general formulas for calculating the targets. On the concentration-mass load diagram, the composite water supply line for a total regeneration reuse system is composed of two parts: the part below the pinch concentration and the part above the pinch concentration. These two parts restrict the freshwater consumption (also the regenerated water flowrate) and regeneration load of the system, respectively. Therefore, two intersections arise between the limiting composite curve and the optimal water supply line, which we called limiting freshwater and regenerated water point, and limiting regeneration load point, respectively. The limiting freshwater and regenerated water point is defined as the touching point of the limiting composite water supply line and the limiting composite curve below the pinch. The limiting composite water supply line below the pinch is always beneath the limiting composite curve and possesses the maximum slope. The limiting regeneration load point is defined as the touching point of the limiting composite water supply line and the limiting composite curve above the pinch. These limiting points for total regeneration reuse systems are actually a transformation of those limiting points for regeneration recycling. Since for total regeneration, the flowrate of freshwater is equal to that of regenerated water, the limiting freshwater point and the limiting regenerated water point are unified as the limiting freshwater and regenerated water point. The two limiting points indicate the bottlenecks of a water system with total regeneration. They are virtually the counterparts of pinch for water reuse without regeneration. The optimal regeneration concentration of a water system with total regeneration actually depends on the limiting points of the system, without direct relationships with the pinch concentration of the system. As presented for the three representative water systems, it can be higher than, equal to or lower than the pinch concentration. Since each water-using system has distinctive limiting composite curve, different water systems have different limiting points for total regeneration. In terms of limiting composite curve, water-using systems can be mainly classified into three categories. For the first category, the limiting composite curve touches the limiting water supply line with direct reuse only at the pinch, such as water-using system 1 (Figure 7). The limiting freshwater and regenerated water point and the limiting regeneration load point of this category both correspond to the normal pinch. For the second category, take water-using system 2 (Figure 10) for example. Besides pinch, one turning point
1185
(point E in Figure 10) of the limiting composite curve above the pinch approaches the limiting water supply line with direct reuse. The limiting freshwater and regenerated water point of this category is the pinch of the system, while the limiting regeneration load point in this case corresponds to a certain point above the pinch, such as point E in Figure 10. For the third category, which water-using system 3 belongs to, an approaching point (point G in Figure 14) appears below the pinch. The limiting freshwater and regenerated water point corresponds to a certain point below the pinch, point G in Figure 14, and the limiting regeneration load point refers to the pinch of the system. These three categories of water-using systems can represent all the single-contaminant water systems. Resorting to the concept of limiting points, two general formulas for calculating the targets for total regeneration systems can be concluded. Minimum freshwater consumption (minimum regenerated water flowrate): FR ¼ FW ¼
MR 2CR C0
(7)
Optimal regeneration concentration: CInR ¼
MC F R (CC C0 ) FR
(8)
In equation (7), MR and CR are the contaminant mass load and the concentration at the limiting freshwater and regenerated water point, respectively. In equation (8), MC and CC are the contaminant mass load and the concentration at the limiting regeneration load point. Both total regeneration reuse and regeneration recycling involves regeneration units. Without considering the conceptual distinction between them, their difference only lies in the quantitative relationships between freshwater and regenerated water. Therefore, equations (7) and (8) can also be directly obtained by applying the restriction that the freshwater consumption is equal to the regenerated water flowrate to the general formulas for regeneration recycling systems. Only some simple mathematical transformation is needed. By using these formulas, the targets for any single-contaminant water systems with total regeneration reuse can be obtained. Equations (1) –(5) are actually a variety of specific applications of equations (7) and (8). For a total regeneration reuse water system with a certain post-regeneration concentration, after identifying the limiting freshwater and regenerated water point, and the limiting regeneration load point, the targets for the system can be calculated by using equations (7) and (8) in sequence. Graphical methods can be employed to determine the limiting points for total regeneration. However, it appears to be more complicated. Because for total regeneration reuse systems, the flowrate of freshwater and regenerated water are correlated, one should find those limiting points by trail and error. Here an improved mass problem table, which is easy to handle, is recommended to target for total regeneration reuse systems. It is similar to the mass problem table for regeneration recycling proposed by Feng et al. (2007). The regenerated water flowrate column and the regeneration concentration column are added to the improved mass problem table. The targeting procedure is as follows. Firstly, simple
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178–1187
1186
BAI et al. Table 4. Mass problem table for water-using system 3 with total regeneration reuse.
Concentration ppm
P1
P2
P3
P4
P5
Mass load kg h21
Accumulative mass load kg h21 0
0
Fresh water flowrate t h21 0
Regenerated water flowrate t h21 0
Regeneration concentration ppm —
0.46 20
0.46
23
20.91
—
2.07
59.14
39.81
—
3.45
57.5
33.82
—
5.75
67.65
37.83
77.44
6.9
53.08
—
61.32
1.61 35 1.38 60 2.3 85 1.15 130
calculations are carried out for the mass load, cumulative mass load and freshwater flowrate columns by using the traditional method. Then the pinch of the system can be determined. Secondly, in the regenerated water flowrate column, each concentration lower than the pinch concentration (including pinch concentration) is assumed to be the limiting freshwater and regenerated water point, and the corresponding regenerated water flowrate is calculated by equation (7). The concentration corresponding to the maximum regenerated water flowrate is taken as the actual limiting freshwater and regenerated water point. Thus the minimum freshwater consumption or minimum regenerated water flowrate can be obtained. Thirdly, in the regeneration concentration column, for each concentration higher than the pinch concentration (including pinch concentration) the corresponding regeneration concentration is calculated by equation (8), and the concentration corresponding to the maximum regeneration concentration is taken as the limiting regeneration load point. Then the optimal regeneration concentration can be identified. Take water-using system 3 for example. The post-regeneration concentration is taken to be 18 ppm. Table 4 shows the improved mass problem table for water system 3 with total regeneration reuse. The pinch of the system arises at 85 ppm. From the regenerated water flowrate column, one can see that the limiting freshwater and regenerated water point corresponds to the concentration of 35 ppm, and the minimum regenerated water flowrate (minimum freshwater consumption) of the system is 39.81 t h21. The optimal regeneration concentration is equal to 77.44 ppm, at the limiting regeneration load point of 85 ppm, as is shown in the regeneration concentration column. According to the previous graphical analysis, when the post-regeneration concentration is higher than the interim post-regeneration concentration (18 ppm . 13.75 ppm), the optimal regeneration concentration is lower than the pinch concentration (77.44 ppm , 85 ppm). The conclusion is also demonstrated by the calculation of mass problem table. In the same way, the targets for the other two water systems with total regeneration can be calculated by the improved mass problem table. The details are not stated here and only results are given. For water-using system 1, since the post-regeneration concentration is 14 ppm
(Figure 7), the minimum freshwater consumption (minimum regenerated water flowrate) is 61.64 t h21 and the optimal regeneration concentration is 80 ppm. For water-using system 2, since the post-regeneration concentration is 10 ppm (Figure 10), the minimum flowrate of freshwater and regenerated water both equal to 26.64 t h21 and the optimal regeneration concentration corresponds to 80.44 ppm.
CONCLUSIONS Three representative single-contaminant water systems with regeneration reuse are analysed in this paper. A handy method is proposed to determine whether partial or total regeneration should be utilized. The optimization of partial regeneration reuse systems is identical to that of regeneration recycling systems owing to their similarities in terms of graphical representation. Thus this paper mainly focuses on total regeneration reuse systems. By minimizing the freshwater consumption, which corresponds to the regenerated water flowrate, and regeneration concentration in sequence, the optimal water supply line for total regeneration reuse systems can be constructed and the targets can be obtained. Then general formulas for calculating the targets are developed on the basis of the concept of limiting points for total regeneration reuse systems. These limiting points indicate the bottlenecks of a water system with total regeneration reuse. Generally there are three categories of water-using systems. The introduction of the limiting freshwater and regeneration water point and the limiting regeneration load point assists the identification of different water-using systems. The optimal regeneration concentration, which is unrelated to the pinch concentration, actually depends on these limiting points besides the post-regeneration concentration. Furthermore, the improved mass problem table, which is recommended to target for regeneration reuse systems, excels in accuracy and efficiency.
NOMENCLATURE In,Max
C C Out,Max CInR C0, COutR COutRc
maximum inlet concentration, ppm maximum outlet concentration, ppm regeneration concentration, ppm post-regeneration concentration, ppm interim post-regeneration concentration, ppm
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178– 1187
OPTIMIZATION OF SINGLE-CONTAMINANT REGENERATION REUSE WATER SYSTEMS CPinch FR FW CInR MPinch CE ME CG MG MR CR MC CC
pinch concentration, ppm minimum regenerated water flowrate, t h21 minimum freshwater consumption, t h21 optimal regeneration concentration, ppm contaminant mass load at the pinch, g h21 concentration at the limiting point above pinch, ppm contaminant mass load at the limiting point above pinch, g h21 concentration at the limiting point below pinch, ppm contaminant mass load at the limiting point below pinch, g h21 contaminant mass load at the limiting freshwater and regenerated water point, g h21 concentration at the limiting freshwater and regenerated water point, ppm contaminant mass load at the limiting regeneration load point, g h21 concentration at the limiting regeneration load point, ppm
REFERENCES Bagajewicz, M., 2001, On the use of linear models for the design of water utilization systems in process plants with a single contaminant, Trans IChemE, 79(Part A): 600– 610. Castro, P., Matos, H., Fernandes, M.C. and Nunes, C.P., 1999, Improvements for mass-exchange networks design, Chem Eng Sci, 54, 1649– 1665.
1187
Feng, X. and Chu, K., 2004, Cost optimization of industrial wastewater reuse systems, Process Safety and Environmental Protection, 82(B3): 249–255. Feng, X., Bai, J. and Zheng, X.S., 2007, On the use of graphical method to determine the targets of single-contaminant regeneration recycling water systems, Chem Eng Sci, 62: 2127– 2138. Gunaratnam, M., Alva-Argaez, A., Kokossis, A., Kim, J.-K. and Smith, R., 2005, Automated design of total water systems, Ind Eng Chem Res, 44: 588–599. Huang, C.H., Chang, C.T., Ling, H.C. and Chang, C.C., 1999, A mathematical programming model for water usage and treatment network design, Ind Eng Chem Res, 38: 2666–2679. 1999. Mann, J.G. and Liu, Y.A., 1999, Industrial Water Reuse and Wastewater Minimization (McGraw-Hill, New York, USA). Takama, N., Kuriyama, T., Shiroko, K. and Umeda, T., 1980, Optimal water allocation in a petroleum refinery, Comp Chem Eng, 4: 251– 258. Wang, Y.P. and Smith, R., 1994, Wastewater minimization, Chem Eng Sci, 49(7): 981–1006. Xu, D.M., Hu, Y.D., Hua, B. and Wang, X.L., 2003, Minimization of the flowrate of fresh water and corresponding regenerated water in water-using system with regeneration reuse, Chinese J Chem Eng, 11(3): 257 –263. Xu, D.M., Hu, Y.D., Hua, B. and Wang, X.L., 2004, Optimum design of water-using network with regeneration reuse, Chinese J Chem Eng, 18(2): 202–207.
ACKNOWLEDGEMENTS Financial support provided by the National Natural Science Foundation of China under Grant No. 20436040 is gratefully acknowledged.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A8): 1178–1187