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Ind. Eng. Chem. Res. 2010, 49, 5742–5751
Holistic Approach for Design of Minimum Water Networks Using the Mixed Integer Linear Programming (MILP) Technique Zainatul B. Handani, Sharifah R. Wan Alwi,* Haslenda Hashim, and Zainuddin A. Manan Process Systems Engineering Centre (PROSPECT), Faculty of Chemical and Natural Resources Engineering, UniVersiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia
Minimum fresh water consumption and wastewater generation in a facility can be achieved when all options for water minimization including source elimination, reduction, reuse/recycle, outsourcing, and regeneration have been considered. This work presents the development of a new generic mixed integer linear programming (MILP) model to holistically minimize fresh water consumption and wastewater generation for systems involving multiple contaminants where the various options for water minimization are simultaneously considered in order to ultimately generate a minimum water utilization network. The MILP model proposed in this work can be used to simultaneously generate the minimum water targets and design the minimum water network for global water-using operations for buildings and industry. This work also includes cases where fresh water concentrations for all contaminants are assumed to be either zero or non-zero. The approach has been successfully implemented in case studies involving an urban building (Sultan Ismail Mosque, UTM) and a manufacturing plant (a chlor-alkali plant). 1. Introduction Water system integration has been widely used to minimize freshwater consumption and wastewater generation and assist organizations to maximize water savings and minimize the potential impact of effluents on the environment. Toward these ends, techniques based on graphical water pinch analysis and mathematical programs have been implemented. Wang and Smith1 pioneered the research using a graphical technique for water targeting and design of a maximum water recovery network that is applicable for mass transfer-based water systems. More recently, significant advances on water pinch analysis for global water operations have emerged. These include works on processes with mass transfer-based (MTB) and non-mass transfer-based (NMTB) operations for systems involving a single contaminant.2-8 Wang and Smith1 also extended their targeting and network design procedure for single contaminant systems to problems involving multiple contaminants. However, some of the graphical procedures for targeting and design are rather tedious since they require elaborate shifting of streams in the concentration versus mass load diagram. The mathematical programming technique has emerged primarily to overcome the limitations of the graphical approaches particularly for large-scale and complex problems involving multiple contaminants. In the recent years, much research has been done to synthesize optimal water networks using the mathematical programming approach. Most of the mathematical programming approaches were based on nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP) involving multiple contaminants applicable for MTB9-14 and NMTB systems.15,16 Doyle and Smith10 reported that, for the multiple contaminants case, at least one contaminant has reached its maximum value at the limiting water flow rate. Doyle’s assumption has been supported by Savelski and Bagajewicz17 who set up the monotonicity conditions for multiple contaminants where at least one contaminant has reached its maximum outlet concentration. The problem is solved using algorithmic procedures that guarantee a global optimum. However, it is * To whom correspondence should be addressed. E-mail: shasha@ fkkksa.utm.my.
important to note that these works are limited to cases involving MTB operations. Teles et al.18 proposed two initialization procedures that provide multiple starting points to design an optimal water network for MTB and NMTB operations by reducing NLP to LP during initialization procedures using global optimization methods.19 NLP and MINLP are very dependent on a starting point and do not guarantee a global optimum. Therefore, many authors then solved it using a two-stage optimization to approximate the optimal solution.10,18,20,21 In contrast, Castro et al.22 claimed that their heuristic procedure was able to generate good starting points and find global optimal solutions up to 3 orders of magnitude faster than when using the global optimization BARON to solve the NLP problem. Recently, Handani et al.23 proposed a generic linear programming (LP) model to reduce freshwater target and achieve water minimum network for MTB and NMTB operations based on water network superstructure to simultaneously generate the maximum water recovery (MWR) targets and minimum water network design involving multiple contaminants. It is important to note that, in the past, many researchers have focused on developing techniques for MWR which are associated with the maximum water reuse, recycle, and regeneration. Nevertheless, unless some key options for water minimization including source elimination, source reduction, and outsourcing are also considered, strictly speaking, the MWR could not lead to the minimum water targets as widely claimed by researchers over the years. Moreover, regenerating wastewater without considering the possibility of elimination and reduction may lead to unnecessary treatment units. Takama et al.9 first addressed the problem of optimal water allocation in a petroleum refinery by generating a superstructure of all possible reuse and regeneration opportunities. However, various later works on regeneration have been done using water pinch analysis1,13,22,24 and mathematical programming approaches.25-28 Earlier work on the use of a water minimization strategy beyond recycling had been done by El-Halwagi29 who proposed a targeting technique involving water elimination, segregation, recycle, interception, and source/sink manipulation. Hallale5 gave clear guidelines for process modifications and regeneration
10.1021/ie1000357 2010 American Chemical Society Published on Web 05/11/2010
Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010
through a pinch approach and how a water surplus diagram can offer this insight to the designers. Bandyopadhyay30 reported that appropriate process changes or process modification can further reduce the waste regeneration by changing quality and/ or demands and source flow rates. To date, Wan Alwi and Manan31 and Wan Alwi et al.32 introduced the water management hierarchy (WMH) to give new insights on process modification. The minimum water network (MWN) design not only considers reuse and recycling but all conceivable methods to systematically and holistically reduce fresh water consumption through elimination, reduction, reuse/outsourcing, and regeneration using the WMH and a set of heuristics as a design guide. Nonetheless, the graphical method and heuristics steps can sometimes be quite cumbersome and tedious apart from being limited in application to problems involving a single contaminant. Although fresh water consumption and wastewater generation can be reduced via reuse and recycle, it is important to note that fresh water source may contain dilute concentration of contaminant. Most previous studies assumed pure fresh water feed without any contamination. Foo33 extended the algebraic water cascade analysis (WCA) technique to problems involving impure fresh water feed. Nevertheless, the technique is also limited to a single contaminant system. Later, Handani et al.34 included cases where fresh water concentrations for all contaminants are assumed to be either zero or non-zero. The authors also reported that targeting for the contaminated fresh water source case is higher than the pure fresh water source case. This work presents a new generic MILP model to minimize fresh water consumption and wastewater generation for systems involving multiple contaminants. The model holistically considers process changes via all levels of water management hierarchy including elimination, reduction, reuse, outsourcing, and regeneration in order to select the best water minimization schemes that can achieve the minimum water targets and ultimately lead to a minimum water utilization network. The developed model proposed in this work can be used to simultaneously generate the minimum water targets and design the minimum water network for global water-using operation for various types of buildings. The models are capable of predicting which water source should be eliminated or reduced; how much external source is needed; which wastewater source should be reused/ recycled, regenerated, or discharged; and finally, the minimum water network configuration to achieve the water targets. This work also includes pure and impure fresh water multiple contaminants. Application of the methodology on case studies involving a chlor-alkali plant and a mosque show significant water savings, illustrating the effectiveness of the proposed approach. 2. Problem Statement Given a set of global water operations for various water sources and water demands containing multiple contaminants, it is desired to design a minimum water network that holistically considers all water management hierarchy options. This work is performed using the mathematical programming approach with the primary aim to minimize fresh water consumption. 3. Assumptions and Limitations (a) All contaminants concentrations for each demand and source are fixed to their maximum values. (b) There are no flow rate losses or gains, and hence, no changes in water flow rates in the water operations.
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(c) No contaminant concentration constraints have been introduced for the discharge of effluent. (d) The water system is assumed to be operating continuously. (e) The system operates isothermally. 4. Methodology 4.1. Superstructure Representation for Minimum Water Networks (MWNs). The representative superstructure is based on the water management hierarchy (WMH) options. The MWN considers all conceivable methods to holistically reduce fresh water usage through elimination, reduction, reuse/outsourcing, and regeneration using the WMH as a guide. The MWN superstructure is a combination of superstructures in Figures 1a and b. Figure 1a shows the superstructure for obtaining the adjusted demand flow rate, Bj when source elimination and reduction are considered. Xj,e, Xj,re, and Xj,o are binary variables that represent the selection of water minimization schemes, e.g. elimination, reduction, or original oprions. Meanwhile, Daj,e, Daj,re, and Daj,o denote the flow rate if elimination and reduction schemes are implemented or water flow rate remain unchanged. Hence, the adjusted demand flow rate, Bj, is highly dependent on the selections of these options. It is important to note that only one option can be selected at one time. Figure 1b represents all possible connections among water sources, water demands, and wastewater discharges with inclusion of outsourcing and regeneration options. For each waterusing operation, the water demand, Bj, can be supplied by fresh water, FWj, outsourced resources, OS (e.g., rainwater, river, and melted snow), reused/recycled water, or regenerated water from a regeneration unit, RU. While at the water source, Ai, the generated wastewater may be directly discharged to the endof-pipe treatment, WWi, or reused in the same or different processes or partially treated in the regeneration unit, RU, before being reused/recycled. In this case, the superstructure of every possible configuration of a water-using network is allowed. The combination of Figure 1a and b gives the general superstructure for the minimum water utilization network considering all WMH options. 4.2. Optimization Model for Minimum Water Network. In this case, the objective is to minimize the fresh water target which leads to minimum wastewater generation. Changes can be made to the flow rates and concentrations of water sources and water demands to reduce the maximum water recovery targets and ultimately achieve a minimum water network benchmark. Minimum water targets can be obtained by considering all conceivable methods to reduce water usage through WMH options. It is vital to note that the implementation of process changes options will yield new water targets. In this approach, all the WMH options are considered simultaneously in order to obtain the minimum water targets. Objective Function. The objective function in this work is to minimize fresh water consumption and can be written as min
∑ FW
j
(1)
j
The minimization of the objective functions in eq 1 is subject to the following constraints. Constraints. 1. Demand Constraint. Adjusted demand flow rate, Bj, is equal to the given demand flow rate after selections of elimination, Daj,e, reduction, Daj,re, and original demand flow rate, Daj,o. Binary variables, Xj,e and Xj,re are introduced to
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represent the selection of several possible measures in elimination and reduction levels.
∑ Da
j,eXj,e
e
+
∑ Da
j,reXj,re
re
+
∑DX
j j,o
) Bj
∀j ∈ J (2)
o
where Daj,o is equal to demand j, Dj. 2. Reduction Option Constraint. If a reduction option is selected, the flow rate for the jth demand, Daj,re, is reduced by a certain percentage, σj,re.
Daj,re ) σj,reDj
∀j ∈ J
(3)
Substituting Daj,re in eq 3 into eq 2 will result in linear constraint 3′ and can be written as below,
∑ Da
j,eXj,e
e
+
∑σ
j,reDjXj,re
re
+
∑DX
j j,o
) Bj
∀j ∈ J
o
(3′) 3. Water Balance for Demand. The water supplied for each adjusted demand flow rate, Bj, is a combination of fresh water,
Figure 1. General superstructure for a minimum water utilization network with WMH options that consider both MTB and NMTB operations. (a) Water network superstructure to obtain the adjusted demand flow rate, Bj, when possible source elimination and reduction are considered. (b) Water network superstructure for maximum water recovery that includes outsourcing and regeneration options.
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Figure 2. Water distribution in the chlor-alkali plant. Table 1. Demands, Dj, and Sources, Si, Water Data for Chlor-Alkali Plant Water System flowrate (t/h)
Si
source
0.40
S1
0.40
S2
0.19 0.27
S3 S4
0.27
S5
4.00 1.04 8.33 13.56 0.08
S6 S7 S8 S9 S10
toilet pipes
0.10
S11
D12
office cleaning
0.05
S12
D13 D14
wash basin ablution
0.01 0.12
S13 S14 S15
washing at filling station and road tanker for NaOH washing at filling station and road tanker for HCl demineralized filter backwash regeneration of demineralized water system (after acid injection) regeneration of demineralized water system (after caustic injection) scrubber laboratory uses cooling tower blow down brine filter backwash brine ion exchange regeneration (brine displacement) brine ion exchange regeneration (after acid injection) brine ion exchange regeneration (after caustic injection) wash basin ablution evaporation condensate
Dj
demand
D1
D6 D7 D8 D9 D10
washing at filling station and road tanker for NaOH washing at filling station and road tanker for HCl demineralized filter backwash regeneration of demineralized water system (after acid injection) regeneration of demineralized water system (after caustic injection) scrubber laboratory uses cooling tower makeup water carbon filter inlet toilet flushing
D11
D2 D3 D4 D5
FWj, potential reused/recycle water, Fi,j, other resources, Fosos,j (e.g., rainwater, river, and snow), and regenerated water from regeneration unit, Fr,j. The water balance for each demand, Bj, is given by FWj +
∑F
i,j
i
+
∑ Fos
os,j
os
+
∑F
r,j
) Bj
0.40 0.40 0.19 0.27 0.27 4.00 1.04 0.49 0.50 0.63 0.49 0.62 0.01 0.12 0.01
partially treated in regeneration unit, Fi,r. The water balance for each source i is given by WWi +
∑F
i,j
j
∀j ∈ J
flowrate (t/h)
+
∑F
i,r
) Ai
∀i ∈ I
(5)
r
r
(4) 4. Water Balance for Source. The water generated from each source i, Ai, is either discharged directly as effluent, WWi, direct reuse/recycle water from source i to demand j, Fi,j, or
5. Demand Contaminant Load Satisfaction. Contaminant mass load for adjusted demand j, BjCdmax j,k is supplied from a mixed of contaminant mass load from different sources (e.g., fresh water, FWjCwk, potential reused/recycle water, Fi,jCsmax i,k , outsources, Fosos,jCosos,k, or/and regenerated water, Fr,jCror,k).
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Thus, the contaminant load from all sources must satisfy the contaminant load for demand j. FWjCwk +
∑F
max i,jCsi,k +
i
∑ Fos
os,jCosos,k +
Dj
os
∑F
∀j ∈ J (6)
e BjCdmax j,k
r,jCror,k
Note that the regeneration units employed here use the centralized wastewater treatment concept and the performance of regeneration units are measured with a fixed outlet concentration for all contaminants, Cror,k or contaminant removal ratio, RRr,k.
∑ F Cs + ∑ Fos Cos + ∑ F ((1 - RR )Cri ) e B Cd max i,k
i,j
os,j
i
os,k
os
r,j
r,k
r,k
j
∀j ∈ J (7)
max j,k
r
6. Mass Balance on Regeneration Unit. The amount of wastewater to be regenerated in the regeneration unit, Fi,r, depends on the demand for regenerated water, Fr,j. The total inlet flow rate is equal to the total outlet flow rate for the regeneration unit. Water consumed for regeneration unit cleaning is assumed to be negligible since the cleaning process is only performed once in a while.
∑F
i,r
)
i
∑F
∀r ∈ R
r,j
(8)
os,j
∀os ∈ OS
max e Fosos
(9)
j
8. Selection of Water Minimization Schemes. This constraint is imposed to ensure that only one water minimization schemes is chosen at one time. Binary variables Xj,e, Xj,re, and Xj,o are introduced to represent the water minimization options involving elimination, reduction, or original operation, respectively.
∑X
j,e
+
e
D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14
∑X
j,re
+
re
∑X
j,o
)1
∀j ∈ J
(10)
o
9. MTB Constraint. For MTB operations, the adjusted flow rate of water demand, Bj, is equal to the adjusted water source flow rate, Ai. Bj ) A i
∀j ∈ J
(11)
10. NMTB Constraint. If source streams exist for NMTB operations, the adjusted flow rate of water source, Ai, is equal to water source flow rate before implementation of WMH options, Si. Ai ) S i
∀i ∈ I
(12)
11. Non-negativity Constraints. Variables that have nonzero, positive values include fresh water supply, wastewater generation and reuse/recycle water flow rate, adjusted flow rate of water source, adjusted flow rate of water demand, and flow rate of water reduction options. FWj, WWi, Fi,j, Fosos,j, Fi,r, Fj,r, Ai, Bj, Daj,re g 0
(13)
5. Case Studies Two case studies involving an urban building as well as a manufacturing plant were used to demonstrate the methodology
demand washing at filling station and road tanker for NaOH washing at filling station and road tanker for HCl demineralized filter backwash demineralized ion exchange regeneration (after acid injection) demineralized ion exchange regeneration (after caustic injection) scrubber laboratory uses cooling tower makeup water carbon filter inlet toilet flushing toilet pipes office cleaning wash basin ablution
pH
TDS (ppm)
hardness (ppm)
7.50
65
17.1
7.50
65
17.1
7.50 7.50
65 40
17.1 17.1
7.50
40
17.1
7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50 7.50
100 65 100 60 100 65 65 65 65
17.1 14.0 14.0 14.0 17.1 17.1 17.1 17.1 17.1
max Table 3. Contaminant Concentration Data for Water Sources, Csi,k
Si S1 S2
j
7. External Water Sources Constraint. The total external water sources flow rate distributed to demand, Fosos,j, must be max equal to or lower than maximum design limit, Fosos
∑ Fos
D1 D2
r
FWjCwk +
Table 2. Contaminant Concentrations Data for Water Demands, max Cdj,k
S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15
source washing at filling station and road tanker for NaOH washing at filling station and road tanker for HCl demineralized filter backwash demineralized ion exchange regeneration (after acid injection) demineralized ion exchange regeneration (after caustic injection) scrubber laboratory uses cooling tower blow down brine filter backwash brine ion exchange regeneration (brine displacement) brine ion exchange regeneration after acid injection brine ion exchange regeneration after caustic injection wash basin ablution evaporation condensate
pH
TDS hardness (ppm) (ppm)
10.80 30360
14
2.50
704
16
7.40 1.20
75 3300
20 14
9.30
60
14
0.30 8.30 6.90 10.60 10.20
528 400 3300 6579 526
40 100 147 14 0
0.02
396
0
13.60
1254
0
7.70 7.70 11.10
60 60 76
20 20 0
for holistic design of optimal water networks. The models were coded into GAMS. In order to achieve optimal solution, a GAMS/CPLEX solver was employed for the MILP problem. 5.1. Case Study 1: A Chlor-Alkali Plant. A chlor-alkali plant is used to illustrate the proposed approach. The limiting water data comprises the overall network water sources and demands streams that include plant uses and domestic uses and are listed in terms of water quality and quantity for the chloralkali plant. This problem consists of mass transfer-based and non-mass transfer-based operations. There are 14 water demands and 15 water sources. Figure 2 illustrates the water using processes in terms of water flow rates. The arrow leaving each box represents a water source that can potentially be reused for other processes. The limiting water data flow rate of the system is listed in Table 1. Tables 2 and 3 show the contaminant concentrations for the water demands and sources. The fresh water source is available for the water system with the following contaminant levels: CwpH ) 3.16 × 10-8 ppm (pH ) 7.50), CwTDS ) 40 ppm, Cwhardness ) 14 ppm. 5.1.1. Water Management Hierarchy Implementation. All potential water minimization schemes to improve a chlor-alkali plant water system were considered according to the WMH options. These options are listed in Table 4 and described next.
Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010 Table 4. Various Water Minimization Schemes for a Chlor-Alkali Plant WMH elimination reduction
reuse external water sources regeneration
strategy D10: change 12 L flushing toilet to composting toilet D6: reduce fresh water usage at HCl scrubber D8: replace chemical treatment with new polymer chemical at cooling water system D10: (option 1) change 12 L flushing toilet to dual flush toilet (option 2) change 12 L flushing toilet to vacuum toilet D14: change normal ablution tap to laminar flow tap direct water reuse rainwater harvesting wastewater regeneration
Table 5. Optimal Results for the Chlor-Alkali Water Distribution optimal result water elimination (t/h) water reduction (t/h) total total total total total
reused/recycled water (t/h) external water sources (t/h) regenerated water (t/h) fresh water consumption (t/h) wastewater generation (t/h)
D10 ) 0 R6,1D6 ) 3.72 R8,1D8 ) 7.75 R14,1D14 ) 0.16 2.53 0.21 6.57 18.51 0
5.1.1.1. Source Elimination. Source elimination is concerned with the complete avoidance of fresh water usage. In order to maximize fresh water savings, all possible means for process changes or equipment changes to eliminate water demands were considered. Due to water mainly being used for chemicals’ dilution, the water demands for process and non-process uses
Figure 3. Optimal water network design for a chlor-alkali plant case study.
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cannot be eliminated. It was possible to eliminate water demands for domestic use, D10 (toilet flushing) by changing all 12 L flushing toilets to composting toilets. 5.1.1.2. Source Reduction. The next option to further reduce fresh water demand was through source reduction. It was possible to reduce water demand at D8 by replacing the chemical used for water treatment with a new polymer chemical at the cooling water system. This resulted to 7% fresh water reduction for cooling tower makeup water. In addition, based on plant observation, the current fresh water utilization at HCl scrubbing system, D6, is higher than the actual fresh water required for the scrubbing system. Therefore, it should be noted that the fresh water consumption at the scrubber can be reduced up to 7% fresh water consumption. The reduction of demand D6 also affects the reduction of source S6. Another possibility to reduce fresh water demand at D10 was by changing the 12 L flushing to dual flush toilet. Dual-flush toilet technology allows the user to select a short flush (6 L) or long flush (12 L). One more option to reduce fresh water usage was by changing the 12 L flushing toilet to a vacuum toilet. The vacuum toilet only required 0.4 L water per flushing. Fresh water consumption can be further reduced at D14 (ablution) by changing normal water taps to laminar taps. This will also reduce source S14. 5.1.1.3. External Water Sources. When it was not possible to eliminate or reduce water demands, external water sources should be considered. Rainwater harvesting is one of the possible water sources to be used at the chlor-alkali plant water system. In Johor, the average annual rainfall is approximately 1778 mm.35 On the basis of the plant available roof area and rain distribution, it was possible to harvest 0.21 m3/h (maximum max design limit, Fosos ) of rainwater at a concentration of TDS CosTDS ) 16 ppm, total hardness Coshardness ) 5 ppm, and pH ) 5.50. The rainwater pH is adjusted to pH 7.50 using an acid
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Table 6. Limiting Water Data for Sultan Ismail Mosque Dj
demand
flowrate (t/day)
BOD (ppm)
turbidity (NTU)
Si
source
flowrate (t/day)
BOD (ppm)
turbidity (NTU)
D1 D2 D3 D4 D5 D6 D7 D8
ablution wash basin showering mosque cleaning kitchen irrigation toilet pipes flushing toilet
25.03 0.14 0.14 0.29 0.03 1.46 0.44 1.57
10 10 10 10 0 10 10 10
2 2 2 2 0 2 2 2
S1 S2 S3 S4 S5
ablution wash basin showering mosque cleaning kitchen
25.03 0.14 0.14 0.29 0.03
23 23 216 472 536
43 49 375 444 132
Table 7. Various Water Minimization Schemes for Sultan Ismail Mosque wmh elimination reduction
reuse external water sources regeneration
strategy D8: change 12 L flushing toilet to composting toilet D1: change normal ablution tap to laminar flow tap D8: (option 1) change 12 L flushing toilet to dual flush toilet (option 2) change 12 L flushing toilet to vacuum toilet direct water reuse max rainwater harvesting [Fosos ) 11.14 t/day, CosBOD ) 10 ppm,38 and Costurbidity ) 1.5 NTU39] wastewater regeneration using a microfiltration, activated carbon, and UV system [CroBOD ) 4.2 ppm and Croturbidity ) 1 NTU of turbidity40]
(HCl) or an alkali (NaOH) that are produced by the plant. Note that a rainwater storage tank is already available for the facility. 5.1.1.4. Regeneration Reuse/Recycle. The next level for water minimization is regeneration. Regeneration refers to treatment of wastewater to match the quality of water required for further use. Regeneration can be used to remove contaminants on an intermediate basis. The regeneration units employed here use a centralized wastewater treatment system. In order to adjust the pH of the water streams, the pH adjustment unit using an acid (HCl) or an alkali (NaOH) may be used as regenerators.
Figure 4. Minimum water network design for Sultan Ismail Mosque case study.
An EDI treatment system (electrodialysis-ion exchange) was used to remove hardness and TDS. It was possible to treat wastewater to concentration of TDS CroTDS ) 30 ppm, total hardness Crohardness ) 2 ppm, and pH ) 7.50. 5.1.2. Results and Discussions. Process changes can be made to reduce flow rates and concentrations of water sources and water demands, to further reduce the maximum water recovery targets, and ultimately achieve the MWN benchmark. The minimum water targets can be obtained through process changes according to WMH options. Solving eq 1 with the constraints in eqs 2-13 yielded an optimal solution for designing the minimum water network. The final solution was found in 0.015 s of generation time with 332 continuous variables, 20 binary variables, and 131 constraints. The minimum fresh water and wastewater flowrates after considering all water minimization options are 18.51 and 0 t/h, respectively. The potential for fresh water and wastewater reductions are up to 35.8% and 100%, respectively, toward achieving the MWN design. It is important to note that targeting the MWR through reuse and recycle only resulted in savings of up to 7.2% fresh water and 22.1% wastewater for chlor-alkali plant based on the MWR model proposed by Handani et al.34 In order to obtain the maximum water savings, the optimizer chose to eliminate water demand at D10 (toilet flushing) by changing all 12 L flushing toilet to composting toilet. In addition, the optimizer selected to reduce water demand at D8 by replacing the chemical used for water treatment with a new polymer
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chemical. Meanwhile, the water demand at D6 was reduced by decreasing fresh water usage at HCl scrubbing system since current fresh water consumption at the scrubber is higher than the actual fresh water required for the scrubbing system. Both selections of water reduction yielded the biggest flow rate reductions in the water system. Another possible water reduction, D14 (ablution) was also selected by changing normal water taps to laminar taps as it also contributed toward maximizing water savings. In addition, an external water source was added at the maximum limit of rainwater harvesting. This water source becomes favorable to be used because of its high water quality rather than to be reused and recycled. Regeneration of 8.49 t/h wastewater also resulted in reduction of fresh water consumption. Table 5 shows the optimal results after integration while the corresponding water network design is given in Figure 3. 5.2. Case Study 2: Sultan Ismail Mosque (SIM). Sultan Ismail Mosque (SIM) which is located in Universiti Teknologi Malaysia (UTM), Johor, Malaysia, was selected to demonstrate the applicability of the generic model on an urban building. The SIM limiting water data taken from the work of Wan Alwi36 was modified to include another contaminant in the water system. Contaminants concerned for this water minimization study are biological oxygen demand (BOD) and turbidity. The limiting water data for each operation is listed in terms of water sources and demands as shown in Table 6. The data for water demands was adapted from USEPA water quality standards for water reuse.37 The fresh water source available is assumed to be free of all contaminants (CwBOD ) 0 ppm, Cwturbidity ) 0 NTU). In this case, there are eight water demands and five water sources. Wastewater derived from toilet flushing and toilet pipes is referred to as black water and will not be considered for reuse since it is highly contaminated. Water from irrigation will be assumed to be completely absorbed by the soil. Table 7 lists the various water minimization schemes applied in order to minimize fresh water consumption. Solving eq 1 with constraints in eqs 2-13 yielded an optimal solution for the water system. The MILP model is solved with a total of 100 continuous variables, 12 binary variables, and 100 constraints with 0.031 s of generation time. The minimum fresh water and wastewater flow rate targets were at 0.03 and 0.14 t/day, respectively, after implementing WMH options. This gives reduction as 99.9% for fresh water consumption and 99.5% for wastewater generation. The percentages of water reductions after implementing the proposed model are significantly higher as compared to when only maximum water recovery (MWR) through reuse and recycle was considered. The fresh water and wastewater obtained from MWR approach were 27.75 and 24.28 t/day, respectively, when multiple contaminants were considered.34 In order to obtain the maximum annual savings for the water system, the optimizer favored to eliminate water demand at D8 (toilet flushing) by changing all 12 L flushing toilet to a composting toilet. In addition, changing normal water taps to laminar taps at demand D1 also led to reductions of fresh water consumption. Water outsourcing through rainwater harvesting was employed to take advantage of the high quality of rainwater as compared to quality of reuse and recycle water. Regenerating 12.64 t/day of wastewater also resulted in decreasing wastewater generation. Figure 4 gives the corresponding optimal design of water network. 5.2.1. Results Comparison. Table 8 compares the results obtained using the mathematical programming approach proposed in this work with that obtained using the heuristic
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Table 8. Results Comparison between the Proposed Model and Heuristic Approach32 for Sultan Ismail Mosque Case Study proposed model contaminant approach total fresh water consumption (t/day) total wastewater generation (t/day) total regenerated water (t/day) total external water sources (t/day) selection of elimination option selection of reduction option
approach by Wan Alwi et al.32
multiple contaminant mathematical programming 0.03
single contaminant heuristic
0.14
9.27
12.64
3.13
2.01
11.14
D8
D8
D1
D1
0.03
approach by Wan Alwi et al.32 The proposed model gives higher wastewater reduction than the heuristic approach. This is due to the fact that, for the mathematical programming approach, the algorithm allows for most wastewater to be regenerated in order to satisfy the demand requirement. On the other hand, the same amount of fresh water consumption is achieved for both approaches but it is important to note that mathematical approach more closely reflects the practical situation as far as the assumptions and the numbers of contaminants are concerned. Real-life water systems involve various contaminants that can present additional constraints and prevent wastewater from being reused or recycled. Table 8 also shows that different process changes have been implemented for both approaches. By using the approach proposed by Wan Alwi et al.,32 all process changes are prioritized according to the WMH. The mathematical approach however considers all WMH options simultaneously in order to obtain the minimum water targets and an optimal water utilization network. 6. Conclusion A new generic MILP model has been developed based on water network superstructure to achieve the minimum water targets for systems involving multiple contaminants for both mass transfer-based and non-mass transfer-based problems (i.e., global water-using operations). The model is able to holistically determine water source to be eliminated or reduced, the amount of external water source needed, which wastewater source should be reused/recycled, regenerated or discharged. The model is also able to specify the minimum water network configuration to minimize fresh water consumption. The method has been successfully implemented to an urban building (Sultan Ismail Mosque at UTM) and a manufacturing plant (chlor-alkali plant). For the chlor-alkali plant, impure fresh water was considered. The potential reductions are 35.8% and 100% for fresh water and wastewater respectively. For the mosque case study, the fresh water concentrations for all contaminants were assumed to be zero. The results show that the maximum potential freshwater and wastewater reductions are 99.9% and 99.5%, respectively. Acknowledgment The authors would like to thank Malaysia Ministry of Science, Technology and Innovation (MOSTI), and National Science Fellowship (NSF) for the financial support.
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Nomenclature Subscripts i ) index for water source j ) index for water demand k ) index for water contaminant r ) index for regeneration unit e ) index for water elimination option re ) index for water reduction option o ) index for original water demand os ) index for external water sources Parameters max Csi,k ) maximum concentration of contaminant k from water source i max Csj,k ) maximum concentration of contaminant k in demand j Cwk ) fresh water concentration of contaminant k Cosos,k ) outsource concentration of contaminant k Cror,k ) outlet concentration of contaminant k from regeneration unit r Si ) flow rate of water source i Dj ) flow rate of water demand j max Fosos ) maximum flow rate of outsource os Daj,e ) flow rate of elimination option e for demand j σj,re ) percentage of water reduction re for demand j
Continuous Variables FWj ) fresh water supplied to demand j Fi,j ) water flow rate from source i to demand j WWi ) unused portion of water source i (waste) Fosos,j ) outsource flow rate os to demand j Fi,r ) water flow rate from source i to regeneration unit r Fr,j ) water flow rate from regeneration unit r to demand j Ai ) adjusted flow rate of water source i Bj ) adjusted flow rate of water demand j Daj,re ) flow rate of reduction option re for demand j Daj,o ) original flow rate o for demand j Crir,k ) inlet concentration of contaminant k to regeneration unit r Binary Variables Xj,e ) selection of elimination options e for demand j Xj,re ) selection of reduction options re for demand j Xj,o ) selection of original flow rate o for demand j Acronyms BOD ) biological oxygen demand EDI ) electrodialysis-ion exchange GAMS ) generalized algebraic modeling system LP ) linear programming MILP ) mixed integer linear programming MINLP ) mixed integer nonlinear programming MTB ) mass transfer-based MWN ) minimum water network NLP ) nonlinear programming NMTB ) non-mass transfer-based TDS ) total dissolved solid WCA ) water cascade analysis WMH ) water management hierarchy
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ReceiVed for reView January 7, 2010 ReVised manuscript receiVed April 8, 2010 Accepted April 27, 2010 IE1000357
