Process Water Management - American Chemical Society

Ind. Eng. Chem. Res. 2006, 45, 5287-5297

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PROCESS DESIGN AND CONTROL Process Water Management Santanu Bandyopadhyay* and Mandar D. Ghanekar Energy Systems Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai 400076, India

Harish K. Pillai Department of Electrical Engineering,Indian Institute of Technology, Bombay, Powai, Mumbai 400076, India

Water management addresses the problem of optimal allocation of reusable water among different waterusing operations. Wastewater management deals with optimal design of effluent treatment units to respect environmental norms. However, optimal design of effluent treatment units should be solved in conjunction with the problem of optimal allocation of water among different processes that use water. A new methodology for targeting minimum effluent treatment flow rate satisfying minimum freshwater requirement is proposed in this paper. The proposed methodology can be applied to fixed-flow-rate as well as fixed-contaminant-load problems having a single contaminant. A source composite curve is proposed for directly targeting generation of wastewater. Freshwater can be indirectly targeted using overall mass balance. To target distributed generation of wastewater, wastewater composite curve is proposed. On the basis of this wastewater composite curve, targets for effluent systems can be set. All these targets can be set on a single concentration-contaminant load diagram before designing the detailed water-allocation network. Analytical algorithms are proposed to solve the integrated water and wastewater management problem. The minimum contaminant removal ratio of the effluent treatment system and the minimum number of required effluent treatment units are also reported in this paper. 1. Introduction Because of environmental regulations, water management has become an important issue for process engineers. The cost of treating wastewater streams is increasing steadily as environmental regulations are becoming more and more stringent. This issue can be effectively addressed by process-integration techniques. One of the goals of process integration is to integrate resources, such as energy, materials, etc., with technologies, to minimize emission and wastes. Process water management can be divided into two distinct activities. One activity deals with optimum allocation of reusable water to different processes to minimize freshwater requirement. The other activity aims at optimal treatment of wastewater generated in different processes to meet environmental regulations. The primary objective of this paper is to address these two issues of process water management simultaneously. In literature, methods proposed for freshwater targeting use either conceptual approaches of process integration or use mathematical optimization techniques. Methodologies based on conceptual approaches help in getting a physical insight of the problem through its graphical representations and simplified tableau-based calculation procedures. On the other hand, mathematical-optimization-based methodologies are preferred to address issues such as multiple contaminants, controllability, flexibility, cost-optimality, etc. El-Halwagi and Manousiouthiakis1 proposed systematic composite representations to identify targets for mass exchange * Corresponding author. Tel.: +91-22-25767894. Fax: +91-2225726875. E-mail: [email protected].

network. Wang and Smith2 proposed a systematic graphical method for freshwater targeting. These methods are applicable for units, which can be modeled as mass transfer units (e.g., washing, scrubbing, etc.) with water being used as a massseparating agent. These operations have a fixed contaminant load, and the maximum allowable inlet and outlet concentrations are specified. The flow rate of water entering and leaving the unit is the same and can be calculated using the following expression,

f)

∆m Cout - Cin

(1)

where ∆m is the mass load of the contaminant and Cin and Cout are inlet and outlet concentrations of the contaminant, respectively. Cin and Cout are not allowed to exceed the specified maximum values. The targeting method proposed by Wang and Smith2 consists of plotting the limiting water composite curve with contaminant load as the horizontal axis and the contaminant concentration as the vertical axis. Since the contaminant load and concentration difference obeys a linear relationship (eq 1), the limiting composite curve is a piecewise linear curve. The freshwater is represented as a straight line in this concentration vs contaminant load diagram, as per eq 1. The freshwater line is then rotated with the freshwater inlet concentration as a pivot until it just touches the limiting composite curve. The reciprocal of the slope of this rotated line gives the required minimum freshwater flow rate. The limiting water composite curve sets the lower limit for freshwater utilization, because at no point can the freshwater line cross the limiting composite curve. However, the freshwater

10.1021/ie060268k CCC: $33.50 © 2006 American Chemical Society Published on Web 06/16/2006

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line is allowed to touch the limiting composite curve, as the required driving forces (for mass transfer) are built-in in the limiting curve. Since the inlet flow rate is identical to the outlet flow rate for each unit, the wastewater flow rate for the network equals the targeted freshwater flow rate. This method cannot be applied for processes such as cooling tower, boiler, etc., because these units cannot be modeled as mass transfer operations.3 These operations have specified inlet and outlet flow rates, which may not necessarily be equal and, therefore, can account for water losses or gains. These units may be modeled with outlet streams leaving at a specified concentration, while the inlet streams have a maximum allowable concentration.4 Wang and Smith5 proposed a method for problems with fixedflow-rate operations through local recycling and splitting of water-using operations to meet the flow-rate constraints. For problems with water loss/gain, Wang and Smith5 obtained the limiting composite curve by neglecting changes in water flow rate (through water loss/gain) and then accounted for the changes in the freshwater line. Here, the freshwater line becomes piecewise linear, and the targeting procedure becomes tedious and iterative. The targeting methodology proposed by Dhole et al.3 involves separate plots for source and demand composites, with flow rate as the horizontal axis and contaminant concentration as the vertical axis. The two composites are translated horizontally till they touch each other (at the pinch), and the nonoverlapping portions of the curves determine the targets for minimum freshwater and wastewater flow rates. However, this procedure does not give true targets.6 Mixing of two streams relaxes the pinch and, therefore, increases the overlap of the two composites. This, in turn, decreases the freshwater requirement. Sorin and Bedard7 and Polley and Polley8 proposed a set of rules for solving fixed-flow-rate problems with few water utilization processes. Hallale6 developed a new graphical approach (water surplus diagram) for freshwater targeting. Though it can be considered for fixed-contaminant-load problems as well as fixed-flow-rate problems, it is a graphical iterative procedure. Tan et al.9 developed a tabular iterative approach to ease the exercise of graphical iterations. A rigorous graphical technique, on the cumulative contaminant loadcumulative flow rate diagram, has been developed recently to target freshwater requirement involving separate source and sink composite curves.4,10,11 The two composites are translated horizontally till the source composite lies just below the sink composite curve, and the nonoverlapping portions of the curves determine the targets for minimum freshwater and wastewater flow rates. Mathematical optimization techniques have also been used to solve freshwater minimization problem.12-14 Water targeting for batch processes has been developed by Foo et al.15,16 All the above methods essentially describe the procedure for targeting minimum freshwater requirement. Through the overall mass balance, the amount of generated wastewater is determined. Because of environmental norms, it becomes essential to treat wastewater streams, containing contaminants in large quantities, before discharge to the environment. It is an important part of the process water management to design and target minimum effluent treatment flow rate to guarantee environmental limits. Wang and Smith17 have developed a systematic approach for the design of distributed effluent treatment systems. This procedure has been extended by Kuo and Smith18 for multiple

Figure 1. Water allocation network, as proposed by Polley and Polley,8 satisfying freshwater target for example 1. (The values show flow rate in t/h with contaminant concentrations in ppm within braces.) Table 1. Limiting Process Data for Example 1 inlet/demand

processes

contaminant concentration (ppm)

flow rate (t/h)

outlet/source contaminant concentration (ppm)

flow rate (t/h)

P1 P2 P3 P4

20 50 50 50 50 100 100 100 100 80 150 70 200 70 250 60 concentration of contaminant in freshwater, Cfw ) 0 ppm environmental limit for discharge concentration, Ce ) 50 ppm removal ratio of the treatment unit, r ) 0.95

treatment processes. Mathematical optimization techniques have also been used to design distributed effluent treatment system.19,20 Overall water management in a process industry is usually performed sequentially. The designs of water-using processes are addressed first, and subsequently, on the basis of the designed water-reuse network, the distributed effluent treatment system is designed. This sequential procedure may lead to suboptimal solution for the distributed effluent treatment system. To illustrate the point, let us consider example 1. The limiting process data for example 1 is given in Table 18 with additional assumptions that the environmental limit is 50 ppm and the contaminant removal ratio of the treatment unit is 95%. If freshwater is used to satisfy the demand for each of the individual processes, the freshwater consumption may be estimated to be 300 t/h. However, reusing water from other processes, the minimum freshwater requirement can be calculated as 70 t/h with a corresponding effluent flow rate of 50 t/h. Polley and Polley8 proposed a water-allocation network satisfying the minimum freshwater target (Figure 1). This network produces an effluent stream of 50 t/h with a contaminant concentration of 250 ppm. To meet the environmental regulation, 42.11 t/h of effluent has to be treated in the treatment unit (not shown in Figure 1). However, this is not optimal. It is possible to redesign the network (as demonstrated later in this paper) such that only 35.96 t/h of effluent needs to be treated to meet the environmental regulation (a reduction of 15%). Therefore, it is essential to target effluent treatment simultaneously with the freshwater targeting. In a seminal paper, Takama et al.21 solved the complete water management problem using nonlinear optimization technique. Kuo and Smith22 presented a methodology to discuss the

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interaction between operations that use water and effluent treatment systems. In this method, they plotted limiting composite curve, freshwater curve, and effluent treatment curve on a single concentration-contaminant load diagram. However, this method is only applicable to fixed-contaminant-load operations. In this paper, a novel methodology is developed for simultaneously targeting distributed effluent treatment system and minimum freshwater requirement. A source composite diagram is introduced to target minimum wastewater production both for fixed-contaminated-load and fixed-flow-rate problems. In the proposed methodology, freshwater requirement is calculated through the overall mass balance. The source composite diagram is then used to develop the wastewater composite curve. The minimum effluent flow rate for treatment, minimum contaminant removal ratio, and minimum number of treatment units required for the overall effluent treatment process are also targeted in this paper. Graphical representations as well as analytical algorithms are proposed to address integrated process water management issues. The conceptual approach presented in this paper is restricted to a single contaminant. 2. Wastewater Targets In the following subsections, a new methodology is proposed to target simultaneously the minimum freshwater requirement, maximum water reuse, minimum wastewater generation, and minimum effluent to be treated to meet environmental norms. In the proposed method, minimum wastewater produced is targeted directly. In this method, a novel limiting composite curve, called source composite curve, is proposed. The source composite curve is plotted on a concentration (C) vs contaminant load (∆m) diagram. 2.1. Source Composite Curve and Targeting Wastewater. Every fixed-contaminant-load problem may be converted to a fixed-flow-rate problem at the targeting stage with the limiting water flow rate being the specified flow rate for each process.4 Therefore, a water allocation problem may be modeled with outlet streams leaving at a specified concentration and flow rate (sources of wastewater), while the inlet streams have a maximum allowable concentration and a specified flow rate. The outlet of any process may be viewed as a source of wastewater, while the inlet to any process represents the scope of reusing wastewater or demands of wastewater. The source composite curve represents the maximum contaminant load at different contaminant concentrations. Physically, the source composite curve is equivalent to the grand composite curve in heat-exchanger network synthesis23 and invariant rectifying and stripping curves in distillation.24 An algebraic procedure for the generation of source composite curve and targeting minimum wastewater production is given below. 2.1.a. Minimum Wastewater Targeting Algorithm. Step 1. Arrange all the distinct concentrations (of freshwater, demands, and sources together) in descending order in the first column. Without loss of generality, the entries of the first column are C1 > C2 > C3 > ... > Cn. Step 2. For each concentration Ci (in the first column), put the corresponding net flow Fi in the second column. The net flow Fi is calculated by taking the algebraic sum of flow rates corresponding to a concentration Ci. We adopt the convention of positive flow rates for sources and negative flow rates for demands. Step 3. The corresponding entries in the third column are i cumulative flow rates given by the formula Qi ) ∑j)1 Fj.

Table 2. Generation of Source Composite Curve and Targeting Wastewater for Example 1 contaminant concentration (ppm)

net flow rate (t/h)

cum. flow rate (t/h)

mass load (kg/h)

cum. mass load (kg/h)

wastewater flow rate (t/h)

250 200 150 100 50 20 0

60 -70 70 20 -50 -50 0

60 -10 60 80 30 -20 -20

0 3 -0.5 3 4 0.9 -0.4

0 3 2.5 5.5 9.5 10.4 10

40 35 50 45 10 -20 0

Step 4. Calculate the entries of the fourth column by the formula Pi ) Qi-1(Ci-1 - Ci). Note that Q0 is assumed to be zero. Step 5. The fifth column contains the cumulative contaminant i mass load ∆mi ) ∑j)1 Pj. Step 6. Calculate the corresponding wastewater flow rate fww,i ) (∆mT - ∆mi)/(Ci - Cfw) where Cfw is the concentration of the freshwater and ∆mT ()∆mn) is the total contaminant load of the process. Note that wastewater flow rates are calculated for concentrations such that Ci > Cfw. Now the fifth column (cumulative mass load) may be plotted against the first column (concentration) to obtain the source composite curve. The largest entry in the last column is the minimum wastewater flow-rate target. The last entry in the third column gives water loss/gain in the overall process. A negative entry suggests water loss, and a positive entry indicates an overall water gain in the process. For a fixed-contaminant-load problem, the last entry should be zero. This is expected because there is no water gain/loss in any process. In step 6 of the previous algorithm, minimum wastewater is targeted from the source composite diagram. This is similar to the freshwater targeting approach of Wang and Smith.2 Similar to eq 1, the equation for the wastewater line is given as

∆m ) ∆mT - fww(C - Cfw)

(2)

At any concentration, the wastewater line cannot pickup more contaminant load than what is available (given by the source composite curve). The minimum wastewater can be targeted by rotating the wastewater line with (∆mT, Cfw) as the pivot point such that it just touches the source composite curve. Note that the wastewater line has a negative slope (eq 2), and the slope is inversely proportional to the wastewater flow rate. This is equivalent to targeting nonpoint utilities in a heat-exchanger network. Step 6 represents the analytical procedure equivalent to this graphical targeting of wastewater on the concentration (C) vs contaminant load (∆m) diagram. Minimum wastewater targeting algorithm is applied on example 1. The limiting process data for example 1 is given in Table 1.8 Values calculated by applying this proposed algorithm are shown in Table 2. In Table 2, the last entry in the third column is -20. It suggests that there is an overall water loss of 20 t/h. The bottom entry in the fifth column signifies the total contaminant load of the process, and the same has to be picked up by the wastewater (∆mT ) 10 kg/h). The maximum entry in the sixth column sets the minimum wastewater targets as 50 t/h. The source composite curve and wastewater line for example 1 are shown in Figure 2. The maximum slope of the wastewater line corresponds to the minimum wastewater flow rate, since they have an inverse relationship (eq 2). So the minimum

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Figure 2. Source composite curve and wastewater line for example 1.

Figure 3. Source composite curve, wastewater line, and wastewater composite curve for example 1.

wastewater flow rate target comes out to be 50 t/h, and the corresponding pinch composition (CP) is 150 ppm. Total water demand for this example is 300 t/h, and total available water flow rate is 280 t/h. Therefore, there is a net loss of 20 t/h of water (last entry of third column in Table 2). Thus, the minimum freshwater target comes out to be 70 t/h. It may be noted that, for a fixed-contaminant-load problem, the minimum wastewater target is equal to the minimum freshwater target, as there is no water loss/gain. 2.2. Wastewater Composite Curve. Wastewater line represented by eq 2 gives the total wastewater available from the unit. This information is sufficient for designing a centralized effluent treatment plant and end-of-the-pipe solution. However, for the most efficient effluent treatment plants, the optimal design of treatment units must be solved in conjunction with the optimal freshwater allocation problem.18 It has been observed that, for optimum design of the effluent treatment unit, wastewater streams should not be merged together to form a single wastewater stream.17,18 Therefore, it is of utmost importance to identify wastewater sources at different concentrations. To identify wastewater streams at different concentration, Kuo and Smith18 suggested a simple procedure. First, the minimum freshwater requirement is determined. Since they have addressed problems with fixed contaminant load, the freshwater line and the wastewater line are identical. Up to the pinch point, the minimum freshwater targeted cannot be reduced further. After the pinch point, the limiting composite curve and the freshwater line diverge from each other. Considering the pinch point as a pivot, the freshwater line can be further rotated to minimize the freshwater requirement. This procedure is equivalent to the removal of pockets for the grand composite curve in the context of heat-exchanger network design.23 The previous methodology can be followed on the source composite curve to obtain the wastewater composite curve. This procedure, in essence, removes all local concavities or pockets and produces an outer convex curve. For a problem having only wastewater sources and no demand, the outer convex curve or the wastewater composite curve coincides with the source composite curve. The wastewater composite curve divides the source composite curve into different regions. Each region, in the order of decreasing concentrations, cumulatively produces more wastewater than the previous one. Whenever there is an addition of wastewater at a particular concentration, the slope of the wastewater composite curve decreases. This is essentially due to the convexity of the wastewater composite curve. This property may be used to prove optimality of effluent treatment targets. Similar to the wastewater targeting approach, to avoid a tedious graphical targeting, an analytical algorithm is developed.

Table 3. Generation of Wastewater Composite Curve for Example 1

contaminant conc (ppm)



250 200 150 100 50 20 0

0 3 2.5 5.5 9.5 10.4 10

40 35 50 45 10 -20 0

wastewater flow rate, after first pinch (t/h) 25 -10

cum. wastewater (t/h)

cum. mass load removed (kg/h)

25 25 50 50 50 50 50

0 1.25 2.5 5 7.5 9 10

2.2.a. Algorithm for Wastewater Composite Curve. Step 1. Determine overall wastewater flow rate, corresponding pinch point (CP), and contaminant load removed up to pinch point (∆mTP) using minimum wastewater targeting algorithm. Step 2. Repeat step 6 of previous algorithm considering ∆mT ) ∆mTP and Cfw ) CP. Therefore, wastewater flow rate is calculated using the formula fww,1,i ) (∆mTP - ∆mi)/(Ci - CP) for concentrations such that Ci > CP. The maximum of this column is the wastewater that can be generated (fww,1) that corresponds to a new pinch point (CP,1). Step 3. Repeat step 2 until the pinch concentration coincides with the top concentration (C1). Every repetition produces a wastewater flow rate (fww,k) that corresponds to a pinch point (CP,k). Step 4. Cumulative wastewater flow rates are tabulated in the next column using the formula Ri ) fww,k for Cp,k g Ci > Cp,k-1. Step 5. The last column contains the cumulative contaminant i mass load removed by wastewater ∆mww,i ) ∑j)1 Rj-1(Cj-1 Cj). Note that R0 is assumed to be zero. Similar to the source composite curve, plotting the last column against the concentration gives the wastewater composite curve. Results obtained by using the algorithm for the wastewater composite curve for example 1 are given in Table 3. For better readability, the first, fifth, and sixth columns of Table 2 are reproduced in the first three columns of Table 3. As indicated before, for example 1, minimum wastewater generated is 50 t/h, which corresponds to a pinch concentration of 150 ppm (CP ) 150 ppm), and load removed up to pinch concentration is 2.5 kg/h (∆mTP ) 2.5 kg/h). In example 1, only one step is sufficient for removing all pockets. Step 2 produces a pinch point that coincides with the top concentration of the first column, i.e., 250 ppm. Both the wastewater line and the wastewater composite curve, for example 1, are plotted in Figure 3. From Table 3, it can be interpreted that wastewater is generated at two different concentration levels (corresponding to two pinch points): 25 t/h of wastewater is generated at 250

Ind. Eng. Chem. Res., Vol. 45, No. 15, 2006 5291 Table 4. Generation of Source Composite Curve, Targeting Wastewater, and Generation of Wastewater Composite Curve for Example 1 with Cfw ) 20 ppm

contaminant conc (ppm) 250 200 150 100 50 20

net flow rate (t/h) 60 -70 70 20 -50 -50

cum. flow rate (t/h)

mas load (kg/h)


60 -10 60 80 30 -20

0 3 -0.5 3 4 0.9

0 3 2.5 5.5 9.5 10.4

ppm (second pinch point) and (50 - 25) t/h, i.e., 25 t/h, of wastewater is generated at 150 ppm (first pinch point). A network satisfying fresh and wastewater targets for example 1 may be obtained using the nearest-neighbor algorithm,4 and it is shown in Figure 4. It may be noted that the concept of water mains, introduced by Kuo and Smith,22 is not necessary to design a water-allocation network satisfying distributed wastewater targets. Example 1 is slightly modified to observe the applicability of the proposed methodology and algorithm for contaminated freshwater (Cfw > 0). Freshwater is assumed to have a concentration of 20 ppm (Cfw ) 20). Note that 20 ppm is the maximum limit for concentration up to which freshwater can be supplied. Beyond this, example 1 will become unsolvable, as the maximum allowable concentration limit for the purest demand (P1 in Table 1) is 20 ppm. Results related to source composite curve, wastewater line, and wastewater composite curve are tabulated in Table 4. The minimum wastewater flow rate target comes out to be 61.25 t/h, and the corresponding pinch composition is 100 ppm. Through the overall mass balance, this corresponds to a freshwater target of 81.25 t/h. Note that, because of an increase in the contaminant level in the freshwater, the freshwater requirement increases by 16%. In this case, wastewater is generated at three different concentration levels (corresponding to three pinch points): 25 t/h of wastewater is generated at 250 ppm (third pinch point); (60 25) t/h, i.e., 35 t/h, of wastewater is generated at 150 ppm (second pinch point); and (61.25 - 60) t/h, i.e., 1.25 t/h, of wastewater is generated at 100 ppm (first pinch point). 2.3. Targeting Effluent System. After targeting the wastewater, the next step is to find out the effluent treatment flow rate for a given set of operations. As discussed in previous subsections, the source composite and wastewater composite

wastewater flow rate (t/h) 45.22 41.11 60.77 61.25 30 0

wastewater flow rate, after first pinch (t/h)

wastewater flow rate, after second pinch (t/h)

36.67 25 60

25 -10

cum. wastewater (t/h)

cum. mass load removed (kg/h)

25 25 60 61.25 61.25 61.25

0 1.25 2.5 5.5 8.56 10.4

curves can be obtained simultaneously before designing the water-allocation network. Let us denote Ce as the concentration below which wastewater may be discharged from the treatment plant (as the environmental regulations imposed on the overall plant). The contaminant load has to be treated and removed in the effluent treatment plant. This can be explained better through Figure 5. We then draw a vertical line on the concentration vs contaminant load diagram that meets the wastewater composite curve at Ce. The vertical line divides the wastewater composite curve and, hence, the total contaminant load into two parts. Let us denote the contaminant load left of the vertical line as ∆mTef and the contaminant load right of the vertical line as ∆ms. If the total wastewater is discharged with a contaminant load of ∆ms, the concentration of the wastewater has to be Ce. Therefore, the contaminant load right of the vertical line (∆ms) can be discharged safely to the environment, and the remaining load (∆mTef) has to be treated. Thus, ∆mTef kg/h amount of load has to be removed from the system to satisfy environmental regulation (see Figure 5). The performance of the effluent treatment system is given by the removal ratio (r) of the contaminant load from the system.2 It is defined as

r)

fTCTin - fTCTout CTin - CTout ∆mTef ) ) (3) fTCTin CTin ∆mTef + m0

To remove ∆mTef kg/h of contaminant load in the effluent treatment unit, the input load for the treatment plant must be some (∆mTef + m0) kg/h. Equation 3 may be rewritten to calculate the input load (∆mTef + m0).

∆mTef + m0 )

∆mTef r

(4)

Point “Q” in Figure 5 denotes the point with contaminant load of (∆mTef + m0) kg/h. Any treatment line, i.e., the line

Figure 4. Network satisfying freshwater, wastewater, and effluent treatment targets for example 1. (The values show flow rate in t/h with contaminant concentrations in ppm within braces.)

Figure 5. Targeting effluent treatment flow rate.

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Figure 6. Wastewater composite curve and effluent treatment line for example 1. Figure 7. Network satisfying freshwater, wastewater, and effluent treatment targets for example 1 with Cfw ) 20 ppm. (The values show flow rate in t/h with contaminant concentrations in ppm within braces.)

Table 5. Targeting Minimum Effluent Treatment Flowrate for Example 1 contaminant concentration (ppm)

cumulative mass load removed (kg/h)

treatment flow rate (t/h)

250 200 150 100 50 20 0

0 1.25 2.5 5 7.5 9 10

31.58 33.22 35.96 28.95 7.89 -55.26

that represents the removal of contaminant load on a concentration (C) vs contaminant load (∆m) diagram, must pass through the point for fixed removal ratio. The equation of the treatment line is given as

∆m ) ∆mTef/r - fTC

(5)

The minimum treatment flow rate can be targeted by rotating the treatment line with point Q, i.e., (∆mTef/r, 0), as the pivot point such that it just touches the active wastewater composite curve. The point at which the treatment line touches the wastewater composite curve is called the treatment pinch. Similar to the previous subsections, an algorithmic approach is described below for targeting minimum effluent treatment flow rate. 2.3.a. Algorithm for Targeting Minimum Effluent Treatment Flow Rate Step 1. Determine ∆mTef from the wastewater composite curve that corresponds to the environmentally acceptable concentration (Ce). Step 2. Determine effluent treatment flow rate using the formula fT,i ) [(∆mTef/r) - ∆mww,i]/Ci. The maximum entry in the last column defines the minimum effluent treatment flow rate. To demonstrate the above algorithm, example 1 is considered with the environmental limit as 50 ppm, and the removal ratio of the treatment unit is assumed to be 0.95. Results are tabulated in Table 5. The concentration and corresponding cumulative contaminant mass load removed by wastewater from Table 3 (from the first and last columns, respectively) are tabulated in first two columns for better understanding. Corresponding to Ce ()50 ppm), the cumulative mass load removed wastewater denotes ∆mTef, the contaminated load to be removed in the effluent treatment unit. For example 1, ∆mTef ) 7.5 kg/h. From Table 5, it is evident that the targeted minimum effluent treatment flow rate is 35.96 t/h and corresponding treatment pinch is 150 ppm. Source composite curve, wastewater composite curve, and the treatment line for example 1 are shown in Figure 6. Figure 4 includes the treatment units to represent the network of overall water management for example 1.

Table 6. Targeting Minimum Effluent Treatment Flowrate for Example 1 with Cfw ) 20 ppm contaminant concentration (ppm)


treatment flow rate (t/h)

250 200 150 100 50 20

0 1.25 2.5 5.5 8.56 10.4

36.04 38.80 43.40 35.11 9.01 -69.47

For completeness, the proposed algorithm is applied to example 1 with a contaminated freshwater supply (Cfw ) 20 ppm). Corresponding values are tabulated in Table 6. The target for minimum effluent treatment flow rate is 43.4 t/h, and the corresponding treatment pinch is 150 ppm. Figure 7 represents the process flow diagram for the solution of the entire water management for example 1 with Cfw ) 20 ppm. 2.4. Minimum Removal Ratio (rmin). Observe from eq 4 that, for a fixed ∆mTef, a decrease in removal ratio (r) leads to an increase in m0. Therefore, the pivot point (point Q in Figure 5) shifts horizontally toward the right. The maximum horizontal shift is possible such that the entire wastewater is treated in the effluent treatment plant. This corresponds to end-of-the-pipe effluent treatment with a limiting value of removal ratio. If the removal ratio is lower than this limiting value, then treatment of the entire wastewater in a single treatment unit is not sufficient to remove the required amount of contaminant from the wastewater. In such a situation, either of the following steps may be taken: (i) More freshwater may be used to dilute the effluent. (ii) A local recycle across the effluent treatment may be provided. (iii) Multiple treatment units may be used in series. Other than these three options, the designer may choose an alternative technology with a higher removal ratio. However, in this paper, we restrict attention to the cases where the removal ratio of the wastewater treatment plant is assumed to be fixed. Before discussing the implications of these three cases, it is important to derive the minimum removal ratio for a given problem. At a minimum removal ratio, Ce is going to hold the treatment pinch and the entire wastewater is treated in the treatment plant. Hence, by rearranging eq 5, the minimum removal ratio can be calculated as follows:

rmin )

∆mTef ∆mTef + fwwCe

(6)

Ind. Eng. Chem. Res., Vol. 45, No. 15, 2006 5293 Table 7. Limiting Process Data for Example 2 inlet/demand processes P1 P2 P3 P4 P5 P6


outlet/source

flow rate (t/h)


0 120 100 50 80 140 50 80 140 140 180 170 80 230 240 195 250 Cfw ) 0 ppm, Ce ) 20 ppm, and r ) 0.95

flow rate (t/h) 120 80 140 80 195

CTout ) (1 - r)CTin

Minimum removal ratios for example 1 with freshwater (C0 ) 0 ppm) and contaminated freshwater (C0 ) 20 ppm) are calculated to be 0.75 and 0.737, respectively. It is interesting to note that an increase in contaminant level in freshwater increases the minimum wastewater output by 22.5%. However, in the case with contaminated freshwater, the minimum removal ratio of the treatment unit is reduced slightly (1.8%). The minimum removal ratio indicates the limit up to which only one treatment unit is sufficient to meet the environmental norms. If the removal ratio of a particular treatment unit is (1 - 0.7)2. Therefore, a minimum of two treatment units in series is requited to meet the environmental discharge criterion. The optimal structure for the treatment is generic (for brevity, the proof is not included in this paper). It suggests that a portion of the effluent will pass through one treatment unit, and the combined treated and untreated effluent should pass through the remaining (n - 1) treatment units in series. Since all the effluent is passing through (n - 1) treatment units in series, the minimum effluent-treatment flow rate corresponds to minimal effluent passing through the single unit. To find the minimal effluent-treatment flow rate, the same procedure described above can be employed. However, eq 5 should be modified as follows:

[

∆m ) 1 -

1 - rmin (1 - r)

n-1

]( )

∆mTef - fTC rminr

Figure 8. Source composite curve, wastewater composite curve, and treatment line for example 2.

(14)

For the modified example 1 with two treatment units in series, only 9.52 t/h of most contaminated effluent has to be treated in the first treatment unit, and the combined wastewater has to be treated in the second unit to achieve the environmental discharge limit of 50 ppm. It may be noted that, in thse case of local recycle, the total amount of treated effluent flow rate (64.29 t/h for modified example 1) is always more than that of the last case (for modified example 1, it is 59.52 t/h). The appropriate choice of a particular method to meet the environmental regulation primarily depends on the economic tradeoffs between the operating cost and the capital investment for extra treatment units. The process designer should be able to take a proper decision based on cost of freshwater, availability of freshwater, operating cost of effluent treatment, types of contaminants, capital cost for setting multiple treatment unit, turndown ratio for the overall plant, availability of space, etc. 3. Illustrative Examples To demonstrate the applicability of the methodologies developed in this paper, several published examples are solved in this section.

Figure 9. Water allocation network including treatment unit for example 2. (The values show flow rate in t/h with contaminant concentrations in ppm within braces.)

3.1. Example 2: Six-Process Example. Limiting process data for this example is given in Table 7.7 Freshwater concentration is 0 ppm. The environmental limit and the removal ratio of the effluent treatment unit are assumed to be 20 ppm and 0.95, respectively. Results concerning generation of the source composite curve, wastewater line, and wastewater composite curve are tabulated in Table 8. Wastewater can be targeted directly as 120 t/h. Freshwater targets can be set through overall mass balance as (120 + 80) t/h, i.e., 200 t/h. Interestingly, in this problem, there are two pinches, at 100 and 180 ppm. However, the upper pinch controls for wastewater generation. In this example, wastewater is generated at two concentration levels: 85 t/h of wastewater is generated at 250 ppm and (120 - 85) t/h, i.e., 35 t/h, of wastewater is generated at 180 ppm. Note that no wastewater is generated at 100 ppm. A minimum removal ratio for example 2 is calculated to be 0.913. Hence, only one treatment plant is sufficient. Results for effluent treatment flow-rate targets are also tabulated in Table 8. The target for minimum treatment flow rate is 114.02 t/h. Source

Table 10. Generation of Source Composite Curve, Targeting Wastewater and Generation of Wastewater Composite Curve for Example 3 contaminant concentration (ppm)

net flow rate (t/h)

cumulative flow rate (t/h)

mass load (kg/h)

cumulative mass load (kg/h)

500 300 200 100 20 0

90 -10 50 -80 0 -50

90 80 130 50 50 0

0 18 8 13 4 1

0 18 26 39 43 44

wastewater flow rate (t/h) 88 86.67 90 50 50

wastewater flow rate, after first pinch (t/h)

cumulative wastewater flow rate (t/h)


86.67 80

86.67 86.67 90 90 90 90

0 17.33 26 35 42.2 44

treatment flow rate (t/h) 40.53 9.79 -28.7 -147.3 -1096.7

Ind. Eng. Chem. Res., Vol. 45, No. 15, 2006 5295

Figure 10. Source composite curve, wastewater composite curve, and treatment line for example 3. Figure 11. Water allocation network including three treatment units in series for example 3. (The values show flow rate in t/h with contaminant concentrations in ppm within braces.)

Table 11. Limiting Process Data for Example 4 inlet/demand processes


flow rate (t/h)

outlet/source contaminant conc (ppm)

reactor/thickener 100 80 1000 cyclone 200 50 700 filtration 0 10 100 steam system 0 10 10 cooling system 10 15 100 Cfw ) 0 ppm, Ce ) 50 ppm, and r ) 0.9

flow rate (t/h) 20 50 40 10 5

composite curve, wastewater composite curve, and treatment line are plotted in Figure 8. The corresponding water-allocation network and the treatment unit are shown in Figure 9. 3.2. Example 3: Fixed-Contaminant-Load Problem. Limiting process data for this example is given in Table 9.22 Results concerning generation of the source composite curve, wastewater line, wastewater composite curve, and effluent treatment flow rate are tabulated in Table 10. Wastewater can be targeted directly as 90 t/h. Freshwater targets can be estimated through overall mass balance as (90 + 0) t/h, i.e., 90 t/h. The pinch concentration is 200 ppm. In this example, wastewater is generated at two concentration levels: 86.67 t/h of wastewater is generated at 500 ppm and (90 - 86.67) t/h, i.e., 3.33 t/h, of wastewater is generated at 200 ppm. A minimum removal ratio for example 3 is calculated to be 0.959. Therefore, one treatment unit is not sufficient to meet the environmental regulation. Using eq 7, the additional freshwater requirement is estimated as 460 t/h. On the other hand, 613.33 t/h of treated effluent may be recycled across the treatment unit to satisfy the environmental discharge limit. Alternatively, three treatment units may be operated in series. The target for minimum treatment flow rate is 40.53 t/h for one unit and combined effluent to be treated in two treatment units in series. Source composite curve, wastewater composite curve, and treatment line are plotted in Figure 10. The corresponding water-allocation network and the treatment unit are shown in Figure 11.

Figure 12. Source composite curve, wastewater composite curve, and treatment line for example 4.

3.3. Example 4: Specialty Chemical Plant. Limiting process data for this example is given in Table 11.5 The removal ratio of the effluent treatment unit is assumed to be 0.9. Table 12 shows results related to the generation of the source composite curve, wastewater line, wastewater composite curve, and effluent treatment flow-rate targets. Wastewater can be targeted directly as 50.64 t/h. Freshwater targets can be estimated through overall mass balance as (50.64 + 40) t/h, i.e., 90.64 t/h. Pinch concentration is 700 ppm. In this example, wastewater is generated at two concentration levels: 20 t/h of wastewater is generated at 1000 ppm and (90.64 - 20) t/h, i.e., 70.64 t/h, of wastewater is generated at 700 ppm. A minimum removal ratio for example 4 is calculated to be 0.939. Therefore, a single treatment unit is not sufficient to satisfy the environmental norm. Using eq 7, the additional freshwater requirement is estimated as 32.26 t/h. Using eq 8, the amount of treated effluent that

Table 12. Generation of Source Composite Curve, Targeting Wastewater, and Generation of Wastewater Composite Curve for Example 4 contaminant concentration (ppm)

net flow rate (t/h)

cumulative flow rate (t/h)

mass load (kg/h)

cumulative mass load (kg/h)


1000 700 200 100 50 10 0

20 50 -50 -35 0 -5 -20

20 70 20 -15 -15 -20 -40

0 6 35 2 -0.75 -0.6 -0.2

0 6 41 43 42.25 41.65 41.45

41.45 50.64 2.25 -15.50 -16.00 -20.00 0.00

wastewater flow rate after first pinch (t/h)

cumulative wastewater flow rate (t/h)


20

20 50.64 50.64 50.64 50.64 50.64 50.64

0 6 31.32 36.39 38.92 40.94 41.45

treatment flow rate (t/h) 17.94 17.06 -66.8 -184.3 -419.2 -2298

5296


additional treatment units, a process designer can evaluate different options and take appropriate steps. Proposed methodologies and algorithms are applicable for systems with a single contaminant. In many multicontaminant problems, there exists a limiting component and other components are consistent with the limiting component. In such problems, the proposed methodology can be applied based on the limiting contaminant. Present research is directed toward a general approach for general multicomponent problems. Nomenclature

Figure 13. Water allocation network for example 4 incorporating two treatment units. (The values show flow rate in t/h with contaminant concentrations in ppm within braces.)

may be recycled across the treatment unit is calculated to be 35.85 t/h. On the other hand, two treatment units may be operated in series. Results for effluent treatment flow-rate targets are tabulated in Table 12. The target for minimum treatment flow rate is 17.94 t/h for one unit and combined effluent to be treated in the next treatment unit. Source composite curve, wastewater composite curve, and treatment line are plotted in Figure 12. The corresponding water-allocation network and the treatment unit are shown in Figure 13. 4. Conclusion Integrated water management in a chemical process industry consists of optimal allocation of reusable water among different water-using operations to reduce freshwater requirement and optimal design of effluent treatment units to honor environmental norms. A new methodology for targeting minimum freshwater and minimum effluent treatment flow rate is proposed in this paper. Optimal design of effluent treatment units is addressed in conjunction with the problem of optimal allocation of water among different water-using units. The proposed methodology can be applied to fixed-flow-rate as well as fixedcontaminant-load problems with a single contaminant. For every example, one of the many possible networks has been designed to show that these targets can actually be achieved. A source composite curve is proposed for directly targeting minimum generation of wastewater, and hence, minimum freshwater requirement can be indirectly targeted using overall mass balance. Distributed generation of wastewater can be targeted through wastewater composite curve, generated from the source composite curve. Wastewater composite curve can further lead to targeting effluent systems. All these targets can be set prior to designing the detailed water-allocation network and can be set on a single concentration-contaminant load diagram and through analytical algorithms. The minimum contaminant removal ratio of effluent treatment systems has been identified in this paper. For treatment units with a removal ratio less than the minimum removal ratio, the process designer has to choose and design effluent treatment units based on many possibilities. Additional freshwater may be used to dilute the effluent streams, a portion of the treated effluent may be recycled across the treatment unit, or multiple treatment units may be used in series. Closed-form formulas to calculate additional freshwater requirements, recycle flow rate, and the minimum number of required effluent treatment units are reported in this paper. On the basis of the relative freshwater cost, effluent treatment unit operating cost, and capital cost of

C ) contaminant concentration, ppm f ) flow rate, t/h ∆m ) contaminant mass load, kg/h m0 ) excess mass load of contaminant at treatment unit inlet, kg/h n ) number of treatment units P ) contaminant load in a concentration interval, kg/h Q ) cumulative flow rate, t/h R ) cumulative wastewater flow rate, t/h r ) removal ratio Subscripts add ) additional e ) environmental ef ) effective i, j, k, l ) index number in ) inlet min ) minimum out ) outlet P ) pinch r ) recycle T ) total, treatment w ) water ww ) wastewater 1, 2, ... ) index number fw ) freshwater Literature Cited (1) El-Halwagi, M.; Manousiouthiakis, V. Synthesis of Mass Exchange Network. AIChE J. 1989, 35, 1233. (2) Wang, Y. P.; Smith, R. Wastewater Minimization. Chem. Eng. Sci. 1994, 49, 981. (3) Dhole, V. R.; Ramchandani, N.; Tanish, R. A.; Wasilewski, M. Make Your Process Water Pay for Itself. Chem. Eng. 1996, 103, 100. (4) Prakash, R.; Shenoy, U. V. Targeting and Design of Water Networks for Fixed Flowrate and Fixed Contaminant Load Operations. Chem. Eng. Sci. 2005, 60, 255. (5) Wang, Y. P.; Smith, R. Wastewater Minimization with Flowrate Constraints. Trans. Inst. Chem. Eng. 1995, 73A, 889. (6) Hallale, N. A New Graphical Targeting Method for Water Minimisation. AdV. EnViron. Res. 2002, 6, 377. (7) Sorin, M.; Bedard, S. The global pinch point in water reuse network. Trans. Inst. Chem. Eng. 1999, 77B, 305. (8) Polley, G. T.; Polley, H. L. Design Better Water Networks. Chem. Eng. Prog. 2000, 96, 47. (9) Tan, Y. L.; Zainuddin, A. M.; Chwan, Y. F. Water minimization by pinch technologysWater Cascade Table for Water and Wastewater Targeting. Presented at APCChE Meeting, New Zealand, 2002. (10) Prakash, R. Resources Optimisations in Process Industries: Water Management. M.Tech. Thesis, Department of Chemical Engineering, Indian Institute of Technology, Bombay, India, 2002. (11) El-Halwagi, M. M.; Gabriel, F.; Harell, D. Rigorous graphical targeting for resource conservation via material recycle/reuse networks. Ind. Eng. Chem. Res. 2003, 42, 4019. (12) Alva-Argeaz, A.; Vallianatos, A.; Kokossis, C. A multi-contaminant transshipment model for mass exchange networks and wastewater minimisation problems. Comput. Chem. Eng. 1999, 23, 1439.

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ReceiVed for reView March 6, 2006 ReVised manuscript receiVed May 5, 2006 Accepted May 10, 2006 IE060268K

Process Water Management - American Chemical Society

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