New Structure and Design Methodology for Water Networks

It is accompanied by a new design procedure to generate networks having internal water mains, limited to a ... programming, given a superstructure, or...
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Ind. Eng. Chem. Res. 2001, 40, 6140-6146

PROCESS DESIGN AND CONTROL New Structure and Design Methodology for Water Networks Xiao Feng* Department of Chemical Engineering, Xi’an Jiaotong University, Xi’an 710049, P.R. China

Warren D. Seider Department of Chemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6393

A new network structure is proposed in which internal water mains are utilized. The structure simplifies the piping network, as well as the operation and control of large plants involving many water-using processes, such as petrochemical or chemical complexes. It is accompanied by a new design procedure to generate networks having internal water mains, limited to a single contaminant with water reuse permitted, involving mass balances only and simple strategies for water minimization. Emphasis is placed on positioning of the internal water mains to simplify the networks, with the first internal main usually positioned at the pinch concentration. Strategies to reduce water consumption, through the use of local pipes and outlet concentration shifts, are discussed. Introduction Water scarcity and stricter environmental regulations on industrial effluents underlie the growing emphasis on freshwater minimization in industry, which corresponds to wastewater minimization. New strategies for optimal water allocation have been reported over the past 2 decades, mostly in the last 5 years.1-11 These include methods to design the water network having minimum water consumption and wastewater production using either (1) mathematical programming, given a superstructure, or (2) a graphic method, involving the water pinch. Mathematical programs are gaining effectiveness in optimizing large-scale systems, with many water streams and multiple contaminants. Recently, Bagajewicz and co-workers8,9 and Savelski and Bagajewicz12 show how to reduce a nonlinear program (NLP) to a linear program, by inserting the maximum outlet concentration conditions. In this way, mass balances involving bilinear terms are replaced by linear inequality constraints and global optimality is guaranteed. However, the solutions of mathematical programs can be difficult to interpret, giving designers fewer insights compared with graphical methods. For the graphical, or water pinch, method, important concepts were introduced by Wang and Smith.2 One is the pinch point, which is the bottleneck of the water network. Another is the limiting water profile, using the maximum inlet/outlet concentrations of species in/out of processes that use water, to construct the limiting composite curve. This ensures that all driving forces for mass transfer are satisfied, even when the transfer units, to be designed, have different mass-transfer mechanisms and minimum driving forces for mass transfer. The limiting water profile has been widely * To whom correspondence should be addressed. Tel. 8629-2668980. Fax: 86-29-3237910. E-mail: [email protected].

accepted.5-10 It indicates the minimum freshwater required for an entire process and, hence, shows the designer how close a water network is to optimal, that is, to the minimum freshwater target. However, when multiple contaminants are present, graphical methods require assumptions for ease of implementation, some of which may be difficult to justify. Water networks are designed using strategies similar to those used in the design of networks of heat exchangers, with pipes connecting the unit processes. When the entire plant involves only a few processes, the networks are fairly simple and water savings at or near the maximum are achieved. However, for a large petrochemical or chemical complex, with many unit processes, the piping network becomes very complicated. Difficulties for operators in understanding the flows through many interconnected streams in a network have led Polley and Heggs13 to suggest a “keep it simple” strategy when designing networks. To meet this objective, in this paper, a new structure for a water network is introduced using one or more internal water mains (or reservoirs). Note that Kuo and Smith4 introduced a similar concept, but as will be explained, their use of the water main is totally different. Herein, a new design method is presented to simplify the piping system and the design of the water network. Emphasis is placed on the location of the water main(s). Use of Water Mains The new structure for a water network involves one or more internal water mains. These water mains simplify operation and the control of water quality, as well as the design strategy. The water main is a reservoir at a uniform concentration of contaminant(s). It receives water at contaminant concentrations less than or equal to its contaminant

10.1021/ie000835i CCC: $20.00 © 2001 American Chemical Society Published on Web 11/28/2001

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concentrations and supplies water to unit processes at concentrations greater than or equal to their contaminant concentrations. Like the freshwater main or the steam pipe, the water mains are connected to many unit processes. Note that, in addition to these internal water mains, all plants contain freshwater and wastewater mains. Kuo and Smith4 introduced a design strategy that utilizes water mains as intermediate sinks and sources of water for the unit processes. However, these are removed during the last step of the design strategy “for the sake of simplicity”. The complexity of the plant should be considered when positioning water mains. For a plant with just a few unit processes, operation is often sufficiently simple not to justify the installation of a water main. However, as mentioned above, the use of one or more water mains should be considered for petrochemical or chemical complexes with many unit processes. All unit processes can be connected to the external water supply main (which usually contains freshwater) and a wastewater main (which discharges wastewater to the environment or to a wastewater treatment plant). When water is to be reused in the unit processes downstream (the so-called reuse water), at least one internal water main is introduced. These mains receive water effluent streams from unit processes upstream and provide water for unit processes downstream. Note that these mains also provide water for unit processes upstream when it is desirable to recycle water. Obviously, as a water source, the internal water main should be positioned at a contaminant concentration less than or equal to that needed by the water sinks. Furthermore, as a water sink, each internal water main must receive water from at least one unit process. Consequently, all contaminant concentrations of streams into and out of the unit processes are candidate concentrations for a water main. Usually, less freshwater is consumed, and less wastewater is discharged, as internal water mains are added to the network. When water mains are positioned at every contaminant concentration, water consumption is minimized, corresponding to the target using the limited water profile in the graphical design methods. However, additional internal water mains increase the complexity of the piping network, and consequently, the design is influenced by the tradeoff between the number of mains and water consumption and the corresponding wastewater treatment capacity. Stated differently, the economic optimum may involve a simpler network, with fewer water mains, having slightly larger water consumption. Also, while one or two internal mains usually simplify the water network, reducing water consumption, more complex networks having three or more internal mains are not recommended. With many potential internal water mains, designers must consider multiple sources of water for the unit processes. While some design strategies handle multiple water sources,5,11 no strategies have been reported for determining their contaminant concentrations. Consequently, design strategies, thus far, involve the retrofit of plants in which the contaminant concentrations of the water sources are fixed. For the design of new plants, or for retrofits of plants in which water reuse is not implemented effectively, it is important to position the water mains (that is, to select their contaminant concentrations) as discussed in this paper.

Table 1. Specifications for Example 1 process no.

mass load of contaminant (kg/h)

CIN,max (ppm)

COUT,max (ppm)

1 2 3 4

2 5 30 4

0 50 50 400

100 100 800 800

In this paper, designs involving only a single contaminant are considered. Work to extend the design methodology for multiple contaminants and to permit the use of regenerated water is underway. Furthermore, it is assumed that each water-using process has a contaminant load that must be removed entirely and that maximum values of its inlet and outlet contaminant concentrations have been specified. Design Procedure To begin, example 1 shows the design procedure. This example involves an internal water main whose contaminant concentration is specified, with it being assumed that concentration changes due to sources at lower concentration are negligible because the main (reservoir) is sufficiently large. Subsequently, in the next section, the design procedure is extended to address the positioning of internal water mains. The mass loads and terminal concentrations in example 1 are taken from Wang and Smith.2 Table 1 shows these specifications for the four unit processes. The water pinch occurs at the contaminant concentration, Cpinch ) 100 ppm, and the minimum freshwater required is 90 t/h. Design Steps. The design procedure is comprised of the following seven steps, subject to the two rules that follow, with steps 2-7 repeated as each internal water main is encountered, as discussed below. Step 1. Determine the concentration of the first internal water main, as discussed in the next section, with the number of the internal mains k ) 1. Step 2. Adjust the number of water mains, m ) 2 + k. Create a contaminant concentration diagram, with concentration increasing from left to right that includes a vertical line for each external or internal water main. As shown in example 1, three lines are positioned for (1) freshwater at 0 ppm, (2) an internal main at 100 ppm, and (3) wastewater at 800 ppm, the maximum outlet concentration of the unit processes. The concentrations are annotated above the lines. Step 3. Position a numbered box for each unit process between two of the water mains. Its maximum contaminant concentration in the inlet stream is greater than or equal to that of the water main to the left but lower than that of the main to the right, as shown in Figure 1. Step 4. Position arrows to represent the streams into and out of each unit process. The water sources originate in the mains at its left, as well as from the mains at its right having contaminant concentrations lower than its maximum outlet concentration. The arrow that represents the effluent stream from each unit process enters the main at its right having a concentration greater than or equal to the maximum contaminant concentration of its outlet stream. Step 5. Perform mass balances. For each unit process, the water balance is

FIN,i ) FOUT,i + Li

i ) 1, ..., P

(1)

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Fj )

Figure 1. Water network for example 1.

Here FIN,i and FOUT,i are the water flow rates of the inlet and outlet streams for unit process i, and Li is the water loss in unit process i. When Li is negative, water is generated in the process. Note that values of Li are specified before the water network is designed and P is the number of unit processes. The contaminant balances are

FIN,iCIN,i + Mi ) FOUT,iCOUT,i + LiCL,i

i ) 1, ..., P (2)

where C is the contaminant concentration and Mi is the mass load of contaminant to be removed in unit process i. The inlet mass balances for unit process i are M

FIN,i )

Fjfi ∑ j)1

i ) 1, ..., P

(3)

M

FIN,iCIN,i )

FjfiCj ∑ j)1

Cjfi e COUT,i,max

i ) 1, ..., P

j )1, ..., M; i ) 1, ..., P

(4) (5)

Cjfi e CIN,i,max for 1 or more sources, j ) 1, ..., M; i ) 1, ..., P (6) CIN,i e CIN,i,max COUT,i e COUT,i,max

i ) 1, ..., P i ) 1, ..., P

(7) (8)

where Fjfi and Cjfi are the water flow rate and concentration of the stream from water main j to unit process i. Note that in eq 5 all water mains that are sources for unit process i must have a contaminant concentration below its maximum outlet concentration. Consequently, water is recycled from a main when its concentration is equal to the maximum outlet concentration of the unit to which the water is supplied. In eq 6, at least one source for unit process i must have its contaminant concentration lower than or equal to its maximum inlet concentration. Step 6. Perform water balance for mains. For the external water main, which is assigned the subscript 1 and is usually the source of freshwater, the water consumption is P

F1 )

F1fi ∑ i)1

(9)

For the other mains, the rate of water accumulation is

P

Fjfi ∑ Fjrk - ∑ k)1 i)1

j ) 2, ..., M

(10)

where the subscript j r k denotes that water flows to main j from unit process k and the subscript j f i denotes that water flows from main j to unit process i. Step 7. Compare the water consumption, F1, with the water target; that is, the minimum freshwater required at the water pinch. When sufficiently close, accept the design. When far apart, consider positioning another internal main. In this case, let k ) k + 1,and repeat steps 2-7. During the design procedure, to attain minimum water consumption, two simple rules should be satisfied:5 Rule 1. Use external water sources only when internal water sources are not available, in either quality or quantity. Rule 2. Transfer exactly the amount of mass that needs to be transferred using water for each unit process. The design procedure begins with the unit processes in the first interval, between water mains 1 and 2. In the implementation of step 4, the usage of external water should be minimized. When a unit process has a maximum inlet concentration higher than that of main 1, water from mains having higher contaminant concentrations (j ) 2, 3, ...) should be added to the external water to achieve the maximum inlet concentration. Note that, to reduce the water flow rate, the outlet contaminant concentration for each unit process should reach its maximum. Using the mass balances (1-5), subject to the inequality constraints (5-8), the flow rates of water into and out of each unit process in interval 1 are determined. Having completed the balances for the first interval, the balances for the second interval are performed. Initially, main 2 is the water source. To reduce the demand on main 2, when possible, water is taken from mains at contaminant concentrations that exceed the maximum inlet concentration for each unit process, as was carried out in interval 1. Upon completing the balances for interval 2, eq 10 is used to determine the rate of water accumulation in main 2. When F2 > 0, water from mains having higher contaminant concentration is reduced until F2 ) 0 or no water flows from these mains to the unit processes in this interval. In the latter case, when F2 > 0, the excess water is transferred to a unit process in a higher interval (3, 4, ...) if possible, and when no unit processes demand water in higher concentration intervals, the excess water must be rejected to the wastewater main, as shown in Figure 1. When F2 < 0, water from the external source (usually freshwater) is added to reduce the rate of accumulation in main 2 to zero. Through repetition of steps 2-7 for each interval, the network is constructed. The rate of accumulation is annotated below the vertical line for each main. Then, M Fj, is the total rate of discharged wastewater, ∑j)2 computed. Note that, for the network in Figure 1, the freshwater target is met; that is, the minimum amount of freshwater is consumed. Determining the First Internal Water Main Concentration When positioning the water mains, the choice of the contaminant concentration for the first internal main

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Figure 2. Limiting composite curve of example 2.

Figure 4. Limiting composite curve for example 3. Table 3. Specifications for Example 3

Figure 3. Water network for example 2. Table 2. Specifications for Example 2 process no.

mass load of contaminant (kg/h)

CIN,max (ppm)

COUT,max (ppm)

1 2 3 4

6.25 15 7.5 14

0 50 150 300

250 300 400 500

is most important, because when set appropriately, it can give a simple network structure and guide the choice of the concentrations for the other mains. Furthermore, the first internal main should be positioned such that water flows to and from its main are sufficiently large. This is usually at or in the proximity of the pinch concentration, the point of zero driving force between the limiting composite curve and the freshwater line, at which the water flow rates are usually maximized. This is observed herein. In all of the examples presented, the pinch concentration is chosen for the first internal main except in example 2, where unit processes above the pinch concentration need no water. In such cases, the concentration of the contaminant in the first internal main should be set to the highest terminal concentration below Cpinch, as shown below. Example 2 is taken from Castro and co-workers.5 It involves four unit processes with mass loads and terminal concentrations in Table 2. As is shown on the limiting composite curve in Figure 2, the water pinch occurs at the contaminant concentration, Cpinch ) 400 ppm. The minimum freshwater required is 89.375 t/h.5 As discussed above, the contaminant concentration of the first internal main is set at 300 ppm, the highest outlet concentration below the pinch concentration. Using the design procedure, the network in Figure 3 is obtained. The water consumption and the wastewater discharge are at 94 t/h, 5% higher than the minimum, but the network is much simpler than that designed by Castro and co-workers.5 Some limiting composite curves have multiple pinch concentrations, as shown in example 3, which is taken from Savelski and Bagajewicz.14 This example involves

process no.

mass load of contaminant (kg/h)

CIN,max (ppm)

COUT,max (ppm)

1 2 3 4 5 6 7 8 9 10

2.0 2.88 4.0 3.0 30.0 5.0 2.0 1.0 20.0 6.5

25 25 25 50 50 400 200 0 50 150

80 90 200 100 800 800 600 100 300 300

10 unit processes with mass loads and terminal concentrations in Table 3. Although difficult to see on the limiting composite curve in Figure 4, water pinches occur at the contaminant concentrations, Cpinch ) 100 and 300 ppm. The minimum freshwater required is 166.3 t/h.14 In this case, the first pinch concentration, 100 ppm, is selected as the contaminant concentration for the first internal water main because more water flows to and from the main than when the second pinch composition, 300 ppm, is selected. The resulting water network, with this internal water main, is shown in Figure 5a. Its water consumption is 182.4 t/h, 10% higher than the minimum value. Further Reduction of Water Consumption and Wastewater Production With only one internal water main, water consumption and wastewater discharge are often higher than the minimum value. Hence, the designer should consider the tradeoff between further reducing water consumption and wastewater production at the cost of a more complex piping system that is more difficult to operate. To further reduce water consumption and wastewater discharge, the following strategies should be considered. Add Internal Water Mains. In general, additional internal water mains reduce water consumption and wastewater production, as long as each main is both a sink for and a source of water. When positioning an additional internal water main, it is important to recognize that the new main decreases the water from the next main to the left and the water to and from the next main to the right. This leads to two guidelines that are presented next with examples. (1) When sufficient water flows into an internal main [that is, the net flow rate (total inlet minus outlet) is positive], another main should be placed at the next lower terminal concentration, as shown in example 4 in Figure 6.

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Figure 6. Water network for example 4: (a) one internal water main; (b) two internal water mains. Table 4. Specifications for Example 4

Figure 5. Water network for example 3: (a) one internal water main; (b) two internal water mains.

Example 4 is taken from Olesen and Polley.10 It involves six unit processes with mass loads and terminal concentrations in Table 4. Using the limiting composite curve, the water pinch occurs at the contaminant concentration, Cpinch ) 100 ppm. The minimum freshwater required is 157.1 t/h. (2) When there is a shortage of water in the first internal main, F2 < 0, water is added from the external main such that F2 ) 0. Then, a second internal main is placed on the side of the first internal main that has the higher water demand. On the left side, the second main is positioned at the highest terminal concentration below the concentration of the first internal main, as shown for example 3 in Figure 5b. On the right side, the second main is positioned at the lowest terminal concentration above the concentration of the first internal main, as shown for example 5 below. Example 5 is taken from Savelski and Bagajewicz.14 It involves 20 unit processes with mass loads and terminal concentrations in Table 5. Using the limiting composite curve, the water pinch occurs at the contaminant concentration, Cpinxh ) 120 ppm. The minimum freshwater required is 299.4 t/h. Figure 7a shows the resulting design after the first internal water main has been added. Its water consumption at 373.5 t/h exceeds the minimum by 25%.

process no.

mass load of contaminant (kg/h)

CIN,max (ppm)

COUT,max (ppm)

1 2 3 4 5 6

2 5 4 5 30 4

25 25 25 50 50 400

80 100 200 100 800 800

Table 5. Specifications for Example 5 process no.

mass load of contaminant (kg/h)

CIN,max (ppm)

COUT,max (ppm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1.0 2.0 2.0 2.0 2.88 1.5 3.0 4.0 4.0 10.0 8.0 1.8 20.0 6.5 2.0 30.0 5.0 7.0 2.55 0.6

0 0 0 25 25 40 50 75 25 75 120 200 75 150 200 50 400 400 600 800

80 100 120 80 90 90 100 120 200 150 200 300 300 300 600 800 800 500 850 950

When a second internal main is added, the water consumption is reduced to 325.8 t/h, as shown in Figure 7b. This exceeds the minimum by only 9%.

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Figure 7. Water network for example 5: (a) one internal water main; (b) two internal water mains with a local pipe; (c) two internal water mains without a local pipe; (d) outlet concentration shift.

When additional internal mains are considered, the two guidelines are generalized accordingly. Local Pipe Layout. While internal water mains are intended to simplify the piping system, the alternative of placing pipes between the unit processes should not be overlooked. Usually the addition of local pipes within an interval can reduce water consumption. These function like an internal water main, often obviating the need for such a main. As an example, observe that the water main at 80 ppm in example 4 is actually a local

pipe from unit process 1 to unit process 5, as shown in Figure 6b. Also, in example 5, Figure 7b shows that a local pipe from unit process 14 to unit process 18 saves 8.9 t/h of freshwater, compared with the water consumption for the network without a local pipe in Figure 7c. Note, however, that many local pipes tend to complicate the networks. Outlet Concentration Shifting. Usually, water consumption is reduced when the outlet concentration for each unit process is at its maximum. However, when

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the water demand from an internal main exceeds the total flow rate of the effluent streams sent to it, the possibility of reducing one or more of the outlet concentrations should be considered. Unit processes having maximum outlet concentrations slightly higher than the concentration of the main should be considered first. This is illustrated in example 5, in which the outlet concentration from unit process 10 is reduced from 150 to 120 ppm, permitting its water effluent to be supplied to the main at 120 ppm. As a result, water consumption is decreased from 373.5 t/h (Figure 7a) to 344.2 t/h (Figure 7d) without an additional water main. Conclusions The new network structure, in which internal water mains (reservoirs) are introduced, is shown to provide simpler water networks for plants involving many unit processes, such as those in petrochemical and chemical complexes. The new design procedure, which has been applied to five example plants, shows that water networks having just one internal main at the pinch concentration sharply reduce water consumption, approaching the minimum. When the procedure is generalized to add one or more internal water mains, a savings in water consumption is obtained. However, in the examples herein, the use of local pipes and outlet concentration shifts also provides water reductions, often obviating the need for a second internal water main. While the new design procedure involves mass balances only, it shows effectively how to design networks of process units that reduce water consumption. This procedure decouples the design of the unit processes from the design of the network. Literature Cited (1) Takama, N.; Kuriyama, T.; Shiroko, K.; Umeda, T. Optimal Water Allocation in a Petroleum Refinery. Comput. Chem. Eng. 1980, 4, 251-258.

(2) Wang, Y. P.; Smith, R. Wastewater Minimization. Chem. Eng. Sci. 1994, 49, 981-1006. (3) Wang, Y. P.; Smith, R. Wastewater Minimization with Flowrate Constraints. Trans. Inst. Chem. Eng. 1995, 73, Part A, 889-904. (4) Kuo, W. C. J.; Smith, R. Designing for the Interactions Between Water-use and Effluent Treatment. Trans. Inst. Chem. Eng. 1998, 76, Part A, 287-301. (5) Castro, P.; Matos, H.; Fernandes, M. C.; Nunes, C. P. Improvements for Mass-exchange Networks Design. Chem. Eng. Sci. 1999, 54, 1649-1665. (6) Huang, C.-H.; Chang, C.-T.; Ling, H.-C.; Chang, C.-C. A Mathematical Programming Model for Water Usage and Treatment Network Design. Ind. Eng. Chem. Res. 1999, 38, 2666-2679. (7) Alva-Argaez, A.; Vallianatos, A.; Kokossis, A. A Multicontaminant Transshipment Model for Mass Exchange Networks and Wastewater Minimization Problems. Comput. Chem. Eng. 1999, 23, 1439-1453. (8) Bagajewicz, M. J.; Rivas, M.; Savelski, M. J. A New Approach to the Design of Utilization Systems with Multiple Contaminants in Process Plants. Annual AIChE Meeting, Dallas, TX, 1999. (9) Bagajewicz, M. J.; Rivas, M.; Savelski, M. J. A Robust Method to Obtain Optimal and Sub-optimal Design and Retrofit Solutions of Water Utilization Systems with Multiple Contaminants in Process Plants. Comput. Chem. Eng. 2000, 24, 14611466. (10) Olesen, S. G.; Polley, S. G. A Simple Methodology for the Design of Water Networks Handling Single Contaminants. Trans. Inst. Chem. Eng. 1997, 75, Part A, 420-426. (11) Polley, G. T.; Polley, H. L. Design Better Water Networks. Chem. Eng. Prog. 2000, 96, Feb, 47-52. (12) Savelski, M.; Bagajewicz, M. A New Algorithmic Design Procedure for the Design of Water Utilization Systems in Refineries and Process Plants. Proceedings of PRESS 99 Meeting, Budapest, 1999. (13) Polley, G. T.; Heggs, P. J. Don’t Let the Pinch Pinch You. Chem. Eng. Prog. 1999, 95, Dec, 27-36. (14) Savelski, M.; Bagajewicz, M. Algorithmic Procedure to Design Water Utilization Systems in Refineries and Process Plants. Chem. Eng. Sci. 2000, submitted for publication.

Received for review September 22, 2000 Revised manuscript received September 13, 2001 Accepted September 24, 2001 IE000835I