Two-Step Methodology for Retrofit Design of Cooling Water Networks

Article pubs.acs.org/IECR

Two-Step Methodology for Retrofit Design of Cooling Water Networks Yufei Wang,*,† Khim Hoong Chu,‡ and Zhuofeng Wang† †

State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, China Department of Chemical Engineering, Xi’an Jiaotong University, Xi’an 710049, China

‡

ABSTRACT: Conventional cooling water networks usually operate in a parallel configuration. Converting a parallel design to a series arrangement can yield a significant reduction in fresh cooling water consumption because of water reuse. This paper presents a two-step methodology for retrofit design of cooling water networks. The proposed methodology can convert a parallel configuration to a series arrangement without investment in a new heat-transfer area. The series arrangement is assumed to contain two heat exchangers. The first heat exchanger in the series arrangement is designated as the supplier because it supplies reuse water to the second heat exchanger, which is called the receiver. To retrofit a cooling water network with a parallel arrangement of several heat exchangers, the first step of the methodology uses the concept of flow rate difference curve to classify the heat exchangers into the two categories of supplier and receiver. In the second step, receiver sensitivity graphs provide guidelines for systematic matching of the suppliers and receivers. A case study is presented to illustrate the practical utility of the two-step methodology. water saving across plants. Boix et al.10 considered the simultaneous optimization of water and heat systems. In many industry sectors, a recirculating cooling water system is a typical water-using system that uses large quantities of freshwater as makeup water. A typical recirculating cooling water system includes a cooling water network, a cooling tower, and a pumping system. In the chemical process industries, a cooling water network is a set of heat exchangers that transfer the waste heat from hot process streams to a cooling water utility. A grassroot design method developed by Kim and Smith11 considers the interaction between the cooling water network and the cooling tower in a recirculating cooling water system. However, the minimum cooling water flow rate determined by the design method cannot guarantee the minimum cost. Panjeshahi et al.12 extended the grassroot design method of Kim and Smith11 by developing a methodology based on a combination of pinch technology and mathematical programming. This method allows energy and water consumption to be optimized simultaneously to minimize the overall cost. PonceOrtega et al.13 proposed an optimization model for the simultaneous synthesis and detailed design of recirculating cooling water systems. In their work, pressure drop can be considered in the optimization process. Retrofit of a cooling water network is an important way to reduce water consumption in an existing plant. So far, very few studies have focused on the retrofit of a cooling water system. Kim and Smith11 investigated a number of debottlenecking situations based on their grassroot design methodology. A subsequent study by the same group14 proposed a mathematical programming methodology for retrofit design of recirculating

1. INTRODUCTION Water is a very important resource that is widely used in industrial activities. With the increasing awareness of sustainability through resource conservation, many regulations have been introduced to restrict industrial water consumption. Therefore, it is of importance for industry to adopt efficient water-using systems that minimize freshwater usage. The well-known concept of pinch analysis initially developed for heat exchanger network design has been adapted to tackle a variety of wastewater minimization problems.1−3 These pinchbased methodologies can provide physical insights and optimal design of water-using systems but sometimes generate very complex water-using networks, restricting their practical application in industry. Moreover, pinch-based methodologies are relatively difficult in solving multicomponent systems. The other classical methodology for optimizing an industrial water system is mathematical programming. Doyle and Smith4 proposed a methodology to solve a multicomponent water system based on an assumption that all contaminants are at their maximum outlet concentration. Both linear programming (LP) model and nonlinear programming (NLP) model are used in this method. Alva-Argáez et al.5 combined the water-pinch analysis together with mathematical programming tools to minimize freshwater consumption. By using mathematical programming, the optimal design can be obtained automatically, but the global optimal solution might not be acquired when the problem is complex and the black box model lacks physical insights. Water cascade analysis was proposed by Manan et al.;6 this method can be used to obtain the minimum freshwater and wastewater targets for both mass-transfer-based and non-mass-transferbased networks of single contaminant. More recently, water systems with internal water mains have been considered in the work of Ma et al.7 Water systems integrated with process models were optimized in the study of Deng et al.8 Chew et al.9 optimized several water systems by considering the feasibility of © 2013 American Chemical Society

Received: Revised: Accepted: Published: 274

March 20, 2013 October 12, 2013 December 6, 2013 December 6, 2013 dx.doi.org/10.1021/ie400906r | Ind. Eng. Chem. Res. 2014, 53, 274−286

Industrial & Engineering Chemistry Research

Article

An overview of the two-step design methodology is given as follows. (1) Determine the matching of heat exchangers. (2) Determine the sequence of heat exchanger connection in series arrangement. (3) Calculate fresh cooling water requirement that can maintain the heat duty of each heat exchanger. (4) Calculate the total fresh cooling water requirement of the entire system. (5) Determine the network structure of the retrofit design.

cooling water systems. The optimization problem is formulated as a mixed-integer nonlinear programming (MINLP) model that considers pressure drop constraints, performance of cooling tower, and water consumption. Although some systematic methods have been proposed for the design and retrofit of cooling water systems, as noted above, most are limited in scope and suffer from some deficiencies. For example, the aforementioned retrofit methodologies, which have been derived from grassroot design methodologies, often ignore the specific characteristics of the existing cooling water network. Also, the final design often involves too many modifications to both the network structure and the individual exchangers. Importantly, most of these methods ignore the impact of the change in cooling water flow rate on heat transfer in heat exchangers. In practice, it is undesired to make too many modifications when retrofitting existing cooling water systems. As such, this work presents a systematic methodology to reduce freshwater consumption in a cooling water system without adding any additional heat-transfer area to its cooling water network. The opportunities for reducing water consumption by modifying the pipe lines only are explored first. Also, the cooling water savings potential for each individual heat exchanger is analyzed. A twostep methodology is then used to generate the optimal retrofit design of the cooling water network.

3. RETROFIT DESIGN METHODOLOGY FOR COOLING WATER NETWORKS Conventional design of heat exchangers in cooling water networks is often based on parallel configurations. In a parallel configuration, fresh cooling water is supplied directly to each individual heat exchanger. The hot cooling water exiting the heat exchangers is returned to the cooling tower. Parallel configurations allow every hot stream to be cooled with cooling water at the supply temperature, but cooling water consumption is maximized because there is no water reuse. Changing the exchanger arrangement from parallel to series allows cooling water to be reused in heat exchangers that do not require cooling water at the supply temperature. The overall flow rate of cooling water is therefore reduced.11 This work focuses on the use of series arrangements in retrofit design of cooling water networks. For simplicity, it is assumed that a series arrangement consists of only two heat exchangers. When the exchanger arrangement is changed from parallel to series in retrofit design, the second heat exchanger in the series arrangement will be affected because the inlet temperature of cooling water changes from the supply temperature to the outlet temperature of cooling water from the first heat exchanger. With the increase of cooling water inlet temperature, the temperature difference in the second heat exchanger decreases, resulting in a reduction in the heat-transfer driving force. It is known that the heat exchanged in an exchanger depends on the log mean temperature difference (ΔTLM), overall heat-transfer coefficient (U), and heat-transfer area (A), as shown in eq 1. Normally, the reduction in the heat-transfer driving force is compensated by using additional area or even new heat exchangers. However, adding additional area will result in a higher retrofit investment. Therefore, retrofit design without adding additional area or new heat exchangers is desired.

2. PROBLEM STATEMENT The two-step methodology proposed in this paper considers implications brought by changes in cooling water flow rate when modifying heat exchanger arrangement from parallel to series. In particular, the effects of cooling water flow rate, stream temperatures, and heat-transfer coefficients for each heat exchanger before and after modifying the heat exchanger arrangement are considered, as well as the position of the heat exchanger in a network. Changing the configuration of heat exchangers from parallel to series will decrease the total cooling water flow rate but increase the cooling water flow rate for each individual heat exchanger. The increase in flow rate will result in a higher heat-transfer coefficient so that the heat-transfer driving force in the heat exchanger may be large enough to fulfill the heat duty without applying any additional area. In general, the heat-transfer driving force depends on the stream temperatures, the initial heattransfer coefficients for both sides, and the initial flow rate of cooling water. The major aim of this work is to explore the use of series arrangements in retrofit design of cooling water networks which are often based on parallel configurations. The series arrangement is assumed to contain two heat exchangers. The design methodology aims to maximize the cooling water savings potential and optimize the heat exchanger network structure. Because the retrofit design avoids the need for additional heattransfer area which could pose significant installation problems in an existing network, the cost of retrofit is greatly reduced. In most cases, only some additional pipelines for heat exchanger connection are required, making the retrofit work relatively simple and cheap. To develop the two-step methodology for retrofit design of cooling water networks, the following information is assumed to be given: (1) exchanger data (i.e., area, heat-transfer coefficients, and heat duty), (2) stream data (i.e., flow rates, inlet and outlet temperatures, and heat capacity), and (3) the initial network structure based on a parallel configuration.

Q = UAΔTLM

(1)

3.1. Retrofit Design without Adding Additional Area. When the exchanger arrangement is changed from parallel to series, for the second heat exchanger not only the temperature difference changes but also the flow rate of cooling water. When two heat exchangers (HE 1 and HE 2) are arranged in parallel (Figure 1), the total flow rate Fp for this system is the sum of the flow rates in two branches (F1,p, F2,p), as shown in eq 2. When the exchanger arrangement is changed from parallel to series, one

Figure 1. Parallel and series exchanger arrangements. 275

dx.doi.org/10.1021/ie400906r | Ind. Eng. Chem. Res. 2014, 53, 274−286


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series (F2,S + Fx > F2,p), the heat-transfer coefficient of the cooling water side will also increase. Therefore, the reduction in the heattransfer driving force due to temperature difference reduction can be compensated for by adjusting the total cooling water flow rate of the second exchanger in series rather than by implementing additional area. As such, it is possible to modify the heat exchanger arrangement from parallel to series without having to add any additional area or new heat exchangers.

pipe line is connected between the cooling water outlet in HE 1 and the inlet side of cooling water in HE 2 (Figure 1). Equation 3 gives the total flow rate Fs for this arrangement while eq 4 defines the total flow rate in HE 2 (F2), where F1,s and F2,s indicate the fresh cooling water flow rate of HE 1 and HE 2 in series arrangement, respectively, and Fx denotes the flow rate of reuse water. Fp = F1,p + F2,p

(2)

Fs = F1,s + F2,s

(3)

F2 = Fx + F2,s

(4)

4. SENSITIVITY ANALYSIS FOR FRESH COOLING WATER REDUCTION IN AN INDIVIDUAL HEAT EXCHANGER Kotjabasakis and Linnhoff18 pointed out that when a design change is made in a heat exchanger network, all of the downstream elements in the network will be affected, and the influence is called passive response. Their heat exchanger model is used in this paper to predict the change in heat exchanger performance after modification. The model is shown in eqs 13−16. By using this model, the duty of a heat exchanger can be calculated with known values of (UA), CPh, CPc, and two out of the four temperatures.

From eqs 2−4, it is clear that Fx lies between 0 and F1,s. Because of water reuse, the requirement of fresh cooling water by HE 2 is reduced, which means F2,s is smaller than F2,p. Because no changes are made to HE 1, it follows that F1,p is equal to F1,s. The total fresh cooling water flow rate of the series arrangement is thus smaller than that of the parallel arrangement. These flow relations are summarized in eqs 5−8. 0 ≤ Fx /F1,s ≤ 1

(5)

F2,s ≤ F2,p

(6)

F1,s = F1,p

(7)

Fs ≤ Fp

(8)

(1 − RB)Th,out + (B − 1)RTc,in + (R − 1)Th,in = 0

R(1 − RB)Tc,out + (B − 1)RTh,in + (R − 1)BRTc,in = 0 (14)

where

According to detailed shell and tube heat exchanger models,15,16 change of fluid velocity will exert a great impact on the heat-transfer coefficients for both shell and tube sides. The work of Nie and Zhu17 gives simple correlations between fluid velocity and heat-transfer coefficients, which are shown in eqs 9 and 10. Because fluid velocity is directly proportional to flow rate, the correlations can easily be expressed in terms of flow rate. The new correlations considering the change in flow rate before and after modifying heat exchanger arrangement are shown in eqs 11 and 12. Choosing the appropriate correlation depends on which side the cooling water goes. ⎛ v ⎞0.8 hi = ⎜⎜ i ⎟⎟ h i,0 ⎝ vi,0 ⎠

(tube side)

⎛ v ⎞0.6 ho = ⎜⎜ o ⎟⎟ ho,0 ⎝ vo,0 ⎠

(shell side)

⎛ F ⎞ ho = ⎜⎜ o ⎟⎟ ho,0 ⎝ Fo,0 ⎠

R=

CPc CPh

(15)

B = exp[(UA /CP)( c R − 1)]

(16)

where CP is stream capacity flow rate, T is stream temperature, subscripts c and h denote the cold stream and hot stream in a heat exchanger, respectively, and subscripts in and out indicate the inlet side and outlet side of a stream in a heat exchanger, respectively. In a cooling water system, the duty of each heat exchanger must be maintained. This should be taken into account when minimizing cooling water consumption. In the example shown in Figure 2, two heat exchangers are arranged in series. The duty of

(9)

(10)

0.8 ⎛ F ⎞0.8 ⎛ F2,s + Fx ⎞ hi i ⎟⎟ = ⎜⎜ ⎟⎟ = ⎜⎜ h i,0 ⎝ Fi,0 ⎠ ⎝ F2,p ⎠

0.6

(13)

⎛F + F ⎞ 2,s x ⎟⎟ = ⎜⎜ ⎝ F2,p ⎠

(tube side) (11)

Figure 2. Heat exchangers in series.

0.6

(shell side)

the first heat exchanger HE 1 is unaffected because the cooling water flow rate F1,s is kept constant. The main objective is to reduce fresh cooling water consumption by minimizing flow rate F2,s without affecting the duty of the second heat exchanger HE 2. There are a number of exchanger and stream variables that can affect the minimum flow rate of F2,s significantly, so it is necessary to explore the interactions between these variables and cooling water consumption. We define water saving efficiency in terms of the parameter ε, which can be calculated from eq 17. εmax is the maximum water saving efficiency when minimum flow rate F2,s is achieved. The first exchanger in the series arrangement is

(12)

where v indicates fluid velocity, h is heat-transfer coefficient, subscript 0 means initial value, and subscripts o and i denote shell and tube side, respectively. Because of the increase in inlet temperature of cooling water in HE 2 after changing heat exchanger arrangement from parallel to series, additional area is required to accommodate the heat duty requirement of HE 2 in conventional design methodologies. From eqs 11 and 12, it can be deduced that if there is an increase in the cooling water flow rate of the second exchanger (HE 2) in 276



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Table 1. Exchanger Data for Example 1 duty (kW)

area (m2)

ho (W/(°C·m2))

hi (W/(°C·m2))

Th,in (°C)

Th,out (°C)

Tc,in (°C)

Tc,out (°C)

2000 2000

92.4 92.4

1000 1

1000 1

90 90

50 50

20 20

30 30

HE 1 HE 2

computed from eq 20 while rT from eqs 13−16 when U is known. At the intersection point of the two curves (indicating rU = rT), ε is equal to εmax, as shown in Figure 3. In Figure 3, it can be seen that εmax is 0.52. Also, rU decreases with increasing ε because of reduction in the total flow rate of cooling water. By contrast, rT is largely insensitive to ε. It decreases slightly with increasing ε when ε is relatively small and increases slightly with increasing ε when ε is relatively large. The reasons for the observed tend in rT are quite complex. Basically, rT is affected by three main factors, Tc,in, CPc, and U. An increase in the inlet temperature or heat-transfer coefficient will reduce rT while an increase in the heat capacity flow rate will enhance rT. The basic idea of this work is to utilize an increment in U (due to increased cooling water flow rate) to compensate for reduction in ΔTLM when the series arrangement is adopted so that the heat exchanger duty remains unchanged, as shown in eq 1. Figure 3 indicates that the profiles of rU and rT are rather different. In some regions, a reduction in ΔTLM can be compensated for by an increase in U but in some other parts this is not possible. It is evident that the relative positions of the two curves will lead to different εmax values. It may be seen that a higher rU curve or a lower rT curve can lead to a higher εmax. The factors that affect the respective position of rU and rT curves are discussed next. 4.2. Relation between εmax and Fx/F1,s. The first factor considered is the flow rate of reuse water. It is obvious that cooling water leaving a supplier will have a higher temperature than fresh cooling water. Accordingly, an increase in the value of Fx/F1,s will lead to an increase in the cooling water inlet temperature of a receiver, resulting in a reduction in the heattransfer driving force. However, an increase in Fx/F1,s means a larger inlet flow rate of cooling water, which will result in a rise in heat-transfer coefficients, enhancing heat transfer. Therefore, it is of interest to examine the effect of Fx/F1,s on εmax. Figure 4 illustrates a set of rU and rT curves calculated using example 1 data for a range of Fx/F1,s values. Each solid circle in Figure 4 indicates the intersection point of a pair of rU and rT curves for a given Fx/ F1,s value, giving the value of εmax. It can be seen that εmax decreases with decreasing Fx/F1,s. Figure 4 shows that the rU

designated as supplier because it supplies reuse water to the second exchanger, which is called receiver.

ε=

F2,p − F2,s F2,p

(17)

4.1. Determination of εmax. When the exchanger arrangement is changed from parallel to series, the input variables of HE 2 (Figure 2) that are affected are the cooling water inlet temperature (Tc,in) and the cooling water flow rate. The change in the flow rate of HE 2 will in turn affect the overall heat-transfer coefficient (U) of HE 2 and the heat capacity flow rate (CPc) of cooling water in HE 2. From eq 1, it can be seen that if the exchanger area is a constant, the product of U and ΔTLM must remain unchanged in order to maintain the same heat duty Q after changing the network design from parallel to series arrangements (see eq 18). Equation 18 is rearranged as eq 19, which introduces two new parameters: rU and rT. The former is a ratio of new U to initial U while the latter is a ratio of initial ΔTLM to new ΔTLM. When rU equals rT, the duty of heat exchanger is maintained, and εmax can be found. In other words, according to eq 1, when the heat exchanger area is fixed, the change in U and ΔTLM must be the same in order to maintain the same heat exchanger duty. U0ΔTLM0 = U ΔTLM

rU ≡

ΔTLM0 U = ≡ rT U0 ΔTLM

1 1 1 = + U ho hi

(18)

(19)

(20)

A simple example will be used here to illustrate how εmax can be computed. This example, called example 1, has two identical heat exchangers, and the exchanger data are shown in Table 1. It is assumed that cooling water flows through the tube side in both heat exchangers. To determine εmax, two curves are plotted in Figure 3: one is the relation between ε and rU; the other, the relation between ε and rT. Both rT and rU values are calculated through eqs 11−16 and 18−20. By using eqs 11 and 12, the heattransfer coefficient of the cooling water side after modifying the exchanger arrangement can be calculated. rU can then be

Figure 3. Determination of εmax for example 1.

Figure 4. Effect of Fx/F1,s on εmax. 277



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4.4. Relation between εmax and ΔTLM. The third factor affecting the respective position of rU and rT curves is the temperature difference in the heat exchanger. Equation 21 shows how ΔTLM can be calculated. The nature of natural logarithm dictates that ΔTLM is sensitive to the smaller one of the two ΔT1 and ΔT2 terms. The smaller ΔT term is thus termed the sensitive side. In a typical heat exchanger, the heat capacity of cooling water (Cp,c) is normally larger than that of the hot stream, so ΔT2 is usually the sensitive side. When the sensitive side in a receiver is very small, changing the exchanger arrangement from parallel to series cannot reduce fresh water consumption. It has been mentioned that series arrangements will increase both Tc,in and the flow rate of cooling water in a receiver. Both factors will affect the rT curve, as discussed below.

reduction span is larger than the rT reduction range which explains why εmax decreases with decreasing Fx/F1,s. In Figure 4, the dashed lines indicate rU curves and the continuous ones represent rT curves. The figure shows that a maximum εmax is obtained when Fx/F1,s = 1, suggesting that the entire cooling water flow leaving a supplier should go to a receiver. Normally, an increase in Fx/F1,s will lead to an increase in U. The magnitude of the increase in U is usually larger than the extent of reduction in ΔTLM, causing the receiver to have a higher heat-transfer driving force. It should however be noted that under some extreme conditions of a receiver, such as the heattransfer coefficient on the cooling water side is very large compared with that on the other side or the temperature difference is very small, the condition of Fx/F1,s = 1 may not lead to a maximum εmax. Under such conditions changing the exchanger arrangement from parallel to series will not result in any beneficial effect. These issues are explored further as follows. 4.3. Relation between εmax and the Heat-Transfer Coefficient on the Cooling Water Side (hc). The second factor that affects the respective position of rU and rT curves is the heat-transfer coefficient on the cooling water side. For simplicity, U can be represented as a function of the tube side film coefficient hi and the shell side film coefficient ho, as shown in eq 20. The fouling coefficients are included in hi and ho because for steadystate situation they do not change with time. In addition, the heat-transfer coefficient for the tube wall is ignored. Equation 20 indicates that U is less than either of the two coefficients. If the two film coefficient values are very different, U tends to be closer to the smaller one. The side with the smaller heat-transfer coefficient is called the controlling side. Therefore, when the cooling water side is the controlling side in a receiver, changing heat exchanger arrangement will exert a larger impact on U, resulting in a higher εmax. As such, if hc is far greater than that on the other side in the receiver, changing arrangement from parallel to series cannot reduce water consumption. To illustrate this point, Figure 5 shows the effect of hc on rU for example 1.

ΔTLM =

ΔT1 − ΔT2

( )

(21)

ΔT1 = Th,in − Tc,out

(22)

ΔT2 = Th,out − Tc,in

(23)

ln

ΔT1 ΔT2

First, we examine the effect of Tc,in on rT. The data for example 1 are used here. The cooling water outlet temperature of HE 1 (Tc,in of HE 2) is changed from 25 to 40 °C. The resulting rT curves are shown in Figure 6. It is clear that the rT curve moves

Figure 6. Effect of cooling water inlet temperature of HE 2 on rT curves.

upward with increasing Tc,in. This will lead to a smaller εmax, indicating a smaller reduction in fresh cooling water consumption. Note that the trends of rT curves are rather different. When the cooling water inlet temperature of HE 2 is 40 °C, rT increases monotonically with increasing ε. By contrast, when the cooling water inlet temperature of HE 2 is 25 °C, rT decreases monotonically with increasing ε. rT is affected by different factors. When the temperature is high, e.g., 40 °C, the sensitive side of ΔTLM is very small, so the temperature factor exerts the greatest influence on the profile of rT. Because U decreases with increasing ε, the heat exchanger duty decreases, resulting in a rise in ΔTLM. On the other hand, when the temperature is low, e.g., 25 °C, the sensitive side of ΔTLM is no longer small. Under such conditions U becomes the controlling factor. Based on the above discussion, it is concluded that a low cooling water outlet temperature of a supplier, which is equivalent to a low cooling water inlet temperature of a receiver, coupled with a high receiver hot side outlet temperature can promote a significant reduction in fresh cooling water consumption. 4.5. Effect of Cooling Water Flow Rate on εmax. The last factor to be discussed is the flow rate of heat exchangers. As can

Figure 5. Effect of hc (W/(°C·m2)) on rU curves.

This time, we change hc for HE 2 in the example from its initial value of 1000 W/(°C·m2) to a range from 600 to 3000 W/(°C· m2). To maintain a constant value of 500 W/(°C·m2) for U, a corresponding change is made to the heat-transfer coefficient on the other side. In accordance with the discussion above, Figure 5 shows that the rU curve moves downward with increasing hc. Therefore, it can be concluded that the cooling water side should be the controlling side in a receiver in order to reduce cooling water consumption if the design configuration is converted from parallel to series arrangements. 278



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Figure 7. Effect of cooling water flow rate Fx (kg/s) on εmax.

be deduced from eqs 11 and 12, U of a receiver depends on the ratio of (F2,s + Fx) to F2,p. Because different receivers in a network have different F2,p, and different suppliers provide different Fx, the minimum value of F2,s for different sets of supplier−receiver can be quite different, indicating that they could have different εmax. The data for example 1 are again used here to examine the effect of cooling water flow rate on εmax. In this analysis, the cooling water outlet temperature of HE 1 is kept constant; all the cooling water that flowed out of HE 1 is delivered to HE 2 so that we have F1,s = Fx. And Fx is changed from 12 to 95.7 kg/s. The results are shown in Figure 7, which indicate that εmax of HE 2 (denoted by solid circles) increases with increasing Fx. A larger Fx from a supplier leads to a larger εmax for its receiver. In the figure, it can be seen that when Fx = 95.7 kg/s, the rU curve is always higher than the corresponding rT curve, resulting in the maximum value of 1 for εmax. At this particular or higher Fx value, HE 2 does not need to use any fresh cooling water. The two rU and rT curves are denoted by the dashed curves in Figure 7. 4.6. Sequence of Exchanger Connection. From the foregoing analysis, given that cooling water flow rate exerts a significant impact on εmax, it is important to determine the best sequence of connecting two exchangers with different cooling water flow rates in a series arrangement. This will be explored by example 2. The data for this example are shown in Table 2. The

The results show that when HE 1 is the supplier in the series arrangement, εmax for HE 2 (receiver) is 0.78 and a reduction in fresh cooling water consumption of 37.3 kg/s is obtained. Inferior results are obtained when the sequence of exchanger connection is reversed. When HE 2 is the supplier, the calculation yields a smaller εmax of 0.34 for HE 1 (receiver) and a smaller reduction in fresh water consumption of 24.7 kg/s. The different results can be easily explained. When HE 1 with the fresh cooling water flow rate of 71.8 kg/s is the supplier, the cooling water inlet flow rate of the receiver HE 2 is also 71.8 kg/s. This flow rate is much larger than the fresh cooling water flow rate of HE 2 which is 47.8 kg/s. As a result, even if there is no fresh cooling water used in HE 2, the cooling water sent from HE 1 to HE 2 is able to enhance heat transfer in HE 2. By contrast, when HE 2 is the supplier, its smaller cooling water flow rate is unable to boost heat transfer in the receiver HE 1 when its fresh cooling water is not used. Figure 8 shows the rU curves for the two

Table 2. Exchanger Data for Example 2 HE 1 HE 2

duty (kW)

area (m2)

Fcooling water (kg/s)

3000 2000

138.6 92.4

71.8 47.8

Figure 8. rU curves for different exchanger sequences.

different sequences of exchanger connection. It can be seen that placing HE 1 first in the series arrangement gives a higher rU curve, indicating better enhancement in heat transfer. It is clear that the exchanger with the larger cooling water flow rate should be the supplier in a series arrangement of two exchangers in order to achieve a larger reduction in fresh cooling water consumption. 4.7. No Intersection between rU and rT Curves. Besides the situations mentioned previously, in some cases there is no

temperatures and heat-transfer coefficients are the same as those used in example 1 (see Table 1). In this example, HE 1 has larger heat duty, heat-transfer area, and cooling water flow rate than HE 2. The flow rates of HE 1 and HE 2 listed in Table 2 refer to their fresh cooling water flow rates when they are in parallel arrangement. In the calculation, it is assumed that all the cooling water flowed out of the supplier is delivered to the receiver. 279



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intersection between the rU and rT curves. Two such cases are depicted in Figure 9. The set 1 pair of rU and rT depicts the

of two heat exchangers. Based on the results, it can be concluded that the receiver should have a high hot stream temperature and a small cooling water side heat-transfer coefficient while the supplier should have a high cooling water flow rate and a low cooling water outlet temperature. To effectively reuse the cooling water of the supplier, the supplier and receiver must be carefully selected and matched. A two-step methodology is proposed here to carry out the selection and matching process in a systematic manner. 5.1. Step 1: Identifying Receivers and Suppliers. A conventional cooling water network is typically made up of several heat exchangers or coolers in parallel arrangements. Here we describe a systematic two-step methodology for retrofit design of such networks. A new problem (example 3) will be used to illustrate the proposed methodology. The first step involves classifying a set of exchangers into suppliers and receivers by using graphical tools named supply resource curve and receiver requirement curve. The cooling water network in example 3 has four heat exchangers. The temperature, heat-transfer coefficient, and duty of hot and cold streams are given in Table 3. To construct the curves for example 3, the four heat exchangers are ranked in ascending order of hot stream outlet temperature. The ranking order is as follows: E2, E1, E4, and E3. Consideration of the temperature implication suggests that the top ranked exchanger (E2) is the least preferred receiver while the bottom ranked exchanger is the most preferred one (E3). Also, given that small heat-transfer coefficients are controlling, exchangers with the smallest hot side heat-transfer coefficient should be ranked as high as possible. To take this into consideration, the previous ranking order may be adjusted accordingly. However, in this example E1 with the smallest hot side heat-transfer coefficient (600 W/(m2·°C)) is already ranked second; elevating E1 to the top position would not make a discernible difference. With the ranking order in place, it is assumed that all of the heat exchangers are suppliers and their individual outlet cooling water flows are mixed into one stream. The flow rate and temperature of the mixed stream can be calculated from eqs 24 and 25.

Figure 9. No interaction between rU and rT curves.

scenario whereby the entire rU curve lies above the rT curve. Such a scenario is ideal for reducing fresh cooling water consumption because the receiver does not need any fresh cooling water. However, as mentioned previously, the basic idea of this work is to utilize increased U value (due to increased cooling water flow rate) to compensate for decreased temperature difference (ΔTLM) so that the receiver duty remains unchanged (see eq 1). In the case of the set 1 curves, it is evident that εmax = 1 for the receiver and there is still an excess of cooling water. In this situation, the surplus cooling water may be diverted to another receiver in the network, as shown in Figure 10. The set 2 pair of rU

Figure 10. Heat exchangers in a mixed arrangement.

NS

and rT in Figure 9 illustrates another scenario whereby the entire rU curve lies below the rT curve. This situation must be avoided because changing the exchanger arrangement from parallel to series will not result in any reduction in fresh cooling water consumption.

Fmixed =

∑ Fj (24)

j=1

N

Tmixed =

5. TWO-STEP METHODOLOGY FOR RETROFIT DESIGN OF COOLING WATER NETWORKS The above sensitivity analysis describes in considerable detail the relations between the cooling water saving performance and the characteristics of the receiver and supplier in a series arrangement

∑ j =S 1 Fj·Tj ,c,out N

∑ j =S 1 Fj

(25)

where NS is the number of exchangers, j is the index for the stream that participated in mixing. The mixed stream is called the supplier resource.

Table 3. Exchanger Data for Example 3 exchanger no.

side

Tin (°C)

Tout (°C)

heat-transfer coefficient (W/(m2·°C))

flow rate (kg/s)

duty (kW)

area (m2)

E1

cold hot cold hot cold hot cold hot

20 60 20 45 20 80 20 75

23 45 25 30 30 60 28 50

1200 600 1100 1000 1000 800 1200 1200

95.7

1200

98.0

38.3

800

105.9

35.9

1500

75.3

26.9

900

39.6

E2 E3 E4

280



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rate of the supplier resource and the flow rate of the receiver requirement. Accordingly, a flow rate difference curve plot may be conveniently constructed by utilizing the ordinate to indicate the difference between the flow rate of the supplier resource and the flow rate of the receiver requirement and using the abscissa to denote the number of suppliers. The data for the three cases in Figure 11 are replotted as a flow rate difference curve, as shown in Figure 12. It can be easily seen that the middle point representing

Next, the supplier status of the bottom ranked exchanger (E3) is changed to Receiver. The cooling water flows of the three higher ranked exchangers are mixed to form the supplier resource whose flow rate and temperature are calculated using eqs 24 and 25. The calculation procedure is repeated by having the third (E4) and last (E3) ranked exchangers as receiver. A final round of calculation is conducted by having the second (E1), third (E4), and last (E3) ranked exchangers as receiver. So, there are three cases with different numbers of suppliers and receivers: (1) three suppliers (E1, E2, and E4) plus one receiver (E3); (2) two suppliers (E1 and E2) plus two receivers (E3 and E4); and (3) one supplier (E2) plus three receivers (E1, E3, and E4). The flow rate and temperature of the supplier resource for each case are plotted in Figure 11 (solid line). This plot is called the supplier resource curve.

Figure 12. Flow rate difference curve for example 3.

the case with two suppliers (plus two receivers) is closest to the intersection point on the abscissa at which the flow rate difference is zero. The flow rate difference curve shows that the cooling water flow rate is redundant when the number of suppliers is large, but it becomes limiting with a decreasing number of suppliers. The desired case identified from Figure 12 is of course the same case identified from Figure 11. For a system with a large number of heat exchangers, computer programming may be used to generate the supplier resource curve, receiver requirement curve, and flow rate difference curve for different distributions of suppliers and receivers following the approach described above. In the flow rate difference curve, the part of the curve above the zero flow rate difference abscissa indicates the reused water provided by suppliers can satisfy the cooling water requirement of receivers, and the deviation between the curve and the zero flow rate difference abscissa means the surplus reused water provided by suppliers. The part of curve below the zero flow rate difference abscissa indicates the reused water supplied by suppliers cannot satisfy the cooling water requirement of receivers, and the deviation between the curve and the zero flow rate difference abscissa means the required reused water provided by supplier. The optimal supplier and receiver distribution point is the point which is most close to the zero flow rate difference abscissa. By using the flow rate difference curve, the optimal supplier and receiver distribution can be obtained. 5.2. Step 2: Using the Receiver Sensitivity Graph to Match Receivers and Suppliers. After identifying individual heat exchangers in a cooling water network as either supplier or receiver, the next step in the proposed two-step methodology aims to match the supplier exchangers with the receiver exchangers. As mentioned in previous sections, ε for a receiver is a function of the cooling water flow rate and the cooling water inlet temperature. The sensitivity of a receiver to the cooling water flow rate and inlet temperature parameters may be quantified in terms of a receiver sensitivity graph, which can be constructed using eqs 11−16. For a given receiver cooling water

Figure 11. Supplier resource curve and receiver requirement curve for example 3.

The flow rate of the supplier resource is then adjusted to obtain εmax = 1 for each receiver in the three cases by using eqs 11−16. This adjusted supplier resource is called the receiver requirement. The flow rates of receiver requirement for all of the receivers in each case are summed up. The resulting total flow rate and temperature of the receiver requirement for each case are plotted in Figure 11 (dashed line), giving the receiver requirement curve. Note that the temperature of the receiver requirement is equivalent to the temperature of the supplier resource. As can be seen in Figure 11, the supplier resource curve and receiver requirement curve intersect at a particular point (solid circle). At the interaction point the flow rate of the supplier resource matches exactly the flow rate of the receiver requirement. In other words, the supplier resource is fully utilized to satisfy the receiver requirement. Among the three cases, the two points of the case with two suppliers (E1 and E2) plus two receivers (E3 and E4) are closest to the interaction point in terms of flow rate. This indicates that this particular case gives the optimal distribution of suppliers and receivers for example 3. From the supplier resource curve and receiver requirement curve, it can be found that with an increasing number of suppliers in the supplier and receiver distribution, the total cooling water flow rate supplied to the suppliers increases while the total cooling water flow rate required by a decreasing number of receivers decreases. As discussed above, the interaction point of the supplier resource curve and receiver requirement curve indicates the presence of a certain supplier and receiver distribution that minimizes the difference between the flow 281



Article

inlet temperature, the cooling water flow rate at which εmax = 1 (i.e., no consumption of fresh cooling water) can be computed. Such pairs of temperature and flow rate are then plotted to give the receiver sensitivity graph, as shown by the solid line in Figure 13.

the receiver sensitivity graph. For example, points 1, 2, and 3 in Figure 13 represent three individual suppliers with different cooling water flow rates and outlet temperatures. The suitability of a supplier is assessed by considering its location on the receiver sensitivity graph, as discussed below. (1) The location of point 1 is close to the receiver sensitivity curve, indicating that this supplier with a relatively low outlet temperature and large flow rate will be a good match for the receiver. However, because point 1 is located in the white area (above the curve), fresh cooling water is needed in order for the receiver to have a high εmax value. (2) The location of point 2 is above and far from the receiver sensitivity curve, indicating that this supplier with a rather high outlet temperature and small flow rate will be a poor choice for the receiver. (3) The location of point 3 is in the gray area (under the curve), indicating that this supplier with a rather low outlet temperature will be a suitable match for the receiver. Its location reflects the fact that the supplier cooling water flow rate is much larger than the cooling water flow rate needed in order for the receiver to have εmax = 1. When the cooling water flows of several suppliers are combined to form a single mixed stream, and the resulting mixed stream is used for matching with a single receiver, it is straightforward to plot the location of the mixed stream point on the receiver sensitivity graph. The flow rate and temperature of the mixed stream can be easily computed given the flow rates and

Figure 13. Receiver sensitivity graph.

In the case of a single receiver, when several suppliers are available for matching and their cooling water flows are not combined to form a single mixed stream, their cooling water flow rates and outlet temperatures are plotted as separate points on

Figure 14. Flowchart for the proposed two-step approach. 282



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Table 4. Exchanger Data for the Case Study exchanger no.

side

inlet temp (°C)

outlet temp (°C)

heat-transfer coefficient (W/(m2·°C))

flow rate (kg/s)

duty (kW)

order

E1

cold hot cold hot cold hot cold hot cold hot cold hot cold hot cold hot cold hot cold hot cold hot

20 59 20 44 20 50 20 50 20 74 20 75 20 69 20 77 20 79 20 68 20 69

34 35 27 31 34 44 27 40 22 70 39 69 32 38 22 33 25 30 32 36 27 63

1200 900 1100 1000 1000 700 1200 1200 1100 900 1000 1000 1200 600 1000 1300 1200 900 1200 600 1000 800

16.4

960

4

13.1

410

2

18.4

1460

8

19.7

576

7

81.7

683

11

10.2

831

10

39.5

1980

6

62.2

202

3

41.3

950

1

18.7

978

5

74.5

2179

9

E2 E3 E4 E5 E6 E7 E8 E9 E 10 E 11

matching procedures will be illustrated by using a case study, as described below.

temperatures of individual suppliers. For example, point 4 in Figure 13 represents the location of the mixed stream obtained by combining the supplier cooling water flows designated by points 1 and 2. Point 4 is obviously superior to point 2 given its close proximity to the receiver sensitivity curve. This proximity of point 4 to the receiver sensitivity curve is comparable to that of point 1, but point 4 has both a larger temperature and a larger flow rate compared to point 1. We now consider in some detail how several suppliers should be matched with multiple receivers in a systematic manner. Recall that in step 1 multiple heat exchangers are ranked in ascending order of hot stream outlet temperature. Given that the bottom ranked receiver exchanger, which has the highest hot stream outlet temperature, can accommodate cooling water with a high supplier outlet temperature, the matching process should start by first matching the bottom ranked receiver with the supplier with the highest cooling water outlet temperature. This particular supplier can be easily identified by plotting the location points of all available suppliers on the receiver sensitivity graph of the bottom ranked receiver. The point of doing this is to let the best receiver match with the worst supplier because those suppliers may not be suitable for other receivers. When a supplier cannot satisfy the requirement of the receiver (e.g., point 2 in Figure 13), its cooling water should be combined with other supplier cooling water streams to generate a more suitable location point (e.g., point 4 in Figure 13). If the supplier cooling water flow rate is larger than the receiver flow rate requirement (any point located under the receiver sensitivity graph), the cooling water flow should be split, one part of which goes to the most suitable receiver to satisfy its requirement, and the remaining fraction goes to the next preferred receiver according to the rank. After satisfying the first receiver, the receiver sensitivity graph is applied to the next preferred receiver in the rank. The same procedure is applied to match this receiver with the remaining suppliers. After all the receivers and suppliers are matched, the final retrofit design can be obtained. The flowchart for the proposed two-step approach is shown in Figure 14. The

6. CASE STUDY Table 4 presents the data of an existing cooling water network in a refinery. The network has 11 heat exchangers arranged in parallel. The retrofit objective is to reduce its fresh cooling water consumption, which amounts to a total of 370.3 kg/s for the parallel configuration. The temperature of fresh cooling water is 20 °C. The retrofit design will be conducted using the proposed two-step methodology. The first step of the methodology ranks the 11 exchangers in ascending order of hot stream outlet temperature. The ranking order is shown in the last column of Table 4. Based on this order, the flow rate difference curve is generated, as shown in Figure 15. From the flow rate difference curve, it can be seen that the location point for eight suppliers is closest to the intersection point on the abscissa which signifies the zero flow rate difference. As a result, the first eight heat exchangers in the ranking order are designated as supplier and the last three heat exchangers are classified as receiver. The order of the eight supplier exchangers is

Figure 15. Flow rate difference curve for the case study. 283



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requirement of E5. It is thus necessary to combine E1 and E3 with other suppliers with high cooling water outlet temperature. Calculation shows that a mixed cooling water stream that can satisfy the requirement of E5 can be obtained by combining E1, E3, E10, E7, E2, E4, and part of E9 (designated as E9′ in Figure 16a). The location of this mixed cooling water stream is given by the blue circle on the receiver sensitivity curve in Figure 16a. At this location point, εmax for E5 is equal to 1, indicating that no fresh cooling water is needed to fulfill the cooling water requirement of E5. The temperature of the mixed cooling water stream is 30.7 °C. The next receiver to be matched is E6, which has the second highest hot side outlet temperature (69 °C). The receiver sensitivity graph of E6 is shown in Figure 16b. The locations of the remaining suppliers, remaining portion of E9 (i.e., E9 − E9′) and E8, are also plotted in the same figure. As can be seen in Figure 16b, the two supplier points are located under the receiver sensitivity curve, indicating that the cooling water flow rate of (E9 − E9′) or E8 is much larger than the requirement of E6. Since the cooling water outlet temperature of (E9 − E9′) is higher than that of E8, the former should be matched with E6. Calculation shows that a fraction of (E9 − E9′), designated as E9″ in Figure 16b, is sufficient to meet the requirement of E6. The location of the match is given by the blue circle in Figure 16b. At this location point, εmax for E6 is equal to 1. Again, no fresh cooling water is needed to satisfy the requirement of E6. The final receiver to be matched is E11, which has the lowest hot side outlet temperature (63 °C) among the three receiver exchangers. Figure 16c shows the receiver sensitivity graph of E11 as well as the location points of the remaining suppliers, which are (E9 − E9′ − E9″) and E8. Given that the two supplier points are located above and far away from the receiver sensitivity curve, their cooling water flows are obviously insufficient to meet the requirement of E11. In this case, it is necessary to combine the two suppliers with fresh cooling water. The location of the mixed cooling water stream is given by the blue circle in Figure 16c. At this location point, εmax for E11 is equal to 1, which can only be achieved with the addition of fresh cooling water. This completes the retrofit design. A schematic diagram of the retrofit design is shown in Figure 17. It is worth pointing out that supplier E9 serves all three receivers and only receiver E11 requires fresh cooling water.

given by E9, E2, E8, E1, E10, E7, E4, and E3, and the order of the three receiver exchangers is E11, E6, and E5. The second step of the proposed methodology matches the eight supplier exchangers with the three receiver exchangers in the ranking order using receiver sensitivity graphs. First, the receiver sensitivity graph of E5, which is the bottom ranked receiver with the highest hot side outlet temperature (70 °C), is constructed, as shown by the solid line in Figure 16a. Also shown

Figure 16. Receiver sensitivity graphs for the case study.

in Figure 16a are the location points of the eight suppliers (red circles). The temperature range in the sensitivity graph goes from 22 °C (lowest supplier cooling water outlet temperature) to 34 °C (highest supplier cooling water outlet temperature). As mentioned previously, E5 with the highest hot side outlet temperature (70 °C) should be matched with suppliers with the highest cooling water outlet temperature, which in this case are E1 and E3 (34 °C), as can be seen in Figure 16a. Unfortunately, the points of E1 and E3 are located above and too far away from the receiver sensitivity curve. As a result, even the sum of these two cooling water streams is insufficient to meet the flow rate

Figure 17. Schematic diagram of the retrofit design for the case study. 284



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h F Fx NS rT rU T U v ΔTLM

Converting the cooling water network from parallel to series arrangements has led to a total fresh cooling water consumption of 242.1 kg/s. This compares favorably to the total fresh cooling water consumption of 370.3 kg/s for the parallel configuration. The cooling water reuse design has therefore yielded a 34.6% reduction in fresh cooling water consumption. From the viewpoint of integration, in the retrofit design suppliers with high cooling water temperature should provide cooling water to receivers with high hot stream outlet temperature. Because such suppliers may not be able to satisfy the flow rate requirement of receivers with low hot stream outlet temperature, a large amount of cooling water may be required to increase heat transfer in this type of receiver in order to attain εmax = 1. As such, it is quite normal to see several suppliers providing cooling water to a single receiver. In summary, it is noteworthy that the water savings for the case study has been achieved without investment in new heattransfer area. Furthermore, in the retrofit design only a small quantity of new pipelines between certain supplier and receiver matches need to be installed.

Greek Letters

ε water saving efficiency εmax maximum water saving efficiency Subscript

0 1 2 c h i j in mixed o out p s

7. CONCLUSION Changing the cooling water network design from parallel to series arrangements can reduce water consumption significantly as a result of water reuse. For a series arrangement consisting of two heat exchangers, it is important to determine the sequence of exchanger connection so that the water savings potential is maximized. The results of this work show that the heat exchanger with the larger cooling water flow rate should be placed first in the series configuration. The entire cooling water flow of the first heat exchanger (supplier) should be sent to the second heat exchanger (receiver). The second heat exchanger in the series design should have a high hot stream temperature and a small cooling water side heat-transfer coefficient. A two-step methodology for retrofit design of cooling water networks has been developed. A parallel configuration can be converted to a series arrangement without investment in a new heat-transfer area. The first step of the methodology uses the concept of flow rate difference curve to identify suppliers and receivers in a cooling water network with multiple heat exchangers. The second step employs receiver sensitivity graphs for matching of the identified suppliers and receivers. Systematic matching procedures have also been developed. A case study demonstrates that the two-step methodology can achieve a significant reduction in fresh cooling water consumption. The retrofit design generated for the case study requires modest pipework modifications.

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heat-transfer coefficients (kW/(m2·°C)) mess flow rate (kg/s) mess flow rate for reused water (kg/s) number of streams a ratio of initial ΔTLM to new ΔTLM a ratio of new U to initial U stream temperature (°C) overall heat-transfer coefficient (kW/(m2·°C)) fluid velocity (m/s) log mean temperature difference (°C)

■

initial value heat exchanger 1 in the example heat exchanger 2 in the example cold side of heat exchanger hot side of heat exchanger tube side of heat exchanger the index for stream participated in mixing inlet of stream after mixing streams shell side of heat exchanger outlet of stream parallel arrangement series arrangement

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the National Basic Research Program of China (973 Program: 2012CB720500) and the National Natural Science Foundation of China under Grant No. 21306228 is gratefully acknowledged

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NOMENCATURE A heat-transfer area of heat exchanger (m) CP stream capacity flow rate (kW/°C) 285



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(15) Bhatti, M. S.; Shah, R. K. Turbulent and Transition Convective Heat Transfer in Ducts; Wiley: New York, 1987. (16) Taborek, J. Shell-and-Tube Heat Exchangers. Heat Exchanger Design Handbook; Hemisphere: New York, 1988. (17) Nie, X.; Zhu, X. Heat Exchanger Network Retrofit Considering Pressure Drop and Heat-transfer Enhancement. AIChE J. 1999, 45 (6), 1239−1254. (18) Kotjabasakis, E.; Linnhoff, B. Sensitivity Tables for the Design of Flexible Processes (1)How Much Contingency in Heat Exchanger Networks is Cost-Effective. Chem. Eng. Res. Des. 1986, 64 (a), 197−211.

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Two-Step Methodology for Retrofit Design of Cooling Water Networks

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