Synthesis of heat exchanger networks featuring batch streams

Synthesis of heat exchanger networks featuring batch streams

Applied Energy 114 (2014) 30–44 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy Synthes...

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Applied Energy 114 (2014) 30–44

Contents lists available at ScienceDirect

Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Synthesis of heat exchanger networks featuring batch streams Yufei Wang a, Ying Wei b, Xiao Feng a,⇑, Khim Hoong Chu b a b

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

h i g h l i g h t s  Heat integration of heat exchanger networks featuring batch streams is firstly considered.  A new method based on the heat duty–time (Q–t) diagram is proposed.  Energy targeting and network design can be obtained easily.  Both direct and indirect heat integration of batch streams are considered.

a r t i c l e

i n f o

Article history: Received 30 May 2013 Received in revised form 27 August 2013 Accepted 17 September 2013 Available online 13 October 2013 Keywords: Heat exchanger network Graphical method Batch stream Intermediate media Energy target

a b s t r a c t A new method based on the heat duty–time (Q–t) diagram is proposed for heat integration of heat exchanger networks featuring batch streams. Using the Q–t diagram method, the energy targets and the structure of the initial heat exchanger network can be easily obtained. The method can be used both for direct and indirect heat integration of batch streams. For indirect heat integration, the heat degradation of intermediate media is considered. A case study on optimizing the heat exchanger network of a hydrazine hydrate plant is used to illustrate the application of the method. The results show that integration of this heat exchanger network without considering its batch streams can limit the total energy savings. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Chemical processes can be broadly divided into continuous and batch operations. Although not common, there exist some continuous processes featuring batch streams. Notable examples include the hydrazine hydrate production process and the delayed coking process. Because chemical processes consume large amounts of finite energy resources, many heat integration techniques have been developed over the years to improve their energy efficiency. For example, heat exchanger networks in numerous continuous and batch processes in the chemical industry have become highly energy efficient as a result of heat integration. Nevertheless, despite this remarkable success, heat integration analysis has not yet been applied to continuous processes featuring batch streams. Although usually only a limited number of key batch streams are present in such processes, the heat content of these batch streams could be quite substantial. As such, heat integration analysis that treats this type of hybrid processes as strictly continuous by ignoring the small number of batch streams can limit the total energy savings. ⇑ Corresponding author. Tel.: +86 15811168976. E-mail addresses: [email protected], [email protected] (X. Feng). 0306-2619/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2013.09.040

Synthesis of heat exchanger networks of continuous processes has been studied extensively, either by pinch technology [1,2] or by mathematical programming techniques [3,4]. Because pinch technology offers the advantages of intuitiveness, simplicity and clarity when compared to the mathematical programming approach, it is widely used in industry. In recent development of heat exchanger networks synthesis of continuous processes, Wang et al. [5] proposed a methodology to consider heat transfer enhancement in the optimization of heat exchanger network. Zhang et al. [6] developed a method for optimizing the operation condition of heat exchanger network and distillation columns simultaneously. This methodology allows the industry to improve its economic and environment performance at the same time. Vaskan et al. [7] developed a multi-objective design method for heat exchanger network by using a MILP based model. Life cycle assessment and environment were involved in this method. Markowski et al. [8] proposed a heat exchanger network synthesis methodology considering fouling. This methodology can monitor long-term changes in the heat exchanger network efficiency. With suitable adaptations, most of the heat integration methods developed for continuous processes can be used to search for heat integration opportunities in batch processes which are

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characterized by their time-dependent mode of operation. A variety of models have been developed for heat integration of batch processes since the 1980s [9], some of which are described below. (1) Time average model [10]: This model is also called pseudocontinuous process model. The heat duties of all streams in the batch process are time averaged in the production cycle, and the utility targets are then obtained by pinch technology. Because the time-dependent features of batch streams are not considered, the targets are highly ideal and can only be approached with extensive use of heat storage. (2) Time segmentation model [11]: In this model, batch streams are re-arranged in a limited manner to recover more waste heat and avoid heat storage. This method is constrained by whether the actual process allows the re-arrangement of batch streams. (3) Time and temperature cascade analysis [12,13]: The method considers simultaneously time and temperature. Heat integration in the same time interval is considered first, followed by consideration of the time sequence. Although intermediate heat storage is included in the method, the heat degradation of intermediate media is not considered. (4) Time pinch method [14]: The heat recovery target is obtained by using time as the main constraint and heat transfer driving force as the secondary factor. The method includes direct and indirect heat recovery. The heat degradation of intermediate media is not considered. In this paper, a new graphical method based on the heat duty–time diagram will be provided for the heat integration of continuous processes featuring batch streams. The proposed method is largely based on the many heat integration concepts and tools arising from the research on continuous and batch processes. The method can be used both for direct and indirect heat integration.

2. The heat duty–time diagram The heat duty–time diagram (Q–t diagram) method developed in this work expresses the time and thermal features of batch streams intuitively and provides a practical graphical tool for heat exchanger network synthesis. As will be explained below, the method is based essentially on a combination of the Gantt chart and the temperature–enthalpy diagram (T–H diagram) commonly used in traditional pinch analysis to represent continuous streams. The Q–t diagram will now be illustrated by application to a batch process reported by Kemp and Deakin [12]. The stream data are given in Table 1. In this four-stream example, the batch period is 1 h with each stream only existing for a limited time period. Representing the streams graphically will allow a better appreciation of their time-dependent nature. A handy method of visualization is the Gantt chart, which is a type of time event chart. The Gantt chart is useful for visualizing which streams exist in which periods. As pointed out earlier, the T–H diagram is a key tool of energybased pinch analysis which is used to represent the thermal features of continuous streams. And the proposed Q–t diagram is a hybrid of the Gantt chart and the T–H diagram which is able to represent the thermal features as well as the time-dependent

nature of batch streams on the same plot. Fig. 1 shows a cold stream (Fig. 1a) and a hot stream (Fig. 1b) plotted on Q–t diagrams, which use the stream heat load (Q) for the vertical axis and time for the horizontal axis. The arrowheads in Fig. 1 indicate the direction of temperature increase for the cold stream and the direction of temperature decrease for the hot stream. The temperature of the cold and hot streams increases and decreases with time, respectively. Therefore, the cold stream line has a positive slope while the hot stream line a negative slope. The vertical axis length defined by the stream boundaries gives the stream heat load while the horizontal axis length defined by the stream boundaries provides the stream time interval. Like T–H diagrams, in the Q–t diagrams, moving the cold and hot streams upward or downward will not affect their heat loads. They can therefore be plotted anywhere on the vertical axis. For multiple batch streams, a systematic procedure for constructing the Q–t diagram is given below. (1) Calculate the heat load of each stream. (2) Rank the streams in ascending order of supply temperature. The top ranked stream is the one with the lowest supply temperature and must thus be a cold stream (If the stream with lowest supply temperature is a hot stream, it should be kept outside the heat recovery project). If two streams have the same supply temperature, rank the one with the lower target temperature first. If two streams have identical supply temperature and target temperature, rank the one with the lower heat duty first. (3) Plot the top ranked stream on the Q–t diagram using its calculated heat duty value and time interval. Begin with the start time. Its y-coordinate (initial heat duty value) at the start time is assumed zero. Its y-coordinate (final heat duty value) at the end time is the computed heat duty value. The plotted line will have a positive slope. (4) Plot the next stream on the Q–t diagram. If it is a cold stream, begin with the start time. Its y-coordinate at the start time is given by the largest y-coordinate of the preceding stream. Its y-coordinate at the end time is given by the sum of its heat duty and the largest y-coordinate of the preceding stream. The plotted line will have a positive slope. If it is hot stream, begin with the end time. Its y-coordinate at the end time is given by the largest y-coordinate of the preceding stream. Its y-coordinate at the start time is given by the sum of its heat duty and the largest y-coordinate of the preceding stream. The plotted line will have a negative slope. Plot the remaining streams in the ranking order using the above procedure. With the four-stream example given in Table 1, let us illustrate how the Q–t diagram can be constructed using the procedure described above. (1) The heat load of each stream is calculated from the following equation:

Q i ¼ CPi DT i Dti

ð1Þ

where Qi = heat load of stream i (kW h), CPi = heat capacity flow rate of stream i (kW °C1), DTi = difference of target and supply

Table 1 Stream data. No.

Type

Supply temperature (°C)

Target temperature (°C)

Heat capacity flow rate (kW °C1)

Start time (h)

End time (h)

Heat duty (kW h)

1 2 3 4

H1 H2 C1 C2

170 150 20 80

60 30 135 140

4 3 10 8

0.25 0.3 0.5 0

1 0.8 0.7 0.5

330 180 230 240

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Y. Wang et al. / Applied Energy 114 (2014) 30–44

Fig. 1. Q–t diagrams for batch streams without phase change.

temperatures of stream i (°C), and Dti = time interval of stream i (h). The computed values of heat loads are listed in the last column of Table 1. (2) Ranking the four streams in ascending order of supply temperature gives C1, C2, H2 and H1. (3) We begin by plotting the top ranked stream C1. Its start time, end time, and heat duty are 0.5 h, 0.7 h, and 230 kW h, respectively. The y-coordinate at 0.5 h is zero kW h while that at 0.7 h is 230 kW h. Hence, the coordinates of the C1 plot are given by (0.5, 0) and (0.7, 230), as shown in Fig. 4. (4) Next, we plot C2 on the Q–t diagram. Its time interval is 0– 0.5 h and heat duty is 240 kW h. Because C2 is a cold stream, we begin with the start time. The y-coordinate at 0 h is given by the largest y-coordinate of the preceding stream, which is 230 kW h. The y-coordinate at 0.5 h is 470 kW h, which is the sum of C1’s heat duty (240 kW h) and the largest y-coordinate of the preceding stream (230 kW h). So, C2 can now be plotted in Fig. 4 using the following two points: (0, 230) and (0.5, 470). (5) H2 is the next stream to be plotted. Its time interval is 0.3– 0.8 h and heat duty is 180 kW h. Because H2 is a hot stream, we begin with the end time. The y-coordinate at 0.8 h is given by the largest y-coordinate of the preceding stream, which is 470 kW h. The y-coordinate at 0.3 h is 650 kW h, which is the sum of H2’s heat duty (180 kW h) and the largest y-coordinate of the preceding stream (470 kW h). Fig. 4 shows the H2 plot with the coordinates (0.3, 650) and (0.8, 470). (6) We now plot the bottom ranked stream H1. Its start time, end time and heat duty are respectively 0.25 h, 1 h, and 330 kW h. Because H1 is also a hot stream, we begin with the end time. The y-coordinate at 1 h is given by the largest y-coordinate of the preceding stream, which is 650 kW h. The y-coordinate at 0.25 h is 980 kW h, which is the sum of H1’s heat duty (330 kW h) and the largest y-coordinate of the preceding stream (650 kW h). The coordinates (0.25, 980) and (1, 650) are used to plot the H1 line in Fig. 4. As can be seen in Fig. 2, the two cold steam lines have positive slopes while the two hot stream plots have negative slopes. The proposed procedure for constructing the Q–t diagram gives a useful representation of when streams coexist as well as the heat duties of the streams unambiguously. To make the stream heat duties even more obvious, the actual heat duties of the streams except C1 are given in parentheses by the side of the respective heat load interval on the vertical axis (Fig. 2). However, it is not possible to plot stream temperatures on the Q–t diagram. To include temperature details, the supply temperature and target temperature of

Fig. 2. Q–t diagram for the four-stream example given in Table 1.

each stream are given in parentheses at the boundaries of each stream plot, as shown in Fig. 2. Note that a continuous stream at steady-state can also be plotted on the Q–t diagram. In this case, the stream exists for the entire time period. It is also needed to note that in the Q–t diagrams, the temperature of streams change from its supply temperature to target temperature in every time interval it exists. It does not mean the temperature of stream changes throughout from supply temperature in its start time to target temperature in its end time.

3. Application of the Q–t diagram – direct heat integration Heat recovery is possible when hot and cold streams of a batch process exist in the same time interval. This is known as direct heat integration. After maximum heat recovery in a time interval is achieved, the remaining heat in the hot streams is removed by cold utility and the balance of heat required by the cold streams is provided by hot utility. Heat cannot be exchanged across different time intervals, that is, a hot and a cold stream in different time intervals cannot be matched. Rescheduling of streams to allow some heat to be recovered by direct heat integration is not considered here.

3.1. Energy targets and initial network synthesis The calculation steps for direct heat integration based on the Q– t diagram are as follows.

Y. Wang et al. / Applied Energy 114 (2014) 30–44

(1) Specify DTmin and calculate energy targets: The energy targets, QHj and QCj for time interval j, are determined from the Q–t diagram. For each time interval, the network is synthesized according to the principles of pinch technology (no utility coolers above the pinch, no utility heaters below the pinch, and no heat exchangers transferring heat across the pinch). P (2) Determine the energy targets for the whole cycle (QH = QHj P and QC = QCj). Direct heat integration of the four-stream example given in Table 1 will now be illustrated using the Q–t diagram in Fig. 2. As can be seen in Fig. 2, there is a total of six time intervals over the batch period of 1 h. In the following calculation, a DTmin of 10 °C is assumed. (1) Calculate QHj and QCj for each time interval: In this step, the time interval [0.5–0.7 h] is used as an example. Fig. 2 shows that three batch streams, H1, H2 and C1 coexist in this time interval. The heat load of stream i in time internal j can be calculated from the following equation:

Q ij ¼ Q i

Dt j Dt i

ð2Þ

where Qij = heat load of stream i in time interval j (kW h), Qi = heat load of stream i (kW h), Dtj = time length of interval j (h) and Dti = time length of stream i (h). So values of Qij for H1, H2 and C1 for the period 0.5–0.7 h are 330(0.2/ 0.75) = 88 kW h, 180(0.2/0.5) = 72 kW h, and 230(0.2/0.2) = 230 kW h, respectively. Knowing the Qij values and temperatures of H1, H2 and C1, heat exchange matches can now be identified. Splitting C1 into three branches according to duties of the hot streams in the same time interval, one branch with a heat load of 88 kW h cools H1 to its target temperature at the end of the time interval (104 °C), another with a heat load of 72 kW h cools H2 to its target temperature at the end of the time interval (54 °C), and the last one with a heat load of 70 kW h is heated by hot utility. The heat capacity flow rates of the three branches are 10(88/230) = 3.83 kW °C1, 10(72/ 230) = 3.13 kW °C1 and 10(70/230) = 3.04 kW °C1, respectively. The heat exchange matches and the heat duty of each match for this time interval are shown in Fig. 3. In this figure, numbers in bold refer to the heat duties of direct heat exchange between hot

Fig. 3. Direct heat integration in the [0.5–0.7 h] time interval.

33

and cold streams and the underlined number denotes the required hot utility. The direct heat integration of hot and cold streams for the other five time intervals can be determined in the same way described above. A summary is given below. [0–0.25 h]: A single cold stream exists in this interval. C2 needs 120 kW h hot utility. [0.25–0.3 h]: One cold stream and one hot stream exist in this interval. H1 and C2 exchange 16 kW h heat (due to minimum temperature approach, they cannot exchange all 22 kW h heat), the remaining 8 kW h heat duty required by C2 is supplied by hot utility, and the remaining 6 kW h heat duty of H1 is removed by cold utility. [0.3–0.5 h]: One cold stream and two hot streams exist in this interval. C2 is split into two branches, one of which with a heat load of 60 kW h cools H1 and the other with a heat load of 36 kW h cools H2. The remaining heat duties of H1 (28 kW h) and H2 (36 kW h) are removed by cold utility. [0.7–0.8 h]: Two hot streams exist in this interval. H1 needs 44 kW h cold utility and H2 needs 36 kW h cold utility. [0.8–1.0 h]: A single hot stream exists in this interval. H1 needs 88 kW h cold utility. In summary, three time intervals require hot utility and four require cold utility. The results of direct heat integration for the whole cycle are shown in Fig. 4. As noted above, numbers in bold refer to the heat duties of direct heat exchange between hot and cold streams, underlined numbers signify heating utilities needed by cold streams, and numbers in normal font denote cold utilities needed by hot streams. (2) Determine the energy targets for the whole cycle (QH and QC): The hot utility target for the whole cycle, QH, can be obtained simply by summing all the underlined numbers in Fig. 4. Similarly, the minimum cold utility for the whole cycle is given by the sum of all the numbers in normal font in Fig. 4. The two overall utility targets are shown below.

QH ¼ QC ¼

X X

Q Hj ¼ 120 þ 8 þ 70 ¼ 198 kW h Q Cj ¼ 6 þ 28 þ 44 þ 88 þ 36 þ 36 ¼ 238 kW h

The corresponding heat recovery is 272 kW h. These targeting results are the same as those obtained by using the cascade analysis method proposed by Kemp and Deakin [12]. From the Q–t diagram in Fig. 4, the structure of the initial heat exchanger network can be

Fig. 4. Indirect heat integration for the entire batch period [0–1 h].

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Y. Wang et al. / Applied Energy 114 (2014) 30–44

easily obtained, as shown in Fig. 5. Therefore, the Q–t diagram approach proposed in this work is superior to the cascade analysis method. It is noted that in Fig. 5, the stream in a time interval indicates that the stream exists in this time interval, two streams will exchange heat with each other only when they both exist in that time interval. 3.2. Network optimization To reduce the capital cost of heat exchanger networks, the number of matches or units should be minimized. In general, this can be done by breaking loops and removing units. The minimum number of matches or units can be determined by Euler’s network theorem. In this work, a simplified form of Euler’s network theorem is used for heat exchanger network analysis, which is expressed as U = N  1. In this equation, U denotes the number of units (heat exchangers) and N indicates the number of streams including utility streams. As shown in previous sections, streams in batch processes exist in different time intervals and some streams exist across several time intervals. As a result, some of their heat exchange matches will also exist in several time intervals. For example, Fig. 4 shows that streams H1 and C2 and their matches appear in the [0.25– 0.3 h] and [0.3–0.5 h] time intervals. When the total numbers of matches are counted by Euler’s network theorem for different time intervals, those matches existing in several time intervals will be counted several times, leading to a larger number of heat exchangers. Exchangers due to miscounting are known as additional exchangers [15]. To reduce the number of matches, a useful method is to use one exchanger to exchange heat for the same hot and cold streams that exist in different time intervals, that is, additional exchangers should be removed. Accordingly, the minimum number of matches for the whole cycle can be expressed in the following way.

U min ¼ U min;0 

X

Uþ ¼

X X U min;j  Uþ

ð3Þ

j

where Umin = minimum number of matches for the whole cycle, Umin,0 = sum of minimum number of matches counted by Euler’s

P network theorem for each time interval, and U+ = sum of additional exchangers. Using Eq. (3), the minimum number of matches P P for the four-stream example is Umin = jUmin,j  U+ = 13  6 = 7. From Fig. 5 it can be seen that there are five heat exchangers (E1, E2, E3, E4, E5), six coolers (E1, E3, E6, E7, E8, E9) and three heaters (E2, E4, E5) in the network, giving a total of 14 heat exchange units. This is seven units more than the minimum number of matches. It can be deduced from Fig. 5 that there are seven loops in the network, in which the four coolers for stream H1 form three, the two coolers for stream H2 form one, the two heaters for stream C2 form one, two heat exchanger pairs, E1–E2 and E2–E3, each forming one, and coolers E6 and E7 form one, as shown in Fig. 6. When optimizing the network, firstly, additional exchangers should be combined, and only the unit with the biggest heat load is retained. Therefore, cooler E8 is chosen for stream H1, cooler E3 for stream H2, heater E2 for stream C2 and exchanger E2 for the match between streams H1 and C2, as shown in Fig. 7. Now the network still has one loop left, that is, E8 ? E2 ? E3 ? E3. Breaking this loop will increase the utility requirements. So the loop is retained.

4. Application of the Q–t diagram – indirect heat integration As mentioned above, heat recovery by direct heat integration is not possible when streams do not coexist in the same time interval. To recover heat from streams that exist in different time intervals, indirect heat integration should be considered. Indirect heat integration can be realized by using thermal storage and intermediate media, that is, hot streams in a certain time interval release heat to an intermediate medium for storage, and the intermediate medium discharges the stored heat to cold streams that exist in other time intervals. In this way, heat recovery is feasible across different time intervals. Because heat transfer temperature differences are needed for the intermediate medium, compared with the original hot stream, the intermediate medium has a lower temperature, which means that using an intermediate medium will cause heat degradation.

Fig. 5. Initial heat exchanger network for the entire batch period.

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Y. Wang et al. / Applied Energy 114 (2014) 30–44

6

H1

44

88

E-7

E-9

E-8

36

36

28

E1

E4

E2 E-1 E3

H2

E5 E-6

E-3

E2 120

8 E1

C2 E-2

E3 E-4

E4 E5

C1 70

E-5

0

0.25

0.3

0.5

0.7

0.8

1.0

Fig. 6. Two of the loops in the initial heat exchanger network.

Fig. 7. The heat exchanger network after optimization.

Two different cases of heat recovery in batch processes by indirect heat integration will be analyzed: intra-batch and inter-batch. The former refers to the situation where the stored heat is used within the same batch. In this case, cold streams that exist in a certain time interval can only be heated by heat sources that have already appeared in some previous time intervals. In other words, matches between hot and cold streams are restricted by the sequence of stream appearance. Heat sources must appear in time intervals that are earlier than those for heat sinks in order to achieve intra-batch heat recovery. In the case of inter-batch heat recovery, heat released in a certain batch is stored and then used to heat the next batch [16]. There is thus no restriction on the sequence of stream appearance. For example, when a batch process is repeated, heat recovered in the second time interval of the first batch may be used to heat cold streams that appear in the first time interval of the second batch.

4.1. Intra-batch heat recovery Based on the Q–t diagram, the steps for carrying out an intrabatch heat recovery analysis are as follows. (1) Based on the results of direct heat integration, determine all potential hot streams which can release heat and potential cold streams which can receive heat. (2) Transform these streams into media streams. (3) Draw the Q–t diagram for these media streams. (4) Apply direct heat integration to these media streams on the Q–t diagram. The four-stream example given in Table 1 will again be used to illustrate how intra-batch heat recovery analysis can be carried out.

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Table 2 Potential heat sources and heat sinks. Type

Time interval (h)

Host stream

Temperature interval (°C)

Heat load (kW h)

HR1 HR2 HR3 HR4 HR5 HR6 HS1 HS2 HS3

0.25–0.3 0.3–0.5 0.3–0.5 0.7–0.8 0.7–0.8 0.8–1.0 0–0.25 0.25–0.3 0.5–0.7

H1 H1 H2 H1 H2 H1 C2 C2 C1

90–60 95–60 90–30 170–60 150–30 170–60 80–140 80–140 20–135

6 28 36 44 36 88 120 8 70

Table 3 Heat sources and sinks in different time intervals. 0–0.25 h

HS1

0.25–0.3 h

0.3–0.5 h

HR1

HR2 HR3

HS2

0.5–0.7 h

0.7–0.8 h

0.8–1.0 h

HR4 HR5

HR6

HS3

(1) Determination of potential streams for indirect heat integration: The results for direct heat integration of the fourstream example have already been presented in Fig. 4. We recall that the underlined number of each cold stream denotes hot utility requirement and the number in normal font of each hot stream indicates cold utility requirement. When indirect heat integration is considered, these numbers take on different meanings. Now, the numbers in normal font are viewed as potential heat sources that can release heat and the underlined numbers represent potential heat sinks that can receive heat. This new interpretation is shown in Table 2, where HR stands for potential heat source and HS denotes potential heat sink. The most data in Table 2 are directly read from Fig. 4. And for temperature intervals, from Table 2, it can be seen that different HR from same host stream have different time intervals. The reason is that the hot streams exchanges heat with cold streams in same time interval first and the remained heat is considered as potential heat sources. In order to intuitively see the time sequence of heat source and heat sink appearances, Table 3 shows the time intervals in which the heat sources and heat sinks appear. As explained previously, intra-batch heat recovery is feasible only if heat sources appear in time intervals that are earlier than those for heat sinks. We can only find one such scenario in Table 3: heat sources HR1, HR2 and HR3 appear in the second and third time intervals and heat sink HS3 appears in the fourth time interval. Consequently, it is possible to match HS3 with HR1, HR2 or HR3. (2) Transformation into media streams: For simplicity, two assumptions for thermal storage are made, as described below. (a) There is no heat loss in the heat transfer process, regardless of whether the thermal storage medium absorbs heat from a heat source or releases heat to a heat sink. (b) There is no heat loss in the thermal storage. Therefore, the heat from a certain heat source can be transferred to a heat sink without loss by a thermal storage medium. From step 1, we see that HR1, HR2, HR3 and HS3 are potential sources and sinks. The temperature of each source is lowered by DTmin to form a media hot stream (h) and that of each sink remains unchanged to form a media cold stream (c). In this way, the case of

indirect heat integration between sources and sinks is transformed into a case of direct heat integration between media hot streams and media cold streams. The media hot and cold streams transformed from HR1, HR2, HR3 and HS3 are listed in Table 4. (3) The Q–t diagram for media streams: All the media streams in Table 4 are plotted on the Q–t diagram, as shown in Fig. 8. (4) Direct heat integration of media streams: In Fig. 8, the media hot streams prepared in the second and third time intervals can now be used in the fourth time interval to match with the media cold stream. DTmin is again taken as 10 °C. By considering the temperature and heat load of each stream, two different match schemes are possible, as shown in Fig. 9. In scheme 1 stream c3 is heated by h1 and h2 while in scheme 2 stream c3 is heated only by h3. Scheme 1 yields a total heat recovery of 33.5 kW h, which is slightly higher than the 30 kW h heat recovery of scheme 2. 4.2. Inter-batch heat recovery As explained above, in the case of inter-batch heat recovery, the sequence of stream appearance is not important. A heat source that appears in any time interval in a certain batch can be used to match with a heat sink that appears in any time interval in the next batch. The steps for analyzing intra-batch heat recovery are therefore directly applicable to inter-batch heat recovery. We will use the previous results obtained for intrabatch heat recovery to demonstrate the steps involved in analyzing inter-batch heat recovery. We will look at the case of two consecutive batches. (1) Determination of potential streams for indirect heat integration: It is clear from Table 3 that in the case of intra-batch heat recovery the heat sources that appear in the fifth and sixth time intervals (HR4, HR5 and HR6) cannot be used to match with the heat sinks that appear in earlier time intervals (HS1, HS2 and HS3). When the batch process is repeated, these heat sources can obviously be used to match with heat sinks appearing in the next batch. Table 5 shows heat sources and sinks for two consecutive batches. The heat sources and sinks in the second batch are marked with a prime. It is clear from Table 5 that inter-batch heat recovery can be achieved by matching HR4, HR5 and HR6 in the first batch with HS1’ HS2’ and HS3’ in the second batch. (2) Transformation into media streams: The heat sources and sinks identified above are transformed into media streams in just the same way as for the intra-batch heat recovery case, as shown in Table 6. (3) The Q–t diagram for media streams: Given that the sequence of stream appearance is no longer a factor in inter-batch heat recovery, it is convenient to plot the media streams in Table 6 on the Q–t diagram over a single batch period of 1 h, as

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Y. Wang et al. / Applied Energy 114 (2014) 30–44 Table 4 Media hot and cold streams for intra-batch heat recovery. Original name

Name after transformation

Supply temperature (°C)

Target temperature (°C)

Heat capacity flow rate (kW °C1)

Start time (h)

End time (h)

Heat load (kW h)

HR1 HR2 HR3 HS3

h1 h2 h3 c3

80 85 80 20

50 50 20 135

4 4 3 3.04

0.25 0.3 0.3 0.5

0.3 0.5 0.5 0.7

6 28 36 70

heat recovery of 99 kW h. Scheme 2 provides a similar amount of heat recovery, heating c3’ using h4 and c1’ using h5 and h6 leads to a total heat recovery of 101 kW h. 5. Network synthesis procedure The Q–t diagram is a valuable tool for the synthesis of heat exchanger networks featuring batch streams. The main synthesis steps are as follows. First, appropriate integration modes are determined. Second, an initial network is generated. Finally, the network is optimized. 5.1. Integration modes

Fig. 8. Q–t diagram for media streams of intra-batch heat recovery.

Heat exchanger networks featuring batch streams offer a number of heat recovery opportunities, including (1) integration of continuous streams without considering batch streams, (2) direct integration of batch streams, and (3) indirect integration of batch streams. For the second and third modes, one may also consider other energy saving opportunities such as matching of batch and continuous streams. Selecting an appropriate integration mode for a given heat exchanger network featuring batch streams requires careful economic consideration. In general, only a limited number of batch streams are present in a continuous process. As a result, integration of a small number of batch streams may not give significant energy savings. Nevertheless, if the heat content of these batch streams is substantial, energy and cost savings from heat recovery may become attractive. Of the two integration modes for batch streams, indirect integration carries a significant cost disadvantage because thermal storage is generally much more costly than heat exchange. 5.2. Synthesis of initial network

Fig. 9. Direct heat integration of media streams of intra-batch heat recovery.

shown in Fig. 10. Note that to reduce number of matches, c2’ with a relatively small heat load is not plotted the Q–t diagram. (4) Direct heat integration of media streams: By considering the temperature and heat load of each stream, two different match schemes can be devised, as shown in Fig. 11. In scheme 1, h4, h5 and h6 are used to heat c1’, giving a total

If integration of batch streams is considered for a heat exchanger network featuring batch streams, synthesizing the initial network of the process can be readily achieved using a combination of the Q–t diagram method and pinch analysis. 5.3. Optimization of network Breaking loops can be done in this step. For retrofit cases, the initial network can be adjusted according to some engineering considerations. For example, a match between streams in close proximity has priority for consideration if other conditions (temperature, heat duty, etc.) are similar.

Table 5 Heat sources and sinks in different time intervals for two consecutive batches. First batch 0–0.25

HS1

Second batch 0.25–0.3

0.3–0.5

HR1

HR2 HR3

HS2

0.5–0.7

HS3

0.7–0.8

0.8–1.0

HR4 HR5

HR6

0–0.25

HS1’

0.25–0.3

0.3–0.5

HR1’

HR2’ HR3’

HS2’

0.5–0.7

HS3’

0.7–0.8

0.8–1.0

HR4’ HR5’

HR6’

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Table 6 Media hot and cold streams for inter-batch heat recovery. Original name

Name after transformation

Supply temperature (°C)

Target temperature (°C)

Heat capacity flow rate (kW °C1)

Start time (h)

End time (h)

Heat load (kW h)

HR4 HR5 HR6 HS1’ HS2’ HS3’

h4 h5 h6 c1’ c2’ c3’

160 140 160 80 80 75

50 20 50 140 140 135

4 3 4 8 2.67 3.04

0.7 0.7 0.8 0 0.25 0.5

0.8 0.8 1.0 0.25 0.3 0.7

44 36 88 120 8 36.5

Fig. 10. Q–t diagram for media streams of inter-batch heat recovery.

rine absorber, in which they react to form hypochlorite. The hypochlorite solution enters the hypochlorite tank (V1102) after cooling. At a certain ratio, the hypochlorite solution and urea solution from the urea tank (V1101) are pumped to a mixer (V1103) through the hypochlorite pump (P1102) and urea pump (P1101), respectively. After vigorous mixing, they go into the synthesis reactor (H1101), where they react after being heated to 104–108 °C by steam in the reactor jacket. The reaction product is a mixture of hydrazine hydrate and some other by-products, called synthesis fluid. The synthesis fluid enters the synthesis fluid tank (V1104) through the synthesis fluid buffer tank. The synthesis fluid is then cooled to 2 °C to remove sodium carbonate through crystallization before flowing to the evaporation fractionation system. In the evaporation fractionation system, shown in Fig. 13, the synthesis fluid is pumped from the feed tank (V1302) to the evaporator (E1301). The evaporated vapor (mixture of hydrazine hydrate and water) is separated in the vapor–solid separator (V1304). After that, the separated vapor enters the bottom of the fractionator (T1301) to increase concentration. The top vapor of T1301 is condensed in a condenser (E1303), part of which goes back to the top of the fractionator as reflux, the other remaining part enters the semi-finished product tank. In the fractionation concentration system, the product hydrazine hydrate solution with a concentration of 80% is obtained through distillation. Fig. 14 shows a simplified flow chart of the system. 6.2. Stream data The heat exchanger network of the hydrazine hydrate plant has 11 hot and 13 cold streams, in which there are four batch hot streams and two batch cold streams, giving a total of six batch streams. Note that this network is not a typical network featuring batch streams as the number of batch streams forms a sizeable fraction of the total number of streams. Table 7 lists all the streams, in which the heat loads of batch streams are assigned to a 24-h period according to the time-average model. Table 8 gives the temperatures, heat load, and time interval of each batch stream.

Fig. 11. Direct heat integration of media streams of inter-batch heat recovery.

6. Case study The heat exchanger network of the hydrazine hydrate plant in Yibin Tianyuan Group Company Limited, Sichuan, China, is used as a case study to illustrate the utility of the proposed method.

6.3. Integration modes Because this particular heat exchanger network has not been systematically integrated in the past, significant scope for energy saving exists. In order to save more energy, indirect heat integration is considered. 6.4. Analysis of the heat exchanger network

6.1. Brief introduction of the hydrazine hydrate plant The plant consists of three parts, the synthesis reaction system, evaporation fractionation system and fractionation concentration system. The synthesis reaction system is mainly used to generate synthesis fluid. A simplified flow chart of the system is shown in Fig. 12. Dilute caustic soda solution and chlorine go into the chlo-

Pinch analysis is applied to the existing heat exchanger network. When determining the pinch location, the heat loads of batch streams are assigned to a 24-h period. At DTmin = 10 °C, the modified pinch temperature is calculated as 50 °C, that is, the pinch temperature of hot streams is 55 °C and that of cold streams is 45 °C. The corresponding temperature–enthalpy diagram is shown in Fig. 15.

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Y. Wang et al. / Applied Energy 114 (2014) 30–44

Synthetic fluid V1101 E1105

P1101

Synthetic fluid

E1106 Crystallizer

buffer tank

NaOH solution V1103 Mixer

Cl2 Absorber

Synthetic fluid

H1101 Synthesis Reactor E1107

V1102

P1102

E1108 Crystallizer

V1104

Fig. 12. Flow chart of the synthesis reaction system.

V1304 Vapor-solid separator Hydrazine hydrate and water

E1303 Condenser

Distillate

P1304 Flowmeter T1301 Fractionator

E1301 Evaporator

V1302

Fig. 13. Flow chart of the evaporation fractionation system.

1# Condenser

Semiproduct tank

1# Reboiler

Prefractionator

2# Condenser

2# Reboiler

Product column

Distillate tank

Fig. 14. Flow chart of the fractionation concentration system.

From Fig. 15 it can be seen that the minimum hot utility is 21,293 kW and the minimum cold utility is 10,168 kW. The current heat exchange network consumes 44,195 kW hot utility and 33,070 kW cold utility. Therefore, the potential energy saving is 22,902 kW, which accounts for 51.8% of the current hot utility. The existing heat exchanger network of the hydrazine hydrate plant is shown in Fig. 16. According to the principles of pinch technology, we can see from Fig. 16 that heat is transferred across the pinch. These pinch violations are listed in Table 9. In the existing network configuration, ten coolers, two exchangers and three heaters are pinch violators because they are inappropriately placed.

6.5. Retrofit of the heat exchanger network (1) Retrofit scheme for continuous streams: It is necessary to retrofit the network to eliminate heat transfer across the pinch. Firstly, a retrofit scheme is proposed for the continuous streams involved in the pinch violations. These continuous streams are shown in Table 10, in which the temperature range between the inlet and outlet temperatures is that of the heat transferred across the pinch for each stream.

The heat loads of streams C3 and C5 are quite small, so they are not considered for recovery in order to reduce capital cost. The retrofit scheme devised for the continuous streams is described below. For the coolers above the pinch, the following measures are adopted.  Addition of a new heat exchanger (E11) with a heat load of 1666.67 kW for heat exchange between H5 (85–55 °C) and C3 (44–75 °C).  Addition of a new heat exchanger (E12) with a heat load of 2666.67 kW for heat exchange between H6 (85–55 °C) and C5 (44–75 °C).  Addition of a new heat exchanger (E13) with a heat load of 4500.00 kW for heat exchange between H7 (85–55 °C) and C7 (45–68.4 °C).  Addition of a new heat exchanger (E14) with a heat load of 4500.00 kW for heat exchange between H8 (85–55 °C) and C9 (45–68.4 °C).  Addition of a new heat exchanger (E15) with a heat load of 4500.00 kW for heat exchange between H9(100–83.6 °C) and C11(70–90 °C). The rest part of H9 is cooled by cooling water through the existing E1122.

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Table 7 Stream data for the hydrazine hydrate plant. No.

Stream

Supply temperature (°C)

Target temperature (°C)

Heat load (kW)

H1 H2 H3

Hypochlorite Synthesis fluid Synthesis fluid

H4

Synthesis fluid

H5 H6 H7 H8 H9 H10 H11 C1 C2

Overhead product of fractionator Overhead product of fractionator Overhead product of fractionator Overhead product of fractionator Semi-finished product Distillate from product column Distillate from product column Mixture of hypochlorite and urea Synthesis fluid

C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13

Synthesis fluid Mixture of hydrazine hydrate Synthesis fluid Mixture of hydrazine hydrate Synthesis fluid Mixture of hydrazine hydrate Synthesis fluid Mixture of hydrazine hydrate Mixture of hydrazine hydrate Semi-finished product Semi-finished product

20 100 80 65 45 80 67 50 30 85 85 85 85 100 113 113 12 5 30 44 95 44 95 45 95 45 95 70 60 60

10 80 65 45 2 67 50 30 2 30 30 30 30 70 70 70 108 30 44 110 105 110 105 95 105 95 105 110 123 123

555.56 1388.89 471.06 636.57 135.42 444.44 597.22 694.44 57.87 3055.56 4888.89 8250.00 8250.00 2361.11 1362.85 1753.47 2527.78 1388.89 444.44 6042.50 611.11 5694.44 972.22 9611.11 1638.89 9611.11 1638.89 2583.33 1423.61 1840.28

and water and water and water and water and water

Table 8 Batch stream data. No.

Stream

Supply temperature (°C)

Target temperature (°C)

Start time (h)

End time (h)

Heat load (kW)

H3 H4 H10 H11 C12 C13

Synthesis fluid Synthesis fluid Distillate from product column Distillate from product column Semi-finished product Semi-finished product

80 80 113 113 60 60

2 2 70 70 123 123

0:00 11:30 3:00 9:00 3:00 9:00

11:00 23:30 18:00 24:00 18:00 24:00

2712.11 3587.94 2180.56 2805.55 2277.78 2944.45

For the heater below the pinch, because stream C1 contains NaClO, which is unstable and easily decomposable, the heater is left as it is. The above retrofit saves 16,014 kW of heating and cooling utilities. (2) Retrofit schemes for batch streams: From Tables 8 and 9, we get the batch streams involved in the heat transfer across the pinch situation and they are shown in Fig. 17. In this figure the heat load for each stream is given in parentheses and placed beside the vertical axis. Numbers placed next to the arc arrows indicate inappropriately exchanged heat.

Fig. 15. Temperature–enthalpy diagram based on the stream data of the case study.

 For the exchangers across the pinch, the following measures are implemented.  Addition of a new heat exchanger (E16) with a heat load of 1388.89 kW for heat exchange between H2 (100–80 °C) and C9 (68.4–75.6 °C).  H2 (55–46 °C) is cooled by C2 (5–30 °C) through the existing E1104 with a heat load of 1388.89 kW.

The batch process is cyclic with a batch period of 24 h. Two retrofit schemes are considered: matches between batch streams and matches between batch and continuous streams. Matches between batch streams: To recover more energy, indirect heat integration is adopted for this retrofit scheme. The procedures for indirect heat integration are as follows. (a) Determination of potential streams for indirect heat integration: The potential heat sources are all the hot streams involved in the inappropriate heat exchange matches

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Fig. 16. Existing heat exchanger network of the case study.

Table 9 The heat transfer across the pinch situation in the hydrazine hydrate plant. Heat exchanger

Stream

Heat transfer across the pinch/kW

Type of inappropriate match

E1105a E1105b E1107b E1111abc E1114abc E1117abcde E1120abcde E1122 E1124 E1126 E1104 E1107a E1102abc E1109 E1112

Synthesis fluid Synthesis fluid Synthesis fluid Overhead product of fractionator Overhead product of fractionator Overhead product of fractionator Overhead product of fractionator Semi-finished product Distillate from product column Distillate from product column Synthesis fluid Synthesis fluid Mixture of hypochlorite and urea Synthesis fluid Synthesis fluid

471.06 318.29 421.57 1666.67 2666.67 4500.00 4500.00 2361.11 1362.85 1753.47 1388.89 444.44 868.92 91.56 86.28 Total = 22901.80

Use of cold utility above the pinch

depicted in Fig. 17, and the potential heat sinks are the cold streams that can cool the sources. The results are shown in Table 11.

Heat transfer across the pinch Use of hot utility below the pinch

(b) Transformation into media streams: The temperature of each source is lowered by DTmin (10 °C) to form a media hot stream (h) and that of each sink remains unchanged to

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Table 10 Continuous streams involved in the heat transfer across the pinch situation. No.

Stream

Heat exchanger

Inlet temperature (°C)

Outlet temperature (°C)

Heat load (kW)

H2 H5 H6 H7 H8 H9 C1 C3 C5

Synthesis fluid Overhead product of fractionator Overhead product of fractionator Overhead product of fractionator Overhead product of fractionator Semi-finished product Mixture of hypochlorite and urea Synthesis fluid Synthesis fluid

E1104 E1111abc E1114abc E1117abcde E1120abcde E1122 E1102abc E1109 E1112

100 85 85 85 85 100 12 44 44

80 55 55 55 55 70 45 45 45

1388.89 1666.67 2666.67 4500.00 4500.00 2361.11 868.92 91.56 86.28

Fig. 17. Batch streams involved in the heat transfer across the pinch situation.

Table 11 Potential heat sources and heat sinks for the case study. Type

Time interval (h)

Host stream

Temperature interval (°C)

Heat load (kW)

HR11 HR10 HR4 HR3 HS13 HS12

9:00–24:00 3:00–18:00 11:30–23:30 0:00–11:00 9:00–24:00 3:00–18:00

H11 H10 H4 H3 C13 C12

113–70 113–70 80–55 80–55 60–123 60–123

2805.55 2180.56 1093.88 826.86 2944.45 2277.78

Table 12 Media hot and cold streams for the case study. Original name

Name after transformation

Supply temperature (°C)

Target temperature (°C)

Start time (h)

End time (h)

Heat load (kW)

HR11 HR10 HR4 HR3 HS13 HS12

h11 h10 h4 h3 c13 c12

103 103 70 70 60 60

60 60 45 45 123 123

9:00 3:00 11:30 0:00 9:00 3:00

24:00 18:00 23:30 11:00 24:00 18:00

2805.55 2180.56 1093.88 826.86 2944.45 2277.78

form a media cold stream (c). The sources and sinks in Table 11 are transformed into the corresponding media hot and cold streams in Table 12. (c) The Q–t diagram for media streams: All the media streams in Table 12 are plotted on the Q–t diagram, as shown in Fig. 18. The streams can be matched without time sequence constraints.

(d) Direct heat integration of media streams: As before, a DTmin of 10 °C is used. According to the stream temperatures and heat loads, h11 and h10 can be matched with c13 and c12. Because the original streams of c13 and h11 are C13 and H11, which appear in the same column (the product column), such matching of streams belonging to the same column should have first priority. This is also true for streams

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Fig. 18. Q–t diagram for media streams of the case study.

Table 13 Batch streams involved in inappropriate heat exchange matches. No.

Name

Heat exchanger

Supply temperature (°C)

Target temperature (°C)

Start time (h)

End time (h)

Heat load (kW h)

H11 H10 H4

Distillate from product column Distillate from product column Synthesis fluid

113 113 80

70 70 55

9:00 3:00 11:30

24:00 18:00 23:30

2805.55 2180.56 1093.88

H3

Synthesis fluid

E1126 E1124 E1107a E1107b E1105a E1105b

80

55

0:00

11:00

826.86

H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13

E1101abc E16

E1104 E1107a

E1107bc

E1105ab E1108

E11

E1111abc E1114abc E1117

E12 E13 E14

E1120 E15

E1122

E1122 E18

E1124 E1126

E17 E1102abc E1107a E1109

E1104

E11

E1110 E1112

E12

E1113 E1115 E1116 E1118 E1119 E1121

E13

E16

E14

E15

E1123 E1125

E18 E17 Fig. 19. Retrofited heat exchanger network of the case study.

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c12 and h10. Accordingly, h11 is used to heat c13 and h10 is used to heat c12. In this way, 2735 kW (15 h/24 h) utilities or 1710 kW (24 h) can be saved. Matches between batch and continuous streams: When a batch stream matches with a continuous stream, they can only exchange heat during the time interval in which the batch stream exists. The continuous stream will have to exchange heat with utilities in other time intervals. Because continuous streams exist in all time intervals, direct heat integration can be used. The hot batch streams involved in the inappropriate heat exchange matches are listed in Table 13, in which the supply and target temperatures only cover the inappropriate heat exchange. A DTmin of 10 °C is again used. According to the temperatures of the batch streams in Table 13, continuous streams C7 and C9 are the suitable ones for matching with the batch streams. Because the temperature and heat load of C7 and C9 are identical (45–95 °C, 9611.11 kW), and the heat load of either stream is sufficient to cool all the four batch streams in Table 13, only one continuous stream can be selected. The retrofit scheme is developed using C7 as example stream. C7 is split into five sub-streams. The one with a heat load of 2805.55 kW, i.e. C71, cools H11 through the existing E1126 and the one with a heat load of 2180.56 kW, i.e. C72, cools H10 through the existing E1124. C73 (45–70 °C, 1093.88 kW) cools H4 through the existing E1107a and E1107b, C74 (45–70 °C, 826.86 kW) cools H3 through the existing E1105a and E1105b, and the last one, i.e. C75, together with the remaining heat load of the other four sub-streams, will have to be heated by hot utility through the existing E1115. In summary, a saving of 4094 kW of hot and cold utilities is achieved. (3) Choice of retrofit schemes: Three retrofit schemes have been devised for the heat exchanger network of the hydrazine hydrate plant. From the energy saving standpoint, the retrofit scheme for continuous streams is a good choice because it gives significant energy savings. The two retrofit schemes for batch streams provide additional heat recovery opportunities. Of the two schemes, the one based on matches between batch and continuous streams is more attractive as it gives a bigger energy saving. The energy saving from this retrofit scheme is about 25% of that from the retrofit scheme for continuous streams. It is evident that integration of this heat exchanger network without considering its batch streams can limit the total energy saving. Fig. 19 shows the network structure after retrofit. The dished lines and exchangers indicate the indirect heat integration. The structure consider the retrofit scheme for continuous streams and the indirect heat integration schemes. From the figure, the network is much more integrated than the original one. 7. Conclusions In this paper, heat integration of continuous processes featuring batch streams has been studied. A list of major findings is given below. (1) The proposed heat duty–time (Q–t) diagram can intuitively and fully express the time and thermal features of batch streams and provide a graphical basis for heat integration of continuous processes featuring batch streams.

(2) The energy targets for a batch process example identified by the Q–t diagram method are identical to those obtained from the cascade analysis method. The Q–t diagram method has the further advantage that the structure of the initial heat exchanger network can be easily obtained. (3) By considering heat degradation in the intermediate heat storage, the concept of media streams is used to transform indirect heat integration of batch streams into direct heat integration of media streams. This transformation allows indirect heat integration analysis to be carried out on the Q–t diagram. (4) The heat exchanger network of a hydrazine hydrate plant has been analyzed and optimized using the proposed method. This network has 18 continuous and six batch streams. The following three retrofit schemes have been considered: (a) scheme based on matches between continuous streams, (b) scheme based on matches between batch streams, and (c) scheme based on matches between batch and continuous streams. The retrofit analysis reveals that the third scheme can give substantial heat recovery. As such, heat integration of this network without considering its batch streams can limit the total energy saving.

Acknowledgements Financial support from the National Basic Research Program of China (973 Program: 2012CB720500) and the National Natural Science Foundation of China under Grant No. 20936004 is gratefully acknowledged. References [1] Linnhoff B, Hindmarsh E. The pinch design method for heat exchanger networks. Chem Eng Sci 1983;38(5):745–63. [2] Asante NDK, Zhu XX. An automated and interactive approach for heat exchanger network retrofit. Chem Eng Res Des 1997;75(3):349–60. [3] Ciric AR, Floudas CA. Heat exchanger network synthesis without decomposition. Comput Chem Eng 1991;15(6):385–96. [4] Yee TF, Grossmann IE. Simultaneous optimization models for heat integration – II. Heat exchanger network synthesis. Comput Chem Eng 1990;14(10):1165–84. [5] Wang Y, Pan M, Bulatov I, Smith R, Kim J-K. Application of intensified heat transfer for the retrofit of heat exchanger network. Appl Energy 2012;89(1):45–59. [6] Zhang N, Smith R, Bulatov I, Klemeš JJ. Sustaining high energy efficiency in existing processes with advanced process integration technology. Appl Energy 2013;101:26–32. [7] Vaskan P, Guillén-Gosálbez G, Jiménez L. Multi-objective design of heatexchanger networks considering several life cycle impacts using a rigorous MILP-based dimensionality reduction technique. Appl Energy 2012;98:149–61. [8] Markowski M, Trafczynski M, Urbaniec K. Identification of the influence of fouling on the heat recovery in a network of shell and tube heat exchangers. Appl Energy 2013;102:755–64. [9] Fernández I, Renedo CJ, Pérez SF, Ortiz A, Mañana M. A review: energy recovery in batch processes. Renew Sustain Energy Rev 2012;16(4):2260–77. [10] Linnhoff B, Ashton G, Obeng E. Process integration of batch processes. In: 79th AIChE annual meeting. New York; 1987. [11] Obeng E, Ashton G. On pinch technology based procedures for the design of batch processes. Chem Eng Res Des 1988;66(3):255–68. [12] Kemp I, Deakin A. The cascade analysis for energy and process integration of batch processes, Part 1: Calculation of energy targets. Chem Eng Res Des 1989;67(5):495–509. [13] Kemp I, Deakin A. The cascade analysis for energy and process integration of batch processes, Part 2: Network design and process scheduling. Chem Eng Res Des 1989;67(5):510–6. [14] Wang Y, Smith R. Time pinch analysis. Chem Eng Res Des 1995;73(8):905–14. [15] Foo DCY, Chew YH, Lee CT. Minimum units targeting and network evolution for batch heat exchanger network. Appl Therm Eng 2008;28(16):2089–99. [16] Chen C-L, Lee J-Y. A graphical technique for the design of water-using networks in batch processes. Chem Eng Sci 2008;63(14):3740–54.