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Synthesis of heat exchanger networks featuring batch streams
Yufei Wang a, Ying Wei b, Xiao Feng a,⇑, Khim Hoong Chu b
a State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, Chinab 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 2013Received in revised form 27 August 2013Accepted 17 September 2013Available online 13 October 2013
Keywords:Heat exchanger networkGraphical methodBatch streamIntermediate mediaEnergy 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 heatexchanger networks featuring batch streams. Using the Q–t diagram method, the energy targets andthe structure of the initial heat exchanger network can be easily obtained. The method can be used bothfor direct and indirect heat integration of batch streams. For indirect heat integration, the heat degrada-tion of intermediate media is considered. A case study on optimizing the heat exchanger network of ahydrazine hydrate plant is used to illustrate the application of the method. The results show that integra-tion of this heat exchanger network without considering its batch streams can limit the total energysavings.
� 2013 Elsevier Ltd. All rights reserved.
1. Introduction
Chemical processes can be broadly divided into continuous andbatch operations. Although not common, there exist some contin-uous processes featuring batch streams. Notable examples includethe hydrazine hydrate production process and the delayed cokingprocess. Because chemical processes consume large amounts of fi-nite energy resources, many heat integration techniques have beendeveloped over the years to improve their energy efficiency. Forexample, heat exchanger networks in numerous continuous andbatch processes in the chemical industry have become highly en-ergy efficient as a result of heat integration. Nevertheless, despitethis remarkable success, heat integration analysis has not yet beenapplied to continuous processes featuring batch streams. Althoughusually only a limited number of key batch streams are present insuch processes, the heat content of these batch streams could bequite substantial. As such, heat integration analysis that treats thistype of hybrid processes as strictly continuous by ignoring thesmall number of batch streams can limit the total energy savings.
Synthesis of heat exchanger networks of continuous processeshas been studied extensively, either by pinch technology [1,2] orby mathematical programming techniques [3,4]. Because pinchtechnology offers the advantages of intuitiveness, simplicity andclarity when compared to the mathematical programming ap-proach, it is widely used in industry. In recent development of heatexchanger networks synthesis of continuous processes, Wang et al.[5] proposed a methodology to consider heat transfer enhance-ment in the optimization of heat exchanger network. Zhang et al.[6] developed a method for optimizing the operation condition ofheat exchanger network and distillation columns simultaneously.This methodology allows the industry to improve its economicand environment performance at the same time. Vaskan et al. [7]developed a multi-objective design method for heat exchangernetwork by using a MILP based model. Life cycle assessment andenvironment were involved in this method. Markowski et al. [8]proposed a heat exchanger network synthesis methodology con-sidering fouling. This methodology can monitor long-term changesin the heat exchanger network efficiency.
With suitable adaptations, most of the heat integration meth-ods developed for continuous processes can be used to search forheat integration opportunities in batch processes which are
0306-2619/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.apenergy.2013.09.040
⇑ Corresponding author. Tel.: +86 15811168976.E-mail addresses: [email protected], [email protected] (X. Feng).
Applied Energy 114 (2014) 30–44
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characterized by their time-dependent mode of operation. A vari-ety of models have been developed for heat integration of batchprocesses since the 1980s [9], some of which are described below.
(1) Time average model [10]: This model is also called pseudo-continuous process model. The heat duties of all streams inthe batch process are time averaged in the production cycle,and the utility targets are then obtained by pinch technol-ogy. Because the time-dependent features of batch streamsare not considered, the targets are highly ideal and can onlybe approached with extensive use of heat storage.
(2) Time segmentation model [11]: In this model, batch streamsare re-arranged in a limited manner to recover more wasteheat and avoid heat storage. This method is constrained bywhether the actual process allows the re-arrangement ofbatch streams.
(3) Time and temperature cascade analysis [12,13]: The methodconsiders simultaneously time and temperature. Heat inte-gration in the same time interval is considered first, followedby consideration of the time sequence. Although intermedi-ate heat storage is included in the method, the heat degrada-tion of intermediate media is not considered.
(4) Time pinch method [14]: The heat recovery target isobtained by using time as the main constraint and heattransfer driving force as the secondary factor. The methodincludes direct and indirect heat recovery. The heat degrada-tion of intermediate media is not considered.
In this paper, a new graphical method based on the heatduty–time diagram will be provided for the heat integration ofcontinuous processes featuring batch streams. The proposed meth-od is largely based on the many heat integration concepts and toolsarising from the research on continuous and batch processes. Themethod 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 developedin this work expresses the time and thermal features of batchstreams intuitively and provides a practical graphical tool for heatexchanger network synthesis. As will be explained below, themethod is based essentially on a combination of the Gantt chartand the temperature–enthalpy diagram (T–H diagram) commonlyused in traditional pinch analysis to represent continuous streams.
The Q–t diagram will now be illustrated by application to abatch process reported by Kemp and Deakin [12]. The stream dataare given in Table 1. In this four-stream example, the batch periodis 1 h with each stream only existing for a limited time period. Rep-resenting the streams graphically will allow a better appreciationof their time-dependent nature. A handy method of visualizationis the Gantt chart, which is a type of time event chart. The Ganttchart is useful for visualizing which streams exist in which periods.
As pointed out earlier, the T–H diagram is a key tool of energy-based pinch analysis which is used to represent the thermalfeatures of continuous streams. And the proposed Q–t diagram isa hybrid of the Gantt chart and the T–H diagram which is able torepresent the thermal features as well as the time-dependent
nature of batch streams on the same plot. Fig. 1 shows a coldstream (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 forthe horizontal axis. The arrowheads in Fig. 1 indicate the directionof temperature increase for the cold stream and the direction oftemperature decrease for the hot stream. The temperature of thecold and hot streams increases and decreases with time, respec-tively. Therefore, the cold stream line has a positive slope whilethe hot stream line a negative slope. The vertical axis length de-fined by the stream boundaries gives the stream heat load whilethe horizontal axis length defined by the stream boundaries pro-vides the stream time interval. Like T–H diagrams, in the Q–t dia-grams, moving the cold and hot streams upward or downwardwill not affect their heat loads. They can therefore be plotted any-where on the vertical axis.
For multiple batch streams, a systematic procedure for con-structing 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 supplytemperature and must thus be a cold stream (If the streamwith lowest supply temperature is a hot stream, it shouldbe kept outside the heat recovery project). If two streamshave the same supply temperature, rank the one with thelower target temperature first. If two streams have identicalsupply temperature and target temperature, rank the onewith the lower heat duty first.
(3) Plot the top ranked stream on the Q–t diagram using its cal-culated heat duty value and time interval. Begin with thestart time. Its y-coordinate (initial heat duty value) at thestart time is assumed zero. Its y-coordinate (final heat dutyvalue) 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 isgiven by the largest y-coordinate of the preceding stream. Itsy-coordinate at the end time is given by the sum of its heatduty 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 isgiven by the largest y-coordinate of the preceding stream. Itsy-coordinate at the start time is given by the sum of its heatduty and the largest y-coordinate of the preceding stream.The plotted line will have a negative slope. Plot the remain-ing streams in the ranking order using the above procedure.
With the four-stream example given in Table 1, let us illustratehow the Q–t diagram can be constructed using the procedure de-scribed above.
(1) The heat load of each stream is calculated from the followingequation:
Q i ¼ CPiDTiDti ð1Þ
where Qi = heat load of stream i (kW h), CPi = heat capacity flow rateof stream i (kW �C�1), DTi = difference of target and supply
Table 1Stream data.
No. Type Supply temperature (�C) Target temperature (�C) Heat capacity flow rate (kW �C�1) Start time (h) End time (h) Heat duty (kW h)
1 H1 170 60 4 0.25 1 3302 H2 150 30 3 0.3 0.8 1803 C1 20 135 10 0.5 0.7 2304 C2 80 140 8 0 0.5 240
Y. Wang et al. / Applied Energy 114 (2014) 30–44 31
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 ofTable 1.
(2) Ranking the four streams in ascending order of supply tem-perature gives C1, C2, H2 and H1.
(3) We begin by plotting the top ranked stream C1. Its starttime, end time, and heat duty are 0.5 h, 0.7 h, and230 kW h, respectively. The y-coordinate at 0.5 h is zerokW h while that at 0.7 h is 230 kW h. Hence, the coordinatesof the C1 plot are given by (0.5, 0) and (0.7, 230), as shown inFig. 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 givenby the largest y-coordinate of the preceding stream, which is230 kW h. The y-coordinate at 0.5 h is 470 kW h, which isthe sum of C1’s heat duty (240 kW h) and the largest y-coor-dinate of the preceding stream (230 kW h). So, C2 can nowbe 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 isgiven 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 larg-est y-coordinate of the preceding stream (470 kW h). Fig. 4shows 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, and330 kW h. Because H1 is also a hot stream, we begin withthe end time. The y-coordinate at 1 h is given by the largesty-coordinate of the preceding stream, which is 650 kW h.The y-coordinate at 0.25 h is 980 kW h, which is the sumof H1’s heat duty (330 kW h) and the largest y-coordinateof 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 positiveslopes while the two hot stream plots have negative slopes. Theproposed procedure for constructing the Q–t diagram gives a usefulrepresentation of when streams coexist as well as the heat dutiesof the streams unambiguously. To make the stream heat dutieseven more obvious, the actual heat duties of the streams exceptC1 are given in parentheses by the side of the respective heat loadinterval on the vertical axis (Fig. 2). However, it is not possible toplot stream temperatures on the Q–t diagram. To include temper-ature details, the supply temperature and target temperature of
each stream are given in parentheses at the boundaries of eachstream plot, as shown in Fig. 2. Note that a continuous stream atsteady-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 tonote that in the Q–t diagrams, the temperature of streams changefrom its supply temperature to target temperature in every timeinterval it exists. It does not mean the temperature of streamchanges throughout from supply temperature in its start time totarget 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 batchprocess exist in the same time interval. This is known as direct heatintegration. After maximum heat recovery in a time interval isachieved, the remaining heat in the hot streams is removed by coldutility and the balance of heat required by the cold streams is pro-vided by hot utility. Heat cannot be exchanged across differenttime intervals, that is, a hot and a cold stream in different timeintervals cannot be matched. Rescheduling of streams to allowsome heat to be recovered by direct heat integration is not consid-ered 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.
Fig. 1. Q–t diagrams for batch streams without phase change.
Fig. 2. Q–t diagram for the four-stream example given in Table 1.
32 Y. Wang et al. / Applied Energy 114 (2014) 30–44
(1) Specify DTmin and calculate energy targets: The energy tar-gets, QHj and QCj for time interval j, are determined fromthe Q–t diagram. For each time interval, the network is syn-thesized according to the principles of pinch technology (noutility coolers above the pinch, no utility heaters below thepinch, and no heat exchangers transferring heat across thepinch).
(2) Determine the energy targets for the whole cycle (QH =P
QHj
and QC =P
QCj).
Direct heat integration of the four-stream example given in Ta-ble 1 will now be illustrated using the Q–t diagram in Fig. 2. As canbe seen in Fig. 2, there is a total of six time intervals over the batchperiod of 1 h. In the following calculation, a DTmin of 10 �C isassumed.
(1) Calculate QHj and QCj for each time interval: In this step, thetime interval [0.5–0.7 h] is used as an example. Fig. 2 showsthat three batch streams, H1, H2 and C1 coexist in this timeinterval. The heat load of stream i in time internal j can becalculated from the following equation:
Q ij ¼ Q iDtj
Dtið2Þ
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, heatexchange matches can now be identified. Splitting C1 into threebranches according to duties of the hot streams in the same timeinterval, one branch with a heat load of 88 kW h cools H1 to its tar-get temperature at the end of the time interval (104 �C), anotherwith a heat load of 72 kW h cools H2 to its target temperature atthe end of the time interval (54 �C), and the last one with a heatload of 70 kW h is heated by hot utility. The heat capacity flowrates of the three branches are 10(88/230) = 3.83 kW �C�1, 10(72/230) = 3.13 kW �C�1 and 10(70/230) = 3.04 kW �C�1, respectively.The heat exchange matches and the heat duty of each match forthis time interval are shown in Fig. 3. In this figure, numbers inbold refer to the heat duties of direct heat exchange between hot
and cold streams and the underlined number denotes the requiredhot utility.
The direct heat integration of hot and cold streams for the otherfive time intervals can be determined in the same way describedabove. A summary is given below.
[0–0.25 h]: A single cold stream exists in this interval. C2 needs120 kW h hot utility.
[0.25–0.3 h]: One cold stream and one hot stream exist in thisinterval. H1 and C2 exchange 16 kW h heat (due to minimum tem-perature approach, they cannot exchange all 22 kW h heat), theremaining 8 kW h heat duty required by C2 is supplied by hot util-ity, and the remaining 6 kW h heat duty of H1 is removed by coldutility.
[0.3–0.5 h]: One cold stream and two hot streams exist in thisinterval. C2 is split into two branches, one of which with a heatload of 60 kW h cools H1 and the other with a heat load of36 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 needs44 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 needs88 kW h cold utility.
In summary, three time intervals require hot utility and four re-quire cold utility. The results of direct heat integration for thewhole cycle are shown in Fig. 4. As noted above, numbers in boldrefer to the heat duties of direct heat exchange between hot andcold streams, underlined numbers signify heating utilities neededby cold streams, and numbers in normal font denote cold utilitiesneeded by hot streams.
(2) Determine the energy targets for the whole cycle (QH andQC): The hot utility target for the whole cycle, QH, can beobtained simply by summing all the underlined numbersin Fig. 4. Similarly, the minimum cold utility for the wholecycle is given by the sum of all the numbers in normal fontin Fig. 4. The two overall utility targets are shown below.
Q H ¼X
Q Hj ¼ 120þ 8þ 70 ¼ 198 kW h
Q C ¼X
Q Cj ¼ 6þ 28þ 44þ 88þ 36þ 36 ¼ 238 kW h
The corresponding heat recovery is 272 kW h. These targeting re-sults are the same as those obtained by using the cascade analysismethod proposed by Kemp and Deakin [12]. From the Q–t diagramin Fig. 4, the structure of the initial heat exchanger network can be
Fig. 3. Direct heat integration in the [0.5–0.7 h] time interval. Fig. 4. Indirect heat integration for the entire batch period [0–1 h].
Y. Wang et al. / Applied Energy 114 (2014) 30–44 33
easily obtained, as shown in Fig. 5. Therefore, the Q–t diagram ap-proach proposed in this work is superior to the cascade analysismethod. It is noted that in Fig. 5, the stream in a time interval indi-cates that the stream exists in this time interval, two streams willexchange heat with each other only when they both exist in thattime interval.
3.2. Network optimization
To reduce the capital cost of heat exchanger networks, the num-ber of matches or units should be minimized. In general, this canbe done by breaking loops and removing units. The minimumnumber of matches or units can be determined by Euler’s networktheorem. In this work, a simplified form of Euler’s network theo-rem is used for heat exchanger network analysis, which is ex-pressed as U = N � 1. In this equation, U denotes the number ofunits (heat exchangers) and N indicates the number of streamsincluding utility streams.
As shown in previous sections, streams in batch processes existin different time intervals and some streams exist across severaltime intervals. As a result, some of their heat exchange matcheswill also exist in several time intervals. For example, Fig. 4 showsthat 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 ofmatches are counted by Euler’s network theorem for different timeintervals, those matches existing in several time intervals will becounted several times, leading to a larger number of heat exchang-ers. Exchangers due to miscounting are known as additionalexchangers [15]. To reduce the number of matches, a useful meth-od is to use one exchanger to exchange heat for the same hot andcold streams that exist in different time intervals, that is, additionalexchangers should be removed. Accordingly, the minimum num-ber of matches for the whole cycle can be expressed in the follow-ing way.
Umin ¼ Umin;0 �X
Uþ ¼X
j
Umin;j �X
Uþ ð3Þ
where Umin = minimum number of matches for the whole cycle,Umin,0 = sum of minimum number of matches counted by Euler’s
network theorem for each time interval, andP
U+ = sum of addi-tional exchangers. Using Eq. (3), the minimum number of matchesfor the four-stream example is Umin =
PjUmin,j �
PU+ = 13 � 6 = 7.
From Fig. 5 it can be seen that there are five heat exchangers(E1, E2, E3, E4, E5), six coolers (E�1, E�3, E�6, E�7, E�8, E�9)and three heaters (E�2, E�4, E�5) in the network, giving a totalof 14 heat exchange units. This is seven units more than the min-imum number of matches. It can be deduced from Fig. 5 that thereare seven loops in the network, in which the four coolers for streamH1 form three, the two coolers for stream H2 form one, the twoheaters for stream C2 form one, two heat exchanger pairs, E1–E2and E2–E3, each forming one, and coolers E�6 and E�7 formone, as shown in Fig. 6.
When optimizing the network, firstly, additional exchangersshould be combined, and only the unit with the biggest heat loadis retained. Therefore, cooler E�8 is chosen for stream H1, coolerE�3 for stream H2, heater E�2 for stream C2 and exchanger E2for the match between streams H1 and C2, as shown in Fig. 7.Now the network still has one loop left, that is,E�8 ? E2 ? E3 ? E�3. Breaking this loop will increase the utilityrequirements. So the loop is retained.
4. Application of the Q–t diagram – indirect heat integration
As mentioned above, heat recovery by direct heat integration isnot 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 inte-gration can be realized by using thermal storage and intermediatemedia, that is, hot streams in a certain time interval release heat toan intermediate medium for storage, and the intermediate med-ium discharges the stored heat to cold streams that exist in othertime intervals. In this way, heat recovery is feasible across differenttime intervals. Because heat transfer temperature differences areneeded for the intermediate medium, compared with the originalhot stream, the intermediate medium has a lower temperature,which means that using an intermediate medium will cause heatdegradation.
Fig. 5. Initial heat exchanger network for the entire batch period.
34 Y. Wang et al. / Applied Energy 114 (2014) 30–44
