Improved Targeting Procedure To Determine the Indirect Interplant

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An improved targeting procedure to determine the indirect inter-plant heat integration with parallel connection pattern among three plants Runrun Song, Yufei Wang, Marc Panu, Mahmoud M El-Halwagi, and Xiao Feng Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04327 • Publication Date (Web): 12 Jan 2018 Downloaded from http://pubs.acs.org on January 12, 2018

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Industrial & Engineering Chemistry Research

An improved targeting procedure to determine the indirect inter-plant heat integration with parallel connection pattern among three plants

Runrun Song a, Yufei Wang a*, Marc Panu b, Mahmoud M. El-Halwagi b, Xiao Feng c a

State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, China

b

Artie McFerrin Chemical Engineering Department, Texas A&M University, College Station, TX 77843, United States

c

School of Chemical Engineering & Technology, Xi’an Jiaotong University, Xi’an 710049, China

ABSTRACT The inter-plant heat integration (IPHI) problem has received growing interest for its potential to reduce energy consumption and emissions beyond heat integration within individual plants. Indirect IPHI using an intermediate energy carrier (intermedium) allows for practical implementation as opposed to direct IPHI, which may consist of multiple piping loops using process streams. Various inter-plant connection patterns of intermedium loops present differences in inter-plant heat recovery potential, pipeline costs and the reliability of IPHI system. This work addresses the parallel connection pattern for it presents the maximum inter-plant heat recovery potential and is a flexible pattern. An improved targeting procedure is proposed to determine the parallel connection pattern. This method can determine the real maximum inter-plant heat recovery potential for indirect IPHI among three plants and simultaneously minimize the corresponding intermedium flowrates. Two examples from prior literatures, as well as the modified cases, are solved to demonstrate the proposed method. The proposed method can always present multiple feasible solutions for IPHI problems. Compared with the previous results for the certain case, under the same inter-plant heat recovery potential, a better solution in terms of the overall intermedium flowrate and/or the number of heat exchanger used can be found from all the feasible ones. Key words: Inter-plant; Heat integration; Pinch; Connection pattern; Parallel; Intermedium; Heat recovery loop *

Corresponding author. E-mail address: [email protected] (Y. Wang).

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1. Introduction Heat Integration (HI) is a systematic method for designing integrated energy systems ranging from individual processes within one plant to entire facilities. Rising energy demands and growing concern regarding environmental sustainability have made the energy conservation via HI an essential way of industrial process grassroots design and retrofit. Facility-wide HI or Total Site Heat Integration (TSHI), was introduced by Dhole and Linnhoff [1] to determine additional reductions in energy use across multiple plants at one site. TSHI is typically defined as HI implemented by the site utility system [2]. Excess heat from a process can be transferred to another process via the site utility system by generating steam or using intermediate fluids [3]. A subsection of TSHI, Inter-Plant Heat Integration (IPHI), focuses on inter-plant heat exchange opportunities between streams from different plants [4]. Klemeš et al.[2] and Liew et al.[3] reviewed the development in forty years of HI and TSHI through Pinch Analysis (PA) and Mathematical Programming (MP) until 2012 and 2016, respectively. Direct IPHI is defined as an HI implementation in which heat is transferred from a process stream in one plant directly to a process stream in another plant [5]. However, a major capital investment may be required to construct a piping network across plants due to the long distances among them. Moreover, multiple piping loops may be required for a direct IPHI problem with multiple participating streams, which will also increase the piping costs. Indirect IPHI is similar to direct IPHI except that indirect IPHI using intermediate fluids (such as utility system [6], hot oil [7] or hot water [8]) to exchange heat. In indirect IPHI, heat is first transferred from heat source to intermedium and then is transferred from intermedium to heat sink. One advantage of indirect IPHI is that it can reduce the cost of building extensive piping loops. However, indirect IPHI requires a bigger approach temperature (∆Tmin) than direct IPHI, therefore leading to potentially smaller maximum heat recovery potential than direct IPHI. In this work, hot water or hot oil is used as the heat transfer intermedium. The connection pattern is defined as the inter-connection of intermedia among plants. The connection pattern and the heat capacity flowrate (CP) of each intermedium loop are the key design variables to be optimized. These decision variables directly determine the energy target and the piping and pumping costs of the IPHI system [9]. In fact, the case study


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results from Chang et al. [9] showed that the piping and pumping costs account for 12% of the Total Annual Cost (TAC). That is almost as expensive as the costs of the heat exchanger units used. Most of the previous methodologies for IPHI focused on exploiting the theoretical maximum inter-plant heat recovery potential or synthesizing the IPHI configuration with different constraints and objectives. Bade and Bandyopadhyay [10] proposed a graphical method to minimize the hot oil flowrate for IPHI between two plants. In their work, the intermedium line with minimum CP in each heat recovery region is selected, which might still lead to multiple Heat Recovery Loops (HRLs) between plants. Wang et al. [11] proposed three basic connection patterns for IPHI among three plants: parallel, split and series connection patterns. Different energy recovery performances and pipeline length requirements are compared among these three different connection patterns. However, the pipeline length is not the only factor which affects the piping investment. The intermedium flowrate, which affects the piping size and thus the piping investment, should also be considered. Wang et al. [5] also presented a framework combining direct and indirect IPHI. It showed that the combined method presented a lower TAC than that of single use of direct or indirect IPHI under certain cases. Among the three basic connection patterns, the parallel connection pattern can always recover more heat than the other two patterns. However, the parallel connection pattern requires the longest pipelines [11]. Nevertheless, the pipeline length is not the only factor that affects the piping investment. The cost of the intermedium and the diameter of the pipelines are also significant contributors to the total cost of the piping. Considering the same set of plants, the flowrate of each intermedium needed in the parallel connection pattern is much smaller than that of the split and series connection patterns. Although the length of the pipelines is longer, the cost may be less due to smaller diameter of pipeline and less flowrate of intermedium. Moreover, the engineers may choose to use two different intermedia for the different temperature intervals in the parallel pattern. For instance, instead of utilizing one single intermedium for indirect IPHI in the split and series connection patterns, a parallel connection pattern may use hot oil to transfer the high temperature heat and hot water to transfer the low temperature heat. This may help to reduce the TAC because less expensive intermedia and piping may be used where appropriate. Furthermore, the three plants are connected by two independent intermedium loops in the parallel connection pattern. This is also beneficial for the control and safety of IPHI



system because of the parallel connection pattern presents fewer inter-connections than the split and series connection patterns. In this work, the parallel connection pattern is selected to implement the indirect IPHI. In the method of Wang et al. [11], in order to determine the energy target and flowrates of intermedia for different connection patterns, two simplified curves are drawn separately for the two heat sink (or source) composite curves in the very beginning. The simplified curve is a straight line that formed by two convex points (including the starting and the terminal points of the corresponding composite curve). The simplified curve is also used as the intermedium line for each heat sink (or source) plant. The parallel structure is determined through compositing two simplified curves together and then get pinched with the heat source (or sink) composite curve. However, the drawing of the simplified curves may change the original site pinch, and thus, may miss the real maximum inter-plant heat recovery potential. Moreover, such an action definitely leads to a multiple pinch problem between each heat sink (or source) and intermedium. The Heat Exchanger Network (HEN) design of multiple pinch problem [12] is usually more difficult and more complicated than that of the single pinch problem or threshold problem. Therefore, further research should focus on the determination of the real maximum inter-plant heat recovery potential and the corresponding connection pattern/ minimum flowrates of intermedia for indirect IPHI. In this work, an improved targeting procedure is proposed to simultaneously target the maximum interplant heat recovery potential and minimum intermedium flowrates for indirect IPHI using a parallel connection pattern among three plants. Before developing the detailed inter-plant HENs, more attentions should be focused on how to extract participating streams for IPHI and how to mitigate the complexities of solving a large-scale IPHI problem.

Usually, there are two basic methods to extract participating streams for IPHI. The first method is searching available heat sources/sinks from the Grand Composite Curves (GCCs), while the second is utilizing the waste heat sources/sinks. The first effort in TSHI composed Site Source Sink Profiles (SSSP) by the sections of GCCs with “pockets” removed is to determine the different temperature levels of generated steams [1]. After that, this pioneering work was extended by Hu and Ahmad [6] to include not only the existing process streams but also the utility systems. Klemeš et al. [13] further developed SSSP


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to Total Site Profiles (TSP) and Site Composite Curve (SCC). These new analytical tools can be used to obtain the total site pinch as well as the heat recovery and cogeneration potential for a total site. Researchers from all over the world continue to contribute their efforts into the development of TSHI based on TSP [14] and SCC [15]. Bandyopadhyay et al. [16] contributed with a new graphical tool named Site Grand Composite Curve (SGCC). In essence, the SGCC provided a graphical expression for the concept of assisted heat transfer and thus had the same inter-plant heat recovery potential with the results from Rodera and Bagajewicz [17]. Note that a mathematical method was used in [17]. However, such a stream data extraction method for IPHI based on GCCs may lead to complicated HEN designs or retrofits of individual plants [18]. Besides, the waste heat sources/sinks, which are the parts cooled or heated by utilities in the existing HENs, can be extracted for IPHI directly. Walmsley et al. [19] proposed an HRL design method with variable temperature storage. For a large-scale dairy case, indirect IPHI was combined with renewable solar heating and gaseous waste heat. In their further work [20], three integration options were modelled using historical stream data from a large multi-plant dairy case to integrate solar thermal directly into HRLs. It was demonstrated that the best location for integrating solar heating into an HRL was in series with the heat sources. Oluleye et al. [21] introduced energy efficiency to identify the site waste heat recovery. However, the utilization of waste heat sources and sinks may lead to a smaller inter-plant heat recovery potential than that of using GCC segments [18]. Song et al. [18] reported another simple solution to extract higher energy level heat sources/sinks than waste heat sources/sinks for IPHI from both integrated and nonintegrated HENs. This method can maintain the existing HEN structures and can be applied to both grassroots design and retrofit projects. This method is used in this work, and its advantages are examined by Example 1 of the case study. Chang et al. [9] used the process streams to implement simultaneous intra- and inter-plant heat integration. However, the practical IPHI problems present complexities as boundaries for simultaneous intra- and inter-plant heat integration are considered, especially for a large-scale IPHI problem [4]. One significant factor contributes to the impracticality is the timeline at which different plants are developed. Simultaneous design of intra- and inter- plant heat integration is difficult when the plants considered for



IPHI are developed in different periods. Furthermore, when multiple plants are connected together via a single IPHI system, process control and safety are still a great challenge. One solution that address the challenge is to divide a large-scale IPHI problem with multiple plants into several smaller sections instead of simultaneously considering all the plants. The detailed designs of these smaller sections are then developed separately. Such an action allows for easier calculation and avoids the non-convergence that is often encountered when attempting to solve a large-scale IPHI problem. However, the segregation must follow specific rules and give a reasonable result. Song et al. [4] proposed a screening algorithm named Nearest and Largest Q rec -based Screening Algorithm (NLQSA) which can be applied to divide a largescale IPHI problem into several smaller sections with each section including two or three plants. In this work, this screening method is recommended to be applied before the design of IPHI system. Further details of this screening and segregation method can be seen in [4] and [22].

2. General procedure The aim of IPHI is to reduce energy consumption and emissions beyond the levels that can be achieved with intra-plant heat integration only. In this work, the general procedure to determine the indirect IPHI is illustrated by Figure 1. The first step of solving an IPHI problem is extracting the participating hot/cold streams for IPHI from individual plants. In this work, it is assumed that individual plants are designed or retrofitted using intra-plant heat integration techniques, and then the collected data of plants is integrated using IPHI techniques. However, if the HEN retrofits are difficult to implement, a simple method proposed by Song et al. [18] is adopted to extract streams which have higher energy levels than waste heat sources/sinks for IPHI from both integrated and nonintegrated HENs. Note that this method can be applied to both grassroots design and retrofit projects. Utilizing this method, the HEN structure can be maintained in the retrofit projects. This method will be reviewed in Section 3.1. The advantages of this method will be demonstrated by Example 1 of the case study. In this work, all the stream data for IPHI are assumed to be constant and to be extracted from continuous processes.


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Figure 1. The overall procedure for the implementation of IPHI.

The second step of solving an IPHI problem is dividing a large-scale IPHI problem into several smaller sections. This work focuses on the determination of maximum inter-plant heat recovery potential and corresponding minimum intermedium flowrates for an indirect IPHI problem with parallel structure among three plants. Hence, those cases with only three plants are selected for the case study. The segregation method for a large-scale IPHI problem proposed by Song et al. [4] is not necessary for the case study. However, for a large-scale IPHI problem, this method is effective in reducing the computational burden and can be implemented before the detailed design of the IPHI system. Note that it is assumed that different participating plants can be connected together through IPHI when the segregation method is applied. The third step of solving an IPHI problem is determining the inter-plant connection pattern, and targeting the inter-plant heat recovery potential and intermedium flowrates. If one plant provides hot streams for IPHI, it is defined as a heat source plant, whereas the plant is defined as a heat sink plant if it provides cold streams for



IPHI. As reviewed in the Introduction, three basic connection patterns (shown in Figure 2) are proposed by Wang et al. [11] for indirect IPHI among three plants. In this work, the parallel structure is used. The energy target and the corresponding minimum flowrates of intermedia are determined by the newly proposed graphical tool, which is presented in Section 3.2. In the fourth step of solving an IPHI problem, the final inter-plant HEN configuration of each IPHI section achieved in the second step can be easily established using PA or MP.

Figure 2. Parallel (2-a), split (2-b) and series (2-c) connection patterns between one heat source plant and two heat sink plants [11].

By applying the proposed method, a large-scale IPHI problem, no matter how many plants involved, can be solved in four steps. Compared with the previous methods for IPHI problem, the non-convergence that is

often encountered when attempting to solve a large-scale IPHI problem is largely avoided in the proposed method. In the mean time, easier calculation and practical solution are presented.

3. Methodology The method for each step in Figure 1 is introduced in detail in the following Sections. Note that, since only the cases with three plants are considered in this work. The detailed presentation for step 2 in Figure 1 is excluded in the Section 3 and can be seen in [4] and in [22].

3.1. The intra-plant heat integration before IPHI and the extraction of the hot/cold streams for IPHI


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In this work, the HEN designs or retrofits for individual plants are implemented first, followed by the IPHI system design. The HEN designs or retrofits can be implemented by using various well-established PA or MP methods. Then, the waste heat source/sinks, which are the parts cooled/heated by utilities, can be extracted as the participating streams for IPHI from these integrated HENs. However, if the HEN retrofits are difficult to implement, a simple method proposed by Song et al. [18] is adopted in this work to extract streams which have higher energy levels than waste heat sources/sinks for IPHI. The hot/cold streams for IPHI extracted by a simple method in one previous work [18] is called redundant heat sources/sinks. Moreover, the utilization of the redundant heat sources/sinks may lead to a higher heat recovery potential than that of waste heat sources/sinks [18]. This method [18] can be applied to extract streams for IPHI from nonintegrated HENs or the scenario that “pocket” appears on GCC and is shown in Figure 3. The advantages of this method will be demonstrated by Example 1 of the case study. Moreover, the surplus heat sources/sinks are the GCC sections after “pockets” removed.

Figure 3. The stream extraction method for IPHI from individual HENs [18].

3.2. The presentation of the parallel connection pattern for indirect IPHI among three plants Sections 3.2.1, 3.2.2 and 3.2.3 illustrate the concepts using a case including one heat source plant and two heat sink plants. The scenario including two heat source plants and one heat sink plant can be analyzed in a similar way as introduced in Section 3.2.4.



3.2.1. The drawing of the inter-plant composite diagram (IPCD) For the three participating plants in IPHI, each one has its own ∆Tmin. In order to draw the composite curves in a single T-H diagram, the temperatures of each stream should be shifted by the ∆Tmin. This value is subtracted from the hot streams and added to the cold streams. The shifted composite curves are shown in Figure 4a as dashed lines. Next, the two shifted cold composite curves are composited together and get pinched with the hot shifted composite curve in one single T-H diagram. This is an idea called inter-plant shifted composite curves (ISCC) from previous work [18]. Instead of setting a fixed ∆Tmin in the very beginning of calculation for indirect IPHI problem, such an action allows for the different ∆Tmin for the different participating plants. This method does not change the original ∆Tmin for each participating plant. As shown by the shadow region in Figure 4b, the common region between the hot shifted composite curve and cold shifted composite curve is the feasible region of intermedia. Note that the temperatures of intermedia on ISCC are their real temperatures but not the shifted temperatures. However, this is not enough to determine the parallel connection pattern. As two shifted composite curves are composited together, using ISCC to guide the design of inter-plant HEN configuration may lead to multiple intermedium loops between the two heat sink plants. For the parallel connection pattern, each intermedium loop should only be implemented between one heat source plant and one heat sink plant. Therefore, the two shifted cold composite curves should be presented on ISCC separately. Before that, the shifted temperature intervals of the heat sources which are lower than the minimum shifted temperature of the heat sinks and the shifted temperature intervals of the heat sinks which are greater than the maximum shifted temperature of the heat sources should be deleted. There is no inter-plant heat transfer opportunity for these temperature intervals. As shown in Fig.5, the two shifted composite curves of two sinks are drawn on ISCC by end to end. The new graph is called inter-plant composite diagram (IPCD) which is the tool to determine the parallel connection pattern. The right and left cold composite curves in Figure 5 are defined as Sink 1 and Sink 2, respectively.


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Figure 4. The illustration for the construction of ISCC.

Fig.5. The inter-plant composite diagram (IPCD).

3.2.2. The flow chart to determine the indirect IPHI with parallel connection pattern among one heat source plant and two heat sink plants By utilizing the IPCD, one determining procedure for indirect IPHI with parallel connection pattern is introduced as shown in Figure 6. Instead of drawing the simplified curves for two heat sink plants in the very beginning [11], one idea with iteration is introduced. Under specific constraints and certain maximum inter-



plant heat recovery potential, drawing the intermedium line for one heat sink plant with minimum possible CP first and then determining the intermedium line for the another heat sink plant. Through applying continuous increasing of intermedium CP or increasing of the intermedia feasible region area until both of the two intermedium lines are feasible, the parallel connection pattern can be determined. By utilizing this flow chart, the maximum inter-plant heat recovery potential and the corresponding minimum intermedium CP can be determined simultaneously for the indirect IPHI with parallel connection pattern. The constraints and explanations for the determining procedure are presented in the following Section 3.2.3.

Figure 6. The flow chart to determine the indirect IPHI with parallel connection pattern among one heat source plant and two heat sink plants.


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3.2.3. The constraints and explanations for the determining procedure of the parallel connection patter on IPCD For the parallel connection pattern, there are two independent intermedium lines for the two heat sinks separately. The two independent intermedium lines can be composited together in a single T-H diagram. As shown in Figure 7a, the composite intermedium line is usually a polyline with two turning points when these two lines are composited together in a T-H diagram. It can also be a polyline with only one turning point as shown in Figure 7b and Figure 7c or a straight line as shown in Figure 7d in the T-H diagram. No matter what shape the composite intermedium line is, the two intermedium lines usually have a common temperature interval (CTI). The starting temperature point on the composite intermedium line within CTI is defined as “inflection point”. The scenario whereas there is no CTI between the two heat sinks will be analyzed in the end of this section. In fact, this interval is the key region for determining the parallel connection pattern for indirect IPHI. It should be noted that in this region, each intermedium loop should be applied to one single heat sink. As shown in Figure 8, the inter-connection between the two heat sinks should be avoided.

Figure 7. The different shapes of composite intermedium line.



Figure 8. The undesired inter-connection of indirect IPHI with parallel connection pattern among one heat source plant and two heat sink plants.

Therefore, the two feasible intermedium lines for Sink 2 and Sink 1 are determined successively. In order to guarantee the flowrates of the two intermedium lines are as small as possible, the intermedium line for Sink 2 with minimum possible CP is drawn in the first step. The minimum temperature of Sink 1 is set as the initial temperature of the inflection point. Then, the initial inflection point can be found on the intermedium line of Sink 2. The region, formed by the intermedium line of Sink 2, the hot/cold shifted composite curves and two horizontal lines whose temperatures are the supply temperature (cold end) and target temperature (hot end) of the intermedium line of Sink 2, is defined as the key region for determining parallel connection pattern (KRP). The KRP is shown as the shade area in Figure 9. Note that it is not the same as the feasible region of intermedia, which is shown in Figure 4b. In the second step, a composite intermedium line that passes the inflection point with the minimum possible CP is drawn within CTI. The terminal point (hot end) of the composite intermedium line within CTI is named as point A. Besides that, the abscissa of point B is the same as that of the lowest point of Sink 1 on IPCD, and the ordinate of point B is the temperature of the inflection point. In the third step, the intermedium line of Sink 1 is determined by drawing a straight line joining point A and point B. The intermedium line of Sink 1 is feasible only when it is located between the hot shifted composite curve and the shifted composite curve of Sink 1.


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Figure 9. The graphical illustration on IPCD for the determination of indirect IPHI with parallel connection pattern among one heat source plant and two heat sink plants.

The improved targeting procedure for indirect IPHI with parallel connection pattern among three plants is introduced as shown in the flow chart of Figure 6 and Figure 9. Moreover, in the flow chart of Figure 6, there are some steps labeled as ①-⑥. These labels give more details of the proposed targeting procedure, which can be found in the supporting information. For the scenario whereas there is no CTI between the two sinks, each CP of two intermedium lines with parallel connection pattern can be simply determined by drawing a straight line with the largest possible slope within the region between the hot shifted composite curve and each cold shifted composite curve. This procedure is shown in Figure 10. Note that the IPCD is the same to ISCC under this case. In fact, under this case, it can be examined that the two determining methods shown in Figure 9 and Figure 10 present the same result.



Figure 10. The determining method for parallel connection pattern when the two sinks have no CTI.

3.2.4. The flow chart to determine the indirect IPHI with parallel connection pattern among two heat source plants and one heat sink plant Compared with the scenario including one heat source plant and two heat sink plants, the scenario including two heat source plants and one heat sink plant can be determined by a similar way. The two shifted composite curves of the two sources are drawn on ISCC by end to end to form the IPCD. The right and left hot composite curves are defined as Source 1 and Source 2, respectively. The intermedium line of Source 1 is drawn first. Then, the composite intermedium line within CTI and the intermedium line of Source 2 are determined successively. One of the convex points which has the highest temperature on the shifted composite curve of Source 1 is selected first. Then, the intermedium line with the minimum possible CP (largest possible slope) which passes this point and fully covers the demand of Source 1 is drawn. The supply temperature (cold end) of the intermedium line for Source 1 should be greater than the minimum temperature of the heat sink plant (For the intermedium line of Source 2, its supply temperature (cold end) should be equal to or greater than the minimum temperature of the heat sink plant). For the intermedium line of Source 1, its supply temperature


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(cold end) is also the starting temperature (cold end) of the composite intermedium line within CTI. The KRP is the region that formed by the intermedium line of Source 1, the hot/cold shifted composite curves and two horizontal line whose temperatures are the supply temperature and target temperature (hot end) of the intermedium line of Source 1. If the intermedium line which fully covers the heat demand of Source 1 or follows the constraints mentioned above cannot be drawn as passing this convex point, another convex point (including the lowest starting point of the shifted composite curve for Source 1) with lower temperature on the shifted composite curve of Source 1 will be selected, until one feasible intermedium line for Source 1 can be drawn. For the later steps of increasing the intermedium CP (decreasing the slope of the intermedium line), the selected point is used as the rotation point for the increment of the intermedium line of Source 1. The inflection point is found from the intermedium line of Source 1. The maximum temperature on the shifted composite curve of Source 2 is set as the temperature of the initial inflection point. The starting point of the composite intermedium line within CTI is named as point A. Besides that, the abscissa of point B is the same as that of the highest point of Source 2 on IPCD, and the ordinate of point B is the temperature of the inflection point. The intermedium line of Source 2 is determined by drawing a straight line joining point A and point B. The intermedium line of Source 2 is feasible only when it is located between the shifted composite curve of Source 2 and the cold shifted composite curve.



Figure 11. The flow chart to determine the indirect IPHI with parallel connection pattern among two heat source plants and one heat sink plant.

For the determination of indirect IPHI with parallel connection pattern among two heat source plants and one heat sink plant, its flow chart is shown in Figure 11. Compared with Figure 6, an underline has been added for each change. Note that the flow chart of Figure 11 is also for the scenario that the two heat sources have CTI. For the scenario in which there is no CTI between the two heat sources, the determination method is the same as the method presented in Figure 10. Each CP of the two intermedium lines with parallel connection pattern can be simply determined by drawing a straight line with a largest possible slope within the region between each hot shifted composite curve and cold shifted composite curve on IPCD.

4. Case study Example 1


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A case given by Chang et al. [9] is used to illustrate the applicability of the newly proposed graphical method in Section 3.2 and to illustrate the advantages of the stream extraction method for IPHI presented in Section 3.1. The stream data of Example 1 is listed in Table 1. Tୱ and T୲ are the supply temperature and target temperature of streams respectively. CP is the heat capacity flowrate of each stream. All of the three plants’ approach temperature (∆Tmin) is 10 ºC.

Table 1. The stream data of Example 1. Stream

Tୱ

T୲

CP

Plant

(ºC)

(ºC)

(kW/ºC)

H11

250.0

120.0

500.00

1

C11

125.0

185.0

500.00

1

H21

500.0

120.0

250.00

2

C21

139.0

500.0

150.00

2

C22

20.0

250.0

100.00

2

H31

200.0

30.0

200.00

3

H32

125.0

119.0

2500.00

3

C31

110.0

160.0

250.00

3

C32

195.0

205.0

2500.00

3

For the case study of this example, a mixed integer nonlinear programming (MINLP) model is applied to implement simultaneous intra- and inter-plant heat integration in the work of Chang et al. [9]. As mentioned above, the intra-plant heat integration is implemented before IPHI and a simple method proposed by Song et al. [18] is used to extract stream data for IPHI in this work. Hence, the HENs for these three plants, which can be seen in the Figure S2, Figure S3 and Figure S4, are established by PA firstly. The stream data extracted from these HENs for IPHI are shown in Table 2. Note that Plant 1 and Plant 2 are only used as heat source plants and Plant 3 is only used as the heat sink plant for IPHI, which is the same as that of [9].

Table 2. The stream data for IPHI of Example 1.



Tୱ

T୲

CP

(ºC)

(ºC)

(kW/ºC)

H1 (Plant 1)

250.0

195.0

500.00

H2 (Plant 1)

135.0

120.0

500.00

H3 (Plant 2)

500.0

306.5

100.00

C1 (Plant 3)

195.0

205.0

2500.00

Stream

This is an IPHI problem among two heat source plants and one heat sink plant. There is no CTI between the two heat sources. The IPCD for the stream data listed in Table 2 is shown in Figure 12. Utilizing the proposed method, one intermedium line with CP of 68.44 kW/ºC between Plant 1 and Plant 3, and another intermedium line with CP of 161.43 kW/ºC between Plant 2 and Plant 3, are achieved for indirect IPHI with parallel connection pattern. The final inter-plant HEN configuration, as shown in Figure 13, is established by utilizing PA. The design from [9] (seen in Figure S5) are compared with the result of this work, as shown in Table 3. Compared with the previous design, although these two designs have the same heat recovery potential. the design of this work has less heat exchanger units and less overall CP of intermedium lines.


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Figure 12. The IPCD and the two intermedium lines with parallel connection pattern for Example 1.

Table 3. The comparison between the designs from [9] and from this work. Items

Design from [9]

This work

Connection pattern of intermedia

Series

Parallel

Total number of inter-connection lines

3

4

Total number of heat exchanger units

13

12

Overall CP of intermedium lines (kW/ºC)

488.4

459.73

Hot utility requirement (kW)

1500

1500

In fact, a single intermedium line with minimum possible CP of 161.43 kW/ºC can be drawn within the feasible region of intermedia before the determination of parallel connection pattern (seen in Figure S6). Due to the fact that there is no CTI between the two heat source plants, the shifted composite curves of the two heat source plants are independent on IPCD. This single intermedium line can be applied to implement the indirect IPHI with the series connection pattern. The inter-plant HEN configuration with series connection pattern is shown in Figure S7. Compared with the design for Example 1 from [9] which also presents a series connection



pattern, this new design still presents a better result with the same heat recovery but a lower CP (161.43 kW/ºC) of intermedium loop and fewer numbers of heat exchange units (11). This result demonstrates that the simple stream data extraction method [18] is an effective and beneficial way for IPHI.

Figure 13. The final inter-plant HEN design for Example 1.

Example 2 A case including one heat source plant and two heat sink plants from Wang et al. [11] is used as Example 2. In the work of Wang et al., three basic connection patterns (shown in Figure 2) are determined from drawing the simplified curves for the two heat sinks in the very beginning. The stream data of Example 2 are listed in Table 4. All of the three plants’ approach temperature is 5 ºC. Note that all the stream data listed in Table 4 are


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the ones extracted for IPHI from individual plants. Hence, the stream data extraction method presented in Section 3.1 is not applied in Example 2.

Table 4. The stream data of Example 2. Stream

Tୱ

T୲

Duty

(ºC)

(ºC)

(kW)

H1 (Refinery)

162.5

95.0

9000

H2 (Refinery)

135.0

75.0

6000

H3 (Refinery)

115.0

65.0

8000

C1 (Rubber plant)

85.0

100.0

2000

C2 (Rubber plant)

115.0

135.0

6000

C3 (Rubber plant)

100.0

120.0

2500

C4 (Rubber plant)

95.0

105.0

1500

C5 (Tank field)

55.0

70.0

1500

C6 (Tank field)

65.0

80.0

1000

C7 (Tank field)

65.0

90.0

2000

C8 (Tank field)

85.0

105.0

2000

Table 5. Three feasible solutions with parallel connection pattern for Example 2. Item

Qrec

Qrec

Qrec

(=17835 kW)

(=17775 kW)

(=17562.5 kW)

Tୱ of the intermedium line for Sink 1 (ºC)

97.1

95.9

93.5

T୲ of the intermedium line for Sink 1 (ºC)

145.7

146.41

148.1

CP of the intermedium line for Sink 1 (kW/ºC)

233.33

223.44

202.79

Tୱ of the intermedium line for Sink 2 (ºC)

62.7

62.5

61.8

T୲ of the intermedium line for Sink 2 (ºC)

110

111.5

115

CP of the intermedium line for Sink 1 (kW/ºC)

137.50

132.53

122.22

Overall CP of intermedia (kW/ºC)

741.67

711.942

650.01



As mentioned above, the theoretical maximum heat recovery potential of IPHI can be found on ISCC. For Example 2, it is 17875 kW. Applying the proposed method of this work, the first feasible solution is found with the overall intermedia CP of 741.67 kW/ºC and the total inter-plant heat recovery is 17835 kW. In fact, more feasible solutions will be found when continuously moving the hot shifted composite curve left-ward (decreasing the total inter-plant heat recovery potential). Some of the feasible solutions with detailed features are given in Table 5.

Figure 14. The determination of the third solution (listed in Table 5) on IPCD.

The determination of the third solution (listed in Table 5) on IPCD is shown in Figure 14. The inter-plant HEN design under this situation is established by PA and presented in Figure 15. Determined by applying the method of Wang et al. [11], 17562.5 kW heat in total can be recovered via IPHI with the parallel connection pattern. In fact, this inter-plant heat recovery potential is the same to that of the third solution yet lower than that of the first and the second solutions in Table 5. The result from Wang et al. [11] is compared with that of this work in Table 6. The overall CP of intermedia is 679.17 kW/ºC in [11] for the parallel connection pattern. This is more than that of this work. The CP of each intermedium line is 137.50 kW/ºC and 202.08 kW/ºC respectively in their result. Compared with the result of parallel connection pattern from Wang et al. [11], the


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design in this work presents multiple inter-plant heat recovery potentials. Under the same heat recovery potential, the result in this work needs a lower overall CP of intermedium lines than that of Wang et al. [11].

Figure 15. The inter-plant HEN design of the third solution (listed in Table 5).



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Table 6. The comparisons between the designs from Wang et al. [11] and from this work for Example 2. Item

Design by applying the method from [11]

This work


Parallel

Parallel


4

4


Not available

21


679.17

650.12

Total inter-plant heat recovery (kW)

17562.5

17562.5

Table 7. The modified stream data of Sink 1. Stream

Tୱ

T୲

Duty

(ºC)

(ºC)

(kW)

C2 (Rubber plant)

115.0

135.0

6000

C3’ (Rubber plant)

105.0

120.0

1875

Table 8. The comparisons between the designs by applying the method from Wang et al. [11] and from this work for the modified Example 2. Item

Design by applying the method from [11]

This work


Parallel

Parallel


4

4


16

15


937.50

713.07

Total inter-plant heat recovery (kW)

13380.5

13750.0

However, a big difference is shown if the stream data of Sink 1 in Example 2 are modified. The modified stream data for Sink 1 are shown in Table 7. The streams C1 and C4 are deleted and the Tୱ of C3 is changed. The determination of parallel connection pattern on IPCD for the modified Example 2 is shown in Figure S8. The final inter-plant HEN designs determined by applying the two different methods (from [11] and this work)


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are shown in Figure S9 and Figure S10 respectively. The comparisons are shown in Table 8. Compared with the inter-plant HEN design by applying the method from [11], this work presents a bigger heat recovery potential but less number of heat exchanger units and lower overall CP of intermedium lines. This is because the method of Wang et al. [11] draws the simplified curves (which are also used as the intermedium lines) and thus fixates the flowrates of intermedium lines and inter-plant heat recovery potential in the very beginning. Such an action may mislead the maximum inter-plant heat recovery potential. However, multiple possibilities of intermedium lines and inter-plant heat recovery potential are presented in the certain case. The method of this work mitigates the drawbacks of the previous method and can always present the real maximum heat recovery potential and the corresponding minimum flowrates of intermedia.

5. Conclusion This paper presents an improved targeting procedure for the determination of indirect IPHI with parallel connection pattern among three plants. By applying the proposed method, the real maximum inter-plant heat recovery potential for the indirect IPHI with parallel connection pattern among three plants and the corresponding minimum flowrates of the two heat recover loops can be achieved simultaneously. This method is a subsequent work of [18] and [4]. Since all the participating plants of an IPHI problem may not be developed in the same period, the advantages of the stream data extraction method from [18], which allows the inner- and inter- plant heat integration to be implemented successively, are also examined by Example 1. A

large-scale IPHI problem including multiple plants is divided into several smaller sections with each section including two or three plants by the method from [4]. Thus only such cases including three plants are discussed in this paper. This also allows for an easier calculation as this method does not lump the calculations for all of the plants into a single complicated calculation. Moreover, the parallel connection pattern which is a good and flexible way for the control and safety of IPHI system is selected. Since the two heat recovery loops are independent, compared with the series and split connection pattern, the parallel connection pattern might be more reliable when some operation parameters in one plant fluctuate. In this work, the inter-plant HEN configuration is established by PA or MP methods. In future, a



mathematical programming will be presented to provide the optimal inter-plant HEN design considering the multiple objectives and the inter-plant connection patterns simultaneously in the same time.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: http://pubs.acs.org/. The more details for the proposed targeting procedure and the complementary figures for the two examples in the Case Study.

Acknowledgements Financial support from the National Natural Science Foundation of China under Grant No.21476256 is gratefully acknowledged. Sponsorship from China Scholarship Council (201606440032) is also deeply appreciated. We are also very grateful to Mr. Qiushi Liang and Ms. Ashritha Rao for their valued comments.

Nomenclatures CP

Heat capacity flow rate of streams or intermedium, kW/ ºC

CTI

Common temperature interval

GCC

Grand composite curve

HEN

Heat exchanger network

HI

Heat integration

HRL

Heat recovery loop

IPCD

Inter-plant composite diagram

IPHI

Inter-plant heat integration

ISCC

Inter-plant shifted composite curve


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KRP

Key region for determining parallel connection pattern

MINLP

Mixed integer nonlinear programming

MP

Mathematical programming

NLQSA

Nearest and largest Qrec -based screening algorithm

PA

Pinch analysis

Qrec

The maximum inter-plant heat recovery potential via each IPHI scheme, kW

SCC

Site composite curve

SGCC

Site grand composite curve

SSSP

Site source sink profiles

TAC

Total annual costs

TSHI

Total site heat integration

TSP

Total site profiles

Tୱ

Supply temperature of stream, ºC

T୲

Target temperature of stream, ºC

ΔT୫୧୬

Minimum approach temperature of individual plant, ºC

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Improved Targeting Procedure To Determine the Indirect Interplant

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