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Simultaneous synthesis of utility system and heat exchanger network incorporating steam condensate and boiler feedwater Xianglong Luo a, *, Xiaojian Huang a, Mahmoud M. El-Halwagi b, María Ponce-Ortega c, Ying Chen a Jose a

School of Material and Energy, Guangdong University of Technology, No. 100 Waihuan Xi Road, Guangzhou Higher Education Mega Center, Panyu District, Guangzhou 510006, China The Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX 77843, USA c s de Hidalgo, Morelia, Michoaca n 58060, Mexico Chemical Engineering Department, Universidad Michocana de San Nicola b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 30 April 2016 Received in revised form 2 July 2016 Accepted 21 July 2016

A heat exchanger network (HEN) is an important part in processing plants used to recover heat from process streams. A utility system supplies heating and cooling utilities and introduces additional hot and cold streams for the processes. The HEN and utility system (e.g., Rankine cycle-based cogeneration system) are closely interconnected primarily through steam, steam condensate leaving the turbines, and process surplus heat. The recovery of the sensible heat from the steam condensate and process surplus heat through an integration technique may contribute signiﬁcantly to the reduction of the heating and cooling utility consumption in the heat exchanger network as well as in the primary energy consumption in the utility system. In this paper, a systematic methodology for the simultaneous synthesis and design of a utility system and HEN is proposed. The heat recovery from the steam condensate and boiler feedwater preheating are integrated into the HEN synthesis together with the design optimization of a Rankine cycle-based utility system. In addition to the simultaneous design of the utility and heatrecovery systems, the optimization variables include the steam condensate target temperature, the steam level for process heating, the energy demand for the utility system, the returning temperature of the steam condensate, and the ﬁnal temperature of the boiler feed water. The total site HEN is composed of several interlinked sub-HENs. A model for the new hot utility-process cold stream HEN is formulated together with the hot -cold process streams of the HEN. The linking constraints between sub-HENs and the utility system are formulated. Several case studies are elaborated to demonstrate the effectiveness and applicability of the proposed methodology. Compared with the former design methods without integrating steam condensate sensible heat and boiler feedwater preheating, meaningful economic beneﬁts can be achieved by applying the proposed framework. © 2016 Elsevier Ltd. All rights reserved.

Keywords: HEN Rankine cycle Utility system MINLP Integration Optimization

1. Introduction The growing emphasis on sustainable design is leading industrial facilities to conserve energy and reduce greenhouse gas emissions. Heat exchanger networks (HENs) form an important part in the energy management system for a process plant. The goal of the HEN design is to recover energy from the process by economically matching hot streams with cold streams. Any energy still needed is then supplied by hot and cold utilities. The utility

* Corresponding author. E-mail address: [email protected] (X. Luo). http://dx.doi.org/10.1016/j.energy.2016.07.109 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

system undertakes the role of supply hot and cold utilities for the HENs in a form of multiple pressure levels of steam and cooling water. In the process industries, the HEN and utility system are usually treated as two separate parts and sequentially designed. In fact, most of the steam streams used in HEN as hot utility may return to the utility system in a form of condensate water after heating the cold streams. The recovery of steam condensate sensible heat is helpful in reducing the consumption of steam as hot utility in the HEN and steam as heat source for boiler feedwater (BFW) preheating. In addition, the surplus heat of process hot stream can be used as heat source for utility streams (boiler feed water preheating, cold utility generation and power generation) of the utility system instead of directly cooled by additional cold

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utility. The HEN and utility system are close interacted and the simultaneous synthesis of the HEN and utility system is crucial to improve the energy efﬁciency and economic competition of process industry. In this paper, there is presented a new methodology based on a new superstructure and a mathematical model for the simultaneous synthesis and optimization of integrated HEN and utility systems accounting for practical and feasibility considerations. 2. Literature review The goal of the synthesis and design of HEN is to recover heat from the process by matching hot streams and cold streams to minimize the economic objective. Hot and cold utilities are imported to supply any energy requirement for the HEN after the energy recovery between hot and cold streams. The synthesis and design methodology of HEN was introduced by Hohmann [1] and later improved by Linnhoff and Flower [2,3]. Since then, the synthesis and design of HEN has been very well studied. The solution approach for the HEN synthesis problem can be generally grouped into pinch analysis approaches, sequential approaches, and simultaneous approaches [4e6]. According to the pinch analysis approach, a HEN can be designed following a series of rules based on the ﬁrst and second law of thermodynamics. The objective of the pinch analysis is to maximize the heat recovery and at the same time minimize the total hot and cold utilities. Any violation of these rules results in an increment in the utility consumption. The pinch analysis is a powerful tool that can provide targets through a graphical interpretation and visualization for the problem, and makes the HEN problem easier to understand [5]. The sequential synthesis approaches decompose the HEN design problem into sub-problems. For example, the targets for the minimum utility requirement, the minimum number of exchanger units and the minimum capital cost of the network are obtained sequentially [7]. Mathematical programming based on pinch theory is usually used in sequential synthesis approaches. Papoulias and Grossmann [8] developed a transshipment model to predict the minimum utility consumption using linear programming and the minimum number of units using mixed-integer linear programming (MILP). Cerda et al. [9] proposed a transportation model for determining the minimum utility cost using a linear programming technique. Floudas et al. [10] proposed a model to minimize the total annual cost (TAC) of a HEN in a two-stage procedure. A mixedinteger linear programming model was ﬁrst formulated to minimize the number of heat exchangers and a non-linear programming model was used to obtain the minimum TAC of the network by ﬁxing heat exchanger structure. Zhu [11] proposed an automated sequential synthesis approach for the HEN. In their approach, an MILP model was formulated to select the matches and a mixed-integer non-linear programming (MINLP) model for determining the cost-optimal network. The simultaneous optimization techniques solve the HEN synthesis problem without any decomposition. The trade-offs between the capital and operational costs of the HEN can be handled by MINLP formulations. Simultaneous approaches have shown to be superior to sequential approaches in most of the cases. Ciric and Floudas [12] combined the transshipment model [8] with a nonlinear programming model [10] into one MINLP formulation for a speciﬁed minimum temperature difference. In this method, all the involved variables were optimized simultaneously. At the same time, Yee et al. [13] developed a stage-wise simpliﬁed superstructure formulation and then Yee and Grossmann [14] extended it to the HEN synthesis. Subsequent works incorporated different assumptions and considerations, such as isothermal mixing [15,16], non-isothermal mixing assumption [17,18] and multiple utilities

[19]. In the past decades, the synthesis and design of HEN have been well studied and applied in the practical design. To further recover energy or improve the energy utilization for a total site, there has been considered the integration between the HEN and its associated energy system accounting for the integration of HEN with organic Rankine cycles (ORC) [20,21], absorption cycle [22] trigeneration systems [23], thermal membrane distillation systems [24], and water network [25]. It is worth noting that any additional energy needed after the HEN synthesis is supplied by hot and cold utilities generated from the utility system. The utility system is the heart of an industrial site energy system. Fig. 1 shows a close interconnection between the HEN and the utility system. The synthesis and optimization of the utility system has been the focus of many researchers [26]. Particularly, the integrated design of a utility system and a HEN has been accepted and more attention and various powerful methodologies have been developed over the recent years. Klemes et al. [27] extended the pinch analysis methodology to the total site plant by incorporating multiple processes linked by a common central utility system. The cogeneration potential and the emission from a centralized utility system were achieved using the proposed methodology. Liew et al. [28] proposed an improved Total Site Sensitivity Table (TSST) to determine the optimal size of a utility generation system, to design the backup generators and piping in the system and to assess external utilities that might need to be bought and stored. Zhang et al. [29] proposed a coupled mixed integer nonlinear programming model to integrate process plants and utility systems. The mathematical model includes three parts: the heat integration of the process plants, the optimization of the utility system, and the coupling equations for the site-scale steam integration. Later, Zhang et al. [30] proposed a multi-period mathematical model for the simultaneous optimization of materials and energy on a reﬁning site scale. A bi-level MILP framework was presented to minimize the total hot and cold utilities of the up and down plants and to maximize the steam generation in the total site. Goh et al. [6] proposed a multiple cascades automated targeting method to determine the minimum total operating cost of a trigeneration system. The above mentioned researches aim to ﬁnd a cogeneration potential of a total site or a design scheme with the minimum operating cost. Other works are focused on the simultaneous minimization of investment and operating costs or the environmental impact for the utility system and the HEN. Chen and Lin [31] presented a systematic methodology for the synthesis of an entire energy system for chemical plants. The entire energy system is composed of a gas-steam cycle-based utility network and a HEN. Bamuﬂeh et al. [32] presented a multi-objective optimization approach for the design of a cogeneration system accounting for

Fig. 1. Interaction between the HEN and the utility system.

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economic, environmental, and social tradeoffs. Na et al. [33] developed a modiﬁed superstructure containing a utility substage considering multiple utilities in a simultaneous MINLP model. They suggested ﬁxed utility locations according to temperature and series connections between utilities to improve the model size and convergence. As mentioned above, the simultaneous synthesis and design of the utility system and the HEN have been studied in different perspectives and scales. However, these methods are based on the assumption that only steam latent heat is used as hot utility. These targets are unrealistic excluding many practical considerations, such as steam condensate for process heating [34]. In practice, the temperature of steam condensate is high enough to heat some process cold stream. In addition, the BFW is a potential heat sink to absorb process surplus heat. The consideration of integrating steam condensate and BFW in the design of utility system and HEN may achieve signiﬁcant beneﬁts in energy savings or cost savings. Sternberg et al. [35] presented a hybrid graphical and mathematical technique for targeting and synthesizing steam-process cold stream networks, where the saturated liquid was used to meet the cold process duty requirements. A case study showed that a steam saving of 29.6% was obtained compared with using just saturated steam. Peng et al. [36] presented an extended Total Site Problem Table Algorithm to target the minimum utility requirements in a steam system that considers the water sensible heat. Several case studies showed that the accuracy of the total site targeting methodology can be improved using the developed new tool considering water sensible heat. Sun et al. [34] presented a practical graphical approach based on the extended site composite curves to provide a realistic utility targeting method accounting for BFW preheating, steam superheating, and steam desuperheating. Steam condensate heat recovery has been included in the graphical method. Luo et al. [37] proposed a combined graphical targeting method and a mathematical model for the heat integration of regenerative Rankine cycle and process surplus heat. The analyzed case study showed that, for the studied steam power plant, 13.34% of fuel consumption can be reduced if all the steam used to preheat BFW is substituted by process surplus heat. Based on the previous literature review, it has been noted that so far most of the works on the synthesis of utility system and HEN

877

have considered only the latent heat of steam generation or steam utilization. There are very limited targeting methodologies considering the integration of water sensible heat and give only heat integration target instead of optimal network synthesis or design scheme. To the best of our knowledge, the synthesis and design optimization of utility systems and HEN incorporating simultaneously the recovery of steam condensate sensible heat and process surplus heat has not been addressed yet. Therefore, this paper presents a systematic approach, develops an improved superstructure, and formulates an MINLP model for the synthesis and design optimization of Rankine cycle based utility system and HEN integrating the steam condensate and the BFW. The objective is to minimize the TAC of the total energy system. A case study based on the proposed methodology is solved and the merits are shown by comparing the results with those without integrating steam condensate and BFW. 3. Problem description Fig. 2 shows a schematic representation of the traditional relation of process HEN and utility system. In Fig. 2, the process HEN and the utility system are sequentially designed. For the process HEN, the hot streams and the cold streams are ﬁrst matched to exchange heat. Some process heat is recovered. The cold streams are then heated to their target temperatures by hot utilities (e.g., steam at different pressure levels); while the hot streams are cooled to their target temperatures by cold utilities (e.g., cooling water). The hot and cold utilities are usually presented in the process HEN synthesis with speciﬁc parameters and costs. In the HEN, only steam latent heat is used as hot utility. For the utility system, the BFW is preheated, evaporated, and superheated by steam (extracted from steam turbine) in a deaerator or other regenerative heaters [37] and ﬂue gas in a boiler. The superheated steam expands in a steam turbine and releases steam at one or more pressure levels used as hot utilities for the HEN. For the design method shown in Fig. 2, the HEN and the utility system are linked only by steam. However, a steam condensate contains much available energy that can be partly or totally recovered before returning to the utility system as BFW. In addition, the surplus heat of hot streams is potential heat source for BFW preheating.

Fig. 2. A general design representation of the relation of a HEN and the utility system. bfwdboiler feedwater; CUdcold utility; Edexchanger; hdhot stream; cdcold stream; HUdhot utility; HPdhigh pressure; MPdmedium pressure; LPdlow pressure.

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Therefore, the HEN and the utility system are closely linked by steam, steam condensate, BFW, and process surplus heat. In this paper a systematic methodology is proposed to design the HEN and the utility system and simultaneously incorporating steam condensate heat recovery and BFW preheating. Fig. 3 shows a general representation of the proposed entire energy system. In Fig. 3, the HEN is grouped into four sections: process hot stream eprocess cold stream HEN (PPHEN), process cold stream - hot utility HEN (PHUHEN), process hot stream - BFW HEN (PBFWHEN) and process hot stream e cold utility HEN (PCUHEN). The PPHEN is a traditional HEN that the hot stream and cold stream are matched to recover process heat. In the PHUHEN, different from traditional structure, the cold stream is heated by not only steam latent heat but also steam condensate sensible heat. The hot utilities and process cold streams conform a new HEN with link constraints that are different from the PPHEN. In the PBFWHEN, the surplus heat from process hot streams is used to heat BFW and consequently reduce the consumption of steam extraction from the turbine. The PCUHEN is the same as that of the traditional HEN. The goal of this paper is to model and solve this proposed simultaneous synthesis and design problem shown in Fig. 3. Based on the above description, the entire problem can be stated as follows: Given: (1) Hot and cold process streams in process plants, their supply and target temperatures, and heat capacities. (2) A basic conﬁguration of utility system available to produce steam and power. The pressure and the temperature of the steam generated in boiler. The extraction pressure and the condensing pressure of the steam turbine. The operating pressure of the deaerator. The low heat value and the unitary cost of the fuel source. (3) Supply temperatures for the steam as hot utility and lower bounds for the target temperatures of these steams after heating cold streams when both steam latent heat and steam condensate sensible heat are used simultaneously. (4) Supply temperatures and upper bounds for the target temperatures of the BFW to be heated by process hot streams.

(5) Cooling water used as cold utility with known supply and outlet temperatures as well as unitary cost. (6) Film heat transfer coefﬁcients for all process streams, hot utilities, cold utilities, and BFW. (7) Investment cost expression of all utility component and all types of heat exchangers. (8) Minimum temperature difference (DTmin) for all HENs. Determine: (1) The optimum structure for the PPHEN, PHUHEN, PBFWHEN and PCUHEN. (2) The heat exchangers installed in all the structure. (3) The splitting and mixing of process streams, and hot utilities (steam and condensate). (4) The target temperature for hot utilities and process hot streams heated by the BFW. (5) The heat load and design for the utility components; inlet, extraction, outlet steam ﬂowrate from the turbine and the yielded power in the turbine. (6) The requirement of cold utilities from the HEN and the condenser of the utility system. (7) The minimum TAC. Assumptions: (1) (2) (3) (4)

All parameters are deterministic. Non-isothermal mixing for process streams. Fixed pressure of steam extraction used as hot utilities. The investment cost for the deaerator and pump in the utility system are neglected due to their relatively minor investment cost compared with the boiler and turbine. (5) There is no centralized utility system available and the selfsupplied utility system is necessary to be designed together with the process HEN. Fig. 4 shows in detail the proposed superstructure for the energy integration of HENs and utility system. In this ﬁgure, the process

Fig. 3. A general representation of the integration of a HEN and the utility system. bfwdboiler feedwater; CUdcold utility; Edexchanger; hdhot stream; cdcold stream; LSdlatent heat of steam; SS-sensible heat of steam condensate; HPdhigh pressure; MPdmedium pressure; LPdlow pressure.

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879

Fig. 4. Superstructure of the proposed integrated system.

hot streams can releaser their surplus heat to the BFW after exchange heat with cold stream in the PPHEN. Then, the hot streams are cooled by cold utility in PCUHEN to reach their target temperatures. The cold streams are heated by a set of steam and condensate in PHUHEN after be heated by hot streams in the PPHEN. The energy interconnection between the HENs and the utility system shown in Fig. 4, which is helpful in maximizing the heat integration and minimizing the consumption of primary energy sources.

PHUHEN, huk denotes any stage in PPHEN, bfwk denotes any stage in PBFWHEN. Other subscripts as well as parameters and variables can be found in Nomenclature Section. The formulated model is composed of the model of HENs, the model of utility system, the linking constraints between HENs and the utility system, and the objective function. The mathematical programming model is formulated as a MINLP problem, and the objective is to minimize the TAC for an entire energy system. 4.1. Model for the HENs

4. Model formulation The proposed optimization formulation is based on the superstructure presented in Fig. 4. As shown in Fig. 4, the HENs are divided into three sub-HENs (PPHEN, PHUHEN, and PBFWHEN) and one for the cooling subsystem (PCUHEN). The models for the PPHEN, PBFWHEN, and PCUHEN are similar to that of traditional process HEN. For the PHUHEN, both saturate steam latent heat and steam condensate water sensible heat of a steam stream are used as hot utilities. The steam stream is decomposed into a saturate steam stream and a steam condensate water stream due to their different temperatures change the performance when release heat. Therefore, the number of hot streams in PHUHEN is twice as the number of steam extractions used as hot utilities. Consequently, the model of PHUHEN is somewhat different to that of PPHEN. To simplify the model description, all the streams that release heat are deﬁned as hot streams (i.e., process hot stream, hot utilities) while all streams that absorb heat are deﬁned as cold streams (i.e., process cold streams and BFW). One hot or cold stream may occur in different sub-HENs. To make the modeling process more clear, some important subscripts used in the model formulation are elaborated here; pi denotes any hot process stream, pj denotes any cold process stream, hui denotes any hot utility stream (include steam stream and steam condensate), bfwj denotes any BFW stream, i denote any hot stream that can be part or all of pi and hui, j denotes any cold stream that can be part or all of pj and bfwj, pk denotes any stage in

Based on the proposed structure, the left side of each subnetworks corresponds to the hottest parts; the right side is the coldest part. In this regards, the hot streams entering each subnetwork from left to right in a descending temperature trend; while the cold streams entering each subnetwork from right to left is in an increasing temperature trend. 4.1.1. Total energy balance for the hot and cold process streams As shown in Fig. 4, any hot process stream can be cooled from its supply temperature to its target temperature by cold process streams, BFW, and cold utilities [see Eq. (1)]. Similarly, any hot process stream can be heated from its supply temperature to its target temperature by hot process streams and hot utilities [see Eq. (2)].

X

X

qpi;pj;pk þ

pj2PJ pk2PK

X

pi2PI pk2PK

qpi;pj;pk þ

qpi;bfwj;bfwk þ QCpi

bfwj2BFWJ bfwk2BFWK

¼ FHpi Tpi;in Tpi;out ;

X X

X

X

cpi2PI X

(1) qhui;pj;huk ¼ FCpj Tpj;in Tpj;out

hui2HUI huk2HUK

(2)

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4.1.2. Mass and energy balances for each internal stage of three sub-HENs Eqs. (3) and (4) denote the energy balance of internal stages for PPHEN and PBFWHEN. In Eq. (3), topi,j,kþ1 denotes the outlet temperature of non-isothermal split hot stream after exchange heat with cold stream j at stage k. Similarly, in Eq. (4), tipi,j,k denotes the outlet temperature of non-isothermal split cold stream after exchange heat with hot stream. Eqs. (5) and (6) denote the mass balances of hot and cold split streams for PPHEN and PBFWHEN. Eqs. (7) and (8) give the mixing energy balances of hot and cold split stream after heat exchange in PPHEN and PBFWHEN.

qpi;j;k ¼ FHSpi;j;k tpi;k topi;j;kþ1

qpi;j;k ¼ FCSpi;j;k tipi;j;k tj;kþ1

X

FHSpi;j;k ¼ FHpi

cpi2PI; k2PK∪BFWK

(3)

FCSpi;j;k ¼ FCpj

(12)

X

FHShui;pj;huk ¼ FHhui chui2HUI; ORDðhuiÞ > CARDðhuiÞ=2;

pj2PJ

chuk2HUK (13) X

FCShui;j;huk ¼ FCpj

(14)

(5)

FHhui ¼ FHhuiþCARDðhuiÞ=2 chui2HUI; ORDðhuiÞ CARDðhuiÞ=2

(6)

(15) FHShui;j;huk tohui;j;hukþ1 ¼ FHhui thui;hukþ1 chui2HUI;

j2PJ

ORDðhuiÞ > CARDðhuiÞ=2; huk2HUK (16)

FHSpi;j;k topi;j;kþ1 ¼ FHpi tpi;kþ1

cpi2PI; k2PK∪BFWK

j2PJ∪BFWJ

(7) X

cj2PJ; huk2HUK

hui2HUI

i2PI

X

chui2HUI;

ORDðhuiÞ CARDðhuiÞ=2

X

cj2PJ∪BFWJ; k2PK∪BFWK

FHShui;pj;huk ¼ FHhui

pj2PJ huk2HUK

(4)

j2PJ∪BFWJ

X

X

Eq. (15) shows that the mass ﬂowrate of saturate stream and steam condensate stream from the same steam level are equal. Eqs. (16) and (17) give the mixing energy balance of split steam condensate streams and cold process stream in PHUHEN.

cj2PJ∪BFWJ; k2PK∪BFWK

cpi2PI; k2PK∪BFWK

X

X

FCShui;j;huk tohui;j;huk ¼ FCpj tpj;huk

cj2PJ; huk2HUK

hui2HUI

(17) FCSpi;j;k tipi;j;k ¼ FCpj tj;k

cj2PJ∪BFWJ; k2PK∪BFWK

(8)

i2PI

The isothermal split and mix model of hot utilities is different from those of hot and cold streams. The steam stream must be separated into saturate steam stream (release latent heat) and condensate stream (release sensible heat) when the steam condensate is used as hot utility and integrated into the HEN. For the set of hot utility streams, the ﬁrst half elements are assigned to saturate steam streams in a descending pressure and the left half elements are assigned to steam condensate streams in the same order as those of the saturate steam streams. Eq. (9) gives the heat balance of saturate steam streams and Eq. (10) gives the energy balance of steam condensate streams, where ORD denotes the order of the element in a set and CARD denotes the total amount of elements in a set. Eq. (11) shows the energy balance of cold stream in each internal stage for PHUHEN. Eqs. (12) and (13) give the mass balance of hot utilities at each internal stage in PHUHEN. For saturate steam stream, one split stream can exchange heat only at one stage in the whole network of PHUHEN as shown in Eq. (13). Eq. (14) gives mass balance of mass split cold stream in PHUHEN.

qhui;j;huk ¼ FHShui;j;huk LHhui

chui2HUI;

ORDðhuiÞ CARDðhuiÞ=2; j2PJ; huk2HUK

(9)

qhui;j;huk ¼ FHShui;j;huk Cphui thui;huk tohui;j;hukþ1 chui2HUI; ORDðhuiÞ > CARDðhuiÞ=2; j2PJ; huk2HUK

qhui;j;huk ¼ FCShui;j;huk tihui;j;huk tj;hukþ1

(10)

4.1.3. Energy balances for hot streams-cold utilities Eq. (18) gives the cold utility requirement equation for the hot process streams.

QCpi ¼ FHpi tpi;pk¼CARDðPKÞþ1 Tpi;out

cpi2PI

(18)

4.1.4. Constraints for temperature feasibility As shown in Fig. 4, the temperatures involved in the superstructure must have a monotonically reduction from left to right for any hot process stream, split hot stream, cold stream, and cold split stream. It should be noted that the outlet temperatures for the steam condensate streams and the ﬁnal temperatures of process surplus heat heated by BFWs are all variables. They are deﬁned by their lower bounds (for hot utilities) and upper bounds (for BFWs).

ti;k ti;kþ1

ci2PI∪HUI; k2PK∪HUK∪BFWK

(19)

tj;k tj;kþ1

cj2PJ∪BFWJ; k2PK∪HUK∪BFWK

(20)

ti;k¼CARDðkÞþ1 Ti;out

ci2PI∪HUI; k2PK∪BFWK

(21)

tj;k¼1 Tj;out

cj2PJ∪BFWJ; k2PK∪HUK∪BFWK

(22)

ti;k toi;j;kþ1

ci2PI∪HUI; j2PJ∪BFWJ; k2PK∪HUK∪BFWK (23)

chui2HUI; j2PJ; huk2HUK

(11)

tj;kþ1 tii;j;k

ci2PI∪HUI; j2PJ∪BFWJ; k2PK∪HUK∪BFWK (24)

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toi;j;k¼CARDðkÞþ1 Ti;out tii;j;k¼1 Tj;out

ci2PI∪HUI; k2PK∪BFWK

(25)

cj2PJ∪BFWJ; k2PK∪HUK∪BFWK

(26)

881

temperature of generated steam are known. However, the temperature of the BFW is variable and depends on the heating network in the PBFWHEN. It should be noted that the boiler efﬁciency is a nonlinear function of the boiler operating load [37,38].

FB LHVF ¼ ð1 þ BCoeffa þ BCoeffbÞ MB ðHBGen Cpw tBFWÞ

4.1.5. Logic constraints for the existence of heat exchanger Eq. (27) shows the existence of any heat exchanger. Similarly, Eq. (28) shows the existence of any cooler.

Qi;j;k QMAXi;j Zi;j;k ci2PI∪HUI; j2PJ∪BFWJ; k2PK∪HUK∪BFWK (27) QCpi QCMAXpi ZCpi

ci2PI

(28)

4.1.6. Feasibility for the temperature differences The exchanger must satisfy the minimum temperature differences that directly relate to the investment cost. Therefore, the temperature differences of both sides of all types of heat exchangers in all sub-HENs must be greater than or equal to the minimum allowable temperature difference.

dtii;j;k ti;k tii;j;k þ DTMAXi;j 1 Zi;j;k

ci2PI∪HUI;

(29)

j2PJ∪BFWJ; k2PK∪HUK∪BFWK dtoi;j;kþ1 toi;j;kþ1 tj;kþ1 þ DTMAXi;j 1 Zi;j;k

ci2PI∪HUI;

j2PJ∪BFWJ; k2PK∪HUK∪BFWK (30)

(37) 4.2.2. Turbine model Most of the industrial utility systems use multiple extraction and condensing steam turbines [37,39e41]. However, to simplify the synthesis procedure, the multiple extraction and condensing turbine is decomposed into cascade connected subsections, which can be modeled as simple turbines [37,42,43]. The pressure and temperature of the inlet steam of the ﬁrst subsection are known. The known parameters also include the pressure of the extractions steams and the condensing steam. However, the enthalpies of outlet and inlet (except the ﬁrst subsection) steams are variables. Eq. (38) gives the power generation model of the steam turbine. Eq. (39) gives the outlet steam enthalpy of each subsection. Eq. (40) shows that the inlet steam enthalpy of subsection zþ1 is equal to the outlet steam enthalpy of subsection z. Eq. (41) gives the isentropic efﬁciency model of the steam turbine, which is converted from the THM [44,45] by setting the operating load equal to its design load. Eq. (42) gives a correlation for the isentropic enthalpy difference for a turbine subsection as a function of the inlet steam enthalpy. Eq. (43) shows that the steam generated from the boiler must be greater than or equal to the inlet steam ﬂowrate to the turbine.

WT ¼

X MTz;in MTz;ext HTz;in HTz;out

(38)

z

dtcuipi ¼ tpi;bfwk¼CARDðbfwkÞþ1 TCUout

dtcuopi ¼ Tpi;out TCUin dtii;j;k DTMIN

cpi2PI; bfwk2BFWK

cpi2PI

(31)

HTz;out ¼ HTz;in DLTHisz EFFisz

(39)

(32)

HTzþ1;in ¼ HTz;out

(40)

EFFisz ¼ ½1 Aisz =ðDLTHisz MTz Þ=Bisz

(41)

DLTHisz ¼ aisz HTz;in þ bisz

(42)

MB MT1;in

(43)

ci2PI∪HUI; j2PJ∪BFWJ; k2PK∪HUK∪BFWK (33)

dtoi;j;kþ1 DTMIN ci2PI∪HUI; j2PJ∪BFWJ; k2PK∪HUK∪BFWK (34) dtcuipi DTMIN

cpi2PI

(35)

dtcuopi DTMIN

cpi2PI

(36)

4.2. Modeling for Rankine cycle-based utility system The structure of the Rankine cycle-based utility system is shown in Fig. 4, which is composed of a boiler, an extraction and condensing steam turbine, and a deaerator. There are three levels of steam extractions, two for process hot utilities (MP and IP) and one for a deaerator heating (LP). The extracted superheated MP steam and IP steam are desuperheated using BFW leaving the deaerator before supplied to HENs as hot utilities. 4.2.1. Boiler model The BHM model [38] is applied in this paper with its operating load equal to its design load. For the boiler, the pressure and

4.2.3. The cold utility requirement in the utility system Eq. (44) gives the cold utility required to condense the exhaust steam.

QCconds ¼ MTz¼CARDðzÞ;out HTz¼CARDðzÞ;out HCONDS

(44)

4.3. Model of the cold utility system The cooling utility used in this paper is cooling water which is generated from the cooling tower [46]. The cooling tower is mainly composed of tower, circulation pump, draft fan and heat exchange unit. The main energy consumption of cooling tower is power for cooling water circulating pump and draft fan. Eq. (45) gives the mass ﬂaw rate of cooling water. Eq. (46) gives the power consumption of cooling water circulation pump (the ﬁrst term in the right hand) and draft fan (the second term in the right hand). Eq.

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X. Luo et al. / Energy 113 (2016) 875e893 Table 3 Information about process streams and utilities of Case 1. Streams

TIN( C)

TOUT( C)

FC(KW/ C)

h(KW/m2K)

pi1 pi2 pj1 pj2 hui1 hui2 hui3 hui4 CU

195 155 125 110 263.9 198.3 263.9 198.3 30

90 65 240 160 263.9 198.3 80a 80a 38

360 290 500 320 e e e e e

1 1 1 1 5 5 1 1 1

Exchanger capital cost ¼ 3800 þ 1020 (area)0.86, annualization factor ¼ 0.2. a Lower bound of steam condense used as hot utility which is equal to the minimum inlet temperature of cold streams. Fig. 5. Representation of steam and sink proﬁles with ﬂash steam recovery in process HEN [34].

system and enters to the deaerator after releasing heat in the HENs. Eqs. (48)e(51) give the mass and energy balances for MP and IP extractions. Eqs. (52) and (53) give the mass and energy balance for the deaerator.

Table 1 Parameters for the utility system and cold utility. Streams

Description

Boiler fuel

Natural gas; low heat value, 37681.2 kJ/kg; unitary cost, 0.227 $/kg [6] Sell price, 0.076 $/kWh [6] Turbine inlet steam; pressure, 9.5 MPa; temperature, 530 C Hot utility; pressure, 5 MPa; saturate temperature, 263.9 C Hot utility; pressure, 1.5 MPa; saturate temperature, 198.3 C Deaerator heating steam; pressure, 0.8 MPa; saturate temperature, 170.4 C Operating temperature, 158 C Turbine condense steam; pressure, 0.008 MPa; saturate temperature, 41.5 C Unitary cost, 0.02 $/m3 [6]

Power HP steam MP extraction IP extraction LP extraction Deaerator Condense Cooling water

(49)

FHhui¼2 ¼ MTIP;ext þ MWIP

(50)

FHhui¼2 HSatIP ¼ MTIP;ext HT2;out þ MWIP HWDEA

(51)

(52)

MTLP;ext HT1;out þ MTz¼CARDðzÞ;out HCONDSz¼CARDðzÞ;out þ 4:2FHhui¼1 thui¼3;huk¼CARDðhukÞþ1

HP

MP

IP

LP

0.5968 1.2770 0.1351 259.4439

0.4019 1.2432 0.2419 467.9333

0.2504 1.2170 0.1360 264.3370

0.2200 1.2117 0.3722 349.8806

(47) gives the ﬂow rate of the make-up water attributed to the water evaporation loss in cooling tower.

X QCpi þ QCconds ðCpcw DTcw Þ

(45)

pi2PI

PWct ¼ DPcw Mcw

FHhui¼1 HSatMP ¼ MTMP;ext HT1;out þ MWMP HWDEA

¼ MB þ MWMP þ MWIP

Table 2 Coefﬁcients for turbine models.

Mcw ¼

(48)

MTLP;ext þ MTz¼ORDðzÞ;out þ FHhui¼1 þ FHhui¼2

Boiler investment cost ¼ 251409 þ 20916 (steam generation). Turbine investment cost ¼ 103471 þ 1.5761 (power generation).

Ais Bis ais bis

FHhui¼1 ¼ MTMP;ext þ MWMP

.

rcw hpump þ SPfan Mcw

Mmk ¼ CPcw DTcw Mcw =LHcw

(46) (47)

4.4. The connection of the HENs and the utility system, and the assignment of temperature for the border of HENs As shown in Fig. 4, the extracted superheated steams from the turbine are ﬁrst desuperheated by the BFW and are then transported to the HENs. The steam condensate ﬂows back to the utility

þ 4:2FHUhui¼2 thui¼4;huk¼CARDðhukÞþ1 ðMB þ MWMP þ MWIP Þ HWDEA

(53)

Eq. (54) shows that the inlet temperature of any hot process stream at the ﬁrst stage in the PPHEN is equal to the inlet temperature of the hot process stream. Eq. (55) shows that the inlet temperature of any cold process stream at the last stage of the PPHEN is equal to the inlet temperature of the cold process stream. Eq. (56) shows that the temperature of saturate steam stream is equal to the steam saturate temperature throughout the stages in the PHUHEN. Eq. (57) shows that the inlet temperature of the steam condensate stream at the ﬁrst stage of the PHUHEN is equal to the steam saturate temperature. Eq. (58) shows that the inlet temperature of any cold process stream at the last stage of the PHUHEN is equal to the outlet temperature of the same stream at the ﬁrst stage of the PPHEN. Eq. (59) shows that the inlet temperature of hot process stream at the ﬁrst stage of the PBFWHEN is equal to the outlet temperature of the same stream at the last stage of the PPHEN. Eq. (60) shows that the inlet temperature of the BFW stream at the last stage of the PBFWHEN is equal to the supply temperature of the BFW from the utility system. Assuming that two streams of the BFW are possible to be heated in the PBFWHEN by hot process streams. One is steam condensate turbine condenser and makeup water. It is heated to at most the deaerator operating

X. Luo et al. / Energy 113 (2016) 875e893 Table 4 Information about process streams and utilities of Case 2.

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tpj;pk¼CARDðPKÞþ1 ¼ Tpj;in

Streams

TIN( C)

TOUT( C)

FC(KW/ C)

h(KW/m2K)

pi1 pi2 pi3 pi4 pj1 pj2 pj3 pj4 hui1 hui2 hui3 hui4 hui5 hui6 CU

195 150 130 190 100 90 80 100 263.9 198.3 170.4 263.9 198.3 170.4 30

65 70 80 95 210 170 180 205 263.9 198.3 170.4 80a 80a 80a 38

330 310 290 300 450 280 300 370 e e e e e e e

1 1 1 1 1 1 1 1 5 5 5 1 1 1 1

thui;huk ¼ Thui;in

cpj2PJ; pk2PK

(55)

chui2HUI; ORDðhuiÞ

CARDðhuiÞ=2; huk2HUK thui;huk¼1 ¼ Thui;in

(56)

chui2HUI; ORDðhuiÞ > CARDðhuiÞ=2;

huk2HUK (57) tpj;huk¼1 ¼ tpj;pk¼CARDðPKÞþ1 chui2HUI; ORDðhuiÞ > CARDðhuiÞ=2; huk2HUK (58)

0.86

, annualization factor ¼ 0.2. Exchanger capital cost ¼ 3800 þ 1020 (area) a Lower bound of steam condense used as hot utility which is equal to the minimum inlet temperature of cold streams.

tpi;bfwk¼1 ¼ tpi;pk¼CARDðPKÞþ1

cpi2PI; bfwk2BFWK; pk2PK (59)

temperature. The other is the water that leaves the deaerator. It is heated from the deaerator operating temperature to at most the allowable boiler inlet temperature.

tpi;pk¼1 ¼ Tpi;in

cpi2PI; pk2PK

(54)

tbfwj;bfwk¼CARDðBFWKÞþ1 ¼ Tbfwj;in

cbfwj2BFWJ; bfwk2BFWK (60)

Eq. (61) shows that the temperature of the BFW entering to the boiler is equal to the outlet temperature of BFW stream at the ﬁrst stage of the PBFWHEN. Eq. (62) shows that the ﬂowrate of the ﬁrst BFW stream is equal to the mass ﬂowrate of the turbine outlet steam. Eq. (63) shows that the ﬂowrate of the second BFW stream is

Fig. 6. Design conﬁguration of the UH-SSHNN (the scenario that the condensing water leaving the HENs is partly recovered at atmospheric pressure) system of Case 1.

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X. Luo et al. / Energy 113 (2016) 875e893

equal to the mass ﬂowrate of the boiler steam generation when the boiler blowdown is not considered for simpliﬁcation.

minTAC ¼ INVHE þ INVUS þ INVCU þ OPFUEL þ OPCU WSELL (64)

tBFW ¼ tbfwj¼2;bfwk¼1

(61) INVHE ¼

FCbfwj¼1 ¼ MTz¼CARDðzÞ;out

(62)

FCbfwj¼2 ¼ MB

(63)

X

X

i2PI∪HUI j2PJ∪BFWJ k2PK∪HUK∪BFWK

. n .h dtii;j;k dtoi;j;kþ1 dtii;j;k þ Qi;j;k 1=hi þ 1 hj . i1=3 ob i Xh 2þd þ CF ZCpi þ dtoi;j;kþ1

The objection function of the proposed problem is the minimization of the TAC. The TAC is equal to the sum of the total investment costs and the operating cost minus the power selling proﬁt [see Eq. (64)]. The investment cost includes the capital cost for all the types heat exchangers [see Eq. (65)], the capital cost of hot utility [see Eq. (66)] [47], the capital cost of cooling tower [see Eq. (67)] which is composed of direct capital costs DCC, soft cost (0.04 DCC) and contingency cost (0.05 DCC) [46]. The direct capital costs DCC is given by Eq. (68). Eq. (69) gives the fuel cost of the utility system. Eq. (70) gives the operating cost of cooling tower which is composed of power cost (the ﬁrst term in the right hand), make-up water cost (the second term in the right hand) and the ﬁxed operating cost (the third term in the right hand). Eq. (71) gives the power selling proﬁt model.

pi2PI

. þ QCpi 1 hpi þ 1=hCU dtcuipi dtcuopi dtcuipi 1=3 ob i h þ CF þ dtcuopi 2 þ d . n þ QCconds =ð1=hconds þ 1=hCU Þ ½ð2Tconds TCUin ob i TCUout Þ=2 þ d1=3 n

4.5. Objective functions

h CF zi;j;k

X

(65) INVUS ¼ CBCoeffa þ MB CBCoeffb þ CTCoeffa þ WT CTCoeffb (66) INVCU ¼ 1:09DCC AFct

Fig. 7. Design conﬁguration of the UH-SSHND (the scenario that the condensing water leaving the HENs is directly pumped to the deaerator) system of Case 1.

(67)

X. Luo et al. / Energy 113 (2016) 875e893

0:7 0:65 DCC ¼ 3714 Mcw þ 3516 PWpump

(68)

OPFUEL ¼ FB cfuel AHour

(69)

OPCU ¼ PWpump þ PWfan cpower AHour þ Mmk cmk AHour þ 0:01DCC

(70)

WSELL ¼ WT cpower AHour

(71)

5. Case study 5.1. Case description In this section, a case study is presented to demonstrate the proposed synthesis and design methodology. In this case, two hot streams and two cold streams as well as two pressure levels of steam used as hot utilities are considered. As mentioned in Literature Review section, only latent heat of steam is used as hot utility in most of the previous works. The sensible heat of steam condensate and BFW has not been considered simultaneously integrated into the HENs in the previous studies. The recovery or utilization of steam condensate (e.g., where the steam condensate ﬂows to and how the steam condensate is recovered and sent back to the utility system) was not well addressed in the literature. There are several possible ways to

885

recover steam condensate heat. The most possible way is ﬂashing at atmosphere pressure (the steam is vented and the saturate water go back to deaerator) or at the pressure higher than atmosphere pressure (the steam is again used as hot utility and the saturate water go back to deaerator). It is usually difﬁcult to effectively recover the process condense if its temperature is high. Therefore, lots of heat energy or mass stream is usually wasted. To demonstrate the synthesis and design problem of the entire system, three schemes are considered in terms of different ways for steam condensate utilization in the process HEN. In the ﬁrst scheme, the steam condensate is not used in the HEN to heat any cold process stream but directly ﬂows to the steam condensate recovery process. In the second scheme, the steam condensate is directly used as hot utility together with the saturate steam. After heating the cold process streams, the steam condensate goes to the steam condensate recovery process at a temperature lower than its saturate temperature. In the third scheme, the MP steam is ﬁrst depressurized to IP steam in a ﬂash tank. The IP steam is used as hot utility together with the IP steam from the utility plant; while the saturated water is sent to the steam condensate recovery process. Fig. 5 gives a general representation of steam and sinks proﬁle with ﬂash steam recovery in process HEN [34]. For each scheme, two scenarios are considered in terms of different steam condensate recovery process after the steam condensate leaving the process HEN. In the ﬁrst scenario, the steam condensate is directly returned to the utility system and entered to the deaerator. No steam condensate sensible heat is wasted. In the second scenario, the steam condensate is partly recovered at atmosphere pressure and then pumped to the deaerator [31]. Therefore, totally six design schemes for the entire energy system are demonstrated and

Fig. 8. Design conﬁguration of the UH-SSHIN (the scenario that the condensing water leaving the HENs is partly recovered at atmospheric pressure) system of Case 1.

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compared in this case. Table 1 gives the basic parameters of utility system and cooling water. It should be noted that the utility plant in Table 1 is a typical industrial utility plant of a petrochemical plant, especially in China [37,39e41]. The utility plant can supply both heat and power for the processes. The high pressure steam is generated in a boiler. The extraction and condensing steam turbine is used to cogenerate steam and power with more ﬂexibility than the utility plant and it contains only back pressure turbines. Table 2 gives the model coefﬁcients for the steam turbine as shown in Eqs. (41) and (42). For the gas ﬁred boiler, BCoeffa ¼ 0.0126 and BCoeffb ¼ 0.2156 [38]. In this paper, two cases are studied. Case 1 is a case with two hot streams, two cold streams and two steam levels as hot utilities. Case 2 is a case with four hot streams, four cold streams and three steam levels as hot utilities. Tables 3 and 4 give the information of hot and cold process streams as well as the information for the hot and cold utilities reported in Table 1 for Case 1 and Case 2. The upper bound of the temperature of the BFW heated by process hot streams in the PBEWHEN is 158 C (equals to the operating temperature of deaerator shown in Table 1) because the air dissolved in the BFW should be removed in the deaerator before entering the boiler. The annual operation time is 8000 h/year. The minimum allowable temperature difference is 2 C. The MINLP models are formulated in GAMS [48] on a 3.0 GHz Intel(R) Core(TM) 2 PC. Solver DICOPT [49] and ANTIGONE [50] are used to solve the MINLP model. DICOPT is ﬁrst used to get a feasible solution. Then the feasible solution is taken as starting point for ANTIGONE. The number of variables and constraints of this optimization scheme are 344 and 593.

5.2. Results and discussion 5.2.1. The synthesis of the HEN and utility system without integrating steam sensible heat and BFW of case 1 In this case, two scenarios are demonstrated. In the ﬁrst scenario (UH-SSHNN), the output water from the HENs is partly recovered at atmosphere pressure. In the second scenario (UH-SSHND), the output water from the HENs is directly pumped to the deaerator. Fig. 6 presents the design conﬁguration of the UH-SSHNN. For the PPHEN, three hot-cold stream heat exchangers are selected. Totally 35323 kW process heat is recovered. Cold stream pj2 is heated by pi1 and pi2 in sequent. For the PHUHEN, two utility heaters are selected. After be heated by pi1 and pi2, pj1 is ﬁrst heated from 165 C to 196.3 C by hui2 (16325 kW) and then heated to its target temperature by hui1 (21852 kW). Two options of steam levels give more ﬂexible choices for the PHUHEN than that of one steam level. Much MP steam can be saved to cogenerate power before it letdown to lower pressure (e.g., IP). The condense water of MP and IP steam return to the utility plant at their saturate temperature, respectively. It is supposed that 70% of the condensate of MP and IP steam is recovered at 90 C and return to the utility plant. Totally 28577 kW of cold utility is required to cool pi1 and pi2 to their target temperature. For the utility plant, 4.5 kg/s of LP steam is extracted from the deaerator because the temperature of the returned steam condenses and the makeup water are relatively low. Therefore, the boiler generation steam ﬂowrate is 28.3 kg/s. As a result, the turbine generated power is 12.937 MW. The TAC of the entire energy system is 13708.6 k$. Fig. 7 shows the design conﬁguration of the UH-SSHND. For the PPHEN, it is observed that two hot-cold stream heat exchangers are selected in the design scheme. Totally 35729 kW process heat is

Fig. 9. Design conﬁguration of the UH-SSHID (the scenario that the condensing water leaving the HENs is directly pumped to the deaerator) system of Case 1.

X. Luo et al. / Energy 113 (2016) 875e893

recovered. For the PHUHEN, three utility heaters are selected. After heated by pi1 and pi2, pj1 is ﬁrst heated from 173.2 C to 196.3 C by hui2 (11546 kW) and then heated to its target temperature by hui1 (21852 kW). The condense water of MP and IP steam returns to utility plant at their saturate temperatures, respectively. Totally 28171 kW of cold utility is required to cool pi1 and pi2 to their target temperatures. For the utility plant, the boiler generation steam ﬂowrate is 32.8 kg/s. No LP steam extraction is required for the deaerator because the steam sensible heat back from the HENs is enough to heat the deaerator to its operating temperature. The turbine generated power is 21.054 MW. The total number of heat exchangers in the UH-SSHND system is 7. The TAC of the entire energy system is 12151.8 k$, which is 11.4 % lower than that of the UH-SSHNN system. 5.2.2. Synthesis of the US and HEN systems integrating steam sensible heat and BFW of case 1 In this case, two scenarios are also presented. In the ﬁrst scenario (UH-SSHIN), the water leaving the HENs is partly recovered at atmospheric pressure. In the second scenario (UH-SSHID), the water leaving the HENs is directly pumped to the deaerator. Fig. 8 presents the design conﬁguration of the UH-SSHIN. For the PPHEN, it is observed that three hot-cold stream heat exchangers are selected. Totally 36839 kW process heat is recovered. For the PHUHEN, ﬁve utility heaters are selected, of which two are steam latent heat heater and three are steam condensate sensible heat heater. Totally 38500 kW of hot utility energy is used of which 5913 kW is steam condensate sensible heat. The temperatures of

887

the steam condense returning to utility plant for MP and IP are 165.5 C and 165.8 C, respectively. In other words, the steam condensate temperature is reduced from 263.9 C to 165.5 C for MP and from 198.3 C to 165.8 C for IP in the PHUHEN system. For the PBFWHEN, the turbine condensate water is heated by process hot stream in one heat exchanger from 45.8 C to 125.3 C. In other words, 3353 kW process surplus heat is recovered by heating BFW and the same amount of cold utility is saved. Totally 25548 kW of cold utility is needed. For the utility plant, the boiler generation steam ﬂowrate is 22.3 kg/s. About 2.3 kg/s of LP steam is extracted from the turbine used for deaerating the BFW. The turbine generated power is 9.438 MW. The TAC of the entire energy system is 11689.6 k$, which is 14.7 % lower than that of the UH-SSHNN. Fig. 9 presents the design conﬁguration of the UH-SSHID. For the PPHEN, two hot-cold stream heat exchangers are selected. Totally 35654 kW process heat is recovered. The conﬁgurations for the PPHEN, PBFWHEN and PCUHEN of UH-SSHID systems are similar to those of the UH-SSHIN. It should be noted that in the UH-SSHID, 1103 kW of heat from pi1 is recovered by heating BFW. In comparison, the amount of heat recovered in the PBFWHEN of the UHSSHIN is much higher than that of the UH-SSHID because of the additional 5.6 kg/s of makeup required in the UH-SSHIN. As shown in Fig. 9, totally 27142 kW of cold utility is needed. For the utility plant, the boiler generation steam ﬂowrate is 19.8 kg/s. The turbine generated power is 7.864 MW. The total number of heat exchangers of the UH-SSHID is 10. The TAC of the entire energy system is 10951.3 k$, which is 20.1 % lower than that of the UH-SSHNN and 6.3 % lower than that of the UH-SSHIN.

Fig. 10. Design conﬁguration for the UH-SSHFN (the scenario that the condensing water leaving the HENs is partly recovered at atmospheric pressure) system of Case 1.

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5.2.3. Synthesis of the US and HEN considering ﬂash steam sensible heat recovery of case 1 In this case, two scenarios are again demonstrated. In the ﬁrst scenario (UH-SSHFN), the water leaving the HENs is partly recovered at atmosphere pressure. In the second scenario (UH-SSHFD), the water leaving the HENs is directly pumped to the deaerator. Fig. 10 presents the design conﬁguration of the UH-SSHFN. Totally eight heat exchangers are selected, of which two for PHUHEN, four for PPHEN and two for PCUHEN. The TAC of the UHSSHFN is 12664.7 k$, which is 8.3 % higher than that of the UHSSHIN. Similarly, Fig. 11 presents the design conﬁguration of the UH-SSHFD. Totally eight heat exchangers are selected, of which two for PHUHEN, four for PPHIN and two for PCUHEN. The TAC of UHSSHFD is 11361.8 k$ which is 3.7% higher than that of UH-SSHID. 5.2.4. Synthesis of the US and HEN systems of case 2 In this case, two integration scenarios are demonstrated with the consumption that the condensate water leaving the HENs is directly pumped to the deaerator. In the ﬁrst scenario (UH-SSHND), the synthesis of US and HENs is conducted without integrating steam sensible heat and BFW. In the second scenario (UH-SSHID), the synthesis of US and HENs is conducted integrating steam sensible heat and BFW. Fig. 12 presents the design conﬁguration of the UH-SSHND for Case 2. For the PPHEN, ﬁve hot-cold stream heat exchangers are selected. Totally 61569 kw process heat is recovered. For the PHUHEN, eight utility heats are selected. Totally 56556 kw hot utility energy is used. For the utility plant, the boiler generation

steam ﬂowrate id 39.1 kg/s. The turbine generated power is 18.192 MW. The TAC of the entire energy system is 18261.0 k$. Fig. 13 presents the design conﬁguration of the UH-SSHID for Case 2. For the PPHEN, it is observed that six hot steam-cold stream heat exchangers are selected in the design scheme. Totally 83767 kw process heat is recovered. For the PHUHEN, eight utility heaters are selected, of which ﬁve are steam latent heat heater and three are steam condensate sensible heat heater. Totally 7845 kw sensible heat is used. For the PBFWHEN, only one hot-cold heat exchanger is selected. The 2501 kw waste heat from pi1 is recovered. For the utility plant, 29.5 kg/s steam ﬂow rate is generated by boiler. The turbine generated power is 12.741 MW. The TAC of the entire energy system is 15664.4 k$ which is 14.2% lower than that of the UH-SSHND system mainly due to the used of steam sensible heat and recovered the waste heat from pi1. The optimization results for the case studies are summarized in Table 5. It can be seen from Table 5 that the TACs of the entire energy system design with direct integration of steam condensate sensible heat and the BFW are much lower than the design without integration or integration with steam condensate ﬂash recovery. The savings of the TAC are mainly attributed to the saving of steam extraction consumption due to the direct integration of steam condensate sensible heat and partly attributed to the reduction of cold utility due to the integration of BFW. Furthermore, the optimal design schemes achieved from the proposed methodology do not feature much more complex structure compared with the schemes achieved from traditional methodologies. On the contrary, the temperatures of the steam condensate ﬂow to the condensate

Fig. 11. Design conﬁguration for the UH-SSHFD (the scenario that the condensing water leaving the HENs is directly pumped to the deaerator) system of Case 1.

X. Luo et al. / Energy 113 (2016) 875e893

889

Fig. 12. Optimal design conﬁguration for the UH-SSHND (the scenario that without integrating steam sensible heat and BFW, and the condensing water leaving the HENs is directly pumped to the deaerator) system.

recovery process reduces greatly after the direct integration in the process HEN. And consequently, the steam condensates are easy recovered in the steam condensate process. Table 5 also shows that the solution of the formulated MINLP model can be achieved within an acceptable computation time.

6. Conclusions The coupling of the utility system design with that of the HEN introduces noticeable complexities. The paper has presented an optimization approach to the simultaneous design of the HEN and a steam Rankine power plant. In this design process, the steam condensate target temperature, the steam level for process heating, the energy demand for the utility system, the returning temperature of the steam condensate, and the ﬁnal temperature of the BFW are all set as optimization variables to be determined in a way that minimizes the cost of the integrated utility and heat recovery systems. . In this study, a systematic methodology, an improved superstructure and an MINLP model are developed for the synthesis of an integrated HEN to a utility system. A case study is addressed and several schemes are compared. The following conclusions are drawn. Compared with the traditional concept of design without incorporating the integration of steam condensate sensible heat

in the HENs, the direct integration of steam condensate sensible heat can signiﬁcantly reduce the steam requirement of process HENs without heavily increases the number of heat exchangers. Consequently, the fuel consumption and the utility system investment cost are reduced. Although the utilization of steam condensate sensible heat by ﬂash recovery gives a possible way to recover steam condensate sensible heat, the TAC of the design with steam condensate ﬂash recovery is much higher than that of the direct integration case. Furthermore, the temperatures of the steam condensates leaving the HENs, after direct integration, are reduced greatly and make the condensate recovery process, after integration in the HEN, much easier in practical operation. The process surplus heat can be further recovered by preheating the BFW after the integration of hot and cold process streams. Consequently, the cooling utility consumption is reduced. It should be noted that the amount of recovered process surplus heat from the BFW preheating is mainly dependent on the ﬂowrate of the turbine steam condensate and makeup water. Much more process heat energy can be recovered if more power is generated when the power demand is high. The hot and cold utility consumptions as well as the TAC are reduced without heavily increasing the complexity of the ﬁnal design conﬁguration for the studied cases. Therefore, the formulated MINLP model can be effectively used for the

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Fig. 13. Optimal design conﬁguration for the UH-SSHID (the scenario that integrating steam sensible heat and BFW, the condensing water leaving the HENs is directly pumped to the deaerator) system.

Table 5 Comparative economic parameters and statistics of the illustrative examples. Case 1

INVHE (k$) INVUS (k$) INVCU (k$) OPCU (k$) OPFUEL (k$) WSELL (k$) TAC (k$) CPU time (S)

Case 2

UH-SSHNN

UH-SSHND

UH-SSHFN

UH-SSHFD

UH-SSHIN

UH-SSHID

UH-SSHID

UH-SSHND

1494.7 2509.4 31.3 667.2 16871.5 7865.5 13708.6 50

1529.9 2860.0 40.8 980.3 19541.6 12800.8 12151.8 87

1501.6 2255.5 30.2 636.2 14888.8 6647.6 12664.7 47

1418.7 1904.6 29.7 619.0 12153.5 4763.7 11361.8 37

1530.1 2045.5 28.2 576.3 13247.6 5738.1 11689.6 80

1472.6 1858.3 28.6 586.1 11787.1 4781.4 10951.3 125

2629.9 2594.8 29.3 608.2 17548.7 7746.5 15664.4 53

1824.5 3326.9 37.4 865.0 23268.2 11061.0 18261.0 141

synthesis and design of utility systems and HENs. The solution of the formulated MINLP model can be achieved within acceptable computation time. As demonstrated in the Problem description Section, the integration and design of HEN and utility system in this paper is based on the assumption of known and ﬁxed process hot and cold streams. Since the ﬂexibility of the utility system is an important issue in the operation, our future work will focus on

the multi-period integration of HEN and utility system to improve the ﬂexibility and operability.

Acknowledgment The authors gratefully acknowledge the ﬁnancial support from the National Natural Science Foundation of China (Grant No. 51476037).

X. Luo et al. / Energy 113 (2016) 875e893

Nomenclature Sets BFWJ BFWK HUI HUK I J K PI PJ PK

{bfwj j BFW streams heated by process surplus heat} {bfwk j stages in PBFWHEN} {hui j hot utility streams} {hui j stages in PHUHEN} {i j hot streams} {j j cold streams} {k j stages in HENs} {pi j process hot streams} {pj j process cold streams} {pk j stages in PPHEN}

Parameters: AFct investment cost annualization factor of cooling tower Ahour 8000 h per a year aisz model coefﬁcients for isentropic enthalpy difference of subsection z Aisz model coefﬁcients for isentropic efﬁciency of subsection z BCoeffa boiler model coefﬁcients BCoeffb boiler model coefﬁcients Bisz model coefﬁcients for isentropic efﬁciency of subsection z bisz model coefﬁcients for isentropic enthalpy difference of subsection z CCU unit cost of cold utility Cfuel unit cost of fuel Cpower unit price of power exportation Cwater unit price of water CBCoeffa coefﬁcients for boiler investment cost equation CBCoeffb coefﬁcients for boiler investment cost equation CF ﬁxed charge for heat exchangers Cpw heat capacity of bfwj Cphui heat capacity of hui CPcw heat capacity of water CTCoeffa coefﬁcients for turbine investment cost equation CTCoeffb coefﬁcients for turbine investment cost equation DTMAXi,j upper bound for temperature difference for exchangers DTMIN minimum approach temperature difference FB fuel consumption of boiler FHpi heat capacity ﬂow rate for process hot stream pi FCpj heat capacity ﬂow rate for process cold stream pj hconds ﬁlm heat transfer coefﬁcient of turbine waste steam hCU ﬁlm heat transfer coefﬁcient of cold utility hi ﬁlm heat transfer coefﬁcient for hot stream i hj ﬁlm heat transfer coefﬁcient for cold stream j hpi ﬁlm heat transfer coefﬁcient for hot process stream pi HBGen enthalpy of steam generated in boiler HCONDS enthalpy of turbine condensing water HSatlp saturate steam enthalpy of LP steam extracted from turbine HSatMP saturate steam enthalpy of MP steam extracted from turbine HWDEA enthalpy of BFW leaving deaerator LHhui latent heat of hot utility hui LHcw latent heat of water evaporation LHVF low heat value of fuel MB boiler steam generation ﬂow rate QCMAXpi upper bound for the cold utility requirement for hot process stream pi QMAXi,j upper heat bound for the heat exchange unit Tbfwj,in inlet temperature of cold stream bfwj Tconds temperature of condensing water from turbine Thui,in inlet temperature of hot stream hui Ti,out outlet temperature of hot stream i

Tj,out Tpi,in Tpi,out Tpj,in Tpj,out tBFW TCUin TCUout

891

outlet temperature of cold stream j inlet temperature of hot process stream pi outlet temperature of hot process stream pi inlet temperature of cold process stream pj outlet temperature of cold process stream pj temperature of BFW after heat integration inlet temperature of cold utility outlet temperature of cold utility

Greek letters b exponent for area of exchangers in cost equation d small number rcw density of cooling water hpump efﬁciency of pump in the cooling tower DTcw temperature difference of cooling water DPCT cooling water pressure drop in the cooling tower Binary variables Zi,j,k binary variables denote the existence of heat exchange units ZCpi binary variables denote the existence of coolers Variables DCC direct capital costs DLTHisz isentropic enthalpy difference of turbine subsection z dtcuipi temperature difference at hot end of the match between hot process stream pi and the cold utility dtcuopi temperature difference at cold end of the match between hot process stream pi and the cold utility dtii,j,k temperature difference at hot end of the match (i,j) at temperature location k dtoi,j,kþ1 temperature difference at cold end of the match (i,j) at temperature location k EFFisz isentropic efﬁciency of turbine subsection z FCbfwj mass ﬂow rate for cold stream bfwj FHhui mass ﬂow rate for hot stream hui FCSpi,j,k split ratio of heat capacity ﬂow rate of cold j that is connected to hot pi in stage k FCShui,j,huk split ratio of heat capacity ﬂow rate of cold j that is connected to hot hui in stage huk FHSpi,j,k split ratio of heat capacity ﬂow rate of hot pi that is connected to cold j in stage k FHShui,j,huk split ratio of mass ﬂow rate of hot pi that is connected to cold j in stage huk FHShui,pj,huk split ratio of mass ﬂow rate of hot pi that is connected to cold pj in stage huk HT1,out outlet enthalpy in Subsection 1 HT2,out outlet enthalpy in Subsection 2 HTz,in inlet enthalpy of turbine subsection z HTz,out outlet enthalpy of turbine subsection z INVCU investment cost of cold utility INVHE investment cost of exchanger heat network INVUS investment cost of hot utility Mcw outlet mass ﬂow rate of water from tower Mmk mass ﬂow rate of make-up water MT1,in turbine inlet steam ﬂow rate MTz inlet steam ﬂow rate of turbine subsection z MTlp,ext LP steam extraction ﬂow rate MTMP,ext MP extraction steam ﬂow rate MTz,ext extraction steam ﬂow rate of turbine subsection z MTz,in inlet steam ﬂow rate of turbine subsection z MTz,out outlet steam ﬂow rate of turbine subsection z MWlp water ﬂow rate for cooling superheated LP steam MWMP water ﬂow rate for cooling superheated MP steam OPCU operating cost for cold utility

892

X. Luo et al. / Energy 113 (2016) 875e893

OPFUEL PWct PWpump PWfan qhui,j,huk

operating cost for fuel the total power consumption of cooling tower the power of pump in the cooling tower the power of draft fan in the cooling tower heat exchanged between hot stream hui and cold stream j in stage huk qhui,pj,huk heat exchanged between hot stream hui and cold stream pj in stage huk Qi,j,k heat exchanged between hot stream i and cold stream j in stage k qpi,bfwj,bfwk heat exchanged between hot stream pi and cold stream bfwj in stage bfwk qpi,j,k heat exchanged between hot stream pi and cold stream j in stage k qpi,pj,pk heat exchanged between hot stream pi and cold stream pj in stage pk QCconds turbine condenser heat load QCpi cold utility requirement for hot process stream pi SPfan unit power consumption of draft fan tbfwj,bfwk temperature of cold stream bfwj at the temperature location bfwk thui,huk temperature of hot stream hui at the temperature location huk ti,k temperature of hot stream i at the temperature location k tj,k temperature of cold stream j at the temperature location k tpi,bfwk temperature of cold stream pj at the temperature location bfwk tpi,k temperature of hot stream pi at the temperature location k tpi,pk temperature of hot stream pi at the temperature location pk tpj,huk temperature of cold stream pj at the temperature location huk tpj,pk temperature of cold stream pj at the temperature location pk TAC total annual cost tii,j,k outlet temperature of non-isothermal split cold stream j after exchange heat with hot stream i at stage k tipi,j,k outlet temperature of non-isothermal split cold stream j after exchange heat with hot stream pi at stage k tohui,j,huk outlet temperature of non-isothermal split hot stream hui after exchange heat with cold stream j at stage huk toi,j,k outlet temperature of non-isothermal split hot stream i after exchange heat with cold stream j at stage k topi,j,k outlet temperature of non-isothermal split hot stream pi after exchange heat with cold stream j at stage k WSELL the proﬁt of selling electricity WT power generation of turbine

Abbreviation UH-SSHIN the scenario that without integrating steam sensible heat and BFW, and the water condensate leaving the HENs is partly recovered at atmospheric pressure UH-SSHI the scenario that without integrating steam sensible heat and BFW, and the water condensate leaving the HENs is directly pumped to the deaerator UH-SSHIN the scenario that integrating steam sensible heat and BFW, and the water condensate leaving the HENs is partly recovered at atmospheric pressure UH-SSHID the scenario that integrating steam sensible heat and BFW, and the water condensate leaving the HENs is directly pumped to the deaerator

UH-SSHFN the scenario that considering ﬂash steam sensible heat recovery, and the water condensate leaving the HENs is partly recovered at atmospheric pressure UH-SSHFD the scenario that considering ﬂash steam sensible heat recovery, and the water condensate leaving the HENs is directly pumped to the deaerator References [1] Hohmann EC. Optimum networks for heat exchange [PhD Thesis, USA]. University of Southern California; 1971. [2] Linnhoff B, Flower JR. Synthesis of heat exchanger networks I: systematic generation of energy optimal networks. AIChE J 1978;24(4):633e42. [3] Linnhoff B, Flower JR. Synthesis of heat exchanger networks II: evolutionary generation of networks with various criteria of optimality. AIChE J 1978;24(4): 642e54. [4] Furman KC, Sahinidis NV. A critical review and annotated bibliography for heat exchanger network synthesis in the 20th Century. Ind Eng Chem Res 2002;41:2335e70. [5] Verheyen W, Zhang N. Design of ﬂexible heat exchanger network for multiperiod operation. Chem Eng Sci 2006;61:7730e53. [6] Goh WS, Wan YK, Tay CK, Ng RTL, Ng DKS. Automated targeting model for synthesis of heat exchanger network with utility systems. Appl Energy 2016;162:1272e81. nez-Gutie rrez A, Grossmann IE. Optimal synthesis of [7] Ponce-Ortega JM, Jime heat exchanger networks involving isothermal process streams. Comput Chem Eng 2008;32:1918e42. [8] Papoulias SA, Grossmann IE. A structural optimization approach in process synthesisdII, heat recovery networks. Comput Chem Eng 1983;7(6):707e21. [9] Cerda J, Westenberg AW, Mason D, Linhoff B. Minimum utility usage in heat exchanger network synthesis. A transportation problem. Chem Eng Sci 1983;38(3):373e87. [10] Floudas CA, Ciric AR, Grossmann IE. Automatic synthesis of optimum heat exchanger network conﬁgurations. AIChE J 1986;32(2):276e90. [11] Zhu XX. Automated design method for heat exchanger network using block decomposition and heuristic rules. Comput Chem Eng 1997;21(10): 1095e104. [12] Ciric AR, Floudas CA. Heat exchanger network synthesis without decomposition. Comput Chem Eng 1991;15(6):385e96. [13] Yee TF, Grossmann IE, Kravanja Z. Simultaneous optimisation models for heat integrationdI, area and energy targeting and modelling of multi-stream exchangers. Comput Chem Eng 1990;14(10):1151e64. [14] Yee TF, Grossmann IE. Simultaneous optimisation models for heat integrationdII, heat exchanger network synthesis. Comput Chem Eng 1990;14(10): 1165e84. [15] Zamora JM, Grossmann IE. A global MINLP optimization algorithm for the synthesis of heat exchanger networks with no stream splits. Comput Chem Eng 1998;22:367e84. nez-Gutie rrez A, Grossmann IE. Optimal synthesis of [16] Ponce-Ortega JM, Jime heat exchanger networks involving isothermal process streams. Comput Chem Eng 2008;32:1918e42. [17] Hasan MMF, Jayaraman G, Karimi IA, Alfadala HE. Synthesis of heat exchanger networks with nonisothermal phase changes. AIChE J 2010;56:930e45. [18] Huang KF, Al-mutairi EM, Karimi IA. Heat exchanger network synthesis using a stagewise superstructure with non-isothermal mixing. Chem Eng Sci 2012;73:30e43. nez-Gutie rrez A. Synthesis of heat [19] Ponce-Ortega JM, Serna-Gonz alez M, Jime exchanger networks with optimal placement of multiple utilities. Ind Eng Chem Res 2010;49:2849e56. lito-Valencia BJ, Rubio-Castro E, Ponce-Ortega JM, Serna-Gonza lez M, [20] Hipo N apoles-Rivera F, El-Halwagi MM. Optimal integration of organic Rankine cycles with industrial processes. Energ Convers Manag 2013;73:285e302. [21] Chen CL, Chang FY, Chao TH, Chen HC, Lee JY. Heat-exchanger network synthesis involving organic Rankine cycle for waste heat recovery. Ind Eng Chem Res 2014;53(44):16924e36. [22] Lira-Barrag an LF, Serna-Gonz alez M, El-Halwagi MM. Optimum heat storage design for solar-driven absorption refrigerators integrated with heat exchanger networks. AICHE J 2014;60(3):909e30. lito-Valencia BJ, Lira-Barraga n LF, Ponce-Ortega JM, Serna-Gonz [23] Hipo alez M, El-Halwagi MM. Multiobjective design of interplant trigeneration systems. AICHE J 2014;60(60):213e36. [24] Gonzalez-Bravo M, Elsayed NA, Ponce-Ortega JM, Napoles-Rivera F, ElHalwagi MM. Optimal design of thermal membrane distillation systems with heat integration with process plants. Appl Therm Eng 2015;75:154e66. [25] Ahmetovic E, Kravanja Z. Simultaneous synthesis of process water and heat exchanger networks. Energy 2013;57:236e50. [26] Klemes JJ, Varhanov PS, Kravanja Z. Recent developments in process integration. Chem Eng Res Des 2013;9:2037e53. [27] Klemes JJ, Dhole VR, Raissi K, Perry SJ, Puigjaner L. Targeting and design methodology for reduction of fuel, power and CO2 on total sites. Appl Therm Eng 1997;17:993e1003. [28] Liew PY, Wan Alwi SR, Varbanov PS, Manan ZA, Klemes JJ. Centralised utility

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