- Email: [email protected]

Xiaojian Huang, Pei Lu, Xianglong Luo, Jianyong Chen, Zhi Yang, Yingzong Liang, Chao Wang, Ying Chen PII:

S0360-5442(20)30029-3

DOI:

https://doi.org/10.1016/j.energy.2020.116922

Reference:

EGY 116922

To appear in:

Energy

Received Date:

21 April 2019

Accepted Date:

06 January 2020

Please cite this article as: Xiaojian Huang, Pei Lu, Xianglong Luo, Jianyong Chen, Zhi Yang, Yingzong Liang, Chao Wang, Ying Chen, Synthesis and simultaneous MINLP optimization of heat exchanger network, steam Rankine cycle, and organic Rankine cycle, Energy (2020), https://doi.org /10.1016/j.energy.2020.116922

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Synthesis and simultaneous MINLP optimization of heat exchanger network, steam Rankine cycle, and organic Rankine cycle Xiaojian Huanga, Pei Lua, Xianglong Luoa,*, Jianyong Chena, Zhi Yanga, Yingzong Lianga, Chao Wanga, Ying Chena aSchool

of Material and Energy, Guangdong Provincial Key Laboratory of Functional Soft Condensed Matter, Guangdong University of Technology, Guangzhou, China

Abstract Process plants are typically energy intensive plants and pollutant emission contributors. Energy integration in process plants effectively reduces energy consumption and pollutant emission. In a traditional energy integration concept, a heat exchanger network (HEN) is typically constructed for heat recovery between process streams. However, a large amount of medium-to-low-temperature surplus heat usually occurs in hot streams, where further internal heat integration is impossible, and is inevitably cooled by external cold source. Integrating organic Rankine cycle (ORC) into the process HEN is an effect way in further enhancing the energy recovery. However, the HEN, utility plant, and ORC are traditionally designed and optimized separately or sequentially, resulting in local energy integration or optimization. In the present study, ORC is integrated into a HEN to generate power energy from surplus heat. An improved superstructure is constructed and a mixed integer non-linear programming model is developed for the synthesis and simultaneous optimization of the integration system containing process-process HEN, hot utility-cold stream HEN, process hot stream-ORC HEN, steam utility plant, and cold utility plant. Two case studies of different scale in complexity are elaborated to validate the proposed methodology. Sensitivity analysis of carbon tax and fuel price are finally conducted. Keywords: HEN; MINLP; Organic Rankine cycle; Optimization; Heat recovery.

1. Introduction The limited fossil fuel reserves and increasing concern on the greenhouse effect push the industrial energy system toward a sustainable direction. In process plants, heat and cold streams must be cooled and heated, respectively, to their target temperatures. Heat integration (HI) under certain rules between hot and cold streams can be performed to maximize the heat recovery and minimize the hot and cold utility requirements for process plants [1]. Hot and cold streams compose a heat exchanger network (HEN). The extra heat and cold demand after HI between hot and cold streams in HENs are provided from the utility plants. In the traditional HI concept, the utility plant is generally designed separately from the HEN. Cerda et al. [2] presented a transportation model for the minimization of the utility cost after the HEN is designed. A transshipment model was developed by Papoulias and Grossmann [3] to minimize the utility cost for a process system with a pre-defined HEN. Recently, the design of utility plant together with a HEN has received significant attention, and many innovative methods have been proposed. Zhang et al. [4] presented a mixed-integer nonlinear programming (MINLP) model that integrate the process plants and utility systems. Luo et al. [5] presented a novel method for the simultaneous synthesis and optimization of a HEN and utility system. Steam condensate and boiler feed water (BFW) were incorporated to recover the surplus heat in the HEN. These studies showed that integration or optimization of HENs and utility systems saves remarkable energy or cost compared with the conventional separate design concept. However, previous research showed that a mass of lowtemperature surplus heat is available after HI in HENs, and must be cooled by external cold utility. The use of external technology to further recover surplus heat in HENs is significant in further reducing fuel consumption and pollutant emission. Recently, numerous studies have been conducted to integrate HENs with energy systems (e.g., absorption cycle [6], heat pumps and engines [7], thermal membrane distillation systems [8], multiple-effect evaporation system [9] and organic *Corresponding

author. School of Material and Energy, Guangdong University of Technology, Guangzhou, 510006, China. Tel.: +86-

020-39322570. E-mail address: [email protected] (X. Luo). 1

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Rankine cycle (ORC) [10]) to recover surplus heat. In a variety of heat recovery technologies, ORC has been regarded as one of the widely accepted low-grade heat driven power generation technology [11]. In ORC, organic fluids are used as working medium, different from the use of water as the working fluid in Rankine cycle. The utilization of ORC to recover waste heat from process plants has drawn considerable attention in the past few years [12]. Yari et al. [13] conducted a comparison of the thermodynamic and exergoeconomic performances of ORC, Kalina cycle, and trilateral Rankine cycle. Their findings showed that ORC is the most advantageous of the three options in term of economic performance. For the integration of HEN and ORC, some studies proposed step-by-step methods. Gutiérrez–Arriaga et al. [14] proposed a two-stage HI approach. In the first stage, a grand composite curve was established for the process streams to determine the HI targets, waste heat available to drive ORC, cold utility load, and refrigeration load. In the second stage, a genetic algorithm was used to determine the optimal ORC structure and operating conditions. Desai and Bandyopadhyay [15] proposed a manual trial-and-error optimization for the integration of ORC and HEN to recover surplus heat of chemical processes. The operating conditions of ORC were determined manually using pinch technology, and a heuristic method was used to derive the HEN. Chen et al. [16] proposed a two-step method for optimizing ORC and synthesizing HEN. In the first step, a stand-alone HEN was synthesized to minimize the demand for hot utility. In the second step, ORC was incorporated into the surplus heat zone to maximize the power output below the pinch point. The design parameters (e.g., condensation temperature, evaporation temperature) of ORC were fixed, and the rigorous thermodynamic models of ORC were not included. Stijepovic et al. [17] proposed a pinch analysis and mathematical programming combined method to determine the optimum structure of ORC and working mediums for various heat sources. The number of ORC stages, HEN configuration, operating parameters, and the working medium used in each cascade were considered to maximize the power output in ORC. The step-by-step method mainly focused on the synthesis of ORC with the surplus heat from the HEN. The simultaneous optimization of HEN and ORC have drawn more and more attention. Hipolito–Valencia et al. [10] proposed a procedure for the integration of ORC and process plants. Their studies showed that the proposed procedure is more cost-saving than an earlier developed method using a sequential approach for discovering optimally integrated systems. Chen et al. [18] proposed a superstructure for HEN synthesis; the superstructure contains ORCs which are used to recover low-grade waste heat through a circulating heat transfer fluid. And a unified MINLP model was developed for the synthesis and optimization of the integration system. A case study of crude-preheat train example demonstrated the effectiveness of the proposed superstructure and MINLP formulation. Yu et al. [19-21] presented several studies for the integration of ORC and HEN. Integration of ORC and HEN was performed based on pinch technology in Yu et al. [19]. A mathematical programming model integrating ORC into background process was proposed to maximize the net power output of ORC in Yu et al. [20]. It was proposed that hot-water stream be used as an intermediate to recover multiple waste heat streams. Hot water was considered a cold stream in the HEN and as heat source in the ORC system in Yu et al. [21]. Previous studies showed the considerable attention paid to the integration of HEN and ORC to further improve the HI on the basis of traditional HEN. Most of these studies applied the concept of pinch integration and sequential method. The synthesis and design of HEN and ORC are typically conducted with pre-specified ORC structure, or the HEN and ORC are designed in sequence. Given that the earning of ORC is power or electricity, and that of HENs is heat recovery, the inconsistent objectives cause difficulty in evaluating the HEN–ORC integration system. Recently, the HI of HEN and the utility plants has been substantially studied [22]. However, the integration of HEN, utility plants and ORC was not reported [23]. To fill the research gap, the present study proposes the integration of hot and cold utility plants, HENs, and ORC with various working fluids. Fig. 1 shows the relationship among the HEN, ORC, and utility plants. Heat recoveries of hot and cold streams are determined according to pinch integration rules. The hot utility plant provides hot utility energy for cold streams. ORC is integrated into the HEN to absorb surplus heat and cogenerate power. Hot stream is finally cooled to its target temperature using cold utility provided by cold utility plant. Fig. 1 indicates the strong interlinkage between HEN, ORC, and utility plants. Appropriate modeling and optimization method are required to maximize the global performance of the integrated system. Thus, an improved modelling framework and solution strategy is proposed to integrate and simultaneous optimize the 2

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process HEN, SRC, ORC and cold utility system. A MINLP model is constructed to synthesize and simultaneously optimize the proposed integration system. The method incorporates rigorous thermodynamic models of steam Rankine cycle (SRC)-based utility plant with condensate heat recovery, ORC for the surplus heat recovery, and cold utility plant for the cooling of hot streams. The objective is to minimize the total annual cost (TAC) consists of capital investment cost, operating cost, and environmental cost. The synthesis and optimization aim to determine a design scheme for the HEN (the number of heat exchangers, and heat exchange between hot and cold streams), SRC (steam flow rate at all inlet/outlet of turbine, and final temperature for hot utilities), and ORC (working fluid flow rate, evaporating temperature, and condensing temperature). Two case examples are elaborated to demonstrate the superiority of the proposed methodology, and sensitivity analyses of carbon tax and fuel price is also conducted. To the best of our knowledge, considering the system model for the efficient integration of HEN with SRC, ORC and cold utility system which simultaneously exploits the structural features, working fluids, and thermo-economic-environmental objectives has not been found in the open literature. T (oC) Cold utility system

Utility system

ORC system

Boiler Expander Cooling tower

Turbine C

Pinch point

C

Pump

H (kW)

Deaerator

Fig. 1 General relationship between HEN, ORC, and utility plants

2. Problem description The entire problem can be described as follows: Presetting hot streams which must be cooled and cold streams which must be heated, with given properties (their inlet temperatures, outlet temperatures, and heat-capacity flow rate). And the basic structure of SRC and ORC are specified, including three types of working mediums and their thermo-physical properties. Additional data consists of investment cost for the utility components and heat exchangers, unit price for fuel, electric power generated from SRC and ORC, heat transfer coefficients for all streams, and minimum allowable temperature differences (ΔTmin) of the entire HENs. Then the integration problem contains in achieving the optimum configuration of the PPHEN, PHUHEN, PCUHEN, and PORCHEN; areas of all the heat exchangers; design load and operation parameters of components in the utility system; cold utilities requirement from the HEN, condensers of SRC, and ORC and the minimum total annual cost (TAC). Fig. 2 shows the superstructure of the proposed integration system. The integration system comprises five sections: a HEN consists of process hot and cold streams (PPHEN), a HEN consists of cold streams leaves PPHEN and hot utility streams (PHUHEN), a HEN consists of hot stream leaves PPHEN and ORC (PORCHEN), and a HEN consists of hot streams leave PORCHEN and cold utility streams (PCUHEN). The constructed PPHEN is a traditional HEN in which process heat recovery is achieved by reasonably matching hot and cold streams. In the PHUHEN, both latent and sensible heat of steam are used as hot utilities. SRC-based utility plant [5] is used to cogenerate steam and power [24-27]. The SRCbased utility plant is easily extended to other types of utility plants when necessary. In PORCHEN, an ORC is integrated to recover surplus heat from hot streams. A general ORC comprises an evaporator, an expander, a condenser, and a pump. After heat recovery in PORCHEN, hot streams are cooled to their target temperatures by cold utility. Fig. 3 displays the schematic and T–S diagram of a simple ORC. In PCUHEN, the surplus heat of hot streams after releasing heat in PORCHEN is cooled by cold utility. A cooling tower is designed to provide cold utility for cooling the process hot streams, steam leaves the turbine in the SRC, and vapor leaves the ORC. The aim of the present study is to model and solve the proposed synthesis and optimization problem depicted in Fig. 2. 3

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Though the integration system is decomposed into several sub-HENs from high to low temperature in cascade, the simultaneous optimization of four HENs, ORC, and SRC presents difficulty in solving the problem. Traditional pinch technology is difficult to guarantee the optimal solution when solving this kind of HI problem, thus requiring a solution strategy. The following two sections will present a detailed model and a strategy for solving the MINLP problem. huk1

PHUHEN ... hukn

PPHEN pk1

...

PORCHEN orck1

pkn

...

PCUHEN

orckn

pi1

hui

C

... pin

C

pj1 ... pjn

orcj

Turbine Fuel

Boiler

Cooling tower

Expander

Makeup water

Condenser

Condenser

Pump

Pump Deaerator

Fig. 2 Superstructure of the proposed integration system (a)

(b)

Evaporator

4

Expander

3

5 Condenser

2

1 Pump

Fig. 3 Representation of a simple ORC: a) Schematic; b) T–S diagram

3. Model formulation The models for process integration and optimization are formulated based on the superstructure shown in Fig. 2 The entire system can be divided into four subsystems, i.e., PPHEN, PHUHEN, PORCHEN, and PCUHEN. Thus, the optimization model of the entire integration system consists of four sub-HENs, SRC, ORC, cooling tower, coupling constraints of these sub-systems, and objective functions. In the present study, PPHEN is a conventional HEN, whereas PHUHEN and PORCHEN differ from the conventional HEN to a certain extent. Both latent and sensible heat of steam generated from the SRC are simultaneously used as hot utilities [5]. Thus, a steam stream is divided into latent condensing stream and sensible condensate stream. For the latent condensing stream, the temperature remains unchanged. For the sensible condensate heat stream, inlet temperature is the same as the saturate temperature, whereas the outlet temperature varies. In PORCHEN, the working fluid is heated in the evaporator from a subcooled liquid to saturation liquid, saturation vapor, and finally superheating vapor. Thus, the working 4

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fluid stream should be divided into pre-heating, evaporating, and superheating sections. In preheating and superheating stages, the heat exchange process is similar to that of hot–cold streams. In the evaporating section, the working fluid temperature shows no change. Generally, hot streams represent all the streams that release heat and cold streams represent all the streams that absorb heat. In the present paper, i represents hot streams, which can be part of or consist the entire hot process stream (pi) and hot utility stream (hui); and j represents cold streams, which can be part of or make up the whole cold process stream (pj) and ORC stream (orcj). Each subsystem is divided into two heat transfer stages. pk, huk and orck denote stage in PHUHEN, PPHEN and PORCHEN, respectively. Nomenclature Section lists all other subscripts, variables and parameters. The model is composed of the HEN model, SRC model, cooling tower model, ORC model, interlink constraints between sub-HENs, and objective functions. The HEN, SRC, and cooling tower models are commonly used models and are described in detail in the previous study [5] and is not repeated in this study. The ORC model, the entire energy system integration model, constraints, and objective functions are formulated in this section. Notably, the proposed integration problem is formulated into mathematical programming model and deterministic optimization method is applied as shown in Fig. 4. Start Model formulation and validation HEN, utility system and ORC model formulation and validation

Data input

Input data -Process streams properties -Thermophysical properties of working fluids -Film heat transfer coefficients -Minimum temperature difference Objective Min =TAC

Initial solution

Solve relaxed model (RMINLP) using solver CONOPT, MINOS and SNOPT in sequence Next solver Is the solution of RMINLP “optimal ” or “locally optimal”

Local solution

Global solution

No

YES Initialize original model and solve model using solver DICOPT

Solve model using solver ANTIGONE

Final Solution

Fig. 4. Problem solution strategy and procedure

3.1 Energy balances for process streams According to the proposed structure, hot streams enter from the left side of each subsystem, whereas cold streams enter from the right side. Hot streams release heat, whereas cold streams absorb it. Hot streams show a downward trend in temperature, whereas cold streams exhibit an upward trend. As shown in Fig. 2, process hot streams are cooled from their supply temperatures to their target temperatures sequentially by process cold streams, ORC working fluid, and cold utility. The heat balances of process hot–cold streams are formulated by Eq. (1), where qpi,pj,pk denotes the quantity of heat transferred between hot stream pi and cold stream pj at 5

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stage pk; qpi,orcj,orck denotes the quantity of heat transferred between hot stream pi and cold stream orcj at stage orck; QCpi denotes the cold utility load used to cool hot stream pi; FHpi, Tpi,in, and Tpi,out, represent the heat capacity flow and inlet/outlet temperatures of hot stream pi, respectively. Similarly, Eq. (2) indicates that process cold streams are heated by process hot streams and/or hot utilities, where qhui,pj,huk denotes the quantity of heat transferred from stream hui to stream pj at stage huk; FCpi, Tpj,in, and Tpj,out, stand for the heat capacity flow and inlet/out temperature of stream pj, respectively. ∑𝑝𝑗 ∈ 𝑃𝐽∑𝑝𝑘 ∈ 𝑃𝐾𝑞𝑝𝑖,𝑝𝑗,𝑝𝑘 + ∑𝑜𝑟𝑐𝑗 ∈ 𝑂𝑅𝐶𝐽∑𝑜𝑟𝑐𝑘 ∈ 𝑂𝑅𝐶𝐾𝑞𝑝𝑖,𝑜𝑟𝑐𝑗,𝑜𝑟𝑐𝑘 + 𝑄𝐶𝑝𝑖 = 𝐹𝐻𝑝𝑖(𝑇𝑝𝑖,𝑖𝑛 ― 𝑇𝑝𝑖,𝑜𝑢𝑡) ∀𝑝𝑖 ∈ 𝑃𝐼 ∑𝑝𝑖 ∈ 𝑃𝐼∑𝑝𝑘 ∈ 𝑃𝐾𝑞𝑝𝑖,𝑝𝑗,𝑝𝑘 + ∑ℎ𝑢𝑖 ∈ 𝐻𝑈𝐼∑ℎ𝑢𝑘 ∈ 𝐻𝑈𝐾𝑞ℎ𝑢𝑖,𝑝𝑗,ℎ𝑢𝑘 = 𝐹𝐶𝑝𝑗(𝑇𝑝𝑗,𝑖𝑛 ― 𝑇𝑝𝑗,𝑜𝑢𝑡)

(1) (2)

3.2 Modeling for ORC ORC is a promising low-grade heat driven power generation technology. ORC has also recently been a hot topic in energy-related fields; modeling of a simple ORC is not a difficult task. However, specific constraints and rules must be constructed when integrating ORC into HENs. In addition, working fluid properties are typically extracted from a database, such as Refprop, or calculated from the equation of states. In the present study, to guarantee simultaneous optimization of the integrated system, regression method is used to correlate the properties of working fluid as a function of operating parameters. 3.2.1 Energy balances of ORC The energy balance of the internal stages for PORCHEN differs from that for PPHEN because the working fluid heating typically consists of preheating, evaporating, and superheating processes. As discussed in previous studies [28, 29], superheating of working fluid usually causes no improvement in the ORC performance; thus, working medium superheating is not considered in the present study. In this section, a working fluid stream is separated into preheating and evaporating streams. Eq. (3) denotes the heat balance for hot process stream pi in PORCHEN. Eq. (4) provides the heat balance of working fluid preheating, and Eq. (5) calculates the heat balance of evaporating working fluid, where Morcj is the mass ratios of the working fluid, ORD and CARD represent the order and total element amount in a set respectively, and LHorcj indicates the evaporation latent heat. Eq. (6) constrains that the mass flow rate of working medium is equal for preheating and evaporating streams. 𝑞𝑝𝑖,𝑜𝑟𝑐𝑗,𝑜𝑟𝑐𝑘 = 𝐹𝐻𝑝𝑖(𝑡𝑝𝑖,𝑘 ― 𝑡𝑜𝑝𝑖,𝑜𝑟𝑐𝑗,𝑜𝑟𝑐𝑘 + 1) ∀𝑝𝑖 ∈ 𝑃𝐼, ∀𝑜𝑟𝑐𝑗 ∈ 𝑂𝑅𝐶𝐽,𝑜𝑟𝑐𝑘 ∈ 𝑂𝑅𝐶𝐾 (3) ( ) 𝑞𝑝𝑖,𝑜𝑟𝑐𝑗,𝑜𝑟𝑐𝑘 = 𝐹𝐶𝑜𝑟𝑐𝑗 𝑡𝑖𝑝𝑖,,𝑜𝑟𝑐𝑗,𝑜𝑟𝑐𝑘 ― 𝑡𝑜𝑟𝑐𝑗,𝑜𝑟𝑐𝑘 + 1 ∀𝑝𝑖 ∈ 𝑃𝐼, ∀𝑜𝑟𝑐𝑗 ∈ 𝑂𝑅𝐶𝐽,𝑂𝑅𝐷(𝑜𝑟𝑐𝑗) = 𝐶𝐴𝑅𝐷(𝑜𝑟𝑐𝑗)/2,𝑜𝑟𝑐𝑘 ∈ 𝑂𝑅𝐶𝐾 (4) (5) (6) The working fluid in ORC (Fig. 3) is integrated in PORCHEN to recover surplus heat of hot stream after process hot– cold stream integration. Eq. (7) expresses the energy balance in ORC evaporators, and Eq. (8) yields the power generation of ORC. Eq. (9) calculates the heat load of the cold utility for the ORC condenser, and Eq. (10) expresses the power consumption of the pump in the ORC system. h1, h2, h4 and h5 are enthalpies of the corresponding state points. Eq. (11) shows the thermal efficiency of the ORC system. 𝑞𝑝𝑖,𝑜𝑟𝑐𝑗,𝑜𝑟𝑐𝑘 = 𝑀𝑜𝑟𝑐𝑗𝐿𝐻𝑜𝑟𝑐𝑗 ∀𝑝𝑖 ∈ 𝑃𝐼, ∀𝑜𝑟𝑐𝑗 ∈ 𝑂𝑅𝐶𝐽,𝑂𝑅𝐷(𝑜𝑟𝑐𝑗) > 𝐶𝐴𝑅𝐷(𝑜𝑟𝑐𝑗)/ 2,𝑜𝑟𝑐𝑘 ∈ 𝑂𝑅𝐶𝐾 𝑀𝑜𝑟𝑐𝑗 = 𝑀𝑜𝑟𝑐𝑗 + 𝐶𝐴𝑅𝐷(𝑜𝑟𝑐𝑗)/2 ∀𝑜𝑟𝑐𝑗 ∈ 𝑂𝑅𝐶𝐽,𝑂𝑅𝐷(𝑜𝑟𝑐𝑗) = 𝐶𝐴𝑅𝐷(𝑜𝑟𝑐𝑗)

𝑄𝐻𝑜𝑟𝑐𝑗 = ∑𝑝𝑖 ∈ 𝑃𝐼∑𝑜𝑟𝑐𝑗 ∈ 𝑂𝑅𝐶𝐽∑𝑜𝑟𝑐𝑘 ∈ 𝑂𝑅𝐶𝐾𝑞𝑝𝑖,𝑜𝑟𝑐𝑗,𝑜𝑟𝑐𝑘 = 𝑀𝑜𝑟𝑐𝑗(h2 ― ℎ4)

(7)

𝑊𝑇𝑜𝑟𝑐𝑗 = 𝑀𝑜𝑟𝑐𝑗(ℎ4 ― ℎ5) 𝑄𝐶𝑜𝑟𝑐𝑗 = 𝑀𝑜𝑟𝑐𝑗(ℎ5 ― ℎ1) 𝑊𝑇𝑝𝑢𝑚𝑝 = 𝑀𝑜𝑟𝑐𝑗(ℎ2 ― ℎ1) 𝜂𝑂𝑅𝐶 = (𝑊𝑇𝑜𝑟𝑐𝑗 ― 𝑊𝑇𝑝𝑢𝑚𝑝)/𝑄𝐻𝑜𝑟𝑐𝑗

(8)

(9) (10) (11) Eqs. (12)–(21) provide the fitting formula for the state points in Fig. 3. Suppose that the working fluid entering the expander at saturate vapor state, all properties of working fluid can be formulated as a function of evaporation temperature Te and/or condensing temperature Tc. The specific enthalpy of saturated state points (i.e., points 1, 3, 4, and 6) are regressed 6

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as a formulation of one independent variable (e.g., Te or Tc) as shown by Eqs. (12), (15), (16) and (19). The isentropic enthalpy rise in the pump Δh1-2s and isentropic enthalpy drop in the expander Δh4-5s can be fitted as a function of Te and Tc as formulation by Eqs. (13) and (17). Then the enthalpies of point 2 and 5 can be calculated from Eqs. (14) and (18), where ηe and ηp are the isentropic efficiencies of the expander and pump, respectively. T2 is regressed as a function of Te and h2 while T5 is regressed as a function of Tc and h5 as given by Eqs. (20) and (21). The fitting parameters are listed in Appendix A. As shown in Appendix A, all of the determination coefficients (R2) of the regressed equations exceed 0.99, indicating the accuracy and reliability of the formulated model. ℎ1 = 𝑐𝑓𝑎𝑎 +𝑐𝑓𝑏𝑏𝑇𝐶 +𝑐𝑓𝑐𝑐𝑇2𝐶 (12) 2 2 ∆ℎ1 ― 2𝑠 = 𝑐𝑓𝑑𝑑 +𝑐𝑓𝑒𝑒𝑇𝐸 +𝑐𝑓𝑓𝑓𝑇𝐸 +𝑐𝑓𝑔𝑔𝑇𝐶 +𝑐𝑓ℎℎ𝑇𝐶 (13) ℎ2 = ℎ1 +∆ℎ1 ― 2𝑠/𝜂𝑝 (14) ℎ3 = 𝑐𝑓𝑎𝑎 +𝑐𝑓𝑏𝑏𝑇𝐸 +𝑐𝑓𝑐𝑐𝑇2𝐸 (15) 2 ℎ4 = 𝑐𝑓𝑖𝑖 +𝑐𝑓𝑗𝑗𝑇𝐸 +𝑐𝑓𝑘𝑘𝑇𝐸 (16) 2 2 ∆ℎ4 ― 5𝑠 = 𝑐𝑓𝑙𝑙 +𝑐𝑓𝑚𝑚𝑇𝐸 +𝑐𝑓𝑛𝑛𝑇𝐸 +𝑐𝑓𝑜𝑜𝑇𝐶 +𝑐𝑓𝑝𝑝𝑇𝐶 (17) ℎ5 = ℎ4 ―∆ℎ4 ― 5𝑠𝜂𝑒 (18) 2 ℎ6 = 𝑐𝑓𝑖𝑖 +𝑐𝑓𝑗𝑗𝑇𝐶 +𝑐𝑓𝑘𝑘𝑇𝐶 (19) 𝑇2 = 𝑐𝑓𝑞𝑞 +𝑐𝑓𝑟𝑟𝑇𝐸 +𝑐𝑓𝑠𝑠ℎ2 (20) 𝑇5 = 𝑐𝑓𝑡𝑡 +𝑐𝑓𝑢𝑢𝑇𝐶 +𝑐𝑓𝑣𝑣ℎ5 (21) 3.2.2 Temperature feasibility constraints in ORC system Eq. (21) guarantees that the temperature of streams orcj is higher than or equal to the condensing temperature (Tc). Eq. (22) guarantees that the temperature of process cold streams orcj is less than or equal to the evaporation temperature (Te). Eq. (23) indicates that the evaporation temperature (Te) is higher than the condensing temperature (Tc). 𝑡𝑜𝑟𝑐𝑗,𝑜𝑟𝑐𝑘 ≥ 𝑇𝑐 ∀𝑜𝑟𝑐𝑗 ∈ 𝑂𝑅𝐶𝐽,orck ∈ 𝑂𝑅𝐶𝐾 (21) 𝑡𝑖𝑝𝑖,𝑜𝑟𝑐𝑗,𝑜𝑟𝑐𝑘 ≤ 𝑇𝑒 ∀𝑝𝑖 ∈ 𝑃𝐼,∀𝑜𝑟𝑐𝑗 ∈ 𝑂𝑅𝐶𝐽, orck ∈ 𝑂𝑅𝐶𝐾 (22) 𝑇𝑒 > 𝑇𝑐 (23) 3.4 Connection of HENs, SRC, and ORC as well as the border temperature setting for HENs As demonstrated in Fig. 2, the superheating steams extracted from turbine are first de-superheated to saturated steams and then delivered to the HENs. After cooled by the cold stream, the saturated steam become condensate water and returns to the SRC and enters the deaerator. Eqs. (24)–(27) express the mass balance and energy balance for medium pressure (MP) and intermediate pressure (IP) extractions, where Mhui is the mass flow rate for hot stream, and MTMP,ext and MTIP,ext are the MP and IP steam extraction flow rates, respectively. MWMP and MWIP are the mass flow rates of water for cooling superheated MP and IP steam, respectively. HT1,out, HT2,out, and HWDEA are the steam enthalpies of subsection 1 outlet, subsection 2 outlet, and the enthalpy of BFW leaving the deaerator, respectively. Eqs. (28) and (29) indicate the mass and energy balances of deaerator, respectively, where MB is the boiler steam generation flow rate, HCONDSz=CARD(z),out is the enthalpy of turbine condensing water, thui is the temperature of hot stream hui, and HBGEN is the enthalpy of steam generated in the boiler. 𝑀ℎ𝑢𝑖 = 1 = 𝑀𝑇𝑀𝑃,𝑒𝑥𝑡 + 𝑀𝑊𝑀𝑃 (24) 𝑀ℎ𝑢𝑖 = 1𝐻𝑆𝑎𝑡𝑀𝑃 = 𝑀𝑇𝑀𝑃,𝑒𝑥𝑡𝐻𝑇1,𝑜𝑢𝑡 + 𝑀𝑊𝑀𝑃𝐻𝑊𝐷𝐸𝐴 (25) 𝑀ℎ𝑢𝑖 = 2 = 𝑀𝑇𝐼𝑃,𝑒𝑥𝑡 + 𝑀𝑊𝐼𝑃 𝑀ℎ𝑢𝑖 = 2𝐻𝑆𝑎𝑡𝐼𝑃 = 𝑀𝑇𝐼𝑃,𝑒𝑥𝑡𝐻𝑇2,𝑜𝑢𝑡 + 𝑀𝑊𝐼𝑃𝐻𝑊𝐷𝐸𝐴 𝑀𝑇𝐿𝑃,𝑒𝑥𝑡 + 𝑀𝑇𝑧 = 𝑂𝑅𝐷(𝑧),𝑜𝑢𝑡 + 𝑀ℎ𝑢𝑖 = 1 +𝑀ℎ𝑢𝑖 = 2 = 𝑀𝐵 + 𝑀𝑊𝑀𝑃 + 𝑀𝑊𝐼𝑃 𝑀𝑇𝐿𝑃,𝑒𝑥𝑡𝐻𝑇1,𝑜𝑢𝑡 + 𝑀𝑇𝑧 = 𝐶𝐴𝑅𝐷(𝑧),𝑜𝑢𝑡𝐻𝐶𝑂𝑁𝐷𝑆𝑧 = 𝐶𝐴𝑅𝐷(𝑧),𝑜𝑢𝑡 + 4.2𝑀ℎ𝑢𝑖 = 1𝑡ℎ𝑢𝑖 = 3,ℎ𝑢𝑘 = 𝐶𝐴𝑅𝐷(ℎ𝑢𝑘) + 1 + 4.2𝑀ℎ𝑢𝑖 = 2 𝑡ℎ𝑢𝑖 = 4,ℎ𝑢𝑘 = 𝐶𝐴𝑅𝐷(ℎ𝑢𝑘) + 1 ≥ (𝑀𝐵 + 𝑀𝑊𝑀𝑃 + 𝑀𝑊𝐼𝑃) ∗ 𝐻𝐵𝐺𝑒𝑛 (29)

(26) (27) (28)

Eq. (30) shows the modelling rules for the starting inlet temperature, outlet temperature, and interlink temperature for the streams in PPHEN and PHUHEN, where thui,huk, and Thui,in represent the temperature of stream hui at stage huk and inlet 7

Journal Pre-proof

temperature of stream hui, respectively, tpj,huk is the temperature of stream pj at stage huk. 𝑡𝑝𝑖,𝑝𝑘 = 1 = 𝑇𝑝𝑖,𝑖𝑛 ∀𝑝𝑖 ∈ 𝑃𝐼, 𝑝𝑘 ∈ 𝑃𝐾 𝑡𝑝𝑗,𝑝𝑘 = 𝐶𝐴𝑅𝐷(𝑃𝐾) + 1 = 𝑇𝑝𝑗,𝑖𝑛 ∀𝑝𝑗 ∈ 𝑃𝐽, 𝑝𝑘 ∈ 𝑃𝐾 𝑡ℎ𝑢𝑖,ℎ𝑢𝑘 = 𝑇ℎ𝑢𝑖,𝑖𝑛 ∀ℎ𝑢𝑖 ∈ 𝐻𝑈𝐼, 𝑂𝑅𝐷(ℎ𝑢𝑖) ≤ 𝐶𝐴𝑅𝐷(ℎ𝑢𝑖)/2, ℎ𝑢𝑘 ∈ 𝐻𝑈𝐾 𝑡ℎ𝑢𝑖,ℎ𝑢𝑘 = 1 = 𝑇ℎ𝑢𝑖,𝑖𝑛 ∀ℎ𝑢𝑖 ∈ 𝐻𝑈𝐼, 𝑂𝑅𝐷(ℎ𝑢𝑖) > 𝐶𝐴𝑅𝐷(ℎ𝑢𝑖)/2, ℎ𝑢𝑘 ∈ 𝐻𝑈𝐾 𝑡𝑝𝑗,ℎ𝑢𝑘 = 1 = 𝑡𝑝𝑗,𝑝𝑘 = 𝐶𝐴𝑅𝐷(𝑃𝐾) + 1 ∀ℎ𝑢𝑖 ∈ 𝐻𝑈𝐼, 𝑂𝑅𝐷(ℎ𝑢𝑖) > 𝐶𝐴𝑅𝐷(ℎ𝑢𝑖)/2, ℎ𝑢𝑘 ∈ 𝐻𝑈𝐾

(30) (31) (32) (33)

(34) Eq. (35) indicates that the inlet temperature of the first stream orcj (torcj=1, orck=CARD (ORCK)+1) equals to the outlet temperature of working fluid from the pump (T2) in ORC. Eq. (36) denotes that the temperature of the second stream orcj (tipi,orcj=2,orck) and the evaporating temperature in the ORC system are equal. Eq. (37) expresses that the outlet temperature of the first stream orcj (tipi,orcj=1,orck=1) and the temperature of the evaporating temperature in the ORC system are equal. Notably, all the inlet/outlet temperatures of streams orcj are design variables. 𝑡𝑜𝑟𝑐𝑗 = 1,𝑜𝑟𝑐𝑘 = 𝐶𝐴𝑅𝐷(𝑂𝑅𝐶𝐾) + 1 = 𝑇2 ∀𝑜𝑟𝑐𝑗 ∈ 𝑂𝑅𝐶𝐽,orck ∈ 𝑂𝑅𝐶𝐾 (35) 𝑡𝑖𝑝𝑖,𝑜𝑟𝑐𝑗 = 2,𝑜𝑟𝑐𝑘 = 𝑇𝑒 ∀𝑝𝑖 ∈ 𝑃𝐼,∀𝑜𝑟𝑐𝑗 ∈ 𝑂𝑅𝐶𝐽, orck ∈ 𝑂𝑅𝐶𝐾 (36) 𝑡𝑖𝑝𝑖,𝑜𝑟𝑐𝑗 = 1,𝑜𝑟𝑐𝑘 = 1 = 𝑇𝑒 ∀𝑝𝑖 ∈ 𝑃𝐼,∀𝑜𝑟𝑐𝑗 ∈ 𝑂𝑅𝐶𝐽, orck ∈ 𝑂𝑅𝐶𝐾 (37) 3.5 Objective functions In the present study, the aim of the proposed problem is to design an optimal integration system by minimizing the TAC. The TAC comprises the investment costs of all components and the operating cost derive from the fuel and water consumptions minus the profit achieved from power export [see Eq. (38)]. The investment cost is composed of the purchase cost of heat exchangers in all the HENs [see Eq. (39)], components in the SRC-based utility plant [see Eq. (40)] [30], components in the ORC [see Eq. (41)] [10], and cooling tower [see Eq. (42)] [31]. The operating cost consists of the boiler fuel cost [see Eq. (43)], pump power consumption cost in the ORC system [see Eq. (44)], cooling utility cost (including pump power consumption cost, draft fan power consumption cost, make-up water cost, and fixed cost) [see Eq. (45)]; and environmental cost [see Eq. (47)]. Eq. (46) shows the CO2 emitted from a gas-fired boiler, where CN refers to the carbon content of fuel, and Ccarbontax represents the carbon emission charge [32]. Eq. (48) presents the power export profit from the SRC and ORC. min 𝑇𝐴𝐶 = 𝐼𝑁𝑉𝐻𝐸 + 𝐼𝑁𝑉𝑈𝑆 + 𝐼𝑁𝑉𝑂𝑅𝐶 + 𝐼𝑁𝑉𝐶𝑇 + 𝑂𝑃𝐹𝑈𝐸𝐿 + 𝑂𝑃𝑂𝑅𝐶 + 𝑂𝑃𝐶𝑇 + 𝑇𝐴𝐶𝑐𝑎𝑟𝑏𝑜𝑛𝑡𝑎𝑥 ―𝑊𝑆𝐸𝐿𝐿 (38) 𝐼𝑁𝑉𝐻𝐸 =

[

∑𝑖 ∈ 𝑃𝐼 ∪ 𝐻𝑈𝐼∑𝑗 ∈ 𝑃𝐽 ∪ 𝑂𝑅𝐶𝐽∑𝑘 ∈ 𝑃𝐾 ∪ 𝐻𝑈𝐾 ∪ 𝑂𝑅𝐶𝐾 𝐶𝐹 ∗ 𝑧𝑖,𝑗,𝑘 + {𝑄𝑖,𝑗,𝑘/(1/ℎ𝑡𝑐𝑖 + 1/ℎ𝑡𝑐𝑗)/[𝑑𝑡𝑖𝑖,𝑗,𝑘𝑑𝑡𝑜𝑖,𝑗,𝑘 + 1(𝑑𝑡𝑖𝑖,𝑗,𝑘 + 𝑑𝑡𝑜𝑖,𝑗,𝑘 + 1)/2 + 𝛿]1/3}

[

+ ∑𝑝𝑖 ∈ 𝑃𝐼 𝐶𝐹 ∗ 𝑍𝐶𝑝𝑖 + {𝑄𝐶𝑝𝑖/(1/ℎ𝑡𝑐𝑝𝑖 + 1/ℎ𝑡𝑐𝐶𝑊)/[𝑑𝑡𝑐𝑢𝑖𝑝𝑖𝑑𝑡𝑐𝑢𝑜𝑝𝑖(𝑑𝑡𝑐𝑢𝑖𝑝𝑖 + 𝑑𝑡𝑐𝑢𝑜𝑝𝑖)/2 + 𝛿]1/3}

]

𝛽

[𝐶𝐹 + {𝑄𝐶𝑐𝑜𝑛𝑑𝑠/(1/ℎ𝑡𝑐𝑐𝑜𝑛𝑑𝑠 + 1/ℎ𝐶𝑊)/[(𝑇𝑐𝑜𝑛𝑑𝑠 ― 𝑇𝐶𝑊𝑖𝑛)(𝑇𝑐𝑜𝑛𝑑𝑠 ― 𝑇𝐶𝑊𝑜𝑢𝑡)(2𝑇𝑐𝑜𝑛𝑑𝑠 ― 𝑇𝐶𝑊𝑖𝑛 ― 𝑇𝐶𝑊𝑜𝑢𝑡)/2 + 𝛿]1/3}𝛽]

[𝐶𝐹 + {𝑄𝐶𝑜𝑟𝑐𝑗/(1/ℎ𝑜𝑟𝑐𝑐𝑜𝑛𝑑𝑠 + 1/ℎ𝑡𝑐𝐶𝑊)/[(𝑇5 ― 𝑇𝐶𝑊𝑖𝑛)((𝑇1 ― 𝑇𝐶𝑊𝑜𝑢𝑡)((𝑇5 ― 𝑇𝐶𝑊𝑖𝑛) + (𝑇1 ― 𝑇𝐶𝑊𝑜𝑢𝑡))/2 + 𝛿]1/3}𝛽] (39) 𝐼𝑁𝑉𝑈𝑆 = 𝐶𝐵𝐶𝑜𝑒𝑓𝑓𝑎 + 𝑀𝐵 ∗ 𝐶𝐵𝐶𝑜𝑒𝑓𝑓𝑏 + 𝐶𝑇𝐶𝑜𝑒𝑓𝑓𝑎 + 𝑊𝑇 ∗ 𝐶𝑇𝐶𝑜𝑒𝑓𝑓𝑏 𝐼𝑁𝑉𝑂𝑅𝐶 = 𝐾𝐹𝐶𝑉𝑒𝑥𝑝𝑎𝑛𝑑𝑒𝑟(𝑊𝑇𝑜𝑟𝑐𝑗)𝛾 + 𝐾𝐹𝐶𝑉𝑝𝑢𝑚𝑝(𝑊𝑇𝑝𝑢𝑚𝑝)𝛾 𝐼𝑁𝑉𝐶𝑇 = (3714 × 𝑀𝑐𝑤0.7 +3516 × 𝑃𝑊𝑝𝑢𝑚𝑝0.65)(1 + 0.04 + 0.05)/𝐿 𝑂𝑃𝐹𝑈𝐸𝐿 = 𝐹𝐵 ∗ 𝑐𝑓𝑢𝑒𝑙𝐴𝐻𝑜𝑢𝑟 𝑂𝑃𝑂𝑅𝐶 = 𝑊𝑇𝑝𝑢𝑚𝑝 ∗ 𝑐𝑝𝑜𝑤𝑒𝑟𝐴𝐻𝑜𝑢𝑟 𝑂𝑃𝐶𝑇 = 𝑃𝑊𝑝𝑢𝑚𝑝 ∗ 𝑐𝑝𝑜𝑤𝑒𝑟𝐴𝐻𝑜𝑢𝑟 + 𝑃𝑊𝑑𝑟𝑎𝑓𝑡 𝑓𝑎𝑛𝑠 ∗ 𝑐𝑝𝑜𝑤𝑒𝑟𝐴𝐻𝑜𝑢𝑟 + 𝑀𝑚𝑎𝑘𝑒 ― 𝑢𝑝𝑐𝑤𝑎𝑡𝑒𝑟𝐴𝐻𝑜𝑢𝑟 + (3714 × 𝑀𝑐𝑤0.7 +3516 × 𝑃𝑊𝑝𝑢𝑚𝑝0.65) × 0.01 𝑀𝑐𝑜2 = 3.667 ∗ 𝐹𝐵 ∗ 𝐴𝐻𝑜𝑢𝑟 ∗ 𝐶𝑁

(40) (41) (42) (43) (44) (45) (46) (47)

𝑇𝐴𝐶𝑐𝑎𝑟𝑏𝑜𝑛𝑡𝑎𝑥 = 𝑀𝑐𝑜2 ∗ 𝐶𝑐𝑎𝑟𝑏𝑜𝑛𝑡𝑎𝑥 8

]

𝛽

Journal Pre-proof

(48)

𝑊𝑆𝐸𝐿𝐿 = 𝑊𝑇 ∗ 𝑐𝑝𝑜𝑤𝑒𝑟𝐴𝐻𝑜𝑢𝑟 +𝑊𝑇𝑜𝑟𝑐𝑗 ∗ 𝑐𝑝𝑜𝑤𝑒𝑟𝐴𝐻𝑜𝑢𝑟

4. Model characteristics and solution strategy 4.1 Characteristics of the formulated model The model of the proposed problem consists of the constraint formulated by Eqs. (1)–(37) and the objective functions formulated by Eqs. (38)–(48). The optimization variables include the following: existence of all candidate heat exchanger, heat load for each heat exchanger, flow rate and enthalpy of extraction steam, operating parameters in ORC, and the power generated from the turbine and ORC. Among the optimization variables, the existence or absence of candidate heat exchanger is 0/1 variable. Eqs. (1)–(5), (7)–(20), (24)–(29), (39)–(45) and (48) are all non-linear equations. At the same time, the undescribed models (e.g., HEN model, SRC model and cooling tower model) in this paper also have a large number of non-linear equations. Thus, the formulated optimized model is a MINLP model. 4.2 Solution procedure and strategy The formulated model for the synthesis and optimization problem contains continuous variables (e.g., heat exchange for each heat exchanger, flow rate, enthalpy of extraction steam, and operating parameters in ORC), binary variables (e.g., existence of all candidate heat exchanger), and integer variables (e.g., heat exchanger number in the HEN). Several discrete variables exist in the model of the proposed problem. Eqs. (1)–(5), (7)–(20), (24)–(29), (39)–(45) and (48) are all non-linear equations. And, there are a large number of non-linear equations which are undescribed in this paper. The formulated MINLP optimization model is non-convex. To ensure a feasible solution, an extension of the previously developed solution strategy [5] is used and demonstrated in Fig. 4. A relaxation model of the original MINLP model is first solved using multiple solvers in sequence to achieve an initial solution. Then, DICOPT [33], an effective local MINLP solver, is applied to achieve a local solution for the original MINLP model. Finally, global solver ANTIGONE [34] is used to obtain a global solution based on the local solution achieved from using DICOPT solver. The MINLP models were coded in the software GAMS [35] on a 3.0 GHz Intel(R) Core(TM) 2 PC.

5. Case study 5.1 Case description The cases in Luo et al. [5] are studied in this study to demonstrate the superiority of the developed methodology. In a previous work, the steam condensate and boiler feedwater were simultaneously integrated into the HENs. However, a remarkable amount of surplus heat remains in the hot process streams. Therefore, an integration of hot SRC, HENs, ORC with various working fluids, and cold utility plant is proposed. In order to test the synthesis and optimization method of the entire system, two scenarios are studied. Four solutions (i.e., IHU, IHUO, OIHU, and OIHUO) are achieved (see Table 1). Solutions IHU and OIHU have been studied in Luo et al. [5]. Then, the influences of carbon tax and fuel price on the optimization results are conducted. In this case, three working fluids are investigated and compared (i.e., R245fa, n-butane, and R123). These working fluids possess the following properties: (1) dryness; (2) high critical temperature; (3) relatively low boiling point in the atmosphere [15]. In addition, these working fluids exert desirable effects on the temperature range of surplus heat from HENs. Thus, these working fluids are widely used in studies focusing on the integration of HEN with ORC. This paper aims not to study the properties of working fluids but to present a simultaneous optimization of a novel integration process energy system. Therefore, these three working fluids (i.e., R245fa, n-butane, and R123) are considered in this paper. The stream parameters of Case 1 and Case 2 can be found in Luo et al. [5]. Case 1 is a small case with two hot streams and two cold streams. Case 2 is a relatively large case with four hot streams and four cold streams. The hot utilities of both cases are provided by SRC with two steam levels and the inlet and outlet temperatures of cold utility is 20 and 28 oC. To compare with a previous method, a case in our previous study is restudied [5]. The basic parameters of SRC, process streams, cold utility, and the coefficients shown in Eqs. (B6) and (B7) of for steam turbine model can be found in Luo et al. [5]. 9

Journal Pre-proof

Scenario Scenario 1 Scenario 2

IHUO

Table 1 Description of scenarios Solution description Latent heat of steam is used as hot utility. BFW is heated by the steam extracted from steam turbine. ORC is integrated into the IHU to recover surplus heat from the HEN.

OIHU

Condensate heat and BFW are integrated into the system.

OIHUO

The proposed integration system in the present study.

Solution IHU

5.2 Synthesis, integration, and optimization of Case 1 5.2.1. Syntheses of HEN, SRC, and ORC Two solutions are demonstrated. The first solution denotes the IHU from a published article [5]. The second solution denotes the IHUO. The two solutions aim to minimize the TAC and carbon tax is excluded in the economic cost objective function. The numbers of variables and equations of the proposed IHUO model are 426 and 729, respectively. The solution time is 22.88 seconds. The design configuration of IHU presented in Fig. 5 is composed of seven units (three heat exchangers in PHUHEN, two heat exchangers in PPHEN and two heat exchangers in PCUHEN). The process-to-process heat recovery is 35729 kW, and the corresponding cold utility is 28171 kW. For the SRC, the produced electricity is 21054kW. The TAC is 12151.8 k$. Fig. 6 depicts the structure of IHUO using n-butane as working fluid. Two heat exchangers are included in the PPHEN. The recovered heat in process heat is 35762 kW. And pi1 and pi2 do not require cold utility. Four heat exchangers are equipped between the hot streams and ORC working fluid. The quantity of heat exchangers of the integration system is two more than that of IHU. ORC produces 3218 kW of power. The TAC is 10579 k$, which is 12.94% lower than that of IHU. Table 2 summarizes the optimization results for Case 1. As shown in Table 2, the TAC of IHUO reduces remarkably compared with that of IHU. Table 3 summarizes the comparative statistics of various working fluids in ORC. ORCs with different working fluids feature different operating parameters, resulting in different thermal efficiencies. The ORC with nbutane as working fluid demonstrates the highest heat removed from process hot streams. The ORC with n-butane as working fluid features the highest pump power consumption and consequently, the highest operating cost as shown in Table 2. However, the TACs of the three solutions with ORC integration are inconsistent with the performances of ORCs. IHUOn-butane holds the lowest TAC, followed by IHUO-R245fa and IHUO-R123. These solutions are achieved from the tradeoff among the four sub-HENs. The results depicted in Fig. 6 show that the surplus heat from the EHN is absorbed by ORC streams. Then, ORC can produce power to yield profit and improve the entire system performance. The TAC of IHUO can be reduced compared with the IHU. Therefore, the economy of IHU can be effectively improved by integrating HEN with ORC.

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21852 kW

hui1

hui2

263.9 oC

pi1 195 oC

11546 kW 198.3 oC 4373 kW

pi2 155 oC

24102 kW

11627 kW

128.1 oC

13698 kW

114.9 oC

14473 kW C

240 oC

173.2 oC

125 oC pj1

160 oC

146.3 oC

110 oC pj2

8.1 kg/s 198.3 oC

7.3 kg/s

13.3 kg/s 263.9 oC 9.5 MPa

10.7 kg/s

TAC (k$) 12151.8

90 oC

65 oC

3056 kJ/kg 3309 kJ/kg 32.8 kg/s 5.0 MPa

1.5 MPa

Turbine Fuel

C

Boiler

0.008 MPa 2341 kJ/kg

0 kg/s 2945 kJ/kg

C

Pump

673 kJ/kg

Cooling Makeup water tower

21054 kW

Deaerator

Fig. 5 Design configuration of general integration of HEN and SRC 21852 kW

hui1

11531 kW

hui2 240.0 oC

263.9 oC

4355kW 198.3 oC

pi2 155 oC

196.3 oC

160.0 oC 8.2 kg/s 198.3 oC

7.2 kg/s

3074.4 kJ/kg

13.3 kg/s 263.9 oC

10.7 kg/s

3315.4 kJ/kg

9.5 MPa 22.4 kg/s

Fuel 2.0kg/s

5.0 MPa

11645 kW

1884 kW 95.2 oC

146.4 oC

110.0 oC pj2

93.2 oC

orcj2

8984.5 kW 0.008 MPa 2403.5 kJ/kg 4.5 kg/s C

Deaerator

TAC (k$) 10579.0

32.6 oC orcj1

93.2℃

1.5 MPa

90.0 oC

5688 kW o 8768 kw 65.0 oC 95.2 C

114.8 oC 125.0 oC pj1

0.8 MPa 0.0 kg/s 2993.9 kJ/kg Pump

11799 kW

173.2 oC

Turbine 2341kJ/kg

Boiler

672.5 kJ/kg

24117 kW 128.0 oC

pi1 195 oC

3218 kW Expander 2341kJ/kg

C

Cooling Makeup water tower

32.0 oC Pump

Fig. 6 Design configuration of general integration of HEN, SRC, and ORC using n-butane Table 2 Comparative economic statistics of various working fluids IHU IHUO-R245fa IHUO-n-butane IHUO-R123 Investment cost of heat exchangers (k$) 1529.9 1383.1 1302.2 1372.6 Investment cost of utility plant components (k$) 2860.0 2039.7 2053.5 2041.4 Investment cost of cold utility components (k$) 40.8 89.7 90.3 89.8 Investment cost of ORC component (k$) 450.6 456.5 415.5 Operating cost for cold utility (k$) 980.3 682.5 689.5 684.9 Operating cost for fuel (k$) 19541.6 13208.5 13316.6 13221.7 ORC operating cost (k$) 62.6 89.4 34.5 Profit from selling electricity (k$) 12800.8 7306.9 7419.0 7241.6 Total annual cost (k$) 12151.8 10609.8 10579.0 10618.9

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Table 3 Comparative statistics of various working fluids in ORC Items IHUO-R245fa IHUO-n-butane Thermal efficiency (%) 10.9 10.9 Heat absorbed from process hot stream (kW) 27822.8 28138.3 Heat removed in the ORC condenser (kW) 24788.5 25067.5 Turbine power (kW) 3137.3 3217.9 Pump power (kW) 103.0 147.1 Evaporation temperature (°C) 93.2 93.2 Condensing temperature (°C) 32.0 32.0

IHUO-R123 10.6 27861.6 24901.3 3017.0 56.8 88.0 32.0

5.2.2. Integration and simultaneous optimization of HEN, SRC, and ORC In this scenario, two solutions are compared. The first solution indicates the OIHU from the published article [5], and the second solution indicates the OIHUO proposed in this paper. The two solutions aim to minimize the TAC and carbon tax is excluded in the economic cost objective functions. Fig. 7 presents the optimization results of OIHU achieved from Luo et al. [5]. There are two heat exchangers in PPHEN, five heat exchangers in PHUHEN, one heat exchanger recovering heat from process stream pi1 in PBFWHEN and two heat exchangers in PCUHEN. The process-to-process heat recovery is 35654 kW. The external cooling requirement is 27142 kW. For the utility plant, the power output is 7864 kW and the recovered heat from pi1 for BFW preheating is 1103 kW. The solution yields the TAC of 10951.3 k$. Fig. 8 shows the optimum results of OIHUO with ORC using n-butane as working fluid. Three heat exchangers exist in PPHEN. The process-to-process heat recovery is 36008 kW and the external cold utility for pi1 and pi2 is zero. Four heat exchangers exist between the hot streams and ORC working fluid. The surplus heat recovered by ORC measures 27892 kW, and the quantity of heat exchangers of the integration system is two more than that in OIHU. ORC produces 3183 kW of power, and the TAC is 9502.0 k$, which is 13.23% lower than that of OIHU. Table 5 summarizes the optimization results for the case. As shown in Table 4, the TAC of OIHUO in different working fluids remarkably reduces compared with that of OIHU. Table 5 summarizes the comparative statistics of various working fluids in ORC. As shown in Table 4, the ORC using different working fluids features different operating parameters. The ORC using R245fa and n-butane as working fluid holds the same and highest thermal efficiency and the highest heat recovered from hot process streams. Consequently, the ORC using n-butane as working fluid features the highest power generation. The ORC using R123 as working fluid holds the lowest pump power consumption and consequently, the lowest operating cost. Among the three solutions using different working fluids, OIHUO- n-butane yields the lowest TAC, followed by OIHUO-R123 and OIHUO-R245fa. The comparison between OIHUO and OIHU shows that TAC can also be reduced. OIHU exhibits the optimal results achieved from Luo et al. [5]. Therefore, more potential or optimization freedom for energy and cost reduction can be achieved by using the design configuration of OIHUO proposed in this paper. Table 4 Comparative economic statistics of various working fluids Items OIHU OIHUO-R245fa OIHUO-n-butane Investment cost of heat exchangers (k$) 1472.6 1497.0 1358.6 Investment cost of utility plant components (k$) 1858.3 1833.8 1846.7 Investment cost of cold utility components (k$) 28.6 82.9 83.5 Investment cost of ORC component (k$) 447.0 453.7 Operating cost for cold utility (k$) 586.1 654.7 662.0 Operating cost for fuel (k$) 11787.1 11594.7 11696.4 ORC operating cost (k$) 61.7 88.2 Profit from selling electricity (k$) 4781.4 6606.0 6687.2 Total annual cost (k$) 10951.3 9565.7 9502.0

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OIHUO-R123 1339.0 1857.5 84.1 441.3 669.2 11780.7 34.9 6652.5 9554.3

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Table 5 Comparative statistics of various working fluids Items ORC-R245fa ORC-n-butane Thermal efficiency (%) 10.9 10.9 Heat absorbed from process hot stream (kW) 27547.9 27891.7 Heat removed in the ORC condenser (kW) 24550.4 24853.9 Turbine power (kW) 3098.9 3182.9 Pump power (kW) 101.4 145.1 Evaporation temperature (°C) 93.0 93.0 Condensing temperature (°C) 32.0 32.0 19166 kW

hui1

263.9 oC

3073 kW

hui3

24069 kW

pi1195 oC

hui2

11585 kW

o pi2155 C

198.3 oC

3114 kW 156.2 oC 1301 kW 195.5 C 173.1 oC

125 oC pj1

160 oC

146.2 oC

110 oC pj2

o

198.3 oC

7.4 kg/s 11.7 kg/s

6.5 kg/s

3079 kJ/kg

263.9 oC 9.4 kg/s

3318 kJ/kg

112.1 oC

65 oC

bfwj

1.5 MPa

19.8 kg/s

9.5 MPa

14515 kW C

115.1 oC

240 oC

5.0 MPa Fuel

TAC (k$) 10951.3

1103 kW 125.1 oC 12627 kW 90 oC C

128.1 oC

201.3 oC 11191 kW

hui4

ORC-R123 10.6 28138.3 25148.7 3047.0 57.4 88.0 32.0

Turbine

7864 kW

Boiler 0 kg/s 3005 kJ/kg

673 kJ/kg

Pump

Cooling tower

Makeup water

0.008 MPa 2416 kJ/kg C

Deaerator

Fig. 7 Configuration of simultaneous and integration optimization of HEN and SRC 19739 kW

hui1

hui3 2485 kW

263.9 oC 214.8 oC

9271 kW

95.0 oC

1815 kW

90.0 oC TAC (k$) 9502.0

3144 kW o 152.6 C

11245 kW 198.3 oC

hui2

pi1195 oC 24031 kW128.2 oC 2683 kW 120.8 oC

9294 kW o 123.0 C

pi2155 oC

8094 kW

8712 kW 95.0 oC

65.0 oC

879 kW o 162.1 C

hui4 240.0 oC

195.6 oC

160.0 oC

157.3 oC o

173.1 oC

125.0 oC

o 125 oC pj1 93.0 C

147.4 oC

118.4 oC

110 oC pj2 93.0 oC

5.8 kg/s

198.3 C 5.1 kg/s

3018.4 kJ/kg

12.0 kg/s

263.9 oC 9.7 kg/s

3318.3 kJ/kg

9.5 MPa

19.6 kg/s

1.5 MPa

orcj1

orcj2

Expander 3183kW

5.0 MPa 7815.9kW Turbine

Fuel 2.0 kg/s

Boiler

672.5 kJ/kg

0.8 MPa 1.0 kg/s 2996.0 kJ/kg Pump

0.008 MPa 2410.6 kJ/kg 3.9 kg/s

C

Deaerator

C

Cooling tower

32.0 oC

Pump

Makeup water

32.6 oC

Fig. 8 Configuration of simultaneous integration and optimization of HEN, SRC, and ORC using R123 as working fluid 13

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5.3 Synthesis, integration, and simultaneous optimization of HEN, SRC, and ORC for Case 2 As shown in the results of Case, the superiority and effectiveness of the proposed integration system and technology has been well demonstrated in a small-scale Case 1. In this section, Case 2 is studied to apply the proposed method to relatively large-scale problem. For simplification, two scenarios, IHU and OIHUO, are demonstrated and compared. The two solutions aim to minimize the TAC and carbon tax is excluded in the economic cost objective functions. The numbers of variables and equations of the proposed IHUO model are 739 and 1216, respectively. The solution time is 46.92 seconds. Fig. 9 presents the optimization and results of IHU for Case 2. There are seven heat exchangers in PPHEN, five heat exchangers in PHUHEN, four heat exchangers in PCUHEN. The process-to-process heat recovery is 85163 kW. The cold utility requirement is 25537 kW. For the utility plant, the power output is 15088 kW. The solution yields the TAC of 16763.0 k$. Fig. 10 shows the optimum results of OIHUO using R245fa as working fluid in the ORC. Seven heat exchangers exist in PPHEN. The process-to-process heat recovery is 83094 kW. Three heat exchangers exist between the hot streams and ORC working fluid. The surplus heat recovered by ORC measures 16593 kW, and the quantity of heat exchangers in the integration system is three more than that in IHU. ORC produces 1433 kW of power, and the TAC is 14919.0 k$, which is 11.1% lower than that of IHU. Table 6 summarizes the optimization results for the case. As shown in Table 6, the TAC of OIHUO in different working fluids remarkably reduces compared with that of IHU. Table 7 summarizes the comparative statistics of various working fluids in ORC. As shown in Table 8, the ORC using different working fluids features different operating parameters. The ORC using R123 as working fluid holds the highest thermal efficiency and the highest heat recovered from hot process streams. Consequently, the ORC using R123 as working fluid features the highest power generation. Among the three solutions using different working fluids, OIHUO-R245fa yields the lowest TAC, followed by OIHUO-R123 and OIHUO-n-butane. These solutions are achieved from the trade-off among the four sub-HENs, SRC, and cold utility plant. The comparison between OIHUO and IHU shows that TAC can be remarkably reduced by integrating HEN with ORC for a large-scale problem. Noting that the saving ratio of TAC of Case 2 is lower than that of Case 1 because the available surplus heat and the temperature level of the hot stream are lower in Case 2. The result for Case 2 show that the proposed model and solution strategy is also effective in solving large-scale complex problem. Table 6 Comparative economic statistics of various working fluids Items IHU IHUO-R245fa IHUO-n-butane Investment cost of heat exchangers (k$) 2696.3 2444.9 2086.3 Investment cost of utility plant components (k$) 2831.8 2382.4 2576.4 Investment cost of cold utility components (k$) 231.4 162.0 180.6 Investment cost of ORC component (k$) 270.6 279.0 Operating cost for cold utility (k$) 783.7 748.6 856.9 Operating cost for fuel (k$) 19393.3 15902.3 17417.8 ORC operating cost (k$) 21.4 33.5 Profit from selling electricity (k$) 9173.6 7013.4 7964.3 Total annual cost (k$) 16762.9 14918.7 15466.1 Table 7 Comparative statistics of various working fluids in ORC Items IHUO-R245fa IHUO-n-butane IHUO-R123 Thermal efficiency (%) 8.4 8.6 8.8 Heat added (kW) 16593.0 17098.9 23486.8 Heat removed (kW) 15195.1 15634.6 21409.0 Turbine power (kW) 1433.2 1519.3 2044.8 Pump power (kW) 35.2 55.0 33.0 Evaporation temperature (°C) 74.4 75.3 75.7 Condensing temperature (°C) 32.0 32.0 32.0

14

IHUO-R123 1914.7 2743.9 165.2 355.6 870.2 18713.2 20.0 9713.4 15069.3

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3221 kW 4943 kW 104.2 oC

263.9 oC pi1195.0 oC 29964 kW

16604 kW

hui1

7993 kW

89.2 oC

11948 kW 2933 kW

o 263.9 oCpi2 150.0 C

hui3

102.0 oC

15379 kW 138.7 oC

o 198.3 oC pi4 190.0 C

hui4 210.0 oC

205.0 oC

196.3 oC

90.0 oC pj2

136.3 oC

96.5 oC

80.0 oC pj3

169.6 oC

128.0 oC

100.0 oC pj4

18.4 kg/s

198.3 C 16.3 kg/s

3055.6 kJ/kg

12.1 kg/s

263.9 oC 9.7 kg/s

3308.8 kJ/kg

9.5 MPa

80.0 oC

C

95.0 oC

C

124.4 oC

o

4863 kW

100.0 oC pj1

170.0 oC

136.3 oC

70.0 oC

C

10360 kW 2761 kW 104.2 oC

173.1 oC

170.0 oC

96.8 oC

TAC (k$) 16763.0

9920 kW

102.0 oC

9637 kw

13109 kW 12763 kW 198.3 oC pi3 130.0 oC 9890 kW

hui2

65.0 oC

C

32.6 kg/s

1.5 MPa

Cooling Makeup water tower

5.0 MPa 15088.1 kW Turbine

Fuel 3.0 kg/s

0.008 MPa 2369.2 kJ/kg 6.5 kg/s

Boiler 0.8 MPa 0.0 kg/s 2962.8 kJ/kg

672.5 kJ/kg

C

Deaerator

Pump

Fig. 9 Configuration of simultaneous and integration optimization of HEN and SRC for Case 1 24314 kW

19679 kW 6801 kW 5925 kW

hui1

263.9 oC pi1195.0 oC

hui2

11784 kW pi2 150.0 oC 122.0 oC 12107 kW 198.3 oC pi3 130.0 oC

hui4

1361 kW o pi4 o 146.2 C 190.0 C

hui3

o

210.0 C 170.0 C

106.0 oC

12992 kW 5686kW 108.1 oC 130.0 oC

25546 kW o 104.8 C

144.0 C

180.0 oC

19.8 kg/s

263.9 oC 15.9 kg/s

9.5 MPa

C

6122 kW

89.7 C

C

2613 kW o 4500 kW 80.0 oC 95.5 C

104.5 oC o

o

97.8 C

97.8 C

65.0 oC

TAC (k$) 14919.0

o

70.0 C 80.0 oC

831 kW

C

95.0 oC

90.0 oC pj2

97.6 C

151.8 oC 198.3 oC 5.5 kg/s

4060 kW

77.3 oC o

89.7 C

2123kw

o

180.0 oC

6.2 kg/s

77.3 oC

100.0 oC pj1

o

170.0 C

9480 kW

o

7387kW

168.0 C

o

205.0 oC

106.0 oC

o

194.9 oC

o

5046 kW

99.0 oC

80.0 oC pj3

74.4 oC

120.0 oC

100.0 oC pj4 74.4 oC

orcj1 orcj2

3073.9 kJ/kg 3312.0 kJ/kg 26.7 kg/s

1.5 MPa

Expander 1433 kW

5.0 MPa 10102.1 kW Turbine

Fuel 2.4 kg/s

Boiler 0.0kg/s

672.5 kJ/kg

Pump

0.8 MPa 2986.0 kJ/kg

0.008 MPa 2391.4 kJ/kg 5.3 kg/s

C

Deaerator

C

Cooling tower

32.0 oC

Pump

32.2 oC

Fig. 10 Configuration of simultaneous and integration optimization of HEN and SRC for Case 2

15

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5.4. Influence of carbon tax on the synthesis and optimization results In the proposed design configuration, ORC is used to recover surplus heat for energy conservation and cost reduction. Another feature of ORC is its environmental friendliness. Therefore, the environmental performance of the proposed system is considered. In this section, carbon tax is added to the objective function. To investigate the influence of carbon tax on the proposed system, three different kinds of carbon emission charge standards [36] in China are considered. The first carbon emission charge standard based on China’s standard was established in 2003 [37]. The second carbon emission charge standard is derived from the cost of reducing pollution based on mature technologies [38]. The third carbon emission charge standard is based on the cost of total pollution damage in Shandong Province and is carried out through ExternE project [39, 40]. The three emission charge costs of CO2 are 0, 3.3, and 50 $/t. To demonstrate the influence of carbon tax on the synthesis and optimization results, Case 1 is re-studied by incorporating different carbon tax in the objective function. Fig. 11 shows the influence of carbon tax on the investment cost of HEN, surplus heat recovered by ORC, fuel cost, carbon tax, and TAC. For n-butane and R123, the investment cost of HEN increases with the increase of carbon tax to increase the heat integration in the PHEN and thus reduce the fuel consumption. As the fuel cost and environment cost are directly related to the fuel consumption, the fuel cost decreases and the environmental cost increment rate decreases. The surplus heat recovered by ORC decreases with the increase in carbon tax because the available surplus heat decreases with the intensification of process-process integration. For R245fa, the investment cost of HEN first decreases then increases with the increase of carbon tax. Unsurprisingly, the fuel cost first increases and then decreases with the increase of carbon tax. Also, the surplus heat recovered by ORC first increases and then decreases with the carbon tax. Correspondingly, the fuel cost of 3.3 and 50$/t is lower than that of 0$/t. Among the solutions with three working fluids, the solution with nbutane features the maximum increment in investment cost of HEN (34.6%). It is easy to understand that both environmental cost and TAC increase as carbon tax increases. Among the solutions with three working fluids, the solution with working fluid n-butane holds the maximum increment in TAC (75.6%). 5.5 Sensitivity analysis of fuel price Natural gas prices vary widely across regions and time. Fuel price significantly affects the results of the proposed system. Thus, performing sensitivity analysis of the fuel price on the proposed system is necessary. To demonstrate the effect of fuel price on the synthesis and optimization results, Case 1 is re-studied by incorporating different fuel price in the objective function. In the analysis, natural gas prices vary from 227 $/t to 694.6 $/t with a fixed carbon charge of 3.3 $/t (the second carbon emission charge standard proposed in Wei and Zhou [38]). Fig. 12 presents the influence of natural gas price on the investment of HEN, waste heat recovered by ORC, fuel cost, environmental cost, and TAC for working fluids n-butane, R245fa, and R123. Usually, to minimize the TAC, the fuel consumption should be minimized, the heat integration between process hot streams and cold streams should be maximized, and the heat recovery by ORC should be maximized. As shown in Fig. 12, the investment cost of PPHEN increases with the increase of fuel price for three working fluids. This indicates that the heat integration between process hot-cold streams is further intensified with the increase of fuel price. As a result, the hot utility demand decreases and the fuel consumption decreases. Subsequently, the environmental cost decreases with the increase of fuel price. However, the heat recovery by ORC decreases with the increase of fuel price. The reason is that the available surplus heat in the PPHEN decreases with the further heat integration intensification compare to the scheme based on the base fuel price. It is unsurprising that the fuel cost increase monotonously with the increase of fuel price for all working fluids. From Tables 3, 5, and 7, we can see that the fuel cost occupies largest proportion among the total cost, thus, the TAC also increases monotonously with the increase of fuel price for all working fluids. Though the ORC with different working fluids feature similar change trends in costs and surplus heat recovery by ORC, the change rates are different. The surplus heat recovered by ORC using n-butane decreases slightly with fuel price while those of ORC using R245fa and R123 decreases first sharply and then slowly with fuel price. The comparison between the ORCs using different working fluids shows that the ORC using n-butane features lower surplus heat recovery than those of ORCs using R245fa and R123. The surplus heat recovered in ORC using n-butane is 21.6-25.1% and 22.2-25.1% lower 16

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than those of ORCs using R245fa and R123 under the same fuel price. However, the TACs of three integration systems using different working fluids do not deviate significantly from each other. For the studied scenarios shown in Fig. 12, the maximum deviation of TAC over the average TAC under the same fuel price condition is 1.04%. The sensitivity analysis results shown in Figs. 13 indicates that the optimal results of the proposed system are influenced significantly by fuel price. The heat recovered from process hot-process cold stream integration increases with increasing fuel price. The surplus heat recovered by ORC and hot utility demand decreases with the increase in fuel price. This finding reflects that the proposed system features a better advantage in the lower fuel prices compared with OIHU. Though the integration schemes are different for different working fluids due to their different thermo-physical properties, the TAC does not deviate significant from each other as the TAC is determined from the trade-off among PPHEN, PHUHEN, PPORC, SRC, and PCUHEN. 1600

R245fa

n-butane

11900

R123

1200 1000 800 600

n-butane

R123

11700 11600 11500 11400

400

11300

200 0 0

3.3

11200

50

Carbon tax ($/t)

0

28000

3.3

n-butane

50

Carbon tax ($/t)

800 R245fa

R245fa

R123

n-butane

R123

700

27800

Environmental cost (k$)

Surplus heat recovered by ORC (kW)

R245fa

11800

Fuel cost (k$)

Investment cost of HEN (k$)

1400

27600

27400

27200

27000

600 500 400 300 200 100 0

26800 0

3.3

0

50

3.3

50

Carbon tax ($/t)

Carbon tax ($/t) 18000

R245fa

n-butane

R123

16000

Total annual cost (k$)

14000 12000 10000 8000 6000 4000 2000 0 0

3.3

Carbon tax ($/t)

50

Fig. 11 Influence of carbon tax on: a) investment cost of HEN; b) surplus heat recovered by ORC; c) fuel cost; d) environmental cost; and e) TAC

17

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30000

30000

28000

25000

24000 15000 22000 10000 20000

5000

0

(b)

18000 227

340.5

454

567.5

681

35000

30000

30000

28000

25000

Cost (k$)

26000 20000 24000 15000 22000 10000

20000

5000

0

18000 227

(c)

340.5

454

567.5

681

35000

30000

30000

28000

25000 26000 20000

Cost (k$)

Surplus heat recovered by ORC (kW)

Cost (k$)

26000 20000

Surplus heat recovered by ORC (kW)

35000

Investment of HEN (k$) Environmental cost (k$)

24000 15000 22000 10000

Surplus heat recovered by ORC (kW)

(a)

Fuel cost (k$) Total annual cost (k$) Surplus heat recovered by ORC(kW)

20000

5000

0

18000 227

340.5

454

567.5

681

Unit price of fuel ($/t)

Fig. 12 Influence of natural gas price on surplus heat recovery and costs for integration solution using different working fluids: (a) n-butane; (b) R245fa; (c) R123 18

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6. Conclusion This paper developed a superstructure containing PHEN, PHUHEN, PORCHEN, PCUHEN, SRC, and cold utility system. Different to the previous sequential optimization method, a MINLP optimization model was formulated for the synthesis and simultaneous optimization of the proposed integration system. Two cases with different scale in complexity were investigated and compared with the schemes without integrating ORC. The influence of carbon tax and fuel price on the integration scheme were conducted. Following conclusions were drawn. In the small-scale Case 1, the optimization scheme IHUO and OIHUO were achieved using the proposed method. The comparison showed that the TAC of IHUO is 12.61-12.94 lower than that of IHU and t the TAC of OIHUO is 12.6513.23% lower than that of OIHU. The TAC of OIHUO is 21.28-21.81% lower than that of IHU. In the large-scale Case 2, the TAC of OIHUO is 7.74-11.00% lower than that of IHU. The optimization schemes are quite different when using different working fluid. However, the TACs of the optimization schemes do not deviate significantly from each other because the TAC is minimized under the best trade-off among all the sub-HENs using the proposed simultaneous optimization method. These comparison results indicated that the integration and optimization of ORC, SRC, and HEN using the proposed method are effective in improving the performance of industrial energy system. The sensitivity analysis showed that carbon tax exerts remarkable influence on the optimization results. For n-butane and R123, the fuel consumption reduces with the increase of carbon tax to minimize the TAC and the surplus heat recovered by ORC decreases with carbon tax. For R245fa, the change trends of fuel cost, surplus heat, and investment cost of HEN are different to those of n-butane and R123. However, the TACs of integration system using three working fluids do not deviate from each other due to the simultaneous optimization and best trade-off of the integration system. The sensitivity analysis of fuel price showed that minimizing the fuel consumption is the direction of minimize the TAC as the fuel price increase. The fuel cost and TAC unsurprisingly increase with the increase of fuel price; however, the increase rate of the former is lower that of the latter as the minimizing the fuel consumption is attributed to the increase of other costs. The surplus heat recovered by the ORC decreases with the increase of fuel price because the available surplus heat decreases with the decrease of fuel consumption. Acknowledgment The authors gratefully acknowledge the financial support from the State Key Program of National Natural Science Foundation of China (Grant No. 51736005), National Natural Science Foundation of China (Grant No. 51876043), and Science and Technology Program of Guangzhou (201704030108). Appendix A. Regression correlations of ORC working fluids

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Table A1. Fitting correlations of the properties of working fluids Coefficients

Items R245fa cfaa, cfbb, cfcc for h1 and h3 cfdd, cfee, cfff, cfgg, cfhh for Δh1-2s cfii, cfjj, cfkk for h4 and h6 cfll, cfmm, cfnn, cfoo, cfpp for Δh4-5s cfqq, cfrr, cfss for T2 cftt, cfuu, cfvv for T5 n-butane cfaa, cfbb, cfcc for h1 and h3 cfdd, cfee, cfff, cfgg, cfhh for Δh1-2s cfii, cfjj, cfkk for h4 and h6 cfll, cfmm, cfnn, cfoo, cfpp for Δh4-5s cfqq, cfrr, cfss for T2 cftt, cfuu, cfvv for T5 R123 cfaa, cfbb, cfcc for h1 and h3 cfdd, cfee, cfff, cfgg, cfhh for Δh1-2s cfii, cfjj, cfkk for h4 and h6 cfll, cfmm, cfnn, cfoo, cfpp for Δh4-5s cfqq, cfrr, cfss for T2 cftt, cfuu, cfvv for T5

R2

202.1920, 1.1723, 0.0021 0.4083, -0.0132, 1.7542E-04, 0.0014, -7.6094E-05 400.9362, 0.8925, -0.0017 0.3191, 0.7336, -0.0016, -0.7679, 0.0019 -146.4921, -0.0054, 0.7392 -408.1944, 0.2126, 1.0135

0.9999 0.9994 0.9994 0.9999 0.9999 0.9996

204.7597, 2.0933, 0.0050 0.8567, -0.0248, 3.9495-E04, 0.0007, -1.8693E-04 577.9352, 1.7568, -0.0034 -1.5775, 1.4493, -0.0033, -1.4605, 0.0035 -77.4780, -0.0072, 0.3967 -303.0088, 0.2065, 0.5213

0.9999 0.9994 0.9993 0.9999 0.9998 0.9996

200.7101, 0.9582, 0.0009 0.2302, -0.0074, 9.9283E-05, 0.0007, -4.4291E-05 379.9826, 0.6722, -0.0008 1.3876, 0.6173, -0.0011, -0.6715, 0.0015 -191.9116, -0.0051, 0.9649 -522.1370, 0.1399, 1.3725

1 0.9996 0.9999 0.9999 1 0.9998

Nomenclature Subscripts: CW= index for cooling water conds= index for condenser DEA=index for deaerator draftfans= index for daft fans in cooling tower ext= index for extraction steam from tribune MP= index for MP steam hui=index for process streams from steam turbine HUI= index for process streams from steam turbine hui huk=index for the stages of process cold stream that matches process stream from steam turbine HUK= index for stages of process cold stream that matches process stream from steam turbine i=index for hot streams and process streams from steam turbine in= index for inlet IP= index for IP steam out= index for outlet j=index for cold streams and ORC working fluid stream k=index for all stages, including HUK, ORCK, and PK and temperature locations orcj= index for process streams from ORC ORCK= index for stages for cold process stream from ORC that matches the hot stream pump= index for pump Pi=index of process hot streams PI= index of hot streams pi Pj=index of process cold streams PJ= index of hot streams pj 20

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Pk=index of stages in matching of hot and cold process PK= index of stages in matching of hot and cold process pk carbontax= index of carbon tax Binary variables Z = existence of candidate process heat exchanger unit, ZC= existence of heat exchange between cold utility and hot stream, Parameters: Ahour= annual operation time, h CF=fixed charge for exchangers, $ CCU=purchasing specific price of cold utility, $/kW Cfuel= purchasing specific price of fuel, $/kW Cpower= specific price of produced electricity, $/kWh CBCoeffa, CBCoeffb = cost coefficients for BT, $ cfaa- cfvv = fitting correlations of working fluid, FH=heat capacity of process hot stream, kJ/ oC FC=heat capacity of process cold stream, kJ/ oC HSat= saturated enthalpy of steam extracted from turbine, kJ/kg KF= factor used to annualize capital costs, LH=latent heat, kJ/kg Greek letters ηe= isentropic efficiencies of expander in ORC, ηp=isentropic efficiencies of pump in ORC, β= cost exponent of exchanger area, δ=very small value, Variables: dtcui=temperature difference between the hot side of hot stream-cold utility, oC dtcuo=temperature difference between the cold sede of hot stream-cold utility, oC dti=temperature difference between the hot side of hot-cold stream, oC dto= temperature difference between the cold side of hot-cold stream, oC FB= fuel consumption of boiler, kg/s h= enthalpy of state point in the ORC, kJ/kg htc=film heat transfer coefficient, kW/(m2∙oC) INVCT=investment of cold utility components, $ INVHE= heat exchanger investment cost, $ INVUS= utility component investment cost, $ INVORC= ORC component investment cost, $

M= flow rate, kg/s MT = turbine inlet or extraction steam flow rate, kg/s MW= water for cooling superheat steam, kg/s OPCU= cold utility operating cost, $ OPORC= ORC operating cost, $ OPFUEL=operating cost for fuel, $ 21

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q = heat exchanging quantity, kW QC=cold utility requirement, kW PW= power consumption in cooling tower, kW TAC= total annual cost, $ T = inlet or outlet temperature, oC Tc= condensing temperature, oC Te=evaporation temperature, oC t = temperature of stream at temperature location, oC ti = outlet temperature of cold stream split after exchange heat with hot stream, oC to =outlet temperature of hot stream split after exchange heat with cold stream, oC WT= power generation or consumption, kW WSELL= profit of selling electricity, $ References [1] Chen Y., Eslick J.C., Grossmann I.E., Miller D.C. Simultaneous process optimization and heat integration based on rigorous process simulations. Comput Chem Eng. 2015;81:880-99. [2] Cerda J., Westerberg A.W., Mason D., Linnhoff B. Minimum utility usage in heat exchanger network synthesis: A transportation problem. Chem Eng Sci;38(3):373-87. [3] Papoulias S.A., Grossmann I.E. A structural optimization approach in process synthesis--II: Heat recovery networks. Computers and Chemical Engineering. 1983;7(6):707-21. [4] Zhang B.J., Luo X.L., Chen X.Z., Chen Q.L. Coupling process plants and utility systems for site scale steam integration. Ind Eng Chem Res. 2013;52(41):14627-36. [5] Luo X.L., Huang X.J., El-Halwagi M.M., Ponce-Ortega J.M., Chen Y. Simultaneous synthesis of utility system and heat exchanger network incorporating steam condensate and boiler feedwater. Energy. 2016;113:875-93. [6] Lira-Barragan L.F., Ponce-Ortega J.M., Serna-Gonzalez M., El-Halwagi M.M. Optimum heat storage design for solar-driven absorption refrigerators integrated with heat exchanger networks. AICHE. 2014;60(3):909-30. [7] Townsend D.W., Linnhoff B. Heat and Power Networks in Process Design. Part I: Criteria for placement of heat engines and heat pumps in process networks. AICHE. 1983;29(5):742-8. [8] González-Bravo R., Elsayed N.A., Ponce-Ortega J.M., Nápoles-Rivera F., El-Halwagi M.M. Optimal design of thermal membrane distillation systems with heat integration with process plants. Appl Therm Eng. 2015;75:154-66. [9] Jiang Y.H., Kang L.X., Liu Y.Z. Simultaneous synthesis of a multiple-effect evaporation system with background process. Chemical Engineering Research and Design;133:79-89. [10] Hipólito-Valencia B.J., Rubio-Castro E., Ponce-Ortega J.M., Serna-González M., Nápoles-Rivera F., El-Halwagi M.M. Optimal integration of organic Rankine cycles with industrial processes. Energ Convers Manage. 2013;73:285-302. [11] Zhang C., Liu C., Wang S.K., Xu X.X., Li Q.B. Thermo-economic comparison of subcritical organic Rankine cycle based on different heat exchanger configurations. Energy. 2017;123:728-41. [12] Lecompte S., Huisseune H., van den Broek M., Vanslambrouck B., de Paepe M. Review of organic Rankine cycle (ORC) architectures for waste heat recovery. Renewable and Sustainable Energy Reviews. 2015; 47:448-61. [13] Yari M., Mehr A.S., Zare V., Mahmoudi S.M.S., Rosen M.A. Exergoeconomic comparison of TLC (trilateral Rankine cycle), ORC (organic Rankine cycle) and Kalina cycle using a low grade heat source. Energy. 2015;83:712-22. [14] Gutierrez-Arriaga C.G., Abdelhady F., Bamufleh H.S., Serna-Gonzalez M., El-Halwagi M.M., Ponce-Ortega J. Industrial waste heat recovery and cogeneration involving organic Rankine cycles. Clean Techn Environ Policy. 2015;17(3):767-79. [15] Desai N.B., Bandyopadhyay S. Process integration of organic Rankine cycle. Energy. 2009;34(10):1674-86. 22

Journal Pre-proof

[16] [17]

[18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]

[32] [33]

Chen C., Chang F., Chao T., Chen H., Lee J. Heat-exchanger network synthesis involving organic Rankine cycle for waste heat recovery. Ind Eng Chem Res. 2014;53:16924-36. Stijepovic M.Z., Papadopoulos A.I., Linke P., Stijepovic V., Grujic A.S., Kijevčanin M., et al. Organic Rankine Cycle system performance targeting and design for multiple heat sources with simultaneous working fluid selection. J Clean Prod. 2017;142:1950-70. Chen C.L., Li P.Y., Le S. Organic Rankine cycle for waste heat recovery in a refinery. Ind Eng Chem Res. 2016;55:3262-75. Yu H.S., Feng X., Wang Y.F., Biegler L.T., Eason J. A systematic method to customize an efficient organic Rankine cycle (ORC) to recover waste heat in refineries. Appl Energ. 2016;179:302-15. Yu H.S., Eason J., Biegler L.T., Feng X. Process integration and superstructure optimization of Organic Rankine Cycles (ORCs) with heat exchanger network synthesis. Comput Chem Eng. 2017;107(Supplement C):257-70. Yu H.S., Eason J., Biegler L.T., Feng X. Simultaneous heat integration and techno-economic optimization of Organic Rankine Cycle (ORC) for multiple waste heat stream recovery. Energy. 2017;119:322-33. Goh W.S., Wan Y.K., Tay C.K., Ng R.T.L., Ng D.K.S. Automated targeting model for synthesis of heat exchanger network with utility systems. Appl Energ. 2016;162(1272–1281). Martelli E., Elsido C., Mian A., Marechal F. MINLP model and two-stage algorithm for the simultaneous synthesis of heat exchanger networks, utility systems and heat recovery cycles. Comput Chem Eng. 2017;106:663-89. Andiappan V., Ng D.K.S. Synthesis of tri-generation systems: Technology selection, sizing and redundancy allocation based on operational strategy. Comput Chem Eng. 2016;91:380-91. Liew P.Y., Theo W.L., Alwi S.R.W., Lim J.S., Manan Z.A., Klemeš J.J., et al. Total Site Heat Integration planning and design for industrial, urban and renewable systems. Renewable and Sustainable Energy Reviews. 2016. Li Z.Q., Du W.L., Zhao L., Qian F. Modeling and optimization of a steam system in a chemical plant containing multiple direct drive steam turbines. Ind Eng Chem Res. 2014;53(27):11021-32. Luo X.L., Zhang B.J., Chen Y., Mo S.P. Operational planning optimization of steam power plants considering equipment failure in petrochemical complex. Appl Energ. 2013;112(SI):1247-64. Quoilin S., Declaye S., Tchanche B.F., Lemort V. Thermo-economic optimization of waste heat recovery Organic Rankine Cycles. Appl Therm Eng. 2011;31(14-15):2885-93. Mago P.J., Chamra L.M., Srinivasan K., Somayaji C. An examination of regenerative organic Rankine cycles using dry fluids. Appl Therm Eng. 2008;28(8-9):998-1007. Luo X.L., Hu J.H., Zhao J., Zhang B.J., Chen Y., Mo S.P. Multi-objective optimization for the design and synthesis of utility systems with emission abatement technology concerns. Appl Energ. 2014;136:1110-31. Gabriel K.J., El-Halwagi M.M., Linke P. Optimization across the water-energy nexus for integrating heat, power, and water for industrial processes, coupled with hybrid thermal-membrane desalination. Ind Eng Chem Res. 2016;55(12):3442-66. Smith R., Delaby O. Targeting flue gas emissions. Chemical Engineering Research and Design. 1991;69(A6):492505. Grossman I.E., Viswananthan J., Vecchietti A., Raman R., Kalvelagen E. GAMS/DICOPT: A discrete continuous optimization package. Math. Method. Appl. Sci. 2001, 11, 649−664. 2001.

[34] [35] [36] [37]

Misener R., Floudas C.A. ANTIGONE: algorithms for coNTinuous / integer global optimization of nonlinear equations. J Global Optim. 2014;59(2-3):503-26. GAMS: a user's guide. Washington DC: GAMS Development Corp. 2008. Luo X.L., Zhang B.J., Chen Y., Mo S.P. Operational planning optimization of multiple interconnected steam power plants considering environmental costs. Energy. 2012;37(1):549-61. Liu D.H., Yang Y.P., Yang K., Li D.Q., Yang Z.P. Research on the production cost of coal-fired power generating unit with consideration of environmental costs. Electric Power. 2005;38(9):23-8. 23

Journal Pre-proof

[38] [39] [40]

Wei X.H., Zhou H. Evaluating the environmental value schedule of pollutants mitigated in china thermal power industry. Research of Environmental Science. 2003;16(1):53-6. Zhang Q.Y., Tian W.L., Wei Y.M., Chen Y.X. External costs from electricity generation of China up to 2030 in energy and abatement scenarios. Energ Policy. 2007;35(8):4295-304. Hirschberg S., Heck T., Gantner U., Lu Y.Q., Spadaro J.V., Trukenmuller A., et al. Health and environmental impacts of China's current and future electricity supply, with associated external costs. International Journal of Global Energy Issues. 2004;22(2/3/4):155.

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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Journal Pre-proof An integration system of HEN, ORC, SRC, and cold utility system is proposed. A MINLP model is formulated to simultaneous optimize the proposed system. Two case studies of different scale are elaborated to validate the proposed method. Influence of carbon tax and fuel price on the optimization schemes is conducted.

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