Energy and Economic Optimization of the Multistage Condensation

Research Article Cite This: ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

pubs.acs.org/journal/ascecg

Energy and Economic Optimization of the Multistage Condensation Rankine Cycle That Utilizes LNG Cold Energy: Considerations on Working Fluids and Cycle Configurations Tong Yuan, Chunxiao Song, Ruixiang Zhang, Xiaopeng Zhang, Ning Zhang, and Junjiang Bao* State Key Laboratory of Fine Chemicals, School of Petroleum and Chemical Engineering, Dalian University of Technology, No. 2 Dagong Road, New District of Liaodong Bay, Panjin 124221, P. R. China Downloaded via UNIV OF SOUTHERN INDIANA on July 27, 2019 at 04:07:03 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: To improve the performance of LNG cold energy power generation systems, scholars have made great efforts to enhance the cycle configuration and select the suitable working fluid. In this process, the improvement of the configuration and the selection of the working fluid are mostly independent, so that the possibility of missing the optimal combination is great. To solve the problem, the superstructures of the two-stage condensation Rankine cycle (2C-ORC) and the three-stage condensation Rankine cycle (3C-ORC) are established in this work, which contain different compression and expansion layouts. The selection coefficients of the working fluids are also introduced at the same time, which can optimize the compositions of mixed working fluids. In this way, the system configuration improvement and working fluid selection can be realized simultaneously. In this work, the net power output and the total cost are taken as the objective functions for the single-objective optimization, respectively. The optimal cycle configurations and mixed working fluids respectively corresponding to the maximum net power output and the minimum total investment cost are determined under different LNG regasification pressures. Then multiobjective optimization is carried out to determine the optimal design parameters under different LNG regasification pressures. The results show that when the LNG gasification pressure is 70 bar, 30 bar, 25 bar, and 6 bar, the maximum net power output of 3C-ORC is 6.21%, 3.24%, 2.25%, and 2.86% higher than that of 2C-ORC, respectively, and the minimum cost of 2C-ORC is 33.60%, 32.13%, 27.70%, and 27.93% lower than that of 3C-ORC, respectively. Finally, after the comprehensive consideration for the economy and generating capacity, at any gasification pressure of LNG, 2C-ORC of a binary mixture with C2H4 or C2H6 as the main component is recommended. KEYWORDS: LNG cold energy, Multistage condensation cycle, Superstructure, Selection coefficient, Mixed working fluid

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INTRODUCTION World energy consumption is increasing with the development of the society.1 Primary energy consumption surged by 2.2% in 2017, which is much higher than the 1.3% in 2016, and natural gas (NG) is the biggest source of this increase.2 NG is an environmentally friendly primary energy source and has been widely used in recent years,3 so optimizing and developing the NG industry chain is particularly important.4 In the industry chain, NG is often liquefied to −162 °C to facilitate transportation due to the uneven distribution throughout the world.5 Liquefied natural gas (LNG) is generated with a large consumption of electric energy and releases cold energy when being regasified before being distributed to residents.6 Therefore, utilizing the LNG cold energy in the regasification process is an important part of the optimization of the NG industry chain.7 There are many ways to utilize the LNG cold energy, including air separation,8 food freezing,9 and seawater desalination10 and so on. Mehrpooya et al.11 conducted a © XXXX American Chemical Society

series of studies using LNG cold energy. Several kinds of high energy integrated cryogenic systems have been proposed.12 But in most cases, the cold energy in the LNG regasification process is recovered by a power generation cycle, which is one of the most effective methods.13 The Rankine cycle, with its simple structure and mature technology, has been studied by most scholars at present. Song et al.14 proposed a trans-critical Rankine cycle power generation system driven by solar energy and using LNG as the cold source. The effects of some of the key parameters on the thermodynamic performance of the system were studied. Qu et al.15 proposed a hybrid power generation system using organic Rankine cycle to recover LNG cold energy, and established a one-dimensional numerical model to describe the conjugate heat transfer and thermodynamic characteristics of the components in the system. Received: June 4, 2019 Revised: July 13, 2019 Published: July 17, 2019 A

DOI: 10.1021/acssuschemeng.9b03146 ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

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ACS Sustainable Chemistry & Engineering

Figure 1. Superstructure of 2C-ORC.

sources. Antonio et al.26explored the best working fluids for three subsystems in a polygeneration plant recovering LNG cold energy. Kanbur et al.27 gave an overview of LNG cold energy power generation systems. They summarized some pure working fluids commonly used in these systems and suggested a criterion for working fluid selection. The zeotropic mixtures have better temperature matching with LNG than pure ones because of their temperature-varying phase transition process. Thus, zeotropic mixtures perform better than pure working fluids. Shi et al.28 proposed a system using ammonia−water mixture as the working fluid and found that the peak value of the maximum net electrical efficiency increased as the ammonia mass fraction increased. Kim et al.29 proposed a cascade power generation system with Rankine cycle and used binary mixture as the working fluid. It was found that R14/propane is the best working fluid for the first stage cycle and ethane/n-pentane is the best working fluid for the second and third stage cycles. Sun et al.30 presented a new type of Rankine cycle using LNG cold energy. The working fluid was a mixture of three hydrocarbons, and the optimum mole fraction of each component was given. Lee31 used ethane and propane as a mixed working fluid to analyze the thermodynamic properties and economics of single and twostage LNG-FSRU cold energy recovery systems. Optimizing cycle configuration and working fluid is a complex process. Recently, there have been some studies about the improvements of the optimization method. On the aspect of cycle configuration optimization, Wang et al.32 proposed a thermodynamic cycle separating method, where the organic Rankine cycle was separated into the Triangle cycle, Carnot cycle, and Brayton cycle. They saved optimization time through a special working fluid selection criterion and the prediction of cycle performance. Bao et al.33 and Lee et al.34 proposed the superstructure to simplify the optimization process of the cycle configuration. The superstructure contained many different cycle configurations and automatically selected the best configuration according to the objective

However, Rankine cycle still has a lot of room for improvement for the recovery of LNG cold energy.13 The ways to improve the performance of the Rankine cycle mainly include the improvement of configuration and the proper selection of a working fluid.16,17 On the aspect of cycle configuration, Mosaffa et al.18 presented the thermo-economic analysis for four different types of Rankine cycles utilizing LNG cold energy, including single-stage Rankine cycle, regenerative Rankine cycle, Rankine cycle with internal heat exchanger, and cascaded Rankine cycle. The regenerative Rankine cycle was recommended after comprehensive consideration. Zhang et al.6 proposed a system combined withing three Rankine cycles to use LNG cold energy. The study found that the new cycle had high output power and lower investment cost. Selecting a suitable working fluid is also important for improving the cycle performance.19 Working fluids can be divided into pure working fluids and zeotropic mixtures. The literature optimized the working fluid for proposing the new cycle configuration or comparing the existing cycles. For example, based on the series cycle, Sadreddini et al.20 selected 9 kinds of working fluids and found that the best working fluids were CO2/Pentane. Yu et al.21 studied the performance of an organic Rankine cycle system with 22 working fluids under the condition that seawater and waste heat were used as heat sources, respectively. It was concluded that R125, R143a, R290, and R1270 were better when seawater was used as a heat source. R170, R134a, and R290 were better when waste heat was used as a heat source. Habibi et al.22 studied the effect of six working fluids on parallel systems performance. Badami et al.23 compared three combination cycles and analyzed the effects of different working fluids on system performance. Yao et al.24studied the thermodynamics and economics of three kinds of working fluids in LNG cold energy power generation system using geothermal heat source, and found that the performance of the system was best when working fluid was R600. Sun et al.25 selected eight working fluids to explore the applicability of the combined system under different heat B


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Figure 2. Superstructure of 3C-ORC.

function. On the aspect of the working fluid selection, Lee et al.35 proposed a two-step method to select the working fluid and the performance of the optimal ternary working fluid was about 7.7% higher than that in the referred literature after being optimized by the method. Lampe et al.36 proposed a framework of the simultaneous optimization for the cycle parameters and configuration, which was achieved by exploiting the rich molecular picture underlying the PCSAFT equation of state in a continuous-molecular targeting approach (CoMT-CAMD). According to the above review of the literature, it can be known that scholars have done a lot on improving cycle configuration and selecting suitable working fluid. However, in this process, the configuration improvement and working fluid selection are mostly conducted independently, so that it is easy to miss the real optimal solution. In order to solve the problem, the present study introduced the superstructure and working fluid selection coefficients. A one-step optimization method is adopted to optimize the system, which means that the system configuration improvement and working fluid selection are realized at the same time. On the basis of the multistage condensation Rankine cycles proposed earlier,17,37the superstructures of the two-stage condensation Rankine cycle (2CORC) and the three-stage condensation Rankine cycle (3CORC) are constructed in this work, which contain different compression and expansion layouts. In addition, the model of the working fluid selection coefficients is established. A onestep optimization method is used to simultaneously optimize the cycle configuration and select the mixed working fluid for the multistage condensation Rankine cycle. First, single objective optimization is carried out with the net power output and total investment cost as the objective function, respectively. Then the multiobjective optimization is carried out, which takes both power generation capacity and economy into account. Finally, some suggestions on the configuration selection and working fluid selection of the multistage

condensation Rankine cycle are given under different LNG gasification pressures.

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SYSTEM DESCRIPTION The superstructures of 2C-ORC and 3C-ORC are shown as Figures 1 and 2 and their corresponding T-s diagram are given in the Supporting Information (SI) Figures 1S and 2S, respectively, which contain all possible compression and expansion layouts. It should be noted that the purpose of this work is to compare the performance of four 2C-ORCs17 and nine 3C-ORCs33 based on mixed working fluids. Because the turbines with low inlet temperature (such as Turb-2B, etc.) easily have liquid at the inlet, which will damage the turbines, the cycles proposed in this work17,33 are improved, that is, adding heat exchangers at the inlet of the low-temperature turbines to heat the two-phase working fluid into a saturated gas. Figure 1 is the superstructure of 2C-ORC. The heat sink of the cycle is LNG. LNG is first pressurized to the distribution pressure by the pump P-5, and then sequentially passes through the first-stage condenser Cond1 and the second-stage condenser Cond2, in which the cold energy is supplied to the working fluid. Meanwhile, LNG absorbs the heat of the working fluid and is finally heated to the normal temperature by seawater. The heat source of the cycle is seawater. The first part of seawater SW-1 enters the evaporator Evap to heat the working fluid, and then is selected by the selection module SP2. When the expansion layout is A, the seawater directly flows out of the system. When the expansion layout is B, the seawater enters into the heat exchanger Heater to heat the twophase working fluid to saturated gas. The other part of the seawater SW-1′ is pressurized by P4̅ and is used to heat the LNG. In the superstructure of 2C-ORC, the working fluid is heated to vapor in the evaporator Evap. Then it enters into the C


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ACS Sustainable Chemistry & Engineering expansion layout A or B selected by the selection module SP2, and the working fluid is divided into two streams. The two streams of the working fluid respectively enter into Cond 1and Cond2 to be condensed by the LNG. After that, the two streams are compressed by the compression layout a or b selected by the selection module SP1 and are mixed into one stream entering the evaporator to start a new cycle. In the compression layout a, the two streams of the working fluid from the condensers are pressurized by the pumps P-1a and P2a, respectively. After that, they merge into one stream. In the compression layout b, the working fluid from the second-stage condenser is pressurized by the pump P-2b. It is mixed with the working fluid from the first-stage condenser and then pressurized by the pump P-1b. In the expansion layout A, the working fluid is divided into two parts, which are expanded in Turb-1A and Turb-2A and then enter the second-stage and the first-stage condensers, respectively. In expansion layout B, the working fluid is first expanded by Turb-1B, and then it is divided into two streams. One of them enters the second-stage condenser and the other one enters the Heater where it is heated by the seawater. After that it is expanded in Turb-2B and enters the first-stage condenser. Figure 2 shows the superstructure of the 3C-ORC. The LNG is first pressurized to the distribution pressure by the pump P6̅, and then passes through the first-stage condenser Cond1, the second-stage condenser Cond2, and the third-stage condenser Cond3. Finally, the LNG is heated by the seawater to the normal temperature. In the superstructure of 3C-ORC, the working fluid is heated in the evaporator Evap, and then enters into the expansion layout A, B, or C selected by the selection module SP2. The working fluid is divided from one stream into three streams after expansion process. They enter into the three condensers to be condensed by the LNG, respectively. After that, the three streams are compressed by compression layout a, b, or c selected by the selection module SP1 and they are mixed into one stream entering the evaporator to start a new cycle. In compression layout a, the three streams of the working fluid from the three condensers are compressed by the pumps P-1a, P-2a, and P-1C, respectively, and are merged into one stream to enter into the evaporator. In compression layout b, the two streams of the working fluids from the first-stage and second-stage condensers are pressurized by pumps P-3b and P2b, respectively, and they are merged with the working fluid from the third-stage condenser. After that, the working fluid is pressurized by pump P-1b and enters into the evaporator. In compression layout c, the working fluid from the first-stage condenser is pressurized by the pump P-3c and is mixed with the working fluid from the second-stage condenser. Then it is pressurized by pump P-2c and is mixed with the working fluid from the third stage condenser. After that, the working fluid is pressurized by the pump P-3c and enters into the evaporator. For the expansion layout, the principle is similar and will not be further described.

Table 1. Input Parameters for the Simulation parameters

values

The inlet temperature of LNG (°C) inlet pressure of LNG (bar) terminal temperature of NG (°C) inlet temperature of seawater (°C) inlet pressure of seawater (bar) outlet temperature of seawater (°C) outlet pressure of seawater (bar) temperature differences at the pinch points (°C) isentropic efficiency of the pumps isentropic efficiency of the turbines

−162 1 10 15 1 10 3 5 80% 80%

Table 2. Physical Properties of All the Working Fluids Involved in This Study working fluids

chemical name

Tcrit (°C)

Pcrit (bar)

CH4 R32 R14 C2H4 C2H6 R123 R152a R290 R245fa R245ca R236ea R227ea R600 R600a R601 R601a

methane difluoromethane tetrafluoromethane ethene ethane 2,2-dichloro-1,1,1-trifluoroethane 1,1-difluoroethane propane 1,1,1,3,3-pentafluoropropane 1,1,2,2,3-pentafluoropropane 1,1,1,2,3,3-hexafluoropropane 1,1,1,2,3,3,3-heptafluoropropan n-butane i-butane n-pentane i-pentane

−82.57 78.10 −45.64 9.20 32.17 183.7 113.26 96.7 154.0 174.4 139.3 101.8 152.0 134.7 196.6 187.2

44.98 57.82 36.49 50.42 47.71 36.6 45.17 42.5 36.5 39.3 35.0 30.0 38.0 36.3 33.7 33.8

3. The heat losses and friction losses are ignored. 4. For the pumps and the turbines, the conversion between the work and the electrical energy is assumed to be 100%. 5. Each condenser condenses the working fluid to the saturated liquid and the evaporator heats the working fluid to saturated vapor. In the simulation process, the input parameters are shown in Table 1. The mole fractions of LNG38are 91.33% for CH4, 5.36% for C2H6, 2.14% for C3H8, 0.47% for i-C4H10, 0.46% for n-C4H10, 0.01% for i-C5H12, 0.01% for n-C5H12, and 0.22% for N2. It is necessary to emphasize that the terminal pressure of NG is also different in different applications. When the NG application39 uses the following scenes: long distance transmission, local distribution, combined cycle stations, and steam power stations, the vaporization pressures are 70, 30, 25, and 6 bar, respectively. Energy Analysis. The energy analysis is carried out based on the first law of thermodynamics. The net output power is equal to the difference between the output power of all the turbines and that of all the pumps. The basic formula is as follows:

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SYSTEM MODELING AND SIMULATION Assumptions. To simply the calculation, some assumptions are made:

Wnet =

1. All of the systems are operated in a steady state and the parameters of each state point do not change with time. 2. The pressure changes of the components other than pumps and turbines are ignored.

∑ WTurb − ∑ WP

(1)

where WTurb is the output power of the turbines, and WP is the consumed power of pumps. Detailed energy analysis of each components can be found in Table S1 of the SI. D


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ACS Sustainable Chemistry & Engineering Table 3. All the Variables Involved in This Study and Their Ranges ranges optimization variables

for 2C-ORC

first-stage condensation temperature (°C) second-stage condensation temperature (°C) third-stage condensation temperature (°C) selection module SP1and SP2 selection coefficient and mole fraction for CH4, R32, R14, C2H4, C2H6, R123, R152a, R290, R245fa, R245ca, R245ca, R236ea, R227ea, R600, R600a, R601, R601a

Exergy Analysis. The second law of thermodynamics isused to analyze the irreversibility in the system. The exergy balance formula40,41 of each component is as follows: ExD = EQ − W + Ex in − Ex out

where ED is the exergy destruction, EQ is the exergy flow caused by the heat input, W is the power output, Exin is the exergy into, and Exout is the exergy out. The calculation formula of Ex is as follows: (3)

• )i ∑ (ZCI• + ZOM

(4)

where ZCI and ZOM are the initial investment cost and the maintenance cost of a component, respectively. For a certain component, they can be calculated by the following formula:18 • • (ZCI )i = + ZOM

Zi × φ CRF 3600 × N

(5)

where Zi is the initial cost of the component i, Φ is the maintenance factor, and the value is 0.15, N is the annual operating time of the system, and the value is 7300 h, and CRF is the initial investment recovery factor, which is calculated by the following formula:42 CRF =

λ(1 + λ)n (1 + λ)n − 1

(6)

where λ is annual interest rate, and the value is 14%, and n is system life, and the value is 20 year. Therefore, the formula 4 can be deduced as follows: C tot =

λ(1 + λ)n φ × × 3600 × N (1 + λ)n − 1

∑ Zi

[−140, −60] [−100, −30] [−60, 0] {(1, 0), (0, 1)} {(1, 0, 0), (0, 1, 0), (0, 0, 1)} ai = {0,1}, xi = [0, 1]

where Wnet,max and Ctot,min are the maximum net output power and the minimum total cost obtained by the single objective optimization, respectively. The obtained Wnet and Ctot by the multiobjective optimization are the corresponding net output power and total cost of the optimal design point, respectively. Details of Simulation and Optimization. The superstructures of 2C-ORC and 3C-ORC are established by ASPEN HYSYS. The physical properties are calculated by the Peng− Robinson equation and the heat exchanger model uses the built-in “Weighted” model of HYSYS. The principle of the selection module is described in detail in previous work,33which can simplify the comparison of different cycle configurations. In the superstructure of 2CORC, both SP1 and SP2 are binary variables with the set of {(1, 0), (0, 1)} representing the two compression layouts and the two expansion layouts, respectively, as shown in Figure 1. In the superstructure of 3C-ORC, both SP1 and SP2 are ternary variables with the set of {(1, 0, 0), (0, 1, 0), (0, 0, 1)}. It is because that there are three compression layouts and three expansion layouts. Different values of SP1 and SP2 correspond to different compression and expansion layouts, respectively, as shown in Figure 2. In this way, SP1 and SP2 are optimized as variables, and their optimal values can reflect the optimal configuration of the cycle in the two systems. The selection module is implemented by the splitter in HYSYS. It is decided by the flow ratio that the working fluid flows into which compression or expansion layout. The principle of the working fluid selection coefficient is given in the SI. The constraints on the condensation pressures and the fraction of the vapor phase at the outlets of the turbines are also considered during the optimization of the cycle. The condensation pressures of the working fluid in the condensers are not less than 100 kPa. In addition, the vapor phase fractions at the outlets of the turbines are constrained to be more than 90% to prevent excessive liquid phase to damage the turbine. In order to make a comprehensive comparison between 2CORC and 3C-ORC, some working fluids that are common in actual production are selected as the candidates. The physical properties of all the working fluids involved in this study are shown in Table 2. The case using pure working fluids has been discussed in detail in previous works.17,33 This study is based on mixed working fluid. The enhancement of the cycle performance by using mixed working fluid is gradually weakened as the number of components increases according to the work.19 The enhancement of the quaternary working

where m is the mass flow rate of the stream, h is the special enthalpy, T is the temperature, s is the special entropy, and subscript 0 represents the environmental state. Economic Analysis. In the economic model established in this work, the total investment cost Ctot of the system is equal to the sum of the investment costs of all components, and its basic formula is as follows:18 C tot =

[−140, −40] [−120−20]

defined as F. The Pareto front that corresponds to the minimum value of F is the optimal design point. The mathematical expression is as follows: ÄÅ ÉÑ Å Ñ MinÅÅÅF = (Wnet − Wnet,max )2 + (C tot − C tot,min)2 ÑÑÑ (8) ÅÇ ÑÖ

(2)

Ex = m[(h − h0) − T0(s − s0)]

for 3C-ORC

(7)

Detailed economic analysis of each components can be found Table S2 of the SI. Multiobjective Optimization. This work also carries out the multiobjective optimization43 for the superstructures of 2C-ORC and 3C-ORC, because the maximum net output power and the lowest cost are conflicting. The ideal point method44−47 is used to calculate the optimum design point, which is included in the SI. For the ideal point method, the best design point is the point that is the closest to the ideal point among the Pareto fronts. The distance between Pareto fronts and the ideal point is E


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−34.33 −29.04

−16.03 −23.42

−24.36 −27.28

−26.40 −27.15

94.89 90.34 100.78 100.41 146.61 142.17 151.36 150.78 158.48 154.47 162.04 159.28 198.61 198.05 204.29 202.92

Tcond2

−53.79 −57.33 −60.25 −58.27 −43.11 −48.92 −54.61 −58.48 −47.04 −49.75 −53.90 −55.00 −46.30 −45.61 −66.47 −67.43

Tcond1

0.87/0.13 0.80/0.01/0.19 0.23/0.77 0.26/0.73/0.01 0.94/0.06 0.30/0.52/0.18 0.34/0.66 0.31/0.45/0.24 0.90/0.10 0.52/0.32/0.16 0.27/0.73 0.02/0.94/0.05 0.92/0.08 0.90/0.01/0.09 0.95/0.05 0.45/0.49/0.06 3C-ORC

2C-ORC 6

3C-ORC

2C-ORC 25

3C-ORC

2C-ORC 30

2C-ORC 70

3C-ORC

mole fraction components superstructure LNG gasification pressure (bar)

component number

b+B b+B c+C c+C b+B b+B c+C c+C b+B b+B c+C c+C b+B b+B c+C c+C

−101.86 −100.35 −99.61 −99.39 −87.75 −92.85 −95.45 −94.76 −94.70 −97.10 −97.45 −87.80 −102.70 −102.46 −100.42 −116.86

Tcond3

Wnet(kW) Ctot($/h) F

optimal working fluid

Table 4. System Parameters When the Net Output Power Is Maximum

optimal cycle configuration (compression+ expansion)

RESULTS AND DISCUSSION Single Objective Optimization. In this section, the single-objective optimizations for the superstructures of 2CORC and 3C-ORC are carried out with the maximum net output power and minimum total cost as the objective function, respectively. The optimization results with the maximum net output power as the objective function are shown in Table 4. First of all, with the decrease of LNG gasification pressure, the maximum net power output of each system increases. In terms of cycle configuration, when the net output power is maximum, the optimal compression and expansion layouts are series layouts for all the systems. Under different LNG gasification pressures (from 70 to 6 bar), the maximum net output power of 3C-ORC is 6.21%, 3.24%, 2.25%, and 2.86% higher than that of 2C-ORC, respectively. Furthermore, in terms of the working fluid, it can be seen from Table 4 that the maximum net output power the system using a binary working fluid is greater than that of the system using a ternary working fluid when the number of condensation stage is same. Under different LNG gasification pressures, the maximum net output power of the 2C-ORC using a binary working fluid is 5.04%, 3.12%, 2.30%, and 0.28% higher than that using a ternary working fluid, and the maximum net output power of the 3C-ORC using a binary working fluid is 0.37%, 0.38%, 1.73%, and 0.68% higher than that using a ternary working fluid. Besides, the difficulty of operation in practice will be significantly increased as the number of the components of the mixed working fluid increases. Therefore, the binary working fluid is recommended. As can be seen from Table 4, the binary working fluid corresponding to the maximum net output power is usually mixed by C2H4 or C2H6 with the other candidates, and C2H4 or C2H6 is also the main component with a high molar fraction in the mixture. As a result, C2H4 or C2H6 are the component preferred by the mixed working fluid for the system energy output when the binary mixture is used. The optimization results with the minimum total cost as the objective are shown in Table 5. With the decrease of LNG gasification pressure, there’s no significant change for the minimum total cost. In terms of cycle configuration, when the total cost is minimum, the optimal compression and expansion layouts are parallel layouts for all the systems. In addition, the total cost of 2C-ORC is obviously less than that of 3C-ORC.

C2H4/R152a C2H4/C2H6/R290 R32/C2H4 R32/C2H4/C2H6 C2H6/R227ea C2H4/C2H6/R290 R32/C2H4 R32/C2H4/C2H6 C2H4/R152a C2H4/C2H6/R290 R32/C2H4 R32/C2H6/R227ea C2H4/R152a C2H4/C2H6/R152a C2H4/R600 R14/C2H6/R227ea

condensation temperatures (°C)

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2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3

fluid can be negligible compared the ternary working fluid. Therefore, this study only involves the binary mixed working fluid and the ternary working fluid. It should be pointed out that it will be obtained the optimal number of working fluids, including their components and compositions if the constraint condition of the number of working fluids is removed. The optimization is carried out through the built-in genetic algorithm toolbox of MATLAB. The parameters of the genetic algorithm are shown in Table S3 of the SI. All the variables involved in the optimization process of the 2C-ORC and 3CORC and their ranges are shown in Table 3. For each superstructure, the optimal cycle configuration, operating parameters, and working fluid can be obtained by optimizing the condensation temperature, the selection module, the selection coefficient and molar fraction simultaneously. This method is called one-step optimization method, which greatly simplifies the optimization process of the cycle configuration and working fluid.

16.07 15.67 17.86 17.42 19.86 18.41 20.05 20.20 20.75 19.26 20.98 20.72 19.29 19.23 21.19 21.84



3C-ORC

2C-ORC

3C-ORC

2C-ORC

3C-ORC

2C-ORC

2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3

component number mole fraction 0.95/0.05 0.27/0.71/0.02 0.98/0.02 0.55/0.23/0.22 0.52/0.48 0.46/0.17/0.37 0.38/0.62 0.05/0.55/0.40 0.76/0.24 0.14/0.63/0.23 0.47/0.53 0.02/0.70/0.41 0.86/0.14 0.52/0.28/0.20 0.59/0.41 0.58/0.28/0.14

components C2H6/R601 CH4/ C2H6/R123 C2H6/R236ea C2H4/ C2H6/R290 C2H6/R290 C2H6/R152a/R227ea C2H6/R290 R32/C2H6/R290 C2H6/R152a R32/C2H6/R152a C2H6/R290 R32/C2H6/R290 C2H6/R152a CH4/C2H6/R290 C2H6/R290 R32/C2H6/R600a

G

6

25

30

2C-ORC

70

3C-ORC

2C-ORC

3C-ORC

2C-ORC

3C-ORC

2C-ORC

3C-ORC

superstructure

LNG gasification pressure (bar) 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3

component number mole fraction 0.78/0.22 0.25/0.63/0.12 0.26/074 0.69/0.15/0.16 0.38/0.62 0.33/0.46/0.21 0.36/0.64 0.36/0.63/0.01 0.32/0.68 0.04/0.86/0.10 0.33/0.67 0.25/0.44/0.31 0.93/0.07 0.69/0.17/0.14 0.21/0.79 0.18/0.79/0.03

components C2H4/R290 C2H4/C2H6/R152a R32/C2H4 C2H4/C2H6/R290 R32/C2H4 C2H4/C2H6/R290 R32/C2H4 R32/C2H4/C2H6 R32/C2H4 R32/C2H6/R290 R32/C2H4 R32/C2H4/C2H6 C2H4/R227ea C2H4/C2H6/R290 R32/C2H4 R14/C2H4/R245fa


Table 6. Parameters at the Optimal Design Points of Different Sysytems

6

25

30

2C-ORC

70

3C-ORC

superstructure

LNG gasification pressure (bar)


Table 5. System Parameters When the Total Cost Is Minimum

b+B b+A c+C c+C b+B b+B a+C c+C b+B b+B a+C c+A b+B b+B c+C a+C


a+A a+A a+A a+A a+A a+A a+A a+A a+A a+A a+A a+A a+A a+A a+A a+A


Tcond2 −57.46 −52.99 −54.83 −59.08 −48.03 −55.22 −57.77 −52.95 −45.56 −43.49 −53.03 −62.65 −38.78 −40.67 −44.18 −66.23

Tcond1 −99.18 −92.80 −99.34 −98.20 −96.86 −92.97 −97.14 −96.67 −98.00 −86.31 −97.80 −94.76 −102.91 −99.58 −99.98 −108.11

−18.33 −36.95

−31.32 −32.79

−31.11 −14.21

−24.67 −27.63

Tcond3


Tcond2 −35.34 −44.48 −55.45 −67.91 −21.10 −22.65 −40.35 −34.94 −20.24 −20.95 −32.77 −40.88 −20.07 −23.97 −40.06 −40.03

Tcond1 −61.19 −136.32 −79.11 −91.52 −40.99 −64.39 −61.03 −60.96 −49.49 −48.76 −60.56 −65.30 −40.17 −45.17 −60.19 −63.53

23.99 37.22 69.20 65.40 50.35 55.07 88.32 91.42 60.06 60.03 90.53 104.04 64.64 68.10 102.15 106.43

89.51 89.09 99.34 98.01 144.32 140.51 149.64 148.26 154.63 146.88 160.36 157.84 196.61 184.91 193.38 202.38

14.96 15.08 17.05 17.10 18.13 17.94 19.73 19.66 18.64 18.11 20.25 20.04 19.26 18.24 20.46 20.81

8.59 5.63 4.82 5.37 9.20 8.11 6.18 6.56 9.80 11.21 7.12 5.90 10.16 15.59 13.28 7.80

F

8.26 9.59 12.44 12.60 9.23 10.00 13.60 13.67 9.63 9.86 13.32 14.33 9.29 9.86 12.89 13.03

Wnet(kW) Ctot($/h)

Wnet (kW) Ctot ($/h)

−8.31 −12.00

−9.61 −18.10

−5.80 −9.63

−50.36 −16.80

Tcond3


ACS Sustainable Chemistry & Engineering Research Article


Research Article


Figure 3. Comparison between multiobjective optimization results and single-objective optimization results when the LNG gasification pressure is 70 bar: a) the comparison of the net output power and b) the comparison of the total cost.

the system have a relatively low cost and a high net output power, representative. As shown in Figure3, the number of the components of the mixed working fluid has little effect on the optimum design point, and the number of the condensation stage has a significant effect on the optimum design point. Therefore, the average values of the binary and ternary working fluid are used to compare the optimum design parameters. The average values of the net output power and total cost at the optimal design point in 3C-ORC are respectively 10.55% and 13.68% higher than those in 2C-ORC. The increase of net output power is less than the cost, so 2C-ORC is recommended. In 2C-ORC, the net output power of binary working fluid is higher than that of the ternary working fluid and the cost is also lower. The binary working fluid is obviously better than the ternary working fluid. Therefore, when the LNG gasification pressure is 70 bar, the 2C-ORC using a binary working fluid is recommended. Similarly, under different LNG gasification pressures, 2C-ORC using the binary working fluid is also recommended. It is because that either the increase of the net output power is greater than that of the cost or the reduction of the cost is less than that of the net output power when 2C-ORC is compared with the other systems. Using a small increase in cost to exchange a greater increase in power generation capacity is preferred. Therefore, on the basis of the analysis of the parameters at the optimum design point, under all LNG gasification pressures, 2C-ORC using a binary working fluid is recommended. In addition, the optimal compression and expansion layouts of the 2C-ORC using the binary working fluid are both serial layouts and the corresponding binary working fluid is mainly composed of C 2 H 4 or C 2 H 6 . Therefore, the 2C-ORC with serial compression and expansion layouts and a binary working fluid mainly composed of C2H4 or C2H6 are recommended. The optimization result when LNG vaporization pressure is 6 bar is taken as an example to analyze the irreversible loss of each components of the systems, as shown in Figure 4. Detailed exergy analysis of each components in other LNG vaporization pressure can be found Tables S16−S17 in the SI. It is obvious from the Figure 1 that the irreversible losses of the condenser, evaporator and turbine are relatively large. When the net power output is the objective function, the irreversible loss of the system is the smallest; when the cost is the objective function, the irreversible loss of the system is the largest. The optimization result of multiobjective function is between the results of the previous two. This is because the system’s

Under different LNG gasification pressures, the minimum total cost of 2C-ORC is 33.60%, 32.13%, 27.70%, and 27.93% less than that of 3C-ORC, respectively. Furthermore, in terms of the working fluid, it can be seen from Table 5 that the minimum total cost of the system using a binary working fluid is less than that of the system using a ternary working fluid when the number of condensation stage is the same. Under different LNG gasification pressures (from 70 to 6 bar), the minimum total cost of the 2C-ORC using a binary working fluid is 13.87%, 7.70%, 2.33%, and 5.78% less than that using a ternary working fluid, and the minimum total cost of the 3C-ORC using a binary working fluid is 1.27%, 0.51%, 7.05%, and 1.07% less than that using a ternary working fluid. Besides, the practical operation of the ternary working fluid is more difficulty than the binary working fluid. Therefore, the binary working fluid is recommended. As can be seen from Table 5, the mixed working fluid in different systems is also mainly composed of C2H4 or C2H6, which is similar to the condition when the net output power is maximum. As a result, the binary working fluid with C2H4 or C2H6 as the main component is recommended. Multiobjective Optimization. From the previous section, it can be found that the parameters corresponding to maximum net output power are in conflict with the minimum total cost. To comprehensively balance the power generation capacity and economy of the systems, the multiobjective optimization is carried out. Under different LNG gasification pressures, the optimal design parameters of each system by the multiobjective optimization are shown in Table 6. The comparisons between multiobjective optimization results and single-objective optimization results under the LNG gasification pressure of 70 bar are shown in Figure 3. The results under the other LNG regasification pressure and stream parameter of systems optimization results could be found in the SI. It can be seen that the net output power and total cost by the multiobjective optimization are between the results of single objective optimization, respectively. The net output power at the optimal design point for 2C-ORC with binary working fluid, 2C-ORC with ternary working fluid, 3C-ORC with binary working fluid, and 3C-ORC with ternary working fluid is about 5.67% 1.38% 1.43%, and 2.39% lower than their maximum net output power, respectively, and is about 273.11%, 139.36%, 43.55%, and 49.86% higher than the net output power with the lowest total cost, respectively. Therefore, the optimal design parameters obtained by multiobjective optimization can make H


Research Article


Figure 4. Exergy destruction of different components when the LNG vaporization pressure is 6 bar a) when the net put power is maximum, b) when the cost is minimum, and c) multiobjective optimization results. I


Research Article

ACS Sustainable Chemistry & Engineering Table 7. Comparisons between This Study and the Literature Tseawater (°C) PNG (bar) TNG (°C) ηpump (%) this study this study Ferreira etal49 Choi et al.50 Xue et al.51 Lee et al.52 Yu et al.53 Sun et al.48

15 25 16 15 30 15 25

70 60 82 60 120 60 70 60

10 10 10 10 5 10 10 10

80 80 70 80 80 80 75 80

ηturbie (%)

working fluid

△T (°C)

80 80 80 80 85 80 80 80

R32/C2H4 (0.23/0.7) R32/C2H4 (0.45/0.5) R290 R290 R290 R290 R1270 propane/ethane

5 5 5 5 5

equipment is more inclined to make the device model smaller size when the cost is taken as the objective function. A smaller heat exchanger leads to the poor matching for the heat exchange between the LNG and the working fluid, which causes the irreversible loss of the heat exchanger to become large. The irreversible loss of the condenser in the three-stage condensing Rankine cycle system is less than that of the twostage condensing Rankine cycle system, mainly because the three-stage condensing Rankine cycle reduces the irreversible loss between the working fluid and the LNG by increasing the number of condensation stages. For the same system, the irreversible loss of the ternary mixed working fluid is less than that of the binary mixture, mainly because the heat exchange between the ternary mixture and the LNG is better. To clarify the advancement of the studied system, the threestage condensation Rankine cycle of the series compression and expansion layouts with binary working fluid is compared with the data of other literatures. The comparison results are shown in Table 1. In this work, the heat source is seawater, so only the data of the seawater as heat source in the literature is compared. It can be seen from Table 7 that the net power output of the three-stage condensation Rankine cycle proposed in this work is superior to most of the literature. The net power output obtained by Sun et al.48 is higher than that of our work, but the parameters selected in the two papers are different. To conduct a fair comparison, the three-stage condensation Rankine cycle is optimized under the same condition as reference.48 From the optimization results in Table 1, the net power output of the system under the same condition is 17% higher than that of the literature.

■

seawater pump

Wnet (kW/(kg/s)

economic

yes yes no yes no yes no no

100.78 138.65 53.02 64.70 87.33 96.10 64.53 118.3

yes yes no no no no no no

3 5

with the serial compression and expansion layouts and the binary working fluid mainly composed of C2H4 or C2H6 are recommended. 3. The optimum design point is obtained after considering the power generation capacity and economy comprehensively and its parameters are representative. According to the analysis of the optimum design parameters, the 2C-ORC with serial compression and expansion layouts and a binary working fluid mainly composed of C2H4 or C2H6 are recommended.

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acssuschemeng.9b03146. T−s diagrams of systems, energy, and economic formulas; working fluid selection coefficient; ideal point method; results of multiobjective optimization; stream parameters; and the exergy destructions of component (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*Phone: +86 0427 2631518. E-mail: [email protected] (J.B.). ORCID

Xiaopeng Zhang: 0000-0002-6267-9851 Ning Zhang: 0000-0003-2893-5505 Junjiang Bao: 0000-0002-0123-1252

■

CONCLUSIONS In this paper, the superstructures of 2C-ORC and 3C-ORC are constructed, which contain different compression and expansion layouts. At the same time, the working fluid selection coefficients are introduced. The cycle configuration and working fluid are optimized simultaneously by the onestep optimization method. First, the net output power and the total cost are taken as the objective functions for the singleobjective optimizations, respectively. Then multiobjective optimization of the systems is carried out to determine the optimal design parameters. The following conclusions can be obtained after the present work: 1. When the maximum net output power is taken as the objective, under different LNG gasification pressures, the 3C-ORC with the serial compression and expansion layouts and the binary working fluid mainly composed of C2H4 or C2H6 are recommended. 2. When the minimum total cost is taken as the objective, under different LNG gasification pressures, the 2C-ORC

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research was financially supported by the National Natural Science Foundation of China (No. 51606025), MOST innovation team in key area (No. 2016RA4053) and the Fundamental Research Funds for the Central Universities (Grant No. DUT19JC05).

■ A ai h h m N n U J

NOMENCLATURE area (m2) the selection coefficient specific enthalpy (J/kg) specific enthalpy (J/kg) mass flow rate (kg/s) annual operating time system life heat transfer coefficient (W·m−1·K−1) DOI: 10.1021/acssuschemeng.9b03146 ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

Research Article

ACS Sustainable Chemistry & Engineering W xi Ż CI Ż OM Ż i φ λ

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power output (kW) the molar fraction of component i of the working fluid initial investment cost of a component maintenance cost of a component the initial cost of the component i maintenance factor annual interest rate

ABBREVIATIONS Cond condenser C investment cost CRF initial investment recovery factor Evap evaporator LNG liquefied natural gas NG natural gas ORC organic Rankine cycle SW Sea water WF working fluid Subscripts

i j k min max net tot

■

the number of turbine or pump the number of compression layout the number of expansion layout minimum maximum net power output total

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L


Energy and Economic Optimization of the Multistage Condensation

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