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Optimal design and thermo-economic analysis of an integrated power generation system in natural gas pressure reduction stations
Energy Conversion and Management 200 (2019) 112079
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Optimal design and thermo-economic analysis of an integrated power generation system in natural gas pressure reduction stations Chenghao Li, Siyang Zheng, Jie Li, Zhiyong Zeng
T
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School of Energy Science and Engineering, Central South University, Changsha, Hunan 410083, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Natural gas Pressure reduction stations Thermo-economic analysis Low-grade heat Multi-objective optimization
A massive amount of byproduct energy of natural gas including pressure and cold energy is released during the natural gas depressurization process in pressure reduction stations. In this paper, a novel integrated power generation system is proposed to make joint use of the byproduct energy in pressure reduction stations and lowgrade heat. The integrated system consists of two subsystems: a natural gas expansion subsystem recovers the pressure energy of natural gas, an organic Rankine cycle subsystem retrieves the cold energy of natural gas and low-grade heat. A multi-objective optimization model which comprehensively considers the thermodynamic and economic performance of the proposed system is established. Optimal determination of key design parameters including intermediate temperature and minimum approach temperatures is investigated under different heat source conditions. Based on the optimization results, the thermo-economic analysis of the proposed system is conducted to give guidance for further optimization. The simulation result shows that there exhibit positive linear correlations between optimal intermediate temperature and minimum approach temperatures with heat source conditions. With the optimized parameters, the performance of the proposed system is enhanced compared to the separated natural gas expansion and organic Rankine cycle systems. Net power output and exergy efficiency are improved by 17.15% and 22.37%. The cost of electricity is reduced by 42.23%. This paper provides an efficient solution to retrieve the byproduct energy in pressure reduction stations as well as low-grade heat.
1. Introduction Over the past decade, the shortage and environmental pollution of conventional fossil fuels such as coal and petroleum have stimulated the transformation of the energy structure. The clean energies emerge as promising supplements in which natural gas is an ideal choice for its cleanness, extensive reserves, vast distribution, and, high caloric value [1]. Natural gas now has gathered global concentration, the exploitation and utilization are developing at a high speed. It is reported that natural gas will become the second leading primary energy by 2030 [2]. With the rapid progress of natural gas trade, transportation industries of natural gas have developed quickly. Conveying through high-pressure pipeline is a dominant method which occupies about 70% of the trade market worldwide [3]. For the sake of reducing energy loss and constructing investment, natural gas is usually compressed before pipeline transportation which consumes a great amount of energy [4]. When the high-pressure natural gas reaches the demand region, it requires to be depressurized in pressure reduction stations (PRSs) or city gate stations (CGSs). During the natural gas depressurization process, a
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great mass of byproduct energy releases including pressure energy and extra cold energy obtained due to the adiabatic expansion effect [5]. In most practical PRSs, a pressure regulator is employed for gas decompression. By this means, the byproduct energy of natural gas is abandoned, in contrast, additional energy is required for gas heating [6]. Hence, the effective recovery of the byproduct energy in PRSs has become a focus, and heightens the need for the developments of novel system designs. Many researchers have explored high-efficiency energy recovery systems. There are mainly two kinds of systems used for utilizing the byproduct energy in PRSs which are pre-heating and post-heating scheme (as shown in Fig. 1). The pre-heating scheme requires external heat sources to heat natural gas before its expansion process. The general method is to employ an indirect water bath heater [7], electric heater [8], or a gas boiler [9] to realize this aim. The high-pressure natural gas depressurizes in an expander and electricity is generated [10]. The post-heating scheme is a novel idea in which the pressure and cold energy of natural gas are both retrieved [11]. The cold energy can be used for power generation, building cooling, liquefaction of natural
Corresponding author. E-mail address: [email protected] (Z. Zeng).
https://doi.org/10.1016/j.enconman.2019.112079 Received 11 July 2019; Received in revised form 11 September 2019; Accepted 15 September 2019 Available online 19 September 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.
Energy Conversion and Management 200 (2019) 112079
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Nomenclature
Subscript
Symbol
1–7 hs ng wf eva cond tur exp reh pump sup cw OM FOM in
Q m h E e P T s W Wnet ηex C Ea Ta i N A U ΔTLM CRF COE H α β
heat duty, kW mass flow rate, kg/s specific enthalpy, kJ/kg exergy, kW specific exergy, kJ/kg pressure, bar temperature, K entropy, kJ/(kg*K) power, kW net power output, kW system exergy efficiency capital cost, $ annual electricity generation, kWh annual operation time, h annual interest rate life time of the system, year area of heat exchangers, m2 overall heat transfer coefficient, W/(m2*K) logarithm mean temperature difference capital recovery factor cost of electricity, $/kWh annual operation time, hour weight coefficient of the evaluation function weight coefficient of the evaluation function
N1-N4 state points of the system heat source natural gas working fluid evaporator condenser turbine expander reheater feed pump supply cooling water operation and maintenance expense fixed O&M expense inflection point
Abbreviation IPGS PRS CGS NGE ORC POE COE CRF
integrated power generation system pressure reduction station city gate station natural gas expansion organic Ranking cycle price of electricity cost of electricity capital recovery factor
Fig. 1. The schematic diagram of the energy recovery systems: (a) pre-heating scheme, (b) post-heating scheme.
low-grade heat (50–100 °C). Gord et al. [17] employed a collector array and a storage tank in PRSs, the simulation result shows that the system unveils an acceptable economic performance. They also studied the possibility of employing geothermal as the heat source [18]. Cascio et al. [19] investigated the scenario of using sun-tracking parabolic trough solar collectors in different regions. They found that it is possible to realize carbon-free conditions in summer period. For the PRSs located near industrial regions, using waste heat [20] or co-generative unit [21] to preheat natural gas is also an alternative. However, using low-grade heat to heat the high-pressure directly limits the flexibility of heat source conditions, and may cause energy waste. From the mentioned literature, it is found that there still exists potentials to fully utilize the cold energy of the post-heating scheme, and to combine low-grade heat with energy recovery systems in PRSs. In this paper, a novel integrated power generation system (IPGS) is proposed which consists of a natural gas expansion (NGE) subsystem and an organic Rankine cycle (ORC) subsystem. The NGE subsystem
gas, hydrogen production and other industrial process requiring cold energy [12]. More recent attention has been devoted to proposing different ways to preheat natural gas and optimizing system structures. Howard et al. [13] employed fuel cells to heat natural gas before expansion and to produce more electricity. Based on the simulation results, the maximum efficiency is increased by 10% via adding a fuel cell into the system and better economic performance is attained. An integrated system of an internal combustion engine (ICE) and an ORC system was proposed by Kostowski et al. [14]. They pointed out that the ICE system and ICE/ ORC system have better performance compared to the conventional throttling system. Saadat-Targhi et al. [15] proposed to use an organic Rankine flash cycle and a thermoelectric generator to enhance the power output. Sanaye et al. [16] proposed to use a gas boiler and an engine to co-generate the heat and electricity. Along with the development of industries and prevalence of renewable energies including solar, geothermal energy, of particular massive and extensive is the 2
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recovers the pressure energy of natural gas, while the ORC subsystem retrieves the cold energy which is obtained in the natural gas expansion process, in the meantime, it could effectively convert low-grade heat to electricity. A multi-objective optimization model is built and the optimal key parameters are investigated. The thermo-economic analysis of the system is conducted under various heat source conditions. Results show that two subsystems are mutually enhanced thus the comprehensive performance of the IPGS is better than the separated NGE and ORC systems. This paper aims to explore a potential way to utilize the byproduct energy in PRSs and low-grade heat, and to provide guidance for further system optimization of the IPGS. 2. System description The schematic presentation of the IPGS is illustrated in Fig. 2. The IPGS consists of two subsystems: an NGE and an ORC subsystem. The ORC subsystem includes four components: an evaporator, a condenser, a feed pump, and a turbine. The NGE subsystem is composed of three main parts: a natural gas expander, a heater, and a reheater, in which the heater also works as the condenser in the ORC subsystem. The ORC subsystem utilizes low-grade heat including industrial waste heat, solar energy or shallow geothermal energy. Meanwhile, the cold energy of natural gas obtained due to the adiabatic expansion effect is used as the heat sink. An expander recovers the pressure energy of natural gas in the NGE subsystem. The electricity generated by the turbine and expander is provided for local PRSs or power consumers nearby. The T-s diagram of the IPGS is presented in Fig. 3. The specific working processes are described as follows. In the ORC subsystem, the working fluid is heated to the saturated vapor state in the evaporator (process 2–4), then is sent to the turbine for electricity generation (process 4–5). The exhaust gas released from the turbine then enters the condenser where the gas is cooled to the saturated liquid state by the depressurized natural gas (process 5–1). At last, the fluid is pressurized by the feed pump (process 1–2). The heat source (assuming as hot water) exchanges heat with the working fluid in the evaporator then is released to the environment or for other usages. In the NGE subsystem, the high-pressure natural gas depressurizes in the expander (process N1-N2), the retrievable pressure energy is recovered and extra cold energy is obtained. Then, the natural gas is heated in the condenser and the cooling duty is used for the condensation (process N2-N3). After that, natural gas is further heated by environmental heat sources (i.e. cooling water) to room temperature (process N3-N4), eventually, is sent to next stage PRSs or local natural gas end users. In the IPGS, the natural gas is heated in a cascade approach: the gas released from the expander first heated in the condenser to a certain
Fig. 3. The T-s diagram of the integrated power generation system.
temperature then is reheated in the reheater by cooling water. In this paper, intermediate temperature is used to name the outlet temperature of natural gas in the condenser, which corresponds to TN3 in the T-s diagram (Fig. 3). 3. Mathematical modeling The performance analysis of the system solely from the view of thermodynamics is difficult to describe system performances, comprehensively and realistically, especially for actual engineering projects. Taking economic characteristics of the system into consideration facilitates us to thoroughly evaluate system performances. The thermodynamic and economic models of the IPGS are built in this section. Some reasonable assumptions have been made in this paper: (1) The whole system works in a steady state. (2) The pressure drops in heat exchangers and pipes are ignored. The heat and friction losses are negligible in all components and pipes. (3) The land capital cost and maintenance fees are out of consideration in the economic model. (4) Natural gas is simplified as pure methane.
Fig. 2. The schematic presentation of the integrated power generation system. 3
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so on [23]. These indicators have their suitable scopes of application and merits and there is no precise information about which index could better evaluate economic characteristics of a power generation system [24]. In this study, cost of electricity (COE) is selected as the economic indicator, which considers total expenses during the lifetime of the project and the associated power generation [25]. COE is defined as follows [26].
3.1. Thermodynamic modeling The thermodynamic model consists of an energy and an exergy submodel. The former submodel reveals the energy transfer between the system and the environment, while the latter one evaluates exergy losses in system components. The exergy of a material stream is composed of four parts which are physical exergy (i.e. thermodynamic exergy), chemical exergy, kinetic exergy, and potential exergy. In this paper, only physical exergies of streams are considered since combustion processes are not involved in the system and kinetic and potential exergies are negligible [22]. The physical exergy of each stream is expressed as:
E = m ·e = m [(h − h 0) − T0 (s − s0)]
(1)
The following equations are used for building the energy and exergy submodels of system components. For evaporator:
Qeva = m wf (h4 − h2) = mhs (h6 − h7)
(2)
El, eva = E6 − (E4 − E2)
(3)
(4)
El, cond = E5 − E1 − (EN 3 − EN 2)
(5)
For feed pump:
Wpump = m wf (h2 − h1)
(6)
El, pump = E2 − E1 + Wpump
(7)
(15)
COM = CFOM + Ccw
(16)
CFOM = 0.05 ∗ Ccapital
(17)
E = H ·Wnet
(18)
H = 0.9 ∗ 24 ∗ 365 = 7884 h
(19)
N CRF = i (1 + i) ((1 + i) N − 1)
(20)
where CRF is capital recovery factor, i and N represent annual interest rate and the lifetime of the project, here are set as 5% and 20 years, respectively. E denotes annual electricity generation of the IPGS, H is annual operation time. The operation and maintenance expense consists of fixed O&M expenses and cooling water consumption. The cooling water price is 0.35 $/GJ [27]. The IPGS is composed of six main components: evaporator, condenser, turbine, pump, reheater, and natural gas expander. The capital cost of each component is determined by the following correlations [28–31]:
For condenser:
Qcond = m wf (h5 − h1) = mng (hN 3 − hN 2)
COE = (CRF ·Ccapital + COM ) Ea
0.89 Ceva = Ccond = 1397·Aeva , cond
Creh =
For turbine:
(21)
0.514 2143·Areh
(22)
Wtur = m wf (h4 − h5)
(8)
0.89 Ctur = 4405·Wtur
(23)
El, tur = E4 − E5 − Wtur
(9)
0.8 Cpump = 1120·W pump
(24)
For natural gas expander:
Wexp = mng (hN 1 − hN 2)
(10)
El, exp = EN 1 − EN 2 − Wexp
(11)
(
) (
)
Cex = 1536· mng 0.93 − η ·ln pN 2 p ·[1 − exp(0.036TN 1 − 54.4)] isen, ex N1 (25) where A denotes the area of heat exchangers, which is calculated as follows:
For the IPGS, the overall thermodynamic performance of the system could not be exhibited by a single indicator. The present work uses two indexes namely net power output of the system (Wnet ), and system exergy efficiency (ηex ) for thermodynamical evaluation of the IPGS. Wnet shows the power generation capacity of the IPGS, while ηex reflects the recovering extent of natural gas and low-grade heat. The definitions of the above indicators are as follows.
Wnet = Wtur + Wexp − Wpump ηex = 1 − (El, eva + El, cond + El, pump + El, tur + El, exp ) Esup
A = Q U ΔTLM
where U is the overall heat transfer coefficient, and ΔTLM the logarithm mean temperature difference. 3.3. Multi-objective optimization model
(12) To determine the optimal design parameters from both thermodynamic and economic points of view for achieving a comprehensively optimal system design, Wnet and COE are selected to establish the multiobjective optimization model. The first objective function F1 (X ) is expressed by:
(13)
with
Esup = E6 + (EN 4 − EN 1)
(26)
(14)
Max: F1 (X ) =
where Esup denotes the supply exergy of the system which is composed of heat source and natural gas supply exergy. It is worth to note that the heat source supply exergy only consists of the inlet exergy rather than the exergy change of the heat source. Since recovering low-grade heat is one of the targets of the IPGS, considering the low-grade heat recovering extent is a necessity of system evaluation.
WNGE + WORC WNGE , ref + WORC , ref
(27)
The second objective function F2 (X ) is expressed by:
Max: F2 (X ) =
COENGE , ref + COEORC , ref COENGE + COEORC
(28)
here, NGE and ORC reference systems are built as base cases. The NGE reference system has the same configurations with the NGE subsystem except the heater is absent. That is, the NGE reference system only recovers the pressure energy of natural gas. The ORC reference system utilizes cooling water (25 °C) as the heat sink and this is the general scenario for low-grade heat recovering.
3.2. Economic modeling The economic performance of a power generation system can be revealed by various indicators like total capital cost of the system, net present value (NPV), static or dynamic payback period (SPP/DPP) and 4
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There are many available methods to solve the multi-objective issues including hierarchical sequence method, constraint method, and evaluation function method [31]. Here, the linear weighted evaluation function is adopted in this paper to deal with the optimization process. The evaluation function is determined as:
the hot and cold stream in heat exchangers which is essential for system design. Based on the optimization results, the thermo-economic analysis of the IPGS including the analyses of exergy loss and capital cost are conducted in the last part of this section.
F (X ) = αF1 (X ) + βF2 (X )
4.1. Determination of the intermediate temperature
(29)
where α , β is the weight coefficients of the evaluation function, which is introduced in Ref. [32]. The determination of the coefficients are as follows: 1 2 α = (F2 − F2 ) [(F12 − F11) + (F21 − F22 )]
(30)
2 1 β = (F1 − F1 ) [(F12 − F11) + (F21 − F22 )]
F11
The IPGS makes combined use of the byproduct energy of the highpressure natural gas and low-grade heat. For different application situations, the low-grade heat may derive from adjacent manufacturing factories, industries or distributed renewable energy equipment. Thus, the heat source conditions including temperature, mass flow rate, have a variant. Considering this issue, determining the intermediate temperature regarding various heat source conditions is of great significance.
(31)
F12
where is the maximum value of F1 (X ) , is the value of F1 (X ) when F2 (X ) obtains the maximum value, F22 is the maximum value of F2 (X ) , F21 is the value of F2 (X ) when F1 (X ) gets the maximum value. F1 (X ) and F2 (X ) have clear physical meanings. F1 (X ) is the ratio of net power outputs of the NGE and ORC subsystems to those of the NGE and ORC reference systems. It reveals the thermodynamic performance enhancement of the IPGS, while F2 (X ) indicates the economic performance enhancement. F(X) considers both the thermodynamic and economic performance enhancements of the IPGS compared to the base cases. Thus, F(X) indicates the comprehensive performance enhancement of the IPGS. If F(X) value is greater than 1, the IPGS has better comprehensive performance than base cases.
4.1.1. The heat source temperature analysis In this section, the determination of the intermediate temperature under different heat source temperatures is performed. The minimum approach temperatures are set as 5 K and the heat source mass flow rate is constant at 1 kg/s. Fig. 5 shows the variation of system performances including (a) net power output, (b) system exergy efficiency with different heat source temperatures and intermediate temperatures. It is clearly seen from Fig. 5(a) that, when the heat source temperature is certain, the net power output first increases then decreases with the increase of the intermediate temperature which reveals a peak point. When the heat source temperature varies, the optimal intermediate temperatures corresponding to the peak points make up an optimal line. Interestingly, with the further increase of the heat source temperature, the optimal intermediate temperature is constant at 283 K which equals to the upstream temperature of natural gas. Then an inflection point occurs which indicates that the reheater is excessive for the system. Moreover, the net power output increase with the increase of the heat source temperature. The explanation of the above phenomena is that, as the intermediate temperature increases, the working fluid mass flow rate of the ORC subsystem increases while the enthalpy drop in the turbine decreases, which results in an optimal value. It can be seen from Fig. 5(b) that, when the heat source temperature is constant, with the increase of the intermediate temperature, the system exergy efficiency first increases then decreases and a peak point exists. The optimal intermediate temperatures form an optimal line and an inflection point exists as well. In addition, as the heat source temperature increases, the system exergy efficiency decreases. This can be explained as follows. The higher the heat source temperature, the higher the outlet exergy of heat source, and the greater the exergy loss in the evaporator. Hence, a lower exergy efficiency is obtained. Fig. 6 presents the variation of the objective function F(X) with different heat source temperatures and intermediate temperatures. It can be seen that, with the increase of the heat source temperature, the optimal intermediate temperature increases. There exhibits an optimal line to make the objective function F(X) maximal and an inflection point. Moreover, it is found that, the F(X) value first decreases then
3.4. Selection of the working fluids of the ORC system The ORC system plays an important role in the integrated power generative system which generates electricity as well as recovers lowgrade heat. The choice of working fluids significantly affects the performance of the ORC system. The organic working fluids are mainly categorized into three kinds according to the temperature-entropy diagram, namely dry fluids, wet fluids, and isentropic fluids. The differences are the scopes of the saturated vapor curve in the T-s diagram, where dry fluids have a positive scope while wet fluids show a negative scope and isentropic fluids show a vertical saturated vapor curve. Wet fluids are not adequately suitable for ORC system since they pose a threat to the turbine when the stream quality of the turbine outlet is within the critical value. R141b is a dry fluid and selected as the working fluid of the ORC subsystem in this work. 3.5. Calculation parameters and optimization processes The present work mainly aims to determine the optimal design parameters of the IPGS, which makes use of the byproduct energy of natural gas in PRSs as well as low-grade heat. Natural gas is simplified as pure methane. The basic conditions and calculation parameters relevant to the system components are listed in Table 1. A Matlab program is written for the simulation in the present study. The thermodynamic properties of material streams are calculated on the basis of the Peng-Robinson equation of states. The optimization process is under a specific solution logic given in Fig. 4.
Table 1 The basic conditions and calculation parameters.
4. Results and discussion The determination of the optimal parameters and thermo-economic analysis of the system are performed in this section. The multi-objective optimization method is applied to determine the key parameters of the system including intermediate temperature, and minimum approach temperatures in the condenser and evaporator under different heat source conditions. The intermediate temperature is a critical design parameter since it affects both the performances of the NGE and ORC subsystem. The approach temperature is the temperature difference of 5
Parameters
Value
Mass flow rate of natural gas Upstream and downstream pressure of natural gas Upstream and downstream temperatures of natural gas Isentropic efficiency of the turbine Isentropic efficiency of the natural gas expander Adiabatic efficiency of the feed pump Overall heat transfer coefficient of the evaporator Overall heat transfer coefficient of the condenser Overall heat transfer coefficient of the reheater
1 kg/s 40/20 bar 283 K 85% 80% 80% 850 W/(m2·K) [33] 250 W/(m2·K) [33] 200 W/(m2·K) [33]
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Fig. 5. The variation of system performances including (a) net power output, (b) system exergy efficiency with different heat source temperatures and intermediate temperatures.
Fig. 4. The calculation procedure of the power generation system.
increases along the optimal line which exhibits two peak regions. In the low heat source temperature situation, the COE of the ORC reference system is much greater than that of the ORC subsystem, the economic performance enhancement of the IPGS is more obvious which reveals a peak region. In the high heat source temperature situation, the power output enhancement of the IPGS is more significant which also exhibits a peak region. It is concluded that, setting the net power output, system exergy efficiency or F(X) as objective, the optimal intermediate temperature increases with the increase of heat source temperature, which make up an optimal line. With the further increase of the heat source temperature, an inflection point occurs on the optimal line. This means that the reheater is redundant for the system. Moreover, the economic performance enhancement of the IPGS is pronounced in the low heat source temperature situation, while the thermodynamic performance enhancement is more significant under the high heat source temperature circumstance. Thus, the objective function F(X) shows two peak regions.
Fig. 6. The variation of the objective function F(X) with different heat source temperatures and intermediate temperatures.
4.1.2. The heat source mass flow rate analysis In the present section, the determination of the intermediate temperature under different heat source mass flow rates is performed. The heat source is constant at 373 K and the minimum approach 6
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temperature. The conclusion can be drawn that the comprehensive performance of the IPGS is obviously better than the NGE and ORC reference systems.
temperatures are set as 5 K. Fig. 7 depicts the variation of system performances including (a) net power output, (b) system exergy efficiency with different heat source mass flow rates and intermediate temperatures. It is seen from Fig. 7(a) that the net power output has no obvious change with the mass flow rate under the low intermediate temperature situation. When the intermediate temperature increases, the greater the mass flow rate, the greater the net power output. It is seen from Fig. 7(b) that, the lower the mass flow rate, the higher the system exergy efficiency. This is because that, the lower the mass flow rate, the lower the heat source outlet exergy, which means a higher heat source recovering extent as well as system exergy efficiency are obtained. Fig. 8 shows the variation of the objective function F(X) with different heat source mass flow rates and intermediate temperatures. It is seen that, under a given heat source temperature, the objective function F(X) has no significant variation with heat source mass flow rate. To fully investigate the combined effects of the temperature and mass flow rate of the heat source on determining the intermediate temperature, Fig. 9 illustrates the variation of the optimal intermediate temperature maximizing objective function F(X) under different heat source temperatures and mass flow rates. It is clearly seen that with the increase of the heat source temperature, the optimal intermediate temperature increases. With the further increase of the heat source temperature, the optimal intermediate temperature reaches the inflection point. It is also found that as the mass flow rate increases, the optimal intermediate temperature increases under a given heat source temperature, in addition, the inflection point occurs at a lower heat source temperature.
4.3. The analysis of the exergy loss in system components The exergy analysis of system components is performed in this section. Here, the intermediate temperature and minimum approach temperatures are set as optimal value based on the above analysis. Fig. 11 shows the ratio of exergy loss in the components under different heat source conditions including (a) heat source temperature, (b) heat source mass flow rate. It is seen from Fig. 11(a) that, the exergy loss in the expander has the largest portion, followed by the condenser and evaporator. It is found that with the increase of the heat source temperature, the portion of expander decreases while that of evaporator increases. It is concluded that the exergy loss in the expander has the largest proportion when the heat source temperature is low. For the cases where temperature and mass flow rate of the heat source are high, the exergy loss in the evaporator occupies most of the ratio of total exergy loss. 4.4. The analysis of the capital costs of system components The analysis of capital cost is of great significance in the design stage of the IPGS. The capital costs of system components under different heat source conditions are analyzed in this section. The
4.2. Determination of the minimum approach temperatures Minimum approach temperature is a key parameter that both related to the thermodynamic performance of the system as well as economic performance. Hence, a good design regarding the minimum approach temperatures in the evaporator and condenser could improve the comprehensive performance of the IPGS. In this section, the determination of optimal minimum approach temperatures under various heat source mass flow rates is conducted. The heat source temperature is constant at 373 K, and the intermediate temperature is optimized based on the results of the previous section. In addition, the minimum approach temperatures in the evaporator and condenser are equal and change simultaneously in the following analysis. Fig. 10 presents the variation of objective function F(X) with different heat source mass flow rates and minimum approach temperatures. It is seen that, keeping the mass flow rate constant, the objective function F(X) shows a peak point with the increase of the minimum approach temperature. With the increase of the mass flow rate, the optimal minimum approach temperature increases and forms an optimal line. This is because, under a fixed heat source temperature, a lower minimum approach temperature results in greater power output, however, it also leads to a larger heat transfer area. A higher minimum approach temperature results in poor thermodynamic performance but better economic performance. Thus, the comprehensive performance exhibits an optimal point. Under a certain pressure range (i.e. 20–40 bar), and heat source conditions (temperature = 373 K, mass flow rate = 1 kg/s), the performance comparison of the IPGS and the reference systems is shown in Table 2. It is clearly seen that the net power output and exergy efficiency are enhanced by 17.15% and 22.37%, respectively. The COE is reduced by 42.23%. Compared to the conventional energy recovering systems in PRSs which only utilizes the pressure energy of natural gas and the ORC system utilizing cooling water as the heat sink, the performances of the NGE and ORC subsystems are mutually enhanced. The NGE subsystem is boosted by recovering maximum byproduct energy of natural gas including the pressure and cold energy. At the same time, the ORC subsystem is enhanced as well due to lower condensation
Fig. 7. The variation of system performances including (a) net power output, (b) system exergy efficiency with different heat source mass flow rates and intermediate temperatures. 7
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Table 2 The performance comparison of the IPGS and the reference systems. Heat source conditions: temperature = 373 K, mass flow rate = 1 kg/s Optimal design parameters Intermediate temperature/K Minimum approach temperatures/K
283 6.2
System performance comparison Indicators
The reference systems
The IPGS
Performance enhancement
Net power output/kW Exergy efficiency COE/$·kWh−1
69.78 0.514 0.1177
81.75 0.629 0.068
17.15% 22.37% 42.23%
Fig. 8. The variation of the objective function F(X) with different heat source mass flow rates and intermediate temperatures.
Fig. 9. The variation of the optimal intermediate temperature maximizing objective function F(X) under different heat source temperatures and mass flow rates.
Fig. 11. The ratio of exergy loss in system components under different heat source conditions including (a) heat source temperature, (b) heat source mass flow rate.
intermediate temperature and minimum approach temperatures are optimized. Fig. 12 shows the ratio of capital costs in system components under different heat source conditions including (a) heat source temperature, (b) heat source mass flow rate. It is seen from Fig. 12(a) that the turbine has the largest capital cost ratio, then follows the condenser and evaporator. Moreover, with the increase of the heat source temperature, the ratio of capital cost of the turbine increases while that of the condenser and reheater decrease. From Fig. 12(b), it is found that as
Fig. 10. The variation of objective function F(X) with different heat source mass flow rates and minimum approach temperatures.
8
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increase of the heat source temperature and mass flow rate. when heat source temperature further increases, natural gas is no need to be reheated and the IPGS becomes simpler. In addition, the optimal minimum approach temperature increases with the increase of the heat source mass flow rate. With the optimized design parameters, the performances of the NGE and ORC subsystems are mutually enhanced, the IPGS shows better comprehensive performance than the NGE and ORC reference systems. The net power output and exergy efficiency are improved by 17.15% and 22.37%, respectively. The COE is reduced by 42.23%. Moreover, the thermodynamic performance improvement of the IPGS is more obvious under high heat source temperature situation, while the economic performance improvement of the IPGS is more significant under low heat source temperature circumstance. The thermo-economic analysis of the IPGS shows that the expander and evaporator are the maximum components of exergy loss, accounting for 74.14%–93.67% with the increase of the heat source temperature and mass flow rate. The capital of the turbine takes up the majority of the total capital of the IPGS, accounting for 36.24%–58.04% with the increase of the heat source temperature, and heat source mass flow exerts a non-significant effect on the capital of the turbine. For further optimization of the IPGS, increasing the efficiency of the expander and decreasing the capital of the turbine would dramatically improve the performance and benefit of the IPGS. This paper provides a feasible and efficient solution to recover the byproduct energy in PRSs as well as low-grade heat. All the components in the IPGS are commercially available. There shows no serious obstacle to practical applications. Declaration of Competing Interest 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. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 21506257), the Fundamental Research Funds for the Central Universities of Central South University (No. 2019zzts535).
Fig. 12. The ratio of capital costs of system components under different heat source conditions including (a) heat source temperature, (b) heat source mass flow rate.
heat source mass flow rate increases, the ratio of capital cost of the turbine has a gentle change while that of the evaporator increases. It is concluded that heat source temperature has a more obvious impact on the capital costs of system components than heat source mass flow rate.
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Optimal design and thermo-economic analysis of an integrated power generation system in natural gas pressure reduction stations Chenghao Li, Siyang Zheng, Jie Li, Zhiyong Zeng
T
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School of Energy Science and Engineering, Central South University, Changsha, Hunan 410083, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Natural gas Pressure reduction stations Thermo-economic analysis Low-grade heat Multi-objective optimization
A massive amount of byproduct energy of natural gas including pressure and cold energy is released during the natural gas depressurization process in pressure reduction stations. In this paper, a novel integrated power generation system is proposed to make joint use of the byproduct energy in pressure reduction stations and lowgrade heat. The integrated system consists of two subsystems: a natural gas expansion subsystem recovers the pressure energy of natural gas, an organic Rankine cycle subsystem retrieves the cold energy of natural gas and low-grade heat. A multi-objective optimization model which comprehensively considers the thermodynamic and economic performance of the proposed system is established. Optimal determination of key design parameters including intermediate temperature and minimum approach temperatures is investigated under different heat source conditions. Based on the optimization results, the thermo-economic analysis of the proposed system is conducted to give guidance for further optimization. The simulation result shows that there exhibit positive linear correlations between optimal intermediate temperature and minimum approach temperatures with heat source conditions. With the optimized parameters, the performance of the proposed system is enhanced compared to the separated natural gas expansion and organic Rankine cycle systems. Net power output and exergy efficiency are improved by 17.15% and 22.37%. The cost of electricity is reduced by 42.23%. This paper provides an efficient solution to retrieve the byproduct energy in pressure reduction stations as well as low-grade heat.
1. Introduction Over the past decade, the shortage and environmental pollution of conventional fossil fuels such as coal and petroleum have stimulated the transformation of the energy structure. The clean energies emerge as promising supplements in which natural gas is an ideal choice for its cleanness, extensive reserves, vast distribution, and, high caloric value [1]. Natural gas now has gathered global concentration, the exploitation and utilization are developing at a high speed. It is reported that natural gas will become the second leading primary energy by 2030 [2]. With the rapid progress of natural gas trade, transportation industries of natural gas have developed quickly. Conveying through high-pressure pipeline is a dominant method which occupies about 70% of the trade market worldwide [3]. For the sake of reducing energy loss and constructing investment, natural gas is usually compressed before pipeline transportation which consumes a great amount of energy [4]. When the high-pressure natural gas reaches the demand region, it requires to be depressurized in pressure reduction stations (PRSs) or city gate stations (CGSs). During the natural gas depressurization process, a
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great mass of byproduct energy releases including pressure energy and extra cold energy obtained due to the adiabatic expansion effect [5]. In most practical PRSs, a pressure regulator is employed for gas decompression. By this means, the byproduct energy of natural gas is abandoned, in contrast, additional energy is required for gas heating [6]. Hence, the effective recovery of the byproduct energy in PRSs has become a focus, and heightens the need for the developments of novel system designs. Many researchers have explored high-efficiency energy recovery systems. There are mainly two kinds of systems used for utilizing the byproduct energy in PRSs which are pre-heating and post-heating scheme (as shown in Fig. 1). The pre-heating scheme requires external heat sources to heat natural gas before its expansion process. The general method is to employ an indirect water bath heater [7], electric heater [8], or a gas boiler [9] to realize this aim. The high-pressure natural gas depressurizes in an expander and electricity is generated [10]. The post-heating scheme is a novel idea in which the pressure and cold energy of natural gas are both retrieved [11]. The cold energy can be used for power generation, building cooling, liquefaction of natural
Corresponding author. E-mail address: [email protected] (Z. Zeng).
https://doi.org/10.1016/j.enconman.2019.112079 Received 11 July 2019; Received in revised form 11 September 2019; Accepted 15 September 2019 Available online 19 September 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature
Subscript
Symbol
1–7 hs ng wf eva cond tur exp reh pump sup cw OM FOM in
Q m h E e P T s W Wnet ηex C Ea Ta i N A U ΔTLM CRF COE H α β
heat duty, kW mass flow rate, kg/s specific enthalpy, kJ/kg exergy, kW specific exergy, kJ/kg pressure, bar temperature, K entropy, kJ/(kg*K) power, kW net power output, kW system exergy efficiency capital cost, $ annual electricity generation, kWh annual operation time, h annual interest rate life time of the system, year area of heat exchangers, m2 overall heat transfer coefficient, W/(m2*K) logarithm mean temperature difference capital recovery factor cost of electricity, $/kWh annual operation time, hour weight coefficient of the evaluation function weight coefficient of the evaluation function
N1-N4 state points of the system heat source natural gas working fluid evaporator condenser turbine expander reheater feed pump supply cooling water operation and maintenance expense fixed O&M expense inflection point
Abbreviation IPGS PRS CGS NGE ORC POE COE CRF
integrated power generation system pressure reduction station city gate station natural gas expansion organic Ranking cycle price of electricity cost of electricity capital recovery factor
Fig. 1. The schematic diagram of the energy recovery systems: (a) pre-heating scheme, (b) post-heating scheme.
low-grade heat (50–100 °C). Gord et al. [17] employed a collector array and a storage tank in PRSs, the simulation result shows that the system unveils an acceptable economic performance. They also studied the possibility of employing geothermal as the heat source [18]. Cascio et al. [19] investigated the scenario of using sun-tracking parabolic trough solar collectors in different regions. They found that it is possible to realize carbon-free conditions in summer period. For the PRSs located near industrial regions, using waste heat [20] or co-generative unit [21] to preheat natural gas is also an alternative. However, using low-grade heat to heat the high-pressure directly limits the flexibility of heat source conditions, and may cause energy waste. From the mentioned literature, it is found that there still exists potentials to fully utilize the cold energy of the post-heating scheme, and to combine low-grade heat with energy recovery systems in PRSs. In this paper, a novel integrated power generation system (IPGS) is proposed which consists of a natural gas expansion (NGE) subsystem and an organic Rankine cycle (ORC) subsystem. The NGE subsystem
gas, hydrogen production and other industrial process requiring cold energy [12]. More recent attention has been devoted to proposing different ways to preheat natural gas and optimizing system structures. Howard et al. [13] employed fuel cells to heat natural gas before expansion and to produce more electricity. Based on the simulation results, the maximum efficiency is increased by 10% via adding a fuel cell into the system and better economic performance is attained. An integrated system of an internal combustion engine (ICE) and an ORC system was proposed by Kostowski et al. [14]. They pointed out that the ICE system and ICE/ ORC system have better performance compared to the conventional throttling system. Saadat-Targhi et al. [15] proposed to use an organic Rankine flash cycle and a thermoelectric generator to enhance the power output. Sanaye et al. [16] proposed to use a gas boiler and an engine to co-generate the heat and electricity. Along with the development of industries and prevalence of renewable energies including solar, geothermal energy, of particular massive and extensive is the 2
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recovers the pressure energy of natural gas, while the ORC subsystem retrieves the cold energy which is obtained in the natural gas expansion process, in the meantime, it could effectively convert low-grade heat to electricity. A multi-objective optimization model is built and the optimal key parameters are investigated. The thermo-economic analysis of the system is conducted under various heat source conditions. Results show that two subsystems are mutually enhanced thus the comprehensive performance of the IPGS is better than the separated NGE and ORC systems. This paper aims to explore a potential way to utilize the byproduct energy in PRSs and low-grade heat, and to provide guidance for further system optimization of the IPGS. 2. System description The schematic presentation of the IPGS is illustrated in Fig. 2. The IPGS consists of two subsystems: an NGE and an ORC subsystem. The ORC subsystem includes four components: an evaporator, a condenser, a feed pump, and a turbine. The NGE subsystem is composed of three main parts: a natural gas expander, a heater, and a reheater, in which the heater also works as the condenser in the ORC subsystem. The ORC subsystem utilizes low-grade heat including industrial waste heat, solar energy or shallow geothermal energy. Meanwhile, the cold energy of natural gas obtained due to the adiabatic expansion effect is used as the heat sink. An expander recovers the pressure energy of natural gas in the NGE subsystem. The electricity generated by the turbine and expander is provided for local PRSs or power consumers nearby. The T-s diagram of the IPGS is presented in Fig. 3. The specific working processes are described as follows. In the ORC subsystem, the working fluid is heated to the saturated vapor state in the evaporator (process 2–4), then is sent to the turbine for electricity generation (process 4–5). The exhaust gas released from the turbine then enters the condenser where the gas is cooled to the saturated liquid state by the depressurized natural gas (process 5–1). At last, the fluid is pressurized by the feed pump (process 1–2). The heat source (assuming as hot water) exchanges heat with the working fluid in the evaporator then is released to the environment or for other usages. In the NGE subsystem, the high-pressure natural gas depressurizes in the expander (process N1-N2), the retrievable pressure energy is recovered and extra cold energy is obtained. Then, the natural gas is heated in the condenser and the cooling duty is used for the condensation (process N2-N3). After that, natural gas is further heated by environmental heat sources (i.e. cooling water) to room temperature (process N3-N4), eventually, is sent to next stage PRSs or local natural gas end users. In the IPGS, the natural gas is heated in a cascade approach: the gas released from the expander first heated in the condenser to a certain
Fig. 3. The T-s diagram of the integrated power generation system.
temperature then is reheated in the reheater by cooling water. In this paper, intermediate temperature is used to name the outlet temperature of natural gas in the condenser, which corresponds to TN3 in the T-s diagram (Fig. 3). 3. Mathematical modeling The performance analysis of the system solely from the view of thermodynamics is difficult to describe system performances, comprehensively and realistically, especially for actual engineering projects. Taking economic characteristics of the system into consideration facilitates us to thoroughly evaluate system performances. The thermodynamic and economic models of the IPGS are built in this section. Some reasonable assumptions have been made in this paper: (1) The whole system works in a steady state. (2) The pressure drops in heat exchangers and pipes are ignored. The heat and friction losses are negligible in all components and pipes. (3) The land capital cost and maintenance fees are out of consideration in the economic model. (4) Natural gas is simplified as pure methane.
Fig. 2. The schematic presentation of the integrated power generation system. 3
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so on [23]. These indicators have their suitable scopes of application and merits and there is no precise information about which index could better evaluate economic characteristics of a power generation system [24]. In this study, cost of electricity (COE) is selected as the economic indicator, which considers total expenses during the lifetime of the project and the associated power generation [25]. COE is defined as follows [26].
3.1. Thermodynamic modeling The thermodynamic model consists of an energy and an exergy submodel. The former submodel reveals the energy transfer between the system and the environment, while the latter one evaluates exergy losses in system components. The exergy of a material stream is composed of four parts which are physical exergy (i.e. thermodynamic exergy), chemical exergy, kinetic exergy, and potential exergy. In this paper, only physical exergies of streams are considered since combustion processes are not involved in the system and kinetic and potential exergies are negligible [22]. The physical exergy of each stream is expressed as:
E = m ·e = m [(h − h 0) − T0 (s − s0)]
(1)
The following equations are used for building the energy and exergy submodels of system components. For evaporator:
Qeva = m wf (h4 − h2) = mhs (h6 − h7)
(2)
El, eva = E6 − (E4 − E2)
(3)
(4)
El, cond = E5 − E1 − (EN 3 − EN 2)
(5)
For feed pump:
Wpump = m wf (h2 − h1)
(6)
El, pump = E2 − E1 + Wpump
(7)
(15)
COM = CFOM + Ccw
(16)
CFOM = 0.05 ∗ Ccapital
(17)
E = H ·Wnet
(18)
H = 0.9 ∗ 24 ∗ 365 = 7884 h
(19)
N CRF = i (1 + i) ((1 + i) N − 1)
(20)
where CRF is capital recovery factor, i and N represent annual interest rate and the lifetime of the project, here are set as 5% and 20 years, respectively. E denotes annual electricity generation of the IPGS, H is annual operation time. The operation and maintenance expense consists of fixed O&M expenses and cooling water consumption. The cooling water price is 0.35 $/GJ [27]. The IPGS is composed of six main components: evaporator, condenser, turbine, pump, reheater, and natural gas expander. The capital cost of each component is determined by the following correlations [28–31]:
For condenser:
Qcond = m wf (h5 − h1) = mng (hN 3 − hN 2)
COE = (CRF ·Ccapital + COM ) Ea
0.89 Ceva = Ccond = 1397·Aeva , cond
Creh =
For turbine:
(21)
0.514 2143·Areh
(22)
Wtur = m wf (h4 − h5)
(8)
0.89 Ctur = 4405·Wtur
(23)
El, tur = E4 − E5 − Wtur
(9)
0.8 Cpump = 1120·W pump
(24)
For natural gas expander:
Wexp = mng (hN 1 − hN 2)
(10)
El, exp = EN 1 − EN 2 − Wexp
(11)
(
) (
)
Cex = 1536· mng 0.93 − η ·ln pN 2 p ·[1 − exp(0.036TN 1 − 54.4)] isen, ex N1 (25) where A denotes the area of heat exchangers, which is calculated as follows:
For the IPGS, the overall thermodynamic performance of the system could not be exhibited by a single indicator. The present work uses two indexes namely net power output of the system (Wnet ), and system exergy efficiency (ηex ) for thermodynamical evaluation of the IPGS. Wnet shows the power generation capacity of the IPGS, while ηex reflects the recovering extent of natural gas and low-grade heat. The definitions of the above indicators are as follows.
Wnet = Wtur + Wexp − Wpump ηex = 1 − (El, eva + El, cond + El, pump + El, tur + El, exp ) Esup
A = Q U ΔTLM
where U is the overall heat transfer coefficient, and ΔTLM the logarithm mean temperature difference. 3.3. Multi-objective optimization model
(12) To determine the optimal design parameters from both thermodynamic and economic points of view for achieving a comprehensively optimal system design, Wnet and COE are selected to establish the multiobjective optimization model. The first objective function F1 (X ) is expressed by:
(13)
with
Esup = E6 + (EN 4 − EN 1)
(26)
(14)
Max: F1 (X ) =
where Esup denotes the supply exergy of the system which is composed of heat source and natural gas supply exergy. It is worth to note that the heat source supply exergy only consists of the inlet exergy rather than the exergy change of the heat source. Since recovering low-grade heat is one of the targets of the IPGS, considering the low-grade heat recovering extent is a necessity of system evaluation.
WNGE + WORC WNGE , ref + WORC , ref
(27)
The second objective function F2 (X ) is expressed by:
Max: F2 (X ) =
COENGE , ref + COEORC , ref COENGE + COEORC
(28)
here, NGE and ORC reference systems are built as base cases. The NGE reference system has the same configurations with the NGE subsystem except the heater is absent. That is, the NGE reference system only recovers the pressure energy of natural gas. The ORC reference system utilizes cooling water (25 °C) as the heat sink and this is the general scenario for low-grade heat recovering.
3.2. Economic modeling The economic performance of a power generation system can be revealed by various indicators like total capital cost of the system, net present value (NPV), static or dynamic payback period (SPP/DPP) and 4
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There are many available methods to solve the multi-objective issues including hierarchical sequence method, constraint method, and evaluation function method [31]. Here, the linear weighted evaluation function is adopted in this paper to deal with the optimization process. The evaluation function is determined as:
the hot and cold stream in heat exchangers which is essential for system design. Based on the optimization results, the thermo-economic analysis of the IPGS including the analyses of exergy loss and capital cost are conducted in the last part of this section.
F (X ) = αF1 (X ) + βF2 (X )
4.1. Determination of the intermediate temperature
(29)
where α , β is the weight coefficients of the evaluation function, which is introduced in Ref. [32]. The determination of the coefficients are as follows: 1 2 α = (F2 − F2 ) [(F12 − F11) + (F21 − F22 )]
(30)
2 1 β = (F1 − F1 ) [(F12 − F11) + (F21 − F22 )]
F11
The IPGS makes combined use of the byproduct energy of the highpressure natural gas and low-grade heat. For different application situations, the low-grade heat may derive from adjacent manufacturing factories, industries or distributed renewable energy equipment. Thus, the heat source conditions including temperature, mass flow rate, have a variant. Considering this issue, determining the intermediate temperature regarding various heat source conditions is of great significance.
(31)
F12
where is the maximum value of F1 (X ) , is the value of F1 (X ) when F2 (X ) obtains the maximum value, F22 is the maximum value of F2 (X ) , F21 is the value of F2 (X ) when F1 (X ) gets the maximum value. F1 (X ) and F2 (X ) have clear physical meanings. F1 (X ) is the ratio of net power outputs of the NGE and ORC subsystems to those of the NGE and ORC reference systems. It reveals the thermodynamic performance enhancement of the IPGS, while F2 (X ) indicates the economic performance enhancement. F(X) considers both the thermodynamic and economic performance enhancements of the IPGS compared to the base cases. Thus, F(X) indicates the comprehensive performance enhancement of the IPGS. If F(X) value is greater than 1, the IPGS has better comprehensive performance than base cases.
4.1.1. The heat source temperature analysis In this section, the determination of the intermediate temperature under different heat source temperatures is performed. The minimum approach temperatures are set as 5 K and the heat source mass flow rate is constant at 1 kg/s. Fig. 5 shows the variation of system performances including (a) net power output, (b) system exergy efficiency with different heat source temperatures and intermediate temperatures. It is clearly seen from Fig. 5(a) that, when the heat source temperature is certain, the net power output first increases then decreases with the increase of the intermediate temperature which reveals a peak point. When the heat source temperature varies, the optimal intermediate temperatures corresponding to the peak points make up an optimal line. Interestingly, with the further increase of the heat source temperature, the optimal intermediate temperature is constant at 283 K which equals to the upstream temperature of natural gas. Then an inflection point occurs which indicates that the reheater is excessive for the system. Moreover, the net power output increase with the increase of the heat source temperature. The explanation of the above phenomena is that, as the intermediate temperature increases, the working fluid mass flow rate of the ORC subsystem increases while the enthalpy drop in the turbine decreases, which results in an optimal value. It can be seen from Fig. 5(b) that, when the heat source temperature is constant, with the increase of the intermediate temperature, the system exergy efficiency first increases then decreases and a peak point exists. The optimal intermediate temperatures form an optimal line and an inflection point exists as well. In addition, as the heat source temperature increases, the system exergy efficiency decreases. This can be explained as follows. The higher the heat source temperature, the higher the outlet exergy of heat source, and the greater the exergy loss in the evaporator. Hence, a lower exergy efficiency is obtained. Fig. 6 presents the variation of the objective function F(X) with different heat source temperatures and intermediate temperatures. It can be seen that, with the increase of the heat source temperature, the optimal intermediate temperature increases. There exhibits an optimal line to make the objective function F(X) maximal and an inflection point. Moreover, it is found that, the F(X) value first decreases then
3.4. Selection of the working fluids of the ORC system The ORC system plays an important role in the integrated power generative system which generates electricity as well as recovers lowgrade heat. The choice of working fluids significantly affects the performance of the ORC system. The organic working fluids are mainly categorized into three kinds according to the temperature-entropy diagram, namely dry fluids, wet fluids, and isentropic fluids. The differences are the scopes of the saturated vapor curve in the T-s diagram, where dry fluids have a positive scope while wet fluids show a negative scope and isentropic fluids show a vertical saturated vapor curve. Wet fluids are not adequately suitable for ORC system since they pose a threat to the turbine when the stream quality of the turbine outlet is within the critical value. R141b is a dry fluid and selected as the working fluid of the ORC subsystem in this work. 3.5. Calculation parameters and optimization processes The present work mainly aims to determine the optimal design parameters of the IPGS, which makes use of the byproduct energy of natural gas in PRSs as well as low-grade heat. Natural gas is simplified as pure methane. The basic conditions and calculation parameters relevant to the system components are listed in Table 1. A Matlab program is written for the simulation in the present study. The thermodynamic properties of material streams are calculated on the basis of the Peng-Robinson equation of states. The optimization process is under a specific solution logic given in Fig. 4.
Table 1 The basic conditions and calculation parameters.
4. Results and discussion The determination of the optimal parameters and thermo-economic analysis of the system are performed in this section. The multi-objective optimization method is applied to determine the key parameters of the system including intermediate temperature, and minimum approach temperatures in the condenser and evaporator under different heat source conditions. The intermediate temperature is a critical design parameter since it affects both the performances of the NGE and ORC subsystem. The approach temperature is the temperature difference of 5
Parameters
Value
Mass flow rate of natural gas Upstream and downstream pressure of natural gas Upstream and downstream temperatures of natural gas Isentropic efficiency of the turbine Isentropic efficiency of the natural gas expander Adiabatic efficiency of the feed pump Overall heat transfer coefficient of the evaporator Overall heat transfer coefficient of the condenser Overall heat transfer coefficient of the reheater
1 kg/s 40/20 bar 283 K 85% 80% 80% 850 W/(m2·K) [33] 250 W/(m2·K) [33] 200 W/(m2·K) [33]
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Fig. 5. The variation of system performances including (a) net power output, (b) system exergy efficiency with different heat source temperatures and intermediate temperatures.
Fig. 4. The calculation procedure of the power generation system.
increases along the optimal line which exhibits two peak regions. In the low heat source temperature situation, the COE of the ORC reference system is much greater than that of the ORC subsystem, the economic performance enhancement of the IPGS is more obvious which reveals a peak region. In the high heat source temperature situation, the power output enhancement of the IPGS is more significant which also exhibits a peak region. It is concluded that, setting the net power output, system exergy efficiency or F(X) as objective, the optimal intermediate temperature increases with the increase of heat source temperature, which make up an optimal line. With the further increase of the heat source temperature, an inflection point occurs on the optimal line. This means that the reheater is redundant for the system. Moreover, the economic performance enhancement of the IPGS is pronounced in the low heat source temperature situation, while the thermodynamic performance enhancement is more significant under the high heat source temperature circumstance. Thus, the objective function F(X) shows two peak regions.
Fig. 6. The variation of the objective function F(X) with different heat source temperatures and intermediate temperatures.
4.1.2. The heat source mass flow rate analysis In the present section, the determination of the intermediate temperature under different heat source mass flow rates is performed. The heat source is constant at 373 K and the minimum approach 6
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temperature. The conclusion can be drawn that the comprehensive performance of the IPGS is obviously better than the NGE and ORC reference systems.
temperatures are set as 5 K. Fig. 7 depicts the variation of system performances including (a) net power output, (b) system exergy efficiency with different heat source mass flow rates and intermediate temperatures. It is seen from Fig. 7(a) that the net power output has no obvious change with the mass flow rate under the low intermediate temperature situation. When the intermediate temperature increases, the greater the mass flow rate, the greater the net power output. It is seen from Fig. 7(b) that, the lower the mass flow rate, the higher the system exergy efficiency. This is because that, the lower the mass flow rate, the lower the heat source outlet exergy, which means a higher heat source recovering extent as well as system exergy efficiency are obtained. Fig. 8 shows the variation of the objective function F(X) with different heat source mass flow rates and intermediate temperatures. It is seen that, under a given heat source temperature, the objective function F(X) has no significant variation with heat source mass flow rate. To fully investigate the combined effects of the temperature and mass flow rate of the heat source on determining the intermediate temperature, Fig. 9 illustrates the variation of the optimal intermediate temperature maximizing objective function F(X) under different heat source temperatures and mass flow rates. It is clearly seen that with the increase of the heat source temperature, the optimal intermediate temperature increases. With the further increase of the heat source temperature, the optimal intermediate temperature reaches the inflection point. It is also found that as the mass flow rate increases, the optimal intermediate temperature increases under a given heat source temperature, in addition, the inflection point occurs at a lower heat source temperature.
4.3. The analysis of the exergy loss in system components The exergy analysis of system components is performed in this section. Here, the intermediate temperature and minimum approach temperatures are set as optimal value based on the above analysis. Fig. 11 shows the ratio of exergy loss in the components under different heat source conditions including (a) heat source temperature, (b) heat source mass flow rate. It is seen from Fig. 11(a) that, the exergy loss in the expander has the largest portion, followed by the condenser and evaporator. It is found that with the increase of the heat source temperature, the portion of expander decreases while that of evaporator increases. It is concluded that the exergy loss in the expander has the largest proportion when the heat source temperature is low. For the cases where temperature and mass flow rate of the heat source are high, the exergy loss in the evaporator occupies most of the ratio of total exergy loss. 4.4. The analysis of the capital costs of system components The analysis of capital cost is of great significance in the design stage of the IPGS. The capital costs of system components under different heat source conditions are analyzed in this section. The
4.2. Determination of the minimum approach temperatures Minimum approach temperature is a key parameter that both related to the thermodynamic performance of the system as well as economic performance. Hence, a good design regarding the minimum approach temperatures in the evaporator and condenser could improve the comprehensive performance of the IPGS. In this section, the determination of optimal minimum approach temperatures under various heat source mass flow rates is conducted. The heat source temperature is constant at 373 K, and the intermediate temperature is optimized based on the results of the previous section. In addition, the minimum approach temperatures in the evaporator and condenser are equal and change simultaneously in the following analysis. Fig. 10 presents the variation of objective function F(X) with different heat source mass flow rates and minimum approach temperatures. It is seen that, keeping the mass flow rate constant, the objective function F(X) shows a peak point with the increase of the minimum approach temperature. With the increase of the mass flow rate, the optimal minimum approach temperature increases and forms an optimal line. This is because, under a fixed heat source temperature, a lower minimum approach temperature results in greater power output, however, it also leads to a larger heat transfer area. A higher minimum approach temperature results in poor thermodynamic performance but better economic performance. Thus, the comprehensive performance exhibits an optimal point. Under a certain pressure range (i.e. 20–40 bar), and heat source conditions (temperature = 373 K, mass flow rate = 1 kg/s), the performance comparison of the IPGS and the reference systems is shown in Table 2. It is clearly seen that the net power output and exergy efficiency are enhanced by 17.15% and 22.37%, respectively. The COE is reduced by 42.23%. Compared to the conventional energy recovering systems in PRSs which only utilizes the pressure energy of natural gas and the ORC system utilizing cooling water as the heat sink, the performances of the NGE and ORC subsystems are mutually enhanced. The NGE subsystem is boosted by recovering maximum byproduct energy of natural gas including the pressure and cold energy. At the same time, the ORC subsystem is enhanced as well due to lower condensation
Fig. 7. The variation of system performances including (a) net power output, (b) system exergy efficiency with different heat source mass flow rates and intermediate temperatures. 7
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Table 2 The performance comparison of the IPGS and the reference systems. Heat source conditions: temperature = 373 K, mass flow rate = 1 kg/s Optimal design parameters Intermediate temperature/K Minimum approach temperatures/K
283 6.2
System performance comparison Indicators
The reference systems
The IPGS
Performance enhancement
Net power output/kW Exergy efficiency COE/$·kWh−1
69.78 0.514 0.1177
81.75 0.629 0.068
17.15% 22.37% 42.23%
Fig. 8. The variation of the objective function F(X) with different heat source mass flow rates and intermediate temperatures.
Fig. 9. The variation of the optimal intermediate temperature maximizing objective function F(X) under different heat source temperatures and mass flow rates.
Fig. 11. The ratio of exergy loss in system components under different heat source conditions including (a) heat source temperature, (b) heat source mass flow rate.
intermediate temperature and minimum approach temperatures are optimized. Fig. 12 shows the ratio of capital costs in system components under different heat source conditions including (a) heat source temperature, (b) heat source mass flow rate. It is seen from Fig. 12(a) that the turbine has the largest capital cost ratio, then follows the condenser and evaporator. Moreover, with the increase of the heat source temperature, the ratio of capital cost of the turbine increases while that of the condenser and reheater decrease. From Fig. 12(b), it is found that as
Fig. 10. The variation of objective function F(X) with different heat source mass flow rates and minimum approach temperatures.
8
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increase of the heat source temperature and mass flow rate. when heat source temperature further increases, natural gas is no need to be reheated and the IPGS becomes simpler. In addition, the optimal minimum approach temperature increases with the increase of the heat source mass flow rate. With the optimized design parameters, the performances of the NGE and ORC subsystems are mutually enhanced, the IPGS shows better comprehensive performance than the NGE and ORC reference systems. The net power output and exergy efficiency are improved by 17.15% and 22.37%, respectively. The COE is reduced by 42.23%. Moreover, the thermodynamic performance improvement of the IPGS is more obvious under high heat source temperature situation, while the economic performance improvement of the IPGS is more significant under low heat source temperature circumstance. The thermo-economic analysis of the IPGS shows that the expander and evaporator are the maximum components of exergy loss, accounting for 74.14%–93.67% with the increase of the heat source temperature and mass flow rate. The capital of the turbine takes up the majority of the total capital of the IPGS, accounting for 36.24%–58.04% with the increase of the heat source temperature, and heat source mass flow exerts a non-significant effect on the capital of the turbine. For further optimization of the IPGS, increasing the efficiency of the expander and decreasing the capital of the turbine would dramatically improve the performance and benefit of the IPGS. This paper provides a feasible and efficient solution to recover the byproduct energy in PRSs as well as low-grade heat. All the components in the IPGS are commercially available. There shows no serious obstacle to practical applications. Declaration of Competing Interest 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. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 21506257), the Fundamental Research Funds for the Central Universities of Central South University (No. 2019zzts535).
Fig. 12. The ratio of capital costs of system components under different heat source conditions including (a) heat source temperature, (b) heat source mass flow rate.
heat source mass flow rate increases, the ratio of capital cost of the turbine has a gentle change while that of the evaporator increases. It is concluded that heat source temperature has a more obvious impact on the capital costs of system components than heat source mass flow rate.
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5. Conclusion In this paper, a novel integrated power generation system making joint use of the byproduct energy of natural gas in PRSs and low-grade heat is proposed. By the integrated system, the cold energy obtained during the natural gas depressurization process is utilized, at the same time, a wide range of low-grade heat (< 100 °C) such as shallow geothermal energy, solar energy or residual waste heat can be recovered to boost power generation. The electricity generated can be supplied to the pressure reduction station itself or nearby consumers. To comprehensively evaluate and optimize the IPGS, a new multiobjective optimization model is established. Compared to conventional models, the indicators in the optimization model could better reveal the thermodynamic and economic performance enhancements to the separated NGE and ORC reference systems. Based on the optimization model, the optimal determination of key design parameters is explored including intermediate temperature and minimum approach temperatures. The optimal intermediate temperature first increases with the 9
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