Design and optimization of combined gasoline vapor recovery, cascade power and Rectisol wash for liquid natural gas cold energy utilization

Energy Conversion and Management 207 (2020) 112511

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Design and optimization of combined gasoline vapor recovery, cascade power and Rectisol wash for liquid natural gas cold energy utilization ⁎

Tiancheng Ouyanga,b, , Binxu Gaoa, Zixiang Sua, Feng Wanga, Jiawei Lia, Haozhong Huanga, a b

T ⁎

College of Mechanical Engineering, Guangxi University, Nanning, PR China School of Mechanical Engineering, Southeast University, Nanjing, PR China

A R T I C LE I N FO

A B S T R A C T

Keywords: Liquid natural gas Cold energy Gasoline vapor recovery Rectisol wash Binary zeotropic mixtures Optimization

The worldwide energy crisis and environmental pollution have led to an enormous demand for liquid natural gas. The recovery and application of cold energy released from the liquid natural gas vaporization process can play a significant role in solving these issues. In this study, a new configuration is proposed to realize the cascade utilization of cold energy, which includes five subsystems: gasoline vapor recovery, cascade Rankine power generation, Rectisol wash, air conditioning and liquefied air energy storage. Each subsystem is validated by the published literature of experiment and simulation, and parameters that are critical to the system are studied in depth. The genetic algorithm is then used to obtain the maximum net output power, using the working fluid composition, mass flow and fraction as optimization variables. As a result, the recovery rate of oil-gas is 95%, which meets environmental regulations for vapor recovery. When a binary zeotropic mixture (fluoromethane/ carbon dioxide, 0.2247/0.7753) is selected in an actual case, the specific work and exergy efficiency of power generation are 135.16 kJ/kg and 31.57%, respectively, and 2639 kg/h of raw coal-gas can be purified to remove carbon dioxide. Under the coordination of liquefied air energy storage system coupled with an allocation algorithm, the demands and supplies of electricity and air conditioning have been matched. Therefore, the cascade utilization model provides a novel idea for cold energy recovery in natural gas stations.

1. Introduction With the announcement of the 21st Conference of Parties (COP), the Central Government of China has committed to reduce carbon dioxide (CO2) emissions 60% relative to 2005 emissions by 2030 and set a target for increasing the share of natural gas (NG) to 15% by 2040 [1]. According to the statistics reported in International Energy Outlook 2016 [2], NG consumption in Asia is predicted to increase from 15.1 trillion cubic feet (Tcf) in 2012 to 50.8 Tcf in 2040 (a 336% increase over 28 years), and China accounts for almost two-thirds of the predicted growth in Asia’s NG consumption. To meet future demands, China is actively pursuing multiple sources for NG imports. One method is transporting liquid natural gas (LNG) by ship [3]. LNG is considered an environmentally friendly fuel because of its high combustion efficiency and peculiar hydrogen-to-carbon ratio. One rationale for expanding the application of LNG is the convenience of transporting NG across long distances when pipelines are not available [4]. Because the volume of LNG at −162 °C is 600 times lower than its ambient volume [5], transporting LNG stored in tanks to gas stations or power generation plants is feasible.

⁎

To use LNG as a fossil fuel in an NG car, it must be regasified, a process that releases a significant amount of LNG cold energy. In conventional regasification devices, LNG at a cryogenic temperature of −162 °C is regasified at inland locations using air or at LNG receiving stations near the sea with seawater [6]. Owing to the temperature difference between LNG and the heat source (air or seawater), the release of LNG cold energy from the regasification of 1 ton of LNG is equivalent to 240 kWh [7]. Therefore, in the past 20 years, recovering the LNG cold energy from the process of regasification has received much attention. In the last few decades, several methods have been proposed and studied regarding the recovery of LNG cold energy, such as integrated air separation processes [8], power generation [9], production of dry ice [10], seawater desalinization [11], air conditioning [12], cold warehouses [13], and other processes. However, in the field of LNG cold energy utilization, most scholars have focused on LNG satellite receiving stations and have seldom considered inland NG stations. The recovery of LNG cold energy in NG stations is facing challenges, and it is worthwhile devoting effort to addressing these challenges. Furthermore, compressed natural gas (CNG) vehicles have been shown to have

Corresponding authors at: College of Mechanical Engineering, Guangxi University, Nanning, PR China (T. Ouyang). E-mail addresses: [email protected] (T. Ouyang), [email protected] (H. Huang).

https://doi.org/10.1016/j.enconman.2020.112511 Received 11 September 2019; Received in revised form 13 January 2020; Accepted 17 January 2020 0196-8904/ © 2020 Elsevier Ltd. All rights reserved.

Energy Conversion and Management 207 (2020) 112511

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an advanced three-stage RC that increased thermal efficiency from 7.16% to 25.7%, and ternary mixtures of 1,1,1,2-tetrafluoromethane (C2H2F4) and n-Pentane (n-C5H12) performed with a thermal efficiency of 29.56% in a two-stage condensation combined cycle. However, this approach seemed to yield less pronounced improvement when more components were mixed, as reported by Bao et al. [41]. The results from the cases cited above indicate that mixed working fluids with a higher of temperature glide match degree can improve the energy conversion efficiency; working fluids with a lower temperature glide match degree yield negative effects. According to the published literature, most scholars regard LNG satellite stations near the sea as the research object and focus on cold energy power generation systems that are arranged in series or parallel and include an air separation plant. With the increasing popularity of CNG vehicles, gas stations in cities will be required. Meanwhile, to reduce construction costs and improve space utilization, natural gas stations should be built with oil stations. However, research in this field of cold energy recovery is rare. Challenges exist for energy conversion and emission reduction, that is, how to efficiently use this aspect of LNG cold energy. In addition, the traditional condensation units for gasoline vapor recovery and Rectisol wash consume a large amount of electric energy, and there is a mismatch between the supply of energy and the demand of users during a day. Therefore, the goal of this study is to investigate the recovery and application of cold energy released in LNG regasification at natural gas stations to meet the requirements of power generation, air conditioning, gasoline vapor recovery and Rectisol wash. In this study, a novel model is proposed to recover cold energy in a natural gas station built in conjunction with an oil station, including gasoline vapor recovery, cascade Rankine power generation, Rectisol wash, air conditioning and liquefied air energy storage. Firstly, the condensing temperature of the gasoline vapor recovery subsystem is discussed to find the best parameters under the conditions of a standard recovery rate of 95%. Secondly, to optimize the cascade Rankine power generation subsystem, the boundary conditions of outlet pressure of the evaporator and turbines are analyzed, and parameters of the working fluid that are critical to the system are optimized by using the genetic algorithm (GA). For further recovery of cold energy, Rectisol wash and air conditioning subsystems are simulated. Then, the irreversibility of the entire system is calculated to find out the parts with the greatest exergy loss. Furthermore, because the inlet mass flow of LNG will vary with the demands of terminal users, variations of the five subsystems and the efficiency of the entire system are analyzed to demonstrate the daily by-products of cold energy recovery in practice. Finally, in order to solve the issue that the power generation and the refrigeration capacity fluctuate greatly with the daily changes of mass flow of LNG, matching demands and supplies of electricity and air conditioning is carried out by utilizing the allocation function of liquefied air energy storage system integrated genetic algorithm. The novelty and motivation of the proposed design are to realize the cascade utilization of LNG cold energy for introducing Rectisol wash to improve energy efficiency and to balance the demands and supplies of electricity and air conditioning for users. Therefore, the cascade utilization model represents a novel idea for cold energy recovery in natural gas stations built in conjunction with oil stations.

the lowest emissions among hydrocarbon fueled vehicles [14] and play an important role in reducing CO2 emissions [15]. As the use of CNG vehicles increases, NG stations are being rapidly constructed in Chinese cities, therefore, one approach is to build stations that offer both NG and petrol to decrease investment and conserve space. Similar to natural gas, the composition of coal-gas primarily consists of carbon monoxide and hydrogen and is used as fuel in many urban homes. However, before being distributed to a terminal user, CO2, sulfur, and other impurities in coal-gas need to be removed by Rectisol wash technology, which is a physical absorption method that uses methanol as a solvent [16]. Power generation from LNG cold energy has attracted extensive interest [17]. Virtually all constructions of LNG power generation are based on one of three cycles: a direct expansion cycle (DEC) [18], a Rankine cycle (RC) [19], or a Brayton cycle (BC) [20]. In a DEC, LNG expands in a turbine directly to generate electricity, without other auxiliary working fluids, as reported by Gomez and Romero. [21]. Consequently, DEC processes have no extra working fluid and heat exchangers, and such plants are the simplest to construct and have the lowest cost [22]. However, DEC also has the lowest efficiency, which is why this cycle has been abandoned by the industry [23]. In an RC, LNG cold energy is employed as a cold source to cool auxiliary working fluids, which are converted from a gaseous to a liquid state in a condenser [24]. Moreover, to utilize the low-grade and high-grade cold energy of LNG, the cascade Rankine cycle (CRC) and the parallel RC have been proposed as solutions [25]. For instance, Li et al. [26] showed that the performance of CRC was better than a conventional RC (an increase of 9.3% and 7.33% in net output power and thermal efficiency, respectively). However, the economics of the CRC need to improve, and a balance point between costs and benefits should be determined [27]. A Brayton cycle (BC), differs from an RC in that a BC uses CO2 as a working fluid to transform the exergy to mechanical energy in a turbine [28]. CO2 is cooled and condensed by using LNG cold energy at the entrance to the compressor, thus reducing the compression work [29]. However, only CO2 can guarantee the energy efficiency of a BC, therefore, its utility is limited. Hence, this cycle has been typically studied in combination with other cycles [30]. For example, Koku et al. proposed a combined cycle power plant (a BC combined with an RC) that achieved an efficiency of 60.4% [31]. From an analysis of literature, an important parameter that affects the efficiency of the power generation cycle is the working fluid. Recently, perfluoropropane (R245fa) was shown to perform best in a tripartite cycle composed of three single RCs, as proposed by Zhang et al. [24]. When a cascade power generation cycle using solar energy as a heat source was applied, as reported by Li et al. [32], pentafluoroethane (R125) was found to be the optimal working fluid. In Lee et al. [33], a combined cycle composed of an RC and a DC was constructed, and the results indicated that isopentane (C5H12) was a suitable working fluid [34]. In addition, C5H12, propylene (C3H6), ethane (C2H6), and propane (C3H8) were selected as optimal working fluids in different cycles [35]. Notably, the optimal working fluid for various constructions is not the same because the construction of the power generation cycle and the boundary conditions strongly affect the working fluid. In terms of energy recovery, it is difficult to achieve high efficiency with a single cycle or pure working fluid, thus recent studies have focused on the properties of mixed working fluids [36] and combinations of mixed working fluids and cycles [37] to improve efficiency further. In 2015, Kim et al. [38] proposed a novel cascade generation system based on a binary working fluid and analyzed the sensitivity of heat source temperature to net output power. The result showed that the net output power per kilogram LNG is 151.78 kJ/h at 25 °C of heat source temperature. The increase in efficiency is attributed to the temperature glide match degree, which reflects the performance of the working fluid in the heat transfer process. These studies have given mixed working fluids more attention [39]. Several years ago, Xue et al. [40] proposed

2. System design The structure of the proposed system and the working fluid used in this study are described in this section. 2.1. Description of the system The combined system, shown in Fig. 1, can be divided into five parts: a gasoline vapor recovery part, where propane (C3H8) is used as the working fluid to carry the cold energy to the oil-gas separator; a 2

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Fig. 1. Sketch of gasoline vapor recovery, cascade power, Rectisol wash, air conditioning and energy storage to recover cold energy of LNG.

MIXER 1 by PUMP 1 and PUMP 2, respectively. In the outlet of MIXER 1, the working fluid initially provides a portion of the cold energy to the air conditioning part to use cold energy efficiently and reduce the irreversibility caused by a large temperature difference at the evaporator. The working fluid is then heated in the evaporator by environmental air to transform it from liquid to gas, which contains high levels of pressure energy and kinetic energy, and sent back to the turbines to begin the next cycle.

power generation part, where a zeotropic mixture is used to drive the expander and generate electricity through phase change; a Rectisol wash part, where cold energy is used to remove hydrogen sulfide (H2S), CO2, carbonyl sulfide (COS), and other impurities from raw coal-gas; an air conditioning part, where a 50% glycol solution is used as the working fluid to transfer LNG cold energy for use in residential and office buildings; and a liquefied air energy storage part, where air is used as the working fluid to store the extra cold energy in the storage tank. The main stream of LNG initially enters HEX 1 and HEX 2 to release cold energy (represented by the blue dotted lines) to FLASH 3 and FLASH 2. In the next part, the main stream passes COND 1 and COND 2 as a cold source to condense the zeotropic mixture from a gaseous to a liquid state. Subsequently, the main stream enters HEX 5, HEX 6, and HEX 4 at relatively high temperatures to use the remaining cold energy for the Rectisol wash and air conditioning. The main stream emerges ready for distribution to the CNG user. Actually, when the supply exceeds demand, the liquefied air energy storage starts to store LNG cold energy, on the contrary, to release cold energy to meet the needs of users.

2.1.3. Part 3: the Rectisol wash The absorption part of a Rectisol wash consists of four towers and five condensers. The four towers have multiple functions: a prewashing, desulfurization, crude decarburization, and fine decarburization (the detailed process and structure are described in Section 3.3, the Rectisol wash subsystem). To maintain the temperature of the methanol in a suitable range, HEX 5 and HEX 6 are employed to provide the cold energy carried by the working fluid C3H8 from the LNG side.

2.1.4. Part 4: air conditioning HEX 7 is introduced between the mixer and evaporator, and HEX 4 is added after HEX 6. HEX 4 and HEX 6 both use a 50% glycol solution as the working fluid. To utilize the high-grade cold energy of LNG and recover a portion of the cold energy from the working fluid in Part 2, the flow from the air conditioning is split into two streams by SPLITTER 2. One stream enters HEX 7 to absorb the cold energy released by the zeotropic mixture; the other stream enters HEX 4 to recover the remaining cold energy from the LNG. The two streams are then merged to form a single stream at MIXER 2, providing and transferring cold energy for use in residential and office buildings.

2.1.1. Part 1: gasoline vapor recovery Part 1 is composed of three flash evaporators and a precooler, each set at a different condensing temperature. To meet oil-gas emission standards and reduce the energy consumption of the equipment, a precooler is used to remove water from raw oil-gas to prevent the pipes from freezing because the condensing temperature is below the freezing point of water. After being cooled by the precooler, the evaporated gas is sent to the flash evaporators that are supplied with cold energy by HEX 1, HEX 2, and HEX 6. The working fluid condenses at different temperatures and then flows out from the bottom of flash evaporators. 2.1.2. Part 2: power generation Part 2 consists of turbines, condensers, pumps, heat exchangers, and evaporators. The stream of working fluid (stream W2) at the outlet of the evaporator is split into two streams through SPLITTER 1. The two streams (W3 and W4) expand in different turbines (turbine 1 and turbine 2), where pressure energy and kinetic energy are transformed into mechanical energy. Mechanical energy is converted into electrical energy by the turbines. The working fluids in the turbine outlets (stream W5 and W6) are condensed by COND 1 and COND 2 to a liquid state. The two streams (W7 and W8) are then pressurized and transmitted to

2.1.5. Part 5: liquefied air energy storage Part 5 is composed of a cooler, a compressor, a heat exchanger and a storage tank. The air in the environmental state first exchanges heat with the cooler, transforming into low-temperature air, and then it enters the compressor, consuming part of energy to change the lowpressure air into high-pressure air. Subsequently, the gaseous air is liquefied by the cold energy released by LNG and stored in the liquefied air tank. The specific scheme of storing and releasing cold energy are controlled by the genetic algorithm shown in Fig. 6, and its results are demonstrated in Section 5.5. 3

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Table 1 Properties of pure working fluid.

Table 3 The components of LNG.

Working fluid

Chemical formula

Critical temperature (°C)

Critical pressure (bar)

Normal boiling point (°C)

Ethane Propylene Propane Trifluoromethane Difluoromethane 1,1,1,2-Tetrafluorethan Fluoromethane 1,1-Difluoroethane 1,1,1-Trifluoroethane Pentafluoroethane Hexafluoroethane Octafluoropropane Carbon dioxide Ammonia

C2H6 C3H6 C3H8 CHF3 CH2F2 C2H2F4 CH3F C2H4F2 C2H3F3 C2HF5 C2F6 C3F8 CO2 NH3

32.17 91.06 96.74 26.14 78.1 101.06 44.1 113.3 101.1 66.02 19.88 71.87 31 132.3

48.72 45.55 42.51 48.32 57.8 40.59 59 45.2 40.6 36.18 30.48 26.4 73.8 48.7

−88.82 −47.62 −42.11 −82.09 −51.65 −26.07 −78.31 −24.02 −26.07 −48.09 −78.09 −36.79 – −33.59

Component Mole fraction/%

̇ ,G = Qtotal

CH4 91.5

C2H6 5

C3H8 3.5

∑ Q̇Flash

(2)

The recovery rate of oil-gas is defined as follows:

η=

Gin − Gout G × 100% = ⎛1 − out ⎞ × 100% Gin Gin ⎠ ⎝ ⎜

⎟

(3)

To establish a simulation model, the assumptions of thermodynamic conditions are listed in Table 2, and the components of LNG and the oilgas are listed in Table 3 and Table 4, respectively.

where Gin is the mass flow of inlet raw oil-gas, and Gout is the mass flow of outlet liquefied oil-gas. In 2007, the National Environmental Protection Agency issued a standard of oil-gas emission control [43], which is displayed in Table 5. The condensing temperature in a flash evaporator plays a significant role in the ability of the gasoline vapor recovery system to meet the oilgas emission standard and reduce the energy consumption of the equipment, as shown in Table 5. The components and pressure of the raw oil-gas at the inlet should remain unchanged. Therefore, it is important to find a suitable condensing temperature for the flash to meet the demand for minimum energy consumption. Fig. 2 illustrates the relationship between the rate of gasoline vapor recovery and the energy consumption of the system at different temperatures. Fig. 2(a) shows that the curve of energy consumption appears as an inverted parabola, and its lowest point corresponds to condensing temperature and gasoline vapor recovery rate of −37 °C and 95%, respectively. A gasoline recovery rate of 95% meets the standard; therefore, −37 °C is determined to be the optimal temperature for FLASH 1. Similarly, the optimal temperature for FLASH 2 is determined to be −64 °C, as shown in Fig. 2(b). As shown in Fig. 2(c), energy consumption tends to decrease as the temperature rises; therefore, to meet the standard for gasoline vapor recovery rate (95%), a condensing temperature of −117 °C is most suitable for FLASH 3. In conclusion, the condensing temperatures of FLASH 1, 2, and 3 are set as −37, −64, and −117 °C, respectively, and the energy consumption of the system is 68.71 kW under the condition of 800 kg/h gasoline vapor recovery.

3.2. Gasoline vapor recovery subsystem

3.3. Cascade Rankine cycle subsystem

2.2. Characteristics of pure working fluid The properties of pure working fluid are displayed in Table 1. From an analysis of the literature, several alternative working fluids were selected for comparison [21]. According to the range of LNG temperature and based on the previous studies [42], fourteen pure working fluid types are chosen for this study. These working fluids consist of hydrocarbons and inorganics, such as fluoride, CO2 and ammonia (NH3). 3. Modeling and optimization The process and result of modeling and optimization are described in this section. 3.1. Assumptions and components

The thermal power of each flash evaporator is determined by the following equation:

Q̇Flash, i = ṁ Gasoline (hin, Flash, i − hout , Flash, i )

In Rankine cycle, the net power is calculated using the equation as:

̇ = Wnet

(1)

̇ − ∑ Ẇ pump ∑ Wturb

(4)

̇ and pump power Ẇ pump can be expressed where the turbine power Wturb as follows:

where the subscript i = 1, 2, 3, and corresponds to the serial number of each flash evaporator, as shown in Fig. 1; Q̇Flash denotes the thermal power of flash evaporator; ṁ Gasoline denotes the mass flow of vaporized oil-gas; and hin,Flash,i and hout,Flash,i denote the inlet and outlet enthalpies, respectively, of the vaporized oil-gas. The total energy consumption of gasoline vapor recovery subsystem is defined as:

̇ , i = ṁ turb, i (hin, turb, i − hout , turb, i ) Wturb

(5)

Ẇ pump, i = ṁ pump, i (hout , pump, i − hin, pump, i )

(6)

where the subscript i = 1, 2, corresponds to the serial number of turbine and pump in Rankine cycle, as shown in Fig. 1. ṁ turb, i and ṁ pump, i

Table 2 Thermodynamic conditions considered in modeling process. Parameters

Value

Parameters

Value

LNG mass flow rate LNG temperature LNG pressure NG temperature Minimum approach temperature of HEX and COND Discharge pressure of PUMP 1 and PUMP 2 Efficiency of pump

2880 kg/h −162 °C 60 bar 5 °C 5 °C 0.8 0.8

Efficiency of turbine Ambient pressure Ambient temperature Heat losses in pipeline and heat exchanger Pressure drop in pipeline and heat exchanger The working fluid in the outlet of evaporator The working fluid in the outlet of condenser

0.8 1 bar 293 K Negligible Negligible Gaseous state Liquid state

4

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Table 4 The components of oil-gas. Component

Mole fraction/%

Component

Mole fraction/%

Component

Mole fraction/%

Methane Ethane Propane Isobutane n-butane

0.68 1.24 1.40 0.30 5.60

cis-2-Butene Trans-2-Butene 2-Methyl-butane n-pentane n-hexane

3.10 2.50 6.00 0.68 4.10

Oxygen Nitrogen 1-Butene 2-Methyl-propene

13.8 51.9 3.30 5.40

While the thermal efficiency is defined as follows:

Table.5 The standard of oil-gas emission [44]. Gasoline vapor recovery rate Oil-gas emission limits

η=

≥95% ≤25 g/Nm3

̇ Wnet ̇ ) (Q̇HEX 7 + Qevap

(11)

The specific exergy is calculated, at each component, as:

ex j = (hin, j − hout , j ) − Tamb (sin, j − sout , j )

denote the mass flow rate of turbine and pump, respectively. hin,turb,i and hin,pump,i denote the inlet enthalpy of turbine and pump, respectively. hout,turb,i and hout,pump,i denote the outlet enthalpy of turbine and pump, respectively. The specific work is then calculated as:

w=

̇ Wnet ṁ LNG

where j represents the name of each component in Fig. 1. Tamb represents the ambient temperature that is 293 K. hin,j and hout,j denote the inlet enthalpy and outlet enthalpy of each component, respectively. sin,j and sout,j denote the inlet entropy and outlet entropy of each component, respectively. For each component, the irreversibility is expressed as follows:

(7)

T I ̇ = mj ex j + ⎛1 − amb ⎞ Qj̇ − Ẇ j T ⎠ ⎝

where ṁ LNG denotes the mass flow of LNG The thermal power of each condenser is defined by the following equation:

̇ , i = ṁ cond, i (hin, cond, i − hout , cond, i ) Qcond

(8)

ηex =

w ex in − ex out

(14)

where exin and exout denote the inlet exergy and outlet exergy of cascade Rankine cycle. 3.4. Rectisol wash subsystem

(9) The construction of the Rectisol wash subsystem is represented in Fig. 3. Before entering the absorption tower, the raw coal-gas is cooled to −23 °C by E05 for better absorption. In C01A, the water in the raw coal-gas is absorbed by a small amount of rich methanol, which is saturated with CO2 from C01C. In the condition of low temperature and high pressure, the solubility of sulfide in methanol is much higher than that of CO2. Therefore, sulfur is easily removed from the raw coal-gas when rich methanol is used as an absorbent upon entering C01B. Inversely, the stages of C01C and C01D require more methanol because its absorption capacity for CO2 is less than that of sulfide.

where Q̇HEX 7 represents the thermal power of HEX 7. ṁ HEX 7 denotes the mass flow rate of HEX 7. hin,HEX 7,i and hout,HEX 7,i denote the inlet enthalpy and outlet enthalpy of HEX7, respectively. The cold energy released to the air is expressed by:

̇ Qevap = ṁ evap (hin, evap − hout , evap)

(13)

where I ̇ is the irreversibility that the component creates. Qj̇ and Ẇ j are the heat and mechanical power that the component creates. T represents the temperature of 273 K The exergy efficiency of the system is defined as:

where the subscript i = 1, 2, corresponds to the serial number of ̇ condenser in Rankine cycle, as shown in Fig. 1. Qcond represents the thermal power of each condenser. ṁ cond, i denotes the mass flow rate of condenser. hin,cond,i and hout,cond,i denote the inlet enthalpy and outlet enthalpy of condenser, respectively. The cold energy removed by the air conditioning in HEX7 is determined as:

Q̇HEX 7 = ṁ HEX 7 (hin, HEX 7 − hout , HEX 7)

(12)

(10)

̇ represents the thermal power of evaporator. ṁ evap denotes where Qevap the mass flow of evaporator. hin,evap,i and hout,evap,i denote the inlet enthalpy and outlet enthalpy of evaporator, respectively.

Fig. 2. Relationship between the gasoline vapor recovery rate and energy consumption at different temperatures. 5

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Table 6 Optimization parameters of genetic algorithm. Parameter

Value

Parameter

Value

Number of individuals Number of variables Generation gap

40 3 0.9

Maximum number of generations Precision of variables

200 200

Etotal = EGR + Wnet + ERW + EAC

(18)

where the EGR, ERW and EAC denote the equivalent electricity power of gasoline vapor recovery subsystem, Rectisol wash subsystem and air conditioning subsystem, respectively. KGR, KRW, and KAC denote the equivalent coefficient of gasoline vapor recovery, equivalent coefficient of Rectisol wash and equivalent refrigeration coefficient, respectively, which are represented the transformation efficiency between refrigeration capability and energy consumption, and decided by the technical level of modern electrical refrigeration. In this study, KGR [16], KRW [44], and KAC [47] are set as 1.6, 1.7, and 4.7, respectively. The thermal efficiency of system is determined as:

Fig. 3. Flow chart of Rectisol wash (yellow lines represent the methanol, black lines represent the coal-gas, C01A-prewashing, C01B-desulfurization, C01Ccrude decarburization, C01D-fine decarburization). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

At the top of C01D, poor methanol at −56.9 °C and rich methanol at −47 °C are injected into C01D for absorption. After absorbing the CO2, the methanol is cooled to approximately −35 °C by E03 and then sent to the C01C to absorb the CO2 continuously. Subsequently, the methanol solution releases a large amount of heat; consequently, its temperature increases and its absorption capacity decreases. Therefore, a heat exchanger (E04) is introduced between C01C and C01B to reduce the temperature of methanol to −35 °C and maintain its absorption ability. The stream at the bottom of C01C is divided into two parts: the first part enters the subsequent towers for CO2 desorption; the second part is fed into C01B to absorb sulfur and is cooled to approximately −35 °C by E04, before sending it into C01A to absorb water. Finally, the methanol solution from the bottom of C01A and C01B is sent to the subsequent towers to complete the cycle. The purified gas is sent to the pipeline from the top of the C01D, and the component ratio of this gas after Rectisol wash is displayed in Fig. 4. The ratio of CO2 sharply decreases from 34% to 1%, representing the effective capacity of the Rectisol wash.

ηsystem, th =

∑ QHEX , i + Wnet QLNG

(19)

where the subscript i = 1, 2, 3, 4, 5, 6 corresponds to the serial number of each heat exchanger, as shown in Fig. 1. QLNG denotes the theoretical cold energy released by the process that LNG regasification from −162 °C to 5 °C. The exergy efficiency of system is defined as:

ηsystem, ex =

∑ mj (ex in, j − ex out , j ) + Wnet mLNG (exLNG − ex dist )

(20)

where j represents the name of each component in Fig. 1. exLNG denotes the exergy of inlet LNG, exdist denotes the exergy of CNG distributed to terminal user.

3.5. Evaluation of equivalent energy

3.6. Optimization strategy

In order to analysis the recovery of LNG cold energy for the whole system, the equivalent output energy, including gaseous vapor recovery subsystem, Rectisol wash subsystem, power generation subsystem, and air conditioning subsystem, is defined to evaluate the performance of entire system. The equivalent output energy is defined as follows:

In this study, Aspen Plus software was used to simulate the chemical process with which the combined model was constructed. Due to the accuracy of the design and calculation required in the four subsystems, the Segregated Runge–Kutta (SRK) method was used to simulate the gasoline vapor recovery, RC, and air conditioning subsystems. The Predictive Soave-Redlich-Kwong (PSRK) method was used as the algorithm to construct the Rectisol wash subsystem. The net output power was defined as the objective function; the working fluid composition, mass flow, and mass fraction of the RC subsystem were selected as the optimization variables. The GA is less time-consuming than the traditional method of exhaustion because the essential principle of the GA follows the evolutionary law of “natural selection and survival of fittest” of biological

EGR =

∑ QFlash,i × KGR

(15)

ERW =

∑ Qheater ,i × KRW

(16)

EAC =

∑ Q̇HEX , i KAC

(17)

Fig. 4. Composition of raw coal-gas. 6

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Fig. 5. Schematic of optimization process by genetic algorithm.

Fig. 6. Schematic of optimization process by modified genetic algorithm for allocation of energy. Table 7 Model validation: Power generation subsystem. Temperature of heat source (K)

293.15 303.15 Average difference

Working fluid

CH2F2 CH2F2

Table 9 Model validation: Rectisol wash subsystem. Present model

[24]

Wnet (kW)

Wnet (kW)

122.18 124.76 0.07%

122.16 124.61

systems [45]. Therefore, the GA using the computational parameters listed in Table 6 was used to maximize the objective function. The calculation process of the GA is displayed in Fig. 5. Because Aspen Plus lacks the programming required for the GA, the GA is performed with Matlab. Firstly, a connecting program is used to link Matlab and Aspen Plus; these two software products each play a different role in the GA. Matlab is employed as a program execution software, and Aspen Plus is selected as a computational function package. Once the linkage is successful, the optimization variables will be input to the GA to establish an initial population quickly. A fitness function is then calculated by Matlab, and the results are sent to Aspen Plus. Control is then given to Aspen Plus to calculate the objective function because when Aspen Plus and Matlab are linked, Aspen Plus is a computational function package with no judgment function. However, a judgment program must be used to determine whether the objective function value is correct. After Aspen Plus performs the judgment function, then

Component

Raw coal-gas (Mole fraction)

Present model Purified coal-gas (Mole fraction)

[16] Purified coal-gas (Mole fraction)

Difference

CO2 CO H2 CH4 N2 AR H2S COS H2O MEOH

0.321 0.212 0.455 0.001 0.002 0.001 0.002 7.92E-06 0.002 0.003

0.023 0.306 0.675 0.001 0.003 0.001 trace trace trace trace

0.023 0.309 0.662 0.001 0.003 0.001 trace trace trace trace

0% 0.970% 1.964% 0% 0% 0% – – – –

Trace means the quantity of components is too tiny to ignore.

the correct objective function value is conveyed to Matlab. When control is returned to Matlab, it evaluates whether to terminate GA. Termination occurs when the fitness function value, which is on the optimal point in the proximate population, is less than or equal to 10-6 or the number of generations reaches 200, Matlab outputs the optimal objective function value and its corresponding variables. If these conditions are not met, a new population is created by the process of selecting parents, reproducing offspring, performing crossover and migration, and then restarting a new cycle until the conditions for

Table 8 Model validation: gasoline vapor recovery subsystem.

T0/T1/T2 (K) 276/238/198 276/233/193 303/243/190 Average difference

Present model

[46]

Present model

[46]

Present model

[46]

QFlash1 (kW) 26.6197 30.0157 28.2071 0.4326%

QFlash1 (kW) 26.7501 30.1127 28.3483

QFlash2 (kW) 14.6999 12.3855 20.3226 1.7079%

QFlash2 (kW) 14.4549 12.1661 19.9909

η (%) 92.91 93.50 94.79 1.3679%

η (%) 95.16 94.50 95.44

T0, T1, and T2 represent the temperature of raw oil-gas, Flash 1, and Flash 2. And η represents the recovery ratio of oil-gas. 7

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Fig. 7. Influence of outlet pressures of evaporator and turbine on performance for pure working fluid.

Fig. 8. The relationship between specific work, critical pressure and exergy efficiency under optimal conditions.

termination are satisfied. Fig. 9. Variation of specific work and exergy efficiency with C2H6 mass fraction.

3.7. Matching demands and supplies of electricity and air conditioning In order to address the issue about allocation of the cold energy in the storage system, the calculating algorithm of allocation is displayed in Fig. 6, by means of adding a modified fitness function and a judgement program to the original genetic algorithm shown in Fig. 5. First, the two simulation softwares of Matlab and Aspen will be connected, and the differences of energy demands and energy supplies from system is then calculated to determine whether it is a positive number or a negative number. If the differences are positive, which represents the actual energy supplies are larger than the energy demands. As a result, the extra cold energy will be stored in the energy storage system. If the

differences are negative, which means the energy supplies can not satisfy the energy demands, then the stored energy will be released to make up for the shortage of cold energy. Energy storage and release is controlled by modified genetic algorithm to calculate the optimal scheme of allocation for meeting the energy demands.

4. Model validation To validate the proposed integrated model, all the boundary

Table 10 The maximum specific work of pure working fluid under optimal conditions. Working fluid

QCOND1 (kW)

QCOND2 (kW)

QEVAP (kW)

QHEX7 (kW)

WPUMP (kW)

Wnet (kW)

Specific work(kJ/kg)

Thermal efficiency

Exergy efficiency

C2H6 C3H6 C3H8 CHF3 CH2F2 C2H2F4 CH3F C2H4F2 C2H3F3 C2HF5 C2F6 C3F8 CO2 NH3

191.63 279.59 269.61 207.04 260.82 288.70 513.87 287.85 268.05 237.33 227.00 286.42 190.51 274.23

191.63 279.59 269.61 207.04 260.82 288.70 513.87 287.85 268.05 237.33 227.00 286.42 190.51 274.23

437.96 571.27 558.75 468.83 563.09 580.14 488.19 581.08 572.90 502.98 506.29 585.87 452.70 579.68

43.57 43.57 43.57 43.57 43.57 43.57 43.57 33.66 33.66 33.66 33.66 33.66 33.66 33.66

13.69 15.16 18.32 12.19 10.71 16.26 10.32 14.98 17.32 15.59 19.50 24.43 8.14 5.48

98.27 55.66 63.11 98.32 85.02 43.32 104.02 41.51 70.46 61.98 85.95 46.68 105.34 64.87

122.80 69.56 78.86 122.86 106.25 54.14 129.99 51.87 88.06 77.45 107.41 58.33 131.63 81.06

20.41% 9.05% 10.48% 19.19% 14.01% 6.95% 19.56% 6.75% 11.62% 11.55% 15.92% 7.53% 21.66% 10.58%

30.98% 13.49% 15.51% 27.99% 21.21% 10.39% 29.00% 9.96% 17.37% 16.22% 23.08% 11.22% 31.82% 15.84%

8

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20.29% 20.41% 20.18% 20.57% 21.66% 18.75% 19.76% 19.35% 21.66% 19.71% 15.92% 19.18% 19.56% 21.30% 21.08% 126.08 122.80 131.71 124.44 131.63 127.91 130.97 124.17 131.63 135.95 107.41 135.07 129.99 135.16 125.69

29.62% 30.98% 29.88% 29.88% 31.82% 27.88% 29.31% 28.30% 31.82% 29.44% 23.08% 28.97% 29.00% 31.57% 30.64%

Thermal efficiency

100.90 98.27 105.39 99.58 105.34 102.35 104.80 99.37 105.34 108.79 85.95 108.09 104.02 108.16 100.58

Fig. 10. The maximum specific work of different binary mixtures under optimal conditions.

43.57 43.57 43.57 43.57 33.66 43.57 43.57 43.57 33.66 43.57 33.66 43.57 43.57 43.57 43.57 497.24 437.96 522.30 484.05 452.70 545.87 530.44 513.51 452.70 551.99 506.29 563.59 488.19 507.80 477.20 198.21 191.63 208.46 192.24 190.51 221.76 212.82 207.07 190.51 224.12 227.00 227.75 513.87 199.83 188.32 198.21 191.63 208.46 192.24 190.51 221.76 212.82 207.07 190.51 224.12 227.00 227.75 513.87 199.83 188.32

QHEX7 (kW) QCOND2 (kW) QCOND1 (kW)

QEVAP (kW)

11.31 13.69 9.97 11.85 8.14 10.10 9.20 10.68 8.14 4.38 19.50 7.59 10.32 7.52 8.66

conditions are consistent with the published literature, and then the effectiveness of three subsystems are compared with previous models published in the literature. For the power generation subsystem, the results of comparing the proposed model with those in [24] reveal that the differences in net output power (0.07%) are very small, as shown in Table 7. For the gasoline vapor recovery subsystem, the accuracy and reliability of FLASH 1 and FLASH 2 and the final recovery ratio are verified to the model presented in [46], and the results are presented in Table 8. The differences in FLASH 1, FLASH 2 and recovery ratio are 0.4326%, 1.7079%, and 1.3679%, respectively. For the Rectisol wash subsystem, the simulated results of purified coal-gas after Rectisol wash obtained with the proposed model are compared with those obtained in [16] are basically the same, except for H2 and CH4, where the differences are 0.970% and 1.964%, respectively. By comparing the simulation results of the proposed model with those in the published literature, the accuracy of the proposed model has been validated (Table 9).

Mass fraction

0.4494/0.5506 1/0 0.3258/0.6742 0.8622/0.1378 0/1 0.8741/0.1259 0.3784/0.6216 0.9253/0.0747 0/1 0.2232/0.7768 0/1 0.3267/0.6733 1/0 0.2247/0.7753 0.3659/0.6035 C2H6/CHF3 C2H6/CH2F2 C2H6/CH3F C2H6/C2F6 C2H6/CO2 CHF3/CH2F2 CHF3/CH3F CHF3/C2F6 CHF3/CO2 CH2F2/CH3F CH2F2/C2F6 CH2F2/CO2 CH3F/C2F6 CH3F/CO2 C2F6/CO2

5. Results and discussions

Working fluid

Table 11 Optimized results of different binary mixtures.

WPUMP (kW)

Wnet (kW)

Specific work (kJ/kg)

Exergy efficiency

T. Ouyang, et al.

In this section, gasoline vapor recovery, Rectisol wash, and air conditioning are combined with traditional power generation to make full use of the cold energy released by LNG. Firstly, pure working fluid are discussed. Secondly, we investigate how to optimize binary mixture compositions. Thirdly, the thermodynamics are analyzed to calculate the equivalent thermal efficiency and system exergy efficiency. Finally, by adjusting the mass flow of LNG at different times, subsequent changes in the system parameters are observed. 5.1. Working fluid selection Fig. 7(a) illustrates the relationship between the specific work of various working fluids and evaporator outlet pressure when the evaporating temperature is 10 °C. Every working fluid approaches the maximum specific work when the evaporator outlet pressure is at the critical point, and the specific work of the pump is barely changing. The working fluid in the exit of the evaporator will turn from a gaseous to a liquid state once the outlet pressure is higher than the critical pressure. A turbine does not allow any liquid to contact the impellers. Therefore, setting the evaporator outlet pressure equal to the critical pressure is 9

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Table 12 Thermodynamic results of system under optimal condition.

Equivalent output power (kW)

Power generation subsystem

Gasoline vapor recovery subsystem

Rectisol wash subsystem

Air conditioning subsystem

108.16

111.536

283.9

21.12

Equivalent thermal efficiency

System exergy efficiency

79.05%

48.18%

Table 13 Thermodynamic results of subsystem under optimal conditions. Power generation subsystem Working fluid Mass fraction

Wnet (kW) Thermal efficiency

Exergy efficiency

Equivalent output power (kW)

CH3F/CO2

108.16

31.57%

108.16

0.2247/ 0.7753

21.30%

Gasoline vapor recovery subsystem Mass flow of oil-gas (kg/h)

Condensing temperature (°C) FLASH 1

Equivalent output power (kW)

FLASH 2 FLASH 3

800 −37 −64 Total consumption of flash evaporator 69.71 (kW)

−117

111.536

Rectisol wash subsystem Mass flow of raw coal-gas (kg/h) 2638.97

Mass flow of CO2 (kg/h) 869.46

Equivalent output power (kW) 283.9

Air conditioning subsystem Refrigeration capacity (kW)

Equivalent thermal efficiency 79.05%

97.19

Equivalent output power (kW) 21.12 System exergy efficiency 48.18%

the optimal condition. Fig. 7(b) displays the relationship between the specific work of different working fluids and turbine outlet pressure. The maximum specific work is achieved when the turbine outlet pressure is set to atmospheric pressure. The more turbine outlet pressure drops, the more specific work is obtained. This phenomenon depends primarily on the thermal energy and pressure energy of the working fluid being converted into mechanical energy for the turbine. Therefore, setting the turbine outlet pressure to atmospheric pressure is the optimal condition. Fig. 8 represents the relationship between specific work, exergy efficiency, and critical pressure for different working fluids under optimal conditions. Details of Fig. 8 are listed in Table 10, including the thermal power of each component, specific work, thermal efficiency, and exergy efficiency. Fig. 8 shows that CO2 performs the best in terms of specific work, thermal efficiency, and exergy efficiency, corresponding to 131.63 kJ/ kg, 21.66%, and 31.82%, respectively. By contrast, the worst performance occurs with C2H4F2, corresponding to 51.87 kJ/kg, 6.75%, and 9.96%, respectively. The trend between specific work and critical pressure of the working fluid is identical, meaning that when the power generation cycle operates with a working fluid that has a higher critical pressure, it will obtain higher specific work. Based on these results, the best five working fluids (C2H6, CHF3, CH2F2, CH3F, and CO2) were selected for the optimization of compositions. 5.2. Optimization of compositions for binary mixture The analysis in Section 5.1 showed that the different pure working fluid used in the power generation cycle yielded large differences in specific work and exergy efficiency. The reason for this phenomenon, as reported by Bao [41], is due to the temperature glide match degree, which reflects the performance of a working fluid in the heat transfer process. If the curve of temperature glide match degree between the working fluid and the LNG in the condenser is similar, then higher amounts of specific work and energy efficiency will be obtained. A viable method seems to be changing the temperature glide match degree by mixing pure working fluids to obtain higher amounts of specific work and exergy efficiency. Taking the mixture of C2H6 and CHF3 as an example, the specific work and exergy efficiency with different ratios of C2H6 and CHF3 is illustrated in Fig. 9. The specific work and exergy efficiency of mixtures differ from those of pure working fluid at some ratios. However, the specific work and exergy efficiency decrease rapidly when the ratio is equal to 0.3/0.7. This implies that the ratio of the mixture has an impact on the specific work and exergy efficiency. Therefore, the ratio of binary mixtures needs to be optimized. In this section, the five pure working fluids selected in Section 5.1 are combined to form binary mixtures. The net output power is used as the objective function, and the working fluid composition, mass flow, and mass fraction of the RC subsystem are selected as optimization variables. The optimal condition for each binary mixture and the corresponding system parameters obtained from the GA are shown in Table 11. As shown in Table 11, the binary mixtures of C2H6/CH2F2, C2H6/CO2, CHF3/CO2, CH2F2/C2F6, and CH3F/C2F6 become pure working fluid (mass fraction is equal to 1). Moreover, the specific work

Fig. 11. The ratio of equivalent output power for each subsystem.

Fig. 12. Irreversibility of the components with binary mixtures CH3F/CO2. 10

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Table 14 Irreversibility of the components with binary mixtures CH3F/CO2. HEX1

HEX2

COND1

COND2

HEX5

HEX6

HEX4

HEX7

PUMP1

PUMP2

EVAP

TURBINE

2.08%

4.02%

27.05%

19.86%

6.74%

2.92%

1.85%

2.95%

1.06%

1.06%

7.36%

23.06%

12:00 to 13:00, and 18:00 to 19:00, respectively. The inlet mass flow of LNG has a significant impact on the performance of the entire system, and Fig. 14 illustrates the daily by-products of the resulting variation of cold energy recovery at a gas station. The thermal efficiency and energy efficiency at a gas station is shown in Fig. 15, and the results reveal a strange phenomenon: the best efficiency occurs when the mass flow of LNG is the lowest between 15:00 and 16:00 because the temperature glide match degree is the key element in this boundary condition. In addition, as the mass flow of LNG increases, the efficiency of the entire system approaches a thermal efficiency of approximately 61% and an energy efficiency of 46%, as shown in Fig. 15(b). 5.5. Comparison of the results with or without energy storage Due to the daily changes of mass flow of LNG, the power generation by the system and the refrigeration capability will fluctuate greatly. So the energy storage system and allocation algorithm are designed to make the cold energy to better match the users’ demands. Figs. 16 and 17 show the comparison between the energy allocation with and without the energy storage system. In this diagram, the curve represents the users’ demands, and the bar chart represents the actual energy supply. From the chart, the peak period of users’ demands is from 08:00 to 17:00, and the energy supplied by the system does, however, not match this ranges. It is notice that in 15:00, the system without energy storage supplies the least amount of energy, but the users’ demands are larger than the supplies. On the contrary, in 19:00, the system provides the largest electric power and refrigeration capability. Under this circumstances, with the addition of the energy storage system and the allocation algorithm, energy supplies with energy storage are guaranteed to meet the peak period of users’ demands and as far as possible to provide energy in the low peak period.

Fig. 13. Variation of LNG daily flow at a gas station.

of the power generation subsystem is at a maximum when CH3F/CO2 is selected as the binary mixtures. To observe changes occurring in specific work visually, the results in Table 11 are displayed graphically in Fig. 10. The two horizontal coordinates represent the first and second components of the binary mixtures, respectively, and the vertical coordinate represents the specific work of the binary mixtures. 5.3. Thermodynamic analysis In Section 5.2, the binary mixture of CH3F/CO2, regarded as the optimum working fluid, was discussed in the power generation subsystem. To evaluate the efficiency of the entire system, the gasoline vapor recovery, Rectisol wash, and air conditioning subsystems are transformed into the equivalent output power to evaluate performance with a unified indicator, and the results are displayed in Tables 12 and 13 and Fig. 11. The Rectisol wash subsystem obtains the most significant portion of equivalent output power, and the equivalent thermal efficiency and system exergy efficiency are 79.05% and 48.18%, respectively. Fig. 12 illustrates that the ratio of the irreversibility that is produced in each component during the simulation. The components of COND1 and COND2, as listed in Table 14, contribute the highest irreversibility during the condensation process because the temperature difference between the working fluid and the LNG stream is large in the condenser. The highest irreversibility of components (approximately 82.2%) is produced by the power generation cycle. Therefore, a feasible method that reduces the irreversibility of COND1, COND2, and TURBINE will effectively improve the efficiency of the entire system.

6. Conclusions In this study, a novel design for LNG cold energy recovery is proposed by integrating gasoline vapor recovery, cascade Rankine power generation, a Rectisol wash, air conditioning and liquefied air energy storage. Using the GA, optimal binary zeotropic mixtures that improve the net output power were identified. This method is a new idea for cascade utilization of cold energy. The main conclusions can be summarized as follows: (1) When the condensing temperatures of FLASH 1, 2, and 3 are set as −37, −64, and −117 °C, respectively, the lowest energy consumption under the condition of 800 kg/h gasoline vapor recovery is 68.71 kW. (2) In the Rankine power generation subsystem, setting the outlet pressure of the evaporator and turbine to the critical pressure of the working fluid and ambient pressure, respectively, obtains the maximum value of specific work. (3) The trend between the specific work and critical pressure of working fluid is identical, meaning that when the power generation cycle operates with a working fluid having a higher critical pressure, a higher amount of specific work will be obtained. (4) When CH3F/CO2 (0.2247/0.7753) is selected, the Rankine power generation subsystem performs the best and its specific work and exergy efficiency are corresponding to 135.16 kJ/kg and 31.57%,

5.4. Daily by-products of cold energy recovery Because most gas stations are located in cities, the inlet mass flow of LNG will vary with the demands of terminal users. In other words, there is a fluctuation in the inlet mass flow of LNG. Taking an actual gas station in China as an example, the fluctuation in the inlet mass flow of LNG is displayed in Fig. 13. Three peaks of terminal user demands occur in the morning, noon, and evening, corresponding to 07:00 to 8:00, 11

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Fig. 14. Variation of cold energy recovery daily by-products at a gas station.

Fig. 15. Thermal efficiency and exergy efficiency at a gas station.

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Fig. 16. Allocation of electricity supplies and demands with or without energy storage system.

Fig. 17. Allocation of refrigeration capacity supplies and demands with or without energy storage system.

Postdoctoral Science Foundation [grant numbers 2019T120374]; the Guangxi Natural Science Foundation Program [grant number 2017GXNSFBA198198].

respectively. (5) Condensers and turbines donate the highest irreversibility of entire system, that is 46.91% and 23.06%. (6) The inlet mass flow of LNG will vary with the demands of terminal user. Similarly, the two subsystems of power generation, Rectisol wash have the same tendency as the variation of mass flow of LNG. In air conditioning subsystem, the refrigeration capacity is more evenly distributed at different times. (7) The efficiency of entire system decreases with the increase of LNG mass flow, the equivalent thermal efficiency and exergy efficiency stable at around 61% and 46% finally. (8) Comparing to the whole system without energy storage, the system with energy storage and allocation algorithm can supply enough cold energy to match the users’ demands in the peak periods from 08:00 to 17:00 and as far as possible to provide energy in the low peak period.

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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. Acknowledgements This work was supported by the National Natural Science Foundation of China [grant numbers 2018NSFC51805100]; the China 13

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