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An optimal design methodology for large-scale gas liquefaction
Applied Energy 99 (2012) 484–490
Contents lists available at SciVerse ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
An optimal design methodology for large-scale gas liquefaction Yongliang Li a, Xiang Wang b, Yulong Ding a,b,⇑ a b
Institute of Particle Science & Engineering, University of Leeds, Clarendon Road, Leeds LS2 9JT, United Kingdom State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Haidian District, Beijing 10090, PR China
h i g h l i g h t s " Configuration selection and parametric optimization carried out simultaneously for gas liquefaction systems. " Effective Heat Transfer Factor proposed to indicate the performance of heat exchanger networks. " Relatively high exergy efficiency of liquefaction process achievable under some general assumptions.
a r t i c l e
i n f o
Article history: Received 2 November 2011 Received in revised form 28 March 2012 Accepted 27 April 2012 Available online 28 May 2012 Keywords: Gas liquefaction system Process modelling Thermodynamic optimization Pinch technology
a b s t r a c t This paper presents an optimization methodology for thermodynamic design of large scale gas liquefaction systems. Such a methodology enables configuration selection and parametric optimization to be implemented simultaneously. Exergy efficiency and genetic algorithm have been chosen as an evaluation index and an evaluation criterion, respectively. The methodology has been applied to the design of expander cycle based liquefaction processes. Liquefaction processes of hydrogen, methane and nitrogen are selected as case studies and the simulation results show that relatively high exergy efficiencies (52% for hydrogen and 58% for methane and nitrogen) are achievable based on very general consumptions. Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved.
1. Introduction Gas liquefaction is a process for refrigerating a gas to a temperature below its critical temperature so that liquid can be formed at some suitable pressure below its critical value. Many gases can be turned into the liquid state either at the normal atmospheric pressure or at a pressurized state by simple cooling. The process has been widely used for scientific, industrial and commercial purposes ranging from medical and biological fields, to superconductivity and aerospace engineering [1,2]. Large scale gas liquefaction has also become a key technology in the energy supply field as a result of developments of new energy sources and energy carriers. For instance, Liquefied Natural Gas (LNG) is playing an increasingly important role in countries relying heavily on importing natural gas [3–5]. Liquid hydrogen is considered as an option for bulk transport in the future energy portfolio [6]. Liquid air/nitrogen has been proposed to be a combustion and emission free vehicle ‘fuel’ [7] and an energy carrier in a novel Cryogenic Energy Storage (CES) technology for storing both renewable and off-peak electricity [8–11]. As ⇑ Corresponding author at: Institute of Particle Science & Engineering, University of Leeds, Clarendon Road, Leeds LS2 9JT, United Kingdom. Tel.: +44 113 343 2747. E-mail address: [email protected] (Y. Ding).
liquefaction plants are rather complicated with numerous components interacting with each other and consume a large amount of process energy, it is vital to develop efficient liquefaction processes for improving the overall system performance and economic competitiveness [12]. This development is believed to be achievable as the current exergy efficiency of liquefaction process is only about 41–45% for the most efficient large scale LNG plants [13,14]. Although it is reported that the Snøhvit LNG plant in arctic Norway has an exergy efficiency close to 50%, the decreased power consumption is mainly due to the low ambient temperature instead of technological improvements [15,16]. Meanwhile hydrogen liquefaction plants generally have an even lower efficiency of about 30% [17]. This paper reports an attempt to develop a genetic algorithm based optimal design method for building a large scale gas liquefaction system. As a first step towards building such a system, a thermodynamic design is performed to select suitable configuration and operating conditions. This is an efficient way to improve the overall efficiency of the system as the performance of the components used in the system is largely determined by the level of technology available, which is in turn dependent on their costs [18]. The paper is organized in the following manner. Section 2 briefly describes the gas liquefaction process. The proposed
0306-2619/$ - see front matter Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2012.04.040
Y. Li et al. / Applied Energy 99 (2012) 484–490
methodology is then detailed in Section 3. Case studies are given in Section 4, and finally, conclusions are drawn in Section 5. 2. A brief process description of gas liquefaction Although many methods can be used to liquefy gases, they operate on the same basic principle as shown in Fig. 1. The feed gas is first compressed to an elevated pressure in an ambient-temperature compressor. The high-pressure gas goes through a countercurrent heat exchanger to a decompressor where expansion occurs. Cooling takes place during the decompression, which leads to low pressure gas and also formation of some liquid in the reservoir under right conditions. The cool, low-pressure gas returns to the compressor inlet to repeat the cycle. The purpose of the use of the countercurrent heat exchanger is to warm the low-pressure gas prior to the recompression, and simultaneously to cool the high-pressure gas to the lowest possible temperature prior to expansion. A refrigeration unit is usually involved to produce additional cold energy for the heat balance of the heat exchanger. The expansion process in the decompressor may take place either through a throttling device or in a power-producing device. In a throttling device the working fluid expands through an isenthalpic process (theoretically), leading to either an increase (when
Feed Gas
Compressor
Heat Exchanger (cold box)
Refrigeration Unit
Decompressor
485
the Joule–Thomson coefficient is negative) or a reduction (when the Joule–Thomson coefficient is positive) in temperature; see for example the case for methane as illustrated in Fig. 2. From the figure one can see that the high-pressure fluid can be fully liquefied if it is cooled to a sufficient low temperature prior to the throttle valve. Liquid expanders or the so-called cryoturbines could be used as power-producing devices for near-isentropic expansion where both temperature and enthalpy decrease. Comparing with the throttle valve, this gives an increase of 3–5% of the liquefaction efficiency because it reduces the cold requirement and at the same time produces additional shaft power [19]. Recent improvements on cryoturbine design have resulted in isentropic efficiencies on the test stand of up to 88%. Furthermore, the second generation cryoturbine with a submerged induction generator completely eliminates the need for any dynamic mechanical seals or couplings between the turbine and generator and therefore enables a very efficient shaft power recovery [20,21]. Liquefaction methods can be broadly grouped into Mixed Refrigerant Cycle (MRC) and expander cycle according to the use of the refrigeration unit [13,22]. The former employs a throttle valve with mixed and two-phase refrigerants for the cold production while the latter uses compression and expansion devices with single and gas-phase refrigerant to generate cold power. In this paper the expander cycle is selected for the case studies as it enables relatively rapid and simple startups and shutdowns and a more stable performance [23]. Another reason for doing so is that the ideal gas equation fails to work in the simulation as the liquefaction system runs at an extremely low temperature. The accurate thermodynamic properties of the mixed refrigerant is hard to calculate while these of the working fluid in the expander cycle can be obtained from a commercial software REFPROP 8.0 developed by National Institute of Standards and Technology (NIST). However it should be noted that the proposed methodology works for the design of MRC based liquefaction system as well if accurate thermodynamic properties can be obtained.
3. The proposed methodology 3.1. Thermodynamic modeling
Reservoir
Fig. 1. Principal process of gas liquefaction.
A thermal cycle consists of two elements: the alternative placement of power transfer units and heat transfer units, and the stream splitting and converge. As the stream converge does not
Fig. 2. Isenthalpic process of methane in a temperature–entropy diagram.
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Y. Li et al. / Applied Energy 99 (2012) 484–490
O311
HF21 O21
I21
expansion, and gTC is the isothermal efficiency of the compressor. This process represents an ambient-temperature compression using an air/water cooling system. The throttle valve is neither a power transfer unit nor a heat transfer unit but could be regarded as a zero-output power transfer unit (w = 0). As working fluid expands through an isenthalpic process, the liquefied mass fraction, x, can be calculated as:
C4111
HF311
I311
C311 C411N
C21
C41N1 HF31N
O31N
I31N
C31N C41NN
I1
x¼
C11
HF2N
I3N1
where hO,liquid and hO,gas represent enthalpies of output liquid and gas, respectively. As mentioned before, when hI < hO,liquid, the gas could be fully liquefied with x = 1. In the heat transfer unit the heat flux could be taken as the enthalpy difference of the inlet and outlet flows:
C3N1 C4N1N
C2N O2N
I2N
C4NN1
HF3NN
O3NN
ð6Þ
C4N11
HF3N1
O3N1
hI hO;gas hO;liquid hO;gas
I3NN
C3NN
qi ¼ hI;iþ1 hO;i
C4NNN
Fig. 3. Diagram of generalized thermodynamic cycle (I – inlet, O – outlet, C – power-transfer component, HF – heat flux, Ai – ith value of A).
affect the thermodynamic properties of the fluids while regarding them as different streams, only stream splitting is considered in the systematic optimization. Despite of the specific heat exchanger network, the generalized superstructure of a thermal cycle could be represented as Fig. 3 which is a tree-like structure. In practical applications, this superstructure could be simplified by the use of constrains such as the upper limits of component stages and overall component numbers and/or the stream numbers of each stream split. In a gas liquefaction process the power transfer units include cold expanders (including cryoturbine) and compressors. Power generated by the cold expander could be expressed as:
w ¼ ðhO;isentropic hI Þ gCE
ð1Þ
where hI is the input enthalpy, hO,isentropic is the ideal output enthalpy after an isentropic expansion, gCE is the isentropic efficiency of the cold expander and w is the specific power output of the cold expander. Note the output power of the expander is taken as negative for the convenience of the whole system design. Considering the cold expander works below the ambient temperature, it is reasonable to regard the practical expansion as an adiabatic process. As a result, the actual output enthalpy, hO, can be given as:
hO ¼ ðhO;isentropic hI Þ gCE þ hI
ð2Þ
There are two types of compression processes in liquefaction plants, isentropic compression and isothermal compression. In the present study isentropic compression is applied when the fluid temperature is lower than the ambient temperature and the power consumption is calculated by:
w ¼ ðhO;isentropic hI Þ=gEC
ð3Þ
where gEC is the isentropic efficiency of the compressor. The actual output enthalpy of the isentropic compressor is calculated as:
hO ¼ ðhO;isentropic hI Þ=gEC þ hI
ð4Þ
If the fluid temperature is higher than the ambient temperature, the process is considered as an isothermal compression and the power consumption is expressed as:
w ¼ ðhO;isothermal hI Þ T ambient ðsO;isothermal sI Þ =gTC
ð5Þ
where sI is the input entropy, hO,isothermal and sO,isothermal are respectively the ideal output enthalpy and entropy after an isothermal
ð7Þ
where qi is the ith heat flux, hI,i+1 is the (i + 1)th inlet enthalpy and hO,i is the ith outlet enthalpy. Here, it is assumed that there is neither pressure drop nor heat loss in the heat transfer processes. The thermodynamic models are capable of simulating not only the main open cycle of liquefaction but also the closed-loop refrigeration cycle by setting I1 = ON. In this study, the inlet pressure PI and temperature TI are set to be optimizing variables and other parameters can be calculated using the above equations and the commercial package REFPROP 8.0.
3.2. Optimal design method From the above one can see that giving the inlet parameters (including flow rate, temperature and pressure) and some outlet parameters (e.g. outlet pressure) of a power transfer component, the other state parameters as well as the heat loads and power can be calculated. Therefore, the optimal design of a liquefaction system can be transformed into stream problems and expressed mathematically in the following form:
_ L eL m max P _ i wi m X _ i qi ¼ 0 m
DT pinch P DT approach
ð8Þ ð9Þ ð10Þ
_ i and m _ L represent the mass flow in the ith component and where m the mass flow of liquid product, respectively, eL is the cryogenic exergy of the liquid product, DTpinch is pinch point temperature difference (the minimum temperature difference in the heat exchanger network), and DTapproach is the approach temperature (the minimum allowable temperature difference in the stream profiles for the heat exchanger network). Eq. (8) is the objective function for the optimization, which refers to the exergy efficiency of the liquefaction process. Eqs. (9) and (10) are the constraints for the optimization and imply the heat balance (first law of thermodynamics) and minimum temperature level requirement of the heat exchanger network (second law of thermodynamics). Optimization of liquefaction processes is a very complex nonlinear problem, which may have several local optimal solutions. The genetic algorithm (GA) is an effective approach to this type of problem and has been used for thermal system optimizations in the past [2,24]. In the present work, a programme is developed in the Matlab 7.0 environment, using the GA as a tool for the optimal design of liquefaction processes. The performance of the program will be tested in the next section.
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3.3. Effective Heat Transfer Factor No matter how complex a heat exchanger network can be, the process can be represented by a diagram of temperature against heat load as shown schematically in Fig. 4. Such a diagram is called the composite curves [25]. In the figure TH and TC are the temperature distributions of hot fluid and cold fluid respectively. Consider a reversibly infinitesimal heat transfer process that the cold fluid attains a heat load of DQ (DQ > 0), the exergy change of the cold fluid could be given as:
DQ T ambient ¼ DQ 1 TC TC
ð11Þ
At the same time, as the hot fluid release a heat load of DQ, one has the exergy change of the hot fluid:
DQ T ambient deH ¼ dhH T ambient ¼ DQ 1 TH TH
ð12Þ
As all heat transfer processes produce entropy (consume exergy with deC + deH < 0), flows with a high exergy change reject exergy. As a result, for a hot fluid with a higher exergy change (deC < deH), the ideal heat transfer can be regarded to occur between the hot fluid and a third fluid with a temperature DTpinch lower than that of the hot fluid. On the other hand, for a cold fluid with a higher exergy change (deC > deH), the ideal heat transfer can be regarded to take place between the cold fluid and a third fluid with a temperature DTpinch higher than that of the cold fluid. According to the above, the temperatures of the above-discussed third fluids, T 0H and T 0C , can be defined as:
(
T 0C ¼
TC
1 TH
T H þ DT pinch
1 TH
½T H DT pinch ½T C
þ T1C 6 T þ
1 TC
>T
2
EHTF ¼
Q1
1 TC
Ambient pressure (kPa) Ambient temperature (K) Liquid product pressure (kPa) Temperature approach of heat exchanger network DTapproach (K) Working fluid of the refrigeration cycle Isentropic efficiency of the cold expander gCE (%) Isentropic efficiency of the cryoturbine gLE (%) Isentropic efficiency of the compressor gEC (%) Isothermal efficiency of compressor gTC (%) Component stages of main flow Component stages of refrigeration cycle Max splitting streams of the main flow Max splitting streams of the refrigeration flow
101.325 293.15 101.325 5 Helium 88 70 87 87 3 4 2 2
ð13Þ
ambient
þ dQ T 0H R Q2 1 T1H dQ Q1 TC 1 TH
Table 1 Assumptions of operating condition and performance of the components.
2 ambient
As a result, a dimensionless number named Effective Heat Transfer Factor, EHTF, can be defined as follows according to the above definitions of the third fluids to examine the effectiveness the heat transfer processes:
R Q2 1
In the following, case studies are provided to illustrate the optimal design methodology. To simplify the computation, all the liquefaction systems are assumed to operate in the steady state. Further assumptions for the simulations are listed in Table 1. In the simulations not only the thermodynamic laws (Eqs. (9) and (10)) but also the stream numbers are used as the constraints to
1 T 0C
ð14Þ
where Q1 and Q2 are respectively the initial and final heat load values of the heat transfer process and T H ; T C ; T 0H , and T 0C are all the functions of the heat load. The EHTF has a value ranging between 0 and 1, which represents the exergy loss ratio of ideal heat transfer processes to the actual heat transfer processes. As ideal heat transfer processes are
60
50
40
30
Hydrogen Methane Nitrogen
20
10 0
10
20
30
40
50
Generations Fig. 5. Liquefaction exergy efficiencies versus number of generations.
T 0.5
TH (Q ) 0.4
ΔT pinch T ' H (Q )
EHTF values
½T 0H
4. Case studies
Exergy efficiency of liquefaction (%)
deC ¼ dhC T ambient
unachievable in practice, particularly when there is phase-change, EHTF is a parameter that indicates how close a real process approaches to an ideal heat transfer process.
0.3
0.2
TC (Q )
dQ
Hydrogen Methane Nitrogen
0.1
Tambient
Q1
Q Q + dQ
Q2
0
Q
Fig. 4. Composite curves of heat transfer processes.
10
20
30
40
50
Generations Fig. 6. Corresponding EHTF values versus number of generations.
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Y. Li et al. / Applied Energy 99 (2012) 484–490
simplify the configurations. It is worth mentioning that the boundary conditions of the optimization variables are also additional constraints. However it turns out that as long as the boundary conditions are reasonable their values affect only the simulation time while the final solutions are almost the same. Therefore the specific values of the boundary conditions are not listed in Table 1. As can be seen from Table 1 helium is selected as the model working fluid for the refrigeration cycle in the following simulations due to its wide working temperature range and high heat transfer coefficient. On the other hand it should be noted that practical applications of helium as the working fluid were only found in hydrogen liquefaction and nuclear power plants because of its high cost and poor compressibility. Three gases, hydrogen, methane and nitrogen, are selected as examples for the optimal design and the throttle valve is chosen as the decompressor in the first place. The results are shown in Fig. 5 in the form of liquefaction efficiency versus the number of generations. One can see that all the values of fitness become
Exergy efficiency of liquefaction (%)
60
50
40
30
Using throttle valve Using cryoturbine 20
10 0
10
20
30
40
50
Generation Fig. 7. Optimization decompressors.
processes
of
hydrogen
liquefaction
using
different
Fig. 8. T–Q composite curves for the hydrogen liquefaction process using cryoturbine: (a) initial system and (b) optimal system.
Feed in Hydrogen Gas
Hydrogen flow Helium flow 11
12
13 Expander 1 Compressor
2 Air/water cooling 5 Cryoturbine 4
Possible heat transfer 6
Heat exchanger network
7
10
9
8
3
Liquid Product Fig. 9. Flow chart of optimized liquefaction process of hydrogen.
489
Y. Li et al. / Applied Energy 99 (2012) 484–490 Table 2 Heat flow parameters of the optimized liquefaction process of hydrogen. Flow no.
Mass flow (kg/s)
Pressure (kPa)
Inlet temperature (K)
Outlet temperature (K)
Fluid
1 2 3 4 5 6 7 8 9 10 11 12 13
1.0 1.0 0.546 1.616 1.909 1.616 1.909 1.616 0.995 0.914 1.616 0.995 0.914
1945.4 3064.6 101.3 3001.1 3001.1 2309.8 400.2 767.0 268.3 268.3 101.3 101.3 101.3
293.2 163.1 213.7 293.2 293.2 146.8 133.4 53.6 85.9 85.9 35.2 210.9 107.3
137.6 40.0 293.2 160.7 259.5 80.0 98.7 68.8 293.2 149.7 270.0 270.0 270.0
Hydrogen Hydrogen Hydrogen Helium Helium Helium Helium Helium Helium Helium Helium Helium Helium
constant after about 40 generations. Hydrogen liquefaction shows the lowest exergy efficiency of about 52%, which is reasonable as hydrogen has the lowest condensation point. However the exergy efficiency of methane liquefaction is even slightly lower than that of nitrogen liquefaction although its condensation temperature is a bit higher. This can be explained in the following by referring to the corresponding EHTF value shown in Fig. 6. Fig. 6 shows the evolution of EHTF. One can see the similar trend in the exergy efficiency for all the three gases with some small fluctuations in initial periods. This suggests that the exergy efficiency could be improved through optimizing the heat exchanger network. Look specifically at methane, it has the lowest EHTF value, which decreases its overall liquefaction efficiency. As methane has the highest critical pressure of about 4.596 MPa, a more efficient heat exchanger network can only be achieved by increasing the component stages. This is confirmed by comparing a 6stage refrigeration system with the 4-stage one as mentioned above. By adding two more stages in the refrigeration cycle, the EHTF value increases from 0.23 to 0.45, and the liquefaction exergy efficiency increasing from 58% to 62%. As mentioned before, the liquefaction efficiency can be increased significantly when the throttle valve is replaced by a cryoturbine. Simulation of the use of cryoturbine is therefore carried out and the results are illustrated in Fig. 7 for hydrogen, together with the results for the throttle valve. One can see that the replacement with the cryoturbine increases the liquefaction efficiency from 52% to about 56%. Fig. 8 shows the initial and optimized composite curves for the use of the cryoturbine. One can see that the temperature difference is greatly decreased by the system optimization, especially at temperature below about 200 K. The decreased exergy loss in the heat exchange process in return contributes greatly to the improvement on the overall exergy efficiency. After discussing the liquefaction process, the attention is now drawn to the specific configuration of the system. Fig. 9 shows a flow chart of hydrogen liquefaction process based on the optimization results shown in Fig. 5 and the corresponding heat flow parameters are listed in Table 2. The heat exchanger network of the system is complicated, which is made up of six hot streams and seven cold streams. As one hot stream may exchange heat with more than one cold streams, splitting of the streams into parallel branches is often required. Of course the multi-steam heat exchanger could be used as an alternative. As a result, the capital cost should be considered, which may affect the configuration of the system. This requires a multi-objective optimization of the system with both the exergy efficiency and the capital cost to be optimized. This is underway and the results will be reported in near future.
5. Concluding remarks This paper presents an optimal design methodology for large scale gas liquefaction systems on the basis of the pinch technology and the genetic algorithm. The method enables the selection to be carried out simultaneously of suitable system configuration and the operating conditions. The simulation results show that relatively high exergy efficiencies of liquefaction (52% for hydrogen and 58% for nitrogen and methane) can be achieved under some general assumptions, and the use of a cryoturbine could significantly enhance the exergy efficiency compared with the use of a throttle valve. A parameter named Effective Heat Transfer Factor (EHTF) is found to be able to indicate the performance of heat exchanger networks. The results also indicate that an optimized system configuration may be too complicated and multi-objective optimization is needed to consider both the efficiency and the capital cost.
Acknowledgements The authors gratefully acknowledge the financial support of the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom under Grant EP/F060955/1 and Ministry of Science & Technology of People’s Republic of China under Grant 2012BAA03B00.
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[14] Dubar C et al. A competive offshore LNG scheme utilising a gravity base structure and improved nitrogen cycles. Presented at the Proceedings of the LNG 12, Perth, WA, Australia. [15] Rian AB, Ertesvåg IS. Exergy evaluation of the Arctic Snøhvit liquefied natural gas processing plant in Northern Norway – significance of ambient temperature. Energy Fuel 2012;26:1259–67. 2012/02/16. [16] Mosbergvik OA. Statoil to begin Snøhvit LNG operations by yearend. Oil Gas J 2007;105(2007):48–56. [17] Syed MT et al. An economic analysis of three hydrogen liquefaction systems. Int J Hydrogen Energy 1998;23:565–76. [18] Nandi TK, Sarangi S. Performance and optimization of hydrogen liquefaction cycles. Int J Hydrogen Energy 1993;18:131–9. [19] Liquid expanders in LNG liquefaction plants, vol. 2002. World Pumps; 2002. p. 16. [20] Hylton EH, Kimmel HE. Exducer turbines, the optimized solution for LNG expanders. Nevada, USA: Ebara International Corporation; 2002.
[21] Haesloop B, Kimmel HE. Improved cryogenic gas processing efficiency due to advancements in liquid turbine expanders. In: AIChE Spring National Meeting, Sparks, Nevada, USA; 1998. [22] Chang H-M et al. Thermodynamic design of methane liquefaction system based on reversed-Brayton cycle. Cryogenics 2009;49:226–34. [23] Finn AJ et al. Developments in natural gas liquefaction. Hydrocarb Process 1999;78:47–59. [24] Mohagheghi M, Shayegan J. Thermodynamic optimization of design variables and heat exchangers layout in HRSGs for CCGT, using genetic algorithm. Appl Therm Eng 2009;29:290–9. [25] Kemp IC. Pinch analysis and process integration – a user guide on process integration for the efficient use of energy. 2nd ed.; 2007. [04.05.2010].
Contents lists available at SciVerse ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
An optimal design methodology for large-scale gas liquefaction Yongliang Li a, Xiang Wang b, Yulong Ding a,b,⇑ a b
Institute of Particle Science & Engineering, University of Leeds, Clarendon Road, Leeds LS2 9JT, United Kingdom State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Haidian District, Beijing 10090, PR China
h i g h l i g h t s " Configuration selection and parametric optimization carried out simultaneously for gas liquefaction systems. " Effective Heat Transfer Factor proposed to indicate the performance of heat exchanger networks. " Relatively high exergy efficiency of liquefaction process achievable under some general assumptions.
a r t i c l e
i n f o
Article history: Received 2 November 2011 Received in revised form 28 March 2012 Accepted 27 April 2012 Available online 28 May 2012 Keywords: Gas liquefaction system Process modelling Thermodynamic optimization Pinch technology
a b s t r a c t This paper presents an optimization methodology for thermodynamic design of large scale gas liquefaction systems. Such a methodology enables configuration selection and parametric optimization to be implemented simultaneously. Exergy efficiency and genetic algorithm have been chosen as an evaluation index and an evaluation criterion, respectively. The methodology has been applied to the design of expander cycle based liquefaction processes. Liquefaction processes of hydrogen, methane and nitrogen are selected as case studies and the simulation results show that relatively high exergy efficiencies (52% for hydrogen and 58% for methane and nitrogen) are achievable based on very general consumptions. Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved.
1. Introduction Gas liquefaction is a process for refrigerating a gas to a temperature below its critical temperature so that liquid can be formed at some suitable pressure below its critical value. Many gases can be turned into the liquid state either at the normal atmospheric pressure or at a pressurized state by simple cooling. The process has been widely used for scientific, industrial and commercial purposes ranging from medical and biological fields, to superconductivity and aerospace engineering [1,2]. Large scale gas liquefaction has also become a key technology in the energy supply field as a result of developments of new energy sources and energy carriers. For instance, Liquefied Natural Gas (LNG) is playing an increasingly important role in countries relying heavily on importing natural gas [3–5]. Liquid hydrogen is considered as an option for bulk transport in the future energy portfolio [6]. Liquid air/nitrogen has been proposed to be a combustion and emission free vehicle ‘fuel’ [7] and an energy carrier in a novel Cryogenic Energy Storage (CES) technology for storing both renewable and off-peak electricity [8–11]. As ⇑ Corresponding author at: Institute of Particle Science & Engineering, University of Leeds, Clarendon Road, Leeds LS2 9JT, United Kingdom. Tel.: +44 113 343 2747. E-mail address: [email protected] (Y. Ding).
liquefaction plants are rather complicated with numerous components interacting with each other and consume a large amount of process energy, it is vital to develop efficient liquefaction processes for improving the overall system performance and economic competitiveness [12]. This development is believed to be achievable as the current exergy efficiency of liquefaction process is only about 41–45% for the most efficient large scale LNG plants [13,14]. Although it is reported that the Snøhvit LNG plant in arctic Norway has an exergy efficiency close to 50%, the decreased power consumption is mainly due to the low ambient temperature instead of technological improvements [15,16]. Meanwhile hydrogen liquefaction plants generally have an even lower efficiency of about 30% [17]. This paper reports an attempt to develop a genetic algorithm based optimal design method for building a large scale gas liquefaction system. As a first step towards building such a system, a thermodynamic design is performed to select suitable configuration and operating conditions. This is an efficient way to improve the overall efficiency of the system as the performance of the components used in the system is largely determined by the level of technology available, which is in turn dependent on their costs [18]. The paper is organized in the following manner. Section 2 briefly describes the gas liquefaction process. The proposed
0306-2619/$ - see front matter Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2012.04.040
Y. Li et al. / Applied Energy 99 (2012) 484–490
methodology is then detailed in Section 3. Case studies are given in Section 4, and finally, conclusions are drawn in Section 5. 2. A brief process description of gas liquefaction Although many methods can be used to liquefy gases, they operate on the same basic principle as shown in Fig. 1. The feed gas is first compressed to an elevated pressure in an ambient-temperature compressor. The high-pressure gas goes through a countercurrent heat exchanger to a decompressor where expansion occurs. Cooling takes place during the decompression, which leads to low pressure gas and also formation of some liquid in the reservoir under right conditions. The cool, low-pressure gas returns to the compressor inlet to repeat the cycle. The purpose of the use of the countercurrent heat exchanger is to warm the low-pressure gas prior to the recompression, and simultaneously to cool the high-pressure gas to the lowest possible temperature prior to expansion. A refrigeration unit is usually involved to produce additional cold energy for the heat balance of the heat exchanger. The expansion process in the decompressor may take place either through a throttling device or in a power-producing device. In a throttling device the working fluid expands through an isenthalpic process (theoretically), leading to either an increase (when
Feed Gas
Compressor
Heat Exchanger (cold box)
Refrigeration Unit
Decompressor
485
the Joule–Thomson coefficient is negative) or a reduction (when the Joule–Thomson coefficient is positive) in temperature; see for example the case for methane as illustrated in Fig. 2. From the figure one can see that the high-pressure fluid can be fully liquefied if it is cooled to a sufficient low temperature prior to the throttle valve. Liquid expanders or the so-called cryoturbines could be used as power-producing devices for near-isentropic expansion where both temperature and enthalpy decrease. Comparing with the throttle valve, this gives an increase of 3–5% of the liquefaction efficiency because it reduces the cold requirement and at the same time produces additional shaft power [19]. Recent improvements on cryoturbine design have resulted in isentropic efficiencies on the test stand of up to 88%. Furthermore, the second generation cryoturbine with a submerged induction generator completely eliminates the need for any dynamic mechanical seals or couplings between the turbine and generator and therefore enables a very efficient shaft power recovery [20,21]. Liquefaction methods can be broadly grouped into Mixed Refrigerant Cycle (MRC) and expander cycle according to the use of the refrigeration unit [13,22]. The former employs a throttle valve with mixed and two-phase refrigerants for the cold production while the latter uses compression and expansion devices with single and gas-phase refrigerant to generate cold power. In this paper the expander cycle is selected for the case studies as it enables relatively rapid and simple startups and shutdowns and a more stable performance [23]. Another reason for doing so is that the ideal gas equation fails to work in the simulation as the liquefaction system runs at an extremely low temperature. The accurate thermodynamic properties of the mixed refrigerant is hard to calculate while these of the working fluid in the expander cycle can be obtained from a commercial software REFPROP 8.0 developed by National Institute of Standards and Technology (NIST). However it should be noted that the proposed methodology works for the design of MRC based liquefaction system as well if accurate thermodynamic properties can be obtained.
3. The proposed methodology 3.1. Thermodynamic modeling
Reservoir
Fig. 1. Principal process of gas liquefaction.
A thermal cycle consists of two elements: the alternative placement of power transfer units and heat transfer units, and the stream splitting and converge. As the stream converge does not
Fig. 2. Isenthalpic process of methane in a temperature–entropy diagram.
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O311
HF21 O21
I21
expansion, and gTC is the isothermal efficiency of the compressor. This process represents an ambient-temperature compression using an air/water cooling system. The throttle valve is neither a power transfer unit nor a heat transfer unit but could be regarded as a zero-output power transfer unit (w = 0). As working fluid expands through an isenthalpic process, the liquefied mass fraction, x, can be calculated as:
C4111
HF311
I311
C311 C411N
C21
C41N1 HF31N
O31N
I31N
C31N C41NN
I1
x¼
C11
HF2N
I3N1
where hO,liquid and hO,gas represent enthalpies of output liquid and gas, respectively. As mentioned before, when hI < hO,liquid, the gas could be fully liquefied with x = 1. In the heat transfer unit the heat flux could be taken as the enthalpy difference of the inlet and outlet flows:
C3N1 C4N1N
C2N O2N
I2N
C4NN1
HF3NN
O3NN
ð6Þ
C4N11
HF3N1
O3N1
hI hO;gas hO;liquid hO;gas
I3NN
C3NN
qi ¼ hI;iþ1 hO;i
C4NNN
Fig. 3. Diagram of generalized thermodynamic cycle (I – inlet, O – outlet, C – power-transfer component, HF – heat flux, Ai – ith value of A).
affect the thermodynamic properties of the fluids while regarding them as different streams, only stream splitting is considered in the systematic optimization. Despite of the specific heat exchanger network, the generalized superstructure of a thermal cycle could be represented as Fig. 3 which is a tree-like structure. In practical applications, this superstructure could be simplified by the use of constrains such as the upper limits of component stages and overall component numbers and/or the stream numbers of each stream split. In a gas liquefaction process the power transfer units include cold expanders (including cryoturbine) and compressors. Power generated by the cold expander could be expressed as:
w ¼ ðhO;isentropic hI Þ gCE
ð1Þ
where hI is the input enthalpy, hO,isentropic is the ideal output enthalpy after an isentropic expansion, gCE is the isentropic efficiency of the cold expander and w is the specific power output of the cold expander. Note the output power of the expander is taken as negative for the convenience of the whole system design. Considering the cold expander works below the ambient temperature, it is reasonable to regard the practical expansion as an adiabatic process. As a result, the actual output enthalpy, hO, can be given as:
hO ¼ ðhO;isentropic hI Þ gCE þ hI
ð2Þ
There are two types of compression processes in liquefaction plants, isentropic compression and isothermal compression. In the present study isentropic compression is applied when the fluid temperature is lower than the ambient temperature and the power consumption is calculated by:
w ¼ ðhO;isentropic hI Þ=gEC
ð3Þ
where gEC is the isentropic efficiency of the compressor. The actual output enthalpy of the isentropic compressor is calculated as:
hO ¼ ðhO;isentropic hI Þ=gEC þ hI
ð4Þ
If the fluid temperature is higher than the ambient temperature, the process is considered as an isothermal compression and the power consumption is expressed as:
w ¼ ðhO;isothermal hI Þ T ambient ðsO;isothermal sI Þ =gTC
ð5Þ
where sI is the input entropy, hO,isothermal and sO,isothermal are respectively the ideal output enthalpy and entropy after an isothermal
ð7Þ
where qi is the ith heat flux, hI,i+1 is the (i + 1)th inlet enthalpy and hO,i is the ith outlet enthalpy. Here, it is assumed that there is neither pressure drop nor heat loss in the heat transfer processes. The thermodynamic models are capable of simulating not only the main open cycle of liquefaction but also the closed-loop refrigeration cycle by setting I1 = ON. In this study, the inlet pressure PI and temperature TI are set to be optimizing variables and other parameters can be calculated using the above equations and the commercial package REFPROP 8.0.
3.2. Optimal design method From the above one can see that giving the inlet parameters (including flow rate, temperature and pressure) and some outlet parameters (e.g. outlet pressure) of a power transfer component, the other state parameters as well as the heat loads and power can be calculated. Therefore, the optimal design of a liquefaction system can be transformed into stream problems and expressed mathematically in the following form:
_ L eL m max P _ i wi m X _ i qi ¼ 0 m
DT pinch P DT approach
ð8Þ ð9Þ ð10Þ
_ i and m _ L represent the mass flow in the ith component and where m the mass flow of liquid product, respectively, eL is the cryogenic exergy of the liquid product, DTpinch is pinch point temperature difference (the minimum temperature difference in the heat exchanger network), and DTapproach is the approach temperature (the minimum allowable temperature difference in the stream profiles for the heat exchanger network). Eq. (8) is the objective function for the optimization, which refers to the exergy efficiency of the liquefaction process. Eqs. (9) and (10) are the constraints for the optimization and imply the heat balance (first law of thermodynamics) and minimum temperature level requirement of the heat exchanger network (second law of thermodynamics). Optimization of liquefaction processes is a very complex nonlinear problem, which may have several local optimal solutions. The genetic algorithm (GA) is an effective approach to this type of problem and has been used for thermal system optimizations in the past [2,24]. In the present work, a programme is developed in the Matlab 7.0 environment, using the GA as a tool for the optimal design of liquefaction processes. The performance of the program will be tested in the next section.
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3.3. Effective Heat Transfer Factor No matter how complex a heat exchanger network can be, the process can be represented by a diagram of temperature against heat load as shown schematically in Fig. 4. Such a diagram is called the composite curves [25]. In the figure TH and TC are the temperature distributions of hot fluid and cold fluid respectively. Consider a reversibly infinitesimal heat transfer process that the cold fluid attains a heat load of DQ (DQ > 0), the exergy change of the cold fluid could be given as:
DQ T ambient ¼ DQ 1 TC TC
ð11Þ
At the same time, as the hot fluid release a heat load of DQ, one has the exergy change of the hot fluid:
DQ T ambient deH ¼ dhH T ambient ¼ DQ 1 TH TH
ð12Þ
As all heat transfer processes produce entropy (consume exergy with deC + deH < 0), flows with a high exergy change reject exergy. As a result, for a hot fluid with a higher exergy change (deC < deH), the ideal heat transfer can be regarded to occur between the hot fluid and a third fluid with a temperature DTpinch lower than that of the hot fluid. On the other hand, for a cold fluid with a higher exergy change (deC > deH), the ideal heat transfer can be regarded to take place between the cold fluid and a third fluid with a temperature DTpinch higher than that of the cold fluid. According to the above, the temperatures of the above-discussed third fluids, T 0H and T 0C , can be defined as:
(
T 0C ¼
TC
1 TH
T H þ DT pinch
1 TH
½T H DT pinch ½T C
þ T1C 6 T þ
1 TC
>T
2
EHTF ¼
Q1
1 TC
Ambient pressure (kPa) Ambient temperature (K) Liquid product pressure (kPa) Temperature approach of heat exchanger network DTapproach (K) Working fluid of the refrigeration cycle Isentropic efficiency of the cold expander gCE (%) Isentropic efficiency of the cryoturbine gLE (%) Isentropic efficiency of the compressor gEC (%) Isothermal efficiency of compressor gTC (%) Component stages of main flow Component stages of refrigeration cycle Max splitting streams of the main flow Max splitting streams of the refrigeration flow
101.325 293.15 101.325 5 Helium 88 70 87 87 3 4 2 2
ð13Þ
ambient
þ dQ T 0H R Q2 1 T1H dQ Q1 TC 1 TH
Table 1 Assumptions of operating condition and performance of the components.
2 ambient
As a result, a dimensionless number named Effective Heat Transfer Factor, EHTF, can be defined as follows according to the above definitions of the third fluids to examine the effectiveness the heat transfer processes:
R Q2 1
In the following, case studies are provided to illustrate the optimal design methodology. To simplify the computation, all the liquefaction systems are assumed to operate in the steady state. Further assumptions for the simulations are listed in Table 1. In the simulations not only the thermodynamic laws (Eqs. (9) and (10)) but also the stream numbers are used as the constraints to
1 T 0C
ð14Þ
where Q1 and Q2 are respectively the initial and final heat load values of the heat transfer process and T H ; T C ; T 0H , and T 0C are all the functions of the heat load. The EHTF has a value ranging between 0 and 1, which represents the exergy loss ratio of ideal heat transfer processes to the actual heat transfer processes. As ideal heat transfer processes are
60
50
40
30
Hydrogen Methane Nitrogen
20
10 0
10
20
30
40
50
Generations Fig. 5. Liquefaction exergy efficiencies versus number of generations.
T 0.5
TH (Q ) 0.4
ΔT pinch T ' H (Q )
EHTF values
½T 0H
4. Case studies
Exergy efficiency of liquefaction (%)
deC ¼ dhC T ambient
unachievable in practice, particularly when there is phase-change, EHTF is a parameter that indicates how close a real process approaches to an ideal heat transfer process.
0.3
0.2
TC (Q )
dQ
Hydrogen Methane Nitrogen
0.1
Tambient
Q1
Q Q + dQ
Q2
0
Q
Fig. 4. Composite curves of heat transfer processes.
10
20
30
40
50
Generations Fig. 6. Corresponding EHTF values versus number of generations.
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simplify the configurations. It is worth mentioning that the boundary conditions of the optimization variables are also additional constraints. However it turns out that as long as the boundary conditions are reasonable their values affect only the simulation time while the final solutions are almost the same. Therefore the specific values of the boundary conditions are not listed in Table 1. As can be seen from Table 1 helium is selected as the model working fluid for the refrigeration cycle in the following simulations due to its wide working temperature range and high heat transfer coefficient. On the other hand it should be noted that practical applications of helium as the working fluid were only found in hydrogen liquefaction and nuclear power plants because of its high cost and poor compressibility. Three gases, hydrogen, methane and nitrogen, are selected as examples for the optimal design and the throttle valve is chosen as the decompressor in the first place. The results are shown in Fig. 5 in the form of liquefaction efficiency versus the number of generations. One can see that all the values of fitness become
Exergy efficiency of liquefaction (%)
60
50
40
30
Using throttle valve Using cryoturbine 20
10 0
10
20
30
40
50
Generation Fig. 7. Optimization decompressors.
processes
of
hydrogen
liquefaction
using
different
Fig. 8. T–Q composite curves for the hydrogen liquefaction process using cryoturbine: (a) initial system and (b) optimal system.
Feed in Hydrogen Gas
Hydrogen flow Helium flow 11
12
13 Expander 1 Compressor
2 Air/water cooling 5 Cryoturbine 4
Possible heat transfer 6
Heat exchanger network
7
10
9
8
3
Liquid Product Fig. 9. Flow chart of optimized liquefaction process of hydrogen.
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Y. Li et al. / Applied Energy 99 (2012) 484–490 Table 2 Heat flow parameters of the optimized liquefaction process of hydrogen. Flow no.
Mass flow (kg/s)
Pressure (kPa)
Inlet temperature (K)
Outlet temperature (K)
Fluid
1 2 3 4 5 6 7 8 9 10 11 12 13
1.0 1.0 0.546 1.616 1.909 1.616 1.909 1.616 0.995 0.914 1.616 0.995 0.914
1945.4 3064.6 101.3 3001.1 3001.1 2309.8 400.2 767.0 268.3 268.3 101.3 101.3 101.3
293.2 163.1 213.7 293.2 293.2 146.8 133.4 53.6 85.9 85.9 35.2 210.9 107.3
137.6 40.0 293.2 160.7 259.5 80.0 98.7 68.8 293.2 149.7 270.0 270.0 270.0
Hydrogen Hydrogen Hydrogen Helium Helium Helium Helium Helium Helium Helium Helium Helium Helium
constant after about 40 generations. Hydrogen liquefaction shows the lowest exergy efficiency of about 52%, which is reasonable as hydrogen has the lowest condensation point. However the exergy efficiency of methane liquefaction is even slightly lower than that of nitrogen liquefaction although its condensation temperature is a bit higher. This can be explained in the following by referring to the corresponding EHTF value shown in Fig. 6. Fig. 6 shows the evolution of EHTF. One can see the similar trend in the exergy efficiency for all the three gases with some small fluctuations in initial periods. This suggests that the exergy efficiency could be improved through optimizing the heat exchanger network. Look specifically at methane, it has the lowest EHTF value, which decreases its overall liquefaction efficiency. As methane has the highest critical pressure of about 4.596 MPa, a more efficient heat exchanger network can only be achieved by increasing the component stages. This is confirmed by comparing a 6stage refrigeration system with the 4-stage one as mentioned above. By adding two more stages in the refrigeration cycle, the EHTF value increases from 0.23 to 0.45, and the liquefaction exergy efficiency increasing from 58% to 62%. As mentioned before, the liquefaction efficiency can be increased significantly when the throttle valve is replaced by a cryoturbine. Simulation of the use of cryoturbine is therefore carried out and the results are illustrated in Fig. 7 for hydrogen, together with the results for the throttle valve. One can see that the replacement with the cryoturbine increases the liquefaction efficiency from 52% to about 56%. Fig. 8 shows the initial and optimized composite curves for the use of the cryoturbine. One can see that the temperature difference is greatly decreased by the system optimization, especially at temperature below about 200 K. The decreased exergy loss in the heat exchange process in return contributes greatly to the improvement on the overall exergy efficiency. After discussing the liquefaction process, the attention is now drawn to the specific configuration of the system. Fig. 9 shows a flow chart of hydrogen liquefaction process based on the optimization results shown in Fig. 5 and the corresponding heat flow parameters are listed in Table 2. The heat exchanger network of the system is complicated, which is made up of six hot streams and seven cold streams. As one hot stream may exchange heat with more than one cold streams, splitting of the streams into parallel branches is often required. Of course the multi-steam heat exchanger could be used as an alternative. As a result, the capital cost should be considered, which may affect the configuration of the system. This requires a multi-objective optimization of the system with both the exergy efficiency and the capital cost to be optimized. This is underway and the results will be reported in near future.
5. Concluding remarks This paper presents an optimal design methodology for large scale gas liquefaction systems on the basis of the pinch technology and the genetic algorithm. The method enables the selection to be carried out simultaneously of suitable system configuration and the operating conditions. The simulation results show that relatively high exergy efficiencies of liquefaction (52% for hydrogen and 58% for nitrogen and methane) can be achieved under some general assumptions, and the use of a cryoturbine could significantly enhance the exergy efficiency compared with the use of a throttle valve. A parameter named Effective Heat Transfer Factor (EHTF) is found to be able to indicate the performance of heat exchanger networks. The results also indicate that an optimized system configuration may be too complicated and multi-objective optimization is needed to consider both the efficiency and the capital cost.
Acknowledgements The authors gratefully acknowledge the financial support of the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom under Grant EP/F060955/1 and Ministry of Science & Technology of People’s Republic of China under Grant 2012BAA03B00.
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