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Study of integrated metal hydrides heat pump and cascade utilization of liquefied natural gas cold energy recovery system
international journal of hydrogen energy 35 (2010) 7236–7245
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Study of integrated metal hydrides heat pump and cascade utilization of liquefied natural gas cold energy recovery system Xiangyu Meng a, Feifei Bai a,b, Fusheng Yang a, Zewei Bao a, Zaoxiao Zhang a,* a
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xianning Road 28#, Xi’an, Shaanxi 710049, PR China b China Nuclear Power Design Co., Ltd, Shenzhen 518057, PR China
article info
abstract
Article history:
The traditional cold energy utilization of the liquefied natural gas system needs a higher
Received 17 November 2009
temperature heat source to improve exergy efficiency, which barricades the application of
Received in revised form
the common low quality thermal energy. The adoption of a metal hydride heat pump
1 February 2010
system powered by low quality energy could provide the necessary high temperature heat
Accepted 1 February 2010
and reduce the overall energy consumption. Thus, an LNG cold energy recovery system
Available online 11 March 2010
integrating metal hydride heat pump was proposed, and the exergy analysis method was applied to study the case. The performance of the proposed integration system was eval-
Keywords:
uated. Moreover, some key factors were also theoretically investigated about their influ-
Metal hydrides
ences on the system performance. According to the results of the analysis, some
Waste heat
optimization directions of the integrated system were also pointed out. ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.
LNG Cascade utilization
1.
Introduction
Natural gas is widely used in recent years to solve the shortage problem of oil resources and the severe environment pollution in many areas. Liquefied natural gas (LNG) is produced by cryogenic refrigeration of natural gas after removing acid and water components. LNG should be regasified before used at the receiving site. A great amount of cold energy is released from the gasification process and usually discarded in the seawater or air, which causes a huge energy waste [1]. Meanwhile, much low grade waste heat exists in primary energy source consumption process, whose temperature is not high enough to convert into power efficiently. The combination between LNG regasification and low quality waste heat utilization can bring large economic benefits. It has
been a good topic in the previous years that how to combine the low quality heat source with the LNG cold energy and change them efficiently into electrical energy [2,3]. Because ammonia and water can maintain a temperature profile closer to that of a heat source with decreasing temperature than the profile of a single component fluid, it is possible to recover the higher temperature part cold energy of the LNG efficiently by using the ammonia–water Rankine cycle. Therefore ammonia–water Rankine cycle has been studied for recovering waste heat and LNG cold energy by some researchers [4,5]. Bai and Zhang [6] have proposed two thermal cycles based on Brayton cycle and Rankine cycle respectively, which integrated the recovery of low-level waste heat and LNG cold energy utilization for power generation. The simulation results showed that these two cycles can
* Corresponding author. Tel.: þ86 29 82660689. E-mail address: [email protected] (Z. Zhang). 0360-3199/$ – see front matter ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2010.02.008
international journal of hydrogen energy 35 (2010) 7236–7245
Nomenclature Exin Exout ef eL mf mL P Q r m DH DS DT T Sgen t s Cp Wnet exth exP n Ts G MH MHHP
exergy into the system, kJ exergy out of the system, kJ heat exergy of heat transfer fluids for unit mass, kJ kg1 cold exergy of LNG for unit mass, kJ kg1 mass flow of the heat transfer fluids, kg mass flow of LNG, kg pressure, kPa heat flow from the metal hydrides, kJ the gasification latent heat for unit mass, kJ kg1 mass, kg reaction heat, J mol1 reaction entropy, J (mol K)1 temperature difference temperature, K, C entropy generation, kJ K1 time, s specific entropy, kJ kg1 specific heat, kJ kg1 network output of the system, kJ thermal exergy, kJ kg1 pressure exergy, kJ kg1 specific volume, m3 kg1 phase transition temperature, K, C mass flow rate, kg s1 metal hydrides metal hydrides heat pump
utilize the low quality waste heat and LNG cold energy more efficiently than the conventional Brayton cycle and Rankine cycle. Bai [7] also calculated the heat and exergy efficiencies of these two thermal cycles with varying temperatures (as shown in Fig. 1a,b). Fig. 1 shows that the efficiency of heat and exergy are increasing with the increase temperature of heat source. When the heat source temperature is lower than 250 C, the heat and exergy efficiencies are lower (heat efficiency is about 40–50%, and exergy efficiency is about 40–55%), which indicated that the temperature of heat source must be higher than 250 C in order to obtain acceptable efficiencies. However, the common temperature of waste heat can’t meet that demand, which barricades the application of the new integration system. Therefore, how to improve the exergy efficiency of the system by using of the common low quality heat source is a key point to this new technology development. Metal hydride is a special type of alloy which can absorb and desorb hydrogen reversibly at a wide range of temperature conditions [8]. Saturated hydrogen content in MHs is extremely large, and the hydriding/dehydriding reaction is accompanied with massive reaction heat, thus MHs could be used for various thermal applications, e.g. waste heat recovery, solar energy utilization and refrigeration. Many researchers investigated the application of the metal hydrides not only for its excellent hydrogen storage property, but also for its being environmentally benign [9,10]. MHHPs typically have SCP ¼ 30–50 W kg1, because a relatively small mass fraction of H2 can be contained within the dense adsorbent
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E-1,2,3,4 evaporator IHX internal heat exchanger UP useful period RP recharging period EP-1,2,3 expander P-1,2,3 pump Greek symbols exergy efficiency hE thermal efficiency hT thermal conductivity of the material leff Subscripts i,j ideal gas state h high temperature m moderate temperature l low temperature u temperature upgrading int1,2 intermediate temperature in input; inlet out output; outlet cir circulating water ave average lost the loss of heat or exergy hydrogen H2 0 ambient condition max maximum min minimum
(transition metals). Nuckols [11] verified the feasibility of using pairs of metal hydride canisters as a potential compact cooling source that can be used in combat swimmer operations. From the previous study, we know that MHs offer a number of potential applications, while the specific application of a MH is closely related to its P–C–T property. After decades of study, many kinds of MHs have been developed and their P–C–T properties cover quite a wide range, e.g. for 1 bar hydrogen pressure, the corresponding temperature varies from 160 K to 800 K for different MHs. Therefore, generally it is always possible to make or find suitable MHs for a given application, such as refrigeration, compression, pumping, waste heat storage, electricity generation, hydrogen purification, and isotope separation [12–14]. Although much research has been devoted to refrigeration and heating technologies, no researchers have systematically investigated the exergy improvement of LNG cold energy recovery process by using a temperature upgrading type MHHP. The purpose of this paper is to carry out a theoretical investigation of this feasibility. A cascade utilization system for recovering the cold energy in LNG with the help of an MHHP was proposed in this paper. The working principle of this integrated system is discussed in detail and a pair of metal hydrides is selected according to a step-by-step procedure. Based on a typical operation condition, the models of energy conversion and exergy analysis were set up. The influence of a few parameters on the scheme’s efficiency and the causation are also analyzed. Finally the directions of optimization are also pointed out.
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Fig. 1 – The effect about the temperature of the heat source on the exergy & heat efficiency. (a) Based on Brayton cycle and (b) based on Rakine cycle.
2. Configuration and working principles of the system The proposed scheme of the integration of a metal hydrides system with an LNG cycle plant is shown in Fig. 2. The whole system is comprised of 4 parts, (as shown in Fig. 2), including Part I for the metal hydrides heat pump subsystem and Parts II–IV for the LNG subsystem. The metal hydrides heat pump is supposed to operate with only two fluids: hot (waste heat) water and cold water. This means that the useful effect is achieved through the waste heat water by increasing its outlet temperature Th (MH1 heat exchanger) to a value greater than Tm. The cyclic operations of a metal hydride energy system working as a ‘‘temperature upgrading’’ device are schematically shown in Fig. 3. During the ‘‘useful period’’ UP (from points 1 to 2), the process includes the hydrogen transfer from metal hydride 2 (MH2) to metal hydride 1 (MH1), the heat supplied to MH2 Qm2 (at Tm) and the heat released from MH1 Qh (at Th). After initial cooling of the hydrides (from points 1 to 4 and from points 2 to 3), the recharging process may be started. During this ‘‘recharging
period’’ RP (from points 3 to 4), hydrogen is transferred from MH1 to MH2, thus the latter is recharged. The heat Qm1 is supplied to MH1 at the intermediate temperature Tm, and the heat Ql is released from MH2 at the lower temperature Tl. Finally, the preheating of the hydrides (from points 4 to 1 and from points 2 to 3) restores its initial conditions of the system and all the foregoing operations may be repeated again (cyclic operations). In conclusion, by these cyclic operations, a partial (Qh at Th) upgrading (i.e., temperature increase) of the heat supplied at intermediate temperature (Qm1 and Qm2 at Tm) is achieved [15]. In order to obtain a quasi continuous heat supply, at least 2 pairs of metal hydrides are needed. These two pairs of metal hydrides can provide the heat output alternatively, and their operation modes (UP or RP) can be switched from the solid line to the dotted line as shown in Fig. 2. It should be noted that the internal exchange process is also very important to enhance the performance of MHHP system. The loops for internal heat exchange between reactors are disconnected, and interconnections between reactors and the heat source or sink are switched to the dotted line in Fig. 2. In the mean time, MH1 and MH2 arrive at state points 5–8 (shown in Fig. 3), respectively. In this way, the metal hydrides heat pump cycle system is fed by a continuous water flow rate at temperature Tm, and useful heat can be obtained continuously except for the period of internal heat exchange. The subsystem Part II is a Rankine cycle with the mixture of ethylene and propane as the working fluid. In this subsystem, the heat source is coming from the high temperature heat exchanger Th, and the heat sink is coming from the cold energy of LNG. At first, the mixture of ethylene and propane is heated in heat exchanger E-2 by the high temperature heat source Th. Then the vapor of mixture goes into expander EP-1 to produce work, and is condensed in heat exchanger E-1 by LNG. The liquid then goes to heat exchanger E-3 to release the cold energy, and finally it gets back to heat exchanger E-2 by pump P-3 to restart the next cycle. The subsystem Part III is an LNG direct expansion open cycle, which utilizes the pressure exergy of LNG. Non-pressurized LNG is pumped to high pressure by pump P-1, and then flows into cooler E-1 of Part II cycle, where it is heated to high temperature by the mixture of ethylene and propane. The LNG flows into heat exchanger E-1 for evaporation. Then the vapor expands in expander EP-2 to produce work, afterwards it flows into heat exchanger E-3 to release the cold energy. Finally the vapor is transported to the end user. The subsystem Part IV is a Rankine cycle system with ammonia/water mixture as the working fluid. In this subsystem, the ammonia/water mixture is firstly evaporated by the high temperature heat source Th in heat exchanger E4, and then flows into expander EP-3 to produce work, being condensed in heat exchanger E-3. The ammonia/water mixture is pumped into heat exchanger E-4 by pump P-2 to complete a cycle. All of these subsystem mentioned above are coupled with each other through 4 heat exchangers (E-1,E-2,E-3,E-4 as shown in Fig. 2). The system realizes the cascade utilization of energy in 4 thermal cycles, where low quality waste heat, low-temperature exergy and pressure exergy of LNG are utilized efficiently through the system synthesis.
international journal of hydrogen energy 35 (2010) 7236–7245
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Fig. 2 – Flow chart of the integrated system (R – reactor, IHX – internal heat exchanger).
3. Mathematical models of the proposed system It is necessary to know how much improvement is obtained by the energy integration. The present investigation has been carried out by four models properly connected. These numerical models allow the performance evaluation of Rankine cycle, Metal hydrides (MH) systems, and LNG direct expansion open cycle respectively. These systems are properly connected so that the water temperature at the evaporator inlet of the Rankine cycle is increased by the output heat of MHHP, meanwhile the water temperature at the condenser inlet is decreased through coupling with the LNG direct expansion open cycle system. The increase of the pumping power owing to the water circulation in the metal hydrides is neglected for simplicity. In this section, the first law and second law analysis of each subsystem will be processed sequentially.
3.1.
specific heat capacity are independent of temperature, concentration and hydrogen pressure. 4. The reactors are assumed to be well insulated and no heat transfer takes place between them and the surroundings. 5. The circulation pump of heat transfer fluids is omitted, and the flow friction of hydrogen and heat transfer fluids is also neglected. The hydrogen flow rate between the two coupled hydrides concerns both the useful and recharging periods. With the reference to Fig. 3, the heat quantities exchanged by hydrides are expressed by the following equations:
Metal hydrides heat pump system
In order to simplify the problem, the following assumptions are made in the modeling. 1. Hydrogen is considered to be a perfect gas. 2. Heat transfer through the hydride bed is assumed to be two dimensional conduction and convection. The effect of radiation is negligible. 3. The thermo-physical properties of the metal hydride, such as reaction enthalpy and entropy, thermal conductivity and
Fig. 3 – Working principles of a metal hydrides heat pump.
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For hydrides MH1: hE ¼
Exout Wnet ¼ $100% Exin ml el þ mf ef
(13)
Wnet $100% Q
(14)
Qh ¼ mH2 ;1 DHm1 mMH1 $CP;MH1 ðTh Tint1 Þ
(1)
Qm1 ¼ mH2 ;1 DHm1 þ mMH1 $CP;MH1 ðTint1 Tm Þ
(2)
hT ¼
Qm2 ¼ mH2 ;2 DHm2 þ mMH2 $CP;MH2 ðTm Tint2 Þ
(3)
The Exout and Exin, for the schemes in this article can be expressed as:
Ql ¼ mH2 ;2 DHm2 mMH2 $CP;MH2 ðTint2 Tl Þ
(4)
For hydrides MH2:
where Tint1 and Tint2 are given as Tint1 ¼ ðTm þ Th Þ=2
(5)
Tint2 ¼ ðTl þ Tm Þ=2
(6)
In the above equations, mH2,1 and mH2,2 are hydrogen mass which transferred from hydride MH1 and MH2, respectively, Cp is the specific heat capacity. Knowing the heat quantities and the duration time of the useful/recharging periods, one can evaluate the performances of the MHHP system [16]. For the temperature upgrading process, the COP can be defined as [17]: 1 1 ! Sgen Tm Th 1 COP ¼ 1 1 1 1 Qm1 Tl Tm Tm Th
XQ T
Qh Qm2 þ mH2 ðsMH2 sMH1 Þ Th Tm
Exlost;u ¼ T0
Qh Qm2 þ mH2 T0 ðsMH2 sMH1 Þ Th Tm
Exlost;u Qh 1 TTh0
In the above equations, eL is the cold exergy of LNG for unit mass (kJ kg1), ef is the heat exergy of heat transfer fluid for unit mass (kJ kg1). The exergy of LNG includes two parts: one is the low-temperature exergy, which is defined as the thermal non-equilibrium exergy with the environment under the system pressure, and the other is the pressure exergy, which is defined as the system pressure nonequilibrium exergy with the environment under the ambient temperature exðT; PÞ ¼ exth þ exP
(17)
Z Ts T0 T0 dT 1 rþ CP 1 Ts T T0
exP ¼ exðT0 ; PÞ ¼
Z
(18)
P;T0
v dp
(19)
P0 ;T0
(8)
(9)
(10)
(11)
So the exergy efficiency of the metal hydrides heat pump system is given by hex;u ¼ 1
(16)
eth ¼
Applying the above equations to various components, we have the entropy analysis about high temperature upgrade system, and the entropy generation Sgen,u and the exergy lost Exlost,u of the temperature upgrading system can be accomplished by: Sgen;u ¼
Exin ¼ mL eL þ mfðE2Þ efðE2Þ þ mfðE4Þ efðE4Þ
(7)
For an ideal gas, the entropy difference between any two states, ‘i’ and ‘j’ is given by [18]: Tj Pj R ln Sj Si ¼ mH2 CP;H2 ln Ti Pi
(15)
exth and exp can be calculated as:
For a steady-flow process, the entropy generated Sgen in a control volume is given by: Sgen ¼ mH2 ðSout Sin Þ
Exout ¼Wnet ¼ðWEP1 þWEP2 þWEP3 ÞðWP1 þWP1 þWP3 Þ
(12)
3.2. Cascade utilization system of LNG cold energy recovery In this investigation, both the thermal efficiency hT and the thermodynamic efficiency hE (the second law exergy efficiency) are selected to value the system performance. They can be defined as:
The first part in the right hand side of equation (18) is the latent heat exergy, and the second part is the sensible heat exergy. Usually LNG is a multi-components mixture, and its physical properties such as latent heat of phase transition, average bubble point temperature are related to the pressure and constituents. Here, the RKS equation was selected to describe the phase equilibrium of the LNG, which has a high precision. Particularly, it is suitable to study the problem of liquid–gas phase equilibrium among different components of hydrocarbon mixture. In the study, the parameters analysis of LNG cold energy recovery process can be performed by using equations (15)–(19), and the simulations of LNG subsystem working process were carried out using the commercial software Aspen Plus 10.2.
3.3. Configuration of the metal hydrides reactor and process model of hydrogen transfer The prototype of a metal hydrides reactor which adopted in this investigation is a helix fins type tube reactor [19]. We select the mathematical model which developed by Gambini [20] to simulate the process of hydrogen transfer between two reactors. It has been shown that the model is able to evaluate the performance of the MH energy systems with a good compromise between accuracy and simplicity. The average outlet temperature of the circulating water is evaluated by Gambini [15] R tUP Tcir ðtÞdt (20) Tcir ¼ 0 tUP
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and
Table 1 – The operation parameters of the system.
dQUP ¼ Gcir $CP;w $ Tcir ðtÞ Tcir;in dt
(21)
QUP Gcir $CP;w $tUP
(22)
Using the average temperature of circulating water at MH heat exchanger outlet (Tcir, ave), the temperature of the working fluid of Rankine cycle plant in Part II and Part IV (as shown in Fig. 2) at the E-2 and E-4 inlet may be simply derived. In particular, it results in Tin ¼ Tcir;ave DTwev DTmin;eva
4.
Example and discussion
4.1.
Example and exergy analysis
Value
It results in Tcir;ave ¼ Tcir;in þ
Parameters
(23)
In order to compare the proposed system to the traditional base case systems, operating conditions of the system must be determined. In this article, the operation conditions are shown in Table 1. To improve the performance of MHHP, the pairing alloys used in the system were carefully selected by following a two step procedure [21]. Under the chosen operation conditions, the paired alloys MmNi4.15Fe0.85–LaNi4.7Al0.3 were found viable for application with a relatively high COP. Physical properties of the alloys and hydrogen used in the simulation were shown in Table 2. Fig. 4 is an exergy flow chart of the proposed system under the given operation conditions. It shows that the biggest exergy loss of the system comes from the MHHP, so the main optimization direction of the system is to increase the exergy efficiency of the MHHP. Because the flow friction of hydrogen and heat transfer fluids were neglected, only some factors with regard to the reactor and heat exchange fluids were taken for discussion here. The heat transfer will be enhanced by extending the area of the reactor or increasing the heat transfer coefficient, which is useful to increase the COP value and decrease the heat and exergy loss of the heat pump system. However, the key point of the problem is the heat and mass transfer inside the reactive bed. One major concern with most metal hydride systems is ‘‘decrepitation’’ of the material after several adsorption and desorption cycles. As a result, there will be a significant level of contact resistance between MH particles, which will lower the thermal conductivity of the material (leff ¼ 1 W (m K)1). A low thermal conductivity affects the heat transfer rates severely, which will limit the system performance. The adopted reactor in this investigation could not realize efficient heat transfer inside the reactive bed, thus developing a new prototype of MH reactor with enhanced bed heat transfer is the most effective way to solve the problem, which will be another studied topic. The exergy of the propane and ethylene mixture flows into E-3 of the Part IV which serves as the condenser of the Rankine cycle with ammonia/water mixture as the working fluid. The heat integration here eliminates the exergy loss in the heat accumulator [7], so the whole exergy and heat efficiency
The temperature of heat source/ C The maximum pressure of Part II/MPa The minimum pressure of Part II/MPa The expanding pressure of the LNG The maximum pressure of Part IV/MPa The minimum pressure of Part IV/MPa The isentropic efficiency of pump/% The isentropic efficiency of expander/% The minimum temperature difference of evaporator DTmin,eva/ C The circulating water temperature drop in the evaporator DTwev/ C The initial pressure of LNG/MPa The initial temperature of LNG/ C The transportation pressure of natural gas/MPa The transportation temperature of natural gas/ C The ambient temperature/ C The ambient pressure/MPa
230 4 0.1 2.5 5 0.15 75 85 3 3 0.1 162 0.15 15 25 0.1
increased simultaneously. The uninstall of heat accumulator also increases the economical property of the system. The comparison between the integrated system and the one proposed by Bai [7] shows that the utilization of propane and ethylene mixture as the working fluid of the Rankine cycle can improve the effect of recovering LNG cold energy, because it makes better matching of hot and cold fluids in condenser E-1, at the same time improves the exergy efficiency of condenser E1.
4.2.
Analysis of the influence factors
The main factors affecting the performance of the process include mass ratio of propane in the mixture, expanding pressure of propane and ethylene mixture and temperature of the heat source.
4.2.1.
The propane mass ratio of the mixture
The effect of the propane mass ratio in the mixture on the exergy and heat efficiencies of LNG cold energy recovery subsystem is shown in Fig. 5. The exergy efficiency of the equipment is shown in Fig. 6. From Fig. 6, we can see that the
Table 2 – Physical properties of the alloys and hydrogen data used in the simulation. Parameters
LaNi4.7Al0.3 MmNi4.15Fe0.85
Density, r (kg.m3) Specific heat, Cp (kJ.kg1) Permeability Reaction enthalpy, DH (kJ.mol1) Porosity Universal gas constant, R J (mol K)1 Thermal conductivity, l W.(m.K)1 Efficiency of heat recovery, (b)
7800 410 1.11 1012 3.4 104
8200 408 1.11 1012 2.53 104
0.5
0.5
H2 0.01 14,890 –
8.314 1.3
2.0
0.5
0.5
0.16
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Fig. 4 – Exergy flow chart of the integrated system.
exergy efficiency of equipment E-3 has the maximum value of 72% at the propane mass ratio as 0.55. This phenomenon can be explained as follows. With the increasing of propane mass ratio, the temperature of propane and ethylene mixture also increases gradually. Therefore, the minimum heat transfer temperature difference between the hot fluids and cold fluids decreases gradually. As a result, the final preheat temperature of mixture is limited in the equipment E-3. In other words, when the mass ratio of the propane is beyond 55%, the final heating temperature of mixture in E-3 decreases gradually, and then the overall temperature difference of hot fluids and cold fluids increases, so the exergy efficiency of equipment E-3 decreases. Because the final preheat temperature of the propane and ethylene mixture is decreased, the evaporation temperature at the inlet of E-2 is also decreased, then the overall heat transfer temperature difference is getting larger, so the exergy efficiency of E-2 is decreasing gradually. All of
Fig. 5 – The exergy and heat efficiency of whole LNG subsystem.
the reasons mentioned above indicate that the mass ratio of propane has an optimized value (as shown in Fig. 5), and this value should be set according to the specific operation conditions.
4.2.2. The expanding pressure of propane and ethylene mixture The exergy and heat efficiency of the LNG subsystem with the variation of the mixture expanding pressure were shown in Fig. 7. It shows that the exergy efficiency of LNG subsystem reaches a maximum value when the pressure of mixtures is 4 MPa with the increase of propane/ethylene mixture pressure. The exergy efficiency of each component was shown in Fig. 8. It indicates that the exergy efficiency of equipment E-2 increases rapidly with the expanding pressure during the initial period. When the mixture expanding pressure is
Fig. 6 – The exergy efficiencies of components in the LNG subsystem with the mass ratio of propane in the propane and ethylene mixture.
international journal of hydrogen energy 35 (2010) 7236–7245
Fig. 7 – The schematic diagram of exergy efficiency of LNG subsystem with the expanding pressure of propane and ethylene mixture.
beyond 4 MPa, the improvement on its exergy efficiency becomes insignificant. The exergy efficiency of E-3 initially increases with the expanding pressure, and then decreases gradually when the expanding pressure is beyond 4 MPa. That phenomenon can be explained as follows. When the expanding pressure of propane and ethylene mixture is lower than 4 MPa, the final expanding temperature of the natural gas is higher in equipment EP-2, which leads to the minimum temperature difference between the hot fluid and cold fluid appeared at the low-temperature heat transfer part of E-3. So it restricts the preheat temperature increase of propane and ethylene mixture in the E-3. As a result, the final expanding temperature of natural gas in EP-2 will decrease gradually, and the preheating temperature of propane/ethylene mixture will increase with the expanding pressure. Therefore, the temperature difference at high temperature part of E-3 decreases and the exergy efficiency of E-3 increases gradually. However, when the expanding pressure of propane and
Fig. 8 – The exergy efficiencies of components in the LNG subsystem with the expanding pressure of propane and ethylene mixture.
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Fig. 9 – The diagram of the COP and exergy efficiency of the metal hydrides heat pump system variation.
ethylene is beyond 4 MPa, the minimum temperature difference between the hot fluid and cold fluid appears at the high temperature part of E-3. Because of the temperature limitation of the hot fluids (ammonia/water mixture), the temperature of propane/ethylene mixture cannot going up continuously in E3. At the same time, the final expanding temperature of natural gas decreases with the expanding pressure of propane/ethylene mixture increases, which leads to the enlarged temperature difference at the low-temperature part of E-3. All of these factors make the exergy efficiency of E-3 to reduce continuously. There are two factors which influence the exergy efficiency of E-2. One is the preheating temperature of the propane/ ethylene mixture in E-3; the other is the gasification profile of the propane and ethylene mixture at different pressure conditions. From above exergy efficiency analysis of E-3, we can see that when the expanding pressure of the propane/ ethylene mixture is lower than 4 MPa, the preheating temperature of the propane and ethylene mixture in E-3 is increased continuously; when the expanding pressure of the mixture is beyond 4 MPa, the preheating temperature will
Fig. 10 – The effect of the temperature of the heat source on the LNG subsystem performance.
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equipment are increased with the heat source temperature, because the temperature differences are enlarged. The maximum exergy loss is happened in the equipment E1, and the other optimization direction is to improve the exergy efficiency of E-1.
5.
Fig. 11 – The exergy efficiency of different components of the LNG subsystem.
close to a constant value because of the temperature limitation of the ammonia/water mixture. Thus there are two factors which will influence the exergy efficiency of E-2 simultaneously when the expanding pressure of the propane/ ethylene mixture is lower than 4 MPa, while only one factor influences the exergy efficiency of E-2 when the expanding pressure of the propane and ethylene mixture beyond 4 MPa because the preheat temperature of the mixture is close to a constant value. Therefore, the exergy efficiency of E-2 increasing becomes more gently with the expanding pressure of the propane/ethylene mixture beyond 4 MPa. The inflexion of the profile is located at the point where the expanding pressure equals 4 MPa.
4.2.3.
The temperature of the heat source
The COP value and exergy efficiency of metal hydrides heat pump with the variation of heat source temperature are shown in Fig. 9. It indicates that the COP and exergy efficiency of the MHHP increase gently with the temperature of heat source, which means that the performance of the MHHP can be improved by using higher temperature heat source. In order to compare the cold energy recovery performance between the new system and the traditional system (as shown in Fig. 1), the LNG subsystem and the MHHP system were investigated independently. In other words, we assume that the heat and exergy output from the MHHP are the whole heat and exergy input to the LNG subsystem. Thus the effect of the heat source temperature on the exergy and heat efficiency of the LNG subsystem is calculated based on the heat and exergy output from the MHHP (as shown in Fig. 10). It is obvious that the exergy and heat efficiency of the proposed system are improved in comparison with the traditional system proposed by Bai [7] (as shown in Fig. 1). Fig. 10 also gave the temperature range of the heat source. The temperature of the heat source is from 100 C to 410 C, in all cases the heat efficiency and exergy efficiency are higher (heat efficiency is about 44–60%, and exergy efficiency is about 56–70%), which is desirable in the engineering practice. Fig. 11 is the exergy efficiencies of the components in the system. The exergy efficiencies of most
Conclusions
A prototype of an integrated LNG cold energy recovery system with MHHP was proposed. The system has many merits e.g. cascade energy utilization, environmentally friendly, and easily adapted to the common waste heat recovery. The main optimization direction of the proposed system is to improve the performance of metal hydrides heat pump. Developing new prototype reactor with high heat transfer rate inside the reactive bed is the most effective method. The mass ratio of propane in the mixture has an optimization value with regard to the system performance, and it should be set according to the operation conditions. The expanding pressure of propane/ethylene mixture has also an optimum value which equals 4 MPa in this study. The exergy efficiencies of the equipment in LNG subsystem are increased with heat source temperature, and another optimization direction is to improve the exergy efficiency of the evaporator E-1.
Acknowledgment Financial support from the National Natural Science Foundation of China (Nos. 50976090 and 20936004) is greatly acknowledged.
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[8] Gu¨ther V, Otto A. Recent developments in hydrogen storage applications based on metal hydrides. J Alloy Compd 1999; 293–295:889–92. [9] Askri F, Ben MS, Jemni A, Nasrallah SB. A new algorithm for solving transient heat and mass transfer in metal–hydrogen reactor. Int J Hydrogen Energy 2009;34:8315–21. [10] Mellouli S, Askri F, Dhaou H, Jemni A, Nasrallah SB. Numerical study of heat exchanger effects on charge/ discharge times of metal–hydrogen storage vessel. Int J Hydrogen Energy 2009;34:3005–17. [11] Nuckols ML. The use of metal hydrides as a cooling source for divers, OCEANS 2005. In: Proceedings of MTS/IEEE, vol. 1; 2005. p. 134–9. [12] Wang YQ, Yang FS, Meng XY, Guo QF, Zhang ZX, Park IS, et al. Simulation study on the reaction process based single stage metal hydride thermal compressor. Int J Hydrogen Energy 2010;35:321–8. [13] Klein HP, Groll M. Development of a two-stage metal hydride system as topping cycle in cascading sorption systems for cold generation. Appl Therm Eng 2002;22(6):631–9. [14] Winter CJ. Hydrogen energy – abundant, efficient, clean: a debate over the energy-system-of-change. Int J Hydrogen Energy 2009;34:S1–52.
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Available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Study of integrated metal hydrides heat pump and cascade utilization of liquefied natural gas cold energy recovery system Xiangyu Meng a, Feifei Bai a,b, Fusheng Yang a, Zewei Bao a, Zaoxiao Zhang a,* a
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xianning Road 28#, Xi’an, Shaanxi 710049, PR China b China Nuclear Power Design Co., Ltd, Shenzhen 518057, PR China
article info
abstract
Article history:
The traditional cold energy utilization of the liquefied natural gas system needs a higher
Received 17 November 2009
temperature heat source to improve exergy efficiency, which barricades the application of
Received in revised form
the common low quality thermal energy. The adoption of a metal hydride heat pump
1 February 2010
system powered by low quality energy could provide the necessary high temperature heat
Accepted 1 February 2010
and reduce the overall energy consumption. Thus, an LNG cold energy recovery system
Available online 11 March 2010
integrating metal hydride heat pump was proposed, and the exergy analysis method was applied to study the case. The performance of the proposed integration system was eval-
Keywords:
uated. Moreover, some key factors were also theoretically investigated about their influ-
Metal hydrides
ences on the system performance. According to the results of the analysis, some
Waste heat
optimization directions of the integrated system were also pointed out. ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.
LNG Cascade utilization
1.
Introduction
Natural gas is widely used in recent years to solve the shortage problem of oil resources and the severe environment pollution in many areas. Liquefied natural gas (LNG) is produced by cryogenic refrigeration of natural gas after removing acid and water components. LNG should be regasified before used at the receiving site. A great amount of cold energy is released from the gasification process and usually discarded in the seawater or air, which causes a huge energy waste [1]. Meanwhile, much low grade waste heat exists in primary energy source consumption process, whose temperature is not high enough to convert into power efficiently. The combination between LNG regasification and low quality waste heat utilization can bring large economic benefits. It has
been a good topic in the previous years that how to combine the low quality heat source with the LNG cold energy and change them efficiently into electrical energy [2,3]. Because ammonia and water can maintain a temperature profile closer to that of a heat source with decreasing temperature than the profile of a single component fluid, it is possible to recover the higher temperature part cold energy of the LNG efficiently by using the ammonia–water Rankine cycle. Therefore ammonia–water Rankine cycle has been studied for recovering waste heat and LNG cold energy by some researchers [4,5]. Bai and Zhang [6] have proposed two thermal cycles based on Brayton cycle and Rankine cycle respectively, which integrated the recovery of low-level waste heat and LNG cold energy utilization for power generation. The simulation results showed that these two cycles can
* Corresponding author. Tel.: þ86 29 82660689. E-mail address: [email protected] (Z. Zhang). 0360-3199/$ – see front matter ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2010.02.008
international journal of hydrogen energy 35 (2010) 7236–7245
Nomenclature Exin Exout ef eL mf mL P Q r m DH DS DT T Sgen t s Cp Wnet exth exP n Ts G MH MHHP
exergy into the system, kJ exergy out of the system, kJ heat exergy of heat transfer fluids for unit mass, kJ kg1 cold exergy of LNG for unit mass, kJ kg1 mass flow of the heat transfer fluids, kg mass flow of LNG, kg pressure, kPa heat flow from the metal hydrides, kJ the gasification latent heat for unit mass, kJ kg1 mass, kg reaction heat, J mol1 reaction entropy, J (mol K)1 temperature difference temperature, K, C entropy generation, kJ K1 time, s specific entropy, kJ kg1 specific heat, kJ kg1 network output of the system, kJ thermal exergy, kJ kg1 pressure exergy, kJ kg1 specific volume, m3 kg1 phase transition temperature, K, C mass flow rate, kg s1 metal hydrides metal hydrides heat pump
utilize the low quality waste heat and LNG cold energy more efficiently than the conventional Brayton cycle and Rankine cycle. Bai [7] also calculated the heat and exergy efficiencies of these two thermal cycles with varying temperatures (as shown in Fig. 1a,b). Fig. 1 shows that the efficiency of heat and exergy are increasing with the increase temperature of heat source. When the heat source temperature is lower than 250 C, the heat and exergy efficiencies are lower (heat efficiency is about 40–50%, and exergy efficiency is about 40–55%), which indicated that the temperature of heat source must be higher than 250 C in order to obtain acceptable efficiencies. However, the common temperature of waste heat can’t meet that demand, which barricades the application of the new integration system. Therefore, how to improve the exergy efficiency of the system by using of the common low quality heat source is a key point to this new technology development. Metal hydride is a special type of alloy which can absorb and desorb hydrogen reversibly at a wide range of temperature conditions [8]. Saturated hydrogen content in MHs is extremely large, and the hydriding/dehydriding reaction is accompanied with massive reaction heat, thus MHs could be used for various thermal applications, e.g. waste heat recovery, solar energy utilization and refrigeration. Many researchers investigated the application of the metal hydrides not only for its excellent hydrogen storage property, but also for its being environmentally benign [9,10]. MHHPs typically have SCP ¼ 30–50 W kg1, because a relatively small mass fraction of H2 can be contained within the dense adsorbent
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E-1,2,3,4 evaporator IHX internal heat exchanger UP useful period RP recharging period EP-1,2,3 expander P-1,2,3 pump Greek symbols exergy efficiency hE thermal efficiency hT thermal conductivity of the material leff Subscripts i,j ideal gas state h high temperature m moderate temperature l low temperature u temperature upgrading int1,2 intermediate temperature in input; inlet out output; outlet cir circulating water ave average lost the loss of heat or exergy hydrogen H2 0 ambient condition max maximum min minimum
(transition metals). Nuckols [11] verified the feasibility of using pairs of metal hydride canisters as a potential compact cooling source that can be used in combat swimmer operations. From the previous study, we know that MHs offer a number of potential applications, while the specific application of a MH is closely related to its P–C–T property. After decades of study, many kinds of MHs have been developed and their P–C–T properties cover quite a wide range, e.g. for 1 bar hydrogen pressure, the corresponding temperature varies from 160 K to 800 K for different MHs. Therefore, generally it is always possible to make or find suitable MHs for a given application, such as refrigeration, compression, pumping, waste heat storage, electricity generation, hydrogen purification, and isotope separation [12–14]. Although much research has been devoted to refrigeration and heating technologies, no researchers have systematically investigated the exergy improvement of LNG cold energy recovery process by using a temperature upgrading type MHHP. The purpose of this paper is to carry out a theoretical investigation of this feasibility. A cascade utilization system for recovering the cold energy in LNG with the help of an MHHP was proposed in this paper. The working principle of this integrated system is discussed in detail and a pair of metal hydrides is selected according to a step-by-step procedure. Based on a typical operation condition, the models of energy conversion and exergy analysis were set up. The influence of a few parameters on the scheme’s efficiency and the causation are also analyzed. Finally the directions of optimization are also pointed out.
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Fig. 1 – The effect about the temperature of the heat source on the exergy & heat efficiency. (a) Based on Brayton cycle and (b) based on Rakine cycle.
2. Configuration and working principles of the system The proposed scheme of the integration of a metal hydrides system with an LNG cycle plant is shown in Fig. 2. The whole system is comprised of 4 parts, (as shown in Fig. 2), including Part I for the metal hydrides heat pump subsystem and Parts II–IV for the LNG subsystem. The metal hydrides heat pump is supposed to operate with only two fluids: hot (waste heat) water and cold water. This means that the useful effect is achieved through the waste heat water by increasing its outlet temperature Th (MH1 heat exchanger) to a value greater than Tm. The cyclic operations of a metal hydride energy system working as a ‘‘temperature upgrading’’ device are schematically shown in Fig. 3. During the ‘‘useful period’’ UP (from points 1 to 2), the process includes the hydrogen transfer from metal hydride 2 (MH2) to metal hydride 1 (MH1), the heat supplied to MH2 Qm2 (at Tm) and the heat released from MH1 Qh (at Th). After initial cooling of the hydrides (from points 1 to 4 and from points 2 to 3), the recharging process may be started. During this ‘‘recharging
period’’ RP (from points 3 to 4), hydrogen is transferred from MH1 to MH2, thus the latter is recharged. The heat Qm1 is supplied to MH1 at the intermediate temperature Tm, and the heat Ql is released from MH2 at the lower temperature Tl. Finally, the preheating of the hydrides (from points 4 to 1 and from points 2 to 3) restores its initial conditions of the system and all the foregoing operations may be repeated again (cyclic operations). In conclusion, by these cyclic operations, a partial (Qh at Th) upgrading (i.e., temperature increase) of the heat supplied at intermediate temperature (Qm1 and Qm2 at Tm) is achieved [15]. In order to obtain a quasi continuous heat supply, at least 2 pairs of metal hydrides are needed. These two pairs of metal hydrides can provide the heat output alternatively, and their operation modes (UP or RP) can be switched from the solid line to the dotted line as shown in Fig. 2. It should be noted that the internal exchange process is also very important to enhance the performance of MHHP system. The loops for internal heat exchange between reactors are disconnected, and interconnections between reactors and the heat source or sink are switched to the dotted line in Fig. 2. In the mean time, MH1 and MH2 arrive at state points 5–8 (shown in Fig. 3), respectively. In this way, the metal hydrides heat pump cycle system is fed by a continuous water flow rate at temperature Tm, and useful heat can be obtained continuously except for the period of internal heat exchange. The subsystem Part II is a Rankine cycle with the mixture of ethylene and propane as the working fluid. In this subsystem, the heat source is coming from the high temperature heat exchanger Th, and the heat sink is coming from the cold energy of LNG. At first, the mixture of ethylene and propane is heated in heat exchanger E-2 by the high temperature heat source Th. Then the vapor of mixture goes into expander EP-1 to produce work, and is condensed in heat exchanger E-1 by LNG. The liquid then goes to heat exchanger E-3 to release the cold energy, and finally it gets back to heat exchanger E-2 by pump P-3 to restart the next cycle. The subsystem Part III is an LNG direct expansion open cycle, which utilizes the pressure exergy of LNG. Non-pressurized LNG is pumped to high pressure by pump P-1, and then flows into cooler E-1 of Part II cycle, where it is heated to high temperature by the mixture of ethylene and propane. The LNG flows into heat exchanger E-1 for evaporation. Then the vapor expands in expander EP-2 to produce work, afterwards it flows into heat exchanger E-3 to release the cold energy. Finally the vapor is transported to the end user. The subsystem Part IV is a Rankine cycle system with ammonia/water mixture as the working fluid. In this subsystem, the ammonia/water mixture is firstly evaporated by the high temperature heat source Th in heat exchanger E4, and then flows into expander EP-3 to produce work, being condensed in heat exchanger E-3. The ammonia/water mixture is pumped into heat exchanger E-4 by pump P-2 to complete a cycle. All of these subsystem mentioned above are coupled with each other through 4 heat exchangers (E-1,E-2,E-3,E-4 as shown in Fig. 2). The system realizes the cascade utilization of energy in 4 thermal cycles, where low quality waste heat, low-temperature exergy and pressure exergy of LNG are utilized efficiently through the system synthesis.
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Fig. 2 – Flow chart of the integrated system (R – reactor, IHX – internal heat exchanger).
3. Mathematical models of the proposed system It is necessary to know how much improvement is obtained by the energy integration. The present investigation has been carried out by four models properly connected. These numerical models allow the performance evaluation of Rankine cycle, Metal hydrides (MH) systems, and LNG direct expansion open cycle respectively. These systems are properly connected so that the water temperature at the evaporator inlet of the Rankine cycle is increased by the output heat of MHHP, meanwhile the water temperature at the condenser inlet is decreased through coupling with the LNG direct expansion open cycle system. The increase of the pumping power owing to the water circulation in the metal hydrides is neglected for simplicity. In this section, the first law and second law analysis of each subsystem will be processed sequentially.
3.1.
specific heat capacity are independent of temperature, concentration and hydrogen pressure. 4. The reactors are assumed to be well insulated and no heat transfer takes place between them and the surroundings. 5. The circulation pump of heat transfer fluids is omitted, and the flow friction of hydrogen and heat transfer fluids is also neglected. The hydrogen flow rate between the two coupled hydrides concerns both the useful and recharging periods. With the reference to Fig. 3, the heat quantities exchanged by hydrides are expressed by the following equations:
Metal hydrides heat pump system
In order to simplify the problem, the following assumptions are made in the modeling. 1. Hydrogen is considered to be a perfect gas. 2. Heat transfer through the hydride bed is assumed to be two dimensional conduction and convection. The effect of radiation is negligible. 3. The thermo-physical properties of the metal hydride, such as reaction enthalpy and entropy, thermal conductivity and
Fig. 3 – Working principles of a metal hydrides heat pump.
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For hydrides MH1: hE ¼
Exout Wnet ¼ $100% Exin ml el þ mf ef
(13)
Wnet $100% Q
(14)
Qh ¼ mH2 ;1 DHm1 mMH1 $CP;MH1 ðTh Tint1 Þ
(1)
Qm1 ¼ mH2 ;1 DHm1 þ mMH1 $CP;MH1 ðTint1 Tm Þ
(2)
hT ¼
Qm2 ¼ mH2 ;2 DHm2 þ mMH2 $CP;MH2 ðTm Tint2 Þ
(3)
The Exout and Exin, for the schemes in this article can be expressed as:
Ql ¼ mH2 ;2 DHm2 mMH2 $CP;MH2 ðTint2 Tl Þ
(4)
For hydrides MH2:
where Tint1 and Tint2 are given as Tint1 ¼ ðTm þ Th Þ=2
(5)
Tint2 ¼ ðTl þ Tm Þ=2
(6)
In the above equations, mH2,1 and mH2,2 are hydrogen mass which transferred from hydride MH1 and MH2, respectively, Cp is the specific heat capacity. Knowing the heat quantities and the duration time of the useful/recharging periods, one can evaluate the performances of the MHHP system [16]. For the temperature upgrading process, the COP can be defined as [17]: 1 1 ! Sgen Tm Th 1 COP ¼ 1 1 1 1 Qm1 Tl Tm Tm Th
XQ T
Qh Qm2 þ mH2 ðsMH2 sMH1 Þ Th Tm
Exlost;u ¼ T0
Qh Qm2 þ mH2 T0 ðsMH2 sMH1 Þ Th Tm
Exlost;u Qh 1 TTh0
In the above equations, eL is the cold exergy of LNG for unit mass (kJ kg1), ef is the heat exergy of heat transfer fluid for unit mass (kJ kg1). The exergy of LNG includes two parts: one is the low-temperature exergy, which is defined as the thermal non-equilibrium exergy with the environment under the system pressure, and the other is the pressure exergy, which is defined as the system pressure nonequilibrium exergy with the environment under the ambient temperature exðT; PÞ ¼ exth þ exP
(17)
Z Ts T0 T0 dT 1 rþ CP 1 Ts T T0
exP ¼ exðT0 ; PÞ ¼
Z
(18)
P;T0
v dp
(19)
P0 ;T0
(8)
(9)
(10)
(11)
So the exergy efficiency of the metal hydrides heat pump system is given by hex;u ¼ 1
(16)
eth ¼
Applying the above equations to various components, we have the entropy analysis about high temperature upgrade system, and the entropy generation Sgen,u and the exergy lost Exlost,u of the temperature upgrading system can be accomplished by: Sgen;u ¼
Exin ¼ mL eL þ mfðE2Þ efðE2Þ þ mfðE4Þ efðE4Þ
(7)
For an ideal gas, the entropy difference between any two states, ‘i’ and ‘j’ is given by [18]: Tj Pj R ln Sj Si ¼ mH2 CP;H2 ln Ti Pi
(15)
exth and exp can be calculated as:
For a steady-flow process, the entropy generated Sgen in a control volume is given by: Sgen ¼ mH2 ðSout Sin Þ
Exout ¼Wnet ¼ðWEP1 þWEP2 þWEP3 ÞðWP1 þWP1 þWP3 Þ
(12)
3.2. Cascade utilization system of LNG cold energy recovery In this investigation, both the thermal efficiency hT and the thermodynamic efficiency hE (the second law exergy efficiency) are selected to value the system performance. They can be defined as:
The first part in the right hand side of equation (18) is the latent heat exergy, and the second part is the sensible heat exergy. Usually LNG is a multi-components mixture, and its physical properties such as latent heat of phase transition, average bubble point temperature are related to the pressure and constituents. Here, the RKS equation was selected to describe the phase equilibrium of the LNG, which has a high precision. Particularly, it is suitable to study the problem of liquid–gas phase equilibrium among different components of hydrocarbon mixture. In the study, the parameters analysis of LNG cold energy recovery process can be performed by using equations (15)–(19), and the simulations of LNG subsystem working process were carried out using the commercial software Aspen Plus 10.2.
3.3. Configuration of the metal hydrides reactor and process model of hydrogen transfer The prototype of a metal hydrides reactor which adopted in this investigation is a helix fins type tube reactor [19]. We select the mathematical model which developed by Gambini [20] to simulate the process of hydrogen transfer between two reactors. It has been shown that the model is able to evaluate the performance of the MH energy systems with a good compromise between accuracy and simplicity. The average outlet temperature of the circulating water is evaluated by Gambini [15] R tUP Tcir ðtÞdt (20) Tcir ¼ 0 tUP
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and
Table 1 – The operation parameters of the system.
dQUP ¼ Gcir $CP;w $ Tcir ðtÞ Tcir;in dt
(21)
QUP Gcir $CP;w $tUP
(22)
Using the average temperature of circulating water at MH heat exchanger outlet (Tcir, ave), the temperature of the working fluid of Rankine cycle plant in Part II and Part IV (as shown in Fig. 2) at the E-2 and E-4 inlet may be simply derived. In particular, it results in Tin ¼ Tcir;ave DTwev DTmin;eva
4.
Example and discussion
4.1.
Example and exergy analysis
Value
It results in Tcir;ave ¼ Tcir;in þ
Parameters
(23)
In order to compare the proposed system to the traditional base case systems, operating conditions of the system must be determined. In this article, the operation conditions are shown in Table 1. To improve the performance of MHHP, the pairing alloys used in the system were carefully selected by following a two step procedure [21]. Under the chosen operation conditions, the paired alloys MmNi4.15Fe0.85–LaNi4.7Al0.3 were found viable for application with a relatively high COP. Physical properties of the alloys and hydrogen used in the simulation were shown in Table 2. Fig. 4 is an exergy flow chart of the proposed system under the given operation conditions. It shows that the biggest exergy loss of the system comes from the MHHP, so the main optimization direction of the system is to increase the exergy efficiency of the MHHP. Because the flow friction of hydrogen and heat transfer fluids were neglected, only some factors with regard to the reactor and heat exchange fluids were taken for discussion here. The heat transfer will be enhanced by extending the area of the reactor or increasing the heat transfer coefficient, which is useful to increase the COP value and decrease the heat and exergy loss of the heat pump system. However, the key point of the problem is the heat and mass transfer inside the reactive bed. One major concern with most metal hydride systems is ‘‘decrepitation’’ of the material after several adsorption and desorption cycles. As a result, there will be a significant level of contact resistance between MH particles, which will lower the thermal conductivity of the material (leff ¼ 1 W (m K)1). A low thermal conductivity affects the heat transfer rates severely, which will limit the system performance. The adopted reactor in this investigation could not realize efficient heat transfer inside the reactive bed, thus developing a new prototype of MH reactor with enhanced bed heat transfer is the most effective way to solve the problem, which will be another studied topic. The exergy of the propane and ethylene mixture flows into E-3 of the Part IV which serves as the condenser of the Rankine cycle with ammonia/water mixture as the working fluid. The heat integration here eliminates the exergy loss in the heat accumulator [7], so the whole exergy and heat efficiency
The temperature of heat source/ C The maximum pressure of Part II/MPa The minimum pressure of Part II/MPa The expanding pressure of the LNG The maximum pressure of Part IV/MPa The minimum pressure of Part IV/MPa The isentropic efficiency of pump/% The isentropic efficiency of expander/% The minimum temperature difference of evaporator DTmin,eva/ C The circulating water temperature drop in the evaporator DTwev/ C The initial pressure of LNG/MPa The initial temperature of LNG/ C The transportation pressure of natural gas/MPa The transportation temperature of natural gas/ C The ambient temperature/ C The ambient pressure/MPa
230 4 0.1 2.5 5 0.15 75 85 3 3 0.1 162 0.15 15 25 0.1
increased simultaneously. The uninstall of heat accumulator also increases the economical property of the system. The comparison between the integrated system and the one proposed by Bai [7] shows that the utilization of propane and ethylene mixture as the working fluid of the Rankine cycle can improve the effect of recovering LNG cold energy, because it makes better matching of hot and cold fluids in condenser E-1, at the same time improves the exergy efficiency of condenser E1.
4.2.
Analysis of the influence factors
The main factors affecting the performance of the process include mass ratio of propane in the mixture, expanding pressure of propane and ethylene mixture and temperature of the heat source.
4.2.1.
The propane mass ratio of the mixture
The effect of the propane mass ratio in the mixture on the exergy and heat efficiencies of LNG cold energy recovery subsystem is shown in Fig. 5. The exergy efficiency of the equipment is shown in Fig. 6. From Fig. 6, we can see that the
Table 2 – Physical properties of the alloys and hydrogen data used in the simulation. Parameters
LaNi4.7Al0.3 MmNi4.15Fe0.85
Density, r (kg.m3) Specific heat, Cp (kJ.kg1) Permeability Reaction enthalpy, DH (kJ.mol1) Porosity Universal gas constant, R J (mol K)1 Thermal conductivity, l W.(m.K)1 Efficiency of heat recovery, (b)
7800 410 1.11 1012 3.4 104
8200 408 1.11 1012 2.53 104
0.5
0.5
H2 0.01 14,890 –
8.314 1.3
2.0
0.5
0.5
0.16
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Fig. 4 – Exergy flow chart of the integrated system.
exergy efficiency of equipment E-3 has the maximum value of 72% at the propane mass ratio as 0.55. This phenomenon can be explained as follows. With the increasing of propane mass ratio, the temperature of propane and ethylene mixture also increases gradually. Therefore, the minimum heat transfer temperature difference between the hot fluids and cold fluids decreases gradually. As a result, the final preheat temperature of mixture is limited in the equipment E-3. In other words, when the mass ratio of the propane is beyond 55%, the final heating temperature of mixture in E-3 decreases gradually, and then the overall temperature difference of hot fluids and cold fluids increases, so the exergy efficiency of equipment E-3 decreases. Because the final preheat temperature of the propane and ethylene mixture is decreased, the evaporation temperature at the inlet of E-2 is also decreased, then the overall heat transfer temperature difference is getting larger, so the exergy efficiency of E-2 is decreasing gradually. All of
Fig. 5 – The exergy and heat efficiency of whole LNG subsystem.
the reasons mentioned above indicate that the mass ratio of propane has an optimized value (as shown in Fig. 5), and this value should be set according to the specific operation conditions.
4.2.2. The expanding pressure of propane and ethylene mixture The exergy and heat efficiency of the LNG subsystem with the variation of the mixture expanding pressure were shown in Fig. 7. It shows that the exergy efficiency of LNG subsystem reaches a maximum value when the pressure of mixtures is 4 MPa with the increase of propane/ethylene mixture pressure. The exergy efficiency of each component was shown in Fig. 8. It indicates that the exergy efficiency of equipment E-2 increases rapidly with the expanding pressure during the initial period. When the mixture expanding pressure is
Fig. 6 – The exergy efficiencies of components in the LNG subsystem with the mass ratio of propane in the propane and ethylene mixture.
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Fig. 7 – The schematic diagram of exergy efficiency of LNG subsystem with the expanding pressure of propane and ethylene mixture.
beyond 4 MPa, the improvement on its exergy efficiency becomes insignificant. The exergy efficiency of E-3 initially increases with the expanding pressure, and then decreases gradually when the expanding pressure is beyond 4 MPa. That phenomenon can be explained as follows. When the expanding pressure of propane and ethylene mixture is lower than 4 MPa, the final expanding temperature of the natural gas is higher in equipment EP-2, which leads to the minimum temperature difference between the hot fluid and cold fluid appeared at the low-temperature heat transfer part of E-3. So it restricts the preheat temperature increase of propane and ethylene mixture in the E-3. As a result, the final expanding temperature of natural gas in EP-2 will decrease gradually, and the preheating temperature of propane/ethylene mixture will increase with the expanding pressure. Therefore, the temperature difference at high temperature part of E-3 decreases and the exergy efficiency of E-3 increases gradually. However, when the expanding pressure of propane and
Fig. 8 – The exergy efficiencies of components in the LNG subsystem with the expanding pressure of propane and ethylene mixture.
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Fig. 9 – The diagram of the COP and exergy efficiency of the metal hydrides heat pump system variation.
ethylene is beyond 4 MPa, the minimum temperature difference between the hot fluid and cold fluid appears at the high temperature part of E-3. Because of the temperature limitation of the hot fluids (ammonia/water mixture), the temperature of propane/ethylene mixture cannot going up continuously in E3. At the same time, the final expanding temperature of natural gas decreases with the expanding pressure of propane/ethylene mixture increases, which leads to the enlarged temperature difference at the low-temperature part of E-3. All of these factors make the exergy efficiency of E-3 to reduce continuously. There are two factors which influence the exergy efficiency of E-2. One is the preheating temperature of the propane/ ethylene mixture in E-3; the other is the gasification profile of the propane and ethylene mixture at different pressure conditions. From above exergy efficiency analysis of E-3, we can see that when the expanding pressure of the propane/ ethylene mixture is lower than 4 MPa, the preheating temperature of the propane and ethylene mixture in E-3 is increased continuously; when the expanding pressure of the mixture is beyond 4 MPa, the preheating temperature will
Fig. 10 – The effect of the temperature of the heat source on the LNG subsystem performance.
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equipment are increased with the heat source temperature, because the temperature differences are enlarged. The maximum exergy loss is happened in the equipment E1, and the other optimization direction is to improve the exergy efficiency of E-1.
5.
Fig. 11 – The exergy efficiency of different components of the LNG subsystem.
close to a constant value because of the temperature limitation of the ammonia/water mixture. Thus there are two factors which will influence the exergy efficiency of E-2 simultaneously when the expanding pressure of the propane/ ethylene mixture is lower than 4 MPa, while only one factor influences the exergy efficiency of E-2 when the expanding pressure of the propane and ethylene mixture beyond 4 MPa because the preheat temperature of the mixture is close to a constant value. Therefore, the exergy efficiency of E-2 increasing becomes more gently with the expanding pressure of the propane/ethylene mixture beyond 4 MPa. The inflexion of the profile is located at the point where the expanding pressure equals 4 MPa.
4.2.3.
The temperature of the heat source
The COP value and exergy efficiency of metal hydrides heat pump with the variation of heat source temperature are shown in Fig. 9. It indicates that the COP and exergy efficiency of the MHHP increase gently with the temperature of heat source, which means that the performance of the MHHP can be improved by using higher temperature heat source. In order to compare the cold energy recovery performance between the new system and the traditional system (as shown in Fig. 1), the LNG subsystem and the MHHP system were investigated independently. In other words, we assume that the heat and exergy output from the MHHP are the whole heat and exergy input to the LNG subsystem. Thus the effect of the heat source temperature on the exergy and heat efficiency of the LNG subsystem is calculated based on the heat and exergy output from the MHHP (as shown in Fig. 10). It is obvious that the exergy and heat efficiency of the proposed system are improved in comparison with the traditional system proposed by Bai [7] (as shown in Fig. 1). Fig. 10 also gave the temperature range of the heat source. The temperature of the heat source is from 100 C to 410 C, in all cases the heat efficiency and exergy efficiency are higher (heat efficiency is about 44–60%, and exergy efficiency is about 56–70%), which is desirable in the engineering practice. Fig. 11 is the exergy efficiencies of the components in the system. The exergy efficiencies of most
Conclusions
A prototype of an integrated LNG cold energy recovery system with MHHP was proposed. The system has many merits e.g. cascade energy utilization, environmentally friendly, and easily adapted to the common waste heat recovery. The main optimization direction of the proposed system is to improve the performance of metal hydrides heat pump. Developing new prototype reactor with high heat transfer rate inside the reactive bed is the most effective method. The mass ratio of propane in the mixture has an optimization value with regard to the system performance, and it should be set according to the operation conditions. The expanding pressure of propane/ethylene mixture has also an optimum value which equals 4 MPa in this study. The exergy efficiencies of the equipment in LNG subsystem are increased with heat source temperature, and another optimization direction is to improve the exergy efficiency of the evaporator E-1.
Acknowledgment Financial support from the National Natural Science Foundation of China (Nos. 50976090 and 20936004) is greatly acknowledged.
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