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Exergy recovery during LNG regasification: Electric energy production – Part one
Applied Thermal Engineering 29 (2009) 380–387
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Exergy recovery during LNG regasification: Electric energy production – Part one Celidonio Dispenza a,*, Giorgio Dispenza b, Vincenzo La Rocca a, Giuseppe Panno a a b
DREAM, Università di Palermo, Viale delle Scienze Parco d’Orleans, Ed. 9, 90128 Palermo, Italy ITAE-CNR Nicola Giordano, Salita Santa Lucia Sopra Contesse, 5, 98126 Messina, Italy
a r t i c l e
i n f o
Article history: Received 20 June 2007 Accepted 8 March 2008 Available online 29 April 2008 Keywords: Liquefied natural gas Regasification Exergy recovery Improved CHP cycles Helium Electric energy production
a b s t r a c t In LNG regasification facilities, for exergy recovery during regasification, an option could be the production of electric energy recovering the energy available as cold. The authors propose an innovative process which uses a cryogenic stream of LNG during regasification as a cold source in an improved CHP plant (combined heat and power). Considering the LNG regasification projects in progress all over the World, an appropriate design option could be based on a modular unit having a mean regasification capacity of 2 109 standard m3/yr. This paper deals with an outlook of LNG trading now expanding in the World and gives a concise state of the art with a review of technology seeming that proposed. Then an innovative CHP plant and results pertaining the selection of working fluids, made with an optimization analysis, are presented. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Transport of natural gas by pipeline from a gas field lying far from dry land to the town or industrial sites is often impossible, so need there is to transport LNG by ship. At the terminal of arrival LNG is regasified in a process, which returns it back to gas state before its transport in the pipeline net work. The liquefaction process requires energy1 which is given by the same natural gas, burning a lot of it, or a fuel gas, derived by the boil-off originating in the process as a stream of gas which is considered a by-product. As energy prices have continuous increase, the opportunity of energy recovery during regasification is evident. The recovery of cold is also of capital interest because it has a relevant environmental impact, usually, on the sea near the regasification site. In past years some studies [2] have been carried out on the possibility of cold energy recovery in cold technology application facilities (e.g. air liquefaction producing nitrogen, oxygen, argon, deep freeze warehouse and cold storage warehouse, freezing process of foods, etc.). This kind of application has limitations and usually the demand of cold near the site suitable for the regasification is low. A very suitable option [3,4], instead, is the production of electric energy recovering the energy available as cold, using the cryogenic
* Corresponding author. Tel.: +39 091236117; fax: +39 091484425. E-mail address: [email protected] (C. Dispenza). 1 Note that the liquefaction of a kilogram of natural gas in worldwide facilities, now available, requires as a mean (1.2–1.5) 104 toe [1]. 1359-4311/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2008.03.036
stream of LNG during regasification as a cold source in an improved CHP Plant (combined heat and power). This paper deals with results of feasibility studies2 on ventures based on an appropriate thermodynamic and economic analysis of improved CHP cycles which demonstrates the suitability of the proposal. The process proposed uses the cryogenic stream of LNG during regasification as a cold source in an improved CHP plant (combined heat and power). Considering the LNG regasification projects now proposed all over the World, an appropriate design option can be based on a modular unit having a mean regasification capacity of 2 109 standard3 m3/yr. 2. The future of natural gas, World diffusion of LNG regasification sites, energetic and environmental implication World Energy Outlooks 2005 and 2006 (WEO 2005 and WEO 2006) of the International Energy Agency (IEA) [5,6], expect global energy markets to increase further its demand through 2030. If policies remain unchanged, in the IEA Reference Scenario World energy demand is projected to increase by over 72% between 2003 (10.6 109 toe) and 2030 (18.2 109 toe), although oil prices considered in WEO 2006 scenarios are higher than those in WEO 2005. World energy resources would be adequate to meet this de2 Research developed at DREAM, University of Palermo in the framework of the Program ‘‘ORPA059444: ‘‘Innovazione tecnologica di sistemi energetici e loro componenti; metodologie di progettazione, verifica e simulazione”. 3 At 15 °C and 760 mmHg.
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Nomenclature p Q T CC CHP COP
pressure (bar) cycle power input (kW) temperature (K) gas generator (in the top cycle process) combined heat and power cycle coefficient of performance
mand, but cumulative investment in energy-supply infrastructure of over $20 trillion in real terms over 2005–2030 will be needed to bring these resources to consumers. Oil and gas imports from the Middle East and North Africa will increase, giving rise to a greater dependence for IEA countries and large importers like China and India. Energy-related CO2 emissions also will be 55% higher than today. Imports of oil and gas in the OECD and developing Asia would grow even faster than demand. World oil demand would reach 116 mb/d in 2030, up from 84 mb/d in 2005. Most of the increase in oil supply in the Reference Scenario would met by a small number of major OPEC producers while non-OPEC conventional crude oil output peaks by the middle of the next decade. Global carbon dioxide (CO2) emissions reach 40 Gt in 2030, with a 55% increase over today’s level. China would overtake the United States as the world’s biggest emitter of CO2 before 2010. The International projections in ‘‘Energy Outlook 2006” of the Energy Information Administration (EIA-US: IEO2006) for international energy markets through 2030 are consistent with those published in EIA’s ‘‘Annual Energy Outlook 2006”. Natural gas trails coal as the fastest growing primary energy source. Natural gas share of total world energy consumption increases from 24% in 2003 to 26% in 2030. Consumption of natural gas worldwide increases from 95 trillion ft3 in 2003 to 182 trillion ft3 in 2030 in the reference case. Although natural gas is expected to be an important fuel source in the electric power and industrial sectors, the annual growth rate for natural gas consumption in the projections is slightly lower than the growth rate for coal consumption in contrast to past forecasts. Higher world oil prices make coal a more economical fuel source in the projections. But, natural gas consumption worldwide increases at an average rate of 2.4% annually from 2003 to 2030, as compared with 2.5%/yr for coal and 1.4%/yr for oil. Nevertheless, natural gas remains a more environmentally attractive energy source and burns more efficiently than coal, and it still is expected to be the fuel of choice in many regions worldwide. In a global market perspective of energy resources all this implies the need of a suitable analysis aiming to assure security of supply of demand in consuming countries with a diversification of their energy mix, while natural gas producing countries will continue to seek to diversify economies. Looking forward, the gas demand will increase and it requires big investment to improve both upstream and downstream capacity. There is need of investment to build pipeline for gas transport, liquefaction facilities to produce LNG in producing countries and regasification facilities in consuming countries. Future use of LNG will grow. By 2030, the LNG market would have a big change, with a five-fold increase in volume to nearly 75 billion ft3/day (BCFD), that represents about 15% of the total gas market, up from about 5% in 2000. A past study of California Energy Commission US [8], reports that in August 2005 Worldwide cryogenic storage capacity of LNG in regasification sites was of 22.7 106 m3 (50 facilities worldwide): 2.84 106 m3 (13 facilities with a regasification capacity reaching a 35% of gas demand) in Europe,
LNG NG Wn b ¼ pp2
liquefied natural gas natural gas net work done by cycle (kW) pressure ratio
g ¼ WQn
cycle thermal efficiency
1
18.54 106 m3 (30 facilities) in Asia, 1.00 106 m3 (five facilities) in North America, 0.32 106 m3 (two facilities) in South America. In Italy only a regasification plant at Panigaglia (LNG Italia – ENI Group) there is now, it has a cryogenic storage capacity of 100,000 m3 and during 2004 it processed4 2.0 109 Stm3 of LNG. Available data allow to derive a preliminary forecast for a mean term Scenario pertaining the development of LNG trading in Italy and the energetic and environmental implication. July 6, 2006, the President of italian ‘‘Authority for Electric Energy and Gas, AEEG, in Rome ‘‘Sala della Lupa” presented the ‘‘Annual Report by the Authority for Electricity and Gas on the State of the Services and the Activities Carried Out” [9]. In Italy 10 LNG regasification terminals are planned which have been authorized by AEEG: 3 shall be built offshore (maximum regasification capacity 22 109 Stm3/yr), 5 in Italy Peninsula (maximum regasification capacity 44 109 Stm3/yr) and 2 in Sicily Island (maximum regasification capacity 24 109 Stm3/yr). The whole regasification capacity in the medium term amounts to 90 109 Stm3/yr. The environmental impact of LNG regasification, due to cold reject in the neighbouring sea when operating with Open Rack (OR) units is high.5 The recovery of a part of this energy shall be mandatory looking at environmental planetary problems, both for saving of energy resources and for reducing environmental impact (provisional Cedigaz data available for the year 2004 [7]: the worldwide amount of LNG trade movement was 178 billion ft3). 3. Production of electric energy recovering cold exergy during regasification of LNG in CHP cycles The production of electric energy recovering the energy available as cold, using the cryogenic stream of LNG during regasification as a cold source, is an old idea. A first possibility is that to improve the overall electric efficiency of an electric utility in power stations working with steam turbines, lying near the regasification site. The efficiency improvement is obtained by lowering the temperature of the condenser utilizing cooled water rejected by OR units. This concept has been applied in Japan. Also in Japan, at Himeji LNG terminal, another application pertains to utilization of cold energy of LNG, released during regasification, to cool inlet air in the compressor [4] of a gas turbine power plant. The electric utility having an electric power capacity6 of 51 MW works inside the terminal area and operates with a combined cycle with gas and steam turbine. An improved process was proposed in the past 20 [3] and it was proved in-field in the regasification site at Panigaglia, La Spezia,
4 The regasification capacity is expansible up to 3.6 109 Stm3, it is planned an expansion of the plant to reach in the future a regasification capacity of 12.6 109 Stm3 [4]. 5 A mean amount of 120–140 Tcal/yr for an amount of 1 109 Stm3/yr of LNG regasified [4]. 6 It works with a combined cycle with a gas turbine (producing 40 MW) and a steam turbine fed by steam generated recovering heat of flue gas from gas turbine (producing 11 MW).
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Italy, of SNAM (ENI Group). The process pertains to the use of a CHP binary cycle composed of two Brayton cycles: a top cycle, which is an open cycle working with a conventional gas turbine, and a bottom cycle, which is a closed cycle working with nitrogen. This last is heated recovering the reject heat of the top cycle. The reject heat of the bottom cycle goes into a cryogenic heat exchanger into which LNG is regasified. Now, the development of innovatory technologies in the field of gas turbines, compressors and heat transfer equipment and devices offers a new perspective. Then, it seems very interesting the analysis of some improved cycles of such kind properly designed to recovery exergy of cold during the regasification of LNG and producing electric energy. The feasibility analysis of DREAM, Palermo University, here presented, includes two ventures: one of them pertains to a CHP binary cycle composed of two Brayton cycles, whose bottom cycle works with helium and another has the bottom cycle working with nitrogen. The pressures have been selected after an optimization analysis and they are higher than those pertaining the process described in [3]. Heat transfer equipment proposed was also duly analysed designing a suitable extended heat transfer matrix to improve the processes [4].
4. The regasification process of LNG The Italian natural gas transmission system works with main pipelines at a pressure rating up to more than 70 bar, then the LNG regasified has to be sent in the transport pipeline at a pressure of the same order of magnitude. In principle it is possible (see Fig. 1, path AB0 D0 D) to pump natural gas at this pressure (D0 D) after regasification at a low pressure (AB0 B00 B000 D0 ), but this option is not applied in Europe. When the regasification is carried out at low pressures and, then, the gas is compressed at the pressure required by pipelines, the pumping power (WNG) is very high. Instead, if the LNG is pumped in liquid phase, at a pressure lying in the pressure rating required by pipelines (hypercritical pressures) there is convenience because the pumping power (WLNG) is lower (see Fig. 1, path ABCD). The ratio WNG/WLNG is higher than 20 [4,10]. Moreover, with regasification at hypercritical pressures, the heat exchange by the LNG side is very good and heat transfer equipment is more reliable. The process proposed works at hypercritical pressures (pressure in the LNG regasification loop lies in the range 75–80 bar) [4]. 5. The process proposed The process proposed works with helium and it is shown in Fig. 2. The top cycle includes a modern gas turbine system working with a high temperature at the inlet in the turbine. The inlet air going to the suction side of the compressor is cooled by sea water coming out by Open Rack units. The process is shown in the higher part of Fig. 2 at left. The bottom cycle, which is shown in the higher part of figure at right, works with helium: the higher pressure is 22.7 bar and the lower is 3 bar. The temperature of helium at the inlet in the gas turbine (GTbottom) is 579 °C, then helium coming out of gas turbine gives heat to LNG in the cryogenic regasifiers and it is cooled down to a temperature of 129 °C, it is then pumped by the cryogenic compressor C2 and at the exit it has a temperature of 70 °C. The cryogenic heat exchanger units (cryogenic regasifiers) managing the LNG to be regasified have a heat transfer matrix made with extended surface tubes of special manufacture [4] (see Fig. 3). LNG flows in the units from the tube side while helium flows from the shell side. Tubes have turbulence promoters inside
Fig. 1. Thermodynamic process during regasification of LNG.
and in a cluster of tubes are inserted hollow tie rods (a series of one between three tubes) on the shell side having windows of rectangular shape with rounded corners. This feature assures lateral injection enhancing turbulence in the stream crossing the matrix. In the plant proposed there are four cryogenic heat exchangers: a train of two is in series and then the trains are connected in parallel. The shell of a unit has an external diameter of 1.20 m and it is long 8.60 m, there are 300 tubes of stainless steel suitable for cryogenic exploitation which have an external diameter of (3/4) in. Cryogenic heat exchangers are installed inside a cold box (see Fig. 4) having the following dimensions: 3.70 m 3.70 m 9.20 m. The exchangers for heating helium are two units with a feature of the heat transfer matrix seeming that of cryogenic units, but the inner of tubes has also extended surface and there are inside turbulence promoters. The shell of a unit has an external diameter of 2.90 m and is long 12.00 m, there are 450 tubes of stainless steel which have an external diameter of (1.5) in. The Open Rack facility reported in Fig. 2 is required for operation for which is not produced electric energy or during maintenance operation. The plant layout for a module with a regasification capacity of 2 109 Stm3/yr is reported in Fig. 5, it requires a whole surface area of a 1500 m2. The plant operating with nitrogen has seeming feature, but it requires higher pressures inside the bottom cycle and its performance is lower. The use of helium calls for R&D on the related technology for a large worldwide diffusion of this kind of CHP plant, but it is very interesting to look forward. Helium is easy available in USA, Russia and Italy [11], moreover, as far as it pertains to the technology, much R&D was carried out in past years for nuclear reactors power cycles [11,12]. Helium is much prone to leakage then nitrogen and calls for an appropriate system to prevent leakage (e.g. such as magnetic bearing). Cost of helium now is acceptable and it is available in various countries, but it is worth of mention that now very little power plants are working with it; during next years the scenarios offered by diffusion of nuclear power plants working with helium [12–19] (and the forecasted diffusion of LNG trading, considering the possible development of CHP plants proposed), so calling for industrial production of this gas, can lower its price. The use of nitrogen has the advantage that technology is easy available on commissioning in the Petrochemical World. Also compressors and gas turbines for use with helium can be available on commissioning (e.g.: multi-stage centrifugal or axial compressors electrical driven and power axial multi-stage gas turbine operating in subsonic regime with a reaction degree 0.50).
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Fig. 2. The modular process proposed for regasification of LNG.
Fig. 3. Heat transfer matrix proposed for the cryogenic regasifier of LNG.
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Fig. 4. Layout of cryogenic heat exchanger units inside the cold box.
Fig. 5. Layout of a modular regasification facility proposed.
Technology required is seeming to that for nitrogen and a feasibility study of authors has verified that compressors and gas turbines can be compact and reliable; this equipment can be made in factories belonging to Petrochemical World.
6. The working fluid proposed for the bottom cycle and design parameters For bottom cycle there is need to select a suitable gaseous fluid. Considering that the fluid will work at very low temperatures, the range of variation of specific volume and the order of magnitude of this parameter is of capital interest for design. Working in a suitable range of pressures and with an appropriate cycle pressure ratio it is possible to have a relative compact plant.
When selecting a working fluid it is important that pumping power to heat transfer ratio Wp/q shall be as low as possible [11]. Table A.1 of Appendix 1 shows that helium is a good fluid by this point of view while nitrogen has a higher value of Wp/q compared with helium. Helium is a very good working fluid. Fig. 67 reports specific net work done by an ideal simple Brayton cycle Wn versus pressure ratio b = p2/p1 for a lower cycle temperature T1 = 144 K and a higher cycle temperature T3 = 852 K. These values pertain to the design parameters of the plants proposed. The temperature of 852 K was selected to have a pinch temperature difference of 34 K between T4 of
7
See Appendix 2.
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1600 1400
Wn [kJ/kg]
1200 1000 800 600 400 200 0 1
10
100
β=p2/p1 Helium
Nitrogen
Carbon dioxide
Fig. 6. Specific net work done by an ideal simple Brayton cycle versus pressure ratio for T1 = 144 K and T3 = 852 K.
Helium 1500
0.6 5.5 bar
η
Wn [kJ/kg]
1300 1100
0.5 0.4
Wn
900
0.3 3 bar
700
0.2
500
0.1
300 0
2
4
6
8
10
12
14
0 18
16
β=p2/p1 Fig. 7. Brayton cycle working with helium, specific net work Wn and conventional efficiency g versus pressure ratio b for T1 = 144 K and T3 = 852 K; p1 varying in the range 3– 5.5 bar
Nitrogen 250
Wn
5.5 bar
225
0.5 3 bar
Wn [kJ/kg]
0.6
η
200
0.4
175
0.3 η
150
0.2
125
0.1
100 0
2
4
6
8
10
12
14
16
0 18
β=p2/p1 Fig. 8. Brayton cycle working with nitrogen, specific net work Wn and conventional efficiency g versus pressure ratio b for T1 = 144 K and T3 = 852 K; p1 varying in the range 3–5.5 bar
886 K in top cycle and T3 of 852 K in the Helium cycle and for T1 was selected to have a pinch temperature difference of 31 K between this and the inlet temperature of LNG (113 K). The same statement hold
for plants working with nitrogen. The optimum pressure ratios are, respectively: 9.4 for helium, 22.4 for nitrogen and 52.1 for carbon dioxide.
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It is evident that the specific net work done by helium is very high compared both with nitrogen and carbon dioxide. A steady-state simulation was made, by means of a program compiled in EES language,8 for the real Brayton cycle proposed working with helium for T1 = 144 K and T3 = 852 K. The simulation gives the results, for the net specific work Wn done by the real cycle, which are reported in a set of curves in Fig. 7. Another set of curves gives the trend of cycle conventional efficiency (g = Wn/Q, where Q is the heat supplied to helium). The curves of net specific work done by the cycle have been derived varying the pressure p1 which lies in the range 3–5.5 bar (3 bar the lower curve and 5.5 bar the higher).9 Approximatively, the optimum is obtained for the pressure ratio 7.5, this value has been selected for design. The lower pressure p1 selected for design is 3 bar, the higher pressure is 22.5 bar. The same kind of analysis was made for the Brayton cycle working with nitrogen. The results, which are presented in a format seeming that for helium plant, are reported in Fig. 8. The lower pressure p1 selected for design is 5 bar. The pressure ratio selected is 7.5. The selection is a suitable compromise aiming to have pressures not too high in the plant. The higher pressure is 37.5 bar. Note that the optimum would be obtained for a very high pressure ratio. In any case, the specific work done by the cycle is very low compared with helium, but, nitrogen requires a simpler technology which is available in Petrochemical World. 7. Conclusive remarks The production of electric energy recovering the energy available as cold, using the cryogenic stream of LNG during regasification as cold source in an improved CHP plant (combined heat and power) would be a very suitable option. Feasibility studies of improved CHP cycles10 carried out at DREAM, University of Palermo show the possibility to use as a working fluid in the bottom cycle helium or nitrogen. CHP plants operating with nitrogen have seeming feature of CHP plants working with helium, but, these require higher pressures inside the bottom cycle and performance is lower. In another author’s paper thermodynamic, economic and environmental analysis for the ventures proposed will be presented. The results demonstrate the suitability of the proposal. Appendix 1. Comparison of gaseous fluids on the basis of heat transfer and pumping power Gaseous working fluids have very high pumping power to heat transfer ratio, compared with other fluids. For sake of simplicity, as only comparative relationships are sought [11], it will considered that all fluids to be compared flow and are heated in a circular pipe of diameter D and length L. The pumping power is given by the relationship: ! L pD2 qV 3 ðA:1Þ Wp ¼ k 4 2 D where Wp is the pumping power; k = 0.184Re0.2 is the Weissbach is the Reynolds number; L is the pipe length; friction factor; Re ¼ VDq l D is the pipe diameter; V is the mean fluid velocity in the pipe; q is the fluid density; l is the dynamic viscosity of fluid.
8 Engineering Equation Solver of S.A. Klein and A. Alvarado, Professional version 6.567. 9 Both: for Wn and g curves. 10 CHP cycles: the top cycle is a conventional gas turbine open cycle fed by natural gas and the bottom cycle is an improved gas turbine closed cycle working with helium or nitrogen gas.
The heat transfer can be given by the relationship: q ¼ hðpDLÞDt m
ðA:2Þ
where q is the heat transferred along the pipe; Dtm is the logarithmic mean temperature difference between pipe walls and coolant; h is the heat transfer coefficient, this last can be given for gaseous coolants by the Dittus–Boelter correlation: h ¼ 0:023
k 0:8 0:4 Re Pr D
ðA:3Þ
where Pr is the Prandtl number; k is the thermal conductivity of fluid. Then, it is obtained the relationship: ! ! Wp V2 Pr 0:6 ðA:4Þ ¼ q Dtm cp where cp is the specific heat at constant pressure, Wp/q is an appropriate parameter for comparison of different working fluids. The first term at right in (A.4) accounts for the operating parameters while the second accounts for fluid properties. It is evident that a good fluid must have a low value of the second parameter (e.g. Pr low and cp high). Another alternative relationship can be obtained considering the heat transferred given by the formula: ! pD2 Vcp DT ðA:5Þ q¼q 4 where DT is the temperature rise of fluid along the pipe length. Dividing Wp given by (A.1) by q given by (A.5), rearranging and introducing the volume of fluid within the pipe, V0 = (pD2/4)/L, it is derived the relationship: ! ! Wp q2 L2 Pr0:6 ðA:6Þ ¼ q c3p q2 Dtm DT 2 V 20 This relationship has in the right side two terms: the first accounts for the operating parameters and the second for fluid properties. It is evident that once again to have a low value of Wp/q there is need to have a low value of the second term. It is worth of note that the dependence on temperature and pressure is different for different gases. For sake of simplicity by using the perfect gas laws, the relationship (A.6) can be arranged to give: " 2 #" 3 # Wp 1 1 qLT c1 0:6 Pr ¼ M q R Dtm DTV p0 c
ðA:7Þ
where R is the universal gas constant; M is the molecular mass of gas; c = cp/cv where cv is the specific heat of gas at constant volume; p, T is the average absolute pressure and temperature of gas. Eq. (A.7) shows that, if heat transfer q, Dtm, DT, V0, and L are the same, a good coolant would have a low value of the third term at r.h.s. Relative values of Wp/q for different gases evaluated by means of (A.7) are reported in Table A.1. The values are divided by that for hydrogen (at 1 atm and 27 °C) which has a lower value. Helium is a good coolant, moreover its specific heat, varying the temperature, is almost constant.
Appendix 2. Comparison of gaseous working fluids on the basis of the specific net work done by an ideal Brayton closed cycle For an ideal simple Brayton cycle the specific net work done by it is given by the well known relationship:
C. Dispenza et al. / Applied Thermal Engineering 29 (2009) 380–387 Table A.1 Relative values of Wp/q for different gases evaluated by means of (A.7) Gas
27 °C
315 °C
Hydrogen Helium Carbon dioxide Nitrogen Air
1.0 5.2 11.2 14.3 14.8
0.9 5.3 5.3 12.9 12.7
P = 1 atm.
( W n ¼ W t W c ¼ cp T 1 ½1
bðc1Þ=c p
" #) T3 1 þ 1 ðc1Þ=c T1 bp
ðB:1Þ
where Wn is the specific net work done by cycle; Wt is the specific work done by turbine; Wc is the specific work for driving compressor; c = cp/cv where cp, cv is the specific heat of gas at constant pressure or volume; bp = p2/p1 is the pressure ratio; T1 is the lower temperature along the cycle; T3 is the higher temperature along the cycle. For fixed initial T1 and maximum T3 cycle temperatures the net work goes trough a maximum at the value of bp = p2/p1: c=ðc1Þ c=½2ðc1Þ T2 T3 ¼ ðB:2Þ bpopt ¼ T1 T1 The results for helium, nitrogen and carbon dioxide which have been compared by means of the relationship (B.1) are reported in Fig. 6. Data pertains to a wide range of variation of the pressure ratio and it is evident that helium is very good. References [1] C. Dispenza, G. Dispenza, V. La Rocca, G. Panno, Analisi delle prestazioni termodinamiche e raffronto tecnico economico di impianti per la liquefazione del gas naturale, in: Proceedings of 57° Congresso Nazionale ATI, Pisa, 17–20 Settembre 2002. [2] J.P. Buffiere, R.Vincent, La recuperation des frigories du LNG et l’ajustement du gaz au terminal de Fos sur Mer, on LNG 3, Session III, Paper 8, 1972.
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Exergy recovery during LNG regasification: Electric energy production – Part one Celidonio Dispenza a,*, Giorgio Dispenza b, Vincenzo La Rocca a, Giuseppe Panno a a b
DREAM, Università di Palermo, Viale delle Scienze Parco d’Orleans, Ed. 9, 90128 Palermo, Italy ITAE-CNR Nicola Giordano, Salita Santa Lucia Sopra Contesse, 5, 98126 Messina, Italy
a r t i c l e
i n f o
Article history: Received 20 June 2007 Accepted 8 March 2008 Available online 29 April 2008 Keywords: Liquefied natural gas Regasification Exergy recovery Improved CHP cycles Helium Electric energy production
a b s t r a c t In LNG regasification facilities, for exergy recovery during regasification, an option could be the production of electric energy recovering the energy available as cold. The authors propose an innovative process which uses a cryogenic stream of LNG during regasification as a cold source in an improved CHP plant (combined heat and power). Considering the LNG regasification projects in progress all over the World, an appropriate design option could be based on a modular unit having a mean regasification capacity of 2 109 standard m3/yr. This paper deals with an outlook of LNG trading now expanding in the World and gives a concise state of the art with a review of technology seeming that proposed. Then an innovative CHP plant and results pertaining the selection of working fluids, made with an optimization analysis, are presented. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Transport of natural gas by pipeline from a gas field lying far from dry land to the town or industrial sites is often impossible, so need there is to transport LNG by ship. At the terminal of arrival LNG is regasified in a process, which returns it back to gas state before its transport in the pipeline net work. The liquefaction process requires energy1 which is given by the same natural gas, burning a lot of it, or a fuel gas, derived by the boil-off originating in the process as a stream of gas which is considered a by-product. As energy prices have continuous increase, the opportunity of energy recovery during regasification is evident. The recovery of cold is also of capital interest because it has a relevant environmental impact, usually, on the sea near the regasification site. In past years some studies [2] have been carried out on the possibility of cold energy recovery in cold technology application facilities (e.g. air liquefaction producing nitrogen, oxygen, argon, deep freeze warehouse and cold storage warehouse, freezing process of foods, etc.). This kind of application has limitations and usually the demand of cold near the site suitable for the regasification is low. A very suitable option [3,4], instead, is the production of electric energy recovering the energy available as cold, using the cryogenic
* Corresponding author. Tel.: +39 091236117; fax: +39 091484425. E-mail address: [email protected] (C. Dispenza). 1 Note that the liquefaction of a kilogram of natural gas in worldwide facilities, now available, requires as a mean (1.2–1.5) 104 toe [1]. 1359-4311/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2008.03.036
stream of LNG during regasification as a cold source in an improved CHP Plant (combined heat and power). This paper deals with results of feasibility studies2 on ventures based on an appropriate thermodynamic and economic analysis of improved CHP cycles which demonstrates the suitability of the proposal. The process proposed uses the cryogenic stream of LNG during regasification as a cold source in an improved CHP plant (combined heat and power). Considering the LNG regasification projects now proposed all over the World, an appropriate design option can be based on a modular unit having a mean regasification capacity of 2 109 standard3 m3/yr. 2. The future of natural gas, World diffusion of LNG regasification sites, energetic and environmental implication World Energy Outlooks 2005 and 2006 (WEO 2005 and WEO 2006) of the International Energy Agency (IEA) [5,6], expect global energy markets to increase further its demand through 2030. If policies remain unchanged, in the IEA Reference Scenario World energy demand is projected to increase by over 72% between 2003 (10.6 109 toe) and 2030 (18.2 109 toe), although oil prices considered in WEO 2006 scenarios are higher than those in WEO 2005. World energy resources would be adequate to meet this de2 Research developed at DREAM, University of Palermo in the framework of the Program ‘‘ORPA059444: ‘‘Innovazione tecnologica di sistemi energetici e loro componenti; metodologie di progettazione, verifica e simulazione”. 3 At 15 °C and 760 mmHg.
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Nomenclature p Q T CC CHP COP
pressure (bar) cycle power input (kW) temperature (K) gas generator (in the top cycle process) combined heat and power cycle coefficient of performance
mand, but cumulative investment in energy-supply infrastructure of over $20 trillion in real terms over 2005–2030 will be needed to bring these resources to consumers. Oil and gas imports from the Middle East and North Africa will increase, giving rise to a greater dependence for IEA countries and large importers like China and India. Energy-related CO2 emissions also will be 55% higher than today. Imports of oil and gas in the OECD and developing Asia would grow even faster than demand. World oil demand would reach 116 mb/d in 2030, up from 84 mb/d in 2005. Most of the increase in oil supply in the Reference Scenario would met by a small number of major OPEC producers while non-OPEC conventional crude oil output peaks by the middle of the next decade. Global carbon dioxide (CO2) emissions reach 40 Gt in 2030, with a 55% increase over today’s level. China would overtake the United States as the world’s biggest emitter of CO2 before 2010. The International projections in ‘‘Energy Outlook 2006” of the Energy Information Administration (EIA-US: IEO2006) for international energy markets through 2030 are consistent with those published in EIA’s ‘‘Annual Energy Outlook 2006”. Natural gas trails coal as the fastest growing primary energy source. Natural gas share of total world energy consumption increases from 24% in 2003 to 26% in 2030. Consumption of natural gas worldwide increases from 95 trillion ft3 in 2003 to 182 trillion ft3 in 2030 in the reference case. Although natural gas is expected to be an important fuel source in the electric power and industrial sectors, the annual growth rate for natural gas consumption in the projections is slightly lower than the growth rate for coal consumption in contrast to past forecasts. Higher world oil prices make coal a more economical fuel source in the projections. But, natural gas consumption worldwide increases at an average rate of 2.4% annually from 2003 to 2030, as compared with 2.5%/yr for coal and 1.4%/yr for oil. Nevertheless, natural gas remains a more environmentally attractive energy source and burns more efficiently than coal, and it still is expected to be the fuel of choice in many regions worldwide. In a global market perspective of energy resources all this implies the need of a suitable analysis aiming to assure security of supply of demand in consuming countries with a diversification of their energy mix, while natural gas producing countries will continue to seek to diversify economies. Looking forward, the gas demand will increase and it requires big investment to improve both upstream and downstream capacity. There is need of investment to build pipeline for gas transport, liquefaction facilities to produce LNG in producing countries and regasification facilities in consuming countries. Future use of LNG will grow. By 2030, the LNG market would have a big change, with a five-fold increase in volume to nearly 75 billion ft3/day (BCFD), that represents about 15% of the total gas market, up from about 5% in 2000. A past study of California Energy Commission US [8], reports that in August 2005 Worldwide cryogenic storage capacity of LNG in regasification sites was of 22.7 106 m3 (50 facilities worldwide): 2.84 106 m3 (13 facilities with a regasification capacity reaching a 35% of gas demand) in Europe,
LNG NG Wn b ¼ pp2
liquefied natural gas natural gas net work done by cycle (kW) pressure ratio
g ¼ WQn
cycle thermal efficiency
1
18.54 106 m3 (30 facilities) in Asia, 1.00 106 m3 (five facilities) in North America, 0.32 106 m3 (two facilities) in South America. In Italy only a regasification plant at Panigaglia (LNG Italia – ENI Group) there is now, it has a cryogenic storage capacity of 100,000 m3 and during 2004 it processed4 2.0 109 Stm3 of LNG. Available data allow to derive a preliminary forecast for a mean term Scenario pertaining the development of LNG trading in Italy and the energetic and environmental implication. July 6, 2006, the President of italian ‘‘Authority for Electric Energy and Gas, AEEG, in Rome ‘‘Sala della Lupa” presented the ‘‘Annual Report by the Authority for Electricity and Gas on the State of the Services and the Activities Carried Out” [9]. In Italy 10 LNG regasification terminals are planned which have been authorized by AEEG: 3 shall be built offshore (maximum regasification capacity 22 109 Stm3/yr), 5 in Italy Peninsula (maximum regasification capacity 44 109 Stm3/yr) and 2 in Sicily Island (maximum regasification capacity 24 109 Stm3/yr). The whole regasification capacity in the medium term amounts to 90 109 Stm3/yr. The environmental impact of LNG regasification, due to cold reject in the neighbouring sea when operating with Open Rack (OR) units is high.5 The recovery of a part of this energy shall be mandatory looking at environmental planetary problems, both for saving of energy resources and for reducing environmental impact (provisional Cedigaz data available for the year 2004 [7]: the worldwide amount of LNG trade movement was 178 billion ft3). 3. Production of electric energy recovering cold exergy during regasification of LNG in CHP cycles The production of electric energy recovering the energy available as cold, using the cryogenic stream of LNG during regasification as a cold source, is an old idea. A first possibility is that to improve the overall electric efficiency of an electric utility in power stations working with steam turbines, lying near the regasification site. The efficiency improvement is obtained by lowering the temperature of the condenser utilizing cooled water rejected by OR units. This concept has been applied in Japan. Also in Japan, at Himeji LNG terminal, another application pertains to utilization of cold energy of LNG, released during regasification, to cool inlet air in the compressor [4] of a gas turbine power plant. The electric utility having an electric power capacity6 of 51 MW works inside the terminal area and operates with a combined cycle with gas and steam turbine. An improved process was proposed in the past 20 [3] and it was proved in-field in the regasification site at Panigaglia, La Spezia,
4 The regasification capacity is expansible up to 3.6 109 Stm3, it is planned an expansion of the plant to reach in the future a regasification capacity of 12.6 109 Stm3 [4]. 5 A mean amount of 120–140 Tcal/yr for an amount of 1 109 Stm3/yr of LNG regasified [4]. 6 It works with a combined cycle with a gas turbine (producing 40 MW) and a steam turbine fed by steam generated recovering heat of flue gas from gas turbine (producing 11 MW).
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Italy, of SNAM (ENI Group). The process pertains to the use of a CHP binary cycle composed of two Brayton cycles: a top cycle, which is an open cycle working with a conventional gas turbine, and a bottom cycle, which is a closed cycle working with nitrogen. This last is heated recovering the reject heat of the top cycle. The reject heat of the bottom cycle goes into a cryogenic heat exchanger into which LNG is regasified. Now, the development of innovatory technologies in the field of gas turbines, compressors and heat transfer equipment and devices offers a new perspective. Then, it seems very interesting the analysis of some improved cycles of such kind properly designed to recovery exergy of cold during the regasification of LNG and producing electric energy. The feasibility analysis of DREAM, Palermo University, here presented, includes two ventures: one of them pertains to a CHP binary cycle composed of two Brayton cycles, whose bottom cycle works with helium and another has the bottom cycle working with nitrogen. The pressures have been selected after an optimization analysis and they are higher than those pertaining the process described in [3]. Heat transfer equipment proposed was also duly analysed designing a suitable extended heat transfer matrix to improve the processes [4].
4. The regasification process of LNG The Italian natural gas transmission system works with main pipelines at a pressure rating up to more than 70 bar, then the LNG regasified has to be sent in the transport pipeline at a pressure of the same order of magnitude. In principle it is possible (see Fig. 1, path AB0 D0 D) to pump natural gas at this pressure (D0 D) after regasification at a low pressure (AB0 B00 B000 D0 ), but this option is not applied in Europe. When the regasification is carried out at low pressures and, then, the gas is compressed at the pressure required by pipelines, the pumping power (WNG) is very high. Instead, if the LNG is pumped in liquid phase, at a pressure lying in the pressure rating required by pipelines (hypercritical pressures) there is convenience because the pumping power (WLNG) is lower (see Fig. 1, path ABCD). The ratio WNG/WLNG is higher than 20 [4,10]. Moreover, with regasification at hypercritical pressures, the heat exchange by the LNG side is very good and heat transfer equipment is more reliable. The process proposed works at hypercritical pressures (pressure in the LNG regasification loop lies in the range 75–80 bar) [4]. 5. The process proposed The process proposed works with helium and it is shown in Fig. 2. The top cycle includes a modern gas turbine system working with a high temperature at the inlet in the turbine. The inlet air going to the suction side of the compressor is cooled by sea water coming out by Open Rack units. The process is shown in the higher part of Fig. 2 at left. The bottom cycle, which is shown in the higher part of figure at right, works with helium: the higher pressure is 22.7 bar and the lower is 3 bar. The temperature of helium at the inlet in the gas turbine (GTbottom) is 579 °C, then helium coming out of gas turbine gives heat to LNG in the cryogenic regasifiers and it is cooled down to a temperature of 129 °C, it is then pumped by the cryogenic compressor C2 and at the exit it has a temperature of 70 °C. The cryogenic heat exchanger units (cryogenic regasifiers) managing the LNG to be regasified have a heat transfer matrix made with extended surface tubes of special manufacture [4] (see Fig. 3). LNG flows in the units from the tube side while helium flows from the shell side. Tubes have turbulence promoters inside
Fig. 1. Thermodynamic process during regasification of LNG.
and in a cluster of tubes are inserted hollow tie rods (a series of one between three tubes) on the shell side having windows of rectangular shape with rounded corners. This feature assures lateral injection enhancing turbulence in the stream crossing the matrix. In the plant proposed there are four cryogenic heat exchangers: a train of two is in series and then the trains are connected in parallel. The shell of a unit has an external diameter of 1.20 m and it is long 8.60 m, there are 300 tubes of stainless steel suitable for cryogenic exploitation which have an external diameter of (3/4) in. Cryogenic heat exchangers are installed inside a cold box (see Fig. 4) having the following dimensions: 3.70 m 3.70 m 9.20 m. The exchangers for heating helium are two units with a feature of the heat transfer matrix seeming that of cryogenic units, but the inner of tubes has also extended surface and there are inside turbulence promoters. The shell of a unit has an external diameter of 2.90 m and is long 12.00 m, there are 450 tubes of stainless steel which have an external diameter of (1.5) in. The Open Rack facility reported in Fig. 2 is required for operation for which is not produced electric energy or during maintenance operation. The plant layout for a module with a regasification capacity of 2 109 Stm3/yr is reported in Fig. 5, it requires a whole surface area of a 1500 m2. The plant operating with nitrogen has seeming feature, but it requires higher pressures inside the bottom cycle and its performance is lower. The use of helium calls for R&D on the related technology for a large worldwide diffusion of this kind of CHP plant, but it is very interesting to look forward. Helium is easy available in USA, Russia and Italy [11], moreover, as far as it pertains to the technology, much R&D was carried out in past years for nuclear reactors power cycles [11,12]. Helium is much prone to leakage then nitrogen and calls for an appropriate system to prevent leakage (e.g. such as magnetic bearing). Cost of helium now is acceptable and it is available in various countries, but it is worth of mention that now very little power plants are working with it; during next years the scenarios offered by diffusion of nuclear power plants working with helium [12–19] (and the forecasted diffusion of LNG trading, considering the possible development of CHP plants proposed), so calling for industrial production of this gas, can lower its price. The use of nitrogen has the advantage that technology is easy available on commissioning in the Petrochemical World. Also compressors and gas turbines for use with helium can be available on commissioning (e.g.: multi-stage centrifugal or axial compressors electrical driven and power axial multi-stage gas turbine operating in subsonic regime with a reaction degree 0.50).
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Fig. 2. The modular process proposed for regasification of LNG.
Fig. 3. Heat transfer matrix proposed for the cryogenic regasifier of LNG.
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Fig. 4. Layout of cryogenic heat exchanger units inside the cold box.
Fig. 5. Layout of a modular regasification facility proposed.
Technology required is seeming to that for nitrogen and a feasibility study of authors has verified that compressors and gas turbines can be compact and reliable; this equipment can be made in factories belonging to Petrochemical World.
6. The working fluid proposed for the bottom cycle and design parameters For bottom cycle there is need to select a suitable gaseous fluid. Considering that the fluid will work at very low temperatures, the range of variation of specific volume and the order of magnitude of this parameter is of capital interest for design. Working in a suitable range of pressures and with an appropriate cycle pressure ratio it is possible to have a relative compact plant.
When selecting a working fluid it is important that pumping power to heat transfer ratio Wp/q shall be as low as possible [11]. Table A.1 of Appendix 1 shows that helium is a good fluid by this point of view while nitrogen has a higher value of Wp/q compared with helium. Helium is a very good working fluid. Fig. 67 reports specific net work done by an ideal simple Brayton cycle Wn versus pressure ratio b = p2/p1 for a lower cycle temperature T1 = 144 K and a higher cycle temperature T3 = 852 K. These values pertain to the design parameters of the plants proposed. The temperature of 852 K was selected to have a pinch temperature difference of 34 K between T4 of
7
See Appendix 2.
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1600 1400
Wn [kJ/kg]
1200 1000 800 600 400 200 0 1
10
100
β=p2/p1 Helium
Nitrogen
Carbon dioxide
Fig. 6. Specific net work done by an ideal simple Brayton cycle versus pressure ratio for T1 = 144 K and T3 = 852 K.
Helium 1500
0.6 5.5 bar
η
Wn [kJ/kg]
1300 1100
0.5 0.4
Wn
900
0.3 3 bar
700
0.2
500
0.1
300 0
2
4
6
8
10
12
14
0 18
16
β=p2/p1 Fig. 7. Brayton cycle working with helium, specific net work Wn and conventional efficiency g versus pressure ratio b for T1 = 144 K and T3 = 852 K; p1 varying in the range 3– 5.5 bar
Nitrogen 250
Wn
5.5 bar
225
0.5 3 bar
Wn [kJ/kg]
0.6
η
200
0.4
175
0.3 η
150
0.2
125
0.1
100 0
2
4
6
8
10
12
14
16
0 18
β=p2/p1 Fig. 8. Brayton cycle working with nitrogen, specific net work Wn and conventional efficiency g versus pressure ratio b for T1 = 144 K and T3 = 852 K; p1 varying in the range 3–5.5 bar
886 K in top cycle and T3 of 852 K in the Helium cycle and for T1 was selected to have a pinch temperature difference of 31 K between this and the inlet temperature of LNG (113 K). The same statement hold
for plants working with nitrogen. The optimum pressure ratios are, respectively: 9.4 for helium, 22.4 for nitrogen and 52.1 for carbon dioxide.
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It is evident that the specific net work done by helium is very high compared both with nitrogen and carbon dioxide. A steady-state simulation was made, by means of a program compiled in EES language,8 for the real Brayton cycle proposed working with helium for T1 = 144 K and T3 = 852 K. The simulation gives the results, for the net specific work Wn done by the real cycle, which are reported in a set of curves in Fig. 7. Another set of curves gives the trend of cycle conventional efficiency (g = Wn/Q, where Q is the heat supplied to helium). The curves of net specific work done by the cycle have been derived varying the pressure p1 which lies in the range 3–5.5 bar (3 bar the lower curve and 5.5 bar the higher).9 Approximatively, the optimum is obtained for the pressure ratio 7.5, this value has been selected for design. The lower pressure p1 selected for design is 3 bar, the higher pressure is 22.5 bar. The same kind of analysis was made for the Brayton cycle working with nitrogen. The results, which are presented in a format seeming that for helium plant, are reported in Fig. 8. The lower pressure p1 selected for design is 5 bar. The pressure ratio selected is 7.5. The selection is a suitable compromise aiming to have pressures not too high in the plant. The higher pressure is 37.5 bar. Note that the optimum would be obtained for a very high pressure ratio. In any case, the specific work done by the cycle is very low compared with helium, but, nitrogen requires a simpler technology which is available in Petrochemical World. 7. Conclusive remarks The production of electric energy recovering the energy available as cold, using the cryogenic stream of LNG during regasification as cold source in an improved CHP plant (combined heat and power) would be a very suitable option. Feasibility studies of improved CHP cycles10 carried out at DREAM, University of Palermo show the possibility to use as a working fluid in the bottom cycle helium or nitrogen. CHP plants operating with nitrogen have seeming feature of CHP plants working with helium, but, these require higher pressures inside the bottom cycle and performance is lower. In another author’s paper thermodynamic, economic and environmental analysis for the ventures proposed will be presented. The results demonstrate the suitability of the proposal. Appendix 1. Comparison of gaseous fluids on the basis of heat transfer and pumping power Gaseous working fluids have very high pumping power to heat transfer ratio, compared with other fluids. For sake of simplicity, as only comparative relationships are sought [11], it will considered that all fluids to be compared flow and are heated in a circular pipe of diameter D and length L. The pumping power is given by the relationship: ! L pD2 qV 3 ðA:1Þ Wp ¼ k 4 2 D where Wp is the pumping power; k = 0.184Re0.2 is the Weissbach is the Reynolds number; L is the pipe length; friction factor; Re ¼ VDq l D is the pipe diameter; V is the mean fluid velocity in the pipe; q is the fluid density; l is the dynamic viscosity of fluid.
8 Engineering Equation Solver of S.A. Klein and A. Alvarado, Professional version 6.567. 9 Both: for Wn and g curves. 10 CHP cycles: the top cycle is a conventional gas turbine open cycle fed by natural gas and the bottom cycle is an improved gas turbine closed cycle working with helium or nitrogen gas.
The heat transfer can be given by the relationship: q ¼ hðpDLÞDt m
ðA:2Þ
where q is the heat transferred along the pipe; Dtm is the logarithmic mean temperature difference between pipe walls and coolant; h is the heat transfer coefficient, this last can be given for gaseous coolants by the Dittus–Boelter correlation: h ¼ 0:023
k 0:8 0:4 Re Pr D
ðA:3Þ
where Pr is the Prandtl number; k is the thermal conductivity of fluid. Then, it is obtained the relationship: ! ! Wp V2 Pr 0:6 ðA:4Þ ¼ q Dtm cp where cp is the specific heat at constant pressure, Wp/q is an appropriate parameter for comparison of different working fluids. The first term at right in (A.4) accounts for the operating parameters while the second accounts for fluid properties. It is evident that a good fluid must have a low value of the second parameter (e.g. Pr low and cp high). Another alternative relationship can be obtained considering the heat transferred given by the formula: ! pD2 Vcp DT ðA:5Þ q¼q 4 where DT is the temperature rise of fluid along the pipe length. Dividing Wp given by (A.1) by q given by (A.5), rearranging and introducing the volume of fluid within the pipe, V0 = (pD2/4)/L, it is derived the relationship: ! ! Wp q2 L2 Pr0:6 ðA:6Þ ¼ q c3p q2 Dtm DT 2 V 20 This relationship has in the right side two terms: the first accounts for the operating parameters and the second for fluid properties. It is evident that once again to have a low value of Wp/q there is need to have a low value of the second term. It is worth of note that the dependence on temperature and pressure is different for different gases. For sake of simplicity by using the perfect gas laws, the relationship (A.6) can be arranged to give: " 2 #" 3 # Wp 1 1 qLT c1 0:6 Pr ¼ M q R Dtm DTV p0 c
ðA:7Þ
where R is the universal gas constant; M is the molecular mass of gas; c = cp/cv where cv is the specific heat of gas at constant volume; p, T is the average absolute pressure and temperature of gas. Eq. (A.7) shows that, if heat transfer q, Dtm, DT, V0, and L are the same, a good coolant would have a low value of the third term at r.h.s. Relative values of Wp/q for different gases evaluated by means of (A.7) are reported in Table A.1. The values are divided by that for hydrogen (at 1 atm and 27 °C) which has a lower value. Helium is a good coolant, moreover its specific heat, varying the temperature, is almost constant.
Appendix 2. Comparison of gaseous working fluids on the basis of the specific net work done by an ideal Brayton closed cycle For an ideal simple Brayton cycle the specific net work done by it is given by the well known relationship:
C. Dispenza et al. / Applied Thermal Engineering 29 (2009) 380–387 Table A.1 Relative values of Wp/q for different gases evaluated by means of (A.7) Gas
27 °C
315 °C
Hydrogen Helium Carbon dioxide Nitrogen Air
1.0 5.2 11.2 14.3 14.8
0.9 5.3 5.3 12.9 12.7
P = 1 atm.
( W n ¼ W t W c ¼ cp T 1 ½1
bðc1Þ=c p
" #) T3 1 þ 1 ðc1Þ=c T1 bp
ðB:1Þ
where Wn is the specific net work done by cycle; Wt is the specific work done by turbine; Wc is the specific work for driving compressor; c = cp/cv where cp, cv is the specific heat of gas at constant pressure or volume; bp = p2/p1 is the pressure ratio; T1 is the lower temperature along the cycle; T3 is the higher temperature along the cycle. For fixed initial T1 and maximum T3 cycle temperatures the net work goes trough a maximum at the value of bp = p2/p1: c=ðc1Þ c=½2ðc1Þ T2 T3 ¼ ðB:2Þ bpopt ¼ T1 T1 The results for helium, nitrogen and carbon dioxide which have been compared by means of the relationship (B.1) are reported in Fig. 6. Data pertains to a wide range of variation of the pressure ratio and it is evident that helium is very good. References [1] C. Dispenza, G. Dispenza, V. La Rocca, G. Panno, Analisi delle prestazioni termodinamiche e raffronto tecnico economico di impianti per la liquefazione del gas naturale, in: Proceedings of 57° Congresso Nazionale ATI, Pisa, 17–20 Settembre 2002. [2] J.P. Buffiere, R.Vincent, La recuperation des frigories du LNG et l’ajustement du gaz au terminal de Fos sur Mer, on LNG 3, Session III, Paper 8, 1972.
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[3] Snamprogetti, More Energy from LNG, Electric Energy from LNG Regasification SP/BBC Process 2, Snamprogetti ENI Group, AMSEL, Linate, Italy, 1978. [4] C. Dispenza, G. Dispenza, V. La Rocca, G. Panno, CHP plants for production of electrical energy during regasification of LNG recovering exergy of cold, in: Proceedings of ASME/ATI 2006 Conference Energy: Production, Distribution and Conservation, vol. II, Milan, May 14–17, 2006, pp. 593–603. [5] World Energy Outlook 2005 (WEO 2005), International Energy Agency, IEA.