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Compressed natural gas behavior in a natural gas vehicle fuel tank during fast filling process: Mathematical modeling, thermodynamic analysis, and optimization
Journal of Natural Gas Science and Engineering 20 (2014) 121e131
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Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse
Compressed natural gas behavior in a natural gas vehicle fuel tank during fast filling process: Mathematical modeling, thermodynamic analysis, and optimization Mehrdad Khamforoush*, Rahil Moosavi, Tahmasb Hatami Department of Chemical Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj 66177, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 April 2014 Received in revised form 13 June 2014 Accepted 15 June 2014 Available online
Every CNG station includes two main parts: a compressor equipped with inter- and after-coolers and a fast filling process (FFP). In this study, both processes were simulated in a FORTRAN based computer program. To model the compression process of real natural gas, the polytropic work of a three-stage compressor was considered. Moreover, the FFP was modeled based on mass conservation and first law of thermodynamics for a non-adiabatic cylinder. Due to high operating pressure, AGA-8 equation of state (EOS) was utilized for accurate computation of necessary thermodynamic properties. Both applied models for compression and FFP were compared with the real data. In particular, the FFP model was evaluated using experimental data obtained from an operating compressed natural gas (CNG) station in Sanandaj, Iran. The comparison showed a good agreement between model and experimental data. In the last part of this paper, the best operating condition for attaining either the minimum energy consumption in compressors and coolers or the maximum final accumulated mass of gas within NGV cylinders was determined using particle swarm optimization (PSO) algorithm. © 2014 Elsevier B.V. All rights reserved.
Keywords: Fast filling process Single storage system Cascade storage system Modeling Optimization
1. Introduction From the beginning of 1980s, natural gas as a vehicle fuel has attracted considerable attentions because of its low air pollutants emission, low cost, and availability (Lozano-Castello et al., 2002; Liang et al., 2012; Martins et al., 2014; Khan and Yasmin, 2014). In comparison with liquid fuel vehicles, natural gas vehicles (NGVs) produce 87% less nitrogen oxides, 89% less non-methane organic gas, and 70% less carbon monoxide (Liang et al., 2012). Therefore, natural gas is more environmentally friendly than liquid fuels. It seems that Iran is now the world's leader in terms of natural gas vehicles. The numbers of Iran CNG vehicles in 2011 was 2.86 million. Notably, the number of CNG filling stations active in Iran is 1976 stations up to April 2013. To store natural gas, four techniques namely liquefaction (Gadhiraju et al., 2008), compression (LozanoCastello et al., 2002), hydrate formation (Englezos and Lee, 2005), and adsorption (Lozano-Castello et al., 2002; Molashahi and Hashemipour 2012; Balathanigaimani et al., 2006) have been utilized. Among these techniques, compression is the most widely
* Corresponding author. Tel./fax: þ98 871 6660073. E-mail addresses: [email protected], [email protected] (M. Khamforoush). http://dx.doi.org/10.1016/j.jngse.2014.06.009 1875-5100/© 2014 Elsevier B.V. All rights reserved.
used technique in transport industries. Nowadays, CNG is used as fuel for millions of automobiles (Lozano-Castello et al., 2002; Ma et al., 2013; Khan and Yasmin, 2014). However, there are some issues about CNG filling stations that limit its applications. These issues are high refueling time, lack of natural gas refueling stations, and low driving range in comparison with gasoline (Shipley, 2002). Long refueling time is one of the problems within NGV refueling stations. In a CNG refueling station, the natural gas of distribution pipeline is compressed from 1.5e1.7 MPa to 20.7e25 MPa using a large multi-stage reciprocating compressor. Afterward, the prepared CNG is directly dispensed from compressor to NGV cylinders. This method, which is called slow filling process, has high refueling time in comparison with gasoline dispensers. Gas industries have remedied long refueling time problems using FFP (Shipley, 2002). Filling process occurs in less than 5 minutes in FFP (Farzaneh-Gord et al., 2008). In this method, prepared CNG in compressor is stored in large supply tanks. Then, due to the high pressure difference between CNG reservoirs and NGV cylinder, CNG flows quickly toward NGV tank. There are two techniques for storing CNG in supply tanks: single gas supply tank (single storage system (SSS)) and cascade gas supply tanks (cascade storage system (CSS)). In the first technique, only single pressure reservoir is used for storing CNG. However, CSS usually comprises of three gas reservoirs that are
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termed low, medium, and high pressure supply tanks (LPST, MPST, and HPST) (Farzaneh-Gord et al., 2011). The second problem with CNG as an alternative fuel is the unavailability of enough numbers of CNG stations due to the high exploitation costs to construct a station (Lozano-Castello et al., 2002; Shipley, 2002). On the other hand, CNG compressors are multi-stage reciprocating compressors that compress natural gas to very high pressure. As gas temperature increases during compression, a cooler is arranged after each stage. Hence, in addition to the high cost for constructing a CNG station, the compression process consumes a lot of energy (Lozano-Castello et al., 2002). Low driving range of NGVs relative to liquid fueled vehicles is the other problem for the marketing of these vehicles (LozanoCastello et al., 2002; Shipley, 2002). One reason for this low driving range is the low density of CNG relative to gasoline (LozanoCastello et al., 2002). Additionally, the pressure of gas supply tanks in CNG stations is very effective on the on-board cylinder charged mass (Farzaneh-Gord et al., 2011). However, the main reason for the low driving range of NGVs lies behind the under-filling phenomenon which occurs during FFP in CNG stations. During FFP, the gas temperature within NGV fuel tank increases by 45 K (Kountz, 1994). This temperature increment stops charging process before the cylinder be really fulfilled, and consequently reduces driving range. According to the above explanations, by reducing the filling time, compressor work, and consumed energy in coolers, and increasing the final accumulated mass of CNG in an on-board cylinder, the performance of CNG refueling stations can be significantly improved (Farzaneh-Gord et al., 2011). FFP modeling for analyzing the gas behavior in NGV cylinder provides valuable information for this purpose. This information can be useful in design or improvement of existing systems or creating new systems to ensure 100% full fill in each refueling. Modeling and simulation of compression and FFP can also be utilized as a suitable tool to obtain optimal conditions in the designing of CNG stations. Up to now, a few experimental and theoretical studies have been carried out in the field of current study (Shipley, 2002; FarzanehGord et al., 2008, 2011; Kountz, 1994). Shipley (2002) studied the FFP for a natural gas cylinder. Shipley (2002) studied the effect of ambient temperature on the FFP. He found that NGV cylinder was under filled when it was rapidly recharged. Kountz (1994) modeled the FFP of a NGV cylinder using a single gas supply tank and quantified the cylinder undercharging phenomenon. He used PengRobinson EOS to calculate the compressibility factor of natural gas. Farzaneh-Gord et al. (2008) developed Kountz's model for cascade gas supply tanks. They considered natural gas as pure methane in order to simplify their calculations. It must be mentioned that FFP operation accomplishes at very high pressures up to 25 MPa. In Such condition, Peng-Robinson EOS and other customary cubic EOSs are not valid. Therefore, a suitable and more accurate EOS, such as AGA-8, must be used to predict the required thermodynamic properties at this condition. AGA-8 is an accurate and complex EOS which was developed by Gas Research Institute and American Gas Association (Starling and Savidge, 2003) for calculating the Z-factor of natural gas at very high pressure conditions. The main objective of this study was to apply a reliable mathematical model for a CNG station including compressor, coolers, and FFP. This paper also aimed to determine the best operating conditions in order to attain either the minimum consumed energy in compressor or the maximum accumulated mass in NGV fuel tank. For this purpose, the proposed study by Kountz (1994) and Farzaneh-Gord et al. (2008) were improved by developing a FORTRAN based computer program using AGA-8 EOS. To validate the FFP model, the required experimental data was obtained from a working CNG station.
2. Mathematical model 2.1. FFP FFP was modeled based on mass conservation law together with the first law of thermodynamic. These laws were applied to a NGV fuel tank considered as a control volume with no chemical reaction involved. As NGV fuel tank had no outlet flow, output terms in applied equations were ignored. During FFP, no mechanical power was generated, and the kinetic and potential energy were neglected. On the basis of the above assumptions, mass conservation and the first law of thermodynamic were simplified as follows (Farzaneh-Gord et al., 2008; Kountz, 1994);
_ ¼ dMr M i dt
(1)
_ ur ; _ hs þ dQr ¼ Mr dur þ M M i i dt dt
hs ¼ hi þ
Vi2 2
(2)
_ , Mr, hi, hs, V =2, ur, and dQr/dt denote inlet mass flow rate where M i i to the cylinder, accumulated mass within the cylinder, specific inlet enthalpy, specific stagnation enthalpy, specific inlet kinetic energy, specific internal energy of the mass within the cylinder, and the rate of heat transfer, respectively. Applying gas dynamics laws together with isenthalpic expansion of compressible gases through an orifice, the mass flow rate was determined as follows (Kountz, 1994):
_ ¼C A M i d orifice
2 gþ1
gþ1 2ðg1Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gPs rs Zs gc
if
Pr Ps
2 gþ1
g g1
(3) 391 2 8 2 g1 > 1 > = < g 7 g 6 P 2g P Z P r s s r _ ¼C A 7 61 gc M i d orifice rs 5> g1 Ps > rs 4 Ps ; :
if
Pr 2 > gþ1 Ps
g g1
(4) where, Cd is orifice discharge coefficient, Aorifice is orifice area, g is the ratio of specific heats, gc is dimensionalizing factor, P is pressure, Z is compressibility factor, and r is density. In addition, the subscripts r and s refer to the NGV cylinder and supply tanks, respectively. The heat transferred from gas to the cylinder wall, Qr, and from the cylinder wall to ambient, Qamb, were calculated as follows (Kountz, 1994);
dQr ¼ hcyl Aicyl ðTr Tw Þ dt
(5)
dQamb ¼ hamb Aocyl ðTw Tamb Þ dt
(6)
where, h is heat transfer coefficient, A is surface area of the cylinder, and T is temperature. The subscript cyl, amb, icyl, ocyl, and w refer to cylinder, ambient, inside of the cylinder, outside of the cylinder, and the cylinder wall, respectively. Using Eqs. (5) and (6) along with the energy balance for the cylinder wall, which was imagined as a
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lumped system, the temperature profile of the cylinder wall was calculated by the following equations (Kountz, 1994).
Tw ¼
a a bTw0 expð bðt t0 ÞÞ b b
(7)
a¼
hcyl Aicyl Tr þ hamb Aocyl Tamb Mw cPw
(8)
b¼
hcyl Aicyl þ hamb Aocyl Mw cPw
(9)
where, Mw, cpw , and Tw0 are the mass, specific heat, and initial temperature of the cylinder wall, respectively. Furthermore, t is refueling time and t0 is the initial time of refueling. As the NGV cylinder includes a cylindrical shell with two dished ends, its inside and outside surfaces area, Aicyl and Aocyl, its volume, Vcyl, and its wall volume, VSM, can be calculated by the following equations (Bakar et al., 1907);
Aicyl ¼ pdicyl lcyl þ
pd2icyl
Aocyl ¼ pdocyl lcyl þ pd2ocyl Vcyl ¼ VSM ¼
p 4
d2icyl lcyl þ
p d3 6 icyl
p p d2ocyl d2icyl lcyl þ d3ocyl d3icyl 4 6
(10) (11) (12)
(13)
where, dicyl, docyl, and lcyl are the inside diameter, outside diameter, and length of cylinder, respectively.
2.2. Compression and cooling processes 2.2.1. Consumed work in compressors The block diagram of a three-stage compressors in a CNG station with inter- and after-coolers is shown in Fig. 1. A cooler is installed next to each compression stage to compensate the gas temperature increment due to the compression. In this study, the outlet temperature of each cooling stage, T10 , is assumed to be T10 ¼ T1 þ 10, in which T1 is inlet temperature of the first compression stage. Each compressor is a four-stage cycle including induction, compression, expansion, and delivery. At reversible condition, the polytropic work of a compressor is calculated by the following equation (Hanlon, 2001):
123
0 1 n1 n B P n C B out Work ¼ Pin Vin 1C A n 1 @ Pin 0 1 n1 n B P n C B out ¼ Zin RTin 1C A n 1 @ Pin
(14)
where, V is volume and n is polytropic exponent of natural gas. In addition, the subscripts in and out stand for input and output, respectively. Total consumed work in a three-stage compressor is determined via:
2
2 3 3 n1 1 n2 1 0 n n 6 6 7 7 n2 Z2 RT1 n Z RT P2 1 6 P3 2 17 þ W ¼ 1 1 16 17 4 4 5 5 n1 1 P1 n2 1 P2 2
3 n3 1 6 P4 n3 7 6 þ 17 4 5 n3 1 P3 n3 Z3 RT10
(15)
where, Pi is the outlet pressure from the stage (i 1). The real work of three-stage compressor is equal to the polytropic work divided by polytropic efficiency (hP). The Polytropic efficiency, which is commonly reported by compressors manufacturers, is equal to 0.8 in this study. To minimize the total consumed work in compressor, the optimum amounts of inter-stage pressures (P2, P3) need to be determined. For this purpose, the partial derivatives of work with respect to the aforementioned pressures must be equal to zero.
h i h i 0 vW ða Þ ða 1Þ ða 1Þ P2 1 Z2 RT1 P3a2 P2 2 ¼ Z1 RT1 P1 1 vP2
0 RT P3 a2 vZ2 1 ¼0 þ 1 a2 P2 vP2 T 0 1
(16) h i h ða 1Þ i 0 0 vW ða Þ ða 1Þ P3 2 Z3 RT1 P4 a3 P3 3 ¼ Z2 RT1 P2 2 vP3
0 RT P4 a3 vZ3 1 ¼0 þ 1 a3 P3 vP3 T 0 1
(17) where, a1, a2 and a3 are equaled to n1 1=n1 , n2 1=n2 and n3 1=n3 , respectively. 2.2.2. Heat lost in coolers According to the first law of thermodynamic, heat lost in a cooler is equal to the difference between input and output enthalpy. In this study, pressure drop has been supposed to be neglected in coolers. Therefore, total heat lost, Qcooling, formula in a three-stage compressor has been simplified as follow:
ZT2 Qcooling ¼
ZT3 cm;P dT
T10
ZT4 cm;P dT
T10
cm;P dT
(18)
T10
2.3. Thermodynamic properties
Fig. 1. A schematic illustration of three-stage compressor equipped with inter- and after-coolers.
In the current study, AGA-8 EOS was employed to calculate the compressibility factor, specific heats, internal energy, and other required thermodynamic properties of natural gas. AGA-8 is a
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semi-empirical EOS that is more accurate than most conventional EOSs (Starling and Savidge, 2003). This EOS can be utilized according to either “detail” or “gross characterization” method. The first method described the pressureetemperatureedensity behavior of natural gas mixtures over a wide range of operating conditions and generates more accurate results than the second method (Starling and Savidge, 2003). The required equations for the calculating of these properties are represented in literature (Starling and Savidge, 2003; Hanlon, 2001; ISO-12213-2, 1997; Maric, 2007; DIPPR®801, 2004; Perry and Green, 1999; FarzanehGord et al., 2010).
Table 1 The composition of natural gas. Component
Mole percent (%)
Nitrogen (N2) Methane (C1) Carbon dioxide (CO2) Ethane (C2) Propane (C3) I-butane (IC4) N-butane (NC4) I-pentane (IC5) N-pentane (NC5) Hexane (C6)
4.0 89.8 1.1 3.2 1.2 0.25 0.32 0.07 0.05 0.01
2.4. Solution algorithm of the applied model In the first step, the minimum compressor work was determined using Eq. (15) at a given pressure arrangement and ambient temperature. Before applying this equation, the inter-stage pressures, polytropic exponents, and compressibility factors should be calculated. To determine the inter-stage pressures, Eqs. (16) and (17) were solved using numerical NewtoneRaphson method. The polytropic exponent of each stage was then calculated (Hanlon, 2001; Maric, 2007). To calculate the compressibility factor, AGA-8 EOS was applied for each stage of compression. Then, the molar heat capacity at constant pressure was determined (Maric, 2007; DIPPR®801, 2004; Perry and Green, 1999), and the total heat lost in coolers was calculated by Eq. (18). Afterward, the FFP was simulated as follow. First, the internal energy and the initial mass of the gas in the cylinder were determined at initial conditions. At these conditions, the cylinder was considered adiabatic and its wall temperature was equal to the initial temperature in the cylinder. Furthermore, the surface area and the volume of the cylinder were calculated by Eqs. (10)e(13). After that, the inlet mass flow rate was calculated using Eq. (3) or Eq. (4). Subsequently, the heat transfer from gas to the cylinder wall was calculated using Eqs. (5) and (6). Then, the internal energy and the accumulated mass in the cylinder were obtained by solving differential Eqs. (1) and (2). These two ordinary first-order differential equations were numerically solved using RungeeKutta fourth order method. All the required thermodynamic properties of natural gas were calculated using AGA-8 EOS. Having determined the specific volume and internal energy, the gas temperature was calculated in each time step. Finally, the pressure of NGV tank was calculated using P ¼ ZRT=vm . 3. Results and discussions 3.1. Evaluation of the proposed model for FFP The FFP experimental data of three NGV cylinders from a working CNG station in Sanandaj, Iran were used for model validation. The NGVs were SAIPA Saba, Peugeot RD, and Peugeot 405 with the tank capacity of 48, 60, and 60 l, respectively. The pressures of supply tanks and NGV cylinders were read from station dispensers. The pressures of low, medium, and high pressure supply tanks were averagely 19.5 MPa, 20.0 MPa, and 20.5 MPa, respectively. The initial pressures of NGV cylinders were 0.5516 MPa for SAIPA Saba, 0.3447 MPa for Peugeot 405, and 0.3447 MPa for Peugeot RD. Furthermore, the temperature of gas supply tanks and the initial temperature of NGV cylinders were equaled to ambient temperature, 297.15 K. The natural gas composition was reported by Sanandaj Gas Company and is given in Table 1. Since the temperature and pressure of gas in cylinder were not available during FFP, the comparison was limited to the accumulated mass of gas in cylinder. As mentioned, the required experimental data were read from the CNG dispenser. The comparisons between the simulations and experimental results in the term of
mass of accumulated gas in the cylinder are shown in Fig. 2. For the purposes of better evaluation and data readability, the results of three NGV tanks were revealed individually in three graphs. In this figure, the model results and the experimental data are depicted by solid lines and circle points, respectively. Due to some unrealistic model assumptions such as adiabatic behavior of NGV tanks, deviations were observed in the middle and the end parts of the FFP curves. Despite these errors, reasonable agreements are totally observed between modeling and experimental results. 3.2. Evaluation of the proposed model for consumed work in compressors Two assumptions were considered for evaluating the suggested model: (1) compression process was considered isentropic, (2) natural gas mixture was considered as pure methane due to the high value of methane mole fraction in it, approximately 90%. Evaluations of the results of suggested model for consumed work in compressor are shown in Table 2. The temperature and pressure of inlet gas to the compressor and outlet gas from it are presented in the first, second, third, and fifth column of this table, respectively. Using the first three columns data, the temperature of output gas from the compressor was calculated by the model and reported in the fourth column. The percentage of relative error between model and experimental values of the output gas temperature are presented in the sixth column. It revealed that the proposed model was significant. Since consumed work in an isentropic process is equal to enthalpy change, simulation and real values of compressor work were calculated according to the operating conditions of columns 1e5. The simulation and real values of compressor work together with its relative error are depicted in the last three columns of Table 2. Although the simulation results in general were in acceptable agreement with real work data, reversible and adiabatic assumptions for the compressor besides considering the gas mixture as pure methane were supposed as sources of some deviations in this table. 3.3. Evaluation of the proposed model for heat lost in coolers Comparison between simulation results and real data for cooling process are presented in Table 3. As the exit stream from the compressor goes directly to the cooler, the operating conditions of input stream to the cooler are known. The main adopted assumptions for the coolers is that they acted ideally, their pressure drops are ignored, and their output gas temperatures are equaled to the temperature of the inlet gas to the first stage of compression. Heat lost in the coolers must be equaled to the negative of gas enthalpy changes. Simulated and real heat lost in the coolers were calculated according to the model and real operating conditions, respectively. The percentage of relative errors between simulation and real values of heat lost are presented in the last column of Table 3.
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125
Fig. 2. Comparison between model results and experimental FFP data of accumulated mass in three types of NGV tanks namely (a) SAIPA Saba, (b) Peugeot 405 and (c) Peugeot RD.
According to this table, the average error was 4.3%, and the maximum error was approximately 11.5%.
3.4. Optimization In addition to the simulation of CNG station, determining the best operating condition for either minimization of energy consumption in compressors and coolers or maximization of the final accumulated mass of gas within the NGV cylinder has an unavoidable degree of importance. Using the validated model, determining the optimum point within a 48 l NGV cylinder was studied in the following subsections. The geometrical and thermophysical specifications of the NGV cylinder reported by SAIPA Company are given in Table 4.
The reliability of optimization results is extremely influenced by the optimization method. For performing a perfect estimation, optimization was accomplished by PSO algorithm, which is a famous efficient technique (Kennedy and Eberhart, 1995; Tasgetiren et al., 2004). PSO is able to optimize a problem by maintaining a population of candidate solutions called particles and moving these particles within the search-space (Santos et al., 2012). PSO selects candidate solutions randomly and operates based on the resulting from objective values for each candidate. Each particle could be improved according to its own experiences as well as the experiences of other particles (Panda and Padhy, 2007). For this purpose, two kinds of CSS namely three and four pressure supply tanks were taken into consideration. In order to investigate various pressure arrangements for optimization, the pressures of low and medium pressure supply tanks in three CSS
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Table 2 Comparison between simulation results and real data for compression process. Tin (K)
Pin (MPa)
Pout (MPa)
Tout (Sim) (K)
Tout (Exp) (K)
Error (%)
Work (Sim) (kJ/kg)
Dh ¼ Work (Exp) (kJ/kg)
Error (%)
300 300 300 300 300 300 300 300 300
1.7 2.552 3.782 1.7 3.268 6.044 1.7 4.370 10.226
2.552 3.782 5.5 3.268 6.044 10.5 4.370 10.226 20.5
330.492 329.738 328.585 350.242 347.494 342.383 374.498 365.973 348.938
330.315 331.437 329.914 350.477 349.246 345.632 373.820 369.526 355.436
0.05359 0.51262 0.40283 0.06705 0.50165 0.94002 0.18137 0.96150 1.82818
64.456 61.408 57.276 106.838 97.626 83.733 159.901 137.048 103.734
64.973 65.947 60.082 109.262 101.329 87.676 160.700 139.998 105.038
0.796 6.883 4.670 2.219 3.654 4.497 0.497 2.107 1.241
Table 3 Comparison between simulation heat lost with real data of cooling process. Tin (Sim) (K
Tin (Exp) (K)
Pin (MPa)
Pout (MPa)
Tout (K)
Qcooling (Sim) (kJ/kg)
Dh ¼ Qcooling (Exp) (kJ/kg)
Error (%)
330.492 329.738 328.585 350.242 347.494 342.383 374.498 365.973 348.938
330.315 331.437 329.914 350.477 349.246 345.632 373.820 369.526 355.436
2.552 3.782 5.5 3.268 6.044 10.5 4.370 10.226 20.5
2.552 3.782 5.5 3.268 6.044 10.5 4.370 10.226 20.5
300 300 300 300 300 300 300 300 300
73.400 73.800 74.154 123.757 124.738 123.718 189.299 189.353 163.335
73.486 78.335 77.534 124.971 129.507 132.196 187.561 198.834 184.626
0.117 5.789 4.359 0.971 3.682 6.413 0.927 4.768 11.532
were varied from 4.0 to 8.0 MPa and 8.5e16.0 MPa, respectively. In four CSS, the pressures of low and two medium pressure supply tanks were considered in the ranges of 4.0e7.0 MPa, 7.5e14.0 MPa, and 14.5e17.0 MPa, respectively. Moreover, the pressure of high pressure supply tanks for both kinds of CSS was constant at 20.5 MPa. With the pressure step of 0.5 MPa, 144 and 588 pressure arrangements were made for three and four CSS, respectively. The optimum conditions were obtained in the following subsections according to a couple of criteria. 3.4.1. Case 1: minimizing the total energy consumption in compressors and coolers Minimizing the total consumed work and energy in compressors and coolers in a CNG station was the aim of this section. In refueling stations, CNG is stored in all supply tanks at 20.5 MPa, at first. In SSS, the pressure of supply tanks remains constant during refueling, but the pressure of low and medium supply tanks in CSS reduces to about 5.5 and 10.5 MPa, respectively. On the other hand, the pressure of NGV tanks increased gradually to about 20.5 MPa. As the CNG flows from the compressor to the low or medium supply tanks, its pressure reduces from 20.5 MPa to 5.5 or 10.5 MPa, respectively. At the same time, the pressure of supply tanks increases gradually. It has been assumed that the work and energy consumption for charging one kilogram of CNG in a supply tank is equaled to the work done by the compressor for producing one kilogram of CNG at the same pressure of supply tank.
Table 4 The geometrical, mechanical, and thermophysical specifications of NGV cylinder. Specification
Unit
Quantity
dorifice Cd docyl lcyl tcyl
m e m m m kg/m3 kJ/kg K
0.002 0.9 0.232 0.393 0.0069 7850.0 0.477
rcyl cpw
For three and four CSS, the variations of compressor real work and the heat lost of coolers per one kilogram of charged mass are shown in Figs. 3e6. The effect of various pressure arrangements was investigated at five ambient temperatures of 273.15 K, 288.15 K, 298.15 K, 313.15 K, and 318.15 K. The model results in these figures were mainly influenced by the variation of ambient temperature rather than the pressure arrangement. According to these figures, increment in ambient temperature increases the amount of total energy consumptions in compressor and coolers. The reason can be explained by the fact that the higher the ambient temperature, the higher the compression ratio and total consumed work will be. Moreover, as the compression ratio increases, the gas temperature increases during compression, and more heat should be lost from the gas to compensate the temperature increment. Another important point according to these figures is the parabolic contour of compressor work and coolers heat lost. Each parabola in Figs. 3 and 4 was plotted by changing the pressure of LPST at a constant pressure value of MPST. Each parabola in these two figures was replaced by a group of parabolas in Figs. 5 and 6. This is due to the existing of second medium pressure tanks in four CSS. At the small values of medium pressures in Figs. 3 and 4, the falling region of the parabola is small. Then, it increases with increment of medium pressure till the variations trend will be thoroughly descending. At the low pressure values of MPST, the charging of NGV fuel tank is mainly performed by HPST. In this condition, increasing the pressure of LPST just increases the consumption energy by compressor and coolers but doesn't have any considerable influence on the tanks contribution for charging the NGV tank. On the other hand, at high pressure value of MPST, both MPST and HPST play as an HPST. In this situation, increasing the pressure of LPST to a sufficient high amount can enhance the contribution of LPST for charging the NGV tank. Since the consumption energy of LPST is considerably lower than that of HPST, the consumption energy in compressor and coolers decreases significantly. The above conceptual analyses can be generalized for two or even more number of MPST. The optimum pressure arrangement to minimize the sum of compressor work and heat lost was determined by PSO algorithm.
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127
Fig. 3. Variations of compressor real work of a CNG station per one kilogram of charged mass versus various pressure arrangements under five ambient temperatures for three CSS.
Fig. 4. Variations of heat lost in coolers of a CNG station per one kilogram of charged mass versus various pressure arrangements under five ambient temperatures for three CSS.
Five ambient temperatures from 273.15 K to 318.15 K were considered in optimization. Optimization results for three and four CSS are presented in Tables 5 and 6, respectively. In three CSS, Ps1 ,Ps2 and Ps3 are the pressures of LPST, MPST, and HPST, respectively. However in four CSS, Ps3 is the pressure of second MPST and Ps4 is the pressures of HPST. In these tables, Tamb is ambient temperature, tm is refueling time, Tr is the final temperature of charged gas, Mr is the final accumulated mass of charged gas, FR is fill ratio, which is defined as the final mass of accumulated gas divided by the cylinder capacity, Rwork is compressor real work per unit mass, and Tecooling is heat lost in coolers per unit mass. According to these tables, the optimum pressure points were approximately independent to ambient temperatures. These points were close to the pressure arrangement of 6.0e12.5e20.5 MPa and 4.3e9.1e14.5e20.5 MPa for the case of three and four CSS, respectively. Furthermore, the results showed that lower ambient temperature leads to shorter refueling time, higher fill ratio, and
lower energy consumption. As the minimum elevation of temperature was 54 K, high safety devices and connections should be taken into consideration to prevent any leakage from NGV tank otherwise a terrible explosion might have happened. Comparison between the best results belonging to three and four CSS revealed that in spite of more energy consumption in three CSS, the amount of charged mass was approximately remained constant.
3.4.2. Case 2: maximizing the final accumulated mass of gas within the NGV cylinder The variations of the final accumulated mass of gas against various pressure arrangements are shown in Figs. 7 and 8. As observed, the variations trend was parabolic, which was well illustrated earlier in Section 3.4.1. Furthermore, it can be noticed from these figures that the final amount of gas in the cylinder decreases with increment in ambient temperature. The reason lies
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Fig. 5. Variations of compressor real work of a CNG station per one kilogram of charged mass versus various pressure arrangements under five ambient temperatures for four CSS.
Fig. 6. Variations of heat lost in coolers of a CNG station per one kilogram of charged mass versus various pressure arrangements under five ambient temperatures for four CSS.
Table 5 The optimum values for pressure of supply tanks, refueling time, final temperature and final accumulated mass of charged gas, fill ratio, compressor real work, and heat lost in coolers for three CSS according to the case 1 criterion. Tamb (K) Ps1 (MPa) Ps2 (MPa) Ps3 (MPa) tm (s) Tr (K) Mr (kg) FR Rwork (kJ/kg) Tecooling (kJ/kg)
273.15 6.3 12.5 20.5 63.7 327.581 3.1119 0.7833 295.679 393.663
288.15 6.1 12.6 20.5 60.3 347.048 2.8255 0.7112 316.165 401.075
298.15 6.0 12.4 20.5 58.6 359.803 2.6689 0.6718 329.232 406.784
313.15 5.9 12.5 20.5 56.2 378.582 2.4724 0.6223 348.368 416.510
318.15 5.9 12.4 20.5 55.6 384.710 2.4155 0.6080 354.589 419.973
Table 6 The optimum values for pressure of supply tanks, refueling time, final temperature and final accumulated mass of charged gas, fill ratio, compressor real work, and heat lost in coolers for four CSS according to the case 1 criterion. Tamb (K) Ps1 (MPa) Ps2 (MPa) Ps3 (MPa) Ps4 (MPa) tm (s) Tr (K) Mr (kg) FR Rwork (kJ/kg) Tecooling (kJ/kg)
273.15 4.6 9.4 14.5 20.5 74.9 329.494 3.0808 0.7755 283.058 374.545
288.15 4.5 9.2 14.5 20.5 71.1 348.813 2.8026 0.7054 302.345 381.253
298.15 4.2 9.1 14.5 20.5 69.2 361.394 2.6508 0.6672 314.667 386.666
313.15 4.2 8.9 14.6 20.5 66.4 379.934 2.4595 0.6191 332.808 395.853
318.15 4.1 8.9 14.5 20.5 65.7 385.988 2.4040 0.6051 338.700 399.133
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Fig. 7. Variations of final mass of the gas in a fuel tank versus various pressure arrangements under five ambient temperatures for three CSS.
Fig. 8. Variations of final mass of the gas in a fuel tank versus various pressure arrangements under five ambient temperatures for four CSS.
behind the diminishing of JouleeThomson cooling effect that occurs in the isenthalpic expansion through the orifice. By applying PSO algorithm, the optimum pressure arrangement for maximizing the final mass of gas was determined for the five aforementioned ambient temperatures. The optimum values of Table 7 The optimum values for pressure of supply tanks, refueling time, final temperature and final accumulated mass of charged gas, fill ratio, compressor real work, and heat lost in coolers for three CSS according to the case 2 criterion. Tamb (K) Ps1 (MPa) Ps2 (MPa) Ps3 (MPa) tm (s) Tr (K) Mr (kg) FR Rwork (kJ/kg) Tecooling (kJ/kg)
273.15 4.0 16.0 20.5 62.5 322.028 3.2072 0.8073 308.780 419.562
288.15 4.0 16.0 20.5 59.3 342.405 2.8888 0.7271 329.863 425.317
298.15 4.0 16.0 20.5 57.6 355.693 2.7178 0.6841 343.416 430.398
313.15 4.0 16.0 20.5 55.3 375.099 2.5069 0.6310 363.295 439.621
318.15 4.0 16.0 20.5 54.7 381.424 2.4464 0.6158 369.790 442.997
pressures together with their corresponding values of refueling time, final temperature of charged gas, final accumulated mass, fill ratio, compressor real work, and heat lost in coolers are reported for three and four CSS in Tables 7 and 8, respectively. According to Table 8 The optimum values for pressure of supply tanks, refueling time, final temperature and final accumulated mass of charged gas, fill ratio, compressor real work, and heat lost in coolers for four CSS according to the case 2 criterion. Tamb (K) Ps1 (MPa) Ps2 (MPa) Ps3 (MPa) Ps4 (MPa) tm (s) Tr (K) Mr (kg) FR Rwork (kJ/kg) Tecooling (kJ/kg)
273.15 4.0 14.0 14.5 20.5 67.6 324.725 3.1605 0.7955 299.383 403.200
288.15 4.0 14.0 14.5 20.5 64.0 344.797 2.8561 0.7189 320.077 409.523
298.15 4.0 14.0 14.5 20.5 62.1 357.854 2.6921 0.6776 333.346 414.859
313.15 4.0 14.0 14.5 20.5 59.6 376.929 2.4892 0.6266 352.751 424.274
318.15 4.0 14.0 14.5 20.5 58.9 383.150 2.4300 0.6116 359.047 427.626
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Table 9 Comparison between SSS and three CSS in term of the optimum values for pressure of supply tanks, refueling time, final temperature and final accumulated mass of charged gas, fill ratio, compressor real work, and heat lost in coolers. Three Cascade Gas Supply Tanks
Tamb (K) Ps1 (MPa) Ps2 (MPa) Ps3 (MPa) tm (s) Tr (K) Mr (kg) FR Rwork (kJ/kg) Tecooling (kJ/kg)
Case 1
Case 2
273.15 6.3 12.5 20.5 63.7 327.581 3.1119 0.7833 295.679 393.663
273.15 4.0 16.0 20.5 62.5 322.028 3.2072 0.8073 308.780 419.562
Single Gas Supply Tank
273.15 20.5
31.6 308.687 3.4626 0.8716 373.099 521.076
Table 10 Comparison between SSS and four CSS in term of the optimum values for pressure of supply tanks, refueling time, final temperature and final accumulated mass of charged gas, fill ratio, compressor real work, and heat lost in coolers. Four Cascade Gas Supply Tanks
Tamb (K) Ps1 (MPa) Ps2 (MPa) Ps3 (MPa) Ps4 (MPa) tm (s) Tr (K) Mr (kg) FR Rwork (kJ/kg) Tecooling (kJ/kg)
Case 1
Case 2
273.15 4.6 9.4 14.5 20.5 74.9 329.494 3.0808 0.7755 283.058 374.545
273.15 4.0 14.0 14.5 20.5 67.6 324.725 3.1605 0.7955 299.383 403.200
Single Gas Supply Tank
273.15 20.5
simulation of compression and FFP in CNG stations. The major conclusions from this paper can be summarized as follows. (1) This paper evidenced that the applied mathematical model is a useful tool for predicting temperature, pressure, and the mass of accumulated gas during FFP. (2) Comparison of simulation results with the real data of a CNG station showed good agreements during the refueling process. (3) Despite the advantage of SSS, such as low refueling time and high filling ratio, using CSS was preferred due to its lower energy consumption. (4) Optimization was performed from the two various viewpoints: (1) minimizing the energy consumption of compressor and coolers; (2) maximizing the final accumulated mass of gas within the NGV cylinder. By applying the minimum energy consumption criterion, the optimum pressure arrangements were 6.0e12.5e20.5 MPa for three CSS, and 4.3e9.1e14.5e20.5 MPa for four CSS. On the other side, by applying the maximum mass of gas accumulated within the NGV cylinder, the optimum pressure arrangements were 4.0e16.0e20.5 MPa for three CSS, and 4.0e14.0e14.5e20.5 MPa for four CSS. Acknowledgments Financial support by National Iranian Oil Products Distribution Company is gratefully acknowledged.
31.6 308.687 3.4626 0.8716 373.099 521.076
the presented results, the optimum pressure arrangements were 4.0e16.0e20.5 MPa and 4.0e14.0e14.5e20.5 MPa for three and four CSS, respectively. Interestingly, the optimum results of three and four CSS are compared with the results of SSS in Table 9 and 10. In these tables, the ambient temperature kept constant at 273.15 K. These results indicated that the final temperature of gas in SSS is lower than that of CSS. Therefore, the mass of accumulated gas in SSS is obviously higher. For example, fill ratio in SSS was respectively 10.13% and 7.38% more than that of cases 1 and 2 in three CSS. On the other side, compressor work in SSS was 20.75% and 17.24% more than that of the two studied cases, respectively. Therefore, despite shorter refueling time and higher mass of accumulated gas by SSS, it was not appropriate on account of higher work of compressor as well as higher heat lost by coolers. On the other side, comparing between case 1 and case 2 for three and four CSS showed that notwithstanding more mass was accumulated in case 2, it was not the desirable criterion due to its higher energy consumption. Other important result was the superiority of using four CSS over three ones due to its lower energy consumption. From the whole above discussion it can be concluded that four CSS under pressure arrangement of 4.6e9.4e14.5e20.5 MPa and ambient temperature of 273.15 K provided an extremely efficient FFP process.
4. Conclusion Due to high fuel prices and environmental concerns, the use of CNG as an alternative to liquid fuels has increased around the world. In this study, by using the first law of thermodynamic and the conservation of mass, a mathematical model was applied for
Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.jngse.2014.06.009. References Bakar, R.A., Othman, M.F., Semin, S., Ismail, A.R., 1907. The Compressed Natural Gas, CNG. Cylinder Pressure Storage Technology in Natural Gas Vehicles, NGV Research Trend. University Malaysia Pahang, Pahang. Balathanigaimani, M.S., Kang, H.-C., Shim, W.-G., Kim, C., Lee, J.-W., Moon, H., 2006. Preparation of powdered activated carbon from rice husk and its methane adsorption properties. Korean J. Chem. Eng. 23 (4), 663e668. DIPPR®801, 2004. Evaluated Standard Thermophysical Property Values. Design Institute for Physical Properties. Sponsored by AIChE. Englezos, P., Lee, J.D., 2005. A cleaner source of energy and opportunity for innovative technologies. Korean J. Chem. Eng. 22 (5), 671e681. Farzaneh-Gord, M., Deymi-Dashtebayaz, M., Rahbari, H.R., 2011. Studying effects of storage types on performance of CNG filling stations. J. Nat. Gas Sci. Eng 3, 334e340. Farzaneh-Gord, M., Khamforoush, A., Hashemi, S., Pourkhadem Namin, H., 2010. Computing thermal properties of natural gas by utilizing AGA-8 equation of state. Int. J. Chem. Eng. Appl. 1 (1), 20e24. Farzaneh-Gord, M., Hashemi, S., Farzaneh-Kord, A., 2008. Thermodynamic analysis of cascade reservoirs filling process of natural gas vehicle cylinders. World Appl. Sci. J. 5 (2), 143e149. Gadhiraju, V., Timmerhaus, K.D., Rizzuto, C., 2008. Cryogenic Mixed Refrigerant Processes. Springer, New York. Hanlon, P.C., 2001. Compressor Handbook. McGraw-Hill Publications, New York. ISO-12213-2, 1997. Natural Gas e Calculation of Compression Factor e Part 2: Calculation Using Molar-Composition Analysis. ISO. Ref., No., ISO-12213-2: 1997(E). Kennedy, J., Eberhart, R.C., 1995. Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, vol. 4, pp. 1942e1948. Khan, M.I., Yasmin, T., 2014. Development of natural gas as a vehicular fuel in Pakistan: issues and prospects. J. Nat. Gas Sci. Eng 17, 99e109. Kountz, K.J., 1994. Modeling the fast fill process in natural gas vehicle storage cylinders. In: 207th ACS national meeting-division of fuel chemistry, San Diego. Liang, F.-Y., Ryvak, M., Sayeed, S., Zhao, N., 2012. The role of natural gas as a primary fuel in the near future, including comparisons of acquisition, transmission and waste handling costs of as with competitive alternatives. Chem. Cent. J. 6 (Suppl. 1), S4. Lozano-Castello, D., Alcaniz-Monge, J., de la Casa-Lillo, M.A., Cazorla-Amoros, D., Linares-Solano, A., 2002. Advances in the study of methane storage in porous carbonaceous materials. Fuel 81, 1777e1803.
M. Khamforoush et al. / Journal of Natural Gas Science and Engineering 20 (2014) 121e131 Ma, L., Geng, J., Li, W., Liu, P., Li, Z., 2013. The development of natural gas as an automotive fuel in China. Energy Policy 62, 531e539. Maric, I., 2007. A procedure for the calculation of the natural gas molar heat capacity, the isentropic exponent, and the Joule-Thomson coefficient. Flow Meas. Instrum. 18, 18e26. , J.R., 2014. Cold start and full cycle emissions from Martins, A.A., Rocha, R.A.D., Sodre a flexible fuel vehicle operating with natural gas, ethanol and gasoline. J. Nat. Gas Sci. Eng 17, 94e98. Molashahi, M., Hashemipour, H., 2012. Experimental study and artificial neural network simulation of methane adsorption on activated carbon. Korean J. Chem. Eng. 29 (5), 601e605. Panda, S., Padhy, N.P., 2007. Comparison of particle swarm optimization and genetic algorithm for TCSC-based controller design. Int. J. Elec. Elect. Eng 1 (5), 305e313.
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Perry, R.H., Green, D.W., 1999. Perry's Chemical Engineers' Handbook. McGraw-Hill Publications, New York. Santos, L.S., Biscaia, J.E.C., Pagano, R.L., Calado, V.M.A., 2012. CFD-optimization algorithm to optimize the energy transport in pultruded polymer composites. Braz. J. Chem. Eng 29, 559e566. Shipley, E., 2002. Study of Natural Gas Vehicles, NGV During the Fast Fill Process. MSc Thesis. West Virginia University, Morgantown. Starling, K.E., Savidge, J.L., 2003. Compressibility Factors of Natural Gas and Other Related Hydrocarbon Gases. American Gas Association, Washington. Tasgetiren, M.F., Sevkli, M., Liang, Y.C., Gencyilmaz, G., 2004. Particle swarm optimization algorithm for single machine total weighted tardiness problem. In: Proceedings of the IEEE Congress on Evolutionary Computation, Portland, vol. 2, pp. 1412e1419.
Contents lists available at ScienceDirect
Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse
Compressed natural gas behavior in a natural gas vehicle fuel tank during fast filling process: Mathematical modeling, thermodynamic analysis, and optimization Mehrdad Khamforoush*, Rahil Moosavi, Tahmasb Hatami Department of Chemical Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj 66177, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 April 2014 Received in revised form 13 June 2014 Accepted 15 June 2014 Available online
Every CNG station includes two main parts: a compressor equipped with inter- and after-coolers and a fast filling process (FFP). In this study, both processes were simulated in a FORTRAN based computer program. To model the compression process of real natural gas, the polytropic work of a three-stage compressor was considered. Moreover, the FFP was modeled based on mass conservation and first law of thermodynamics for a non-adiabatic cylinder. Due to high operating pressure, AGA-8 equation of state (EOS) was utilized for accurate computation of necessary thermodynamic properties. Both applied models for compression and FFP were compared with the real data. In particular, the FFP model was evaluated using experimental data obtained from an operating compressed natural gas (CNG) station in Sanandaj, Iran. The comparison showed a good agreement between model and experimental data. In the last part of this paper, the best operating condition for attaining either the minimum energy consumption in compressors and coolers or the maximum final accumulated mass of gas within NGV cylinders was determined using particle swarm optimization (PSO) algorithm. © 2014 Elsevier B.V. All rights reserved.
Keywords: Fast filling process Single storage system Cascade storage system Modeling Optimization
1. Introduction From the beginning of 1980s, natural gas as a vehicle fuel has attracted considerable attentions because of its low air pollutants emission, low cost, and availability (Lozano-Castello et al., 2002; Liang et al., 2012; Martins et al., 2014; Khan and Yasmin, 2014). In comparison with liquid fuel vehicles, natural gas vehicles (NGVs) produce 87% less nitrogen oxides, 89% less non-methane organic gas, and 70% less carbon monoxide (Liang et al., 2012). Therefore, natural gas is more environmentally friendly than liquid fuels. It seems that Iran is now the world's leader in terms of natural gas vehicles. The numbers of Iran CNG vehicles in 2011 was 2.86 million. Notably, the number of CNG filling stations active in Iran is 1976 stations up to April 2013. To store natural gas, four techniques namely liquefaction (Gadhiraju et al., 2008), compression (LozanoCastello et al., 2002), hydrate formation (Englezos and Lee, 2005), and adsorption (Lozano-Castello et al., 2002; Molashahi and Hashemipour 2012; Balathanigaimani et al., 2006) have been utilized. Among these techniques, compression is the most widely
* Corresponding author. Tel./fax: þ98 871 6660073. E-mail addresses: [email protected], [email protected] (M. Khamforoush). http://dx.doi.org/10.1016/j.jngse.2014.06.009 1875-5100/© 2014 Elsevier B.V. All rights reserved.
used technique in transport industries. Nowadays, CNG is used as fuel for millions of automobiles (Lozano-Castello et al., 2002; Ma et al., 2013; Khan and Yasmin, 2014). However, there are some issues about CNG filling stations that limit its applications. These issues are high refueling time, lack of natural gas refueling stations, and low driving range in comparison with gasoline (Shipley, 2002). Long refueling time is one of the problems within NGV refueling stations. In a CNG refueling station, the natural gas of distribution pipeline is compressed from 1.5e1.7 MPa to 20.7e25 MPa using a large multi-stage reciprocating compressor. Afterward, the prepared CNG is directly dispensed from compressor to NGV cylinders. This method, which is called slow filling process, has high refueling time in comparison with gasoline dispensers. Gas industries have remedied long refueling time problems using FFP (Shipley, 2002). Filling process occurs in less than 5 minutes in FFP (Farzaneh-Gord et al., 2008). In this method, prepared CNG in compressor is stored in large supply tanks. Then, due to the high pressure difference between CNG reservoirs and NGV cylinder, CNG flows quickly toward NGV tank. There are two techniques for storing CNG in supply tanks: single gas supply tank (single storage system (SSS)) and cascade gas supply tanks (cascade storage system (CSS)). In the first technique, only single pressure reservoir is used for storing CNG. However, CSS usually comprises of three gas reservoirs that are
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termed low, medium, and high pressure supply tanks (LPST, MPST, and HPST) (Farzaneh-Gord et al., 2011). The second problem with CNG as an alternative fuel is the unavailability of enough numbers of CNG stations due to the high exploitation costs to construct a station (Lozano-Castello et al., 2002; Shipley, 2002). On the other hand, CNG compressors are multi-stage reciprocating compressors that compress natural gas to very high pressure. As gas temperature increases during compression, a cooler is arranged after each stage. Hence, in addition to the high cost for constructing a CNG station, the compression process consumes a lot of energy (Lozano-Castello et al., 2002). Low driving range of NGVs relative to liquid fueled vehicles is the other problem for the marketing of these vehicles (LozanoCastello et al., 2002; Shipley, 2002). One reason for this low driving range is the low density of CNG relative to gasoline (LozanoCastello et al., 2002). Additionally, the pressure of gas supply tanks in CNG stations is very effective on the on-board cylinder charged mass (Farzaneh-Gord et al., 2011). However, the main reason for the low driving range of NGVs lies behind the under-filling phenomenon which occurs during FFP in CNG stations. During FFP, the gas temperature within NGV fuel tank increases by 45 K (Kountz, 1994). This temperature increment stops charging process before the cylinder be really fulfilled, and consequently reduces driving range. According to the above explanations, by reducing the filling time, compressor work, and consumed energy in coolers, and increasing the final accumulated mass of CNG in an on-board cylinder, the performance of CNG refueling stations can be significantly improved (Farzaneh-Gord et al., 2011). FFP modeling for analyzing the gas behavior in NGV cylinder provides valuable information for this purpose. This information can be useful in design or improvement of existing systems or creating new systems to ensure 100% full fill in each refueling. Modeling and simulation of compression and FFP can also be utilized as a suitable tool to obtain optimal conditions in the designing of CNG stations. Up to now, a few experimental and theoretical studies have been carried out in the field of current study (Shipley, 2002; FarzanehGord et al., 2008, 2011; Kountz, 1994). Shipley (2002) studied the FFP for a natural gas cylinder. Shipley (2002) studied the effect of ambient temperature on the FFP. He found that NGV cylinder was under filled when it was rapidly recharged. Kountz (1994) modeled the FFP of a NGV cylinder using a single gas supply tank and quantified the cylinder undercharging phenomenon. He used PengRobinson EOS to calculate the compressibility factor of natural gas. Farzaneh-Gord et al. (2008) developed Kountz's model for cascade gas supply tanks. They considered natural gas as pure methane in order to simplify their calculations. It must be mentioned that FFP operation accomplishes at very high pressures up to 25 MPa. In Such condition, Peng-Robinson EOS and other customary cubic EOSs are not valid. Therefore, a suitable and more accurate EOS, such as AGA-8, must be used to predict the required thermodynamic properties at this condition. AGA-8 is an accurate and complex EOS which was developed by Gas Research Institute and American Gas Association (Starling and Savidge, 2003) for calculating the Z-factor of natural gas at very high pressure conditions. The main objective of this study was to apply a reliable mathematical model for a CNG station including compressor, coolers, and FFP. This paper also aimed to determine the best operating conditions in order to attain either the minimum consumed energy in compressor or the maximum accumulated mass in NGV fuel tank. For this purpose, the proposed study by Kountz (1994) and Farzaneh-Gord et al. (2008) were improved by developing a FORTRAN based computer program using AGA-8 EOS. To validate the FFP model, the required experimental data was obtained from a working CNG station.
2. Mathematical model 2.1. FFP FFP was modeled based on mass conservation law together with the first law of thermodynamic. These laws were applied to a NGV fuel tank considered as a control volume with no chemical reaction involved. As NGV fuel tank had no outlet flow, output terms in applied equations were ignored. During FFP, no mechanical power was generated, and the kinetic and potential energy were neglected. On the basis of the above assumptions, mass conservation and the first law of thermodynamic were simplified as follows (Farzaneh-Gord et al., 2008; Kountz, 1994);
_ ¼ dMr M i dt
(1)
_ ur ; _ hs þ dQr ¼ Mr dur þ M M i i dt dt
hs ¼ hi þ
Vi2 2
(2)
_ , Mr, hi, hs, V =2, ur, and dQr/dt denote inlet mass flow rate where M i i to the cylinder, accumulated mass within the cylinder, specific inlet enthalpy, specific stagnation enthalpy, specific inlet kinetic energy, specific internal energy of the mass within the cylinder, and the rate of heat transfer, respectively. Applying gas dynamics laws together with isenthalpic expansion of compressible gases through an orifice, the mass flow rate was determined as follows (Kountz, 1994):
_ ¼C A M i d orifice
2 gþ1
gþ1 2ðg1Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gPs rs Zs gc
if
Pr Ps
2 gþ1
g g1
(3) 391 2 8 2 g1 > 1 > = < g 7 g 6 P 2g P Z P r s s r _ ¼C A 7 61 gc M i d orifice rs 5> g1 Ps > rs 4 Ps ; :
if
Pr 2 > gþ1 Ps
g g1
(4) where, Cd is orifice discharge coefficient, Aorifice is orifice area, g is the ratio of specific heats, gc is dimensionalizing factor, P is pressure, Z is compressibility factor, and r is density. In addition, the subscripts r and s refer to the NGV cylinder and supply tanks, respectively. The heat transferred from gas to the cylinder wall, Qr, and from the cylinder wall to ambient, Qamb, were calculated as follows (Kountz, 1994);
dQr ¼ hcyl Aicyl ðTr Tw Þ dt
(5)
dQamb ¼ hamb Aocyl ðTw Tamb Þ dt
(6)
where, h is heat transfer coefficient, A is surface area of the cylinder, and T is temperature. The subscript cyl, amb, icyl, ocyl, and w refer to cylinder, ambient, inside of the cylinder, outside of the cylinder, and the cylinder wall, respectively. Using Eqs. (5) and (6) along with the energy balance for the cylinder wall, which was imagined as a
M. Khamforoush et al. / Journal of Natural Gas Science and Engineering 20 (2014) 121e131
lumped system, the temperature profile of the cylinder wall was calculated by the following equations (Kountz, 1994).
Tw ¼
a a bTw0 expð bðt t0 ÞÞ b b
(7)
a¼
hcyl Aicyl Tr þ hamb Aocyl Tamb Mw cPw
(8)
b¼
hcyl Aicyl þ hamb Aocyl Mw cPw
(9)
where, Mw, cpw , and Tw0 are the mass, specific heat, and initial temperature of the cylinder wall, respectively. Furthermore, t is refueling time and t0 is the initial time of refueling. As the NGV cylinder includes a cylindrical shell with two dished ends, its inside and outside surfaces area, Aicyl and Aocyl, its volume, Vcyl, and its wall volume, VSM, can be calculated by the following equations (Bakar et al., 1907);
Aicyl ¼ pdicyl lcyl þ
pd2icyl
Aocyl ¼ pdocyl lcyl þ pd2ocyl Vcyl ¼ VSM ¼
p 4
d2icyl lcyl þ
p d3 6 icyl
p p d2ocyl d2icyl lcyl þ d3ocyl d3icyl 4 6
(10) (11) (12)
(13)
where, dicyl, docyl, and lcyl are the inside diameter, outside diameter, and length of cylinder, respectively.
2.2. Compression and cooling processes 2.2.1. Consumed work in compressors The block diagram of a three-stage compressors in a CNG station with inter- and after-coolers is shown in Fig. 1. A cooler is installed next to each compression stage to compensate the gas temperature increment due to the compression. In this study, the outlet temperature of each cooling stage, T10 , is assumed to be T10 ¼ T1 þ 10, in which T1 is inlet temperature of the first compression stage. Each compressor is a four-stage cycle including induction, compression, expansion, and delivery. At reversible condition, the polytropic work of a compressor is calculated by the following equation (Hanlon, 2001):
123
0 1 n1 n B P n C B out Work ¼ Pin Vin 1C A n 1 @ Pin 0 1 n1 n B P n C B out ¼ Zin RTin 1C A n 1 @ Pin
(14)
where, V is volume and n is polytropic exponent of natural gas. In addition, the subscripts in and out stand for input and output, respectively. Total consumed work in a three-stage compressor is determined via:
2
2 3 3 n1 1 n2 1 0 n n 6 6 7 7 n2 Z2 RT1 n Z RT P2 1 6 P3 2 17 þ W ¼ 1 1 16 17 4 4 5 5 n1 1 P1 n2 1 P2 2
3 n3 1 6 P4 n3 7 6 þ 17 4 5 n3 1 P3 n3 Z3 RT10
(15)
where, Pi is the outlet pressure from the stage (i 1). The real work of three-stage compressor is equal to the polytropic work divided by polytropic efficiency (hP). The Polytropic efficiency, which is commonly reported by compressors manufacturers, is equal to 0.8 in this study. To minimize the total consumed work in compressor, the optimum amounts of inter-stage pressures (P2, P3) need to be determined. For this purpose, the partial derivatives of work with respect to the aforementioned pressures must be equal to zero.
h i h i 0 vW ða Þ ða 1Þ ða 1Þ P2 1 Z2 RT1 P3a2 P2 2 ¼ Z1 RT1 P1 1 vP2
0 RT P3 a2 vZ2 1 ¼0 þ 1 a2 P2 vP2 T 0 1
(16) h i h ða 1Þ i 0 0 vW ða Þ ða 1Þ P3 2 Z3 RT1 P4 a3 P3 3 ¼ Z2 RT1 P2 2 vP3
0 RT P4 a3 vZ3 1 ¼0 þ 1 a3 P3 vP3 T 0 1
(17) where, a1, a2 and a3 are equaled to n1 1=n1 , n2 1=n2 and n3 1=n3 , respectively. 2.2.2. Heat lost in coolers According to the first law of thermodynamic, heat lost in a cooler is equal to the difference between input and output enthalpy. In this study, pressure drop has been supposed to be neglected in coolers. Therefore, total heat lost, Qcooling, formula in a three-stage compressor has been simplified as follow:
ZT2 Qcooling ¼
ZT3 cm;P dT
T10
ZT4 cm;P dT
T10
cm;P dT
(18)
T10
2.3. Thermodynamic properties
Fig. 1. A schematic illustration of three-stage compressor equipped with inter- and after-coolers.
In the current study, AGA-8 EOS was employed to calculate the compressibility factor, specific heats, internal energy, and other required thermodynamic properties of natural gas. AGA-8 is a
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semi-empirical EOS that is more accurate than most conventional EOSs (Starling and Savidge, 2003). This EOS can be utilized according to either “detail” or “gross characterization” method. The first method described the pressureetemperatureedensity behavior of natural gas mixtures over a wide range of operating conditions and generates more accurate results than the second method (Starling and Savidge, 2003). The required equations for the calculating of these properties are represented in literature (Starling and Savidge, 2003; Hanlon, 2001; ISO-12213-2, 1997; Maric, 2007; DIPPR®801, 2004; Perry and Green, 1999; FarzanehGord et al., 2010).
Table 1 The composition of natural gas. Component
Mole percent (%)
Nitrogen (N2) Methane (C1) Carbon dioxide (CO2) Ethane (C2) Propane (C3) I-butane (IC4) N-butane (NC4) I-pentane (IC5) N-pentane (NC5) Hexane (C6)
4.0 89.8 1.1 3.2 1.2 0.25 0.32 0.07 0.05 0.01
2.4. Solution algorithm of the applied model In the first step, the minimum compressor work was determined using Eq. (15) at a given pressure arrangement and ambient temperature. Before applying this equation, the inter-stage pressures, polytropic exponents, and compressibility factors should be calculated. To determine the inter-stage pressures, Eqs. (16) and (17) were solved using numerical NewtoneRaphson method. The polytropic exponent of each stage was then calculated (Hanlon, 2001; Maric, 2007). To calculate the compressibility factor, AGA-8 EOS was applied for each stage of compression. Then, the molar heat capacity at constant pressure was determined (Maric, 2007; DIPPR®801, 2004; Perry and Green, 1999), and the total heat lost in coolers was calculated by Eq. (18). Afterward, the FFP was simulated as follow. First, the internal energy and the initial mass of the gas in the cylinder were determined at initial conditions. At these conditions, the cylinder was considered adiabatic and its wall temperature was equal to the initial temperature in the cylinder. Furthermore, the surface area and the volume of the cylinder were calculated by Eqs. (10)e(13). After that, the inlet mass flow rate was calculated using Eq. (3) or Eq. (4). Subsequently, the heat transfer from gas to the cylinder wall was calculated using Eqs. (5) and (6). Then, the internal energy and the accumulated mass in the cylinder were obtained by solving differential Eqs. (1) and (2). These two ordinary first-order differential equations were numerically solved using RungeeKutta fourth order method. All the required thermodynamic properties of natural gas were calculated using AGA-8 EOS. Having determined the specific volume and internal energy, the gas temperature was calculated in each time step. Finally, the pressure of NGV tank was calculated using P ¼ ZRT=vm . 3. Results and discussions 3.1. Evaluation of the proposed model for FFP The FFP experimental data of three NGV cylinders from a working CNG station in Sanandaj, Iran were used for model validation. The NGVs were SAIPA Saba, Peugeot RD, and Peugeot 405 with the tank capacity of 48, 60, and 60 l, respectively. The pressures of supply tanks and NGV cylinders were read from station dispensers. The pressures of low, medium, and high pressure supply tanks were averagely 19.5 MPa, 20.0 MPa, and 20.5 MPa, respectively. The initial pressures of NGV cylinders were 0.5516 MPa for SAIPA Saba, 0.3447 MPa for Peugeot 405, and 0.3447 MPa for Peugeot RD. Furthermore, the temperature of gas supply tanks and the initial temperature of NGV cylinders were equaled to ambient temperature, 297.15 K. The natural gas composition was reported by Sanandaj Gas Company and is given in Table 1. Since the temperature and pressure of gas in cylinder were not available during FFP, the comparison was limited to the accumulated mass of gas in cylinder. As mentioned, the required experimental data were read from the CNG dispenser. The comparisons between the simulations and experimental results in the term of
mass of accumulated gas in the cylinder are shown in Fig. 2. For the purposes of better evaluation and data readability, the results of three NGV tanks were revealed individually in three graphs. In this figure, the model results and the experimental data are depicted by solid lines and circle points, respectively. Due to some unrealistic model assumptions such as adiabatic behavior of NGV tanks, deviations were observed in the middle and the end parts of the FFP curves. Despite these errors, reasonable agreements are totally observed between modeling and experimental results. 3.2. Evaluation of the proposed model for consumed work in compressors Two assumptions were considered for evaluating the suggested model: (1) compression process was considered isentropic, (2) natural gas mixture was considered as pure methane due to the high value of methane mole fraction in it, approximately 90%. Evaluations of the results of suggested model for consumed work in compressor are shown in Table 2. The temperature and pressure of inlet gas to the compressor and outlet gas from it are presented in the first, second, third, and fifth column of this table, respectively. Using the first three columns data, the temperature of output gas from the compressor was calculated by the model and reported in the fourth column. The percentage of relative error between model and experimental values of the output gas temperature are presented in the sixth column. It revealed that the proposed model was significant. Since consumed work in an isentropic process is equal to enthalpy change, simulation and real values of compressor work were calculated according to the operating conditions of columns 1e5. The simulation and real values of compressor work together with its relative error are depicted in the last three columns of Table 2. Although the simulation results in general were in acceptable agreement with real work data, reversible and adiabatic assumptions for the compressor besides considering the gas mixture as pure methane were supposed as sources of some deviations in this table. 3.3. Evaluation of the proposed model for heat lost in coolers Comparison between simulation results and real data for cooling process are presented in Table 3. As the exit stream from the compressor goes directly to the cooler, the operating conditions of input stream to the cooler are known. The main adopted assumptions for the coolers is that they acted ideally, their pressure drops are ignored, and their output gas temperatures are equaled to the temperature of the inlet gas to the first stage of compression. Heat lost in the coolers must be equaled to the negative of gas enthalpy changes. Simulated and real heat lost in the coolers were calculated according to the model and real operating conditions, respectively. The percentage of relative errors between simulation and real values of heat lost are presented in the last column of Table 3.
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Fig. 2. Comparison between model results and experimental FFP data of accumulated mass in three types of NGV tanks namely (a) SAIPA Saba, (b) Peugeot 405 and (c) Peugeot RD.
According to this table, the average error was 4.3%, and the maximum error was approximately 11.5%.
3.4. Optimization In addition to the simulation of CNG station, determining the best operating condition for either minimization of energy consumption in compressors and coolers or maximization of the final accumulated mass of gas within the NGV cylinder has an unavoidable degree of importance. Using the validated model, determining the optimum point within a 48 l NGV cylinder was studied in the following subsections. The geometrical and thermophysical specifications of the NGV cylinder reported by SAIPA Company are given in Table 4.
The reliability of optimization results is extremely influenced by the optimization method. For performing a perfect estimation, optimization was accomplished by PSO algorithm, which is a famous efficient technique (Kennedy and Eberhart, 1995; Tasgetiren et al., 2004). PSO is able to optimize a problem by maintaining a population of candidate solutions called particles and moving these particles within the search-space (Santos et al., 2012). PSO selects candidate solutions randomly and operates based on the resulting from objective values for each candidate. Each particle could be improved according to its own experiences as well as the experiences of other particles (Panda and Padhy, 2007). For this purpose, two kinds of CSS namely three and four pressure supply tanks were taken into consideration. In order to investigate various pressure arrangements for optimization, the pressures of low and medium pressure supply tanks in three CSS
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Table 2 Comparison between simulation results and real data for compression process. Tin (K)
Pin (MPa)
Pout (MPa)
Tout (Sim) (K)
Tout (Exp) (K)
Error (%)
Work (Sim) (kJ/kg)
Dh ¼ Work (Exp) (kJ/kg)
Error (%)
300 300 300 300 300 300 300 300 300
1.7 2.552 3.782 1.7 3.268 6.044 1.7 4.370 10.226
2.552 3.782 5.5 3.268 6.044 10.5 4.370 10.226 20.5
330.492 329.738 328.585 350.242 347.494 342.383 374.498 365.973 348.938
330.315 331.437 329.914 350.477 349.246 345.632 373.820 369.526 355.436
0.05359 0.51262 0.40283 0.06705 0.50165 0.94002 0.18137 0.96150 1.82818
64.456 61.408 57.276 106.838 97.626 83.733 159.901 137.048 103.734
64.973 65.947 60.082 109.262 101.329 87.676 160.700 139.998 105.038
0.796 6.883 4.670 2.219 3.654 4.497 0.497 2.107 1.241
Table 3 Comparison between simulation heat lost with real data of cooling process. Tin (Sim) (K
Tin (Exp) (K)
Pin (MPa)
Pout (MPa)
Tout (K)
Qcooling (Sim) (kJ/kg)
Dh ¼ Qcooling (Exp) (kJ/kg)
Error (%)
330.492 329.738 328.585 350.242 347.494 342.383 374.498 365.973 348.938
330.315 331.437 329.914 350.477 349.246 345.632 373.820 369.526 355.436
2.552 3.782 5.5 3.268 6.044 10.5 4.370 10.226 20.5
2.552 3.782 5.5 3.268 6.044 10.5 4.370 10.226 20.5
300 300 300 300 300 300 300 300 300
73.400 73.800 74.154 123.757 124.738 123.718 189.299 189.353 163.335
73.486 78.335 77.534 124.971 129.507 132.196 187.561 198.834 184.626
0.117 5.789 4.359 0.971 3.682 6.413 0.927 4.768 11.532
were varied from 4.0 to 8.0 MPa and 8.5e16.0 MPa, respectively. In four CSS, the pressures of low and two medium pressure supply tanks were considered in the ranges of 4.0e7.0 MPa, 7.5e14.0 MPa, and 14.5e17.0 MPa, respectively. Moreover, the pressure of high pressure supply tanks for both kinds of CSS was constant at 20.5 MPa. With the pressure step of 0.5 MPa, 144 and 588 pressure arrangements were made for three and four CSS, respectively. The optimum conditions were obtained in the following subsections according to a couple of criteria. 3.4.1. Case 1: minimizing the total energy consumption in compressors and coolers Minimizing the total consumed work and energy in compressors and coolers in a CNG station was the aim of this section. In refueling stations, CNG is stored in all supply tanks at 20.5 MPa, at first. In SSS, the pressure of supply tanks remains constant during refueling, but the pressure of low and medium supply tanks in CSS reduces to about 5.5 and 10.5 MPa, respectively. On the other hand, the pressure of NGV tanks increased gradually to about 20.5 MPa. As the CNG flows from the compressor to the low or medium supply tanks, its pressure reduces from 20.5 MPa to 5.5 or 10.5 MPa, respectively. At the same time, the pressure of supply tanks increases gradually. It has been assumed that the work and energy consumption for charging one kilogram of CNG in a supply tank is equaled to the work done by the compressor for producing one kilogram of CNG at the same pressure of supply tank.
Table 4 The geometrical, mechanical, and thermophysical specifications of NGV cylinder. Specification
Unit
Quantity
dorifice Cd docyl lcyl tcyl
m e m m m kg/m3 kJ/kg K
0.002 0.9 0.232 0.393 0.0069 7850.0 0.477
rcyl cpw
For three and four CSS, the variations of compressor real work and the heat lost of coolers per one kilogram of charged mass are shown in Figs. 3e6. The effect of various pressure arrangements was investigated at five ambient temperatures of 273.15 K, 288.15 K, 298.15 K, 313.15 K, and 318.15 K. The model results in these figures were mainly influenced by the variation of ambient temperature rather than the pressure arrangement. According to these figures, increment in ambient temperature increases the amount of total energy consumptions in compressor and coolers. The reason can be explained by the fact that the higher the ambient temperature, the higher the compression ratio and total consumed work will be. Moreover, as the compression ratio increases, the gas temperature increases during compression, and more heat should be lost from the gas to compensate the temperature increment. Another important point according to these figures is the parabolic contour of compressor work and coolers heat lost. Each parabola in Figs. 3 and 4 was plotted by changing the pressure of LPST at a constant pressure value of MPST. Each parabola in these two figures was replaced by a group of parabolas in Figs. 5 and 6. This is due to the existing of second medium pressure tanks in four CSS. At the small values of medium pressures in Figs. 3 and 4, the falling region of the parabola is small. Then, it increases with increment of medium pressure till the variations trend will be thoroughly descending. At the low pressure values of MPST, the charging of NGV fuel tank is mainly performed by HPST. In this condition, increasing the pressure of LPST just increases the consumption energy by compressor and coolers but doesn't have any considerable influence on the tanks contribution for charging the NGV tank. On the other hand, at high pressure value of MPST, both MPST and HPST play as an HPST. In this situation, increasing the pressure of LPST to a sufficient high amount can enhance the contribution of LPST for charging the NGV tank. Since the consumption energy of LPST is considerably lower than that of HPST, the consumption energy in compressor and coolers decreases significantly. The above conceptual analyses can be generalized for two or even more number of MPST. The optimum pressure arrangement to minimize the sum of compressor work and heat lost was determined by PSO algorithm.
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Fig. 3. Variations of compressor real work of a CNG station per one kilogram of charged mass versus various pressure arrangements under five ambient temperatures for three CSS.
Fig. 4. Variations of heat lost in coolers of a CNG station per one kilogram of charged mass versus various pressure arrangements under five ambient temperatures for three CSS.
Five ambient temperatures from 273.15 K to 318.15 K were considered in optimization. Optimization results for three and four CSS are presented in Tables 5 and 6, respectively. In three CSS, Ps1 ,Ps2 and Ps3 are the pressures of LPST, MPST, and HPST, respectively. However in four CSS, Ps3 is the pressure of second MPST and Ps4 is the pressures of HPST. In these tables, Tamb is ambient temperature, tm is refueling time, Tr is the final temperature of charged gas, Mr is the final accumulated mass of charged gas, FR is fill ratio, which is defined as the final mass of accumulated gas divided by the cylinder capacity, Rwork is compressor real work per unit mass, and Tecooling is heat lost in coolers per unit mass. According to these tables, the optimum pressure points were approximately independent to ambient temperatures. These points were close to the pressure arrangement of 6.0e12.5e20.5 MPa and 4.3e9.1e14.5e20.5 MPa for the case of three and four CSS, respectively. Furthermore, the results showed that lower ambient temperature leads to shorter refueling time, higher fill ratio, and
lower energy consumption. As the minimum elevation of temperature was 54 K, high safety devices and connections should be taken into consideration to prevent any leakage from NGV tank otherwise a terrible explosion might have happened. Comparison between the best results belonging to three and four CSS revealed that in spite of more energy consumption in three CSS, the amount of charged mass was approximately remained constant.
3.4.2. Case 2: maximizing the final accumulated mass of gas within the NGV cylinder The variations of the final accumulated mass of gas against various pressure arrangements are shown in Figs. 7 and 8. As observed, the variations trend was parabolic, which was well illustrated earlier in Section 3.4.1. Furthermore, it can be noticed from these figures that the final amount of gas in the cylinder decreases with increment in ambient temperature. The reason lies
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Fig. 5. Variations of compressor real work of a CNG station per one kilogram of charged mass versus various pressure arrangements under five ambient temperatures for four CSS.
Fig. 6. Variations of heat lost in coolers of a CNG station per one kilogram of charged mass versus various pressure arrangements under five ambient temperatures for four CSS.
Table 5 The optimum values for pressure of supply tanks, refueling time, final temperature and final accumulated mass of charged gas, fill ratio, compressor real work, and heat lost in coolers for three CSS according to the case 1 criterion. Tamb (K) Ps1 (MPa) Ps2 (MPa) Ps3 (MPa) tm (s) Tr (K) Mr (kg) FR Rwork (kJ/kg) Tecooling (kJ/kg)
273.15 6.3 12.5 20.5 63.7 327.581 3.1119 0.7833 295.679 393.663
288.15 6.1 12.6 20.5 60.3 347.048 2.8255 0.7112 316.165 401.075
298.15 6.0 12.4 20.5 58.6 359.803 2.6689 0.6718 329.232 406.784
313.15 5.9 12.5 20.5 56.2 378.582 2.4724 0.6223 348.368 416.510
318.15 5.9 12.4 20.5 55.6 384.710 2.4155 0.6080 354.589 419.973
Table 6 The optimum values for pressure of supply tanks, refueling time, final temperature and final accumulated mass of charged gas, fill ratio, compressor real work, and heat lost in coolers for four CSS according to the case 1 criterion. Tamb (K) Ps1 (MPa) Ps2 (MPa) Ps3 (MPa) Ps4 (MPa) tm (s) Tr (K) Mr (kg) FR Rwork (kJ/kg) Tecooling (kJ/kg)
273.15 4.6 9.4 14.5 20.5 74.9 329.494 3.0808 0.7755 283.058 374.545
288.15 4.5 9.2 14.5 20.5 71.1 348.813 2.8026 0.7054 302.345 381.253
298.15 4.2 9.1 14.5 20.5 69.2 361.394 2.6508 0.6672 314.667 386.666
313.15 4.2 8.9 14.6 20.5 66.4 379.934 2.4595 0.6191 332.808 395.853
318.15 4.1 8.9 14.5 20.5 65.7 385.988 2.4040 0.6051 338.700 399.133
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Fig. 7. Variations of final mass of the gas in a fuel tank versus various pressure arrangements under five ambient temperatures for three CSS.
Fig. 8. Variations of final mass of the gas in a fuel tank versus various pressure arrangements under five ambient temperatures for four CSS.
behind the diminishing of JouleeThomson cooling effect that occurs in the isenthalpic expansion through the orifice. By applying PSO algorithm, the optimum pressure arrangement for maximizing the final mass of gas was determined for the five aforementioned ambient temperatures. The optimum values of Table 7 The optimum values for pressure of supply tanks, refueling time, final temperature and final accumulated mass of charged gas, fill ratio, compressor real work, and heat lost in coolers for three CSS according to the case 2 criterion. Tamb (K) Ps1 (MPa) Ps2 (MPa) Ps3 (MPa) tm (s) Tr (K) Mr (kg) FR Rwork (kJ/kg) Tecooling (kJ/kg)
273.15 4.0 16.0 20.5 62.5 322.028 3.2072 0.8073 308.780 419.562
288.15 4.0 16.0 20.5 59.3 342.405 2.8888 0.7271 329.863 425.317
298.15 4.0 16.0 20.5 57.6 355.693 2.7178 0.6841 343.416 430.398
313.15 4.0 16.0 20.5 55.3 375.099 2.5069 0.6310 363.295 439.621
318.15 4.0 16.0 20.5 54.7 381.424 2.4464 0.6158 369.790 442.997
pressures together with their corresponding values of refueling time, final temperature of charged gas, final accumulated mass, fill ratio, compressor real work, and heat lost in coolers are reported for three and four CSS in Tables 7 and 8, respectively. According to Table 8 The optimum values for pressure of supply tanks, refueling time, final temperature and final accumulated mass of charged gas, fill ratio, compressor real work, and heat lost in coolers for four CSS according to the case 2 criterion. Tamb (K) Ps1 (MPa) Ps2 (MPa) Ps3 (MPa) Ps4 (MPa) tm (s) Tr (K) Mr (kg) FR Rwork (kJ/kg) Tecooling (kJ/kg)
273.15 4.0 14.0 14.5 20.5 67.6 324.725 3.1605 0.7955 299.383 403.200
288.15 4.0 14.0 14.5 20.5 64.0 344.797 2.8561 0.7189 320.077 409.523
298.15 4.0 14.0 14.5 20.5 62.1 357.854 2.6921 0.6776 333.346 414.859
313.15 4.0 14.0 14.5 20.5 59.6 376.929 2.4892 0.6266 352.751 424.274
318.15 4.0 14.0 14.5 20.5 58.9 383.150 2.4300 0.6116 359.047 427.626
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Table 9 Comparison between SSS and three CSS in term of the optimum values for pressure of supply tanks, refueling time, final temperature and final accumulated mass of charged gas, fill ratio, compressor real work, and heat lost in coolers. Three Cascade Gas Supply Tanks
Tamb (K) Ps1 (MPa) Ps2 (MPa) Ps3 (MPa) tm (s) Tr (K) Mr (kg) FR Rwork (kJ/kg) Tecooling (kJ/kg)
Case 1
Case 2
273.15 6.3 12.5 20.5 63.7 327.581 3.1119 0.7833 295.679 393.663
273.15 4.0 16.0 20.5 62.5 322.028 3.2072 0.8073 308.780 419.562
Single Gas Supply Tank
273.15 20.5
31.6 308.687 3.4626 0.8716 373.099 521.076
Table 10 Comparison between SSS and four CSS in term of the optimum values for pressure of supply tanks, refueling time, final temperature and final accumulated mass of charged gas, fill ratio, compressor real work, and heat lost in coolers. Four Cascade Gas Supply Tanks
Tamb (K) Ps1 (MPa) Ps2 (MPa) Ps3 (MPa) Ps4 (MPa) tm (s) Tr (K) Mr (kg) FR Rwork (kJ/kg) Tecooling (kJ/kg)
Case 1
Case 2
273.15 4.6 9.4 14.5 20.5 74.9 329.494 3.0808 0.7755 283.058 374.545
273.15 4.0 14.0 14.5 20.5 67.6 324.725 3.1605 0.7955 299.383 403.200
Single Gas Supply Tank
273.15 20.5
simulation of compression and FFP in CNG stations. The major conclusions from this paper can be summarized as follows. (1) This paper evidenced that the applied mathematical model is a useful tool for predicting temperature, pressure, and the mass of accumulated gas during FFP. (2) Comparison of simulation results with the real data of a CNG station showed good agreements during the refueling process. (3) Despite the advantage of SSS, such as low refueling time and high filling ratio, using CSS was preferred due to its lower energy consumption. (4) Optimization was performed from the two various viewpoints: (1) minimizing the energy consumption of compressor and coolers; (2) maximizing the final accumulated mass of gas within the NGV cylinder. By applying the minimum energy consumption criterion, the optimum pressure arrangements were 6.0e12.5e20.5 MPa for three CSS, and 4.3e9.1e14.5e20.5 MPa for four CSS. On the other side, by applying the maximum mass of gas accumulated within the NGV cylinder, the optimum pressure arrangements were 4.0e16.0e20.5 MPa for three CSS, and 4.0e14.0e14.5e20.5 MPa for four CSS. Acknowledgments Financial support by National Iranian Oil Products Distribution Company is gratefully acknowledged.
31.6 308.687 3.4626 0.8716 373.099 521.076
the presented results, the optimum pressure arrangements were 4.0e16.0e20.5 MPa and 4.0e14.0e14.5e20.5 MPa for three and four CSS, respectively. Interestingly, the optimum results of three and four CSS are compared with the results of SSS in Table 9 and 10. In these tables, the ambient temperature kept constant at 273.15 K. These results indicated that the final temperature of gas in SSS is lower than that of CSS. Therefore, the mass of accumulated gas in SSS is obviously higher. For example, fill ratio in SSS was respectively 10.13% and 7.38% more than that of cases 1 and 2 in three CSS. On the other side, compressor work in SSS was 20.75% and 17.24% more than that of the two studied cases, respectively. Therefore, despite shorter refueling time and higher mass of accumulated gas by SSS, it was not appropriate on account of higher work of compressor as well as higher heat lost by coolers. On the other side, comparing between case 1 and case 2 for three and four CSS showed that notwithstanding more mass was accumulated in case 2, it was not the desirable criterion due to its higher energy consumption. Other important result was the superiority of using four CSS over three ones due to its lower energy consumption. From the whole above discussion it can be concluded that four CSS under pressure arrangement of 4.6e9.4e14.5e20.5 MPa and ambient temperature of 273.15 K provided an extremely efficient FFP process.
4. Conclusion Due to high fuel prices and environmental concerns, the use of CNG as an alternative to liquid fuels has increased around the world. In this study, by using the first law of thermodynamic and the conservation of mass, a mathematical model was applied for
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