REAL AND IDEAL GAS THERMODYNAMIC ANALYSIS OF SINGLE RESERVOIR FILLING PROCESS OF NATURAL GAS VEHICLE CYLINDERS

Journal of Theoretical and Applied Mechanics, Sofia, 2011, vol. 41, No. 2, pp. 21 36 REAL AND IDEAL GAS THERMODYNAMIC ANALYSIS OF SINGLE RESERVOIR FILLING PROCESS OF NATURAL GAS VEHICLE CYLINDERS Mahmood Farzaneh-Gord Department of Mechanical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran,, e-mail: mahmood.farzaneh@yahoo.co.uk [Received 25 September 2009. Accepted 29 August 2011] Abstract. The accurate modelling of the fast-fill dynamics occurring in Compressed Natural Gas (CNG) fuelled vehicle storage cylinders is a complex process and to date those dynamics have not been thoroughly studied. In this paper, conversation of mass and real and ideal gas assumptions based on first law of thermodynamics, a numerical method has been developed to study fast filling process of natural gas vehicle s (NGV) cylinder. Thermodynamic properties table has been employed for the case of a real gas model. A simple equation has been derived for the case of ideal gas which could be solved analytically. The model has been applied for a single reservoir tank. The results indicated that there is a temperature rise in order 40 K or more for real gas and 80 K or more for the case of ideal gas during charging process. The results also indicated that ambient temperature has big effect on filling process and final NGV cylinder conditions. Key words: Compressed natural gas, CNG cylinder, fast filling process, thermodynamic analysis. 1. Introduction Compressed natural gas is used as a clean alternative to other automobile fuels such as gasoline (petrol) and diesel. The compressed natural gas (CNG) fuelled vehicle storage cylinders encountered a rise in storage gas cylinder temperature (in the range of 40 K or more) during the fast filling due to complex compression and mixing processes. This temperature rise reduces the density of the gas in the cylinder, resulting in an under filled cylinder, relative to its rated specification. The vehicle user will experience a reduced driving

22 Mahmood Farzaneh-Gord range if this temperature rise is not compensated for in the fuelling station dispenser, by transiently over-pressurizing the tank. The on-board storage capacity of natural gas vehicles (NGVs) is a critical issue to the wide spread marketing of these alternate fuelled vehicles. CNG is dispensed to an NGV through a process known as the fast fill process, since it is completed in less than five minutes. During fast fill charging operations can occur under-filling of NGV cylinders, at fuelling stations, at ambient temperatures greater than 30 C. The resulting reduced driving range of the vehicle is a serious obstacle which the gas industry is striving to overcome, without resorting to unnecessarily high fuelling station pressures, or by applying extensive over-pressurization of the cylinder during the fuelling operation. Undercharged storage cylinders are a result of the elevated temperature which occurs in the NGV storage cylinder, due to compression and other processes which have not, to the author s knowledge, been studied, analyzed and documented to date. There have been limited researches in the filed of current study in literatures. Kountz [1] was first who modelled fast filling process of natural gas storage cylinder based on first law of thermodynamics. He developed a computer program to model fast filling process for a single reservoir for real gas. Kountz et al. [2-5] have developed a natural gas dispenser control algorithm that insures complete filling of NGV cylinders under a fast fill scenario. The researches are also under way to model fast filling of hydrogen-based fuelling infrastructure including work of Liss and Richards [6] and Liss et al. [7]. Newhouse and Liss [8] have studied fast filling of hydrogen cylinder using number of experiments. They reported a high temperature increase in the cylinder during the process. A few experimental studies were also carried out to study fast filling of natural gas cylinder including work of Thomas and Goulding [9] and Shiply [10]. Shiply [10] concluded that ambient temperature change can have an affect on the fast fill process. He also concluded that, the test cylinder was under-filled every time it was rapidly recharged. Farzaneh et al. [11] and [12] have also modelled fast filling process. They developed a computer programme based on Peng-Robinson state equation and methane properties table for single reservoir. They investigated effects of ambient temperature and initial cylinder pressure on final cylinder conditions. The number of natural gas fuel based vehicles in Iran growing rapidly recently due to the government policy. Most of owners of those vehicles have reported under-filling charge compared to rated conditions. A computer programme has been developed to understand fast filling process and study effect

Real and Ideal Gas Thermodynamic Analysis... 23 of ambient temperature, based on first law of thermodynamics, conversation of mass and thermodynamics properties table of the gas in this study. This enables us to study effects of various parameters on dynamics change in the NGV cylinder. The fast fill process was assumed to be quasi-static process and the natural gas presumed to be purely Methane for case of real gas model. Ideal gas state equation has been employed for the case of ideal gas assumption and Methane assumed as an ideal gas. 2. CNG Filling station Figure 1 shows a typical CNG filling station. Gas from the distribution pipeline, usually low pressure (< 0.4 MPa) or possibly medium pressure (1.6 MPa), is compressed using a large multi-stage compressor into a cascade storage system. This system is maintained at a pressure higher than that in the vehicle s on-board storage so that gas flows to the vehicle under differential pressure. Typically, the cascade storage will operate in range of 20.5 MPa to 25.0 MPa, while the vehicle s maximum onboard cylinder pressure is 20 MPa. In order to make the utilization of the compressor and buffer storage more efficient, fast fill CNG stations usually operate using a three-stage cascade storage system. Fig. 1. A schematic diagram of NGV Filling Station 3. Compressed natural gas cylinders The natural gas cylinders have various design types based on materials of construction used. Design types include Type 1, which are all-metal, Type 2, which have a metal liner and hoop wrapped composite reinforcement, Type 3, which have a metal liner and a full wrapped composite reinforcement, and Type 4, which have a non-metallic liner and a full wrapped composite

24 Mahmood Farzaneh-Gord reinforcement. Metal containers and liners are typically steel or aluminium. Composite reinforcements are typically carbon or glass fibbers in an epoxy resin matrix. CNG cylinders are designed for a specified nominal service pressure at a specified temperature essentially a specified density (kg/m3) of fuel. This will result in a given mass of natural gas stored in the fuel container. The actual pressure in the fuel container will vary from the nominal service pressure as the temperature of the fuel in the container varies. Fuelling stations normally fill the cylinder up %125 of nominal service pressure to avoid under charging but this highly depends to ambient temperature. The common CNG cylinder type in Iran is Type 1. They have the same inside diameter with various heights depending to their volume. Figure 2 shows dimensions of a typical CNG cylinder. Fig. 2. Dimensions of a typical CNG cylinder 4. Chemical Compositions of Natural Gas Natural gas composition (mixture) varies with location, climate and other factors. The gas is refined before flowing into the pipe lines. Table 1 shows an experimental analysis of typical natural gas composition which flows in Iran pipe lines according to the Khangiran refinery official website [13]. It can be realised that the most of compositions occupied very low percentage by knowing that Methane is occupied about 99% of the gas. For the sake of simplicity it is assumed that Methane is the only substance in the Natural gas.

Real and Ideal Gas Thermodynamic Analysis... 25 Table 1. Experimental analysis of natural gas composition the Khangiran refinery (the Khangiran refinery official website) [13] Component Chemical formula Experimental Analysis (mole Fraction %) Carbon dioxide CO 2 0.055 Nitrogen N 2 0.428 Methane CH 4 98.640 Ethane C 2 H 6 0.593 Propane C 3 H 8 0.065 Iso butane C 4 H 10 0.015 n-butane C 4 H 10 0.034 Iso-Pentane C 5 H 12 0.026 +C 6 +C 6 0.125 Total = 100% 5. Mathematical modelling and Numerical procedure 5.1. Real gas In this study to model the fast filling process and develop a mathematical method, the NGV on-board cylinder is considered as a thermodynamics open system which goes through a quasi-steady process. Figure 3 shows a schematic diagram of the thermodynamic model which has been employed. In actual filling process, an orifice flow meter is employed for accounting purposes. The diameter of current orifice flow meters is varied from 1 to 4 mm. Fig. 3. A schematic diagram of the thermodynamic model The mass conservation equation and first law of thermodynamics has been applied to develop a numerical method to the cylinder to find 2 thermodynamics properties. The mass conservation equation considering the onboard NGV cylinder as a control volume and knowing it has only 1 inlet, may be written as follow: (1) dm c dt = ṁ i In equation 1, ṁ i is inlet mass flow rate and can be calculated by considering an expansion through an orifice. Non-ideality could be modelled

26 Mahmood Farzaneh-Gord by considering a discharge coefficient. Applying gas dynamics laws [15]: (2) ṁ i = C d ρ r A orifice ( p c p r ) 1 γ { ( 2γ γ 1 )( pr ρ r ) [ 1 ( pc p r ) γ 1]} 1 2 γ if ( ) γ p c 2 γ 1 p r γ + 1 ( ) γ+1 2 2(γ 1) (3) ṁ i = C d γpr ρ r A orifice γ + 1 if ( ) γ p c 2 γ 1 >. p r γ + 1 In equations 2, 3 C d, γ are discharge coefficient of the orifice and isentropic exponent, respectively. The subscript c and r stands for NGV in-cylinder and reservoir properties. The First law of thermodynamics for a control volume in general form can be written as follow: (4) Q cv + ṁ i (h i + V 2 i /2 + gz i) = ṁ e (h e + V 2 e /2 + gz e) + d/dt[m(u + V 2 /2 + gz)] cv + Ẇcv. The work term is zero in the filling process and the change in potential and kinetic energy can be neglected. Heat transfer through the cylinder walls into environment can be neglected considering fast filling process time. The equation 4 by applying the above assumptions, can be rewritten as follow: (5) d(mu) cv /dt = ṁ i (h + V 2 /2) i. The equation 5 considering stagnation enthalpy as h r = h i + V 2 i /2 which is actually equal to enthalpy of the reservoir tanks is now as follow (6) u c dm c dt + m c du c dt = ṁ ih r. The following equation combining equation 6 and 1 can be easily driven: (7) u c ṁ i + m c du c dt = ṁ ih r. In theory, it should be possible to calculate all thermodynamics properties by knowing two independent properties. The numerical procedure starts

Real and Ideal Gas Thermodynamic Analysis... 27 by using equation 2 and 3 to calculate the inlet mass flow rate. The differential equations 1 and 6 are solved using Rung-Kuta forth order method to obtain internal energy (u) and mass (m c ) in the next time step. Specific volume (v) can be calculated knowing total mass and volume of the cylinder. Now, other thermodynamic properties can be calculated by knowing two independent thermodynamics properties (v, u), by employing Methane properties table provided by National Institute of Standards and Technology website [14]. Solutions end when the NGV cylinder pressure reaches a user-input pressure (20 MPa) level. 5.2. Ideal gas model The governing equation could be much simplified for the case of assuming ideal gas behaviour. Considering the following ideal gas assumptions: (8) u = c v T, h = c p T, m = PV RT, and knowing that volume of the cylinder, specific heats, reservoir temperature are constant, then equation 5 can be simplified as follow: (9) d(mu) cv /dt = ṁ i h r d(pv/rt c v T) cv /dt = ṁ i c p T r V cv c v /R d(p cv )/dt = ṁ i c p T r. The following simple equation by replacing inlet mass flow rate from equation 2 and 3, could be obtained: (10) (P c )/dt = ṁ i (γr/v cv )T r = ( ) 1 { pc γ (γr/v cv )T r C d ρ r A orifice ( 2γ [ p r γ 1 )(p r ) 1 ( p ]}1 c ) γ 1 2 γ ρ r p r = if ( ) γ p c 2 γ 1 p r γ + 1 ( ) γ+1 2 2(γ 1) (γr/v cv )T r C d γpr ρ r A orifice γ + 1. if ( ) γ p c 2 γ 1 > p r γ + 1 To solve equation (10) analytically it would be a simple task. For the real gas model, once in-cylinder pressure calculated using equation (10),

28 Mahmood Farzaneh-Gord then equation (1) could be employed to find the in-cylinder mass. Finally, incylinder temperature can be obtained by employing ideal gas state equation. 6. Results and discussion In this study, the NGV on-board cylinder has been considered adiabatic as a result, the characteristics of the orifice, will not affect on final in-cylinder temperature. The orifice diameter and the cylinder volume were considered to be 1 mm and 67 litres respectively. Initial temperature of NGV cylinder and reservoir tanks is set to the ambient temperature to study the effect of ambient temperature. The results have been presented here for single reservoir tank at 20.5 MPa. Figures 4 and 5 show effects of initial in-cylinder pressure on dynamic in-cylinder pressure and temperature profiles, respectively during filling process which could describe the topping off of the vehicle cylinder for real gas model. In early filling time as shown in Fig. 4, the cylinder gas temperature dips significantly for an empty cylinder (P i = 0.1 MPa), before rising to a final value of about 350 K. It can be seen also that for other cases, the gas temperature profile doesn t reduce during charging time and final temperature decreases as the initial cylinder pressure gas increases. The reason for the dip in temperature profile, in the early part of the filling of a nearly empty cylinder is a result of the Joule-Thompson cooling effect, which the gas undergoes in the isenthalpic expansion through the orifice, from the 20.5 MPa supply pressure to the initially low 0.1 MPa in-cylinder pressure. This cold gas mixes with and compresses the gas originally in the tank, with the result that the combined mixed gas temperature initially reduces. The mixed gas temperature in the cylinder begins to increase when the compression and conversion of supply enthalpy energy to cylinder internal energy overcomes the Joule- Thompson cooling effect, which becomes smaller as the cylinder pressure increases,. The Joule-Thompson cooling effect is smaller and couldn t overcome the supply enthalpy conversion to cylinder internal energy if the initial gas pressure in the cylinder is relatively high. In this case, the in-cylinder temperature is seen to rise. Figure 5 shows effects of initial in-cylinder pressure on dynamic incylinder pressure for real gas model, as it can be seen as initial pressure increases, filling time decreases. This is due the fact that, the cylinder encountered under-charged filling. Figures 6 and 7 show effects of initial in-cylinder and reservoir tank temperature on dynamic in-cylinder temperature profiles for real and ideal

Real and Ideal Gas Thermodynamic Analysis... 29 Fig. 4. Effect of initial pressure on dynamic in-cylinder temperature profile for a real gas model Fig. 5. Effect of initial pressure on dynamic in-cylinder pressure profile for a real gas model gas model respectively, during filling process which could describe ambient temperature effect. Note, from Fig. 6, that the in-cylinder gas temperature dips during the early stages of charging for all ambient temperature less than 320 K before rising to a final value. The reason for the dip in temperature is described above. There is no dip in the temperature profile for the case of T i = 320, this is due the fact that, at this conditions, the Joule-Thompson cooling effect is not high enough to overcome enthalpy conversion. Note form Fig. 7, that the in-cylinder gas temperature rises sharply during early charging time and flattens after. As expected for ideal gas model, there is no dip in temperature profile due the fact that Joule-Thompson cooling effect is not present for ideal gases. Comparing Figs 6 and 7, it can be

30 Mahmood Farzaneh-Gord Fig. 6. Effect of initial (ambient) temperature on dynamic temperature profile for real gas model Fig. 7. Effect of initial (ambient) temperature on dynamic temperature profile for ideal gas model realized that the temperature profiles are highly different and temperature rise is much more for ideal gas model. So, it can be concluded that thermodynamic properties of the gas has big effect on temperature profile. Figures 8 and 9 show effects of initial in-cylinder and reservoir tank temperature on dynamic in-cylinder pressure profiles for real and ideal gas model, respectively. Effects of initial temperature are higher for case of real gas model. Generally, there are similar trends in pressure profile for both cases. Figure 10 shows effects of initial in-cylinder and reservoir temperature on charging time and final in-cylinder temperature. As it can be seen, as initial temperature increases, the final cylinder temperature increases and charging time decreases. The final in-cylinder temperature for ideal gas model is much higher than for real gas model. The charging time for real gas model is smaller

Real and Ideal Gas Thermodynamic Analysis... 31 Fig. 8. Effect of initial (ambient) temperature on in-cylinder dynamic pressure profile for real gas model Fig. 9. Effect of initial (ambient) temperature on in-cylinder dynamic pressure profile for ideal gas model than for ideal gas case. So it can be concluded that the thermodynamic properties of the gas has big effect on charging time and final in-cylinder temperature. Figure 11 shows in-cylinder temperature rise (difference between final and initial in-cylinder temperature) during filling process. It can be seen that for real gas model, temperature rise varies between 40K and 60K depends to ambient temperature. Temperature rise is between 80K and 87K for ideal gas cases. So it can be deduced, ambient condition has big effects on temperature rise. The cylinder fill ratio is defined as the charged cylinder mass divided by the mass, which the cylinder could hold at the rating condition of 300 K ambient temperature and a pressure of 200 bar (here 11.6 kg). This parameter is directly related to the driving range of the NGV. Figure 12 shows how the

32 Mahmood Farzaneh-Gord Fig. 10. Effect of initial (ambient) temperature on charging time and final cylinder temperature Fig. 11. Effect of initial (ambient) temperature on in-cylinder temperature rise

Real and Ideal Gas Thermodynamic Analysis... 33 fill ratio varies with initial temperature (in NGV cylinder and the reservoir tanks) which could describe effect of ambient temperature. It can be seen as initial temperature increases fill ratio decreases. This means that driving range of an NGV will be decreased for hot weather comparing to the colder conditions. The same conclusion can be made by studying the effect of ambient temperature on the final in-cylinder mass in the same figure. Note from the figure, the final in-cylinder mass decreases as ambient temperature increases. Note again from Fig. 12, the fill ratio and final in-cylinder mass are higher for real gas compared with ideal one. Fig. 12. Effect of initial (ambient) temperature on fill ratio and the amount of charged gas Figure 12 shows also the effects of the gas reservoir temperature. So, it can be realized that by cooling the supply gas, if a practical and cost effective way could be developed, the driving range of the NGV is expected to rise. 7. Conclusion In this study a numerical method has been developed based on first law of thermodynamics, conservation of mass and real and ideal gas assumptions to simulate fast filling process of NGV cylinder. For case of real gas model, thermodynamic table of the methane has been employed. Based on the

34 Mahmood Farzaneh-Gord method, a computer program has been built to study the effect of the ambient temperature and initial NGV cylinder pressure. An expression has been derived for ideal gas model, which could be analytically solved. The model has been applied for single reservoir tank. The results indicated that there is a temperature rise in order 40 K or more for real gas and in order 80K or more for ideal gas model during charging process. This would cause under-filled the NGV cylinder and reduce driving range of the NGV. The results also indicated that ambient temperature has big effect on filling process and final NGV cylinder conditions. As ambient temperature rise, the fill ratio and amount of charged gas drop which cause low driving range as a result, filling the NGV during night probably more efficient than during the day, especially during summer. Fill ratio and final in-cylinder mass which are highly different for real and ideal gas model comparing the temperature profile, it can be concluded that thermodynamic properties of the gas has big effect on final in-cylinder conditions. So, ideal gas assumption may not be valid for fill process of NGV cylinder. However, this model (ideal gas model) may be applicable for fill process of hydrogen vehicles on-board cylinder. REFERENCES [1] Kountz, K. Modelling The Fast Fill Process in Natural Gas Vehicle Storage Cylinders, American Chemical Society Paper at 207th National ACS Meeting, March 1994. [2] Kountz, K. J., C. F. Blazek. NGV Fuelling Station and Dispenser Control Systems, report GRI-97/0398, Gas Research Institute, Chicago, Illinois, November 1997. [3] Kountz, K., W. Liss, C. Blazek. Method and Apparatus For Dispensing Compressed Natural Gas, U. S. Patent 5,752,552, May 19, 1998. [4] Kountz, K., W. Liss, C. Blazek. Automated Process and System For Dispensing Compressed Natural Gas, U.S. Patent 5,810,058, Sept. 22, 1998. [5] Kountz, K., W. Liss, C. Blazek. A New Natural Gas Dispenser Control System, Paper at 1998 International Gas Research Conference, San Diego, November 3, 1998, 135 145. [6] Liss, W. E., M. Richards. Development of a Natural Gas to Hydrogen Fuelling Station, Topical Report for U.S. DOE, GTI-02/0193, Sept., 2002.

Real and Ideal Gas Thermodynamic Analysis... 35 [7] Liss, W. E., M. E. Richards, K. Kountz, K. Kriha. Modelling and Testing of Fast-Fill Control Algorithms for Hydrogen Fuelling, 2003 National Hydrogen Association Meeting, March, 2003. [8] Newhouse, N. L., W. E. Liss. Fast Filling of NGV Fuel Containers, SAE paper 1999-01-3739. [9] Thomas, G., J. Goulding, C. Munteam. Measurement, Approval and Verification of CNG Dispensers, NWML KT11 Report, 2002. [10] Shipley, E. Study of Natural Gas Vehicles (NGV) During the Fast Fills Process, Thesis for Master of Science, 2002, College of Engineering and Mineral Resources at West Virginia University. [11] Farzaneh-Gord, M., H. Eftekhari, S. Hashemi, M. Magrebi, M. Dorafshan. The Effect of Initial Conditions on Filling Process of CNG Cylinders, The second International conference on Modelling, Simulation, And Applied Optimization, Abu Dhabi, UAE, March 24 27 2007. [12] Farzaneh-Gord, M. Compressed Natural Gas Single Reservoir Filling Process. Gas international Engineering and Management, Vol. 48 (2008) Issue 6, 16 18. [13] Khangiran refinery official website, http://khangiran.com/pages/products.htm. [14] National Institute of Standards and Technology website, available at http://webbook.nist.gov/chemistry/fluid/. [15] Oosthuizen, P. H., W. E Carscallen. Compressible Fluid Flow, McGraw- Hill, 1997. Nomenclature A area (m 2 ) C d orifice discharge coefficient c p, c v Constant pressure and volume specific heats (kj/kg K) g gravitational acceleration (m/s 2 ) h specific enthalpy (kj/kg) ṁ mass flow rate (kg/s) M molecular weight (kg/kmol) P Pressure (Pa) Q heat transfer rate (kw) T temperature (K or C) u internal energy (kj/kg)

36 Mahmood Farzaneh-Gord v specific volume (m 3 /kg) V velocity (m/s) W actual work (kj/kg ) Ẇ actual work rate (kw or MW) z height (m) C 6+ all hydrocarbon compounds with more than 5 carbon in their chemical formula ρ density (kg/m 3 ) γ Subscript c r i isentropic exponent NGV cylinder reservoir tank initial or inlet condition