REAL AND IDEAL GAS THERMODYNAMIC ANALYSIS OF SINGLE RESERVOIR

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:[email protected]

[Received 25 September 2009. Accepted 29 August 2011]

Abstract. The accurate modelling of the fast-fill dynamics occurringin Compressed Natural Gas (CNG) fuelled vehicle storage cylinders is acomplex process and to date those dynamics have not been thoroughlystudied. In this paper, conversation of mass and real and ideal gas as-sumptions based on first law of thermodynamics, a numerical methodhas been developed to study fast filling process of natural gas vehicle’s(NGV) cylinder. Thermodynamic properties table has been employed forthe case of a real gas model. A simple equation has been derived for thecase of ideal gas which could be solved analytically. The model has beenapplied for a single reservoir tank. The results indicated that there is atemperature rise in order 40 K or more for real gas and 80 K or more forthe case of ideal gas during charging process. The results also indicatedthat ambient temperature has big effect on filling process and final NGVcylinder 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 auto-mobile fuels such as gasoline (petrol) and diesel. The compressed natural gas(CNG) fuelled vehicle storage cylinders encountered a rise in storage gas cylin-der temperature (in the range of 40 K or more) during the fast filling due tocomplex compression and mixing processes. This temperature rise reduces thedensity of the gas in the cylinder, resulting in an under filled cylinder, relativeto 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 stationdispenser, by transiently over-pressurizing the tank.

The on-board storage capacity of natural gas vehicles (NGVs) is a criti-cal issue to the wide spread marketing of these alternate fuelled vehicles. CNGis dispensed to an NGV through a process known as the fast fill process, since itis completed in less than five minutes. During fast fill charging operations canoccur under-filling of NGV cylinders, at fuelling stations, at ambient tempera-tures greater than 30 ◦C. The resulting reduced driving range of the vehicle is aserious obstacle which the gas industry is striving to overcome, without resort-ing to unnecessarily high fuelling station pressures, or by applying extensiveover-pressurization of the cylinder during the fuelling operation. Underchargedstorage cylinders are a result of the elevated temperature which occurs in theNGV 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 lit-eratures. Kountz [1] was first who modelled fast filling process of natural gasstorage cylinder based on first law of thermodynamics. He developed a com-puter 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 algorithmthat insures complete filling of NGV cylinders under a fast fill scenario. Theresearches are also under way to model fast filling of hydrogen-based fuellinginfrastructure including work of Liss and Richards [6] and Liss et al. [7]. New-house and Liss [8] have studied fast filling of hydrogen cylinder using numberof experiments. They reported a high temperature increase in the cylinderduring the process.

A few experimental studies were also carried out to study fast fillingof natural gas cylinder including work of Thomas and Goulding [9] and Shiply[10]. Shiply [10] concluded that ambient temperature change can have anaffect on the fast fill process. He also concluded that, the test cylinder wasunder-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 equa-tion and methane properties table for single reservoir. They investigated effectsof ambient temperature and initial cylinder pressure on final cylinder condi-tions.

The number of natural gas fuel based vehicles in Iran growing rapidlyrecently due to the government policy. Most of owners of those vehicles havereported under-filling charge compared to rated conditions. A computer pro-gramme 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, conversationof mass and thermodynamics properties table of the gas in this study. Thisenables us to study effects of various parameters on dynamics change in theNGV cylinder. The fast fill process was assumed to be quasi-static processand 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 assumptionand Methane assumed as an ideal gas.

2. CNG Filling station

Figure 1 shows a typical CNG filling station. Gas from the distributionpipeline, 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 inthe vehicle’s on-board storage so that gas flows to the vehicle under differentialpressure. Typically, the cascade storage will operate in range of 20.5 MPa to25.0 MPa, while the vehicle’s maximum onboard cylinder pressure is 20 MPa.In order to make the utilization of the compressor and buffer storage moreefficient, 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 materi-als 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


reinforcement. Metal containers and liners are typically steel or aluminium.Composite reinforcements are typically carbon or glass fibbers in an epoxyresin matrix. CNG cylinders are designed for a specified nominal service pres-sure 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. Theactual pressure in the fuel container will vary from the nominal service pres-sure as the temperature of the fuel in the container varies. Fuelling stationsnormally fill the cylinder up %125 of nominal service pressure to avoid undercharging but this highly depends to ambient temperature.

The common CNG cylinder type in Iran is Type 1. They have thesame inside diameter with various heights depending to their volume. Figure2 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 andother factors. The gas is refined before flowing into the pipe lines. Table 1shows an experimental analysis of typical natural gas composition which flowsin Iran pipe lines according to the Khangiran refinery official website [13]. Itcan be realised that the most of compositions occupied very low percentageby knowing that Methane is occupied about 99% of the gas. For the sake ofsimplicity it is assumed that Methane is the only substance in the Natural gas.


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 CO2 0.055Nitrogen N2 0.428Methane CH4 98.640Ethane C2H6 0.593Propane C3H8 0.065Iso butane C4H10 0.015n-Butane C4H10 0.034Iso-Pentane C5H12 0.026+C6 +C6 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 mathemat-ical method, the NGV on-board cylinder is considered as a thermodynamicsopen system which goes through a quasi-steady process. Figure 3 shows aschematic diagram of the thermodynamic model which has been employed. Inactual 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 hasbeen applied to develop a numerical method to the cylinder to find 2 thermo-dynamics properties. The mass conservation equation considering the onboardNGV cylinder as a control volume and knowing it has only 1 inlet, may bewritten as follow:

(1)dmc

dt= mi

In equation 1, mi is inlet mass flow rate and can be calculated byconsidering an expansion through an orifice. Non-ideality could be modelled


by considering a discharge coefficient. Applying gas dynamics laws [15]:

(2) mi = CdρrAorifice(pc

pr

)1γ

{

(

2γ

γ − 1

)(

pr

ρr

)

[

1 −(

pc

pr

)γ−1

γ

]}

12

ifpc

pr

≤(

2

γ + 1

)γ

γ−1

(3) mi = Cd

√γprρrAorifice

(

2

γ + 1

)γ+1

2(γ−1)

ifpc

pr

>

(

2

γ + 1

)γ

γ−1

.

In equations 2, 3 Cd, γ are discharge coefficient of the orifice and isen-tropic exponent, respectively. The subscript c and r stands for NGV in-cylinderand reservoir properties.

The First law of thermodynamics for a control volume in general formcan be written as follow:

(4) Qcv +∑

mi(hi + V 2

i /2 + gzi)

=∑

me(he + V 2

e /2 + gze) + d/dt[m(u + V 2/2 + gz)]cv + Wcv.

The work term is zero in the filling process and the change in potentialand kinetic energy can be neglected. Heat transfer through the cylinder wallsinto environment can be neglected considering fast filling process time. Theequation 4 by applying the above assumptions, can be rewritten as follow:

(5) d(mu)cv/dt = mi(h + V 2/2)i.

The equation 5 considering stagnation enthalpy as hr = hi + V 2

i /2which is actually equal to enthalpy of the reservoir tanks is now as follow

(6) uc

dmc

dt+ mc

duc

dt= mihr.

The following equation combining equation 6 and 1 can be easily driven:

(7) ucmi + mcduc

dt= mihr.

In theory, it should be possible to calculate all thermodynamics prop-erties by knowing two independent properties. The numerical procedure starts


by using equation 2 and 3 to calculate the inlet mass flow rate. The differentialequations 1 and 6 are solved using Rung-Kuta forth order method to obtaininternal energy (u) and mass (mc) in the next time step. Specific volume (v)can be calculated knowing total mass and volume of the cylinder. Now, otherthermodynamic properties can be calculated by knowing two independent ther-modynamics properties (v, u), by employing Methane properties table providedby National Institute of Standards and Technology website [14]. Solutions endwhen 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 assum-ing ideal gas behaviour. Considering the following ideal gas assumptions:

(8) u = cvT, h=cpT, m =PV

RT,

and knowing that volume of the cylinder, specific heats, reservoir temperatureare constant, then equation 5 can be simplified as follow:

(9) d(mu)cv/dt = mihr → d(PV/RT × cvT )cv/dt

= micpTr → Vcvcv/R × d(Pcv)/dt = micpTr.

The following simple equation by replacing inlet mass flow rate fromequation 2 and 3, could be obtained:

(10) (Pc)/dt = mi(γR/Vcv)Tr =

=

(γR/Vcv)TrCdρrAorifice

(

pc

pr

)1γ

{

(2γ

γ − 1)(

pr

ρr

)

[

1 − (pc

pr

)γ−1

γ

]}12

ifpc

pr

≤(

2

γ + 1

)γ

γ−1

(γR/Vcv)TrCd

√γprρrAorifice

(

2

γ + 1

)γ+1

2(γ−1)

ifpc

pr

>

(

2

γ + 1

)γ

γ−1

.

To solve equation (10) analytically it would be a simple task. Forthe real gas model, once in-cylinder pressure calculated using equation (10),


then equation (1) could be employed to find the in-cylinder mass. Finally, in-cylinder 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 adiabaticas a result, the characteristics of the orifice, will not affect on final in-cylindertemperature. The orifice diameter and the cylinder volume were considered tobe 1 mm and 67 litres respectively. Initial temperature of NGV cylinder andreservoir tanks is set to the ambient temperature to study the effect of ambienttemperature. The results have been presented here for single reservoir tank at20.5 MPa.

Figures 4 and 5 show effects of initial in-cylinder pressure on dynamicin-cylinder pressure and temperature profiles, respectively during filling processwhich 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 sig-nificantly for an empty cylinder (Pi = 0.1 MPa), before rising to a final valueof about 350 K. It can be seen also that for other cases, the gas temperatureprofile doesn’t reduce during charging time and final temperature decreases asthe initial cylinder pressure gas increases. The reason for the dip in temper-ature profile, in the early part of the filling of a nearly empty cylinder is aresult of the Joule-Thompson cooling effect, which the gas undergoes in theisenthalpic expansion through the orifice, from the 20.5 MPa supply pressureto the initially low 0.1 MPa in-cylinder pressure. This cold gas mixes withand compresses the gas originally in the tank, with the result that the com-bined mixed gas temperature initially reduces. The mixed gas temperature inthe cylinder begins to increase when the compression and conversion of supplyenthalpy energy to cylinder internal energy overcomes the Joule- Thompsoncooling effect, which becomes smaller as the cylinder pressure increases,. TheJoule-Thompson cooling effect is smaller and couldn’t overcome the supply en-thalpy conversion to cylinder internal energy if the initial gas pressure in thecylinder is relatively high. In this case, the in-cylinder temperature is seen torise.

Figure 5 shows effects of initial in-cylinder pressure on dynamic in-cylinder pressure for real gas model, as it can be seen as initial pressure in-creases, filling time decreases. This is due the fact that, the cylinder encoun-tered under-charged filling.

Figures 6 and 7 show effects of initial in-cylinder and reservoir tanktemperature on dynamic in-cylinder temperature profiles for real and ideal


Fig. 4. Effect of initial pressure on dynamic in-cylinder temperature profile for a realgas model

Fig. 5. Effect of initial pressure on dynamic in-cylinder pressure profile for a real gasmodel

gas model respectively, during filling process which could describe ambienttemperature effect.

Note, from Fig. 6, that the in-cylinder gas temperature dips during theearly stages of charging for all ambient temperature less than 320 K beforerising to a final value. The reason for the dip in temperature is describedabove. There is no dip in the temperature profile for the case of Ti = 320, thisis due the fact that, at this conditions, the Joule-Thompson cooling effect isnot high enough to overcome enthalpy conversion.

Note form Fig. 7, that the in-cylinder gas temperature rises sharplyduring 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 cool-ing effect is not present for ideal gases. Comparing Figs 6 and 7, it can be


Fig. 6. Effect of initial (ambient) temperature on dynamic temperature profile forreal gas model

Fig. 7. Effect of initial (ambient) temperature on dynamic temperature profile forideal gas model

realized that the temperature profiles are highly different and temperature riseis much more for ideal gas model. So, it can be concluded that thermodynamicproperties of the gas has big effect on temperature profile.

Figures 8 and 9 show effects of initial in-cylinder and reservoir tanktemperature on dynamic in-cylinder pressure profiles for real and ideal gasmodel, respectively. Effects of initial temperature are higher for case of realgas model. Generally, there are similar trends in pressure profile for both cases.

Figure 10 shows effects of initial in-cylinder and reservoir temperatureon charging time and final in-cylinder temperature. As it can be seen, as initialtemperature increases, the final cylinder temperature increases and chargingtime decreases. The final in-cylinder temperature for ideal gas model is muchhigher than for real gas model. The charging time for real gas model is smaller


Fig. 8. Effect of initial (ambient) temperature on in-cylinder dynamic pressureprofile for real gas model

Fig. 9. Effect of initial (ambient) temperature on in-cylinder dynamic pressureprofile for ideal gas model

than for ideal gas case. So it can be concluded that the thermodynamic proper-ties of the gas has big effect on charging time and final in-cylinder temperature.

Figure 11 shows in-cylinder temperature rise (difference between finaland initial in-cylinder temperature) during filling process. It can be seen thatfor real gas model, temperature rise varies between 40K and 60K depends toambient temperature. Temperature rise is between 80K and 87K for ideal gascases. So it can be deduced, ambient condition has big effects on temperaturerise.

The cylinder “fill ratio” is defined as the charged cylinder mass dividedby the mass, which the cylinder could hold at the rating condition of 300 Kambient temperature and a pressure of 200 bar (here 11.6 kg). This parameteris directly related to the driving range of the NGV. Figure 12 shows how the


Fig. 10. Effect of initial (ambient) temperature on charging time and final cylindertemperature

Fig. 11. Effect of initial (ambient) temperature on in-cylinder temperature rise


fill ratio varies with initial temperature (in NGV cylinder and the reservoirtanks) which could describe effect of ambient temperature. It can be seenas initial temperature increases fill ratio decreases. This means that drivingrange of an NGV will be decreased for hot weather comparing to the colderconditions. The same conclusion can be made by studying the effect of ambienttemperature on the final in-cylinder mass in the same figure. Note from thefigure, 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 forreal gas compared with ideal one.

Fig. 12. Effect of initial (ambient) temperature on fill ratio and the amount ofcharged gas

Figure 12 shows also the effects of the gas reservoir temperature. So, itcan be realized that by cooling the supply gas, if a practical and cost effectiveway 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 firstlaw of thermodynamics, conservation of mass and real and ideal gas assump-tions to simulate fast filling process of NGV cylinder. For case of real gasmodel, thermodynamic table of the methane has been employed. Based on the


method, a computer program has been built to study the effect of the ambienttemperature and initial NGV cylinder pressure. An expression has been de-rived for ideal gas model, which could be analytically solved. The model hasbeen applied for single reservoir tank.

The results indicated that there is a temperature rise in order 40 K ormore for real gas and in order 80K or more for ideal gas model during chargingprocess. This would cause under-filled the NGV cylinder and reduce drivingrange of the NGV. The results also indicated that ambient temperature hasbig effect on filling process and final NGV cylinder conditions. As ambienttemperature rise, the fill ratio and amount of charged gas drop which causelow driving range as a result, filling the NGV during night probably moreefficient than during the day, especially during summer.

Fill ratio and final in-cylinder mass which are highly different for realand ideal gas model comparing the temperature profile, it can be concludedthat thermodynamic properties of the gas has big effect on final in-cylinderconditions. So, ideal gas assumption may not be valid for fill process of NGVcylinder. However, this model (ideal gas model) may be applicable for fillprocess of hydrogen vehicles on-board cylinder.

REFEREN CES

[1] Kountz, K. Modelling The Fast Fill Process in Natural Gas Vehicle StorageCylinders, American Chemical Society Paper at 207th National ACS Meeting,March 1994.

[2] Kountz, K. J., C. F. Blazek. NGV Fuelling Station and Dispenser ControlSystems, report GRI-97/0398, Gas Research Institute, Chicago, Illinois, Novem-ber 1997.

[3] Kountz, K., W. Liss, C. Blazek. Method and Apparatus For DispensingCompressed Natural Gas, U. S. Patent 5,752,552, May 19, 1998.

[4] Kountz, K., W. Liss, C. Blazek. Automated Process and System For Dis-pensing Compressed Natural Gas, U.S. Patent 5,810,058, Sept. 22, 1998.

[5] Kountz, K., W. Liss, C. Blazek. A New Natural Gas Dispenser ControlSystem, Paper at 1998 International Gas Research Conference, San Diego, No-vember 3, 1998, 135–145.

[6] Liss, W. E., M. Richards. Development of a Natural Gas to Hydrogen Fu-elling Station, Topical Report for U.S. DOE, GTI-02/0193, Sept., 2002.


[7] Liss, W. E., M. E. Richards, K. Kountz, K. Kriha. Modelling and Testingof Fast-Fill Control Algorithms for Hydrogen Fuelling, 2003 National HydrogenAssociation Meeting, March, 2003.

[8] Newhouse, N. L., W. E. Liss. Fast Filling of NGV Fuel Containers, SAEpaper 1999-01-3739.

[9] Thomas, G., J. Goulding, C. Munteam. Measurement, Approval and Ver-ification 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 Resourcesat West Virginia University.

[11] Farzaneh-Gord, M., H. Eftekhari, S. Hashemi, M. Magrebi, M. Do-

rafshan. The Effect of Initial Conditions on Filling Process of CNG Cylinders,The second International conference on Modelling, Simulation, And AppliedOptimization, 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 athttp://webbook.nist.gov/chemistry/fluid/.

[15] Oosthuizen, P. H., W. E Carscallen. Compressible Fluid Flow, McGraw-Hill, 1997.

Nomenclature

A area (m2)

Cd orifice discharge coefficient

cp, cv Constant pressure and volume specific heats (kj/kg K)

g gravitational acceleration (m/s2)

h specific enthalpy (kj/kg)

m 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)


v specific volume (m3/kg)

V velocity (m/s)

W actual work (kj/kg )

W actual work rate (kW or MW)

z height (m)

C6+

all hydrocarbon compounds with morethan 5 carbon in their chemical formula

ρ density (kg/m3)

γ isentropic exponent

Subscript

c NGV cylinder

r reservoir tank

i initial or inlet condition

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REAL AND IDEAL GAS THERMODYNAMIC ANALYSIS OF SINGLE RESERVOIR