Effects of Natural Gas Compositions on CNG FastFilling Process for Buffer Storage System

M. Farzaneh-Gord, H. Reza Rahbari and M. Deymi-Dashtebayaz

The Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood - Irane-mail: mahmood.farzaneh@yahoo.co.uk - rahbarihamidreza@yahoo.com - meh_deimi@yahoo.com

Résumé — Effets des compositions de gaz naturel sur le processus de remplissage rapide de GNCpour un système de stockage tampon — La modélisation précise du processus de remplissage rapidedes bouteilles de Gaz Naturel Comprimé (GNC) pour l’alimentation de véhicules constitue un processuscomplexe et doit être parfaitement étudiée. Les conditions finales dans la bouteille doivent satisfaire à desnormes de sécurité. La composition du gaz naturel joue un rôle important sur les propriétésthermodynamiques et en conséquence, sur le processus de remplissage rapide et ces conditions finales.Une analyse théorique a été développée pour étudier les effets de la composition du gaz naturel sur leprocessus de remplissage d’une bouteille de Gaz Naturel Véhicule (GNV) embarquée. La bouteille estconsidérée comme un système localisé. L’analyse est basée sur les lois de la thermodynamique et deconservation de masse. Les propriétés requises de mélanges de gaz naturel ont été calculées ens’appuyant sur l’équation d’état (EOS ; Equation of State) AGA8 et les relations de la thermodynamique.Les résultats, présentés pour un système adiabatique, montrent que la composition du gaz naturel a deseffets importants sur le processus de remplissage et les conditions finales dans la bouteille. En outre, legaz présentant un moindre pourcentage de méthane dans sa composition est plus approprié pour leprocessus de remplissage.

Abstract — Effects of Natural Gas Compositions on CNG Fast Filling Process for Buffer StorageSystem — The accurate modeling of the fast-fill process occurring in Compressed Natural Gas (CNG)fuelled vehicle storage cylinders is a complex process and should be thoroughly studied. Finalin-cylinder conditions should meet appropriate cylinder safety standards. The composition of natural gasplays an important role on its thermodynamic properties and consequently, on the fast-fill process andthe final conditions. Here, a theoretical analysis has been developed to study the effects of the natural gascomposition on the filling process of an onboard Natural Gas Vehicle (NGV) cylinder. The cylinder isassumed as a lumped system. The analysis is based on laws of thermodynamics and mass balance. Basedon AGA8 Equation of State (EOS) and thermodynamics relationships, the required properties of naturalgas mixtures have been calculated. The results are presented for an adiabatic system. The results showthat the compositions of natural gas have great effects on the filling process and final in-cylinderconditions. Furthermore, the gas with less methane percentage in its composition is more suitable for thefilling process.

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles,Copyright © 2013, IFP Energies nouvellesDOI: 10.2516/ogst/2012010

Vol. 69 (2014), No. 2, pp. 319-330

320

NOMENCLATURE

A Area (m2)B Second virial coefficientCd Orifice discharge coefficientcp, cv Constant pressure & volume specific heats (kJ/kg.K)g Gravitational acceleration (m/s2)h Specific enthalpy (kJ/kg)Kij Binary interaction parameterm· Mass flow rate (kg/s)M Molecular weight (kg/kmol)Mw Molecular weightN Number of component in gas mixturen Number of experimental dataP Pressure (bar or Pa)Q· Heat transfer rate (kW)T Temperature (K or oC)u Internal energy (kJ/kg) um Molar internal energyh Enthalpy (kJ/kg)s Entropy (kJ/K)t Time (s)v Specific volume (m3/kg)V Velocity (m/s)W Actual work (kJ/kg)W· Actual work rate (kW or MW)z Height (m)Z Compressibility factorρ Density (kg/m3)γ Isentropic exponent

Subscript

C NGV onboard cylinder R Reservoir tanki Initial or inlet conditionr Recents Start of filling processa, ∞ Ambientav Averagegen Generation1 Reservoir tank 12 Reservoir tank 23 Reservoir tank 3

Greek Letters

ρm Molar densityρr Reduce density

γ Gas gravityμJ Joule-Thomson coefficientνm Molar specific volume

INTRODUCTION

Compressed Natural Gas (CNG) is considered as a cleanalternative to other car fuels such as gasoline (petrol) anddiesel [1]. There are millions of Natural Gas Vehicles (NGV)on the streets and that number is growing continuously.Especially for urban vehicles, natural gas is regarded as anenvironmentally friendly fuel [2]. To ensures, safe andefficient use of NGVs, it is essential to investigate the effectsof various parameters on filling process and final in-cylinderconditions.

The NGVs usually receive natural gas from high pressurereservoirs at the fuelling stations during filling. The onboardvehicle storage cylinders encountered a rise in in-cylindertemperature during the filling. This temperature rise decreasesthe density of the gas, resulting in an under-filled cylinder,relative to its rated specification. If this temperature rise isnot compensated for in the fuelling station, by transientlyover-pressurizing the cylinder, the vehicle driver willexperience a reduced driving range.

The onboard storage capacity of NGV is a critical issue tothe wide spread marketing of these alternate fuelled vehicles.CNG is dispensed to an NGV through a process known asthe fast fill process, since it is completed in less than fiveminutes. Under-filling of NGV cylinders could occur at thefuelling stations, at ambient temperatures greater than 30°C.The resulting reduced driving range of the vehicle is a seriousobstacle which the gas industry is striving to overcome,without resorting to unnecessarily high fuelling stationpressures, or by applying extensive over-pressurization of thecylinder during the fuelling operation. Undercharged storagecylinders are a result of the elevated temperature whichoccurs in the NGV storage cylinder, due to compression andother processes.

The standards use a settled service pressure of either20 MPa (2 900 psi) or 24.5 MPa (3 600 psi) for an onboardNGV cylinder. They allow for overfilling to take account ofthe increased temperature generated during fast filling andtherefore, use the overfilled condition as the upper limit inthe pressure cycle tests. A maximum pressure of 26 MPa ispermitted in ISO 11439 regardless of ambient temperature.The cylinders are generally designed to be filled to servicepressure 1 000 times per year of service life, up to a maximumof 20 years [3]. They are expected to operate effectively intemperatures from –40°C to 65°C with occasional temperaturerises up to 82°C.

The NGV industry has made excellent advancements inthe industry to provide a system to refuel a NGV in acomparable to that of a gasoline dispenser. The problem with

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 69 (2014), No. 2

M. Farzaneh-Gord et al. / Effects of Natural Gas Compositions on CNG Fast Filling Process for Buffer Storage System 321

the long refuelling time has been remedied, for the most part,to be comparable to the fill time (< 5 min) taken to fill agasoline powered automobile. This fill time can be referredto as a fast fill or rapid charge.

There have been limited researches in the field of fillingprocess modeling in literature. Kountz [4] were progenitor inthis field that modeled fast filling process of an NGV cylinderbased on first law of thermodynamics. They expanded acomputer program to simulate fast filling process for a singlereservoir based on real gas. Kountz et al. [5-8], have alsodeveloped a natural gas dispenser control algorithm thatinsures complete filling of NGV cylinders under a fast fillscenario. The researchers are also under way to model fastfilling of hydrogen-based fuelling infrastructure, includingwork of Liss and Richards [9], Liss et al. [10] and Newhouseand Liss [11] have studied fast filling of the hydrogencylinder using the number of experiments. They reported ahigh temperature increase in the cylinder during the process.

A few experimental studies were also carried out to studyfast filling of the natural gas cylinder, including work ofThomas et al. [12] and Shiply [13]. Shiply [13] concludedthat ambient temperature change can have an effect on thefast fill process. He also concluded that, the test cylinder wasunder-filled every time it was rapidly recharged.

Farzaneh-Gord et al. [14] and Farzaneh-Gord [15] havealso modeled fast filling process. They developed a computerprogramme based on the Peng-Robinson state equation andmethane properties table for single reservoir. Theyinvestigated effects of ambient temperature and initialcylinder pressure on final cylinder conditions. In anotherstudy, Farzaneh-Gord et al. [16] presented thermodynamicsanalysis of cascade reservoirs filling process of NGVcylinders. The results of this research indicated that ambienttemperature has the big effect on filling process and finalNGV cylinder conditions.

Farzaneh-Gord et al. [17] have employed a theoreticalanalysis to study effects of buffer and cascade storagesystems on performance of a CNG fuelling station. It isfound that the time (filling time) required for bringing up theNGV onboard cylinder to its final pressure in the bufferstorage system is about 66% less than the cascade storagesystem. The charged mass for cascade system is about 80% ofthe buffer system which gives an advantage to buffer systemover cascade one. The biggest advantage of the cascadesystem over the buffer system is 50% less entropy generationfor this configuration, which probably causes much lowerrequired compressor input work for this configurationcomparing to buffer system.

In all previous studies, the natural gas assumed as puremethane or a gas with fixed composition. So the influencesof natural gas compositions on filling process and final in-cylinder values have not been studied. The main purpose of thecurrent study is to investigate the effects of natural gascompositions on filling process and final in-cylinder conditionsfor a buffer storage system.

Natural gas composition plays a big role on CNG fuel. Ina research, Kim et al. [18] have studied the effect of natural gascomposition on the performance of a CNG engine. For studyingthe CNG filling process, it is vital to know thermodynamicproperties of natural gas. To compute the thermodynamicproperties, the AGA8 Equation of State (EOS) [19, 20] hasbeen employed. The AGA8 EOS has been developed by theAmerican Gas Association (AGA), especially for calculatingcompressibility factor and density of natural gas for custodytransfer. It shows good performance and high accuracy in thetemperature range between 143.15 K and 676.15 K and for apressure up to 280 MPa. The AGA8 has been also subject tovarious researches in order to calculate thermodynamicsproperties of natural gas. Isentropic exponent, Joule-Thomsoncoefficient and heat capacities at constant pressure andvolume are calculated by Maríc et al. [21] and Maríc [22, 23].Farzaneh-Gord et al. [24] has employed AGA8 EOS tocalculate the thermal properties of natural gas mixture such asenthalpy and internal energy in addition of the compressibilityfactor.

In this study, the second law has been employed tocalculate the value of the entropy generation theoretically.Entropy generation is corresponded with thermodynamicirreversibilities, which is common in all types of thermalsystems. Various sources are accountable for the entropygeneration. There have been numerous researches in thefield of entropy generation. Bejan [25, 26] haveconcentrated upon the different mechanisms responsible forentropy generation in applied thermal engineering.Generation of entropy reduces the available work of asystem. Therefore, it makes good engineering sense to focuson irreversibilities (see Bejan [25-27]) of heat transfer andfluid flow processes and try to understand the function ofrelated entropy generation mechanisms. Since then, a lot ofstudies have been carried out to compute the entropygeneration and irreversibility profiles for different geometricconfigurations, flow situations and thermal boundaryconditions. Here, entropy generation minimization has beenemployed as a tool to determine the amount of workdestruction during filling process.

In this study, the main objective is to investigate the effectsof natural gas composition on filling process of an NGVonboard cylinder. The cylinder is assumed to be filled byconnecting to a single high pressure reservoir (commonlycalled buffer system). The thermodynamic analysis has beenemployed as a theoretical tool. The theoretical model isdeveloped based on the mass and energy balance and thesecond law of thermodynamic. Thermodynamic propertiesand entropy generation in the cylinder are calculated duringthe filling process. The thermodynamic properties of naturalgas mixture are computed based on AGA8 EOS andthermodynamics relationships.

322

1 NATURAL GAS COMPOSITIONS

Natural gas is a mixture of several components with variousproperties. Therefore, its thermodynamics properties aredependant on its components. To obtain the propertiesaccurately, the effect of the gas compositions must be alsoconsidered. For this purpose, the AGA8 EOS has beenemployed. Table 1 shows the molar percent of four typicalcompositions employed in this study. These gases areextracted from the various regions within Iran [28]. Thesegases have been selected due to highest different in theircompositions among Iranian pipeline natural gases.

TABLE 1

Mole fraction of natural gas extracted from various region of Iran [28]

Mole fraction (%)Component

Khangiran Kangan Turkman gas Pars

CH4 98.6 90.04 94.21 87

C2H6 0.59 3.69 2.25 5.4

C3H8 0.09 0.93 0.53 1.7

iso-C4H10 0.02 0.2 0.36 0.3

n-C4H10 0.04 0.29 0 0.45

iso-C5H12 0.02 0.14 0.26 0.13

n-C5H12 0.02 0.08 0 0.11

n-C6H14 0.07 0.14 0.17 0.07

C7+ 0 0.01 0.18 0.03

N2 0.56 4.48 1.9 3.1

CO2 0 0 0.14 1.85

2 CNG FILLING STATION

Figure 1 shows a typical CNG filling station. Natural gasfrom the distribution pipeline, usually “low” pressure at< 0.4 MPa or possibly “medium” pressure (1.6 MPa), iscompressed using a large multi-stage compressor into astorage system. This system is maintained at a pressurehigher than that in the vehicle’s onboard storage so that gasflows to the vehicle under differential pressures. Typically,the storage system will operate in the range of 20.5 MPa to25 MPa, while the vehicle’s maximum onboard cylinderpressure is 20 MPa. In order to make the utilization of thecompressor and storage system more efficient, fast fill CNGstations usually operate using a three-stage “cascade” storagesystem. In this storage system, reservoir cylinders are put intoan order of ascending pressure. Figure 1 shows a schematicdiagram of a cascade storage system. During fast filling, theonboard cylinder is first connected to the low-pressurereservoir. As the flow rate reaches a pre-set level the systemis first switched to the medium pressure reservoir and then tothe high-pressure reservoir to complete the fill. However, in

refilling the station reservoirs the compressor is automaticallyswitched on to fill the high pressure reservoir first and thenswitches to the medium and the low pressure reservoirs. Thisensures that the high pressure reservoir is maintained atmaximum pressure all the time, ensuring that vehicles arealways supplied with the maximum amount of gas available.Here for sake of simplicity, the pressure assumed to beunchanged during filling processes.

3 THERMODYNAMIC ANALYSIS

3.1 First Law Analysis

To model the fast filling process and develop a mathematicalmethod, the NGV onboard cylinder is considered as athermodynamics open system which goes through a quasi-steady process.

To develop a theoretical analysis, the continuity and firstlaw of thermodynamics have been applied to the cylinder, tofind 2 thermodynamics properties. Considering the onboardNGV cylinder as a control volume and knowing it has only1 inlet, the continuity (conservation of mass) equation may bewritten as follows:

(1)

In Equation (1), m· i is the inlet mass flow rate and can becalculated by considering expansion through an orifice.Applying gas dynamics laws [4]:

(2) P

PC

R

≤+

⎛

⎝⎜

⎞

⎠⎟

−2

1

1

γ

γ

γ

�m C AP

P

Pi d R orifice

C

R

R

R

=⎛

⎝⎜

⎞

⎠⎟

−

⎛

⎝⎜

⎞

⎠⎟ρ

γγ ρ

γ

1

2

1

⎛⎛

⎝⎜

⎞

⎠⎟ −

⎛

⎝⎜

⎞

⎠⎟

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪

−

1

1

P

PC

R

γ

γ

11

2

if:

dm

dtmC

i= �

Gassupply

& meter

Multi-stagecompressor

Reservoir 3

Reservoir 2

Reservoir 1

Cascade reservoirs Dispenser

Figure 1

A schematic diagram of NGV filling station.

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 69 (2014), No. 2

M. Farzaneh-Gord et al. / Effects of Natural Gas Compositions on CNG Fast Filling Process for Buffer Storage System 323

(3)

Equation (2) is valid for subsonic flow while Equation (3)is for sonic condition. Discharge coefficient (Cd) is thenintroduced to consider irreversibility of the flow through anorifice.

The first laws of thermodynamics for a control volume ingeneral form can be written as follow:

(4)

The work term is zero in the filling process and the changein potential and kinetic energy in NGV cylinder (V2/2)cv) canbe neglected. The equation then could be simplified asbelow:

(5)

Applying energy balance for the reservoir tank, one could

obtain . Here, the reservoir conditions are assumed

to be unchanged, consequently hR is constant throughout thefilling process.

Replacing with hR, Equation (5) further could be

simplified as:

(6)

The heat lost from the onboard NGV cylinder to environmentcould be calculated as:

Q· = – UHCAC(TC –T∞) (7)

That UHC is overall heat transfer coefficient of the cylinder.It controls the rate of heat transfer from the gas withincylinder to the ambient. Higher UHC means lower final in-cylinder condition. Combining Equations (1, 6) and (7), onecould obtain an equation as:

(8)

Or in the following form:

(9)

The above equation could be rearranged in the followingform:

d(mCuC – mChR) = – UHCAC(TC –T∞)dt (10)

The above equation could be integrated from “start” offilling, up to “recent” time as:

d m u

dt

d m h

dtU A T TC C C R

HC C C

( ) ( )− = − −( )∞

d m u

dtU A T T

dm

dthC C

HC C CC

R

( )= − −( ) +∞

dU

dtQ m hC

i R= +� �

Vhi

i

2

2+

hV

hRi

i= +2

2

dU

dtQ m

VhC

ii

i= + +⎛

⎝⎜

⎞

⎠⎟� �

2

2

� � �Q m h V gz m h V gzcv i i i i e e e e+ + + = + +

+

∑ ∑( ) ( )2 22 2/ /

dd dt m u V gz Wcv cv/ /[ ( )]+ + +2 2 �

�m C P Ai d R R orifice=+

⎛

⎝⎜

⎞

⎠⎟

+

−γ ρ

γ

γ

γ2

1

1

2 1( ) if:

P

PC

R

>+

⎛

⎝⎜

⎞

⎠⎟

−2

1

1

γ

γ

γ (11)

The integration of the above equation for a single reservoirfuelling station resulted to:

mC(uC – hR) – mCs(uCs – hR) = – UHCACΔTavt (12)

When mC, mCs are mass of charged gas at “recent” and“start” of filling process respectively, ΔTav is average temper-ature difference between cylinder and environment whichdefined as:

(13)

The first law of thermodynamic for the onboard NGVcylinder finally could be written as:

(14)

Equations (2, 3) and (14) could be employed to calculatethe two thermodynamic properties of in-cylinder natural gasat any time.

For an adiabatic system, Equation (14) could be moresimplified as:

(15)

And if mCs = 0, the following relation is valid at any time:

uC = hR (16)

3.2 The Second Law Analysis

The second law of thermodynamic adopted in this study,makes it possible to evaluate the entropy generation rate, S·gen,for flow processes occurring in the storage system of theCNG filling station.

The second law of thermodynamics for an onboard NGVcylinder during filling could be presented as:

S·gen = dSC/dt – Q· /T∞ – m· isi ≥ 0 (17)

Here, all irreversibility assumed to be occurred from inlet toin-cylinder position. This makes an isentropic expansion fromreservoir to inlet position, which means si = sR. Consideringthis assumption and combining Equations (1, 7) and (17), thefollowing equation could be obtained:

(18)

Or in the following form:

(19) �S dt d m s m s U A T T T dtgen C C C R HC C C= − + −( )∞ ∞( ) /

�S d m s

dt

dm

dts U A T T Tgen

C C CR HC C C= − + −( )∞ ∞

( )/

u hm

mu hC R

Cs

CCs R= + −( )

u hU A T t

m

m

mu hC R

HC C av

C

Cs

CCs R= −

Δ+ −( )

Δ = −( )∞∫Tt

T T dtav Co

t1

d m u m h U A T T dtC C C Rs

r

HC C Co

t

( )− = − −( )∫ ∫ ∞

324

The above equation could be integrated from “start” offilling to “recent” time as below:

(20)

For a fuelling station with a single reservoir in which sR

remains constant throughout the filling process, the integrationof the above equation resulted to a simple equation as:

(21)

Equation (21) could be more simplified for an adiabaticsystem as:

(22)

And if the cylinder is empty at start of filling process(mCs = 0) the following relation could be obtained:

(23)

4 COMPUTING NATURAL GAS THERMODYNAMICSPROPERTIES

As discussed, a few thermodynamic properties of natural gashave to be calculated in order to analyze the filling process.These properties are density (or specific volume), internalenergy and entropy. The method for calculating theseproperties are discussed in this section. The detailed methodsfor calculating most of natural gas thermodynamic propertiesare presented in Farzaneh-Gord and Rahbari [29-30]. Thethermodynamics relationship presented here, could be alsofound in most of thermodynamic text books including Moranand Shapiro [31].

4.1 AGA8 EOS

The general form of AGA8 EOS is presented as follows [19]:

P = ZρmRT (24)

In Equation (24), P is pressure, Z is compressibility factor,ρm is molar density, R is universal gas constant and T istemperature.

To calculate compressibility factor, the following equationis presented [19]:

(25)

In Equation (25), ρr is reduced density and defined asfollows:

ρr = K3ρm (26)

Z B C C Dm r n

n

n n

n

= + − += =

∑ ∑113

18

13

18

ρ ρ * * *

S m s sgen C C R,max ( )= −

S m s s m s sgen C C R Cs Cs R= − − −( ) ( )

S m s s m s sU A T t

Tgen C C R Cs Cs RHC C av= − − − +

∞

( ) ( )Δ

S d m s m sU A T T

Tdtgen C C C R

s

rHC C C

s

r

= − +−( )∫ ∫ ∞

∞

( )

where in Equation (26), K is mixture size parameter andcalculated using following equation [19]:

(27)

In Equation (27), xi is mole fraction of component i in themixture, xj is mole fraction of component j in mixture, Ki issize parameter of component i, Kj is size parameter ofcomponent j, Kij is binary interaction parameter for size andN is number of component in gas mixture. The values forthese parameters could be found in [19].

In Equation (25), B is second virial coefficient and givenby the following equation [19]:

(28)

In Equation (28), Bnij* and Eij are defined by the following

equations [19]:

(29)

Eij = Eij*(EiEj)

1/2 (30)

In Equation (29), Gij is defined by the following equation[19]:

(31)

In Equations (27) to (31), N is the number of componentin gas mixture, an, fn, gn, qn, sn, un, wn are the Equation ofState parameters, Ei, Fi, Gi, Ki, Qi, Si, Wi are thecorresponding characterization parameters and Eij

*, Gij* are

corresponding binary interaction parameters.

In Equation (25), Cn*; n = 1, ...,58 are temperature

dependent coefficients and defined by the following equation[19]:

(32)

In Equation (32), G, F, Q, U are the mixture parametersand defined by the following equations [19]:

(33)

(34)G x G x x G Gi i

i

N

i

j i

N

j ij

i

N

i= + − += = +=

−

∑ ∑∑1 11

1

2 1( )(* GGj )

U x E x x Ui i

i

N

i

j i

N

j ij5

5

2

1

2

1

52 1=⎛

⎝⎜⎜

⎞

⎠⎟⎟ + −

= = +

∑ ∑ ( ))( )i

N

i jE E=

−

∑1

1 5

2

C a G g Q q F f U Tn n ngn

nqn

nfn

nun* ( ) ( ) ( )= + − + − + − −1 1 12 uun

GG G G

ijij i j=

+* ( )

2

B G g Q Q q

F F

nij ij ngn

i j nqn

i j

*

/ /

( ) ( )

(

= + − + − ×1 1

1 2 1 2 ++ − + − + −1 1 1f S S s W W wnfn

i j nsn

i j nwn) ( ) ( )

B a T x x B E K Knun

i j nij ijun

i j

j

N

i

N

n

= −

===

∑∑ * ( )3

2

111

118

∑

K x K x x Ki i

i

N

i

j i

N

j ij5

5

2

1

2

1

52 1=⎛

⎝⎜⎜

⎞

⎠⎟⎟ + −

= = +

∑ ∑ ( ))( )i

N

i jK K=

−

∑1

1 5

2

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 69 (2014), No. 2

M. Farzaneh-Gord et al. / Effects of Natural Gas Compositions on CNG Fast Filling Process for Buffer Storage System 325

(35)

(36)

where in Equation (33), Uij is the binary interactionparameter for mixture energy.

In Equation (25), Dn* is defined by the following equation:

(37)

Coefficients of Equation (37) are introduced in Reference[19].

Substituting Equation (25) to (37) in Equation (24), andby knowing the temperature, pressure and composition, theonly unknown parameter is molar density. The modifiedEquation (24) is then solved using Newton-Raphson iterativemethod to calculate the molar density [19].

The density of natural gas is then calculated by thefollowing equation:

ρ = Mwρm (38)

where, Mw is molecular weight of the mixture.

AGA8 EOS is developed for specific range of the naturalgas components. Table 2 shows range of the components towhich AGA8 EOS could be employed [19]. The range ofAGA8 suitability, made it well suited for CNG fillingprocess.

TABLE 2

Range of gas mixture characteristics in AGA8 model [19]

Component (mole%) Normal range Expanded range

Methane 45 to 100 0 to 100

Nitrogen 0 to 50 0 to 100

Carbon dioxide 0 to 30 0 to 100

Ethane 0 to 10 0 to 100

Propane 0 to 4 0 to 12

Total butanes 0 to 1 0 to 6

Total pentanes 0 to 0.3 0 to 4

Hexanes plus 0 to 0.2 0 to Dew point

Helium 0 to 0.2 0 to 3

Hydrogen 0 to 10 0 to 100

Carbon monoxide 0 to 3 0 to 3

Argon 0 0 to 1

Oxygen 0 0 to 21

Water 0 to 0.05 0 to Dew point

Hydrogen sulfide 0 to 0.02 0 to 100

D b c k cn n n n rkn

rbn

n rkn* ( ) exp( )= − −ρ ρ ρ

F x Fi i

i

N

==

∑ 2

1

Q x Qi i

i

N

==

∑1

4.2 Internal Energy Calculation (u)

Assuming internal energy as a function of temperature andmolar specific volume, the internal energy residual functionis defined as follows [31]:

(39)

In Equation (39), um is the molar internal energy for realgas and um,I is the molar internal energy for ideal gas. UsingEquation (24), partial differential relation in Equation (39)could be calculated by below equation [31]:

(40)

Substitute Equation (40) in Equation (39) and changingvariables of νm to ρm, the following equation for calculatinginternal energy could be obtained [31]:

(41)

Molar internal energy for ideal gas could be calculatedusing the following equation:

um,I = hm,I – Pνm = hm,I – RT (42)

In Equation (42), hm,I is the molar enthalpy for ideal gasand calculated using below equation:

(43)

where in Equation (43), hm, ij is the molar enthalpy for

ideal gas and for component j in the mixture. It could berepresented as [31]:

(44)

Coefficients in Equation (44) are given in Reference [31].hm,i0

j is the molar enthalpy for ideal gas of component j in themixture at reference state (25°C, 101.325 kPa).

Also, the internal energy per unit mass is defined asfollows:

(45)

4.3 Joule-Thomson Coefficient Calculation (μJ)

Joule-Thomson coefficient is defined as follows [31]:

(46)μJh

T

P=

∂∂

⎛

⎝⎜

⎞

⎠⎟

uu

Mm

w

=

h h a T b cc

Td em i

jm i

jj j j

jj j, , coth tanh= + +

⎛

⎝⎜

⎞

⎠⎟ −0

ee

Tj⎛

⎝⎜

⎞

⎠⎟

h x hm I j m ij

j

N

, ,==

∑1

u u RTZ

T

dm m I

m

m

m

m

− = −∂∂

⎛

⎝⎜

⎞

⎠⎟∫,

2

0

ρ

ρ

ρρ

∂∂

⎛

⎝⎜

⎞

⎠⎟ =

∂∂

⎛

⎝⎜

⎞

⎠⎟ = +

∂∂

⎛

⎝⎜

⎞

⎠⎟

P

T

P

TR Z T

Z

Tm m

mν ρ ρ

ρmm

⎡

⎣⎢⎢

⎤

⎦⎥⎥

u u TP

TP dm m I

mm I

mm− =

∂∂

⎛

⎝⎜

⎞

⎠⎟ −

⎡

⎣⎢⎢

⎤

⎦⎥⎥→∞∫,

,ν

ν

νν

326

where μJ, is Joule-Thomson coefficient and h is enthalpy.Total differential for enthalpy related to temperature andmolar volume is [31]:

(47)

Considering the definition of Joule-Thomson coefficient,

, one could obtain the following relation for calculating

Joule-Thomson coefficient [31]:

(48)

Maríc [23] calculated Joule-Thomson coefficient fornatural gas mixtures using AGA8 EOS and obtained similarresults.

4.4 Entropy Calculation (s)

Using one of Maxwell’s relations, the following relationship forentropy could be derived [31]:

(49)

In Equation (49), sm is the molar entropy. By integratingEquation (49) to the specific molar volume and changingvariables, the following equation for molar entropy could beobtained [31]:

(50)

In Equation (50), sm is the molar entropy for real gas andsm, I is the molar entropy for ideal gas. Molar entropy for idealgas defines as follow:

(51)

In Equation (51), sm, ij is the molar entropy for ideal gas of

component j in the mixture which could be presented asbelow:

(52)

In Equation (52), sm, ij(T) is the molar entropy for ideal gas

of component j that is a function of the temperature and isdefined by the following equation [31]:

(53)

s T s a Ln T

bc

T

c

T

m ij

m ij

j

jj j

, ,( ) ( )

coth

= +

+⎛

⎝⎜

⎞

⎠⎟

⎛

0

⎝⎝⎜

⎞

⎠⎟ −

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥

−⎛

Lnc

T

de

T

j

jj

sinh

⎝⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟ −

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

⎡

⎣coth cosh

e

TLn

e

Tj j⎢⎢

⎢

⎤

⎦⎥⎥

s T P x s T RLn x Pm ij

j m ij

j, ,( , , ) ( ) ( )= −

s x sm I j m ij

j

N

, ,==

∑1

s s R Z TZ

T

dm m I

m

m

m

m= − +∂∂

⎛

⎝⎜

⎞

⎠⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥

∫,ρ

ρ ρρ0

∂∂

⎛

⎝⎜

⎞

⎠⎟ =

∂∂

⎛

⎝⎜

⎞

⎠⎟

s P

Tm

m T mν ν

μ

νν

Jh

m

Pm

m P

T

P

TT

C=

∂∂

⎛

⎝⎜

⎞

⎠⎟ =

∂∂

⎛

⎝⎜

⎞

⎠⎟ −

⎡

⎣⎢

⎤

⎦⎥

,

∂∂

⎛

⎝⎜

⎞

⎠⎟

T

P h

dh C dT TT

dPm m P mm

P

= + −∂∂

⎛

⎝⎜

⎞

⎠⎟

⎡

⎣⎢

⎤

⎦⎥, ν

ν

In Equation (53), sm, i0j is the molar entropy at reference

temperature. Coefficients for Equation (53) are given inReference [32]. Entropy per unit mass then could be calculatedas follows:

(54)

5 THE NUMERICAL PROCEDURE

The procedure for computing the natural gas in-cylinderproperties begins by knowing the initial conditions (pressureand temperature). The other initial thermodynamic properties(including hR = uR + (pv)R) are calculated by employingAGA8 EOS discussed in Section 4. Equation (2) (or 3) isemployed to calculate the inlet mass flow rate. Equation (1)is then employed to compute the in-cylinder mass andconsequently specific volume within the cylinder using firstorder Euler numerical scheme. Similarly, Equation (15) issolved to calculate the in-cylinder specific internal energy ofhydrogen at the new time step. Upon determination ofspecific internal energy and specific volume, other propertiesare found from the AGA8 EOS by the trial and error method.

6 RESULTS AND DISCUSSION

In this study, the NGV onboard cylinder is considered as alump adiabatic system as a result, the orifice size and inletmass flow rate, have no effect on the final in-cylinder tem-perature and pressure. The orifice diameter and the cylindervolume were considered to be 1 mm and 67 liters respectively.The discharge coefficient is also assumed to be one. Theresults have been presented here for a single reservoir storageas shown in Figure 2.

The Joule-Thomson coefficient (μJ) plays an importantrole during filling process. A gas with positive μJ, cools uponexpansion. The rate of change of temperature with respect topressure directly related to the coefficient value. It is instruc-tive to examine the coefficient during the filling process.Figure 3 shows the effects of natural gas compositions on thein-cylinder μJ coefficient during the filling process with initialconditions of 300 K and 0.101325 MPa. It could be noticed

ss

Mm

w

=

Ti , Pi, m·

iReservoir tankPR , TR

Onboard CNG cylinderPc , Tc

T∞

Figure 2

A schematic diagram of thermodynamic system.

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 69 (2014), No. 2

M. Farzaneh-Gord et al. / Effects of Natural Gas Compositions on CNG Fast Filling Process for Buffer Storage System 327

that, there is a jump in μJ profiles during early part of filling.The μJ coefficient is positive throughout of the filling so thetemperature should drop as pressure reduces. Comparing theμJ values for various gases, the μJ is higher for the gas withlower methane percentage in the composition (for currentstudy, the Pars natural gas).

Figure 4 shows the effects of natural gas compositions ondynamic in-cylinder temperature during filling with initialconditions of 300 K and 0.101325 MPa. Note, from Figure 4,that the in-cylinder temperature dips during the early stagesof charging before rising to a final value. The reason for the

dip in temperature profile, in the early part of the filling isresult of the μJ cooling effect, which the gas undergoes in theisenthalpic expansion through the orifice, from the 20.5 MPasupply pressure to the initially low 1 bar cylinder pressure.This cold gas mixes with and compresses the gas originallyin the tank, with the result that the combined mixed gas tem-perature initially reduces. The lowest in-cylinder temperatureoccurs when the highest coefficient encountered (see Fig. 3).When the compression and conversion of supply enthalpyenergy to cylinder internal energy overcomes the μJ coolingeffect, which becomes smaller as the cylinder pressureincreases (see Fig. 3), the mixed gas temperature in the cylinderbegins to increase. In this case, the cylinder gas temperatureis seen to rise. By comparing the temperature profiles, itcould be realized that the lowest temperature throughout offilling corresponds to the gas with lowest methane percent-age in the compositions (the gas with highest μJ coefficient).There is about 14 K temperature difference in the final in-cylinder temperature for the gas with the highest methanepercentage (Khangiran gas with 98% methane) and the gaswith lowest methane percentage (Pars gas with 87%methane). The figure clearly shows the significant effect ofthe natural gas compositions on the temperature profiles.

Figure 5 shows the mass flow rate profiles during fillingfor various natural gas compositions while initial (ambient)temperature and pressure kept constant at 300 K and 0.101325MPa. According to Figure 5, in early part of filling, mass flowrates are constant due to choking. Note from figure 5 that themass flow rate is highest for the gas with the lowest methanepercentage in the composition.This is mainly due to the higherdensity for such gas. The figure shows the significant effect ofthe natural gas compositions on the mass flow rate profiles.

28 28056 84 112 140 168 196 224 2520

7

2

1

3

4

5

6

Joul

e-T

hom

son

coef

ficie

nt (

K/M

Pa)

Time (s)

Pure methane

Khangiran

Turkman gas

Kangan

Pars

Figure 3

In-cylinder Joule-Thomson coefficient of studied natural gasduring the filling while initial conditions kept constant at 300 Kand 0.101325 MPa.

20151050

In-c

ylin

der

tem

pera

ture

(K

)

350

260

270

280

290

300

310

320

330

340

In-cylinder pressure (MPa)

Pure methane

Khangiran

Turkman gas

Kangan

Pars

Figure 4

In-cylinder temperature profiles for various natural gascompositions during CNG filling process while initialconditions kept constant at 300 K and 0.101325 MPa.

205 10 150

0.045

0.005

0.040

0.035

0.030

0.025

0.020

0.015

0.010

Mas

s flo

w r

ate

(kg/

s)

In-cylinder pressure (MPa)

Pure methane

Khangiran

Turkman gas

Kangan

Pars

Figure 5

Mass flow rate profiles for various natural gas compositionsduring the CNG filling process while initial conditions keptconstant at 300 K and 0.101325 MPa.

328

In Figure 6, the in-cylinder mass variation is shown. It isexpected that the in-cylinder mass would be higher for thegas with higher density. The density is higher for the gas withthe lower temperature and the methane percentage. Thein-cylinder temperature is also lower for the gas with a lowmethane percentage (see Fig. 4). Note from the figure 6 thatthe final in-cylinder mass (charged mass) is higher for thenatural gas with the lowest methane percentage. The chargedmass for the gas with the lowest methane percentage (Parsgas with 87% methane) is about 1.5 kg more than the gaswith the highest percentage (Khangiran gas with 98%methane). This again shows the significant effect of the naturalgas compositions on the filling process.

Figure 7 shows the effect of natural gas compositions ontime profiles. Note form figure 7 that there is a very smalldifference between the time profiles. The small effects of thecomposition on the profiles are due to two opposite effects.The inlet mass flow rate for the gas with lower methanepercentage is higher so the time should be lower. In otherhand, the in-cylinder mass is higher for such gas, so moretime is required for filling.

Previous studies [13-16] show that the initial in-cylinderand reservoir tank temperatures (which could be representedby ambient temperature) have big effects on the final NGVonboard in-cylinder properties. Figure 8 shows the effects ofambient temperature on final NGV onboard in-cylinder tem-perature for various natural gases. As it is evident fromFigure 8, the final in-cylinder temperature is higher for nat-ural gas with the more methane percentage. The significantpoint is that by increasing the initial (ambient) temperature,the final in-cylinder temperatures increases linearly.

Figure 9 shows the effect of the initial temperature on thecharged mass of an empty NGV onboard cylinder for variousnatural gases. As discussed previously, the charged mass hasthe direct impact on driving range of a NGV and one ofmost important problem associated with NGV industry. Asindicated in figure 9 the charged mass decreases sharply asambient temperature increases. The charged mass differenceamong the studied gases decreases as ambient temperatureincreases. There is a sharp increase in charged mass as tem-perature decreases so one could conclude that filling processshould be carried out during colder time (nights rather thandays).

20151050

10

0

1

2

3

4

5

6

7

8

9

In-c

ylin

der

mas

s (k

g)

In-cylinder pressure (MPa)

Pure methane

Khangiran

Turkman gas

Kangan

Pars

Figure 6

NGV onboard in-cylinder mass variations during fillingprocess for various natural gas compositions while initialconditions kept constant at 300 K and 0.101325 MPa.

20151050

Tim

e (s

)

300

0

250

50

100

150

200

Pure methane

Khangiran

Turkman gas

Kangan

Pars

In-cylinder pressure (MPa)

Figure 7

Time profiles for various natural gases during the CNGfilling process while initial conditions kept constant at 300 Kand 0.101325 MPa.

330320310300290280270260

Fin

al in

-cyl

inde

r te

mpe

ratu

re (

K)

400

280

380

300

320

340

360

Initial (ambient) temperature (K)

Pure methane

Khangiran

Turkman gas

Kangan

Pars

Figure 8

Effect of initial (ambient) temperature on final in-cylindertemperature for various natural gases.

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 69 (2014), No. 2

As mentioned previously, entropy generation is associatedwith thermodynamic irreversibilities. Irreversibilities destroythe available work in the filling station. As, the availablework is provided by the compressor, one could conclude thatas entropy generation is decreased, available workdestruction is decreased too. Figure 10 shows the entropygeneration variation for the studied natural gases duringfilling an empty cylinder. As it can be seen, the entropygeneration is highest during the early part of filling when thereservoir and cylinder differential pressure is highest. Itapproaches zero as the value of the differential pressurevanishes.

Figure 11 shows the entropy generation for the wholeprocess of filling of an empty cylinder. The entropygeneration for natural gas with highest methane percentage(Khangiran gas) is about 0.11 kJ/kg.K more than the gas withlowest methane percentage (Pars gas). This means that therequired work by the compressor increases as methanepercentage in natural gas composition increases.

CONCLUSION

The laws of thermodynamics and mass balance have beenused as theoretical tools to study the effects of natural gascompositions on the filling process and the final in-cylinderconditions of an onboard NGV cylinder. Based on AGA8EOS and thermodynamics relationships, the required proper-ties of natural gas mixtures have been computed. As entropygeneration is associated with the compressor input work, it isassumed that, as entropy generation reduces, compressorinput decreases too.

It is found that the time (filling time) required for bringingup the NGV onboard cylinder to its final pressure (20 MPa)for Pars natural gas type (with about 87% methane) is about15 seconds less than Khangiran natural gas (with about 98%methane). As filling time is between 260 to 275 seconds forstudied gases, one could conclude that the composition hassmall effect on the filling time.

The charged mass for the Pars gas (lowest methanepercentage in the composition with 87% methane) and theKhangiran gas (highest methane percentage in the composi-tion with 98% methane) are 8 and 9.6 kg respectively. Thisshows the significantly of natural gas compositions on thecharged mass (20% here). It should be pointed out that thecharged mass is directly related to driving range of a NGV.

M. Farzaneh-Gord et al. / Effects of Natural Gas Compositions on CNG Fast Filling Process for Buffer Storage System 329

330270 280 290 300 310 320260

Cha

rged

mas

s (k

g)15

6

7

8

9

10

11

12

13

14 Pure methane

Khangiran

Turkman gas

Kangan

Pars

Initial (ambient) temperature (K)

Figure 9

Effect of initial (ambient) temperature on charged mass forvarious Iranian natural gases.

Pars

0.38

Ent

ropy

gen

erat

ion

(kJ/

K)

0.60

0.30

0.50

0.40

0.30

0.20

0.10

Kangan

0.42

Turkmangas

0.44

Khangiran

0.49

Puremethane

0.50

Figure 11

Entropy generation for various Iranian natural gases.

30050 100 150 200 2500

Ent

ropy

gen

erat

ion

(kJ/

K)

0.9

0

0.1

0.4

0.5

0.6

0.7

0.8

0.3

0.2

Time (s)

Pure methane

Khangiran

Turkman gas

Kangan

Pars

Figure 10

Entropy generation variations during filling for variousIranian natural gases.

330

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The results also reveal that the entropy generation duringfilling the gas with lowest methane percentage is about 24%less than the gas with highest methane percentage.

Considering the above comments, one could conclude thatthe natural gas composition has big effects on the fillingprocess and the final in-cylinder conditions and should beconsidered as an important parameter for investigating thefilling process.

REFERENCES

1 Chauveron S. De (1996) Natural Gas for Vehicles, Oil Gas Sci.Technol. 51, 5, 729-741.

2 Tilagone R., Venturi S., Monnier G. (2006) Natural Gas - anEnvironmentally Friendly Fuel for Urban Vehicles: the SmartDemonstrator Approach, Oil Gas Sci. Technol. 61, 1, 155-164.

3 ISO 11439 (2000) Gas Cylinders - High Pressure Cylinders forthe Onboard Storage of Natural Gas as a Fuel for AutomotiveVehicles.

4 Kountz K. (1994) Modelling the Fast Fill Process in Natural GasVehicle Storage Cylinders, American Chemical Society Paper at207th National ACS Meeting, San Diego, CA (United States),13-18 Mar 1994.

5 Kountz K., Kenneth J., Blazek C., Christopher F. (1997) NGVFuelling Station and Dispenser Control Systems, report GRI-97/0398, Gas Research Institute, Chicago, Illinois, November.

6 Kountz K., Liss W., Blazek C. (1998) Method and ApparatusFor Dispensing Compressed Natural Gas, U.S. Patent 5,752,552,May 19.

7 Kountz K., Liss W., Blazek C. (1998) Automated Process andSystem For Dispensing Compressed Natural Gas, U.S. Patent5,810,058, Sept. 22.

8 Kountz K., Liss W., Blazek C. (1998) A New Natural GasDispenser Control System, Paper at 1998 International GasResearch Conference, San Diego, November 3.

9 Liss W.E., Richards M. (2002) Development of a Natural Gas toHydrogen Fuelling Station, Topical Report for U.S. DOE, GTI-02/0193, Sept.

10 Liss W.E., Richards M.E., Kountz K., Kriha K. (2003)Modelling and Testing of Fast-Fill Control Algorithms forHydrogen Fuelling, National Hydrogen Association Meeting,Washington DC, March.

11 Newhouse N.L., Liss W.E. (1999) Fast Filling of NGV FuelContainers, SAE Technical Paper 1999-01-3739.

12 Thomas G., Goulding J., Munteam C. (2002) Measurement,Approval and Verification of CNG Dispensers, NWML KT11Report.

13 Shipley E. (2002) Study of Natural Gas Vehicles (NGV) Duringthe Fast Fills Process, Thesis for Master of Science, College ofEngineering and Mineral Resources at West Virginia University.

14 Farzaneh-Gord M., Eftekhari H., Hashemi S., Magrebi M.,Dorafshan M. (2007) The Effect of Initial Conditions on FillingProcess of CNG Cylinders, The Second International Conferenceon Modelling, Simulation and Applied Optimization, AbuDhabi, UAE, March 24-27.

15 Farzaneh-Gord M. (2008) Compressed Natural Gas SingleReservoir Filling Process, Gas Int. Eng. Manage. 48, 6, 16-18.

16 Farzaneh-Gord M., Hashemi S.H., Farzaneh-Kord A. (2008)Thermodynamics Analysis of Cascade Reservoirs FillingProcess of Natural Gas Vehicle Cylinders, World Appl. Sci. J. 5,2, 143-149.

17 Farzaneh-Gord M., Deymi-Dashtebayaz M., Rahbari H.R.(2011) Studying Effects of Storage Types on Performance ofCNG Filling Stations, J. Nat. Gas Sci. Eng. 3, 334-340.

18 Kim K., Kim H., Kim B., Lee K., Lee K. (2009) Effect ofNatural Gas Composition on the Performance of a CNG Engine,Oil Gas Sci. Technol. 64, 2, 199-206.

19 AGA8-DC92 EoS (1992) Compressibility and SuperCompressibility for Natural Gas and other Hydrocarbon Gases,Transmission Measurement Committee Report No. 8, AGACatalog No. XQ 1285, Arlington, VA.

20 ISO-12213-2 (1997) Natural Gas Calculation of CompressionFactor-Part 2: Calculation Using Molar-Composition Analysis,ISO, Ref. No. ISO- 12213-2:1997(E).

21 Maríc I., Galovi´c A., S̆muc T. (2005) Calculation of NaturalGas Isentropic Exponent, Flow Meas. Instrum. 16, 1, 13-20.

22 Maríc I. (2005) The Joule–Thomson Effect in Natural Gas Flow-Rate Measurements, Flow Meas. Instrum. 16, 2, 387-95.

23 Maríc I. (2007) A Procedure for the Calculation of the NaturalGas Molar Heat Capacity, the Isentropic Exponent, and theJoule–Thomson Coefficient, Flow Meas. Instrum. 18, 1, 18-26.

24 Farzaneh-Gord M., Khamforoush A., Hashemi Sh., PourkhademNamin H. (2010) Computing Thermal Properties of Natural Gasby Utilizing AGA8 Equation of State, Int. J. Chem. Eng. Appl. 1,1, 20-24.

25 Bejan A. (1979) A Study of Entropy Generation in FundamentalConvective Heat Transfer, J. Heat Transfer 101, 3, 718-725.

26 Bejan A. (1982) Second-Law Analysis in Heat Transfer andThermal Design, Adv. Heat Transfer 15, 1, 1-58.

27 Bejan A. (1996) Entropy Generation Minimization, CRC, BocaRaton, NY.

28 National Iran Gas Company website available at: www.NIGC.ir.

29 Farzaneh-Gord M., Rahbari H.R. (2012) Numerical Proceduresfor Natural Gas Accurate Thermodynamics PropertiesCalculation, J. Engineer. Thermophys., 21, 3, October.

30 Farzaneh-Gord M., Rahbari H.R. (2011) Developing NovelCorrelations for Calculating Natural Gas ThermodynamicProperties, Chem. Process Engineer. J. 32, 4, 435-452.

31 Moran M.J., Shapiro H.N. (2007) Fundamentals of EngineeringThermodynamics, 6th Ed., Wiley, ISBN: 0471787353.

32 DIPPR® 801 (2004) Evaluated standard thermophysicalproperty values, Design Institute for Physical Properties,Sponsored by AIChE.

Final manuscript received in November 2011Published online in February 2013

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 69 (2014), No. 2