natural gas physical properties

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Natural Gas Physical Properties

Extracted from

•

Section 23: Physical Properties, GPSA Engineering Data Book

•

Tarek Ahmed, Equation of State and PVT Analysis, Gulf Publishing Co. Houston Texas, 2007.

Nomenclature used in natural gas physical properties equations as mentioned in GPSA Data Book

are listed as below.

Natural Gas Physical Properties of 20 Natural Gas Engineering Supplementary course note by Sarithdej PathanasethpongCreated on 10/13/2008 11:34:00 AM



Knowledge of pressure-volume-temperature (PVT) relationships and other physical and chemical

properties of gases are essential for solving problems in natural gas reservoir engineering. The properties

of interest include

• Apparent molecular weight, MW a

• Specific gravity, γ g

•

Compressibility factor, Z •

Gas density, ρ g

• Specific volume, ν

• Isothermal gas compressibility coefficient, c g

• Gas formation volume factor, B g

•

Gas expansion factor, E g

• Viscosity, μ g

Behavior of Ideal Gas

For ideal gas, following assumptions are stated:• The volume of gas molecules is insignificant compared with the total volume

occupied by gas.

•

No attractive or repulsive forces exist between molecules of gas.

• All collision of molecules are perfectly elastic.

Based on kinetic energy of gases, equation of state for ideal gas can be derived to express the

relationship existing between pressure, p, volume,V , and temperature, T , for a given quantity of moles of

gas, n. The mathematical equation is called the ideal gas law can be expressed as following:

pV = nRT

where p = absolute pressure, psia

V = volume, ft3

T = absolute temperature, ºR

n = number of moles of gas, lb-mole

R = universal gas constant = 10.73 psia-ft3/lb-mole. ºR

The number of lb-moles, n, is defined as weight of the gas, m, divided by the molecular weight, MW , or

n = m/MW

The ideal gas law the can be rewritten as

pV = (m/MW) RT

where

m = weight of gas, lb

MW = molecular weight, lb/lb-mole

Gas Density

Since density is defined as the mass per unit volume of substance, then the above equation can be

rearranged to estimate the gas density, lb/ft3 at any given pressure and temperature as following

ρ g = m/V = ( p.MW ) /RT




Apparent Molecular Weight, MW a

For gas mixture of ith component, the apparent molecular weight of the gas mixture is defined as

MW a = ∑ yi . MW i

where

MW a = apparent molecular weight of gas mixture

MW i = molecular weight of the ith component in the mixture

yi = mole fraction of component i in the mixture

Conventionally, mole fraction can be defined as

yi = ni /n = ni / ∑ ni

The weight fraction of a particular component, i, is defined as

wi = mi / m = mi / ∑ mi

The volume fraction of a particular component, i, is defined as

υi = V i / V = V i / ∑ V i

Therefore the mole fraction can be converted to weight fraction and vice versa using the following steps

1. Let the total number of gas in the system , n =1

2. From mole fraction, yi and number of mole, ni

yi = ni /n = ni

mi = ni MW i = yi MW i

3.

Calculate the weight fraction to give

wi = mi / m = mi / ∑ mi = yi MW i / ∑ yi MW i = yi MW i / MW a

4. Similarly,

yi = wi MW i / ∑ wi MW i

Standard Volume, V sc

The standard volume is defined as the volume of gas occupied by 1lb-mole of gas at the standardcondition, usually at 14.7 psia and 60 ºF. The standard volume of gas then can be calculated using the

ideal gas law to give

V sc = (1) RT sc / p sc = (1)(10.73)(520)/ (14.7)

= 379.4 scf/lb-mole

Specific Volume, ν, ft3/lb

The specific volume of gas is defined as the volume occupied by a unit mass of gas. For ideal gas

the property can be calculated using the equation

ν = V / m = RT / (p MW a ) = 1 / ρ g




Specific Gravity, γ g

The specific gravity is defined as the ration of gas density to that of the air. Both densities are

measured or expressed at the same pressure and temperature. Commonly, the standard pressure and

standard temperature are used in defining the gas gravity.

γ g = ρ g / ρair = MW a / 28.96

Behavior of Real Gas

In dealing with gas at very high pressure, the use of the ideal gas law may lead to errors as great as

500%, as compare to errors of 2-3 % at atmospheric pressure. Basically, the magnitude of deviations of

real gases from the conditions of ideal gas law increases with increasing pressure and temperature and

varies widely with composition of the gas.

Numerous equations of state have been developed to correlate pressure –volume – temperature

variables for real gases with experimental data. The gas compressibility factor, Z, has been introduced

into the ideal gas law to account for the departure of gases from ideality. The real gas equation is then

become pV = ZnRT

where the gas compressibility factor , Z , the dimensionless quantity, is defined as the ratio of actual

volume of n-moles of gas at T and p to the ideal volume of the same number of moles at the same T and p

Z = Vactual / Videal

The compressibility factor can be generalized for various composition with sufficient accuracy

using the following two dimensionless properties: pseudo-reduced pressure, p pr , and pseudo-reduced

temperature, T pr . These pseudo–reduced properties are defined as following

p pr = p / p pc

T pr = T / T pc

Where

p = system pressure, psia

p pr = pseudo-reduced pressure, dimensionless

T = system temperature, ºR

T pr = pseudo-reduced temperature, dimensionless

p pc , T pc = pseudo-critical pressure and temperature, respectively, defined as following

p pc = ∑ yi pci

T pc = ∑ yi T ci

Following Figure 23-3 of GPSA Data Book illustrates the calculation of pseudo-critical properties

for a natural gas mixture. Also as it is based on the concept of pseudo-reduced properties, Standing and

Katz(1942) presented a generalized gas compressibility factor chart as shown Figure 23-4. These chart is

generally reliable for natural gas with minor amount of non-hydrocarbon.




In case where the composition of natural gas is not available, the pseudo-critical properties, p pc

and T pc , can be predicted solely from specific gravity of the gas. Brown et al.(1948) presented a

graphical method for convenient approximation of the pseudo-critical pressure and the pseudo-critical

temperature of gases when only specific gravity of gas is available. The correlation is presented in Figure

3-1 . Later Standing (1977) expressed this graphical correlation as following forms.

For Case 1, natural gas system

T pc = 168 + 325 γ g – 12.5 γ g 2

p pc = 677 + 15.0 γ g – 37.5 γ g 2

For Case 2, wet gas system

T pc = 187 + 330 γ g – 71.5 γ g 2

p pc = 706 + 51.7 γ g – 11.1 γ g 2




Nonhydrocarbon Adjustment Methods

Two methods were developed to adjust the pseudo-critical properties of gases to account for the

presence of the presence of the non-hydrocarbon components: the Wichert-Aziz method ans the Carr-

Kobayashi-Burrows method.

Wichert-Aziz’s Correlation MethodFor natural gas contain H2S and/or CO2 frequently exhibit different compressibility factor

behavior than sweet gases. Wichert-Aziz (1972) developed a correlation which permits the use of the

Standing-Katz Z-factor chart by using a pseudo-critical temperature adjustment factor, ε, which is a

function of concentration of CO2 and H2S in the sour gas. This correction factor is then used to adjust the

pseudo-critical temperature and pressure according to the following expressions:

T’ pc = T pc - ε

p’ pc = [ p pc T’ pc] / [T pc + B(1 - B) ε]

whereT pc = pseudo-critical temperature, ºR

p pc = pseudo-critical pressure, psia

T’ pc = corrected pseudo-critical temperature, ºR

p’ pc = corrected pseudo-critical pressure, psia

B = mole fraction of H2S in gas mixture

ε = pseudo-critical temperature adjustment factor, defined mathematically as following

ε = 120[ A0.9 – A1.6] + [ B0.5 – B4.0]

where the coefficient A is the sum of the mole fraction H2S and CO2 in gas mixture:

A = γ H2S + γ CO2

Figure 23-8 below shows pseudo-critical temperature adjustment factor chart.




Carr-Kobayashi-Burrows’ Correction Method

Carr, Kobayashi, and Burrows (1954) proposed a simplified procedure to adjust the pseudo-

critical properties of natural gases when non-hydrocarbon components are present. The method can be

used then the composition of the natural gas is not available. The procedure is summarized into following

steps.1. Knowing the gas specific gravity, calculate pseudo-critical pressure and temperature by

applying Brown et al.’s correlations.

2. Adjust the estimated pseudo-critical properties by using the following expressions

T’ pc = T pc – 80 yCO2 + 130 yH2S – 250 y N2

p’ pc = p pc + 440 yCO2 + 600 yH2S – 170 y N2

where

T’ pc = the adjusted pseudo-critical temperature, ºR

T pc = the un-adjusted pseudo-critical temperature, ºR yCO2 = mole fraction of CO2

yH2S = mole fraction of H2S in the gas mixture

y N2 = mole fraction of N2

p’ pc = the adjusted pseudo-critical pressure, psia

p pc = the un-adjusted pseudo-critical pressure, psia

3.

Use the adjusted pseudo-critical pressure and temperature to calculated pseudo-reduced

properties.

4. Read or calculate the Z-factor from Chart.

Direct Calculation of Compressibility Factors

Several empirical correlations for calculating the Z-factor have been developed over the years

which were intended to accurately reproduce the Standing-Katz Z-factor chart. The most widely used

correlations are: Papay(1985), Hall-Yarborough, Dranchuk-Abu-Kassem, and Dranchuk-Purvis-

Robinson.

The Papay(1985) correlations are expressed as:

Z = 1 – [ 3.53 p pr / 10 0.9813 Tpr ] + [ 0.274 p2 pr / 10 0.8157 Tpr ]

Hall- Yaborough’s Method

Hall and Yaborough (1973) presented an equation of state that accurately represents the Standing

and Katz Z-factor chart. The coefficients of the correlation were determined by fitting the Starling-

Carnahan’s equation of state data with data taken from the Standing and Katz Z-factor chart. The

mathematical expression is as following;

Z = [0.06125 t p pr / Y ] exp[-1.2(1-t )2]

Where

p pr = pseudo-reduced pressuret = reciprocal of pseudo-reduced temperature (i.e. T pc /T )




Y = the reduced density; which can be obtained as a solution of the following term:

F(Y) = X 1 + [(Y + Y 2 + Y 3 – Y 4 ) / (1 – Y)] – X 2 Y 2 + X 3 Y X4 = 0

Where

X 1 = - 0.06125 p pr t exp[-1.2(1-t )2]

X 2 = (14.76 t – 9.76 t 2

+ 4.58 t 3

) X 3 = (90.7 t – 242.2 t 2 + 42.4 t 3)

X 4 = (2.18 + 2.82 t )

The Hall and Yaborough (1973) correlation is nonlinear equation and can be solved conveniently

for the reduced density Y by using the Newton-Raphson iteration technique. The computational

procedure for solving the Z equation at any specified pseudo-reduced pressure and pseudo-reduced

temperature is summarized into following steps.

1. Make an initial guess of unknown parameter, Y k , where k is an iteration counter. An

appropriate initial guess of Y is given by following relationshipY k = 0.0125 p pr t exp[-1.2(1-t )2]

2. Substitute this initial value in equation F(Y) and evaluate the non linear function. Unless

the correct value of Y has been initially selected, the F(Y) will have nonzero value.

3.

A new improved estimate of Y , that is Y k+1 is calculated from the following expression:

Y k+1 = Y k – f(Y k ) / f’(Y k )

where f’(Y k ) is obtained by evaluating the derivative of F(Y)equation at Y k or

f’(Y) = [(1 + 4Y + 4Y 2 -4Y 3 + Y 4 ) / (1-Y)4 ] – 2(X 2 )Y + (X 3 )(X 4 )Y (X 4-1)

4.

repeat step 2 and step 3 until error abs of [Y k - Y k +1] become smaller than the preset

tolerance. (say 10 -12)

5. The correct value of Y is then used to evaluate Z factor:

Z = [0.06125 t p pr / Y ] exp[-1.2(1-t )2]

The Hall and Yaborough (1973) correlation is not recommended for application if pseudo-reduced

temperature is less than 1.

Dranchuk and Abu-Kassem’s Method

Dranchuk and Abu-Kassem (1975) derived an analytical expression for calculating the reduced

gas density that can be used to estimate the gas compressibility factor. The reduced gas density ρr is

defined as the ratio of gas density at specified pressure and temperature to that of gas at its critical

pressure and temperature:

ρr = ρ / ρc = [ pMW a / (ZRT)] / [ pc MW a / (Z c RT c )]

= [ p / (ZT)] / [ pc / (Z cT c )]




The critical gas compressibility factor, Zc, is approximately 0.27 which leads to the following

simplified expression for reduced gas density, ρr , as expressed in terms of the reduce temperature, T r and

reduced pressure, pr :

ρr = 0.27 p pr /( Z T pr )

Dranchuk and Abu-Kassem (1975) proposed the following 11 –constant equation of state forcalculating the reduced gas density:

f ( ρr ) = ( R1) ρr – R2/ ρr +(R3 ) ρr 2 – (R4 ) ρr

5+ (R5 )(1+A11 ρr

2 ) ρr

2 exp[- A11 ρr

2] + 1 = 0

Where the coefficient R1 to R5 are expressed as R1 = A1 + A2/T pr + A3/T pr

3 + A4/T pr 4 + A5/T pr

5

R2 = 0.27 p pr / T pr

R3 = A6 + A7/T pr + A8/T pr 2

R4 = A9 [A7/T pr + A8/T pr 2]

R5 = [A10/T pr 3

]

The coefficient A1 – A11 are given;

A1 = 0.3265, A2 = -1.0700, A3 = -0.5339, A4 = 0.01569, A5 = -0.05165,

A6 = 0.5475, A7 = -0.7361, A8 = 0.1844, A9 = 0.1056, A10 = 0.6134,

A11 = 0.7210

The reduced gas density ρr equation can be solved by applying Newton and Raphson iteration

technique which can be summarized as following:

1.

Make initial guess of unknown reduced gas density ρr k at iteration counter k . an

appropriate initial guess of ρr k is given as

ρr = 0.27 p pr /( T pr )

2. Substitute initial value of ρr k into f ( ρr ) equation and evaluate the nonlinear function.

Unless the correct value of ρr k has been initially selected, the equation will give nonzero

value for the f ( ρr k )

3.

A new improved estimated of ρr , that is ρr k +1 , is calculated from the following expression

ρr k+1 = ρr

k – f( ρr k ) / f’( ρr

k )

where

f ‘( ρr ) = ( R1) + R2/ ρr 2+2(R3 )/ ρr

– 5(R4 ) ρr

4

+ 2(R5 ) ρr exp (-A11 ρr 2 ) [(1+2A11 ρr

3 ) - A11 ρr

2(1+ A11 ρr

2)]

4. Repeat step 2 and 3 n iteration until ther error of abosute( ρr

k - ρr

k+1) become smaller than

a preset tolerance, say 10-12

5. The correct value of ρr , is then used to evaluate for compressibility factor from the reduced

density equation as following expression

Z = 0.27 p pr /( ρr T pr )




The proposed correlation was reported to duplicate compressibility factors from the Standing-Katz

chart with an average absolute error of 0.585% and is applicable over the ranges 0.2 < p pr < 3.0 and 1.0 <

T pr < 3.0 .

Dranchuk-Puvis-Robinson Method

Dranchuk, Puvis, and Robinson (1974) developed a correlation based on the Benedict-Web-Rubintype of equation of state. Fitting the equation to 1500 data points from the Standing and Katz Z-factor

chart optimized the eight equations of the proposed equation. The equation has the following form:

1 + T 1 ρr + T 2 ρr 2+ T 3 ρr

5 + [T 4 ρr

5(1+A8 ρr

2 ) exp(- A8 ρr

2)] - T 5/ ρr = 0

Where

T 1 = A1 + A2/T pr + A3/T pr 3

T 2 = A4 + A5/T pr

T 3 = (A5 A6)/T pr

T 4 = A7/T pr 3

T 5 = 0.27 p pr /( T pr )

The reduced density, ρr is defined by the same function as expressed in Dranchuk and Abu-

Kassem (1975)’s method. The coefficients A1 through A8 have the following values:

A1 = 0.31506237

A2 = -1.0467099

A3 = -0.57832720

A4 = 0.53530771

A5 = 0.31506237

A6 = -1.0467099

A7 = -0.57832720

A8 = 0.53530771

The solution procedure of proposed equation of state is similar to that of Dranchuk and Abu-

Kassem. The method is valid within the following ranges of pseudo-reduced temperature and pressure:

1.05 < T pr < 3.0

0.2 < p pr < 3.0




Compressibility of Natural Gas (c g )Knowledge of the variability of fluid compressibility with pressure and temperature is essential in

performing many reservoir engineering calculations. For the liquid phase, the compressibility is small

and usually assumed to be constant. For gas phase, the compressibility is neither still nor constant.

By definition, the isothermal gas compressibility is the change in volume per unit volume for a

unit change in pressure, or in equation form as following:

c g = (1/V)( ∂V/ ∂ p)T

where c g = isothermal gas compressibility, 1/psi.

Differentiate the real gas equation ( V = nRTZ/p) with respect to pressure at constant

temperature, T gives

(∂V/ ∂ p) = nRT [1/p( ∂Ζ/ ∂ p) –Z/p2]

Substituting into the compressibility definition term produces the following generalized

relationship:

c g = 1/p – 1/Z (∂ Z/ ∂ p)T

for an ideal gas, Z = 1 and (∂ Z/ ∂ p)T = 0; therefore,

c g = 1/p

It is pointed out that the equation (c g = 1/p) is useful in determining the expected order ofmagnitude of the isothermal gas compressibility.

Transforming the generalized equation of gas compressibility in term of the pseudo-reduced

pressure and temperature by replacing p with ( p pr . p pc):

c g = 1/ ( p pr . p pc) – 1/Z (∂ Z/ ∂( p pr . p pc))Tpr

Multiply this equation by p pc , yields

c g . p pc = c pr = 1/ ( p pr ) – 1/Z (∂ Z/ ∂ p pr )Tpr

The term c pr is called the isothermal pseudo-reduced compressibility defined by the definition

c pr = c g . p pc

where

c pr = isothermal pseudo-reduced compressibility

c g = isothermal gas compressibility, psi -1

p pc = the pseudo-reduced pressure, psi

The value of (∂ Z/ ∂ p pr )Tpr can be calculated from the slope of the T pr isotherm line on the Standing and

Katz Z-factor chart.




Gas Formation Volume Factor

The gas formation volume factor is used to relate the volume of gas, as measures at reservoir

conditions, to the volume of gas as measured at standard conditions. This gas property is then defined as

the actual volume occupied by a certain amount of gas at a specified pressure and temperature, divided by

the volume occupied by the same amount of gas at standard conditions. The equation form is expressed

as:

B g = (V ) p,T / Vsc

Where

B g = gas formation volume factor, ft3/scf

(V ) p,T = volume of gas, as measures at pressure p and temperature T

Vsc = volume of gas at standard conditions

Applying the real gas equation of state and substituting for volume V , gives

B g = ( p sc /T sc ) . (ZT/p)

Assuming that the standard conditions are represented by p sc = 14.7 and T sc = 520 ºR, the preceding

expression can be reduced to :

B g = 0.02827 (ZT/p) in ft3/scf

In other field units, the gas formation volume factor can be expressed in bbl/scf to give:

B g = 0.005035 (ZT/p)

Reciprocal of gas formation volume factor, called the gas expansion factor , E g , then:

E g = 1/ B g

In term of scf/ ft3 , the gas expansion factor is

E g = 35.37 (p / ZT) in scf/ ft3

and

E g = 198.6 (p / ZT) in scf/ bbl




Gas Viscosity

The viscosity of fluid is a measure of the internal fluid friction to flow. If the friction between

layers of the fluid is small, that is, low viscosity, an applying shear force will result in a large velocity

gradient. As the viscosity increases, each fluid layer exerts a larger frictional drag on the adjacent layer

and the velocity gradient decreases. The viscosity of fluid is generally defined as the ratio of shear force

per unit area (i.e. shear stress) to the local velocity gradient ( i.e. shear rate). The viscosity is expressed interm of poises, centipoises, or micropoises. One poise equals a viscosity of 1 dyne-sec/cm2 and can be

converted to other units as following:

1 poise = 100 centipoise

= 1 x 106 micropoise

= 6.72 x 10-2 lb mass/ft-sec

= 20.9 x 10-3 lbf – sec/ft2

Gas viscosity is not commonly measured in the laboratory because it can be estimated precisely

from empirical correlations. Two popular methods that are commonly used in the petroleum industry are

the Carr-Kobayashi-Burrows correlation and the Lee-Gonzales-Eakin method which are described below.

Carr-Kobayashi-Burrows’ Method

Carr-Kobayashi-Burrows (1954) developed graphical correlations for estimating the viscosity of

natural gas as a function of temperature, pressure, and gas gravity. The graphical correlations are

presented in Figure 23.22 and Figure 23.24




The step procedures for applying the Carr-Kobayashi-Burrows’ correlations are summarized asfollowing:

1. Calculate pseudo-critical pressure, pseudo-critical temperature and apparent molecular weight

from the specific gravity or the known composition of natural gas. Correction for

nonhydrocarbon gas (N2, H2S,CO2) should be made if they are present in concentration greater

than 5 mole percent.

2. Obtain the viscosity of the natural gas at 1 atm (μ 1 atm) and the temperature of interest from figure

23.22 . The correction for nonhydrocarbon component on the viscosity of the natural gas at 1 atm

can be expressed as following:

μ1 = (μ1)uncorrected + (Δμ) N2 + (Δμ)CO2 + (Δμ)H2S

(Δμ are denoted for the viscosity correction due to the present of non hydrocarbon components)

3. Calculate the pseudo-reduced pressure and temperature.

4.

Obtain (μg/μ1) from Figure 23.24 at pseudo-reduced pressure and temperature. The term μg

represent the viscosity of the gas at required conditions.\

5.

The gas viscosity, μg, at the pressure and temperature of interest, is calculated by multiplying thevalue μ1 to the viscosity ration obtained from step 4.




Lee-Gonzales-Eakin’s Method

Lee-Gonzales-Eakin (1966) presented a semi-empirical relationship for calculating the viscosity

of natural gas. The proposed equation is given as following:

μ g = 10-4 K exp[ X ( ρ g /62.4)Y]

Where

K = [(9.4 + 0.02 MW a)T 1.5 ] / [209 + 19 MW a + T ]

X = 3.5 + (986 / T ) + (0.01 MW a)

Y = 2.4 -0.2 X

ρ g = gas density at reservoir pressure and temperature, lb/ft3

T = reservoir temperature, º R

MW a = apparent molecular weight of the gas mixture

The proposed correlation can predict viscosity value with a standard deviation of 2.7% and a

maximum deviation of 8.99%. The correlation is less accurate for gases with higher specific gravities.

The authors pointed out that the method cannot be used for sour gases.

Specific Gravity of Wet Gas

The specific gravity of wet gas, γg, is described by the weighted-average of the specific gravities

of the separated gas from each separator. This weighted average approach is based on the value of

separator gas/ oil ratio and the expression is shown as following:

γg = [∑ (R sep)i (γ sep)i + R st γst ]/ [∑ (R sep)i + R st ]

Where

n = number of separators

R sep = separator gas / oil ratio, scf/STBγ sep = separator gas gravity

R st = gas/oil ratio from the stock tank, scf/STB

γst = gas gravity from the stock tank

Foe wet gas reservoirs that produce liquid (condensate) at separator conditions, the produced gas

mixtures normally exist as a single gas phase in the reservoir and production tubing. To determine well

stream specific gravity, the produced gas and condensate must be recombined in the correct ratio to find

the average specific gravity of single-phase gas reservoir.

Let,

γw = well-stream gas gravity

γo = condensate (or oil) stock tank gravityγg = average surface gas gravity

MW o = molecular weight of the stock tank condensate (or oil)

r p = producing oil/gas ration (reciprocal of the gas/oil ratio, R s), STB/scf

therefore;

The average specific gravity of well stream is given by

γw = [γg + 4580 r p γo] / [1 + 133,000 r p (γo / MW o)]

In terms of gas/oil ration, R s, then,

γw = [γg R s + 4580 γo] / [ R s + 133,000 (γo / MW o)]




Standings(1974) gave the following correlation for estimating the molecular weight of the stock-

tank condensate:

MW o = 6084 / (API -5.9)

Where API is the API gravity of liquid as given by

API = 141.5/ γo – 131.5

For the range of 45º < API < 60º Eilerts(1947) proposed the following expression for the ratio of

γo/ MW o as a function of condensate stock-tank API gravity:

γo/ MW o = 0.001892 + 7.35 (10-5) API – 4.52 (10-8) (API)2

In retrograde and wet gas reservoir calculations, it is convenient to express the produced separated

gas as a function of the total system produced. The fraction of separated gas produced from the total

system is written as:

f g = n g /nt = n g /(n g + nl )

where

f g = fraction of the separated gas produced in the entire system

n g = number of moles of the separated gas

nl = number of moles of the separated liquid

nt = total number of moles of the well stream

For a total producing gas/oil ratio, R s , scf/STB, the equivalent number of moles of gas per STB asdescribed in specific volume of gas equation is

n g = R s/379.4

The number of moles of 1 STB of the separated condensate is given by

no = mass / molecular weight = (volume)(density) / MW o

or

no = (1)(5.615)(62.4) γo/ MW o = 350.4 γo/ MW o

in term of f g

f g = [ R s ] / [ R s + 133,000 (γo / MW o)]

When applying the material balance equation for gas reservoir, it is assumes that a volume of gas

in the reservoir will remain as a gas at surface conditions. When liquid is separated, the cumulative liquid

volume must be converted into an equivalent gas volume, V eq, and added to the cumulative gas production

for use in the material balance equation. If N p STB of liquid (condensate) has been produced, the

equivalent number of moles of liquid is given as

no = ( N p)(5.615)(62.4) (γo/ MW o) = 350.4 ( N p)( γo/ MW o)




Natural Gas Physical Properties of 20 Natural Gas Engineering Supplementary course note by Sarithdej Pathanasethpong

Expressing this number of moles of liquid as an equivalent gas volume at standard condition by

applying the ideal gas equation of state gives

V eq = no R T sc / p sc = 350.4 ( N p)( γo/ MW o) (10.73) (520) / 14.7

V eq = 133,000 ( N p)( γo/ MW o)

More conveniently, the equivalent gas volume can be expressed in scf/STB as

V eq = 133,000 ( γo/ MW o)

natural gas physical properties

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