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Chapter 3: Gas Properties
Chapter 3 G A S
P R O P E R T I E S
3.1
Introduction
3.2
Composition
3.3
Phase Behaviour
3.4
Real-Gas Law
3.5
Z-Factor
3.6
Compressibility
3.7
Condensate/Gas Ratio
3.8
Formation-Volume Factor
3.9
Viscosity
List of Symbols References
Gas Properties
3.1
INTRODUCTION
In this chapter we discuss the behaviour and properties of natural gas systems insofar as of interest for gas reservoir engineering. Since gas from subsurface reservoirs undergoes a series of changes in pressure and temperature before it is delivered to the sales gas line, the emphasis is on the pressure, volume and temperature (PVT) behaviour and related properties. The PVT behaviour of natural gas depends on its chemical composition. This composition may vary widely from reservoir to reservoir and may result in drastically different production behaviour. Therefore, we start out with a brief discussion on the chemical composition of natural gas. The changing pressures and temperatures encountered in the production of natural gas may precipitate complex phase behaviour phenomena in natural gas systems. For this reason we include here a qualitative discussion on the phase behaviour of hydrocarbon systems. In Chapter 4 we present a more detailed quantitative treatment of this topic. Apart from the general PVT behaviour we also discuss methods and techniques of predicting the gas properties of interest in reservoir engineering analyses and evaluations. They are mostly empirical but have reached a high degree of perfection to the extent that they can be used as a substitute for laboratory measurements. In fact, in many cases the composition is the only information required to evaluate gas properties.
3.2
COMPOSITION
The main constituents of natural gas are the volatile paraffins dominated by methane. In addition, natural gas may contain significant amounts of non-hydrocarbon gases, notably nitrogen, carbon dioxide and hydrogen sulfide. Minor quantities of the rare gases helium, argon and neon may also be present. As liquid water is always present in hydrocarbon-bearing formations, natural gas is also saturated with water vapour. The composition of natural gas is commonly expressed in mole fractions or mole percentages of its constituents. If natural gas and its constituents were to behave as ideal gases, molar volumes of the natural gas mixture and the individual gas components would be equal (Avogadrots Law) and thus mole fractions would be equal to volume fractions. Therefore, as a first approximation mole fractions or percentages may be thought of as volume fractions or percentages. Table 3.1 lists the compositions of natural gas from the Pars field, Iran (Ref. l ) , the Groningen field, The Netherlands (Ref. 2) and the Waterton field, Canada (Ref. 3). Indicated are the non-hydrocarbon components and the hydrocarbon components up to the heptanes. The heavier hydrocarbons are lumped together in the heptanes-plus fraction. This is the standard representation of the composition of a natural gas, as reported by commercial service laboratories. For reservoir engineering purposes, this representation is generally sufficiently detailed.
Gas Properties
Table 3 . 1
-
Composition of natural gas systems Mole Percentage
Component
Pars (Iran)
Nitrogen Carbon Dioxide Hydrogen Sulfide Methane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane Hexanes Heptanes-plus
1.70 3.28 0.66 89.24 2.20 0.51 0.12 0.13 0.06 0.04 0.06 0.24
Groningen Waterton (Netherlands) (Canada) 14.27 0.94
-
81.28 2.82 0.40 0.06 0.08
0.01 0.02 0.04 0.08
0.97 3.48 16.03 65.49 3.93 1.53 0.32 0.92 0.52 0.50 1.12 5.19
The composition of gas as reported by commercial service laboratories is based on measurements of dry (water-free) gas samples and thus does not include the water vapour. Suppose the mole fraction of water vapour in The composition the gas mixture at reservoir conditions is given by y of the gas mixture at reservoir conditions is then obrained by multiplying the reported mole percentages by the factor
.
As a first approximation, the water content of natural gas in the reservoir may be obtained by regarding water vapour and hydrocarbon gas as ideal gases. According to Dalton’s Law, the partial pressure of water in the gas mixture is equal to the vapour pressure of water at the reservoir temperature. The mole fraction of water vapour in the gas is then given by Yw = P,/PR’
py
where p
=
=
vapour pressure of water at reservoir temperature reservoir pressure.
For most practical conditions the mole fraction of water vapour and thus the correction factor Eqn ( 3 . 1 ) is very small indeed (See Exercise 3 . 1 ) and can be safely ignored in reservoir engineering calculations. Table 3 . 1 shows a wide variation in composition. Based on the composition of the gas, the following characterizations are used. Gases with a low content of the heavier hydrocarbons (Pars, Groningen) are called lean or & gases. Dry alludes to the low liquid condensate yield when reservoir gas is brought to the surface. Likewise gases that -29-
Gas Properties
are relatively rich in the heavier hydrocarbons (Waterton) are termed rich or wet.
-
The Groningen gas shows a relatively high concentration of non-hydrocarbons and as a consequence has a low heating value. For this reason it is called a low-calorific gas. The Pars gas is an example of a high-calorific gas.
-
Gases that contain significant amounts of hydrogen sulfide and carbon dioxide (Waterton) are called sour gases. Sweet gases (Groningen) contain negligible quantities of hydrogen sulfide. Sour gas systems are very corrosive and require special treatment to remove the hydrogen sulfide. Exercise 3.1
-
Water Content
Estimate the associated water groduction of a gaswell that is producing at a rate of 1 million m /d at standard conditions (15 degr.C and 1.01325 bar), assuming a reservoir temperature of 100 degr.C and a reservoir pressure of 300 bar. Solution At 100 degr.C the vapour pressure of water is approximately 1 bar. Thus, the mole fraction of water vapour in the mixture is 1/300 = 0.0033 (0.33 mole per cent). 1 kmol of gas at standard conditions occupies 23.63 m3. Hencg 1.0 3 million m /d at standard conditions corresponds to 1.0 x 10 / 5 23.64 = 0.423~105kmol/day. The water production rate is then 0.0033x0.423 x 10 = 139 kmol/day. For a mo ecular mass of water of 18 kg/kmol and a water density of 1000 kg/m the volumetric water rate becomes 139x18/1000 = 2.5 m /day.
i
3.3
PHASE BEHAVIOUR
A multicomponent natural-gas system may occur in the liquid or the gas phase, or both, depending on its pressure, temperature and composition. The phase behaviour of a natural-gas system of given composition is schematically illustrated in the pressure-temperature (PT) diagram shown in Fig. 3.1. In the PT diagram the two-phase area is indicated by the area within the locus B-C-D. Outside this area the system is either in the liquid or the gas state. The curve B-C marks the boundary between the liquid phase area above it and the two-phase area. Imagine a fluid cell charged with hydrocarbon fluid in the liquid state, thus at a pressure and temperature above curve B-C. Expansion of the cell volume causes the pressure within the cell to drop. At a certain pressure gas bubbles appear and move to the top of the cell. This pressure is called the bubble-point pressure and lies on the curve B-C which is therefore called a bubble-point curve.
Gas Properties
TEMPERATURE
Fig. 3.1
-
Pressure-Temperature Diagram of Hydrocarbon Mixture at Constant Composition
The curve C-D delineates the single-phase gas phase area and the twophase area. Here traversing the boundary from above leads to the formation of a liquid. For this reason, the locus C-D is called the dewpoint locus. The phenomenon of liquid formation upon reducing the pressure is known as retrograde condensation. The point C where the bubble-point and the dew-point loci meet is called the critical point. In this point the gas and liquid phases are identical and have equal physical properties. Other characteristic points on the phase boundary are the cricondentherm CT and the cricondenbar CB. The cricondentherm is the maximum temperature on the two-phase boundary; above the cricondenterm single-phase conditions exist regardless of the pressure. The cricondenbar is the maximum pressure on the two-phase boundary; two-phase conditions can only exist below the cricondenbar. Within the two-phase area one can draw curves of equal liquid saturation defined as the fractional volume occupied by liquid. On the bubblepoint locus the saturation is unity and on the dewpoint locus it is zero. Intersection of these iso-saturation lines with a vertical line yields an isothermal, constant-composition depletion curve. The shape of this curve depends greatly on the location of the vertical line with respect to the critical temperature. This is illustrated in Fig. 3.2 showing a depletion curve at a temperature below (curve a) and above the critical temperature (curve b), respectively. For the curve below the critical temperature the liquid saturation decreases with decreasing pressure. Above the critical temperature, however, the depletion curve exhibits a maximum due to retrograde condensation. At pressures below this maximum the curve shows the normal vaporizing behaviour: a decreasing liquid saturation with decreasing pressure.
Gas Properties
1
BUBBLE F
Fig. 3.2 Constant-Composition Depletion Curve at a Temperature Below (a) and Above (b) the Critical Temperature The location of the two-phase locus in the pressure-temperature diagram depends on the composition. This is schematically illustrated in Fig. 3.3 where we have depicted the locus of a lean gas and a rich gas. The locus of the lean gas encloses a relatively small area in the region of low temperatures and pressures. The rich gas exhibits a much larger twophase region extending to higher pressures and temperatures.
TEMPERATURE
Fig. 3.3
-
Phase Behaviour of a Lean and a Rich Natural Gas
Gas Properties
The location of the two-phase locus with respect to the pressure-temperature trajectory of the reservoir gas from reservoir to surface has given rise to the following important classification of hydrocarbon gas reservoirs: (i) dry-gas reservoirs, (ii) wet-gas reservoirs, and (iii) gas-condensate reservoirs. i. Dry-gas reservoirs The pressure-temperature trajectory always lies outside the two-phase boundary. Hence, the composition of the produced gas is always equal to that of the original reservoir gas and no associated liquids are produced. ii. Wet-gas reservoirs The reservoir temperature is higher than the cricondentherm. During reservoir depletion, the gqs mixture within the reservoir remains in the gas phase. Within the borehole or at the surface, however, the pressuretemperature trajectory of the gas enters the two-phase area. Hence condensate will drop out in the tubing or at the surface or both. If conditions at the surface remain constant, the liquid content of the wellstream also remains constant. iii. Gas-condensate reservoirs Here the reservoir temperature is lower than the cricondentherm but higher than the critical temperature. Thus liquid drop-out takes place within the reservoir. As a result the composition of the well stream, the surface gas and the surface condensate change continuously while the reservoir is being depleted. Also the liquid content of the well stream will change with time. From the reservoir engineering viewpoint there is no fundamental difference between dry-gas and wet-gas reservoirs. In both cases single-phase conditions are maintained within the reservoir throughout the depletion period. Dry-gas reservoirs are just a subset of wet-gas reservoirs, viz., wet-gas reservoirs with a zero condensate content in the well stream. 3.4
REAL-GAS LAW
The pressure-volume-temperature behaviour of an ideal gas (no interaction between the gas molecules) is described by the Law of Boyle-Gay Lussac also known as the Ideal-Gas Law
where p = pressure V = volume n = number of moles R T
= =
'
gas constant (8314,413 -or 10.732 psi.ft3 kmol .K 1bmol.degr.R 1 absolute temperature.
Real gases behave as ideal gases only at low pressures. At high pres-
Gas Properties
sures strong deviations from ideal gas behaviour may occur. The pressure-volume-temperature relation of real gases can be described by including in the Ideal-Gas Law a correction factor denoted by z
Equation (3.4) is known as the Real-Gas Law and the correction factor z is commonly called the gas-deviation-factor or simply z-factor. For ideal gases the z-factor is equal to unity. For real gases, it may be greater or less than unity depending on the pressure, temperature and composition of the gas. 2-factors can be measured in the laboratory on a representative gas sample, or alternatively, they may be calculated from the gas composition using empirical correlations (see 3.5 below). The Real-Gas Law combined with the relative molecular mass (molecular weight) provides a relation for gas density. Let the gas molecular mass be denoted by M. Thus, n moles of gas correspond to nM mass units. From Eqn (3.4) it then follows for the gas density that
A widely used parameter to indicate the density ofta gas is the gas
gravity y, defined as the ratio of the gas density and the air density, both taken at standard conditions. At standard conditions the z-factor is very close to unity and the density at standard conditions is therefore given by
Applying Eqn (3.6) to the gas and to (dry) air we obtain for the gas gravity y
where p
M~~~
= =
density of (dry) air at standard conditions molecular mass of (dry) air.
Hence, gas gravity is directly proportional to molecular mass. In the case of pure methane, the gas gravity is 0.0345~16= 0.55. Exercise 3 . 2 - Molecular Mass and Gas Gravity Calculate the molecular mass and gas gravity for the Pars and Waterton gases of Table 3.1. For the molecular mass of the individual gas components refer to Appendix B.
Gas Properties
Solution Pars
Waterton
Component Nitrogen Carbon Dioxide Hydrogen Sulfide Methane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane Hexanes Heptanes-plus Molecular Mass Gas gravity
0.0345x17.8816 = 0.617
Z-factors for natural gases can be obtained from the empirical z-factor chart of Standing and Katz (Ref. 4) which is reproduced in Fig. 3.4. This chart employs as correlation parameters the reduced pressure p and reduced temperature T which are defined by pr = p/pCp
and T
=
T/Tcp,
where p = pseudo-critical pressure T~~ = pseudo-critical (absolute) temperature. CP The pseudo-critical pressure and temperature are defined by PCP
=CyiTci, cP where y = mole fraction of component i in the mixture i p . = critical pressure of component i ::T = critical (absolute) temperature of component i. =
C Yipci
and
T
The choice of these reduced correlation parameters is based on the Principle of Corresponding States. Very briefly, this Principle states that properties of single-component fluids, and thus z-factors, are approximately equal if the fluids are in corresponding states, that is if the ratios of actual to critical pressure and of actual to critical temperature (in absolute units) for each fluid are the same.
Gas P r o p e r t i e s
Pseudo reduced pressure
Fig. 3 . 4
-
Standing-Katz 2-Factor Chart (Courtesy of SPE)
Gas Properties
Kay has shown (Ref. 5) that the Principle of Corresponding States can be extended to gas mixtures. In that case the pressure and temperature are to be expressed as a ratio of the pseudo-critical pressure and temperature of the mixture as defined above. This pseudo-critical pressure and temperature should not be confused with the physical critical pressure and temperature of a gas mixture as defined in the PT diagram. They are fictitious quantities to be used for correlation purposes only. The Standing and Katz chart is based on measured z-factors of natural gases that contained very little non-hydrocarbons. It covers a reduced pressure and temperature range of
<
0
pr
<
15
and
1
<
Tr
<
3.
(3.10)
The Standing and Katz chart may also be used for sour gases, provided the pseudo-critical temperature and pressure are corrected as indicated by Wichert and Aziz (Ref. 6). The corrected pseudo-critical pressure and temperature, denoted by an asterisk, are given by
T
* CP
= T -ATwa, CP
where ATwa
yHZS
=
=
)O. 9
)1.6
a[(yCO2
+
Y~~~
where a
=
120 degr.Rankine or 66.666 Kelvin
-
('~02
+
'~25
mole fraction of H S 2
yCO2 = mole fraction of CO 2' Application of the Standing-Katz chart requires knowledge of the composition of the gas to calculate the pseudo criticals. Alternatively, if the gas composition is not known, the pseudo criticals may be estimated from Standing's correlation for either 'surface gases' or 'condensate gases', in which gas gravity is used as correlation parameter (Ref. 7). The surface-gas correlation is based on measurements of surface trap gases and stock-tank vapours and reads =
P c ~
677.0 + 15.0 y - 37.5 y
2
(pCp in psi)
(3.14)
The condensate-gas correlation is based on measurements of laboratorygenerated gases in equilibrium with crude oils at high pressure and is given by
-
P c ~
706.0-51.7 y - 11.1 y'
(pcp in psi)
(3.16)
Gas Properties
A number of analytical methods have been proposed to reproduce the Standing and Katz chart. A very accurate, powerful and yet simple method is the one advanced by Hall and Yarborough (Ref. 81, according to which z-factors can be approximated by the following relation
where a
=
-0.06125(pr/Tr)exp[-1.2(1
2 - 1/~,) ]
Equation (3.18) is an implicit equation that must be solved iteratively. The following scheme, based on the Newton-Raphson method (Ref. 9 ) , works very well and converges within three to four iterations. Step 1. Take Y
=
0 for the first estimate.
Step 2. Update Y using the Newton-Raphson approximation formula
where the prime denotes differentiation with respect to Y. Step3. Calculate z byz=-a/Y new new' Repeat step 2 until satisfactory precision is obtained. The Hall and Yarborough correlation is valid up to a reduced pressure of 25 which is substantially beyond the Standing and Katz chart range. Using the method below T = 1 is not recommended. Exercise 3.3
-
Gas Density and z-factor
Estimate the z-factor and density for the Pars and Waterton gases of Table 3.1, using the Katz-Standing chart Fig. 3.4 assuming a temperature of 100 degr.C and a pressure of 300 bar. The critical temperature and pressure of the individual components are given in Appendix B.
Gas P r o p e r t i e s
Solution Pars Component
yixlo0
Pci
Yipci
bar
bar
T . cl K
YiTci K
Nitrogen Carbon Dioxide Hydrogen S u l f i d e Methane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane Hexanes Heptanes-plus IyipCi
= 46.1836
Wichert-Aziz c o r r e c t i o n :
From t h e Standing-Katz c h a r t : z = 0 . 9 9 8 The d e n s i t y i s t h e n g i v e n by (Eqn (3.5))
I Y ~= 196.6183 T ~ ~
Gas Properties
Waterton Component
yixl0O
'ci
'iPci
bar
bar
Tci
K
'iTci
K
Nitrogen Carbon Dioxide Hydrogen Sulfide Me thane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane Hexanes Heptanes-plus
Wichert-Aziz correction:
From the Standing-Katz chart: z
3.6
=
0.87
COMPRESSIBILITY
The gas compressibility is defined as the relative volume increase per unit pressure drop at a constant temperature. In formula form
In the case of an ideal gas (pV
For real gases (pV
=
=
nRT), the compressibility becomes
nzRT) Eqn (3.20)
yields
Gas Properties
Hence, for ideal gases the compressibility is simply the reciprocal of the pressure. For real gases a correction is to be applied that depends on the pressure dependence of the z-factor. The derivative in Eqn (3.22) may be approximated with the well-known central difference formula. Let three successive pressures be given by P - ~ ,po and p+ I ' The derivative at the pressure po then follows from
Exercise 3.4
-
Compressibility
Calculate the compressibility of the Pars gas at a pressure of 275 bar and a temperature of 100 degr.C. Solution To calculate the derivative of the z-factor, we take a pressure interval of 50 bar around the pressure of 275 bar. The d-factors at 250, 275 and 300 bar are listed below. pressure
r'
z-factor
According to Eqn (3.221, the compressibility at 275 bar is given by
By comparison, the ideal-gas compressibility at a pressure of 275 bar is given by
The condensate content of natural gas may be expressed by the condensate/gas ratio either on a molar or on a volumetric basis. Suppose that n moles of natural gas, when brought to the surface, split into nG moles of gas and n moles of liquid condensate. The molar condensate/gas ratio, denoteg by RMLG, is then simply defined by
The volumetric condensatei'gas ratio is defined as the ratio of the volume of condensate at stock-tank conditions, VLst, and the volume of gas at standard conditions, VGsc. Thus
Gas Properties
The volume of gas at standard conditions is related to the number of moles of gas by the Ideal-Gas Law and given by
The volume of condensate is related to moles of condensate by
= molecular mass of liquid condensate where ML pLst = density of condensate at stock-tank conditions.
Combining Eqns (3.24) - (3.27), we obtain for the relation between the volumetric and molar condensate/gas ratio
Strictly speaking, the condensate/gas ratio is not a property of natural gas per se, for it depends not only on gas composition but also on the conditions under which separation at the surface is carried out (see Chapter 4 , section 5). If surface conditions remain the same, the condensate/gas ratio is a constant for wet-gas reservoirs and for gas-condensate reservoirs above the dewpoint pressure. In the latter case, the condensate/gas ratio of the produced gas starts declining as soon as the reservoir pressure falls below the dewpoint pressure of the gas. Exercise 3.5
-
Condensate/Gas Ratio
Calculate the molar condensate/gas ratio of a Waterton 3gas well psoducing at a volumetric condensate/gas ratio of 0.5 m /(lo00 m ) at standard conditions for the condensate properties and standard conditions listed below condensate molecular mass: density stock-tank condensate: standard pressure: standard temperature:
125 750 1.013 15
kg/kmol kg/m3 bar degr.C
Solution Application of Eqn (3.28) gives
3.8
FORMATION-VOLUME FACTOR
The formation-volume factor of gas is the ratio of a volume of gas at reservoir conditions to the volume of surface gas at standard conditions that results from bringing that volume to the surface. Let us consider n
Gas Properties
moles of reservoir gas. The volume occupied by these n moles at reservoir conditions, VGR, follows from the Real-Gas Law and is given by
In the case of a dry-gas reservoir, all the reservoir gas is converted to surface gas. According to the Ideal-Gas Law, n moles of surface gas of at standard conditions occupy a volume V Gsc
Combining Eqns ( 3 . 2 9 ) and ( 3 . 3 0 ) , we obtain for the gas formation volume factor
In the case of a wet gas, the well stream splits into a gas and a liquid phase and the expression for the formation-volume-factor becomes slightly more involved. Let us suppose the well stream, consisting of n moles, splits into nL liquid moles and nG gas moles. The volume occupied by the n moles at reservoir conditions again follows from the Real-Gas Law and is given by
Likewise, it follows from the Ideal-Gas Law for the volume of gas occupied by n gas moles at standard conditions that G
Combining Eqns ( 3 . 3 2 ) and ( 3 . 3 3 ) , we then obtain for the formation volume factor of a wet gas
where RHLG = molar condensate/gas ratio ( = n /n ) . L G Hence, the formation-volume factor for wet gas is to be corrected for the condensate content. Gas formation-volume factors are used to convert a volume ervoir conditions to a volume at standard conditions. Let ume of the reservoir occupied by hydrocarbons be given by mount of gas-in-place expressed in the volume at standard then reads
of gas at resthe pore volVhc. The aconditions
Like the condensate/gas ratio, the gas formation-volume-factor is not a
Gas Properties
true gas property either. It depends not only on the type of gas but also on the prescribed standard conditions and on the separator conditions through the condensate/gas ratio. Standard conditions are not standardized and may vary form country to country. In the USA the standard temperature is 60 degr.F, but the standard pressure depends on the geographical location and varies from 14.65 psi (e.g. Texas) to 15.025 psi (e.g. Louisiana). In Canada and Europe the standard conditions are 15 degr.C and 1.01325 bar ( = 1 atm) but in Europe gas reserves are usually reported in 'normal' conditions defined as 1.01325 bar and 0 degr.C. Hence, whenever gas formation-volume factors and gas volumes at standard conditions are reported, the standard conditions must be specified. Exercise 3.6 - Formation-Volume Factor Calculate the formation-volume factor for the Pars and Waterton gas at the following conditions: reservoir temperature: reservoir pressure: standard pressure: standard temperature: molar condensate/gas ratio Pars Waterton
100 300 1.01325 15
degr.C bar bar degr.C
0 rnol/mol 0.071 mol/mol
Solution Pars:
Waterton:
3.9
VISCOSITY
Viscosity of fluids is a measure for the internal resistance of fluids to flow. The viscosity of reservoir gases can be described by Newton's Viscosity Law which states that at any point the shear force per unit area is proportional to the local velocity gradient perpendicular to the flow direction. By definition the proportionality constant is called the viscosity of a fluid. Viscosities depend on pressure, temperature and composition.
A great number of empirical and semi-empirical viscosity prediction methods are available (Ref. 10). One of the most popular methods for the prediction of viscosity of natural gases is that proposed by Lee et al. (Ref. ll), according to which viscosities of natural gases can be predicted by the following relation
Gas Properties
where K =
(9.4 + 0.02 M ) T ~ . ~ 209 + 19M + T
where p = viscosity (microPoise) T = absolute temperature (degr.Rankine M = molecular mass. 3 p = gas density (g/cm )
=
1.8 x K)
Hence as input this relation requires the molecular mass, the gas density, the pressure and the temperature. The relative molecular mass can be obtained from the composition. The density can be calculated using Eqn (3.5) where the z-factor can be obtained from the Standing-Katz chart or from the Hall-Yarborough z-factor correlation Eqn (3.18). Lee et al.'s relation allows of the prediction of viscosities of natural 3 per cent and with a maximum devigases with a standard deviation of ation of approximately 10 per cent. For most reservoir engineering purposes this is sufficiently accurate.
*
Exercise 3.7
-
Viscosity
Calculate the viscosity of the Pars and Waterton gas at a pressure of 300 bar and a temperature of 100 degr.C. Solution The molecular mass, z-factor and density of the Pars and Waterton gas are listed below.
M (g/cm3) Pars :
Waterton:
Pars
Waterton
17.88 0.998 0.173
27.25 0.870 0.305
(Exercise 3.2) (Exercise 3.3) (exercise 3.3)
Gas Properties
Gas Properties
LIST OF SYMBOLS Latin
B
=
c F G n
=
n~ n MG
=
= = = = =
gas formation volume factor gas compressibility correction factor for water content gas-in-place number of moles of reservoir gas number of moles of surface condensate number of moles of surface gas molecular mass (molecular weight) molecular mass of air molecular mass of surface gas molecular mass of surface condensate molecular mass component i pressure critical pressure component i pseudo-critical pressure reduced pressure reservoir pressure standard pressure vapour pressure of water gas constant molar condensate/gas ratio volumetric condensate/gas ratio at standard conditions absolute temperature critical temperature component i pseudo-critical temperature reduced temperature absolute standard temperature volume volume of condensate at stock-tank conditions volume gas at reservoir conditions volume surface gas at standard conditions hydrocarbon pore volume mole fraction component i mole fraction of water gas deviation factor or z-factor
Greek
Y ATwa lJ P
.cs'f
=
=
=
= = =
'asc = P~st
gas gravity Wichert-Aziz correction viscosity gas density gas density at standard conditions air density at standard conditions density of stock-tank condensate
Gas Properties
REFERENCES 1. Nematizadeh, F. and Betpolice, A.: 'Pars Offshore Gas Field Development", EUR paper 104 presented at the European Offshore Petroleum Conference & Exibition, Oct. 24-27, 1978. 2. de Ruiter, H.J., van der Laan, G. and Udink, H.G.: "Development of the North Netherlands Gas Discovery in Groningen", Geologie en Mijnbouw (July 1967) 46, no. 7, 225-264. 3. Castelijns, J.H.P. and Hagoort, J.: "Recovery of Retrograde Condensate from Naturally Fractured Condensate-Gas Reservoirs", Soc. Pet. Eng. J. (December 1984), 719-717. 4. Standing, M.B. and Katz, D.L.: "Density of Natural Gases", Trans. AIME, 146 (1942), 140-149. 5. Kay, W.B. : "Density of Hydrocarbon Gases and Vapors at High Temperature and Pressure", Ind. Eng. Chem., 28, (1936), 1014-1019. 6. Wichert, E. and Aziz, K.: "Calculate 2's for Sour Gases", Hydr. Proc. 51 (May 1972). 7. Standing, M.B.: "Volumetric and Phase Behaviour of Oilfield Hydrocarbon Systems", Soc. Pet. Eng. of AIME Dallas (1977), Appendix 11. 8. Hall, K.R. and Yarborough, L.: "A New Equation-of-state for Z-Factor Calculations", Gas Technology, SPE Reprint Series no. 13, vol. 1 (1977). 9. Scheid, F.: "Numerical Analysis", Schaumls Outline Series, McGrawHill Book Company (1968). 10. Reid, R.C., Prausnitz, J.M. and Sherwood, Th. K.: "The Properties of Gases and Liquids", McGraw-Hill Book Co., Third Edition, 1977. 11. Lee, A.L., Gonzalez, M.H. and Eakin, B.E.: "The Viscosity of Natural Gases", Gas Technology, SPE Reprint Series no 13, vol. 1 (1977).
P R O P E R T I E S
3.1
Introduction
3.2
Composition
3.3
Phase Behaviour
3.4
Real-Gas Law
3.5
Z-Factor
3.6
Compressibility
3.7
Condensate/Gas Ratio
3.8
Formation-Volume Factor
3.9
Viscosity
List of Symbols References
Gas Properties
3.1
INTRODUCTION
In this chapter we discuss the behaviour and properties of natural gas systems insofar as of interest for gas reservoir engineering. Since gas from subsurface reservoirs undergoes a series of changes in pressure and temperature before it is delivered to the sales gas line, the emphasis is on the pressure, volume and temperature (PVT) behaviour and related properties. The PVT behaviour of natural gas depends on its chemical composition. This composition may vary widely from reservoir to reservoir and may result in drastically different production behaviour. Therefore, we start out with a brief discussion on the chemical composition of natural gas. The changing pressures and temperatures encountered in the production of natural gas may precipitate complex phase behaviour phenomena in natural gas systems. For this reason we include here a qualitative discussion on the phase behaviour of hydrocarbon systems. In Chapter 4 we present a more detailed quantitative treatment of this topic. Apart from the general PVT behaviour we also discuss methods and techniques of predicting the gas properties of interest in reservoir engineering analyses and evaluations. They are mostly empirical but have reached a high degree of perfection to the extent that they can be used as a substitute for laboratory measurements. In fact, in many cases the composition is the only information required to evaluate gas properties.
3.2
COMPOSITION
The main constituents of natural gas are the volatile paraffins dominated by methane. In addition, natural gas may contain significant amounts of non-hydrocarbon gases, notably nitrogen, carbon dioxide and hydrogen sulfide. Minor quantities of the rare gases helium, argon and neon may also be present. As liquid water is always present in hydrocarbon-bearing formations, natural gas is also saturated with water vapour. The composition of natural gas is commonly expressed in mole fractions or mole percentages of its constituents. If natural gas and its constituents were to behave as ideal gases, molar volumes of the natural gas mixture and the individual gas components would be equal (Avogadrots Law) and thus mole fractions would be equal to volume fractions. Therefore, as a first approximation mole fractions or percentages may be thought of as volume fractions or percentages. Table 3.1 lists the compositions of natural gas from the Pars field, Iran (Ref. l ) , the Groningen field, The Netherlands (Ref. 2) and the Waterton field, Canada (Ref. 3). Indicated are the non-hydrocarbon components and the hydrocarbon components up to the heptanes. The heavier hydrocarbons are lumped together in the heptanes-plus fraction. This is the standard representation of the composition of a natural gas, as reported by commercial service laboratories. For reservoir engineering purposes, this representation is generally sufficiently detailed.
Gas Properties
Table 3 . 1
-
Composition of natural gas systems Mole Percentage
Component
Pars (Iran)
Nitrogen Carbon Dioxide Hydrogen Sulfide Methane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane Hexanes Heptanes-plus
1.70 3.28 0.66 89.24 2.20 0.51 0.12 0.13 0.06 0.04 0.06 0.24
Groningen Waterton (Netherlands) (Canada) 14.27 0.94
-
81.28 2.82 0.40 0.06 0.08
0.01 0.02 0.04 0.08
0.97 3.48 16.03 65.49 3.93 1.53 0.32 0.92 0.52 0.50 1.12 5.19
The composition of gas as reported by commercial service laboratories is based on measurements of dry (water-free) gas samples and thus does not include the water vapour. Suppose the mole fraction of water vapour in The composition the gas mixture at reservoir conditions is given by y of the gas mixture at reservoir conditions is then obrained by multiplying the reported mole percentages by the factor
.
As a first approximation, the water content of natural gas in the reservoir may be obtained by regarding water vapour and hydrocarbon gas as ideal gases. According to Dalton’s Law, the partial pressure of water in the gas mixture is equal to the vapour pressure of water at the reservoir temperature. The mole fraction of water vapour in the gas is then given by Yw = P,/PR’
py
where p
=
=
vapour pressure of water at reservoir temperature reservoir pressure.
For most practical conditions the mole fraction of water vapour and thus the correction factor Eqn ( 3 . 1 ) is very small indeed (See Exercise 3 . 1 ) and can be safely ignored in reservoir engineering calculations. Table 3 . 1 shows a wide variation in composition. Based on the composition of the gas, the following characterizations are used. Gases with a low content of the heavier hydrocarbons (Pars, Groningen) are called lean or & gases. Dry alludes to the low liquid condensate yield when reservoir gas is brought to the surface. Likewise gases that -29-
Gas Properties
are relatively rich in the heavier hydrocarbons (Waterton) are termed rich or wet.
-
The Groningen gas shows a relatively high concentration of non-hydrocarbons and as a consequence has a low heating value. For this reason it is called a low-calorific gas. The Pars gas is an example of a high-calorific gas.
-
Gases that contain significant amounts of hydrogen sulfide and carbon dioxide (Waterton) are called sour gases. Sweet gases (Groningen) contain negligible quantities of hydrogen sulfide. Sour gas systems are very corrosive and require special treatment to remove the hydrogen sulfide. Exercise 3.1
-
Water Content
Estimate the associated water groduction of a gaswell that is producing at a rate of 1 million m /d at standard conditions (15 degr.C and 1.01325 bar), assuming a reservoir temperature of 100 degr.C and a reservoir pressure of 300 bar. Solution At 100 degr.C the vapour pressure of water is approximately 1 bar. Thus, the mole fraction of water vapour in the mixture is 1/300 = 0.0033 (0.33 mole per cent). 1 kmol of gas at standard conditions occupies 23.63 m3. Hencg 1.0 3 million m /d at standard conditions corresponds to 1.0 x 10 / 5 23.64 = 0.423~105kmol/day. The water production rate is then 0.0033x0.423 x 10 = 139 kmol/day. For a mo ecular mass of water of 18 kg/kmol and a water density of 1000 kg/m the volumetric water rate becomes 139x18/1000 = 2.5 m /day.
i
3.3
PHASE BEHAVIOUR
A multicomponent natural-gas system may occur in the liquid or the gas phase, or both, depending on its pressure, temperature and composition. The phase behaviour of a natural-gas system of given composition is schematically illustrated in the pressure-temperature (PT) diagram shown in Fig. 3.1. In the PT diagram the two-phase area is indicated by the area within the locus B-C-D. Outside this area the system is either in the liquid or the gas state. The curve B-C marks the boundary between the liquid phase area above it and the two-phase area. Imagine a fluid cell charged with hydrocarbon fluid in the liquid state, thus at a pressure and temperature above curve B-C. Expansion of the cell volume causes the pressure within the cell to drop. At a certain pressure gas bubbles appear and move to the top of the cell. This pressure is called the bubble-point pressure and lies on the curve B-C which is therefore called a bubble-point curve.
Gas Properties
TEMPERATURE
Fig. 3.1
-
Pressure-Temperature Diagram of Hydrocarbon Mixture at Constant Composition
The curve C-D delineates the single-phase gas phase area and the twophase area. Here traversing the boundary from above leads to the formation of a liquid. For this reason, the locus C-D is called the dewpoint locus. The phenomenon of liquid formation upon reducing the pressure is known as retrograde condensation. The point C where the bubble-point and the dew-point loci meet is called the critical point. In this point the gas and liquid phases are identical and have equal physical properties. Other characteristic points on the phase boundary are the cricondentherm CT and the cricondenbar CB. The cricondentherm is the maximum temperature on the two-phase boundary; above the cricondenterm single-phase conditions exist regardless of the pressure. The cricondenbar is the maximum pressure on the two-phase boundary; two-phase conditions can only exist below the cricondenbar. Within the two-phase area one can draw curves of equal liquid saturation defined as the fractional volume occupied by liquid. On the bubblepoint locus the saturation is unity and on the dewpoint locus it is zero. Intersection of these iso-saturation lines with a vertical line yields an isothermal, constant-composition depletion curve. The shape of this curve depends greatly on the location of the vertical line with respect to the critical temperature. This is illustrated in Fig. 3.2 showing a depletion curve at a temperature below (curve a) and above the critical temperature (curve b), respectively. For the curve below the critical temperature the liquid saturation decreases with decreasing pressure. Above the critical temperature, however, the depletion curve exhibits a maximum due to retrograde condensation. At pressures below this maximum the curve shows the normal vaporizing behaviour: a decreasing liquid saturation with decreasing pressure.
Gas Properties
1
BUBBLE F
Fig. 3.2 Constant-Composition Depletion Curve at a Temperature Below (a) and Above (b) the Critical Temperature The location of the two-phase locus in the pressure-temperature diagram depends on the composition. This is schematically illustrated in Fig. 3.3 where we have depicted the locus of a lean gas and a rich gas. The locus of the lean gas encloses a relatively small area in the region of low temperatures and pressures. The rich gas exhibits a much larger twophase region extending to higher pressures and temperatures.
TEMPERATURE
Fig. 3.3
-
Phase Behaviour of a Lean and a Rich Natural Gas
Gas Properties
The location of the two-phase locus with respect to the pressure-temperature trajectory of the reservoir gas from reservoir to surface has given rise to the following important classification of hydrocarbon gas reservoirs: (i) dry-gas reservoirs, (ii) wet-gas reservoirs, and (iii) gas-condensate reservoirs. i. Dry-gas reservoirs The pressure-temperature trajectory always lies outside the two-phase boundary. Hence, the composition of the produced gas is always equal to that of the original reservoir gas and no associated liquids are produced. ii. Wet-gas reservoirs The reservoir temperature is higher than the cricondentherm. During reservoir depletion, the gqs mixture within the reservoir remains in the gas phase. Within the borehole or at the surface, however, the pressuretemperature trajectory of the gas enters the two-phase area. Hence condensate will drop out in the tubing or at the surface or both. If conditions at the surface remain constant, the liquid content of the wellstream also remains constant. iii. Gas-condensate reservoirs Here the reservoir temperature is lower than the cricondentherm but higher than the critical temperature. Thus liquid drop-out takes place within the reservoir. As a result the composition of the well stream, the surface gas and the surface condensate change continuously while the reservoir is being depleted. Also the liquid content of the well stream will change with time. From the reservoir engineering viewpoint there is no fundamental difference between dry-gas and wet-gas reservoirs. In both cases single-phase conditions are maintained within the reservoir throughout the depletion period. Dry-gas reservoirs are just a subset of wet-gas reservoirs, viz., wet-gas reservoirs with a zero condensate content in the well stream. 3.4
REAL-GAS LAW
The pressure-volume-temperature behaviour of an ideal gas (no interaction between the gas molecules) is described by the Law of Boyle-Gay Lussac also known as the Ideal-Gas Law
where p = pressure V = volume n = number of moles R T
= =
'
gas constant (8314,413 -or 10.732 psi.ft3 kmol .K 1bmol.degr.R 1 absolute temperature.
Real gases behave as ideal gases only at low pressures. At high pres-
Gas Properties
sures strong deviations from ideal gas behaviour may occur. The pressure-volume-temperature relation of real gases can be described by including in the Ideal-Gas Law a correction factor denoted by z
Equation (3.4) is known as the Real-Gas Law and the correction factor z is commonly called the gas-deviation-factor or simply z-factor. For ideal gases the z-factor is equal to unity. For real gases, it may be greater or less than unity depending on the pressure, temperature and composition of the gas. 2-factors can be measured in the laboratory on a representative gas sample, or alternatively, they may be calculated from the gas composition using empirical correlations (see 3.5 below). The Real-Gas Law combined with the relative molecular mass (molecular weight) provides a relation for gas density. Let the gas molecular mass be denoted by M. Thus, n moles of gas correspond to nM mass units. From Eqn (3.4) it then follows for the gas density that
A widely used parameter to indicate the density ofta gas is the gas
gravity y, defined as the ratio of the gas density and the air density, both taken at standard conditions. At standard conditions the z-factor is very close to unity and the density at standard conditions is therefore given by
Applying Eqn (3.6) to the gas and to (dry) air we obtain for the gas gravity y
where p
M~~~
= =
density of (dry) air at standard conditions molecular mass of (dry) air.
Hence, gas gravity is directly proportional to molecular mass. In the case of pure methane, the gas gravity is 0.0345~16= 0.55. Exercise 3 . 2 - Molecular Mass and Gas Gravity Calculate the molecular mass and gas gravity for the Pars and Waterton gases of Table 3.1. For the molecular mass of the individual gas components refer to Appendix B.
Gas Properties
Solution Pars
Waterton
Component Nitrogen Carbon Dioxide Hydrogen Sulfide Methane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane Hexanes Heptanes-plus Molecular Mass Gas gravity
0.0345x17.8816 = 0.617
Z-factors for natural gases can be obtained from the empirical z-factor chart of Standing and Katz (Ref. 4) which is reproduced in Fig. 3.4. This chart employs as correlation parameters the reduced pressure p and reduced temperature T which are defined by pr = p/pCp
and T
=
T/Tcp,
where p = pseudo-critical pressure T~~ = pseudo-critical (absolute) temperature. CP The pseudo-critical pressure and temperature are defined by PCP
=CyiTci, cP where y = mole fraction of component i in the mixture i p . = critical pressure of component i ::T = critical (absolute) temperature of component i. =
C Yipci
and
T
The choice of these reduced correlation parameters is based on the Principle of Corresponding States. Very briefly, this Principle states that properties of single-component fluids, and thus z-factors, are approximately equal if the fluids are in corresponding states, that is if the ratios of actual to critical pressure and of actual to critical temperature (in absolute units) for each fluid are the same.
Gas P r o p e r t i e s
Pseudo reduced pressure
Fig. 3 . 4
-
Standing-Katz 2-Factor Chart (Courtesy of SPE)
Gas Properties
Kay has shown (Ref. 5) that the Principle of Corresponding States can be extended to gas mixtures. In that case the pressure and temperature are to be expressed as a ratio of the pseudo-critical pressure and temperature of the mixture as defined above. This pseudo-critical pressure and temperature should not be confused with the physical critical pressure and temperature of a gas mixture as defined in the PT diagram. They are fictitious quantities to be used for correlation purposes only. The Standing and Katz chart is based on measured z-factors of natural gases that contained very little non-hydrocarbons. It covers a reduced pressure and temperature range of
<
0
pr
<
15
and
1
<
Tr
<
3.
(3.10)
The Standing and Katz chart may also be used for sour gases, provided the pseudo-critical temperature and pressure are corrected as indicated by Wichert and Aziz (Ref. 6). The corrected pseudo-critical pressure and temperature, denoted by an asterisk, are given by
T
* CP
= T -ATwa, CP
where ATwa
yHZS
=
=
)O. 9
)1.6
a[(yCO2
+
Y~~~
where a
=
120 degr.Rankine or 66.666 Kelvin
-
('~02
+
'~25
mole fraction of H S 2
yCO2 = mole fraction of CO 2' Application of the Standing-Katz chart requires knowledge of the composition of the gas to calculate the pseudo criticals. Alternatively, if the gas composition is not known, the pseudo criticals may be estimated from Standing's correlation for either 'surface gases' or 'condensate gases', in which gas gravity is used as correlation parameter (Ref. 7). The surface-gas correlation is based on measurements of surface trap gases and stock-tank vapours and reads =
P c ~
677.0 + 15.0 y - 37.5 y
2
(pCp in psi)
(3.14)
The condensate-gas correlation is based on measurements of laboratorygenerated gases in equilibrium with crude oils at high pressure and is given by
-
P c ~
706.0-51.7 y - 11.1 y'
(pcp in psi)
(3.16)
Gas Properties
A number of analytical methods have been proposed to reproduce the Standing and Katz chart. A very accurate, powerful and yet simple method is the one advanced by Hall and Yarborough (Ref. 81, according to which z-factors can be approximated by the following relation
where a
=
-0.06125(pr/Tr)exp[-1.2(1
2 - 1/~,) ]
Equation (3.18) is an implicit equation that must be solved iteratively. The following scheme, based on the Newton-Raphson method (Ref. 9 ) , works very well and converges within three to four iterations. Step 1. Take Y
=
0 for the first estimate.
Step 2. Update Y using the Newton-Raphson approximation formula
where the prime denotes differentiation with respect to Y. Step3. Calculate z byz=-a/Y new new' Repeat step 2 until satisfactory precision is obtained. The Hall and Yarborough correlation is valid up to a reduced pressure of 25 which is substantially beyond the Standing and Katz chart range. Using the method below T = 1 is not recommended. Exercise 3.3
-
Gas Density and z-factor
Estimate the z-factor and density for the Pars and Waterton gases of Table 3.1, using the Katz-Standing chart Fig. 3.4 assuming a temperature of 100 degr.C and a pressure of 300 bar. The critical temperature and pressure of the individual components are given in Appendix B.
Gas P r o p e r t i e s
Solution Pars Component
yixlo0
Pci
Yipci
bar
bar
T . cl K
YiTci K
Nitrogen Carbon Dioxide Hydrogen S u l f i d e Methane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane Hexanes Heptanes-plus IyipCi
= 46.1836
Wichert-Aziz c o r r e c t i o n :
From t h e Standing-Katz c h a r t : z = 0 . 9 9 8 The d e n s i t y i s t h e n g i v e n by (Eqn (3.5))
I Y ~= 196.6183 T ~ ~
Gas Properties
Waterton Component
yixl0O
'ci
'iPci
bar
bar
Tci
K
'iTci
K
Nitrogen Carbon Dioxide Hydrogen Sulfide Me thane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane Hexanes Heptanes-plus
Wichert-Aziz correction:
From the Standing-Katz chart: z
3.6
=
0.87
COMPRESSIBILITY
The gas compressibility is defined as the relative volume increase per unit pressure drop at a constant temperature. In formula form
In the case of an ideal gas (pV
For real gases (pV
=
=
nRT), the compressibility becomes
nzRT) Eqn (3.20)
yields
Gas Properties
Hence, for ideal gases the compressibility is simply the reciprocal of the pressure. For real gases a correction is to be applied that depends on the pressure dependence of the z-factor. The derivative in Eqn (3.22) may be approximated with the well-known central difference formula. Let three successive pressures be given by P - ~ ,po and p+ I ' The derivative at the pressure po then follows from
Exercise 3.4
-
Compressibility
Calculate the compressibility of the Pars gas at a pressure of 275 bar and a temperature of 100 degr.C. Solution To calculate the derivative of the z-factor, we take a pressure interval of 50 bar around the pressure of 275 bar. The d-factors at 250, 275 and 300 bar are listed below. pressure
r'
z-factor
According to Eqn (3.221, the compressibility at 275 bar is given by
By comparison, the ideal-gas compressibility at a pressure of 275 bar is given by
The condensate content of natural gas may be expressed by the condensate/gas ratio either on a molar or on a volumetric basis. Suppose that n moles of natural gas, when brought to the surface, split into nG moles of gas and n moles of liquid condensate. The molar condensate/gas ratio, denoteg by RMLG, is then simply defined by
The volumetric condensatei'gas ratio is defined as the ratio of the volume of condensate at stock-tank conditions, VLst, and the volume of gas at standard conditions, VGsc. Thus
Gas Properties
The volume of gas at standard conditions is related to the number of moles of gas by the Ideal-Gas Law and given by
The volume of condensate is related to moles of condensate by
= molecular mass of liquid condensate where ML pLst = density of condensate at stock-tank conditions.
Combining Eqns (3.24) - (3.27), we obtain for the relation between the volumetric and molar condensate/gas ratio
Strictly speaking, the condensate/gas ratio is not a property of natural gas per se, for it depends not only on gas composition but also on the conditions under which separation at the surface is carried out (see Chapter 4 , section 5). If surface conditions remain the same, the condensate/gas ratio is a constant for wet-gas reservoirs and for gas-condensate reservoirs above the dewpoint pressure. In the latter case, the condensate/gas ratio of the produced gas starts declining as soon as the reservoir pressure falls below the dewpoint pressure of the gas. Exercise 3.5
-
Condensate/Gas Ratio
Calculate the molar condensate/gas ratio of a Waterton 3gas well psoducing at a volumetric condensate/gas ratio of 0.5 m /(lo00 m ) at standard conditions for the condensate properties and standard conditions listed below condensate molecular mass: density stock-tank condensate: standard pressure: standard temperature:
125 750 1.013 15
kg/kmol kg/m3 bar degr.C
Solution Application of Eqn (3.28) gives
3.8
FORMATION-VOLUME FACTOR
The formation-volume factor of gas is the ratio of a volume of gas at reservoir conditions to the volume of surface gas at standard conditions that results from bringing that volume to the surface. Let us consider n
Gas Properties
moles of reservoir gas. The volume occupied by these n moles at reservoir conditions, VGR, follows from the Real-Gas Law and is given by
In the case of a dry-gas reservoir, all the reservoir gas is converted to surface gas. According to the Ideal-Gas Law, n moles of surface gas of at standard conditions occupy a volume V Gsc
Combining Eqns ( 3 . 2 9 ) and ( 3 . 3 0 ) , we obtain for the gas formation volume factor
In the case of a wet gas, the well stream splits into a gas and a liquid phase and the expression for the formation-volume-factor becomes slightly more involved. Let us suppose the well stream, consisting of n moles, splits into nL liquid moles and nG gas moles. The volume occupied by the n moles at reservoir conditions again follows from the Real-Gas Law and is given by
Likewise, it follows from the Ideal-Gas Law for the volume of gas occupied by n gas moles at standard conditions that G
Combining Eqns ( 3 . 3 2 ) and ( 3 . 3 3 ) , we then obtain for the formation volume factor of a wet gas
where RHLG = molar condensate/gas ratio ( = n /n ) . L G Hence, the formation-volume factor for wet gas is to be corrected for the condensate content. Gas formation-volume factors are used to convert a volume ervoir conditions to a volume at standard conditions. Let ume of the reservoir occupied by hydrocarbons be given by mount of gas-in-place expressed in the volume at standard then reads
of gas at resthe pore volVhc. The aconditions
Like the condensate/gas ratio, the gas formation-volume-factor is not a
Gas Properties
true gas property either. It depends not only on the type of gas but also on the prescribed standard conditions and on the separator conditions through the condensate/gas ratio. Standard conditions are not standardized and may vary form country to country. In the USA the standard temperature is 60 degr.F, but the standard pressure depends on the geographical location and varies from 14.65 psi (e.g. Texas) to 15.025 psi (e.g. Louisiana). In Canada and Europe the standard conditions are 15 degr.C and 1.01325 bar ( = 1 atm) but in Europe gas reserves are usually reported in 'normal' conditions defined as 1.01325 bar and 0 degr.C. Hence, whenever gas formation-volume factors and gas volumes at standard conditions are reported, the standard conditions must be specified. Exercise 3.6 - Formation-Volume Factor Calculate the formation-volume factor for the Pars and Waterton gas at the following conditions: reservoir temperature: reservoir pressure: standard pressure: standard temperature: molar condensate/gas ratio Pars Waterton
100 300 1.01325 15
degr.C bar bar degr.C
0 rnol/mol 0.071 mol/mol
Solution Pars:
Waterton:
3.9
VISCOSITY
Viscosity of fluids is a measure for the internal resistance of fluids to flow. The viscosity of reservoir gases can be described by Newton's Viscosity Law which states that at any point the shear force per unit area is proportional to the local velocity gradient perpendicular to the flow direction. By definition the proportionality constant is called the viscosity of a fluid. Viscosities depend on pressure, temperature and composition.
A great number of empirical and semi-empirical viscosity prediction methods are available (Ref. 10). One of the most popular methods for the prediction of viscosity of natural gases is that proposed by Lee et al. (Ref. ll), according to which viscosities of natural gases can be predicted by the following relation
Gas Properties
where K =
(9.4 + 0.02 M ) T ~ . ~ 209 + 19M + T
where p = viscosity (microPoise) T = absolute temperature (degr.Rankine M = molecular mass. 3 p = gas density (g/cm )
=
1.8 x K)
Hence as input this relation requires the molecular mass, the gas density, the pressure and the temperature. The relative molecular mass can be obtained from the composition. The density can be calculated using Eqn (3.5) where the z-factor can be obtained from the Standing-Katz chart or from the Hall-Yarborough z-factor correlation Eqn (3.18). Lee et al.'s relation allows of the prediction of viscosities of natural 3 per cent and with a maximum devigases with a standard deviation of ation of approximately 10 per cent. For most reservoir engineering purposes this is sufficiently accurate.
*
Exercise 3.7
-
Viscosity
Calculate the viscosity of the Pars and Waterton gas at a pressure of 300 bar and a temperature of 100 degr.C. Solution The molecular mass, z-factor and density of the Pars and Waterton gas are listed below.
M (g/cm3) Pars :
Waterton:
Pars
Waterton
17.88 0.998 0.173
27.25 0.870 0.305
(Exercise 3.2) (Exercise 3.3) (exercise 3.3)
Gas Properties
Gas Properties
LIST OF SYMBOLS Latin
B
=
c F G n
=
n~ n MG
=
= = = = =
gas formation volume factor gas compressibility correction factor for water content gas-in-place number of moles of reservoir gas number of moles of surface condensate number of moles of surface gas molecular mass (molecular weight) molecular mass of air molecular mass of surface gas molecular mass of surface condensate molecular mass component i pressure critical pressure component i pseudo-critical pressure reduced pressure reservoir pressure standard pressure vapour pressure of water gas constant molar condensate/gas ratio volumetric condensate/gas ratio at standard conditions absolute temperature critical temperature component i pseudo-critical temperature reduced temperature absolute standard temperature volume volume of condensate at stock-tank conditions volume gas at reservoir conditions volume surface gas at standard conditions hydrocarbon pore volume mole fraction component i mole fraction of water gas deviation factor or z-factor
Greek
Y ATwa lJ P
.cs'f
=
=
=
= = =
'asc = P~st
gas gravity Wichert-Aziz correction viscosity gas density gas density at standard conditions air density at standard conditions density of stock-tank condensate
Gas Properties
REFERENCES 1. Nematizadeh, F. and Betpolice, A.: 'Pars Offshore Gas Field Development", EUR paper 104 presented at the European Offshore Petroleum Conference & Exibition, Oct. 24-27, 1978. 2. de Ruiter, H.J., van der Laan, G. and Udink, H.G.: "Development of the North Netherlands Gas Discovery in Groningen", Geologie en Mijnbouw (July 1967) 46, no. 7, 225-264. 3. Castelijns, J.H.P. and Hagoort, J.: "Recovery of Retrograde Condensate from Naturally Fractured Condensate-Gas Reservoirs", Soc. Pet. Eng. J. (December 1984), 719-717. 4. Standing, M.B. and Katz, D.L.: "Density of Natural Gases", Trans. AIME, 146 (1942), 140-149. 5. Kay, W.B. : "Density of Hydrocarbon Gases and Vapors at High Temperature and Pressure", Ind. Eng. Chem., 28, (1936), 1014-1019. 6. Wichert, E. and Aziz, K.: "Calculate 2's for Sour Gases", Hydr. Proc. 51 (May 1972). 7. Standing, M.B.: "Volumetric and Phase Behaviour of Oilfield Hydrocarbon Systems", Soc. Pet. Eng. of AIME Dallas (1977), Appendix 11. 8. Hall, K.R. and Yarborough, L.: "A New Equation-of-state for Z-Factor Calculations", Gas Technology, SPE Reprint Series no. 13, vol. 1 (1977). 9. Scheid, F.: "Numerical Analysis", Schaumls Outline Series, McGrawHill Book Company (1968). 10. Reid, R.C., Prausnitz, J.M. and Sherwood, Th. K.: "The Properties of Gases and Liquids", McGraw-Hill Book Co., Third Edition, 1977. 11. Lee, A.L., Gonzalez, M.H. and Eakin, B.E.: "The Viscosity of Natural Gases", Gas Technology, SPE Reprint Series no 13, vol. 1 (1977).