III Fluid Properties PVT

Fluids Properties

Basic Reservoir Engineering

1

III.

Fluid properties 1.

Basic theory background a)

Review the Gas Laws (Boyles’ Law; Charles’ law; Avogadro’ Hypothesis; Ideal Gas law “Assumptions & limitations”

b)

The law of corresponding sta states

2.

Fluid Systems –Definitions –Definitions

3.

Fluid properties a)

Gas

b)

Oil

c)

Water

4.

PVT Lab Testing

5.

Rese Reserv rvoi oirr hydr hydroc ocar arbo bons ns flui fluid d clas classi sifi fica cati tion on


2

1.Basic Theory background


3

Boyles’ Law

• Boyles’ La Law : For a fixed mass of Gas at constant Temperature PV=Constant (P is proportional to 1/V) 1/V) • This law is based on observation made around 1660, that for a mixed mass of gas at a fixed temperature, the product of pressure and volume is a constant, i.e:

 PV = Constant


4

Charles’ Law •

•

Charles’ Law: Law: For a fixed mass of Gas at constant Pressure V/T=Constant Over a century later (1787) it was observed that for a fixed mass of gas at constant pressure: •

•

•

•

The volume varies linearly with temperature, i.e if the gas had a volume V0 at 0° 0° C at a temperature T: V=V0(1+aT) The gradient, a, is found fo und to have the value 1/273 As a consequence, when T=-273° T=-273°C the gas volume will become Zero. By re-specifying re-specifying a temperature scale T’ with the same spacing of degrees as the centigrade scale, but starting with 0 at 273° 273°C the volume/ temperature relationship becomes: V=VoT’/273

• The scale is the absolute temperature scale, measured in degrees Kelvin (K), where K=C+273 • The Fahrenfeit equivalent is the Rankine Scale, R, R , where R=F+460 Basic Reservoir Engineering

5

Avagadro’s hypothesis Avagadro’s hypothesis

• Equal volumes of gas at the same conditions of temperature and pressure contain the same number of molecules (2.76 1026) • One mole of any gas at standard conditions will occupy a fixed volume • A gram mole weight of a substance occupies a volume of 22400 cm3 at a pressure of 760 mm hg and 0° 0°C • 1 pound mole weight od a substance occupies 379.484 ft3 at a pressure of 14.7 psia and 60° 60°F – Therefore, 2lbs. of hydrogen, 32, lbs. of oxygen and 16 lbs. of methane all occupy 379.484 ft3 :at the specified conditions: assuming they behave ideally!


6

Ideal Gas law

• Combining Boyle’s Boyle’s and Charles’ laws

Ideal Gas Law

PV=nRT R = 10.732 [(psia)(ft3)]/[lb-mole)(° )]/[lb-mole)(°R)] R = 0.0821 [(barsa)(m3)]/[kg-mole)(° )]/[kg-mole)(°K)] • If 1 lb. mole is involved, at a pressure of 14.7 Psia and temperature of 60° 60°F, the volume occupied will be: 0.72×(60:460) 4.7

=379.5 cu. ft.

If n lb. moles are involved then the relationship is simply: PV=nRT Basic Reservoir Engineering

7

Assumptions and limitations • Assumptions of the Ideal Gas law • PV=nRT – Molecules are point-like, i.e., zero volume – No inter-molecular forces • But – Gases are not infinitely compressible – No account of change of phase


8

Compressibility -Z- Factor

• PV=nRT Ideal Gas • PV=ZnRT Real Gas, where Z= compressibility



•

Z=



Deviation of gas from ideal behavior


9

PVT of Mixtures of components

• Apparent Molecular weight of a Gas Ga s mixture Ma=    • Specific Gravity of a gas Ration of the density of the gas to the density of dry air at same temperature and pressure

  =   

/

=





=

/  29


10

The Law of Corresponding States • It was found (by Van der Waals, Waa ls, 1873) that diverse real gases appear app ear to have much more PVT behavior in common, when their equations of state are expressed in reduced form, • That is that the pressures, temperatures and volumes are all expressed as a ration of the critical properties for the gas in question, Pc, Tc and Vc. • This implies that the P-V slices through the phase diagrams of different gases will all appear in the same scale using ‘reduced’ pressures, volumes and temperature (i.e as functions of P/Pc, V/Vc and T/Tc) • Law of corresponding states (applied to gases) means that the same real gas compressibility factor (Z-Factor) can be applied to different gases when they are in the reduced condition • Reduced properties Pr=













, Vr= , Tr=

• Systems are in corresponding states if two of their reduced variables are equal.


11

Non- Ideal Behavior – Behavior –ZZ- Factor

• Z Factor or compressibility factor function of temperature and pressure can relate volume of gas at one pressure to anather pressure:

 22 =  22


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Z- Factor- Kay Mixing Rule • Experimental work by Kay (1936), and correlations based on his data, proved the extension extension of the Law of corresponding corresponding states to the treatment of gaseous mixtures, specifically hydrocarbon gas mixtures. • Based on the composition of the gas mixture, A set of critical constants can be calculated for the mixture from mole fraction weighted constants for the individual components of the mixture. Resulting values are called Pseudo-criticals, denoted Ppc, Tpc and Vpc, and are used in exactly the same way as Pc and Tc in the determination of Zfactors. • For certain purposes, a mixture of gases can ca n be considered as a single gas having properties which are the sum of the mole fraction weighted properties of the individual gas components. • The most common application of the rule is the computation of pseudo-reduced temperatures and pressures for a gas mixture in order to calculate Z-factors: i.e. Basic Reservoir Engineering

T

=







13

Standing Chart (behavior of Oil Field Hydrocarbon Systems) • Chart of Z Factor Vs. Pseudo-reduced pressure, for a range of values of pseudo-reduced temperature. (After M. B. standing, 1942).


14


15

Why Fluid Properties? • To estimate hydrocarbons in place and reserves • To understand reservoir processes and to predict reservoir behavior • To understand well flow performance and surface processing requirements • To identify markets and product prices


16

2. Fluid Systems -Definitions • Phase: any homogeneous and physically distinct part of a system that is separated from any other part of the system by definite bounding surfaces, examples: solid, liquid, gas. Fluids will not mix readily with the other fluid present due to interfacial tension • Component: a pure substance. The number of components in a thermodynamic system is the smallest of independently variable constituents by a means of which the composition of each phase can be expressed for a system in equilibrium. • Bubble point: point (condition of temperature and pressure) at which the first few molecules leave the liquid and form a small bubble of gas. • Dewpoint: point (condition of temperature and pressure) at which only a small drop of liquid is in the fluid system. Basic Reservoir Engineering

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Fluid properties • Substances of interest to the reservoir engineer are oil, gas and water. Normally we would expect these materials to be fluid. • In reservoir studies, we normally prefer to use data obtained from laboratory analysis of actual fluids recovered from the reservoir early in filed life. • Where analyses are not available or the accuracy of the information is in question, the reservoir engineer will need to rely on published correlations, analyses of similar fluids from nearby reservoirs, etc.


18

Properties of naturally occurring petroleum Deposits • Petroleum deposits vary widely in properties as to production horizon, geographical location, and producing depth. The bulk of the chemical compounds present are hydrocarbons and, as the name implies, are comprised of hydrogen and carbon. car bon. • Since the carbon atom has the ability to combine with itself and form long chains, the number of possible compounds is very large. • A typical crude oil contains hundreds of different chemical compounds and normally is separated int crude fractions according to the range of boiling points of the compounds included in each fraction. • Hydrocarbons may be gaseous, liquid, or solid at normal temperature and pressure, Basic Reservoir Engineering

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Properties of naturally occurring petroleum Deposits • The simplest hydrocarbon is methane, a gas consisting cons isting of one carbon atom and four hydrogen atoms. The methane molecule can be represented as:

• This is the first of the so-called paraffin series of hydrocarbons having the general formula CnH2n+2 • Crudes containing mainly paraffin-base materials give good yields of paraffin wax and high grade lubrication oils. • Asphatic base oils are comprised largely of naphthenic (ringed, mostly aromatic) compounds. Asphatic crudes yields lubrication oils that are more viscosity sensitive to temperature and require special refining methods and additives.


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Components of Typical Natural Gases


21

Hydrocarbon mixtures of …


22

Pressure – Pressure – Temperature Temperature Diagram


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Single Component System • P-T Diagram for Pure component


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Component properties


25

2 Component mixture


26

2 Component mixture


27

Typical Hydrocarbon Mixture Compositions


28

Typical Properties of Reservoir Fluid systems


29

C7+ variation in Reservoir Fluid type


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3. Fluid Properties Gas, Oil and Water


31

Key Properties •

Formation Volume Factor: reservoir volume occupied by unit

surface volume. (Bo,g,w) •

Dissolved Gas Oil Ratio: volume of surface gas dissolved in unit

surface liquid volume. (R) •

Viscosity: Resistance of fluid to shear which retards flow. (m)

•

gravity segregation. (r) Density: mass per unit volume. Controls gravity

•

Compressibility: change in fluid volume per unit volume per

unit pressure change. (C) •

Bubble point pressure: saturation pressure pressure in gas reservoir

where liquid first condenses (Pdp)


32

Reservoir and Surface Volumes


33

Gas Equation Of State (EOS)


34

Determination of Z factor


35

Tpc and Ppc for Gas mixture


36

Gas Gravity


37

Formation Volume Factor (Gas) • ‘Bg’ Bg’ is used to signify gas formation factor which is equal to the volume of gas at reservoir temperature and pressure divided by the volume of the same amount of gas at standard conditions of temperature and pressure • This factor relate gas reservoir volume to its surface volume 

Bg=





=

 

• Normally, with field units T sc=520° =520°R, Psc=14.7 psia and Zsc=1   

Bg=0.0283



[

 

]

 

Bg=0.00503



[



]

• Gas Formation Volume factor is non linear • In simulation, insert more points to define non linear portion of the curve Basic Reservoir Engineering

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Formation Volume Factor (Gas)


39

Isothermal Compressibility of Gases(Gas) • In reservoir engineering, we often need to know much of a gas will compress with an increase in pressure or how much it will expand with a decrease in pressure • This nees brings us to compressibility (not compressibility factor, which is the Z-factor). The general mathematical definition for isothermal compressibility for any material is:

C=-

 

  

• For gas 

 



 

Cg= −

Cpr=CgPpc


40

Trube’s graphs Trube’s graphs for estimating compressibility of naturel gases


41

Viscosity Of Gas Mixtures (Carr’s charts for predicting Gas viscosity)

• Gas viscosity can be measured in the laboratory, but usually is not. Relatively good values can be developed from published correlations. • Where a gas contains an inordinately high quantity od non-hydrocarbon components, laboratory measurement could be justified.


42

Viscosity Of Gas Mixtures (Carr’s charts for predicting predicting Gas viscosity)


43

Useful Formulae


44

Useful Formulae


45

Summary on Gas properties • Gas properties are easily correlated by using the theorem of corresponding states. • For Gas mixtures, which all naturally occurring hydrocarbon gases are, the mole fraction of each component is usually determined from a gas chromatographic analysis. • Using the analysis along with the theorem of corresponding states, most of the properties that would be of interest to the reservoir engineer can be calculated


46

Summary on Gas properties •

Chemical composition – Major components – Trace elements

•

Physical properties – Gas gravity – Critical pressure and temperature then knowing T res and Pres, deduce: calculate or correlate: • Gas density and gradient • Dew point pressure • Compressibility Compressibility factor • Viscosity


47

Properties of liquid hydrocarbons • Liquids differ from gases in that higher densities and higher viscosities are involved. Liquids take the shape of their container but do not entirely fill it as do gases. • In the reservoir engineering sense, when speaking of liquid hydrocarbons, we usually mean oil; therefore, when discussing these properties, the subscript will usually be “o”. “o”. • Methods to get these properties of a reservoir oil include – From a sample – From published correlations


48

Density • Density relates the mass per volume of a given substance. The density of a liquid is affected by changes in temperature and pressure, but lee so than is a gas. ga s. However, the density of oil at reservoir conditions is usually quite different than at the surface • Where stock tank liquid composition is available, the stock s tock tank density can be calculated in the following manner. 26.8070

Oil density=

4.09

=53.68

 


49

Specific Gravity • Oil specific gravity, o, (relative density) is defined as the ratio of the density of the given liquid to the density of water, with both taken at specified conditions of temperature and pressure • API Gravity o

4.

API gravity (degres)=

o

− 131.5

For Example: 40° 40° API

o= 0.825


50

Specific Gravity • API gravity is an indicator of crude oil value, but other factor may be important • Surface density is specific gravity times surface density times surface density of pure water.

o,s.c = o X w,s.c o,s.c = o X (62.4) lbs/cf • Surface density is a simulation input. • Relation used in simulation programs prog rams





o =(o,s.c +Rs g,s.c)

Rs in ft 3/ft 3 or m3/ m3


51

Isothermal compressibility of liquid hydrocarbons • As the name name “oil “oil compre compressi ssibil bility ity”” indicate indicates, s, this this propert property y relate relatess how much volume change (compared to a unit volume) occurs with a change in pressure. • Oil compressibility is usually defined as:

• Co=-

    

• Compressibility particularly is important when pressure greater than bubble point CoDBo/Bo/DP Basic Reservoir Engineering

52

Solution Gas/Oil Ratio

• The solution gas/oil ration (Rs) is defined as the volume of gas dissolved in a unit volume of stock oil at reservoir temperature and pressure. Common units are standard cubic feet per stock tank barrel (SCF/STB) and standard cubic meter per stock tank cubic meter. • It could be said that somewhere during the history of the reservoir fluid as pressure was increasing ( with increasing overburden), the bubble point was that pressure where the fluid system “ran “ran out of gas”, or gas”, or all available gas into solution.


53

Solution Gas/Oil Ratio


54

Formation volume Factor for oil

• The volume of liquid entering the stock tank is less than the volume of the same liquid plus dissolved gas ga s in the reservoir. – The main reason for this is that the liquid in the reservoir is swollen due to the solution gas. – A second reason is that the reservoir fluid is in a thermally expanded state due to the higher temperature in the reservoir than in the stock tank.           

Bo=

         


55

Formation volume Factor for oil


56

Oil viscosity • Viscosity is the property of resistance ta shear stress. Alternatively, viscosity may be viewed as a fluid’s internal fluid’s internal resistance to flow. A thick, usually heavy liquid (e.g. tar) has a higher viscosity than a thin one that flows easily. • Reservoir oil viscosity, mo, is directly related to tank-oil gravity, gas gravity, gas in solution in the oil, pressure, and temperature. With the wide variety of compositions of crude oil, we should expect to find a large variation in oil viscosities even with oils of similar gravity, solution gas/oil ratio, and reservoir temperature. • Of the more important oil physical properties that needed in reservoir engineering, crude oil viscosity has the poorest correlation.


57

Oil viscosity


58

Oil PVT Properties Determining oil volume Factor, Dissolved Gas Oil Ratio and Viscosity •

Correlations (Regression Fit of Data)

•

Sampling and Lab analysis


59

Why Correlations ? • • • •

•

•

PVT Analysis may not be avaible Check reasonableness of PVT analysis Discriminate correct PVT analysis among am ong differing tests Extend PVT properties to account for reservoir variations in fluids where no PVT analysis exists Incorporate Incorporate variations in fluid properties due to temperature variations (e.g. flow up tubing) Require:  API oil Gravity  Initial Solution Gas-Oil Ratio  Reservoir Temperature  Separator Gas Gravity, Temperature and pressure Basic Reservoir Engineering

60

Oil Correlations • Procedure: (Vasquez, Beggs Correlations) – Correct Gas Gravity to 100 Psi Separator Equivalent conditions, (gp, API, T & Psep) – Calculate Bubble point Pressure (gp, API, T & Rs) – Define below Pbp (gp, API, P & Tsep) – Define Bo at Pbp (gp, API, Tres & Rs) – Define Co (gp, API, Pres ,Tres & Rs) • Bo=Bobp e-co(p-pb) – Calculate the saturated Oil viscosity below Pbp (API, Tres & Rs) – Calculate the under saturated Oil viscosity above Pbp (Pres / Pbp)


61

Water PVT Properties • Important – Water density affects gravity segregation – water compressibility influences aquifer support – Water viscosity is part of mobility ratio in waterfloods – Water composition for water compatibility (scaling) and tracking • Less important – Water formation volume factor (approximately 1.0) – Dissolved gas-water ratio • Pure water composition – At standard conditions, specific gravity (gw, pure) is 1.0 gm/cc – At standard conditions, density is 62.4 lb/cf


62

Water PVT Properties • Oil field water – Contains dissolved solids – Common cations: Na+, Ca++, Mg++, K+, Ba++, Li+, Fe++, Sr++ – Common anions: Cl-, SO4, HCO3-, CO3, NO3, Br-, I-, NO3,S – Water chemistry useful in identifying source of water and water compatibility compatibility of injected and formation water.

• Concentration of solids – “ppm” is “ppm” is grams solid per million grams of brine – “Wt % solids” is solids” is ppm/10,000 – “Wt %solids” %solids” is is ppm X brine density (gm/cc) at standard conditions conditions

• Water compressibility – Rule of thumb: Cw=0.000003 vol/vol/psi – More precise approch requires knowledge of gas dissolved in water. Correlations Correlations based on hydrocarbon gas. Significantly different for CO2

• Formation volume factor – Rule of thumb: B w=1.03 RB/STB Basic Reservoir Engineering

63

4. PVT Lab Testing


64

Well Sampling •

Types of Samples

– Bottomhole, primarily for oil samples – Surface separator, for (recombination samples)

gas

condensate

and

volatile

oil

samples

– MDT (Downhole wireline sampling tool) •

Collection

– Clean sample containers – Record time when separator temperature approximately constant – Record separator P and T, production rates, reservoir pressure and temperature – Use stainless steel if H2S present – Take multiple samples for consistency check •

Quality Control checks

– Opening pressures Vs. separator pressure at separator sep arator T – Presence of air or heavies in gas sample – Presence of water in oil sample – Consistency of results – Comparison Pbp or Pdp to sampling FBHP


65

Flash Separation Tests • Used to model separation conditions • Sample of bubble point oil “flashed” through “flashed” through one or more stages of separation. Remaining oil volume and produced gas measured. • Pick optimum separator conditiond to maximize oil volume • Measures Bobp and Rsi


66

Flash Vaporization Tests • Normalized with bubble point volume to yield relative volume • Defines Bo above Bubble point – Bo=Bobp X relative volume


67

Differential Vaporization Test •

GOR and relative volume normalized on basis of residual volume. Gas deviation factor measured.

•

Defines how gas evolves out of the oil below the bubble point (Rs) and how the oil volume changes as a function of pressure below the bubble point (Bo)

•

Both need to be adjusted to separator flash volumes

Fluid allowed to expand. Gas displaced from system. Volume of gas and remaining oil volume measured.


68

Combining the flash and depletion tests


69

Flash and Differential Vaporization in the Field


70

Differential Vs. Flash liberation •

In an oil reservoir, or in a laboratory cell, gas will break out of solution from the oil as pressure is reduced. The quantity of gas liberated, as well as its composition, is somewhat dependent on the manner in which the pressure is reduced.

•

Differential liberation is that process where as free gas is liberated, it is removed from the proximity proximity of the oil. It is also known as a Constant Volume, Variable ariable composition composition process.

•

Now, if the gas were not removed at each pressure decrement, but allowed to remain in intimate contact with the liquid, then we would have a flash or equilibrium liberation. This is also called a Constant Composition omposition,, variable volume process.

•

With a normal low shrinkage (black) oil, flash conditions will cause more gas to be liberated (with resultant greater shrinkage of the liquid) down to a given pressure that will the differential process. This is caused by the attraction of the heavy liquid molecules to the light gas molecules in the flash process. Basic Reservoir Engineering

71

Differential Vs. Flash liberation • With a high shrinkage (volatile) oil, this is usually reversed: the differential process liberates more gas. • The trip that the oil makes from the formation through the wellbore and flow line to the separator is not an isothermal process. This is usually regarded as a flash process, but the temperature is decreasing. Et lower temperature, gas solubility is generally increased. Therefore, the quantity of gas coming out of solution with pressure reduction is much reduced over the constant temperature case. It is common with either volatile or black oil, for this type of flash process to liberate less gas than either of the constant (reservoir) temperature processes. • Both high and low shrinkage oils will shrink to the stock tank if they are first passed to a high pressure separator where the gas is removed from the proximity of the oil


72

5. Reservoir hydrocarbons fluid classification The Five Reservoir Fluids

Black Oil

Volatile

Retrograde

Wet

Dry

Oil

Gas

Gas

Gas


73

Phase Diagram of a Typical Black Oil

Pressure path in reservoir a i s p , e r u s s e r P

Critical Point

Dewpoint line

Black Oil % Liquid

Separator

Temperature, °F Basic Reservoir Engineering

74

Phase Diagram of a Typical Volatile Oil

Pressure path in reservoir

1

Critical point

2 Volatile oil e r u s s e r P

% Liquid

3

Separator

Basic Reservoir Engineering III-Fluid Properties

Temperature, °F

75

Phase Diagram of a Typical Retrograde Gas Pressure path in reservoir 1 Retrograde gas

e r u s s e r P

2

Critical point % Liquid

3

Separator


Temperature

76

Phase Diagram of Typical Wet Gas Pressure path in reservoir 1

e r u s s e r P

Wet gas

Critical point

% Liquid 2

Separator

Temperature Basic Reservoir Engineering

77

Phase Diagram of Typical Dry Gas Pressure path in reservoir 1

e r u s s e r P

Dry gas

% Liquid 2

Separator

Basic Reservoir Engineering Temperature

78

Volatile Oil

Black Oil

Pressure path in reservoir a i s p , e r u s s e r P

The Five Reservoir Fluids

Critical 1 point


2 Critical point

Dewpoint line

Black Oil % Liquid

Volatile oil e r u s s e r P

% Liquid

33

Separator

Separator

Temperature

Temperature, °F


Retrograde gas

e r u s s e r P



1

1

1

2

e r u s s e r P

Critical point

Wet gas

% Liquid Liquid Critical point 3

Separator Temperature

Retrograde Gas

% Liquid

e r u s s e r P

Dry gas

% Liquid 2


Basic Reservoir Engineering Wet Gas

2


Dry Gas

79

Relative Positions of Phase Envelopes


80

Three Gases - What Are the Differences?

• Dry gas - gas at surface is same as gas in reservoir • Wet gas - recombined surface gas condensate represents gas in reservoir

and

• Retrograde gas - recombined surface gas and condensate represents the gas in the reservoir but not the total reservoir fluid (retrograde condensate stays in reservoir)


81

Field Identification

Initial Producing Gas/Liquid Ratio, scf/STB Initial Stock-Tank Liquid Gravity, API Color of StockTank Liquid

Black Oil <1750

Volatile Oil 1750 to 3200

Retrograde Gas > 3200

Wet Gas > 15,000*

Dry Gas 100,000*

< 45

> 40

> 40

Up to 70

No Liquid

Dark

Colored

Lightly Colored

Water White

No Liquid



*For Engineering Purposes Basic Reservoir Engineering

82

Field Identification

bitumen

Tar or Heavy oil

Low – shrinkage oils

High-shrinkage crude oil

Condensate Gas

Wet Gas

4<°API<10

10<°API<20

20<°API<30

30<°API<50

50<°API<70

API>60

Rs initial=Rsi ~neglogible

Neglogible
50
50
2 000 to 6 000
15000
Bo .0

1.0
1.1
1.5
1.000.000>mo>5. 000 cp

5.000>mo>00 cp

00>mo>2 up 3 cp

2 to 3 >mo>0.25cp

mo~0.25cp

mo~0.25cp

C7+>20%

C7+:12.5%~20%

C7+<21.5%

C7+: 0.8% to 4%


83

Primary Production Trends

Black Oil R O G

Volatile Oil R O G

Time

I P A

R O G

Time

I P A

Time

Retrograde Gas R O G

Time

I P A

Time

Wet Gas

Dry Gas R O G

Time

I P A

Time Basic Reservoir Engineering

Time

I P A

Time

No liquid

No liquid

Time 84

Pressure-Dependent PVT Properties 1.0

3.2

) 2.8 B T S / f 2.4 c s M ( y 2.0 t i l i b u l o 1.6 S s a G 0.8

0.9 ) ) B B R / R/ 0.8 B B T T (S S( 0.7 r o t t c a F F 0.6 e g g a k k nr i i 0.5 h h S S

p i

Undersaturated Curve

Saturated Curve

0.4 0.3

1

2

3

4

p

i

b

0.4

p b 0

p

5

6

7

8

9

0.0 0

1

2

Pressure (thousands psia)

3

4

5

6

7

8

9


0.50

1.0

0.48

0.9

t ) t ) 0.46 f f i / i / s p p ( ( 0.44 y y t t i i s n e 0.42 D D e s a h h 0.40 P P

) ) p p c ( ( 0.7 y y t i t i s o c 0.6 s i i V V

0.8


p

i


p i

0.5

Saturated Curve 0.38

Saturated Curve

0.4

p

b

0.36 0

1

2

3

4

5

6

7


8

9

p b

0.3 0

1


2

3

4

5

6


7

8

9

85

III Fluid Properties PVT

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