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Phase Behavior of Petroleum Reservoir Fluids


Michael Aide Imiewarin 

ID #:UB26630SP35132

Reservoir Fluids: 

Phase Behavior of Petroleum Reservoir Fluids





         The naturally occurring petroleum deposits comprise of organic chemicals. The chemical composition has of small particles. The small particles mixture is a gas at normal temperatures and pressures. The mixture with large molecules is a liquid at normal temperatures and pressures. The separation of crude oil into fraction is accomplished by knowing the boiling point of each compound in the mixture. The oils are chemically categories according to the large molecule structures in the mixture. Classification includes aromatic, asphaltic, naphthenic and paraffinic. Paraffinic molecules have lubricating oil and residuum wax. The heavier fractions of crude oil are aromatic and asphalt. They are useful for paving asphalts, roofing, and pitching among other applications.

Oil reserves calculation and establishment of the oil physical aspects requires a wide knowledge how the fluid performs under different conditions of temperature and pressure. The most important characteristic of crude oil includes viscosity, solution or gas oil ratio, bubble point pressure, formulation volume factor and surface tension. The flow resistance and surface tension is important to determine how the oil flows in pipes and other transportation medium. In some cases, laboratory research is necessary to determine such properties. However, experiments on the oil are more accurate due to various tools used for analysis. The derivations of the properties of pressure-volume and temperature (PVT) manually or using experientially analyzed correlation is necessary (Garland, Neilson, Stephen & Katherine 103).

Most PVT correlations proposed in the past sixty years assume the gas and oil phase to be a two-component system. The PVT properties of oil include specific gravity, pressure, composition of each component and their temperature. As stated earlier crude oil can either be aromatic, paraffinic or naphthenic depending on the crude oil fractions (Gluyas 78).

Hydrocarbons of the paraffinic nature have straight or open chains and are joined by single or linear bonds. These include all alkanes such as propane, methane, octane and pentane among others. Paraffinic isomers include paraffin or kerosene. The first four members of the alkane group are gaseous at room conditions. However alkanes such as pentane (C5H12), hexane (C6H14) and others that contain more than five carbon bonds are liquids at room pressure and temperature. Other heavier compounds such as wax products are solid at room conditions. Hydrocarbons that are unsaturated have triple or double bounds. These include alkenes and alkynes. These include diolefins, olefins and acetylenes among others. On the other hand, naphthenic hydrocarbons have ringed particles or molecules hence referred as cycloparaffins.

These compounds are stable and saturated like paraffin and make the second fraction of crude

oil. Hydrocarbons of aromatic nature are imitative of benzene structure and properties. These hydrocarbons have rings with alternating double bonds and are relative stable making them the third constituent of the black oil. Examples of paraffinic and naphthenic are the Pennsylvania and United States grade oil respectively. Crude oil may also contain resins and Asphaltenes. Asphaltenes and resins are the black elements found in oil. These elements have aromatic ring molecules that are high in molecular weight, polycyclic and polar. However if the Asphaltenes are pure they tend to be nonvolatile black powders. Resins are sticky r heavy liquids with high volatility rates. Resins of higher molecular weights are red in color, and the color decreases with molecular weight. Asphaltenes are usually suspended in crude oil since they do not dissolve. However, these hydrocarbons are soluble in aromatic systems such as xylene. However, resins are highly and readily soluble in crude oil (Garland, Neilson, Stephen & Katherine 120).


Bubble Point and Dew Point 

         The instant at which little molecules leave the liquid and forms a small effervesce is called bubble point. Dew point is the instant at which only a small drop of liquid remains. In pure matter, the pressure at the dew and bubble point is equal to the pressure of matter vapor at a particular temperature.

The density of ideal gas 

Pg= =          

Dry Gases 

         No liquid condenses from the dry gas as it moves from the oil reservoir to the surface. The properties and specific gravity of the gas at the reservoir be the same as the composition of gas at the surface.

No liquid condenses from the dry gas as it moves from the oil reservoir to the surface. The properties and specific gravity of the gas at the reservoir be the same as the composition of gas at the surface.

Gas formation (reservoir) Volume Factor is the gas volume at reservoir conditions needed to produce one standard cubic foot of gas at the surface.

Formation volume factor of a gas is the volume of the gas at reservoir pressure and temperature divided by volume of the same mass of gas at standard state.

                                      Bg = VR/VSC

The Compressibility Equation of State is used to determine the volume of a specific number of moles at reservoir states.


For the same volume at standard state, number of moles at TSC AND PSC is given by:

Vsc=                      Where N is the number of moles.

The formation gas factor for the gas is:


The coefficient of the isothermal compressibility of gas defined as the fractional change of volume as pressure changes at constant temperature (Donnez & Pierre 108).

Cg= -    (          ) T

Cg= -  ) T


Cg= -    (          ) T

The coefficient of the isothermal compressibility of ideal gases is

PV=n RT or V=          ...... (I)

Deriving from equation (i)

(    ........ (ii)

Using equation (I) and (ii)

Cg= -  )

Cg= -

Coefficient of the isothermal compressibility of Real gases 

Since z- factors changes as pressure changes;




Cg= -    (          ) T

Cg=  () ?

Cg=    -  (          ) T

In some special cases of the ideal gas where the z-factor is a constant and equal to one, the partial derivative of the factor becomes zero.

The Coefficient of Gas Viscosity is a measure of resistance to flow exerted by a fluid. The units of viscosity are centipoises. A unit of centipoises is a g mass/ 100 sec cm.

Kinematic Viscosity v=

Oil Bubble Point Pressure 

The pressure at which natural gas leaves the solution and creates bubbles is called bubble point pressure.

Solution Gas-Oil Ratio 

Saturation of black oil occurs when a small decrease in pressure causes release of gases and occurs initially at bubble point pressure. However, above the bubble-point pressure the oil is under saturated due to few light particles. Gas ratio is the amount of gas dissolved in the oil at reservoir states. Dissolved gas oil ratio or gas solubility is the quantity of gas that oil releases as it is transferred to the reservoir to the surface.


The surface volumes of liquid and gas are in standard conditions. The units of solution gas ratio are standard cubic feet per stock-tank barrel i.e., scf/STB.

Total Formation Volume Factor 

For the analysis of the volume factor; let B0 be the volume at low pressure. The capacity of gas released is the amount in solution at the bubble point, Rsb subtracted from the amount of gas in the remaining solution at a lower pressure, RS. For reservoir conditions volume factor, multiply the result by the formation volume factor of the gas, Bg.

Bt=B0 + Bg (Rsb-Rs).

The gas formation volume factor units are res bbl/scf. The two phase FVF total formation volume factor measurement units is res bbl/STB.

The coefficient of the isothermal compressibility of Oil 

The coefficient of the isothermal compressibility of oil and gas are the same at pressure above bubble point.

Co= -    (          ) T or

Co= -  ) T  or

Co= -    (          ) T

The specific volume for known changes in pressure is

V2=V1 EXP [Co (p1-p2)]

Specific Gravity of a Liquid 

Liquid specific gravity, ?o, is the ratio of a given liquid density to water density at the same temperature and pressure conditions.

?o =

Formation volume factor of oil 


The reciprocal of the volume factor is called shrinkage factor.


The formation of the volume factor is also called the reservoir volume factor.

Oil density 

The division of mass of oil and the crude oil volume is the called the oil density. The definition of density at all conditions is


To determine the PVT properties the above relationship of density becomes


The above equation is applicable to all temperature and oil pressure conditions for known PVT.

Interfacial Tension 

In some case, imbalance between molecular forces at the interface between the phases occurs. These are as a result of physical attraction between molecules. A molecule at the surface is more strongly attracted from below because the molecules of the separation gap of the gas. However, the attraction is inversely propositional to the distance between molecules. Surface tension is used to describe the interfacial tension between gas and liquid.

Weinaug and Katz methods

?1/4go=?Pi (xi?o/Mo - yi?g/Mg)    =>?1/4go=Po (    )-  Pg (            )

The oil mole fraction is

Xo= [1+]-1      Gas mole fraction of the oil    =>Xg =1-xo

Therefore, gas and oil mole fraction is

yo= [1+]-1


The characterization of crude oil is only related to the crude oil specific gravity. The API gravity relates to the specific gravity as follows;

?API= - 131.5

Nelson and Watson found a new ratio also called a correlation factor between the specific gravity and the mean average boiling point to show the chemical composition of the hydrocarbons in the crude oil fractions.


If the characterization factor is greater than 12.5, the hydrocarbons present in the crude oil alkane i.e. paraffinic. Low characterization factor indicate presence of aromatic or naphthenic hydrocarbons. For the characterization of less than ten, aromatic hydrocarbons are present in the crude oil. Therefore, the characterization factor formulated by Watson is important in determining the crude oil paraffinic.

The Molecular weight and specific gravity established by Watson is as follows

Kw= 4.5579 Mo0.15178?o-0.84573

Relationship between API gravity and the Watson characteristics

Bubble point pressure 

The fundamental equation required in the determination of Standing's correlation of bubble point pressure is as follows

                                          Pb=f (T, ?API,?g,Rs) 

The rearrangement of the above correlation yields solution Gas Oil Ratio.

The other methods proposed by Al-Shammasi, Lasater and Velarde regularly determine the impact of corrections of API gravity and GOR (Garland, Neilson, Stephen & Katherine 88).

Relationship between bubble point pressure and solution GOR

The method proposed by Owalabi showed the following correlation. The above relation shows a range of 200-300 scf/STB with 5% to 15% nitrogen. Interpolation of the data shows higher values of GOR using the bubble point pressure given (Donnez & Pierre 87). Owalabi showed the value of impurities found in gases and the results of the impurities to the analyzed results. He stated the importance of adjusting the bubble point pressure to reflect such impurities.

The figure below show the variability of bubble point pressure correlation

The relationship established above shows the difference in low and high results used in the correlation analysis (Donnez & Pierre 102).

Both the Lasater and Whitson characterization factor limits their use to the relationship between specific gravity and molecular weight. Cargoes' relation proposed by Whitson Brule showed the relationship between API gravity and molecular weight of the crude oil.

Mo= 6084/?API-5.

The above equation is applicable on a range of 20 - 800 API especially in condensates.

The characterization factor suggested by Watson of 11.8 is defined in a range of 30 to 40 in the Cargoes' equation. The Whitson equation determines the molecular weight of crude oil from the characterization factor. Therefore, the chemical nature of crude oil determination is possible using the three equations (Ma & Pointe 86). The Lasater correlation used the bubble point pressure factor, Pb?g/T, and the mole percentage of the gas dissolved the crude oil.

To adjust the Glaso's correlation to account for characterization changes, Brule and Whitson modified the equation into:

?oc=?om(kw /11.9)1.1824

Relationship between characterization factor and bubble point pressure according to the above modified equation.

Non hydrocarbon gas effects 

Carbon, hydrogen sulphide and nitrogen are the major non hydrocarbons found in the crude oil. Nitrogen increases the pressure of the bubbles since it is insoluble in the crude oil. However, hydrogen sulphide and carbon dioxide lower the bubble point pressure as they dissolve in the oil (Fitch, Jim & Drew Troyer 69).

The following equation relates nitrogen to the bubble point pressure

PbN2/Pbh= 1.1585+2.86yN2-1.07x10-3T

The nitrogen composition examined by Glaso show the relation between temperature, temperature, and API gravity.

PbN2/Pbh =1.0+ [(-2.65X 10-4?API+5.5 X10-3) T + (0.931?API - 0.8295)] yN2

[(1.954 X10-11?4.699API) T+ (0.027 ?API - 2.366)] y2N2

Also, the carbon dioxide correction shows a relation between temperature and carbon dioxide.


The hydrogen sulphide correction showed the function between crude oil gravity and the gas content.

PbH2S/Pbh= 1.0 - (0.9035 + 0.0015?API) y H2S + 0.019(45- ?API) y2H2S

The volume of oil at storage conditions to oil volume at increased pressure and temperature shows the oil formation volume factor. The values of FVF range from 1.0 to 3.0 bbl/STB.

The FVF correlations factor is a function of the following

                                        Bob = f (T, ?API, ?g, Rs)

Saturated oil FVF correlation vs. solution GOR                        Oil FVF vs.oil API gravity Relationship between Oil FVF and solution gas gravity

For the under saturated oil the isothermal compressibility is define as

co=- (          )T

The equation shows the volume changes as pressure changes under standard conditions of temperature.

For saturated oil, below the bubble point pressure the isothermal compressibility is

co=-) T - Bg (          ) T

The oil formation volume factor is a function of bubble point pressure, isothermal compressibility and bubble point volume factor for under saturated oils.

B0=BOBe[co (pb-p)]

Graphs showing the isothermal compressibility relations


         The fluid internal resistance is called absolute viscosity. Viscosity is necessary for the calculation of all fluid movements. The correlations created to determine viscosity use temperature range of 35 to 300 degrees Celsius (Goodwin, Sengers & Cor 98). The Newtonian fluids' viscosity does not depend on the fluid shear rate. The figure below shows the curve of oil viscosity

Relationship between dead oil viscosity and API gravity with characterization factor

         Dead oil viscosity is always a function of temperature of the crude oil and API gravity. The function of solution gas oil ratio and gas-free oil viscosity determines the saturated oil viscosity. For the under saturated oil viscosity, functions of saturation pressure and saturated oil viscosity are necessary (Caenn, Ryen, Darley, George & George 117).

Dead oil viscosity against temperature                                            Dead oil viscosity against

API gravity 

Connally and Chew determined the correlation of bubble point viscosity. The formula forms a correlation between solution GOR and dead oil viscosity.


Relationship between bubble point          viscosity correlation factors

Bubble point viscosity against solution GOR                        Undersaturated oil viscosity against pressure

Bubble point correlation 

Cragoe formula states;

Mo= 6084/?API-5.9

Properties of wet gases 

The assumption of the analysis of the properties of wet gas is that reservoir gases properties are not similar to surface gas properties. Liquid solidifies from the gas as it advances to the surface from reservoir conditions. The recombination of surface gases and liquid gases is important when establishing the gas properties at the reservoir. Given the composition of the separator gas, gas ratios, stock-tank vent gas and liquid the composition of the reservoir hence calculated. The calculation creates experimental recombination of the gases and liquids. The calculation of the density and molecular weight of the stock-liquid are important. These gas- oil ratios in terms of the lb mole are used to combine the mixtures of the gas and oil (Lyons, William, Tom, Norton, Norton  196).

The separator gas-oil units are in scf/ STB. To convert the separator gas ratio into standard units divide the volume of the separator oil and volume of the stock tank.

There are two methods of estimating specific gravity from data produced from the reservoir if the composition is unknown. In the first example, the properties and quantities of the reservoir gas from production data. In the second part, the only properties of the gas from the primary separator are known.

Separator gas and stock-tank vent gas properties.


Hence the gas ratio is


Properties of stock- tank gas unknown 

The quantity and specific gravity of the stock tank vent be unknown. For example in a threestage system, the amount of the following separator gas is unknown. A correlation is available for use in these situations.


VEQ is the equivalent volume of the stock tank gas and the subsequent separator gas. The unit of equivalent volume is in scf/STB.

For three stage of separation;

VEQ=RSP2 + RST + 133000

AGP is the additional gas produces and is related to the mass of gas released from the separator and stock tank. For three stages of separator,


Specific Gravity of a Liquid 

?o =

Formation volume factor of oil 


The shrinkage factor is the reciprocal of the volume factor.

Formation volume factor of wet gases 

The formation volume factor of wet gas is the volume of the reservoir gas required to produce one stock-tank barrel of liquid at the surface.


The two methods of estimating volume factors for wet gases are:

Composition unknown 

The gas composition of stock gas volume is mostly unknown. In that case, the precise value of the formation volume factor of the wet gas required is usually calculated using equivalent volume, VEQ. However, the primary separator gas-oil ratio is necessary. The second separator and stock tank gas-oil ratios ignored; the VEQ Correlation includes these gases.

Volume of the reservoir wet gas= RSPI +VEQ,    scf/STB.

The Production Trends 

Consider crude oil at reservoir pressure above the bubble point. Production into the wellbore will consist solely of liquid. As the oil is transported from the reservoir to the surface the dissolved air evolves. Above bubble point pressure, the amount of gas released from every barrel of tank oil is constant. The trend remains the same though some variances occur while during gas release. Bubble point pressure reaches as production of oil from the reservoir continues. Gas start forming in the void spaces created. Initially, the trapped gas does not move but as pressure decreases the trapped gas increases and starts moving (Mccain 246).

The production of oil from the reservoir increases and the pressure decreases. Reservoir rocks, water and oil fill the pore spaces created during oil extraction at pressure above the bubble point. A high pressure decrease is important so as the remained liquid and rock can occupy the void left efficiently (Jamshiki, Tayebeh & Zeinab 108). The free gas occupies significantly more spaces than liquid. Gas also readily expands as pressure decreases more. The forming and expanding gas replaces most of the void created in production. Reservoir pressure dies not decrease as rapidly as it does when pressures above the bubble point. Excessive production of the gas is detrimental to the maintenance of reservoir pressure.

The plot of reservoir pressure exhibits two different slopes.

Adjustment of surface Gas data -Example of the graph 

At pressure above bubble point pressure, oil formation volume factors are calculated from recombination of flash vaporization and separator data test.

BO= () F BOSb at p? pb

Solution gas-oil ratio at pressures above bubble-point pressure is a constant equal to the solution gas-oil ratio at the bubble point.

Rs =RsSbat p ? pb

Solution gas-oil ratios at pressure below bubble-point pressure hence estimated from a combination of differential vaporization data and separator test data

RS = RsSb - (RsDb - RSd)  at p< pb

Gas formation volume factors are calculated with z- factors measured with the gases removed from the oil at each pressure step during the differential vaporization.

Bg= 0.0282

Total formation volume factors may be calculated as 

Bg = BO + Bg (Rsb - Rs)

Viscosity of oil and gas viscosities reported in the reservoir fluid study being used directly.

Coefficient of isothermal compressibility of oil 

Co (p2 - p1) = - ln  at p ? pb



The research above focuses on the phase behavior of petroleum. The mathematical tools analyzed are effective, simple to understand and apply in all the calculations of such system. The correlation factors of oil and brine properties developed uses different scientists who developed them. The recombination methods are also a major focus of the paper (Mccain 287). The recombination analyzed include when the composition of separator and stock tank gas are known and unknown.


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