Fluid Properties Oil

4/27/12 2:29 PMFluid Properties

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Fluid PropertiesF.A.S.T. VirtuWell™ is designed to calculate multiphase flow effects, and thus allows the user to input the relevant fluid properties of Gas, Oil (Condensate) and Water.

GasThe Gas Properties that can be entered into F.A.S.T. VirtuWell™ include gas gravity, mol% N2, mol% CO2 and mol% H2S. The use of correct gasproperties is most important in single phase gas wells and Gas/Liquid systems with high Gas to Liquid Ratios. These gas properties are used in calculatingthe gas density, the compressibility factor (Z) and the gas viscosity at various pressures and temperatures

Natural Gas HydratesHydrates are solid (icy) chemical compounds formed of gas trapped in a crystalline structure of water molecules. They represent a problem in productionoperations due to the blockage of pipelines.

In order to perform the detection of natural gas hydrates the only additional information needed is the mol% of C3H8 in the gas stream. This detectionoption is just available for the Wellbore module. The procedure is based on the Baillie-Wichert method. The main advantage of this method is its capabilityto handle the hydrate onset of sour gases. The recommended range of use for this implementation is for sour gases with up to 50% H2S and up to 10%C3H8.

CondensateThe Condensate Properties that can be entered into F.A.S.T. VirtuWell™ include the condensate density, separator pressure and separator temperature.

OilThe Oil Properties that can be entered into F.A.S.T. VirtuWell™ include the API Gravity and, in certain instances, the flowing Gas-Oil Ratio (GOR). TheAPI Gravity is used to determine the Oil Density, the Solution Gas-Oil Ratio, the Oil Viscosity and the Formation Volume Factor at various pressures andtemperatures. The oil properties can be measured in the laboratory or obtained from several published correlations. F.A.S.T. VirtuWell™ has a choice ofoil properties to choose from. The flowing Gas-Oil Ratio affects the pressure drop calculations in multiphase flow.

WaterThe Water Properties that can be entered into F.A.S.T. VirtuWell™ include the Water Gravity and, in certain instances, the flowing Water-Gas Ratio(WGR). The Water Gravity is used to determine the density and the viscosity of water at various pressures and temperatures from published correlations.The flowing water-gas ratio affects the pressure drop calculations in multiphase flow.

The gas, oil and water properties have a significant effect on both the hydrostatic and the friction pressure losses.

Gas PropertiesThe Gas Properties that can be entered into F.A.S.T. VirtuWell include:

gas gravitymol% N2mol% CO2mol% H2S

The use of correct gas properties is most important in single phase gas wells and Gas/Liquid systems with high Gas to Liquid Ratios. These gas properties are used incalculating:

gas densitycompressibility factor (Z)gas viscosity

These, in turn, affect DIRECTLY the calculation of the pressure drops caused by friction and by hydrostatic head.

The Pressure-Volume-Temperature relationship of natural gases is covered in most standard texts. A convenient reference is the ERCB manual :Gas Well Testing, Theory and Practice. Fourth Edition, 1979 (Metric), 1975 (Field). Energy Resources Conservation Board, Alberta, Canada.

Gas GravityGas Gravity is the molar mass (molecular weight) of the natural gas divided by the molar mass of air (28.94). It ranges from 0.55 for dry sweet gas (mostlymethane) to approximately 1.5 for wet, sour gas (includes CO2 and H2S concentration). The Gas Gravity is readily obtained from any laboratory gasanalysis.

In F.A.S.T. VirtuWell™, Gas Gravity affects three variables namely compressibility factor (Z-factor), gas viscosity, and gas density.

The effects on compressibility (Z) and viscosity are not very significant. However, the effect on density is significant in two ways. It affects the frictionpressure drop to some extent, but it affects the hydrostatic pressure drop directly – i.e. doubling the Gas Gravity doubles the density and therefore doublesthe hydrostatic pressure drop.

When the parameter name is displayed in yellow this a warning that the entered value is outside the range.

UNITS: None

LIMITS: 0.5 < G < 1.5

N2Molar Concentration of Nitrogen in the gas stream. It has an effect on the calculation of compressibility factor (z-factor) and viscosity. The concentration of

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Nitrogen must be between 0% and 15% to be within the limits of the correlations. For values outside of this range F.A.S.T. VirtuWell™ will still completethe calculations, however results should be used with caution.


UNITS: Percent (%)

DEFAULT: 0

CO2Molar Concentration of Carbon Dioxide in the gas stream. It has an effect on the calculation of compressibility factor (z-factor) and viscosity. Theconcentration of CO2 must be between 0% and 80% to be within the limits of the correlations for the z-factor, and between the limits of 0 and 15% for theviscosity correlations. For values outside of this range F.A.S.T. VirtuWell™ will still complete the calculations, however results should be used with caution.


UNITS: Percent (%)

DEFAULT: 0

H2SMolar Concentration of Hydrogen Sulfide in the gas stream. It has an effect on the calculation of compressibility factor (z-factor), viscosity and hydrateformation. The concentration of H2S must be between 0% and 80% to be within the limits of the correlations for the z-factor and between the limits of 0 and15% for the viscosity correlations. For values outside of this range F.A.S.T. VirtuWell™ will still complete the calculations, however results should be usedwith caution.


UNITS: Percent (%)

DEFAULT: 0

Gas DensityThe density of a gas varies with the in-situ conditions of pressure and temperature along a pipe. The gas density is calculated from the "real gas" law :

where:

G = Gas Gravity

P = Pressure (psia)

z = compressibility factor

T = temperature (R)

The gas density is used in calculating the pressure drops caused by friction and by hydrostatic head.

UNITS: lb/ft3 (kg/m3)

Gas Compressibility factor (Z)The supercompressibility factor (also often called compressibility factor), z, of a natural gas is a measure of its deviation from ideal gas behavior. Its valueis usually between 0.8 and 1.2, but it can be as low as 0.3 and as high as 2.0. It is used in the calculation of gas densities, and in converting gas volumesand rates from standard conditions to reservoir conditions (and vice-versa).

Gas ViscosityThe viscosity of a fluid refers to the resistance to flow. It causes the pressure to drop in the direction of flow. It is used in the calculation of the "frictionpressure drop". For gas, the viscosity varies with gas gravity, temperature and pressure. Usually it is not measured, but is obtained from the Carr,Kobayashi and Burrows correlations, which include corrections for H2S, CO2 and N2. For sour gases, this correlation is preferred to the Lee, Gonzalez andEakin formulation (which does NOT account for H2S, CO2 and N2). Viscosity enters into the definition of Reynold’s Number, which is used to obtain thefriction factor from the Fanning friction factor charts.

Typically, gas viscosity is in the range of 0.015 to 0.03 centipoise (cp).

UNITS: cp (mPa.s)

Natural Gas HydratesThe detection of hydrate formation is available just in the Wellbore module. The procedure consists in compare the calculated onset temperature (obtained through thepressure at a certain depth in the wellbore) with the temperature in the wellbore at the same depth. If the temperature is below the hydrate temperature hydrates mayform.

C3H8Molar Concentration of Propane in the gas stream. It has a direct effect on the detection of hydrate formation. The concentration of C3H8 must be between0% and 10% to be within the limits of the Baillie-Wichert method for hydrates detection. For values outside of this range F.A.S.T. VirtuWell™ will stop thecalculations and the entered value will be highlited in red.

UNITS: Percent (%)

DEFAULT: 0



Condensate PropertiesThe Condensate Properties that can be entered into F.A.S.T. VirtuWell™ include:

Condensate DensitySeparator PressureSeparator TemperatureCondensate-Gas Ratio (CGR)

The Condensate Properties that are entered into F.A.S.T. VirtuWell™ are used to calculate a Recombined Gas Gravity and a Recombined Gas Rate. These are thenused in single-phase pressure drop calculations. A gas-condensate system is treated as a single-phase system with a recombined gas gravity and a recombined gasrate.

See Also: Recombination

Condensate DensityCondensate Density is the specific gravity in API of condensate at stock tank conditions. It ranges from 60 API to 40 API. The API Gravity is readilyobtained from any laboratory oil analysis. It is a fixed property of the condensate.

In F.A.S.T. VirtuWell™, this variable is used to calculate the Recombined Gas Gravity and the Recombined Gas Rate which are then used in single-phasepressure drop calculations.

The conversion from API Gravity (field units) to Stock Tank Oil Density (metric units) is:

Stock Tank Density (kg/m3) = 1000 * (141.5 / (API + 131.5))

UNITS: API (kg/m3)

DEFAULT: None

Separator PressureThe separator pressure is the pressure in the separator or at wellhead. It is used in the recombination calculations to calculate the vapour equivalent of thecondensate, the recombined gas rate and the recombined gas gravity.

UNITS: psia (kPaA)

DEFAULT: 100 psia

Separator TemperatureThe separator temperature is the temperature in the separator or at wellhead. It is used in the recombination calculations to calculate the vapourequivalent of the condensate, the recombined gas rate and the recombined gas gravity.

UNITS: F (C)

DEFAULT: 100 F

Condensate Gas RatioThis is the condensate to gas ratio produced at surface. It is typically known from direct measurements. If the daily condensate rate is known, it must bedivided by the daily gas rate to obtain the Condensate-Gas Ratio. The CGR is used to calculate the Recombined Gas Gravity and the Recombined GasRate which are used in the wellbore pressure drop calculations.

UNITS: Bbl/MMcf (m3/103m3)

DEFAULT: 0

Oil PropertiesIn this document, the word "oil" is used interchangeably with the word "condensate".

The Oil (Condensate) Properties that can be entered into F.A.S.T. VirtuWell™ include the API Gravity (Oil Density) and, in certain instances, the flowing Gas-Oil Ratio(GOR).

Although every oil has its unique PVT and flowing characteristics, the properties that affect the pressure loss in pipe flow can usually be characterized by the singlevariable, API Gravity. It can be correlated to the Oil Density, the Solution Gas-Oil Ratio, the Oil Viscosity and the Oil Formation Volume Factor at various pressures andtemperatures.

These oil properties can be measured in the laboratory or can be obtained from several published correlations. F.A.S.T. VirtuWell™ uses the "Beggs and Robinson"(1975) correlation for viscosity, and the "Vasquez and Beggs" (1980) correlation for the other oil properties.

The oil properties that can be entered into F.A.S.T. VirtuWell™ include:

Bubble Point PressureAPI Gravity

The API Gravity is used to determine the following at various temperatures and pressures:

Oil DensitySolution Gas-Oil RatioOil ViscosityOil Formation Volume Factor

The oil properties can be measured in the laboratory or obtained from several published correlations. F.A.S.T. VirtuWell™ uses the "Beggs and Robinson" correlation forviscosity, and the "Vasquez and Beggs" correlation for the other oil properties. The flowing Gas-Oil Ratio affects the pressure drop calculations in multiphase flow.

Bubble Point PressureThe Bubble Point Pressure is defined as the pressure at which the oil is saturated with gas. Above this pressure the oil is undersaturated, and the oil actsas a single phase liquid. At and below this pressure the oil is saturated, and any lowering of the pressure causes gas to be liberated resulting in two phase



flow.

The Bubble Point affects the Inflow Performance Relationship Curve (IPR) curve. Above this pressure, the IPR is a straight line, of slope equal to theinverse of productivity index. Below the bubble point pressure, the IPR is a curve based on "Vogel’s" equation. The straight line and the curve aretangential at the bubble point pressure, where they meet.

The bubble point pressure has a SIGNIFICANT effect on PVT correlations. It marks a drastic change, and a discontinuity, in the correlations. For example:

At pressures below the bubble point, the oil viscosity decreases with increasing pressure where as above the bubble point the viscosity increases.The solution gas-oil ratio increases with increasing pressure up to the bubble point and is constant thereafter.The oil formation volume factor increases with increasing pressure and decreases slightly thereafter.

UNITS: psia or kPa (absolute)

DEFAULT: None

API GravityAPI Gravity is the specific gravity (density) of oil at stock tank conditions. It ranges from 60 °API (condensate) to 45 °API (light oil) to 20 °API (mediumdensity) to 10 °API (heavy oil). The API Gravity is readily obtained from any laboratory oil analysis. It is a fixed property of the oil, and is independent of theoperating pressure or temperature, unlike the in-situ oil density that is very dependent on operating pressure and temperature conditions.

In F.A.S.T. VirtuWell™, this variable is the primary variable used for calculating the oil properties at the required pressures and temperatures. API Gravityaffects four variables namely:

Oil viscositySolution gas-oil ratioOil formation volume factorOil density (in situ)

The primary effect of API Gravity is on the in-situ oil density. The density affects the friction pressure drop to some extent, but it affects the hydrostaticpressure drop DIRECTLY.

The conversion from API Gravity (field units) to Stock Tank Oil Density (metric units) is:

Stock Tank Density (kg/m3) = 1000 * (141.5 / (API + 131.5))The API Gravity must be between 16 °API and 58 °API to be within the range of the correlations. When the parameter name is displayed in yellow this awarning that the entered value is outside the range.

UNITS: °API (kg/m3)

DEFAULT: None

LIMITS: 16 °API < G < 58 °API

Oil Density (in-situ)

The in-situ oil density should not be confused with the API Gravity (Stock Tank Oil Density). The in-situ oil density varies with pressure and temperature,but more so with the amount of dissolved gas contained in the oil (Solution Gas-Oil Ratio), whereas the API gravity is a fixed property of the particular oil,independent of operating conditions. The in-situ oil density is obtained by multiplying the density at stock tank conditions by the Formation Volume Factorat the in-situ pressure and temperature conditions. Thus:

Oil density (in-situ) = Oil Density (Stock Tank Conditions) * Oil Formation Volume FactorThe oil density affects the Hydrostatic Pressure Loss and the Friction Pressure Loss.

UNITS: lb/ft3 (kg/m3)

DEFAULT: Vasquez and Beggs correlation

Solution Gas-Oil RatioThis is the amount of gas dissolved in the oil at any pressure. It increases approximately linearly with pressure. It is a function of the oil and gascomposition. A heavy oil contains less dissolved gas than a light oil. In general, the solution gas-oil ratio varies from 0 (dead oil) to approximately 2000SCF/Bbl (very light oil). The solution gas-oil ratio increases with pressure until the bubble point pressure is reached, after which it is a constant, and the oilis said to be under-saturated.

The solution gas-oil ratio has a significant influence on the oil formation volume factor and the oil viscosity.

When a mixture of gas and oil is flowing in a pipe or wellbore, the actual quantity of "free gas" that is flowing increases as the pressure of the gas-oilsystem decreases. This is due to gas "coming out of solution from the oil" and becoming free gas, thus increasing the gas flow rate, and decreasing the oilflow rate. In the F.A.S.T. VirtuWell™ program, the solution gas-oil ratio is used for accounting for the changes in the in-situ gas rate along the pipe orwellbore.

The solution gas-oil ratio is readily obtained from laboratory PVT measurements, or as is done in the F.A.S.T. VirtuWell™ program, it may be calculatedfrom correlations such as "Vasquez and Beggs".

UNITS: SCF/Bbl (m3/m3)

DEFAULT: Vasquez and Beggs correlation

Oil ViscosityThis is the value of the oil viscosity at in-situ conditions. It is a very strong function of temperature, API Gravity (Stock Tank Oil Density) and Solution Gas-Oil Ratio.

Below the bubble point pressure, the amount of gas dissolved in the oil increases as the pressure is increased. This causes the in-situ oil viscosity todecrease significantly. Above the bubble point pressure, oil viscosity increases minimally with increasing pressure.

The oil viscosity can be measured as a function of pressure in most PVT laboratory measurements. In the F.A.S.T. VirtuWell™ program it is calculatedfrom the correlation of "Beggs and Robinson" at the appropriate pressure and temperature. These correlations are very sensitive to solution gas-oil ratioand to oil gravity. The oil viscosity can vary from 10 000 cp for a heavy oil to less than 1 cp for a light oil.

The oil viscosity has a very strong effect on the friction pressure loss, but no effect on the hydrostatic pressure difference.

UNITS: cp (mPa.s)



DEFAULT: Beggs and Robinson correlation

Oil Formation Volume FactorThis is defined as the ratio of the volume of oil at operating conditions to that at stock tank conditions. This factor is used to convert the flow rate and thedensity of oil (both normally reported at stock tank conditions) to in-situ conditions. Thus,

Oil Flow Rate (in-situ Barrels) = Oil Flow Rate (Stock Tank Barrels) * Oil Formation Volume Factor

and

Oil density (in-situ) = Oil Density (Stock Tank Conditions) * Oil Formation Volume Factor

In the equations used in F.A.S.T. VirtuWell™ the oil rate and the oil density should be expressed at in-situ conditions, because the equations apply to thepressure and temperature conditions inside the pipe. However, the oil flow rate is generally measured at the surface, in stock tank barrels. Therefore, thisrate is multiplied by the oil formation volume factor to convert it to in-situ conditions. Similarly, it is the in-situ density that counts, and that is obtained fromthe API Gravity (Stock Tank Oil Density) and the Formation Volume Factor

Below the bubble point pressure, the oil formation volume factor increases with pressure. This is because more gas goes into solution as the pressure isincreased and this causes the oil to swell. Above the bubble point pressure, the oil formation volume factor decreases as the pressure is increased,because there is no more gas available to go into solution, and the oil is being compressed.

The value of the oil formation volume factor is generally between 1 and 2 RB/STB (m3/m3). It is readily obtained from laboratory PVT measurements, or itmay be calculated from correlations such as "Vasquez and Beggs".

In the correlations that are being used to calculate the oil formation volume factor, the Solution Gas-Oil Ratio is the most significant variable.

UNITS: Bbl/Bbl (m3/m3)

DEFAULTS: Vasquez and Beggs correlation

Water PropertiesCurrently, water gravity is the only property that can be entered, but water can potentially have a large effect on a system.

Water GravitySpecific Gravity is defined as the density of the liquid divided by the density of water at standard conditions (62.3 lb/ft3, 1000 kg/m3). The gravity of purewater is therefore 1.0. Often oilfield waters are saline and have a specific gravity slightly greater than 1.0.

The primary effect of water gravity is on the density of water, which in turn affects the hydrostatic pressure difference.

UNITS: None

DEFAULT: 1

Fluid Property CorrelationsKhan et al (Saudi Arabian Oils)The Khan et al correlation contains equations for estimating oil viscosity at, above and below the bubble point for Saudi Arabian oils. The study used datafrom 75 bottom hole samples, which were taken from 65 Saudi Arabian reservoirs. The authors claim that this correlation gives the most accuratepredictions for Saudi Arabian crude oils, as compared to the Beggs and Robinson, Beal, and Chew and Connally correlations.

In order to calculate the viscosity, the solution gas-oil ratio (Rs) at the bubble point is required. There are two methods to calculate the viscosity with theKhan et al correlation. The first way is to input the value of Rs at the bubble point. This can be entered as shown in the following image.



In the case where there is no user selected value, the Rs value will be calculated using the correlation selected for Bo and Rs in the fluid properties tab.

In the correlation for oil viscosity at the bubble point, the oil specific gravity must be less than one in order to prevent division by zero in the equation. Inorder to handle this, we have added a limit that the oil gravity, in API, must be greater than 10 (specific gravity would then equal 1).

Oil Viscosity at the Bubble Point

Oil Viscosity above the Bubble Point

Oil Viscosity below the Bubble Point

NomenclatureThe limits used in the development of the correlation are listed after the symbol.

P = reservoir pressure, psia (14.7 – 5015)Pb= bubble point pressure, psia (107 – 4315)



Rs= solution gas-oil ratio, scf/STB (24 – 1901)T = reservoir temperature, F (75 – 240)

= gas specific gravity (air = 1) (0.752 – 1.367) = oil specific gravity (14.3 – 44.6 degrees API)

= relative temperature, (T+ 459.67)/459.67). (T is in F) = oil viscosity above the bubble point, cp (0.13 – 71.0) = oil viscosity below the bubble point, cp (0.13 – 77.4) = bubble point oil viscosity, cp (0.13 – 17.9)

ReferenceS.A. Khan, M.A. Al-Marhoun, S.O. Duffuaa, and S.A. Abu-Khamsin. "Viscosity Correlations for Saudi Arabian Crude Oils," SPE Paper No. 15720, 1987.

De Ghetto et al (Heavy and Extra-Heavy Oils)The De Ghetto et al correlation contains modified PVT correlations for estimating bubble point pressure, solution gas-oil ratio, oil formation volume factor,oil compressibility, and oil viscosity for heavy and extra-heavy oils. Each correlation is modified specifically for heavy oils (10 < oAPI < 22.3), and extraheavy oils (oAPI < 10). The oils used for developing the correlation came from the Mediterranean Basin, Africa and the Persian Gulf, taken from AGIP’sreservoir fluid samples. When comparing published correlations, De Ghetto et al decided that the Vazquez and Beggs correlation estimated the oilformation volume factor with minimal error, and therefore no further modification was needed. The Vazquez and Beggs correlation for oil formation volumefactor is included in the De Ghetto et al correlation.

Important Note: In contrast with other correlations, the De Ghetto et al correlation requires the pressure and temperature at the separator. Thesevalues may be specified by selecting Properties Calculation Parameters in the Options menu as shown in the following picture.

Bubble Point PressureHeavy oils: Modified Vazquez and Beggs solution gas-oil ratio correlation reversed to solve for the bubble point pressure.

Where



Extra-Heavy oils: Modified Standing’s solution gas-oil ratio correlation, reversed to solve for the bubble point pressure.

Solution Gas-Oil-RatioHeavy oils: Modified Vasquez-Begg's correlation

is calculated the same as above.

Extra-heavy oils: Modified Standing’s correlation

Oil Formation Volume FactorGas saturated: Vazquez and Beggs correlation

Where

Undersaturated:

Oil CompressibilityUndersaturated:

Heavy oils: Modified Vasquez-Begg's correlation

is calculated the same as above.

Extra-heavy oils: Modified Vasquez-Begg's correlation

Gas saturated:

The derivatives dBo/dRs and dRs/dP where taken from the Vazquez and Beggs correlation.

Oil ViscosityDead Oil:

Heavy-oils: Modified Egbogah-Jack’s correlation

Extra-heavy oils: Modified Egbogah-Jack’s correlation



Gas saturated:

Heavy Oils: Modified Kartoatmodjo’s Correlation

Where

Extra-heavy oils: Modified Kartoatmodjo’s correlation

Where

Y is calculated the same as for heavy oils, which is shown above.

Undersaturated:

Heavy Oils: Modified Kartoatmodjo’s correlation

Extra-heavy oils: Modified Labedi’s correlation

NomenclatureIf available, the limits used in the development of the correlation are listed after the symbol.

API = oil gravity, API (6 – 22.3)Bg = gas formation volume factor, bbl/scfBo = oil formation volume factor, bbl/STB (1.057 – 1.362)Bob = oil formation volume factor at the bubble point, bbl/STBCo = oil compressibility, (3.02 x 10-5 – 4.29 x 10-5)

P = reservoir pressure, psia (1038.49 – 7411.54)Pb = bubble point pressure, psia (208.86 – 4021.96)Psp = separator pressure, psia (14.5 – 752.2)Rs = solution gas-oil ratio, scf/STB (17.21 – 640.25)T = reservoir temperature, F(131.4 – 250.7)Tsp = separator pressure, psia (59 – 177.8)X = intermediate variableY = intermediate variable

= gas specific gravity (air = 1) (0.623 – 1.517)

= gas specific gravity at separator pressure of 114.7 psia = undersaturated oil viscosity, cp (2.4 – 354.6) = dead-oil or gas-free oil viscosity, cp (7.7 – 1386.9) = gas-saturated oil viscosity, cp (2.1 – 295.9)

ReferenceGiambattista De Ghetto, Francesco Paone and Marco Villa. "Pressure-Volume-Temperature Correlations for Heavy and Extra Heavy Oils," SPE 30316,1995.

Velarde et al (Reduced Variable Approach)The Velarde et al correlation contains equations for estimating bubble point pressure, solution gas-oil ratio and oil formation volume factor. The correlationfor the solution gas-oil ratio uses a reduced variable approach, and so the final equation is solved for the reduced solution gas-oil ratio. The reducedsolution gas-oil ratio is defined as the solution gas-oil ratio divided by the solution gas-oil ratio at the bubble point. Similarly, the reduced pressure isdefined as the pressure divided by the bubble point pressure.

Note that the reservoir pressure and the bubble point pressure used in the reduced pressure equation are in units of psig.



Bubble Point PressureThe bubble point pressure in this equation is in units of psia.

Where

Solution Gas-Oil Ratio at the Bubble Point Pressure

The bubble point pressure equation is reversed to solve for the solution gas-oil ratio. The bubble point pressure in this equation is in units ofpsia.

Where X is calculated the same as above

Solution Gas-Oil RatioOnce the reduced solution gas-oil ratio has been calculated, the solution gas-oil ratio at the bubble point calculated above is used to solvefor the solution gas-oil ration at any pressure below the bubble point. The pressures used in this correlation are in units of psig. We use apressure of 14.7 psi as our atmospheric pressure.

In order to prevent the calculation of a negative solution gas-oil ratio, we have implemented a limit on the variable . If the value of

is greater than one, it is given a value of one.

where:

Oil Formation Volume FactorGas saturated:

oR can be calculated using the following correlations:

where:



po is calculated through iteration using the following equations. The calculations are done ten times. The values from the ninth and tenthcalculations are averaged to give you a final value for .

Undersaturated:

The oil compressibility used in this equation is obtained from the Vazquez and Beggs correlation.

NomenclatureThe limits used in the development of the correlation are in two tables after the list of symbols. One set of limits was used to develop the solution gas-oilratio correlation, the other used to develop the bubble point pressure correlation.

API = oil gravity, degrees APIBo = oil formation volume factor, bbl/STBBob = oil formation volume factor at the bubble point, bbl/STBP = reservoir pressure, psiaPb = bubble point pressure, psiaPr = reduced pressure, psig/psigRs = solution gas-oil ratio, scf/STBRsb = solution gas-oil ratio at the bubble point, scf/STBRsr = reduced solution gas-oil ratio,

T = reservoir temperature, degrees FX = intermediate variable

= gas specific gravity (air = 1))bs = pseudo liquid density at reservoir pressure and standard temperature, 60 degrees F, lbm/cu ft

po = pseudo liquid density at standard conditions, lbm/cu ft

STO = stock tank oil density, lbm/cu ft

ReferenceJ. Velarde, T.A. Blasingame and W.D. McCain, Jr. "Correlation of Black Oil Properties at Pressures Below Bubble Point Pressure – A New Approach," ThePetroleum Society 97-93, 1997.

Beggs and Robinson



Beggs and Robinson is a generally applicable correlation containing equations for dead, gas-saturated and undersaturated oil viscosity. The correlationwas developed using a wide range of PVT data.

In order to calculate the viscosity, the Beggs and Robinson correlation requires a solution gas-oil ratio (Rs).

Dead Oil Viscosity

where

Gas Saturated Oil Viscosity

where

Undersaturated Oil Viscosity

where

C1 = 2.6C2= 1.187C3 = -11.513C4 = -8.98x10-5


A = intermediate variableAPI = oil gravity, degrees API (16 – 58)B = intermediate variableP = reservoir pressure, psia (0 – 5250)Pb = bubble point pressure, psiaRs = solution gas-oil ratio, scf/STB (20 – 2070)T = reservoir temperature, F (70 – 295)X = intermediate variableY = intermediate variableZ = intermediate variable

= oil viscosity, cp

ob = oil viscosity at the bubble point, cp

oD = dead oil viscosity, cp

ReferenceH.D. Beggs and J.R. Robinson. "Estimating the Viscosity of Crude Oil Systems," JPT 1140-41, September 1975.

Vazquez and Beggs (Generally Applicable)Vazquez and Beggs is a generally applicable correlation containing equations for solution gas-oil ratio, oil formation volume factor, and oil compressibility.The correlation was developed from 600 laboratory PVT analyses from fields all over the world. The data used in the development of the correlationincluded wide ranges of pressure, temperature and oil properties. The correlation divides the data into two groups bases on oil gravity. The division ismade at an oil gravity of 30 degrees API.

Bubble Point Pressure

where:



Solution Gas-Oil Ratio

The coefficients C1, C2 and C3 are the same as for the bubble point pressure equation.

Oil Formation Volume FactorsGas saturated:

where:

Undersaturated:


where

A1 = -1433.0A2 = 5.0A3 = 17.2A4 = -1180.0A5 = 12.61A6 = 105

Gas saturated:

The derivatives dBo / dRs and dRs/dP where taken from the Vazquez and Beggs correlation.


API = oil gravity, degrees API (15.3 – 59.5)Bg = gas formation volume factor, bbl/scfBo = oil formation volume factor, bbl/STBBob = oil formation volume factor at the bubble point, bbl/STBP = reservoir pressure, psia (140.7 – 9514.7)Pb = bubble point pressure, psiaRs = solution gas-oil ratio, scf/STBT = reservoir temperature, degrees F

g = gas specific gravity (air = 1) (0.511 – 1.351)

ReferenceM.E. Vazquez and H.D. Beggs. "Correlations for Fluid Physical Property Prediction," JPT 968-70, June 1980.



Petrosky and Farshad (Gulf of Mexico Oils)The Petrosky and Farshad correlation contains equations for estimating bubble point pressure, solution gas-oil ratio and oil formation volume factor and oilcompressibility for Gulf of Mexico oils. The correlation was developed with fluid samples taken from offshore Texas and Louisiana. The producing areasrepresented are from Galveston Island Eastward through Main Pass.

The authors claim that these correlations provide improved results over other correlations for the Gulf of Mexico, including those published by Standing,Vazquez and Beggs, Glaso and Al-Marhoun.


Where


Where


Undersaturated:

Oil CompressibilityGas saturated:

Undersaturated:

The derivatives dBo/dRs and dRs/dP were taken from the Vazquez and Beggs correlation.


API = oil gravity, degrees API (16.3 – 45.0)Bg = gas formation volume factor, bbl/scfBo = oil formation volume factor, bbl/STB (1.1178 – 1.6229)Bob = oil formation volume factor at the bubble point, bbl/STBco = oil compressibility, psia-1 (3.507 x 10-5 – 2.464 x 10-5)P = reservoir pressure, psia (1700 – 10692)Pb = bubble point pressure, psia (1574 – 6523)Rs = solution gas-oil ratio, scf/STB (217 – 1406)T = reservoir temperature, F (114 – 288)X = intermediate variable


o = oil specific gravity (water = 1)

ReferenceG.E. Petrosky Jr. and F.F. Farshad. "Pressure-Volume-Temperature Correlations for Gulf of Mexico Crude Oils," SPE 26644, 1993.

Ng and Egbogah



The Ng and Egbogah correlation contains two methods for calculating dead oil viscosity, a modified Beggs and Robinson correlation and a correlation thatuses the pour point temperature. When the Ng and Egbogah correlation has been selected or is being displayed on the comparison page, an input cell forthe pour point temperature will appear on the left side of the screen. If a pour point temperature is input, the program uses the pour point correlation tocalculate the viscosity of dead oil.

Pour point temperature is the lowest temperature at which the oil is observed to flow when cooled and examined under conditions prescribed in ASTMD97. The purpose of introducing the pour point temperature into the correlation is to reflect the chemical composition of crude oil into the viscositycorrelation.

The pour point temperature parameter entry is located in the options menu under Properties Calculation Parameters.

If a pour point temperature is not entered, the program uses the modified Beggs and Robinson correlation to calculate the viscosity of dead oil. To obtainthe viscosity for live oil, the dead oil correlations are used with the Beggs and Robinson viscosity correlation. The data used to derive the correlations wastaken from the Reservoir Fluids Analysis Laboratory of AGAT Engineering Ltd., using a total of 394 oil systems.

In order to calculate the viscosity, the Ng and Egbogah correlation requires a solution gas-oil ratio (Rs).

Modified Beggs and Robinson Viscosity Correlation

Pour Point Viscosity Correlation

Gas-Saturated Viscosity

where

Undersaturated Viscosity



where:

C1 = 2.6C2 = 1.187C3 = -11.513C4 = -8.98!10-5


API = oil gravity, API (5 - 58)P = reservoir pressure, psiaPb = bubble point pressure, psiaRs = solution gas-oil ratio, scf/STBT = reservoir temperature, C (15 – 80)TF = reservoir temperature, F (70 – 295)Tp = pour point temperature, C (-50 – 15)X = intermediate variableX = intermediate variableZ = intermediate variable

= oil specific gravity, (water = 1) = oil viscosity, cp

ob = oil viscosity at the bubble point, cp

oD = dead oil viscosity, cp

ReferencesAchong, I., "Revised Bean Performance Formula for Lake Maracaibo Wells", internal co. report, Shell Oil Co., Houston, TX, Oct 1961Ashford, F.E. and Pierce, P.E., "Determining Multiphase Pressure Drops and Flow Capacities in Down-Hole Safety Valves", SPE Paper No. 5161, J. Pet. Tech.,Sep 1975, 1145Baxendell, P.B., "Bean Performance – Lake Maracaibo Wells", internal co. report, Shell Oil Co., Houston, TX, Oct 1967Gilbert, W.E., "Flowing and Gas-Lift Well Performance", Drill. & Prod. Practice, 1954, 126Omana, R., Houssiere, C. Jr., Brown, K.E., Brill, J.P., and Thompson, R.E., "Multiphase Flow Through Chokes", SPE Paper No. 2682, paper presented atAnnual Fall Meeting of the SPE of AIME, Denver, CO, Sep 28 – Oct 1, 1969Ros, N.C.J., "An Analysis of Critical Simultaneous Gas-Liquid Flow Through a Restriction and Its Application to Flowmetering", Appl. Sci. Res. (9), 1960, 374

Standing (California Oils)The Standing correlation contains equations for estimating bubble point pressure, solution gas-oil ratio and oil formation volume factor for California oils.105 experimentally determined data points on 22 different oil-gas mixtures from California were used in the development of the correlations.




Undersaturated:


Nomenclature



The limits used in the development of the correlation are listed after the symbol.

API = oil gravity, API (16.5 – 63.8)Bo = oil formation volume factor, bbl/STB (1.024 – 2.15)Bob = oil formation volume factor at the bubble point, bbl/STBP = pressure, psiaPb = bubble point pressure, psia (200 –6000)Rs = solution gas-oil ratio, scf/STB (20 – 1425)TF = reservoir temperature, F (60 – 260 for bubble point correlation, 100 – 260 for oil formation volume factor correlation)co = oil compressibility, psia-1 (3.507 x 10-5 – 2.464 x 10-5)


o = oil specific gravity (water = 1)

ReferenceM.B. Standing. "A Pressure-Volume-Temperature Correlation for Mixtures of California Oil and Gases," Drill. & Prod. Prac., API, 1947.

Al-Marhoun 1985 (Saudi Arabian Oils)The Al-Marhoun correlation contains equations for estimating bubble point pressure, solution gas-oil ratio and oil formation volume factor for Saudi Arabianoils. 75 bottom hole fluid samples from 62 reservoirs in Saudi Arabia were used in the development of these correlations. The author claims that thecorrelations should be valid for all types of gas-oil mixtures that share similar properties as those used in the derivation. According to the author, theaverage errors and standard deviations were lower with the Al-Marhoun correlation than with the Standing and Glaso correlations for Saudi Arabian crudeoils.


Where

Solution Gas-Oil RatioThe bubble point pressure equation is reversed to solve for the solution gas-oil ratio. X must be solved for using the quadratic equation.

Where


Where

Undersaturated:



Bo = oil formation volume factor, bbl/STB (1.02 – 2.42)Bob = oil formation volume factor at the bubble point, bbl/STBP = reservoir pressure, psiaPb = bubble point pressure, psia (107 – 4315)Rs = solution gas-oil ratio, scf/STB (24 – 1901)T = reservoir temperature, (534.668 – 699.668)X = intermediate variable



Y = intermediate variableg = gas specific gravity (air = 1) (0.752 – 1.367)

o = oil specific gravity (water = 1) (14.3 – 44.6 degrees API)

ReferenceM.A. AL-Marhoun. "Pressure-Volume-Temperature Correlations for Saudi Crude Oils," SPE 13718, 1985

GLASO (North Sea Oils)The Glaso correlation contains equations for estimating bubble point pressure, solution gas-oil ratio and oil formation volume factor for North Sea oils. Theauthor claims that the correlation should be valid for all types of oil and gas mixtures after correcting for non-hydrocarbons in the surface gases and theparaffinicity of the oil. According to the author, the correlation more accurately predicts the oil properties of North Sea oils than the Standing correlation.

Bubble Point Correlation

Where

Solution Gas-Oil RatioThe bubble point pressure equation is reversed to solve for the solution gas-oil ratio. X must be solved for using the quadratic equation.

Where


Where

Undersaturated:



API = oil gravity, degrees API (22.3 –48.1)Bo = oil formation volume factor, bbl/STB (1.087 – 2.588)Bob = oil formation volume factor at the bubble point, bbl/STBP = reservoir pressure, psia (400 – 4000)Pb = bubble point pressure, psia (150 – 7127)Rs = solution gas-oil ratio, scf/STB (90 – 2637)T = reservoir temperature, F (80 – 280)X = intermediate variableY = intermediate variable




o = oil specific gravity (water = 1) (0.788 – 0.920)

ReferenceOistein Glaso. "Generalized Pressure-Volume-Temperature Correlations," Journal of Petroleum Technology, 1980.

Hanafy et al (Egyptian Oils)The Hanafy et al correlation contains equations for estimating bubble point pressure, solution gas-oil ratio and oil formation volume factor and oilcompressibility, oil density and oil viscosity for Egyptian oils. The compressibility correlation assumes constant compressibility after the bubble point. Thiscorrelation is independent of oil gravity and reservoir temperature.

The PVT data used in the derivation of the correlations was distributed along three different regions of Egypt: The Gulf of Suez, Western Desert and Sinairegions. The authors claim that the correlations can be used to estimate oil properties for a wide range of crude oils ranging from heavy to volatile oils.However our observations are that it appears to be closer to the properties of light oils.


Solution Gas-Oil RatioTo prevent the calculation of a negative solution gas-oil ratio, 0 is returned for pressures less than 157.28 psia.


Undersaturated:

Oil DensityNOTE: the density is calculated in metric units, gm/cc.

Gas saturated:

Undersaturated:


This correlation uses only the oil density at the bubble point. Therefore the oil compressibility is constant for pressures greater than thebubble point.

Gas saturated:

The derivatives and were taken from the Vazquez and Beggs correlation.

Oil ViscosityThis correlation calculates the oil viscosity at any pressure using the corresponding oil density.


Bg = gas formation volume factor, bbl/scfBo = oil formation volume factor, bbl/STB (1.032 – 4.35)Bob = oil formation volume factor at the bubble point, bbl/STBco = oil compressibility, ( - ?)P = reservoir pressure, psiaPb = bubble point pressure, psia (36 – 5003)HL = solution gas-oil ratio, scf/STB (7 – 4272)



ob = gas-saturated oil density, gm/cc (0.428 – 0.939)ou = undersaturated oil density, gm/cc (0.648 – 1.071) = oil viscosity, cp (0.119 – 106.6)

ReferenceH.H. Hanafy, S.M. Macary, Y.M. ElNady, A.A. Bayomi and M.H. El Batanony. "A New Approach for Predicting the Crude Oil Properties," SPE 37439, 1997.

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