# PVT

The black oil model is used to calculate PVT properties of fluids. In this model, we treat oil and gas phases as a single component. The requirements for creating a black oil PVT model are described as follows:

The Black Oil PVT engine consumes the oil gravity in degree API which is calculated as:

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where:

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is the oil specific gravity obtained from

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*sc denotes standard conditions usually 14.7 psia and 60 F.

Gas specific gravity is calculated as:

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To improve the gas phase PVT calculations, mole fraction of nitrogen (N2), carbon dioxide (CO2) and hydrogen sulfide (H2S) are used if available. The remaining gas mixture will be assumed as hydrocarbons (HC) as:

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GOR represents the ratio of gas volume to oil volume at standard conditions.

This parameter represents the total dissolved solids in aqueous phase in parts per million (ppm) unit.

Black oil properties are calculated using the following correlations:

Several correlations have been considered for solution-gas-oil-ratio calculation in the Xecta Production V1 as following:1- Standing (1947) correlation,2- Vazquez and Beggs (1980) correlation,3- Lasater (1958) correlation,4- Glasø (1980) correlation

Details of above-mentioned correlations can be found from:

- Standing, M.B. A Pressure-Volume-Temperature Correlation for Mixtures of California Oils and Gases. API Drilling and Production Practice (1947): 275-287.
- Glasø, Ø. Generalized Pressure-Volume-Temperature Correlations. J Pet Technol (1980) 32 (5), 785-795. SPE-8016-PA.
- Lasater, J.A. Bubble Point Pressure Correlations. J Pet Technol (1958) 10 (5), 65–67. SPE-957-G
- Vazquez, M. and Beggs, H.D. Correlations for Fluid Physical Property Prediction. J Pet Technol (1980) 32 (6), 968-970. SPE-6719-PA.

The correlations described for calculation of solution-gas-oil-ratio are re-arranged and utilized for bubble point pressure calculations.

Correlations utilized for calculation of Oil FVF in the Xecta Production V1 as following:1- Standing (1947) correlation,2- Vazquez and Beggs (1980) correlation,3- Glasø (1980) correlation

Details of above-mentioned correlations can be found from:

- Standing, M.B. A Pressure-Volume-Temperature Correlation for Mixtures of California Oils and Gases. API Drilling and Production Practice (1947): 275-287.
- Vazquez, M. and Beggs, H.D. Correlations for Fluid Physical Property Prediction. J Pet Technol (1980) 32 (6), 968-970. SPE-6719-PA.
- Glasø, Ø. Generalized Pressure-Volume-Temperature Correlations. J Pet Technol (1980) 32 (5), 785-795. SPE-8016-PA.

Vazquez and Beggs (1980) correlation is used to calculate the oil isothermal compressibility. Details are given in

- Vazquez, M. and Beggs, H.D. Correlations for Fluid Physical Property Prediction. J Pet Technol (1980) 32 (6), 968-970. SPE-6719-PA.

The following correlations have been implemented in Xecta Production V1 for calculation of oil phase viscosity.1- Beal (1946) correlation,2- Beggs and Robinson (1975) correlation,The details can be found from:

- Beggs, H.D. and Robinson, J.R. 1975. Estimating the Viscosity of Crude Oil Systems. J Pet Technol 27 (9): 1140-1141. SPE-5434-PA
- Beal, C., “The Viscosity of Air, Water, Natural Gas, Crude Oils and its Associated Gases at Oil Field Temperatures and Pressures,” Trans. AIME, 1946, Vol. 165, pp. 94–112.

The following correlation is used to calculatethe oil phase density:

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where:

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shows the specific gravity of gas and oil. The B denoted the formation-volume-factor of the oil phase. Rs shows the solution-gas-oil ratio in scf/STB.

Two correlations have been implemented to calculate gas/oil surface tension as follows:1- Abdul-Majeed and Abu Al-Soof (2000),2- Baker and Swerdloff (1955)Details of the correlations can be found from:

- Abdul-Majeed, G.H. and Abu Al-Soof, N.B. 2000. Estimation of gas–oil surface tension. J. Pet. Sci. Eng. 27 (3–4): 197-200
- Baker, O. and Swerdloff, W. 1955. Calculation of Surface Tension 3—Calculating parachor Values. Oil Gas J. (5 December 1955): 141.

Correlation of Firoozabadi and Rame (1988) has been utilized to calculate the surface tension of oil/water phases. Details can be found from Firoozabadi, A. and Ramey Jr., H.J. Surface Tension of Water-Hydrocarbon Systems at Reservoir Conditions. J Can Pet Technol (1988) 27 (May–June), 41–48

To calculate the gas/water surface tension, two correlations have been utilized in Xecta Production V1:

- Firoozabadi and Rame (1988), and,
- Jennings and Newman (1971) as descibed inH.Y. Jennings Jr., G.H. Newman, The effect of temperature and pressure on the interfacial tension of water against methane-normal decane mixtures. SPE 1971, pp. 171–175

Compressibility factor of the gas phase can be calculated using two equations:

- Hall and Yarborough’s correlation (1973) (Default)
- Dranchuk and Abou-Kassem’s correlation (1975)

The details of correlations can be found from following references:Hall, K. R., Yarborough, L., *A New Equation-of-State for Z-factor Cal- culations*, Oil and Gas Journal, June 18, 1973, 82–92.Dranchuk, P. M., Abu-Kassem, J. H., *Calculation of Z-factors for Nat- ural Gases Using Equations-of-State*, JCPT, July–Sept., 1975, 34–36.

FVF of the gas phase is obtained after calculating of compressibility factor (Z) as:

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where T and P denote absolute temperature (R) and pressure (psia), respectively.

At each temperature and pressure, after calculation of gas compressibility factor (Z), density of gas can be calculated as

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There are two correlations to calculate the gas phase viscosity.**Carr-Kobayashi-Burrows Correlation (1954) **The details and parameters can be found fromCarr, N., Kobayashi, R., Burrows, D., Viscosity of Hydrocarbon Gases Under Pressure, *Trans. AIME*, 1954, Vol. 201, 270–275.**Lee-Gonzalez-Eakin Correlation(1966)**The details and parameters can be found fromLee, A. L., Gonzalez, M. H., Eakin, B. E., The Viscosity of Natural Gases, *JTP*, August 1966, 997–1000.

Details can be found fromOsif, T.L. The Effects of Salt, Gas, Temperature, and Pressure on the Compressibility of Water. *SPE Res Eng*, 1988, 3 (1), 175-181. SPE-13174-PA

Dotson. C.R. and Standing, M.B. 1944. Pressure, Volume, Temperature and Solubility Relations for Natural Gas-Water Mixtures. Drill. & Prod. Prac., API, 173.

Two correlations have been utilized to calculate the water phase FVF including:

- McCoy Correlation (Default),
- McCain CorrelationThe details of correlations can be found from following references:

- McCain, W.D. Jr.: McCain, W.D. Jr. 1990. The Properties of Petroleum Fluids, second edition. Tulsa, Oklahoma: PennWell Books.
- Tarik Ahmed, Reservoir Engineering Handbook, Gulf Professional Publishing (March 15, 2000)

Four correlations are available to calculate the aqueous phase viscosity including:

- McCoy Correlation
- McCain Correlation
- Van Wingen Correlation
- Matthews and Russell (1967)(Default)The details of correlations can be found from following references:

- Matthews, C.S. and Russell, D.G., 1967. Pressure Buildup and Flow Tests in Wells. SPE Monograph: 130-133.
- McCain, W.D. Jr.: McCain, W.D. Jr. 1990. The Properties of Petroleum Fluids, second edition. Tulsa, Oklahoma: PennWell Books.

Two correlations can be used to calculate water density:

This correlation is applied to consider the effect of dissolved solids in aqueous phase as:

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where S denotes the dissolved salts in mass percent. Then, the water density at standard conditions can be converted to reservoir conditions by dividing to water FVF as:

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More details can be found fromMcCain Jr., W.D. *Reservoir-Fluid Property Correlations-State of the Art*, SPE Res Eng 6 (2), 1991, 266-272 (SPE-18571-PA)

This correlation considers effect of both dissolved solid and gas on the density of water as:

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where S is the water salinity in ppm and

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is the solution gas-water ration (scf/STB).

There are two correlations to calculate the dissolved gas in water phase in Xecta black oil PVT package.

This correlation calculates the gas solubility in pure water as:

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where A, B, and C are the temperature dependent parameters.

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Then, effect of water salinity is captured as:

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This correlation calculates the gas solubility in pure water as:

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where A, B, and C are the temperature dependent parameters.

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Gas solubility in saline water is calculated as:

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where S is dissolved solids in water in mass percent.

- Dranchuk PM, Abou-kassem JH (1975) Calculation of z factors for natural gases using equations of state. J Can Pet Technol. Link
- Hall, K.R., Yarborough, L., 1973. A new equation-of-state for Z-factor calculations. Oil Gas J. 71, 82–92.