PVT Correlations Formula

PVT (Pressure-Volume-Temperature) properties describe how reservoir fluids behave under changing conditions. Key properties include bubble point pressure (Pb), solution gas-oil ratio (Rs), oil formation volume factor (Bo), oil viscosity (μo), and gas compressibility factor (Z). Empirical correlation...

Overview

Theory

Black oil PVT correlations use surface measurements (API gravity, GOR, gas gravity, temperature) to estimate subsurface fluid properties. The most common correlations are:

Standing (1947): Bubble point pressure and Rs
Beggs-Robinson (1975): Dead and live oil viscosity
Vasquez-Beggs (1980): Oil FVF and Rs above Pb
Lee-Gonzalez-Eakin (1966): Gas viscosity

Formulas

Bubble Point Pressure — Standing (1947)

Pb = 18.2 * ((Rs/γg)^0.83 * 10^a - 1.4)

a = 0.00091*T - 0.0125*API

where Rs = solution GOR (scf/STB), γg = gas specific gravity, T = temperature (°F), API = oil API gravity.

Solution GOR — Standing

Rs = γg * (Pb/18.2 * 10^(-a) + 1.4)^(1/0.83) ... (inverted form)

Oil Formation Volume Factor — Standing

Bo = 0.9759 + 12e-5 * (Rs * sqrt(γg/γo) + 1.25*T)^1.2

Dead Oil Viscosity — Beggs-Robinson

μod = 10^(10^(3.0324 - 0.02023*API) * T^(-1.163)) - 1

Live Oil Viscosity — Beggs-Robinson

μo = A * μod^B
A = 10.715 * (Rs + 100)^(-0.515)
B = 5.44 * (Rs + 150)^(-0.338)

Gas Viscosity — Lee-Gonzalez-Eakin

μg = K * exp(X * ρg^Y) * 1e-4
K = (9.4 + 0.02*Mg) * T^1.5 / (209 + 19*Mg + T)
X = 3.5 + 986/T + 0.01*Mg
Y = 2.4 - 0.2*X

Worked Example

Given: API = 35°, GOR = 500 scf/STB, γg = 0.75, T = 200°F

Bubble Point (Standing):

a = 0.00091*200 - 0.0125*35 = 0.182 - 0.4375 = -0.2555
Pb = 18.2 * ((500/0.75)^0.83 * 10^(-0.2555) - 1.4)
   = 18.2 * (666.7^0.83 * 0.555 - 1.4)
   = 18.2 * (271.7 * 0.555 - 1.4)
   = 18.2 * (150.8 - 1.4)
   = 18.2 * 149.4
   = 2,719 psia

Dead Oil Viscosity (Beggs-Robinson):

X = 10^(3.0324 - 0.02023*35) = 10^(2.324) = 210.9
μod = 10^(210.9 * 200^(-1.163)) - 1
    = 10^(210.9 * 0.00173) - 1
    = 10^0.365 - 1
    = 2.32 - 1 = 1.32 cp

Valid Ranges

Correlation	Parameter	Range
Standing Pb	API	16.5 – 63.8°
Standing Pb	T	100 – 258°F
Standing Pb	Rs	20 – 1,425 scf/STB
Beggs-Robinson	API	16 – 58°
Beggs-Robinson	T	70 – 295°F
Beggs-Robinson	P	132 – 5,265 psia

References

Standing, M.B. (1947). "A Pressure-Volume-Temperature Correlation for Mixtures of California Oils and Gases." Drilling and Production Practice, API.
Beggs, H.D. & Robinson, J.R. (1975). "Estimating the Viscosity of Crude Oil Systems." JPT, 27(9), 1140–1141.
Vasquez, M. & Beggs, H.D. (1980). "Correlations for Fluid Physical Property Prediction." JPT, 32(6), 968–970.
PetroWiki — Oil PVT correlations: https://petrowiki.spe.org/Oil_fluid_properties

PVT Correlations