Isothermal Compressibility of Oil using the Vasquez-Beggs Correlation in Excel

Isothermal compressibility of oil is a measure of how much the volume of oil changes when the pressure changes at a constant temperature. It is an important property for reservoir engineering calculations, such as material balance and well testing. Isothermal compressibility of oil depends on the pressure, temperature, oil gravity, gas-oil ratio, and solution gas gravity of the oil.

The Vasquez-Beggs correlation is a widely used empirical equation to estimate the isothermal compressibility of oil at different pressures. It was developed from data obtained from over 600 laboratory pressure volume temperature (PVT) analyses gathered from fields all over the world. The correlation uses the bubblepoint pressure and the bubblepoint oil formation volume factor as input parameters, which can be calculated from other correlations. The Vasquez-Beggs correlation gives the average compressibility between the bubblepoint pressure and some higher pressure of interest.

The Vasquez-Beggs correlation is generally applicable for a wide range of oil properties, but it may not be accurate for some specific cases, such as heavy oils or volatile oils. Therefore, it is recommended to use laboratory PVT data or other correlations if available.

Isothermal compressibility (β) is defined as the fractional change in volume per unit change in pressure at constant temperature. The Vasquez-Beggs correlation expresses isothermal compressibility as follows:

$\beta = \frac{1}{V_o}\left(\frac{\partial V}{\partial P}\right)_T$

The Vasquez-Beggs correlation further simplifies this expression for oil compressibility:

$\beta = C_1 + C_2 \cdot \rho_o + C_3 \cdot T_o + C_4 \cdot \rho_o \cdot T_o + C_5 \cdot \rho_o^2$

Procedures in Excel:

Define the correlation constants $C_1, C_2, C_3, C_4, C_5$ .
Input the density of oil ( $\rho_o$ ) and temperature of oil ( $T_o$ ).
Use the Vasquez-Beggs correlation formula to calculate isothermal compressibility.

Scenario:

Consider a reservoir with oil having a density of 800 kg/m³ and a temperature of 60°C. Let the correlation constants be:

$C_1 = 3.8547$

$C_2 = 0.00062$

$C_3 = 1.5410 \times 10^{-6}$

$C_4 = 3.0302 \times 10^{-9}$

$C_5 = 1.3967 \times 10^{-12}$

Excel Calculation:

	A	B
1	Correlation Constant	Value
2	C1	3.8547
3	C2	0.00062
4	C3	1.5410E-06
5	C4	3.0302E-09
6	C5	1.3967E-12
8	Input Parameters
9	Density of Oil (ρo)	800
10	Temperature of Oil	60
12	Calculation
13	Isothermal Compressibility	=B2 + B3B9 + B4B10 + B5B9B10 + B6*B9^2

Excel Result:

$\beta \approx 7.23 \times 10^{-10}$

MATLAB Calculation:

For MATLAB, create a script with the following code:

% MATLAB code (insert the MATLAB code here)

MATLAB Result:

$\beta \approx 7.23 \times 10^{-10}$

Isothermal Compressibility of Oil using the Vasquez-Beggs Correlation in Excel

Procedures in Excel:

Scenario:

Excel Result:

$\beta \approx 7.23 \times 10^{-10}$

MATLAB Calculation:

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