Isothermal Compressibility

Sometimes it is desirable to work with values of the liquid compressibility rather than the formation or relative volume factors. The isothermal compressibility, or the bulk modulus of elasticity of a liquid, is defined by Eq. (2.1):

The compressibility, c, is written in general terms since the equation applies for both liquids and solids. For a liquid oil, c will be given a subscript of c_o to differentiate it from a solid. Because dV/dp is a negative slope, the negative sign converts the oil compressibility, c_o, into a positive number. Because the values of the volume V and the slope of dV/dp are different at each pressure, the oil compressibility is different at each pressure, being higher at the lower pressure. Average oil compressibilities may be used by writing Eq. (2.1) as

The reference volume V in Eq. (2.33) may be V₁, V₂, or an average of V₁ and V₂. It is commonly reported for reference to the smaller volume—that is, the volume at the higher pressure. The following expressions determine the average compressibility of the fluid of Table 2.2 between 5000 psig and 4100 psig

between 4100 psig and 3400 psig

and between 3400 psig and 2695 psig

A compressibility of 13.03 × 10^–6 psi^–1 means that the volume of 1 million barrels of reservoir fluid will increase by 13.03 bbls for a reduction of 1 psi in pressure. The compressibility of undersaturated oils ranges from 5 to 100 × 10^–6 psi^–1, being higher for the higher API gravities, for the greater quantity of solution gas, and for higher temperatures.

Spivey, Valko, and McCain presented a correlation for estimating the compressibility for pressures above the bubble-point pressure.²² This correlation yields the compressibility in units of microsips (1 microsip = 10^–6/psi). The correlation involves the following equations:

The correlation gives good results for the following ranges of data:

11.6 ≤ ρ_o,API ≤ 57.7 °API

0.561 ≤ γ_g,SP ≤ 1.798 (air = 1)

120.7 ≤ p_b ≤ 6658.7 psia

414.7 ≤ p ≤ 8114.7 psia

12 ≤ R_sob ≤ 1808 SCF/STB

70.7 ≤ T ≤ 320 °F

3.6 ≤ c_o ≤ 50.3 microsips

Villena-Lanzi developed a correlation to estimate c_o for black oils.²³ A black oil has nearly all its dissolved gas removed. The correlation is good for pressures below the bubble-point pressure and is given by

where

T = °F

The correlation was developed from a database containing the following ranges:

31.0(10)^–6 < c_o (psia^–1) < 6600(10)^–6

500 < p (psig) < 5300

763 < p_b (psig) < 5300

78 < T (°F) < 330

1.5 < R_sob, gas-oil ratio (SCF/STB) < 1947

6.0 < ρ_{o, API} (°API) < 52.0

0.58 < γ_g < 1.20