Property Correlations for Two-Phase Systems

This subsection presents the most widely used property correlations for two-phase oilfield hydrocarbon systems.

The downhole volumetric flow rate of oil is related to the surface rate through the formation volume factor, B_o:

Here q_l is the actual liquid flow rate at some location in the well or reservoir. The downhole gas rate depends on the solution gas–oil ratio, R_s, according to

where B_g is the gas formation volume factor, addressed further in and R_p is the produced gas–oil ratio in SCF/STB.

The oil-formation volume factor and the solution gas–oil ratio, R_s, vary with temperature and pressure. They can be obtained from laboratory PVT data or from correlations. One common correlation is the one of Standing, given in Figures 3-2 and 3-3. Another correlation that is accurate for a wide range of crude oils is that by Vasquez and Beggs (1990), given here.

First, the gas gravity is corrected to the reference separator pressure of 100 psig (114.7 psia):

where T_sep is in °F, p_sep is in psia, and γ_o is in °API. The solution gas–oil ratio is then, for γ_o ≤ 30°API,

and for γ_o > 30°API,

where

For pressures below the bubble-point pressure, the oil-formation volume factor for γ_o > 30°API is

and for γ_o > 30°API is

where

and for pressure above the bubble point is

where

and B_ob is the formation volume factor at the bubble point. At the bubble point, the solution gas–oil ratio is equal to the produced gas–oil ratio, R_p, so the bubble-point pressure can be estimated from Equations (3-9) or (3-10) by setting R_s = R_p and solving for p. Then Equation (3-12) or (3-13) may be used to calculate B_ob.

3.2.2.1. Liquid Density

The oil density at pressures below the bubble point is

where ρ_o is in lb_m/ft³ and γ_gd is the dissolved gas gravity because of the changing gas composition with temperature. It can be estimated from Figure 3-4 (Katz et al., 1959). Above the bubble point, the oil density is

where B_o is calculated from Equation (3-13) and B_ob from Equation (3-12) or (3-13), with R_s = R_p.

Figure 3-4. Prediction of gas gravity from solubility and crude-oil gravity. (After Katz et al., Handbook of Natural Gas Engineering, Copyright 1959, McGraw-Hill, reproduced with permission of McGraw-Hill.)