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, Bo:
Here ql 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, Rs, according to
where Bg is the gas formation volume factor, addressed further in and Rp is the produced gas–oil ratio in SCF/STB.
The oil-formation volume factor and the solution gas–oil ratio, Rs, 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 Tsep is in °F, psep is in psia, and γo is in °API. The solution gas–oil ratio is then, for γo ≤ 30°API,
and for γo > 30°API,
where
For pressures below the bubble-point pressure, the oil-formation volume factor for γo > 30°API is
and for γo > 30°API is
where
and for pressure above the bubble point is
where
and Bob 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, Rp, so the bubble-point pressure can be estimated from Equations (3-9) or (3-10) by setting Rs = Rp and solving for p. Then Equation (3-12) or (3-13) may be used to calculate Bob.
3.2.2.1. Liquid Density
The oil density at pressures below the bubble point is
where ρo is in lbm/ft3 and γgd 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 Bo is calculated from Equation (3-13) and Bob from Equation (3-12) or (3-13), with Rs = Rp.
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.)
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