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 Chapter 4, 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_l is in °API. The solution gas–oil ratio is then, for γ_l ≤ 30°API,

and for γ_l > 30°API,

where

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

and for γ_l > 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.

(After Katz et al., Handbook of Natural Gas Engineering, Copyright 1959, McGraw-Hill, reproduced with permission of McGraw-Hill.)

Figure 3-4. Prediction of gas gravity from solubility and crude-oil gravity.

3.2.2.2. Oil Viscosity

Oil viscosity can be estimated with the correlations of Beggs and Robinson (1975) and Vasquez and Beggs (1980). The “dead” oil viscosity is

where

The oil viscosity at any other pressure below the bubble point is

where

If the stock tank oil viscosity is known, this value can be used for μ_od.

For pressures above the bubble point, the viscosity at the bubble point is first computed with Equations (3-19) through (3-25). Then

where

Gas viscosity can be estimated with the correlation that will be given in Chapter 4.

3.2.2.3. Accounting for the Presence of Water

When water is produced, the liquid flow properties are generally taken to be averages of the oil and water properties. If there is no slip between the oil and water phases, the liquid density is the volume fraction-weighted average of the oil and water densities. The volume fraction-weighted averages will be used to estimate liquid viscosities and surface tension, though there is no theoretical justification for this approach. The reader should note that in the petroleum literature it has been common practice to use volume fraction-weighted average liquid properties in oil–water–gas flow calculations. Also, the formation volume factor for water is normally assumed to be 1.0 because of low compressibility and gas solubility. Thus, when water and oil are flowing,

where WOR is the water–oil ratio, and σ is the surface tension.

Example 3-3. Estimating Downhole Properties

Suppose that 500 bbl/d of the oil described in Appendix B is being produced at WOR = 1.5 and R_p = 500 SCF/STB. The separator conditions for properties given in Appendix B are 100 psig and 100°F.

Using the correlations presented in Section 3.2.2, estimate the volumetric flow rates of the gas and liquid and the density and viscosity of the liquid at a point in the tubing where the pressure is 2000 psia and the temperature is 150°F.

Solution

The first step is to calculate R_s and B_o. Since the separator is at the reference condition of 100 psig, γ_gs = γ_g. From Equations (3-9) to (3-14),

The gas-formation volume factor, B_g, can be calculated from the real gas law. For T = 150°F and p = 2000 psi, it is 6.97 × 10^–3 res ft³/SCF. (This calculation is shown explicitly in Chapter 4.)

The volumetric flow rates are [Equations (3-28) and (3-7)]

To calculate the oil density, the dissolved gas gravity, γ_gd, must be estimated. From Figure 3-4 it is found to be equal to 0.85. Then, from Equation (3-17),

and, from Equation (3-29),

The oil viscosity can be estimated with Equation (3-19) through (3-25):

The liquid viscosity is then found from Equation (3-30), assuming μ_w = 1 cp:

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