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 Rp = 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 Rs and Bo. Since the separator is at the reference condition of 100 psig, γgs = γg. From Equations (3-9) to (3-14),
The gas-formation volume factor, Bg, 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.
The volumetric flow rates are [Equations (3-28) and (3-7)]
To calculate the oil density, the dissolved gas gravity, γgd, 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 μw = 1 cp:
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