Over the years many correlations have been developed for predicting the pressure drop in two-phase flow. Nearly all of these procedures recognize different possible flow regimes and most of them relate, in some way, the two phase pressure drop to the pressure drop with one phase flowing alone in the pipe. In addition, all of the procedures assume homogeneous flow, or flow in which the velocities of the gas phase and the liquid phase are assumed to be identical. Incorporating "slip" in which the two phases can have different velocities is difficult and mathematically tedious. This paper presents a simple technique by which slip velocity can be incorporated in two-phase flow calculations for pressure drop.

Slip Correlation

Dukler et al. (l,2) presented a method based on similarity analysis for incorporating slip in two-phase flow calculations. If the segment length is sufficiently short, average values for the different variables will result in reasonably accurate predictions of two-phase pressure drop assuming a constant slip velocity. i.e. a constant ratio between the velocity of the liquid phase and the velocity of the gas phase.

Results of Calculation Using the New Procedure

The slip calculations outlined above were incorporated in the two-phase flow program originally programmed and presented by Akashah, Erbar and Maddox (3). Their procedure uses the Soave-Redlich-Kwong (SRK) equation of state for vapor-liquid equilibrium and enthalpy calculations. The SRK also gives gas phase densities. Liquid phase densities are calculated by the method of Hankinson and Thompson (4). Liquid and vapor viscosities are calculated using correlations of Thodos (5.6). Baker (7) presented test data for a two-phase oil pipeline. Two cases reported by Baker will be used to demonstrate the effect of incorporating slip in the two-phase pressure drop calculation. Data from Baker for the first case are shown in Table 1. The second case to be considered is exactly the same in all respects except that the inlet pressure to the line is 975 psia, the measured discharge pressure was 946 psia, and the line was 10.136 inches in diameter and 7.83 miles long. The comparison of calculations and experimental measurements for Case 1 are shown in Table II and Figure I. For that reason, the non-slip technique selected for comparison was that presented by the ASA-API joint study (8). As can be seen, there is a slight improvement in the predicted pressure drop when slip is incorporated in the calculation procedure. In an effort to determine the effect of vapor-liquid ratio on the pressure drop calculation, various vapor-liquid ratios at inlet pipeline conditions were studied. The same pipeline conditions and gas and liquid compositions were used as shown in Table II. The gas flow rate was maintained constant but the amount of oil entering the pipeline was varied over the range shown in Table IV. The resulting pressure drops calculated are shown in Figure 3. Again there is a consistent, but slight difference in the pressure drop calculated using the slip and homogeneous flow approaches.

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