1. Two Phase Pipeline Example
Ref.: Brill & Beggs, Two Phase Flow in Pipes, 6th Edition, Chapter 3.

2. Two Phase Flow Example 1: Description
d1 , L1
DZ1 P1
For the above two-phase pipeline, calculate the exit pressure (P2) based on the Beggs and Brill equation. Compare the manual calculation results with Hysys software results (using Pipe Segment and Pipesys) .
Feed specifications:
T1 = 60 oF, P1 = 1000 psia, qgtsc= 50 MMscfd, qosc = bbl/day, γgt = , γo = 31.3 oAPI,
Pipeline specifications:
L1 = 900 ft, ΔZ1 = 10 ft, d1= 12 in nominal (Mild Steel, Schedule 40), T2 = 60 oF

3. Two Phase Flow Example 1: Description
For using compositional model (in Hysys), the following analysis of produced oil and gas at standard conditions are exist:
Produced Gas at S. C.
Light Ends Analysis
Distillation Curve and Density (oAPI=31.3)
Mole, %
Components
Liquid Vol. %
Density, oAPI
Cut Temp, oF
6.8311 N2
0.0013
----
145
2.85
1.3467
H2S
0.014
57.7
167
3.83
0.9777
CO2
0.0037
56.4
212
5.63 C1
0.0733
55.4
257
7.33
7.5713 C2
0.0803
52.3
302
10.03
2.9463 C3
0.1307
47.8
347
13.43
2.9119
i-C4
0.4177
42.6
392
18.53
1.8989
n-C4
0.3947
39.2
437
24.43
1.2841
i-C5
0.9029
35.8
482
34.23
0.8183
n-C5
0.7487
33.0
527
44.93
0.5388
C6+
Properties of C6+ : Molecular Weight = 89.53, Density = oAPI, N. Boiling point = 210 oF

4. Two Phase Flow Example 1: solution
In hand calculation, a single segment with Pav= P1 was used (for first iteration).
I didn’t find any reliable correlation for calculation of dissolved gas specific gravity, and therefore the specific gravity of free gas was selected from HYSYS software at input conditions: γgf =
Calculation of Rs and γgd needs a try and error, based on these equations:
Therefore:

5. Two Phase Flow Example 1: solution
Volume flow rate of free gas at inlet conditions can be calculated with using Bg:
Viscosity of oil and gas and surface tension between them can be calculated as:

6. Two Phase Flow Example 1: solution
Therefore, the two-phase no slip properties can be calculated as follows:
Flow regimes:
Liquid Hold and ρs:

7. Two Phase Flow Example 1: solution
Pressure gradient due to friction:
Outlet pressure: