Two Phase Pipeline Example Ref.: Brill & Beggs, Two Phase Flow in Pipes, 6th Edition, 1991. Chapter 3.

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 =100000 bbl/day, γgt = 0.7896, γo = 31.3 oAPI, Pipeline specifications: L1 = 900 ft, ΔZ1 = 10 ft, d1= 12 in nominal (Mild Steel, Schedule 40), T2 = 60 oF

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 72.8749 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 = 55.49 oAPI, N. Boiling point = 210 oF

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 = 0.6397 Calculation of Rs and γgd needs a try and error, based on these equations: Therefore:

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:

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

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