1. Two-Phase Flow in Vertical Wells Notes to Accompany Week 5 Lab—Vertical Two-Phase Flow
Multi-Phase Flow in Wells
(see also PPS Ch. 7, pp 184 onward)

2. Multiphase Flow in Wells
The simultaneous flow of 2 or more phases will occur in
Almost all oil wells
Whenever the pressure drops below the bubble point, gas will evolve, and from that point to the surface, 2-phase flow will occur
In many gas wells
Condensation may occur as a result of the reduction of pressure and temperature as fluids flow up the well

3. Two-Phase Flow Is More Complicated Than Single-Phase Flow
The phases tend to separate because of differences in density
Shear stresses at the pipe wall are different for each phase - different density and viscosity
Expansion of the highly compressible gas phase with decreasing pressure increases the in situ volumetric flow rate of the gas

4. Two-Phase Flow—More Complicated
For upward flow, the less dense, more compressible, less viscous gas phase tends to flow at a higher velocity than the liquid phase causing a phenomenon known as slippage
Consider the 2-phase example to the right where both α and β are flowing upwards
α is less dense than β and will move faster than β
This phenomenon is called “holdup” – that is, the denser phase is “held-up” in the pipe relative to the lighter phase
So, the volume of the denser phase in the pipe is disproportionately greater than the volumetric flow rate of the denser phase feeding into the pipe

5. Two-Phase Flow Regimes
The flow regime or flow pattern is a qualitative description of the phase distribution
For gas-liquid, upward flow, 4 flow regimes are generally agreed upon in the two-phase literature
Bubble, Slug, Churn, and Annular
These occur as a progression with increasing gas rate for a given liquid rate
Slug and churn flow are sometimes combined in a flow pattern called intermittent flow
Some investigators have named annular flow as mist or annular-mist flow

6. Flow Regimes in Vertical, Upward Multiphase Flowing Wells is a Qualitative description of the Phase Distribution
Gas in the center
and liquid “hugging” or “climbing” the walls
Increasing
Gas-Liquid Ratio
Mist Flow
Intermittent Flow

7. The flow regime in gas-liquid, vertical flow can be predicted with a flow regime map – a plot relating flow regime to flow rates of each phase, fluid properties, and pipe size
The chart to the right is from Govier and Azis and shows these flow patterns and the approximate regions in which they occur as functions of gas and liquid velocities

8. Taitel-Dukler Flow Regime Map (from PPS Fig. 7-11)
A theoretical flow regime map was developed by Taitel, Barnea, and Dukler in 1980
This map identifies 5 flow regions, again based on gas and liquid velocities
Taitel-Dukler Flow Regime Map (from PPS Fig. 7-11)

9. Bubble Flow
Dispersed bubbles of gas in a continuous liquid phase

10. Slug Flow
At higher gas rates, the bubbles coalesce into larger bubbles, called Taylor bubbles, that eventually fill the entire pipe cross section
Between the large gas bubbles are slugs of liquid that contain smaller bubbles of gas entrained in the liquid

11. Churn Flow
With a further increase in gas rate, the larger gas bubbles become unstable and collapse, resulting in churn flow,
Churn flow is a chaotic flow of gas and liquid in which the shape of both the Taylor bubbles and the liquid slugs are distorted
It is a highly turbulent flow pattern
Churn flow is characterized by oscillatory, up-and-down motions of the liquid

12. Annular Flow
At higher rates, gas becomes the continuous phase, with liquid flowing in an annulus coating the surface of the pipe and with liquid droplets entrained in the gas phase

13. Note Differences in Flow Regimes
in Horizontal Pipes—gravity effects are important (we will look at horizontal two-phase flow in Week 6 Lab)

15. Two-Phase Flow Models
There are many different correlations that have been developed to calculate gas-liquid pressure gradients, most of which are empirically derived
Each correlation was likely derived for a specific set of conditions, so no single correlation will apply to all real-world cases
Become familiar with the assumptions inherent to each correlation and which correlation is best to use

16. Two-Phase Flow Models
The table at the right compares the relative errors of 8 different 2-phase flow correlations for different flow conditions
VW = vertical wells
DW = deviated wells
VNH = vertical well cases w/o Hagedorn and Brown data
Etc.
In this table, the smaller the relative performance factor, the more accurate is the correlations
The different flow correlation models are in the left column

17. Multiple Flow Regimes May Exist in a Well

18. Multiphase Flow Concepts
Flow Regimes
Velocities:
Superficial
Slip
In-situ
Holdup vs. input volume fraction

19. Flow Regimes: Vertical Flow
Four flow regimes:
Bubble
Slug
Churn
Annular
Change based on gas and liquid rate

20. Flow Regime Map: Vertical Flow
Govier and Aziz

21. Flow Regime Map: Vertical Flow
Taitel-Dukler Flow Regime Map (from PPS)

22. Flow Regimes in Horizontal Pipe Good animation:

23. Velocity Concepts

24. Velocity Differences

25. Holdup Vs. Input Fraction

26. Holdup Vs. Input Fraction

27. Two-Phase Flow Pressure Drop Calculation

28. Two-Phase Flow Models Several different empirical correlations:
Separated flow models:
Hagedorn-Brown (1965): only for vertical wells
Beggs-Brill (1973): any wellbore inclination and flow direction
Homogenous flow models:
Poettmann-Carpenter (1952)
Guo-Ghalambor (2005)

29. Two-Phase Gradient Curves
Based on given water/oil ratio (liquid density) and varying gas-liquid-ratio
Includes friction and potential pressure drops
For a fixed size
Affected by GLR

30. Example of Tubing Curve Use (PPS
wh = wellhead
bh = bottom hole