Two-Phase Flow in Vertical Wells Notes to Accompany Week 5 Lab—Vertical Two-Phase Flow

1. Two-Phase Flow in Vertical WellsNotes to AccompanyWeek 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 situvolumetric 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

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: http://www.bing.com/videos/search?q=vertical+two+phase+flow+video+clip&mid=0C1617DA4FC12EBA92610C1617DA4FC12EBA9261&view=detail&FORM=VIRE7

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