Liquid Loading Current Status, New Models and Unresolved Questions

1. Liquid LoadingCurrent Status, New Models and Unresolved Questions Mohan Kelkar and Shu Luo The University of Tulsa

2. Outline • Definition of liquid loading • Literature Survey • Our Data • Model Formulation • Model Validation • Program Demonstration • Summary

3. What is liquid loading? • Minimum pressure drop in the tubing is reached • The liquid drops cannot be entrained by the gas phase (Turner et al.) • The liquid film cannot be entrained by the gas phase (Zhang et al., Barnea) • The answers from different definitions are not the same

4. Traditional Definition IPR Stable OPR Unstable Transition Point Liquid Loading

5. Traditional Definition • As gas flow rate increases • and • At low velocities decreases faster than increase in • When two gradients are equal, minimum occurs

6. Definition Based on Mechanisms • Two potential mechanisms of transition from annular to slug flow • Droplet reversal • Film Reversal • Models are either based on droplet reversal (Turner) or film reversal (Barnea)

7. Literature Data • Air-water data are available • The data reported is restricted to 2” pipe • Very limited data are available in pipes with diameters other than 2” • No data are available for other fluids

8. Generalized Conclusions(2” pipe) • Minimum pressure drop for air-water flow occurs at about 21 m/s • The liquid film reversal starts at around 15 m/s • The dimensionless gas velocity is in the range of 1.0 to 1.1 at minimum point

9. Liquid Film Reversal Westende et al., 2007

10. Liquid Film Reversal At 15 m/s, liquid starts to flow counter current with the gas stream Westende et al., 2007

11. Liquid Film Reversal Minimum is at 20 m/s (blue line) Residual pressure reaches a zero value at lower velocity Zabaras et al., 1986

12. Entrained Liquid Fraction Alamu, 2012

13. Inception of Liquid Loading For vertical pipe OLGA = 12 m/s Exptl = 14 m/s Belfroid et al., 2013

14. Our Data

15. Air-Water Flow • Skopich and Ajani conducted experiments in 2” and 4” pipes • The results observed are different based on film reversal and minimum pressure drop – consistent with literature • However, the experimental results are very different for 2” versus 4” pipe

16. Calculation Procedure • Total pressure drop is measured and gradient is calculated • Holdup is measured and gravitational gradient is calculated • Subtracting gravitational pressure gradient from total pressure gradient to get frictional pressure gradient • By dividing the incremental pressure gradient by incremental gas velocity, changes in gravitational and frictional gradients with respect to gas velocity are calculated.

17. dPG vs. dPFAir-Water, 2 inch, vsl=0.01 m/s Minimum

18. Total dp/dzAir-Water, 2 inch, vsl=0.01 m/s Film Reversal

19. dP/dz)Gvs. dP/dz)FAir-Water, 2 inch, vsl=0.01 m/s dp/dz)F is zero

20. dPT - dPGAir-Water, 2 inch, vsl=0.01 m/s Transition at 16 m/s

21. Pressure at BottomAir-Water, 2 inch, vsl=0.01 m/s Pressure build up No pressure build up

22. dP/dz)G vs. dP/dz)FData from Netherlands (2 inch) dp/dz)F is zero

23. What should we expect for 3” or 4” pipeline? • Based on the above equation, the minimum should shift to right as diameter increases • If the above equation is correct, the ratio of uG/√d at unstable point should be constant

24. dPG vs. dPFAir-Water, 4 inch, vsl=0.01 m/s Minimum

25. Total dp/dzAir-Water, 4 inch, vsl=0.01 m/s Film Reversal

26. dP/dz)G vs. dP/dz)F TUFFP (3 inch, vsl=0.1 m/s) dp/dz)F is zero

27. dP/dz)G vs. dP/dz)FAir-Water, 4 inch, vsl=0.01 m/s dp/dz)F is zero Film reversal

28. Effect of Diameteron Liquid Loading

29. Why diameter impacts?Film thickness? Skopich et al., SPE 164477

30. Liquid Loading Definition • Liquid loading starts when liquid film reversal occurs • We adopt the model of film reversal to predict inception of liquid loading • The reason for this adoption, as we will show later, is because we are able to better predict liquid loading for field data using this methodology.

31. BackgroundTurner’s Equation • The inception of liquid loading is related to the minimum gas velocity to lift the largest liquid droplet in the gas stream. • Turner et al.’s Equation: • This equation is adjusted upward by approximately 20 percent from his original equation in order to match his data.

32. Background Drawbacks with Turner’s Equation • Turner’s equation is not applicable to all field data. Coleman et al. proposed equation (without 20% adjustment ) • Veeken found out that Turner’s results underestimate critical gas velocity by an average 40% for large well bores. • Droplet size assumed in Turner’s equation is unrealistic based on the observations from lab experiments. • Turner’s equation is independent of inclination angle which is found to have great impact on liquid loading.

33. ApproachFilm Model • Two film models are investigated to predict liquid loading: • Zhang et al.’s model(2003) is developed based on slug dynamics. • Barnea’s model(1986) predicts the transition from annular to slug flow by analyzing interfacial shear stress change in the liquid film.

34. ApproachBarnea’s Model • Constructing force balance for annular flow and predict the transition from annular to slug flow by analyzing interfacial shear stress changes. • The combined momentum equation: • Interfacial shear stress with Wallis correlation: Schematic of Annular Flow

35. ApproachBarnea’s Model • Solid curves represent Interfacial shear stress from combined momentum equation • Broken curves represent Interfacial shear stress from Wallis correlation • Intersection of solid and broken curves yields a steady state solution of film thickness and gas velocity at transition boundary • Another transition mechanism is liquid blocking of the gas core. Transition

36. Model Formulation • In inclined wells, the film thickness is expected to vary with radial angle Vertical Well Inclined Well

37. Original Barnea’s Modelat Different Inclination Angles

38. Non-uniform Film Thickness Model

39. Non-uniform Film Thickness Model • Let A1=A2, we can find this relationship. • If film thickness reaches maximum at 30 degree inclination angle

40. Non-uniform Film Thickness Model • We will use the following film thickness equation in the new model:

41. Non-uniform Film Thickness Model • Only maximum film thickness will be used in the model because thickest film will be the first to fall back if liquid loading starts. • Find critical film thickness δTby differentiating momentum equation. δT equals to maximum film thickness δ(π,30).

42. Non-uniform Film Thickness Model

43. Other Film Shape

44. Interfacial Friction Factor • Critical gas velocity calculated by Barnea’s model is conservative compared to other methods. Fore et al. showed that Wallis correlation is reasonable for small values of film thickness and is not suitable for larger film thickness liquid film. • A new correlation is used in the new model :

45. Turner’s Data • 106 gas wells are reported in his paper, all of the gas wells are vertical wells. • 37 wells are loaded up and 53 wells are unloaded. 16 wells are reported questionable in the paper. • Current flow rate and liquid loading status of gas well are reported.

46. Turner’s Model ResultsTurner’s Data Vg < Vg,c Vg > Vg,c

47. Barnea’s Model ResultsTurner’s Data

48. New Model ResultsTurner’s Data

49. Coleman’s Data • 56 gas wells are reported, all of the wells are also vertical wells. • These wells produce at low reservoir pressure and at well head pressures below 500 psi. • Coleman reported gas velocity after they observed liquid loading in gas wells.

50. Turner’s Model ResultsColeman’s Data