1. Liquid Loading Current 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
Talk about the importance of identifying liquid loading and necessary measurements
Transition Point
Liquid Loading

5. Traditional Definition
As gas flow rate increases
𝑑( ∆𝑝 𝑔 ) 𝑑( 𝑉 𝑔 ) and 𝑑( ∆𝑝 𝑓 ) 𝑑( 𝑉 𝑔 )
At low velocities 𝑑( ∆𝑝 𝑔 ) 𝑑( 𝑉 𝑔 ) decreases faster than increase in 𝑑( ∆𝑝 𝑓 ) 𝑑( 𝑉 𝑔 )
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)
2 mechanisms: droplet and film reversal
Droplet model determine liquid loading when droplet falls back
Film model determine liquid loading when liquid film falls back

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
𝑢 𝐺 ∗ = 𝑢 𝐺 𝜌 𝐺 1/2 𝑔𝑑 𝜌 𝐿 − 𝜌 𝐺 1/2

9. Liquid Film Reversal
Westende et al., 2007

10. flow counter current with the gas stream
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. dPF Air-Water, 2 inch, vsl=0.01 m/s
Minimum

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

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

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

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

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

23. What should we expect for 3” or 4” pipeline?
𝑢 𝐺 ∗ = 𝑢 𝐺 𝜌 𝐺 1/2 𝑔𝑑 𝜌 𝐿 − 𝜌 𝐺 1/2
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. dPF Air-Water, 4 inch, vsl=0.01 m/s
Minimum

25. Total dp/dz Air-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)F Air-Water, 4 inch, vsl=0.01 m/s
dp/dz)F is zero Film reversal

28. Effect of Diameter on Liquid Loading

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

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. Background Turner’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.
𝑣 𝐺,𝑇 = 𝜎 𝜌 𝐿 − 𝜌 𝐺 𝜌 𝐺
Turner proposed two models of removal of liquid. One is liquid film move along the walls of pipe, another is liquid droplets entrained in the gas core. And he found the liquid droplet is the dominating mechanism of liquid removal. Then he developed the equation to calculate terminal velocity. Comparing with field data, he suggested that a upward 20% adjustment of the equation will best fit the 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.
𝑣 𝐺,𝑇 = 𝜎 𝜌 𝐿 − 𝜌 𝐺 𝜌 𝐺
most of Turner’s data had well head flow pressure above 500 psi. Coleman focused on low pressure gas wells, WHFP all below 500psi. He predicted critical rate adequately with Turner’s equation without adjustment.
Veeken used TR to examine Turner’s equation. He also proposed a modified Turner expression that best fits this offshore liquid loading field data. He suggested that liquid loading occurs because of liquid film flow reversal rather than droplet flow reversal.

33. Approach Film 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. Approach Barnea’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:
𝜏 𝐼 𝑆 𝐼 1 𝐴 𝐿 𝐴 𝐺 − 𝜏 𝐿 𝑆 𝐿 𝐴 𝐿 − 𝜌 𝐿 − 𝜌 𝐺 𝑔 sin 𝜃 =0
𝜏 𝐼 = 1 2 𝑓 𝐼 𝜌 𝐺 𝑣 𝑆𝐺 2 (1−2𝛿) 4
Schematic of Annular Flow

35. Approach Barnea’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.
Two mechanisms for blockage of core
Instability of annular flow that prevents a stable annular configuration
Liquid film gets large enough to create spontaneous blockage
For low liquid rates, transition occurs due to the first mechanism, whereas, for high liquid rates, transition occurs due to second mechanism
Both mechanisms are checked for transition to slug flow
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 Model at 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
𝛿 𝑐 = 1 2 [𝛿 0,𝜃 +𝛿 𝜋,𝜃 ]

40. Non-uniform Film Thickness Model
We will use the following film thickness equation in the new model:
𝑭𝒐𝒓 𝟎≤𝜽≤𝟑𝟎 𝒅𝒆𝒈𝒓𝒆𝒆
𝑭𝒐𝒓 𝜽>𝟑𝟎 𝒅𝒆𝒈𝒓𝒆𝒆
𝜹 𝜱,𝜽 = 𝜽 𝟑𝟎 𝒔𝒊𝒏 𝜱−𝟗𝟎 +𝟏 𝜹 𝒄
𝜹 𝜱,𝜽 = 𝒔𝒊𝒏 𝜱−𝟗𝟎 +𝟏 𝜹 𝒄

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 δT by differentiating momentum equation. δT equals to maximum film thickness δ(π,30).
𝛿 𝑐 = 1 2 [0+𝛿 𝜋,30 ]= 𝛿 𝑇

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 :
𝑓 𝐼 = 𝑅𝑒 𝐺 ℎ 𝐷 −0.0015

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 Results Turner’s Data
Vg < Vg,c
Vg > Vg,c
This graph shows a plot of boundary velocity calculated by the method vs. actual gas velocity at well head conditions. If boundary velocity is greater than observed velocity, slug flow is present; if less, annular flow is present. The prediction is quite reasonable with 90 % success.

47. Barnea’s Model Results Turner’s Data
This graph shows a plot of boundary velocity calculated by the method vs. actual gas velocity at well head conditions. If boundary velocity is greater than observed velocity, slug flow is present; if less, annular flow is present. The prediction is quite reasonable with 90 % success.

48. New Model Results Turner’s Data
This graph shows a plot of boundary velocity calculated by the method vs. actual gas velocity at well head conditions. If boundary velocity is greater than observed velocity, slug flow is present; if less, annular flow is present. The prediction is quite reasonable with 90 % success.

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 Results Coleman’s Data
Coleman examined the data for wells which were only at critical conditions. Which means every one of these wells were loading. As can be seen, the prediction of the new method is quite good in correctly predicting that all the wells are loading.

51. Barnea’s Model Results Coleman’s Data
Coleman examined the data for wells which were only at critical conditions. Which means every one of these wells were loading. As can be seen, the prediction of the new method is quite good in correctly predicting that all the wells are loading.

52. New Model Results Coleman’s Data
Coleman examined the data for wells which were only at critical conditions. Which means every one of these wells were loading. As can be seen, the prediction of the new method is quite good in correctly predicting that all the wells are loading.

53. Veeken’s Data Veeken reported offshore wells with larger tubing size.
67 wells, which include both vertical and inclined wells, are presented.
Similar to Coleman’s data, critical gas rate was reported.
Liquid rate were not reported in the paper. We assumed a water rate of 5 STB/MMSCF.
Liquid rate will not affect

54. Turner’s Model Results Veeken’s Data
Bad prediction may be pipe diameter and inclination angle

55. Barnea’s Model Results Veeken’s Data
Well deviation angle : Veekan’s data also only shows wells which are producing at critical conditions. Clearly, the method is not working as well and in many wells, the model is predicting annular flow.

56. New Model Results Veeken’s Data
Well deviation angle : Veekan’s data also only shows wells which are producing at critical conditions. Clearly, the method is not working as well and in many wells, the model is predicting annular flow.

57. Chevron Data Production data:
Monthly gas production rate
Monthly water and oil production rate
82 wells have enough information to analyze liquid loading
Two tubing sizes: and inch
Get average gas and liquid production rate when cap string is installed from service history. Assume liquid loading occurred at this point.

58. Production Data

59. Turner’s Model Results Chevron Data

60. New Model Results Chevron Data

61. ConocoPhillips Data
Daily production data and casing and tubing pressure data are available
Select 62 wells including 7 off-shore wells
Two tubing size: and inch
Determine liquid loading by casing and tubing pressure divergence.

62. ConocoPhillips Field Data
liquid loading starts
Pc and Pt diverge
Liquid Loading starts at 400 MCFD

63. Turner’s Model Results ConocoPhillips Data

64. New Model Results ConocoPhillips Data

65. Future Improvements Better interfacial fi correlation

66. Improvements Liquid Entrainment Collection of 5” data
Impact on the inception of liquid loading
Collection of 5” data
Pressure drop inspection for larger diameter pipes
Incorporation of foam data in model

67. Summary
Liquid film reversal is the most appropriate model for defining liquid loading
The effect of diameter on liquid loading is significant and is related to square root of diameter
The film reversal can be detected either by observation of film or residual pressure drop

68. Thank You! Questions…