Shu Luo and Mohan Kelkar 2014 Liquid Loading (Contains Stratified to Annular Transition Double Circle)

Foam Flow Meeting, January 23, 2014 1

Liquid LoadingCurrent Status, New Models and

Unresolved Questions

Mohan Kelkar and Shu Luo

The University of Tulsa


Outline

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


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


Traditional Definition

OPR

IPR

Transition Point

Stable

Unstable

Liquid Loading


Traditional Definition

• As gas flow rate increases and

• At low velocities decreases faster than increase in

• When two gradients are equal, minimum occurs


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)


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


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


Liquid Film Reversal

Westende et al., 2007



Westende et al., 2007

At 15 m/s, liquid starts to flow counter current with the gas stream



Zabaras et al., 1986

Minimum is at 20 m/s (blue line)Residual pressure reaches azero value at lower velocity


Entrained Liquid Fraction

Alamu, 2012


Inception of Liquid Loading

Belfroid et al., 2013

For vertical pipeOLGA = 12 m/sExptl = 14 m/s


Our Data


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


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.


dPG vs. dPF

Air-Water, 2 inch, vsl=0.01 m/s

Minimum


Total dp/dzAir-Water, 2 inch, vsl=0.01 m/s

Film Reversal


dP/dz)G vs. dP/dz)F


dp/dz)F is zero


dPT - dPG


Transition at 16 m/s


Pressure at BottomAir-Water, 2 inch, vsl=0.01 m/s

Pressure build up

No pressure build up


dP/dz)G vs. dP/dz)F

Data from Netherlands (2 inch)

dp/dz)F is zero


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


dPG vs. dPF


Minimum


Total dp/dzAir-Water, 4 inch, vsl=0.01 m/s

Film Reversal


dP/dz)G vs. dP/dz)F

TUFFP (3 inch, vsl=0.1 m/s)

dp/dz)F is zero


dP/dz)G vs. dP/dz)F


dp/dz)F is zero Film reversal


Effect of Diameteron Liquid Loading

1 1.2 1.4 1.6 1.8 2 2.20

5

10

15

20

25

d1/2

uG

, m/s


Why diameter impacts?Film thickness?

(a) vSL=0.01 m/s

(b) vSL=0.05 m/s

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

15.0 20.0 25.0 30.0

δ[m]

vSG [m/s]

ID=2in ID=4in

0

0.0002

0.0004

0.0006

0.0008

0.001

15.0 20.0 25.0 30.0

δ[m]

vSG [m/s]

ID=2in ID=4in

Skopich et al., SPE 164477


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.


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.

𝑣𝐺 ,𝑇=6.558 [ 𝜎 (𝜌𝐿−𝜌𝐺 )𝜌𝐺

2 ]0.25


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.

𝑣𝐺 ,𝑇=5.465 [𝜎 ( 𝜌𝐿− 𝜌𝐺 )𝜌𝐺

2 ]0.25


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.


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

𝜏 𝐼𝑆𝐼 ( 1𝐴𝐿

+ 1𝐴𝐺

)−𝜏𝐿

𝑆𝐿

𝐴𝐿

− ( 𝜌𝐿− 𝜌𝐺 )𝑔 sin𝜃=0

𝜏 𝐼=12𝑓 𝐼 𝜌𝐺

𝑣𝑆𝐺2

(1−2𝛿)4


ApproachBarnea’s Model

Transition

• 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.


Model Formulation

• In inclined wells, the film thickness is expected to vary with radial angle

Vertical Well Inclined Well


Original Barnea’s Modelat Different Inclination Angles


Non-uniform Film Thickness Model



• Let A1=A2, we can find this relationship.

• If film thickness reaches maximum at 30 degree inclination angle

𝛿𝑐=12[𝛿 (0 ,𝜃 )+𝛿 (𝜋 , 𝜃 )]



• We will use the following film thickness equation in the new model:

𝜹 (𝜱 ,𝜽 )=[ 𝜽𝟑𝟎 𝒔𝒊𝒏 (𝜱−𝟗𝟎 )+𝟏]𝜹𝒄

𝜹 (𝜱 ,𝜽 )=[𝒔𝒊𝒏 (𝜱−𝟗𝟎 )+𝟏 ]𝜹𝒄



• 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).

𝛿𝑐=12[0+𝛿 (𝜋 ,30 )]=1

2𝛿𝑇




Other Film Shape


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=0.005 {1+300 [(1+ 17500𝑅𝑒𝐺

) h𝐷−0.0015]}


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.


Turner’s Model ResultsTurner’s Data

Vg < Vg,c Vg > Vg,c


Barnea’s Model ResultsTurner’s Data


New Model ResultsTurner’s Data


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.


Turner’s Model ResultsColeman’s Data


Barnea’s Model ResultsColeman’s Data


New Model ResultsColeman’s Data


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.


Turner’s Model Results Veeken’s Data


Barnea’s Model Results Veeken’s Data


New Model Results Veeken’s Data


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: 1.995 and 2.441 inch• Get average gas and liquid production rate

when cap string is installed from service history. Assume liquid loading occurred at this point.


Production Data


Turner’s Model Results Chevron Data


New Model Results Chevron Data


ConocoPhillips Data

• Daily production data and casing and tubing pressure data are available

• Select 62 wells including 7 off-shore wells• Two tubing size: 1.995 and 2.441 inch• Determine liquid loading by casing and tubing

pressure divergence.


ConocoPhillips Field Data

Pc and Pt diverge

Liquid Loading starts at 400 MCFD

liquid loading starts


Turner’s Model Results ConocoPhillips Data


New Model Results ConocoPhillips Data


Future ImprovementsBetter interfacial fi correlation


Improvements

• Liquid Entrainment Impact on the inception of liquid loading

• Collection of 5” data• Pressure drop inspection for larger

diameter pipes• Incorporation of foam data in model


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


Thank You!

Questions…

Documents

Shu Luo and Mohan Kelkar 2014 Liquid Loading (Contains Stratified to Annular Transition Double Circle)