foam flow meeting, jul.9th, 2013 1 new comprehensive equation to predict liquid loading shu luo the...

Foam Flow Meeting, Jul.9th, 2013 1

New Comprehensive Equation to Predict Liquid Loading

Shu Luo

The University of Tulsa


Outline

• Introduction• Background and Approach• 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)


Air-Water Flow

• Anton Skopich conducted experiments in 2” and 4” pipes

• The results observed are different based on film reversal and minimum pressure drop


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.


Magnitude of Gravitational vs. Frictional Gradient with respect to Gas Velocity


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


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

Data from Netherlands (2 inch)

dp/dz)F is zero


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

TUFFP (3 inch, vsl=0.01 m/s)

dp/dz)F is zero


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

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

dp/dz)F is zero


dPG vs. dPF


Minimum


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

Film Reversal


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


dp/dz)F is zero Film reversal


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.


Outline



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 )𝜌𝐺2 ]

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 )𝜌𝐺2 ]

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.


ApproachZhang et al.’s Model


ApproachZhang et al.’s Model

• Momentum equation for annular flow:

• With other equations and closure relationships, we can solve this momentum equation and calculate critical gas velocity


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 from 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.


Outline



Three Main Modifications

• Accounted for variable liquid film thickness• Changed the equation for liquid film friction

factor• Accounted for presence of liquid in the form

of droplet


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


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]}


Outline



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


Zhang et al.’s Model ResultsTurner’s Data


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


Zhang et al.’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


Zhang et al.’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


Zhang et al.’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


Zhang et al.’s Model Results ConocoPhillips Data


New Model Results ConocoPhillips Data


Outline



Program

• This program is developed in .net framework using c sharp.

• It consists two pages: single well calculation and multiple well calculation.


Summary

• We analyzed various definitions of liquid loading and concluded that definition based on liquid film reversal is most appropriate.

• A new model for liquid loading is developed for gas well using liquid film reversal method.

• The new model is applicable for both vertical and inclined wells.

• The new model is able to better predict the inception of liquid loading compared to most often used Turner et al.’s equation.

• Liquid loading prediction program is developed to determine onset of liquid loading.


Thank You!

Questions…

foam flow meeting, jul.9th, 2013 1 new comprehensive equation to predict liquid loading shu luo the...

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