Foam Flow Meeting, Jul.9th, 2013 1

Foam Flow Instability Analysis

Shu Luo

The University of Tulsa

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Outline

• Introduction• Liquid Holdup in Foam• Foam Flow Stability• Foam Flow Pressure Drop• Summary

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Introduction

• Liquid holdup in foam flow is much lower than air-water flow

• Liquid holdup in foam flow is a function of liquid and gas velocities, as well as surfactant concentration

• At high concentration, liquid holdup almost remains constant at different gas velocities

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Foam Flow Liquid Holdup 2 inch, vsl=0.01 m/s

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Foam Flow Liquid Holdup

• Predicting liquid holdup in large facility based on lab data from small facility

• Half life analysis reveals the effectiveness of surfactant at different concentrations

• Drainage velocity can be calculated from half life data, which relates to the slippage between gas and liquid

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Half Time Analysis Small Scale

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Drainage Velocity Calculation

• Using half time analysis data (thalf) from small scale facility to calculate drainage velocity:

• Then, comparing drainage velocity with liquid holdup in foam flow

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Drainage Velocity vs. Liquid Holdup

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Liquid Holdup Correlation

• Liquid holdup in foam is proportional to drainage velocity and liquid velocity, and inversely proportional to gas velocity

• This correlation Implicitly includes the effect of surfactant concentration through drainage velocity

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Liquid Holdup 800 ppm, 2 inch, vsl=0.01 m/s

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Liquid Holdup 1600 ppm, 2 inch, vsl=0.01 m/s

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Liquid Holdup 3000 ppm, 2 inch, vsl=0.01 m/s

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Liquid Holdup 800 ppm, 2 inch, vsl=0.03 m/s

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Liquid Holdup 1600 ppm, 2 inch, vsl=0.03 m/s

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Liquid Holdup 800 ppm, 4 inch, vsl=0.01 m/s

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Liquid Holdup 1600 ppm, 4 inch, vsl=0.01 m/s

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Liquid Holdup 3000 ppm, 4 inch, vsl=0.01 m/s

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Liquid Holdup 800 ppm, 4 inch, vsl=0.03 m/s

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Liquid Holdup 1600 ppm, 4 inch, vsl=0.03 m/s

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Experiment vs. Calculation

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Liquid Loading for Foam

• Conventional definition is difficult to apply for foam flow

• Definition based on negative frictional pressure gradient (liquid film reversal) can be applied

• We applied this definition to predict the stability of foam flow

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Traditional Definition (dp/dz)2 inch, 0.01 m/s

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Traditional Definition (dp/dz)4 inch, 0.01 m/s

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

400 ppm, 2 inch, vsl=0.01 m/s

6 m/s

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

800 ppm, 2 inch, vsl=0.01 m/s

4.3 m/s

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

1200 ppm, 2 inch, vsl=0.01 m/s

3.2 m/s

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

1600 ppm, 2 inch, vsl=0.01 m/s

1.4 m/s

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

3000 ppm, 2 inch, vsl=0.01 m/s

2.4 m/s

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

400 ppm, 4 inch, vsl=0.01 m/s

15 m/s

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

800 ppm, 4 inch, vsl=0.01 m/s

14 m/s

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

1200 ppm, 4 inch, vsl=0.01 m/s

8 m/s

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

1600 ppm, 4 inch, vsl=0.01 m/s

4 m/s

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

3000 ppm, 4 inch, vsl=0.01 m/s

6 m/s

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Foam Flow Stability(Consistent with Small Scale)

1200 ppm

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Pressure Gradient Calculation

• We subtracted gravitational gradient from overall pressure gradient to calculate frictional gradient.

• We use the frictional pressure gradient to back calculate viscosity

• We plotted the apparent viscosity as a function of gas velocity

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Viscosity vs. Gas Velocity1200 ppm, 2 inch

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Observations

• Viscosity of foam is close to water at low gas velocities

• At very high gas velocities, the viscosity is closer to gas viscosity

• For a simple correlation, we propose

• We used this correlation to calculate the frictional pressure gradient

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Total dP/dz400 ppm, 2 inch, vsl=0.01 m/s

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Total dP/dz800 ppm, 2 inch, vsl=0.01 m/s

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Total dP/dz1200 ppm, 2 inch, vsl=0.01 m/s

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Total dP/dz1600 ppm, 2 inch, vsl=0.01 m/s

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Total dP/dz3000 ppm, 2 inch, vsl=0.01 m/s

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Total dP/dz400 ppm, 2 inch, vsl=0.03 m/s

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Total dP/dz800 ppm, 2 inch, vsl=0.03 m/s

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Total dP/dz1200 ppm, 2 inch, vsl=0.03 m/s

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Total dP/dz1600 ppm, 2 inch, vsl=0.03 m/s

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Summary

• A correlation of liquid holdup in foam flow is developed, which uses information from small facility.

• Foam flow Stability is determined based on film reversal phenomenon

• Critical velocity of foam flow decreases as surfactant concentration increases for both 2” and 4”

• A correlation of viscosity is proposed to calculate pressure gradient of foam flow.

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Thank You!

Questions…