### Foam Flow Instability Analysis - TUCRS

```Foam Flow Instability Analysis
Shu Luo
The University of Tulsa
Foam Flow Meeting, Jul.9th, 2013
1
Outline
• Introduction
• Liquid Holdup in Foam
• Foam Flow Stability
• Foam Flow Pressure Drop
• Summary
Foam Flow Meeting, Jul.9th, 2013
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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
Foam Flow Meeting, Jul.9th, 2013
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Foam Flow Liquid Holdup
2 inch, vsl=0.01 m/s
Foam Flow Meeting, Jul.9th, 2013
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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
Foam Flow Meeting, Jul.9th, 2013
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Half Time Analysis
Small Scale
Foam Flow Meeting, Jul.9th, 2013
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Drainage Velocity Calculation
• Using half time analysis data (thalf) from small
scale facility to calculate drainage velocity:
/
=
(/)
ℎ
• Then, comparing drainage velocity with liquid
holdup in foam flow
Foam Flow Meeting, Jul.9th, 2013
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Drainage Velocity vs. Liquid Holdup
Foam Flow Meeting, Jul.9th, 2013
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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
= 2327
3.83

0.39
• This correlation Implicitly includes the effect
of surfactant concentration through drainage
velocity
Foam Flow Meeting, Jul.9th, 2013
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Liquid Holdup
800 ppm, 2 inch, vsl=0.01 m/s
Foam Flow Meeting, Jul.9th, 2013
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Liquid Holdup
1600 ppm, 2 inch, vsl=0.01 m/s
Foam Flow Meeting, Jul.9th, 2013
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Liquid Holdup
3000 ppm, 2 inch, vsl=0.01 m/s
Foam Flow Meeting, Jul.9th, 2013
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Liquid Holdup
800 ppm, 2 inch, vsl=0.03 m/s
Foam Flow Meeting, Jul.9th, 2013
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Liquid Holdup
1600 ppm, 2 inch, vsl=0.03 m/s
Foam Flow Meeting, Jul.9th, 2013
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Liquid Holdup
800 ppm, 4 inch, vsl=0.01 m/s
Foam Flow Meeting, Jul.9th, 2013
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Liquid Holdup
1600 ppm, 4 inch, vsl=0.01 m/s
Foam Flow Meeting, Jul.9th, 2013
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Liquid Holdup
3000 ppm, 4 inch, vsl=0.01 m/s
Foam Flow Meeting, Jul.9th, 2013
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Liquid Holdup
800 ppm, 4 inch, vsl=0.03 m/s
Foam Flow Meeting, Jul.9th, 2013
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Liquid Holdup
1600 ppm, 4 inch, vsl=0.03 m/s
Foam Flow Meeting, Jul.9th, 2013
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Experiment vs. Calculation
Foam Flow Meeting, Jul.9th, 2013
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• 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
Foam Flow Meeting, Jul.9th, 2013
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2 inch, 0.01 m/s
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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
Foam Flow Meeting, Jul.9th, 2013
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dP/dz)G vs. dP/dz)F
800 ppm, 2 inch, vsl=0.01 m/s
4.3 m/s
Foam Flow Meeting, Jul.9th, 2013
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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
Foam Flow Meeting, Jul.9th, 2013
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dP/dz)G vs. dP/dz)F
3000 ppm, 2 inch, vsl=0.01 m/s
2.4 m/s
Foam Flow Meeting, Jul.9th, 2013
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dP/dz)G vs. dP/dz)F
400 ppm, 4 inch, vsl=0.01 m/s
15 m/s
Foam Flow Meeting, Jul.9th, 2013
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dP/dz)G vs. dP/dz)F
800 ppm, 4 inch, vsl=0.01 m/s
14 m/s
Foam Flow Meeting, Jul.9th, 2013
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dP/dz)G vs. dP/dz)F
1200 ppm, 4 inch, vsl=0.01 m/s
8 m/s
Foam Flow Meeting, Jul.9th, 2013
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dP/dz)G vs. dP/dz)F
1600 ppm, 4 inch, vsl=0.01 m/s
4 m/s
Foam Flow Meeting, Jul.9th, 2013
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dP/dz)G vs. dP/dz)F
3000 ppm, 4 inch, vsl=0.01 m/s
6 m/s
Foam Flow Meeting, Jul.9th, 2013
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Foam Flow Stability
(Consistent with Small Scale)
1200 ppm
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• We subtracted gravitational gradient from
•
•
We use the frictional pressure gradient to
back calculate viscosity
We plotted the apparent viscosity as a
function of gas velocity
Foam Flow Meeting, Jul.9th, 2013
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Viscosity vs. Gas Velocity
1200 ppm, 2 inch
Foam Flow Meeting, Jul.9th, 2013
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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
4

= 0.0026 −0.24 ∗
1200
We used this correlation to calculate the
Foam Flow Meeting, Jul.9th, 2013
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Total dP/dz
400 ppm, 2 inch, vsl=0.01 m/s
Foam Flow Meeting, Jul.9th, 2013
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Total dP/dz
800 ppm, 2 inch, vsl=0.01 m/s
Foam Flow Meeting, Jul.9th, 2013
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Total dP/dz
1200 ppm, 2 inch, vsl=0.01 m/s
Foam Flow Meeting, Jul.9th, 2013
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Total dP/dz
1600 ppm, 2 inch, vsl=0.01 m/s
Foam Flow Meeting, Jul.9th, 2013
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Total dP/dz
3000 ppm, 2 inch, vsl=0.01 m/s
Foam Flow Meeting, Jul.9th, 2013
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Total dP/dz
400 ppm, 2 inch, vsl=0.03 m/s
Foam Flow Meeting, Jul.9th, 2013
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Total dP/dz
800 ppm, 2 inch, vsl=0.03 m/s
Foam Flow Meeting, Jul.9th, 2013
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Total dP/dz
1200 ppm, 2 inch, vsl=0.03 m/s
Foam Flow Meeting, Jul.9th, 2013
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Total dP/dz
1600 ppm, 2 inch, vsl=0.03 m/s
Foam Flow Meeting, Jul.9th, 2013
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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