Transcript Liquid Loading - TUCRS - The University of Tulsa

Liquid Loading
Current Status, New Models and
Unresolved Questions
Mohan Kelkar and Shu Luo
The University of Tulsa
Foam Flow Meeting, January 23, 2014
1
Outline
• Definition of liquid loading
• Literature Survey
• Our Data
• Model Formulation
• Model Validation
• Program Demonstration
• Summary
Foam Flow Meeting, January 23, 2014
2
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
•
Foam Flow Meeting, January 23, 2014
3
Traditional Definition
IPR
Stable
OPR
Unstable
Transition
Point
Liquid Loading
Foam Flow Meeting, January 23, 2014
4
Traditional Definition
• As gas flow rate increases

𝑑(∆𝑝𝑔 )
𝑑(𝑉𝑔 )
and
𝑑(∆𝑝𝑓 )
𝑑(𝑉𝑔 )
• At low velocities
increase in
𝑑(∆𝑝𝑔 )
𝑑(∆𝑝𝑓 )
𝑑(𝑉𝑔 )
decreases faster than
𝑑(𝑉𝑔 )
• When two gradients are equal, minimum
occurs
Foam Flow Meeting, January 23, 2014
5
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)
Foam Flow Meeting, January 23, 2014
6
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
Foam Flow Meeting, January 23, 2014
7
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
1/2
𝜌𝐺
∗
𝑢𝐺 = 𝑢𝐺
𝑔𝑑 𝜌𝐿 − 𝜌𝐺 1/2
Foam Flow Meeting, January 23, 2014
8
Liquid Film Reversal
Westende et al., 2007
Foam Flow Meeting, January 23, 2014
9
Liquid Film Reversal
At 15 m/s, liquid starts to
flow counter current with the gas stream
Westende et al., 2007
Foam Flow Meeting, January 23, 2014
10
Liquid Film Reversal
Minimum is at 20 m/s (blue line)
Residual pressure reaches a
zero value at lower velocity
Zabaras et al., 1986
Foam Flow Meeting, January 23, 2014
11
Entrained Liquid Fraction
Alamu, 2012
Foam Flow Meeting, January 23, 2014
12
Inception of Liquid Loading
For vertical pipe
OLGA = 12 m/s
Exptl = 14 m/s
Belfroid et al., 2013
Foam Flow Meeting, January 23, 2014
13
Our Data
Foam Flow Meeting, January 23, 2014
14
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
•
Foam Flow Meeting, January 23, 2014
15
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.
Foam Flow Meeting, January 23, 2014
16
dPG vs. dPF
Air-Water, 2 inch, vsl=0.01 m/s
Minimum
Foam Flow Meeting, January 23, 2014
17
Total dp/dz
Air-Water, 2 inch, vsl=0.01 m/s
Film Reversal
Foam Flow Meeting, January 23, 2014
18
dP/dz)G vs. dP/dz)F
Air-Water, 2 inch, vsl=0.01 m/s
dp/dz)F is
zero
Foam Flow Meeting, January 23, 2014
19
dPT - dPG
Air-Water, 2 inch, vsl=0.01 m/s
Transition at
16 m/s
Foam Flow Meeting, January 23, 2014
20
Pressure at Bottom
Air-Water, 2 inch, vsl=0.01 m/s
Pressure
build up
No pressure
build up
Foam Flow Meeting, January 23, 2014
21
dP/dz)G vs. dP/dz)F
Data from Netherlands (2 inch)
dp/dz)F is
zero
Foam Flow Meeting, January 23, 2014
22
What should we expect for
3” or 4” pipeline?
𝑢𝐺∗ = 𝑢𝐺
1/2
𝜌𝐺
𝑔𝑑 𝜌𝐿 − 𝜌𝐺 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
Foam Flow Meeting, January 23, 2014
23
dPG vs. dPF
Air-Water, 4 inch, vsl=0.01 m/s
Minimum
Foam Flow Meeting, January 23, 2014
24
Total dp/dz
Air-Water, 4 inch, vsl=0.01 m/s
Film Reversal
Foam Flow Meeting, January 23, 2014
25
dP/dz)G vs. dP/dz)F
TUFFP (3 inch, vsl=0.1 m/s)
dp/dz)F is
zero
Foam Flow Meeting, January 23, 2014
26
dP/dz)G vs. dP/dz)F
Air-Water, 4 inch, vsl=0.01 m/s
dp/dz)F is zero
Film reversal
Foam Flow Meeting, January 23, 2014
27
Effect of Diameter
on Liquid Loading
25
uG, m/s
20
15
10
5
0
1
1.2
1.4
1.6
1.8
2
2.2
d1/2
Foam Flow Meeting, January 23, 2014
28
Why diameter impacts?
Film thickness?
0.0006
0.001
0.0005
0.0008
0.0004
0.0003
δ [m]
δ [m]
0.0006
0.0004
0.0002
0.0002
0.0001
0
15.0
20.0
25.0
30.0
0
15.0
20.0
30.0
vSG [m/s]
vSG [m/s]
ID=2in
25.0
ID=4in
(a) vSL=0.01 m/s
ID=2in
ID=4in
(b) vSL=0.05 m/s
Skopich et al., SPE 164477
Foam Flow Meeting, January 23, 2014
29
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.
Foam Flow Meeting, January 23, 2014
30
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:
𝑣𝐺,𝑇
•
𝜎 𝜌𝐿 − 𝜌𝐺
= 6.558
𝜌𝐺2
0.25
This equation is adjusted upward by
approximately 20 percent from his
original equation in order to match his
data.
Foam Flow Meeting, January 23, 2014
31
Background
Drawbacks with Turner’s Equation
•
Turner’s equation is not applicable to all field data. Coleman
et al. proposed equation (without 20% adjustment )
𝑣𝐺,𝑇
•
•
•
𝜎 𝜌𝐿 − 𝜌𝐺
= 5.465
𝜌𝐺2
0.25
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.
Foam Flow Meeting, January 23, 2014
32
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.
Foam Flow Meeting, January 23, 2014
33
Approach
Barnea’s Model
•
•
𝜏𝐼 𝑆𝐼
•
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:
1
1
𝑆𝐿
+
− 𝜏𝐿
− 𝜌𝐿 − 𝜌𝐺 𝑔 sin 𝜃 = 0
𝐴𝐿 𝐴𝐺
𝐴𝐿
Interfacial shear stress with Wallis
correlation:
2
1
𝑣𝑆𝐺
𝜏𝐼 = 𝑓𝐼 𝜌𝐺
2
(1 − 2𝛿)4
Foam Flow Meeting, January 23, 2014
Schematic of Annular Flow
34
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.
Foam Flow Meeting, January 23, 2014
Transition
35
Model Formulation
•
In inclined wells, the film thickness is expected to vary
with radial angle
Vertical Well
Foam Flow Meeting, January 23, 2014
Inclined Well
36
Original Barnea’s Model
at Different Inclination Angles
Foam Flow Meeting, January 23, 2014
37
Non-uniform Film Thickness Model
Foam Flow Meeting, January 23, 2014
38
Non-uniform Film Thickness Model
•
•
Let A1=A2, we can find this relationship.
1
𝛿𝑐 = [𝛿 0, 𝜃 + 𝛿 𝜋, 𝜃 ]
2
If film thickness reaches maximum at 30 degree
inclination angle
Foam Flow Meeting, January 23, 2014
39
Non-uniform Film Thickness Model
•
We will use the following film thickness equation in
the new model:
𝑭𝒐𝒓 𝟎 ≤ 𝜽 ≤ 𝟑𝟎 𝒅𝒆𝒈𝒓𝒆𝒆
𝜹 𝜱, 𝜽 =
𝜽
𝒔𝒊𝒏 𝜱 − 𝟗𝟎 + 𝟏 𝜹𝒄
𝟑𝟎
𝑭𝒐𝒓 𝜽 > 𝟑𝟎 𝒅𝒆𝒈𝒓𝒆𝒆
𝜹 𝜱, 𝜽 = 𝒔𝒊𝒏 𝜱 − 𝟗𝟎 + 𝟏 𝜹𝒄
Foam Flow Meeting, January 23, 2014
40
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).
1
1
𝛿𝑐 = [0 + 𝛿 𝜋, 30 ] = 𝛿𝑇
2
2
Foam Flow Meeting, January 23, 2014
41
Non-uniform Film Thickness Model
Foam Flow Meeting, January 23, 2014
42
Other Film Shape
Foam Flow Meeting, January 23, 2014
43
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 :
𝑓𝐼 = 0.005 1 + 300
Foam Flow Meeting, January 23, 2014
1+
17500 ℎ
− 0.0015
𝑅𝑒𝐺 𝐷
44
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.
Foam Flow Meeting, January 23, 2014
45
Turner’s Model Results
Turner’s Data
Vg < Vg,c
Foam Flow Meeting, January 23, 2014
Vg > Vg,c
46
Barnea’s Model Results
Turner’s Data
Foam Flow Meeting, January 23, 2014
47
New Model Results
Turner’s Data
Foam Flow Meeting, January 23, 2014
48
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.
Foam Flow Meeting, January 23, 2014
49
Turner’s Model Results
Coleman’s Data
Foam Flow Meeting, January 23, 2014
50
Barnea’s Model Results
Coleman’s Data
Foam Flow Meeting, January 23, 2014
51
New Model Results
Coleman’s Data
Foam Flow Meeting, January 23, 2014
52
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.
Foam Flow Meeting, January 23, 2014
53
Turner’s Model Results
Veeken’s Data
Foam Flow Meeting, January 23, 2014
54
Barnea’s Model Results
Veeken’s Data
Foam Flow Meeting, January 23, 2014
55
New Model Results
Veeken’s Data
Foam Flow Meeting, January 23, 2014
56
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.
Foam Flow Meeting, January 23, 2014
57
Production Data
Foam Flow Meeting, January 23, 2014
58
Turner’s Model Results
Chevron Data
Foam Flow Meeting, January 23, 2014
59
New Model Results
Chevron Data
Foam Flow Meeting, January 23, 2014
60
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.
Foam Flow Meeting, January 23, 2014
61
ConocoPhillips Field Data
liquid loading starts
Pc and Pt diverge
Liquid Loading starts at
400 MCFD
Foam Flow Meeting, January 23, 2014
62
Turner’s Model Results
ConocoPhillips Data
Foam Flow Meeting, January 23, 2014
63
New Model Results
ConocoPhillips Data
Foam Flow Meeting, January 23, 2014
64
Future Improvements
Better interfacial fi correlation
Foam Flow Meeting, January 23, 2014
65
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
Foam Flow Meeting, January 23, 2014
66
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
Foam Flow Meeting, January 23, 2014
67
Thank You!
Questions…
Foam Flow Meeting, January 23, 2014
68