Post on 16-Apr-2017
Comparison of mechanistic modelsin gas-liquid flow in vertical and
deviated wells
Pablo Adames, SPT Group CanadaPAdames@slb.com
Brent Young, The University of Aucklandb.young@auckland.ac.nz
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Table of Contents
Introduction
Objectives
Methodology
Results
Conclusions
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Landmarks in the developmentof comprehensive gas-liquid flow models
Models became more complex…more interconnected and using more closures
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Table of Contents
Introduction
Objectives
Methodology
Results
Conclusions
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
About using publishedcomprehensive mechanistic models
Are the results of the more recentmodels better?Can they work in a wellbore simulatorwithout modifications?How do they perform againstindustry-accepted models?
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Table of Contents
Introduction
Objectives
Methodology
Results
Conclusions
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
The criteria for selectionamong flow models
Connection between flow patternprediction and hydrodynamic calculation
uses predecessor’s logicuses similar models for both
After Ansari, it uses a unit cell model forslug flowBetter results against a similar data setas the predecessor’s
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
The model implementationsSeqMMFLO, C++ library
Hasan and Kabir: SPE Production &Facilities, 3(2):263–272, 1988 and SPEProduction & Facilities, 3(4):474–482, 1989
Ansari et al.: SPE Production & Facilities,9(2):143–152, 1994
Gomez et al.: SPE Journal, 5(3):339–350,2000
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
The well cases456 in total
BHR 2002: 119 gas-water andgas-condensate wells
SPE 13297: 68 deep, high rate, high watercut wells from Germany
SMFDB: 269 wells from the StanfordMultiphase Flow Data Bank
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Description of the well cases
DataSource
d i Angle MD Oilrate
Gasrate
WGR Oilden-sity
BHPf
mm ◦ %data
msm3
d
e3sm3
dm3
106m3◦API kPaa
BHR 2002 50.8to
101.6
90 97.3 1,120to
3,680
1 to254
3 to776
0 to823
17to
112
4,502to
28,034
SPE-13279 60to
152
90to80
94.0 3,073to
4,940
0 12to
1,205
4 to780
8,100to
48,200
SMFDB 44to
179
90to80
80.4 908to
4,000
9.5to
3,657
1.1to
4,974
0 to42.4
11to96
2,309to
45,479
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Solved casesas relative performance index
The total number of wells solved by a model,nk, by setting the bottom hole pressureand computing the well head pressure,can be used to construct an additional index:
indexnk =max nj − nk
max nj − min nj
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Relative performance index
Irp,k =|e rk | − min |e rj |
max |e rj | − min |e rj |+
σ er k − minσ er j
maxσ er j − minσ er j
+|e r|k − min |e r|j
max |e r|j − min |e r|j+
σ|er |k − minσ|er |j
maxσ|er |j − minσ|er |j
+|ek| − min |e j|
max |e j| − min |e j|+
σ ek − minσ ej
maxσ ej − minσ ej
+|e|k − min |e|j
max |e|j − min |e|j+
σ|e|k − minσ|e|j
maxσ|e|j − minσ|e|j
+max nj − nk
max nj − min nj
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Relative performance index
Irp,k =|e rk | − min |e rj |
max |e rj | − min |e rj |+
σ er k − minσ er j
maxσ er j − minσ er j
+|e r|k − min |e r|j
max |e r|j − min |e r|j+
σ|er |k − minσ|er |j
maxσ|er |j − minσ|er |j
+|ek| − min |e j|
max |e j| − min |e j|+
σ ek − minσ ej
maxσ ej − minσ ej
+|e|k − min |e|j
max |e|j − min |e|j+
σ|e|k − minσ|e|j
maxσ|e|j − minσ|e|j
+max nj − nk
max nj − min nj
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Table of Contents
Introduction
Objectives
Methodology
Results
Conclusions
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
I rp
with the original model implementations
BB AGF GREGHasan-Kabir
Ansari Gomez OLGAS
BHR 2002 7.51 4.57 0.24 2.93 4.36 1.44 0.97
SPE-13279 8.19 3.35 1.75 1.32 3.24 0.74 0.42
SMFD 3.32 1.20 1.04 9.00 0.93 1.14 0.26
TOTAL 8.12 2.83 0.58 3.14 3.35 0.76 0.05
Relative performance Index,
Data source
𝐼𝑟𝑝
Irp,k =Q∑
q=1
indexxq,k
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
I rp
with the original model implementations
BB AGF GREGHasan-Kabir
Ansari Gomez OLGAS
BHR 2002 7.51 4.57 0.24 2.93 4.36 1.44 0.97
SPE-13279 8.19 3.35 1.75 1.32 3.24 0.74 0.42
SMFD 3.32 1.20 1.04 9.00 0.93 1.14 0.26
TOTAL 8.12 2.83 0.58 3.14 3.35 0.76 0.05
Relative performance Index,
Data source
𝐼𝑟𝑝
Irp,k =Q∑
q=1
indexxq,k
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
I rp
with the original model implementations
BB AGF GREGHasan-Kabir
Ansari Gomez OLGAS
BHR 2002 7.51 4.57 0.24 2.93 4.36 1.44 0.97
SPE-13279 8.19 3.35 1.75 1.32 3.24 0.74 0.42
SMFD 3.32 1.20 1.04 9.00 0.93 1.14 0.26
TOTAL 8.12 2.83 0.58 3.14 3.35 0.76 0.05
Relative performance Index,
Data source
𝐼𝑟𝑝
Irp,k =Q∑
q=1
indexxq,k
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
G9
with the original model implementations
BB AGF GREGHasan-Kabir
Ansari Gomez OLGAS
BHR 2002 16.5 49.2 97.3 67.4 51.6 84.0 89.2
SPE-13279 9.0 62.7 80.6 85.3 64.1 91.8 95.4
SMFD 63.0 86.2 88.6 0.0 88.3 87.1 97.1
TOTAL 9.8 68.6 93.6 65.2 62.8 91.6 99.5
Relative performance Grade,
Data source
𝐺9
GQ,k = (1− Irp,k
Q )× 100
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
G9
with the original model implementations
BB AGF GREGHasan-Kabir
Ansari Gomez OLGAS
BHR 2002 16.5 49.2 97.3 67.4 51.6 84.0 89.2
SPE-13279 9.0 62.7 80.6 85.3 64.1 91.8 95.4
SMFD 63.0 86.2 88.6 0.0 88.3 87.1 97.1
TOTAL 9.8 68.6 93.6 65.2 62.8 91.6 99.5
Relative performance Grade,
Data source
𝐺9
GQ,k = (1− Irp,k
Q )× 100
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
G9
with the original model implementations
BB AGF GREGHasan-Kabir
Ansari Gomez OLGAS
BHR 2002 16.5 49.2 97.3 67.4 51.6 84.0 89.2
SPE-13279 9.0 62.7 80.6 85.3 64.1 91.8 95.4
SMFD 63.0 86.2 88.6 0.0 88.3 87.1 97.1
TOTAL 9.8 68.6 93.6 65.2 62.8 91.6 99.5
Relative performance Grade,
Data source
𝐺9
GQ,k = (1− Irp,k
Q )× 100
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
G9
with the Gas-lift subgroup
BB AGF GREGHasan-Kabir
Ansari Gomez OLGAS
BHR 2002 16.5 49.2 97.3 67.4 51.6 84.0 89.2
SPE-13279 9.0 62.7 80.6 85.3 64.1 91.8 95.4
SMFD 63.0 86.2 88.6 0.0 88.3 87.1 97.1
Gas lift 57.1 45.5 59.2 43.7 80.1 30.3 86.1
TOTAL 9.8 68.6 93.6 65.2 62.8 91.6 99.5
Data sourceRelative performance Grade, 𝐺9
Gas Lift 30.3
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
G9
with the Gas-lift subgroup
BB AGF GREGHasan-Kabir
Ansari Gomez OLGAS
BHR 2002 16.5 49.2 97.3 67.4 51.6 84.0 89.2
SPE-13279 9.0 62.7 80.6 85.3 64.1 91.8 95.4
SMFD 63.0 86.2 88.6 0.0 88.3 87.1 97.1
Gas lift 57.1 45.5 59.2 43.7 80.1 30.3 86.1
TOTAL 9.8 68.6 93.6 65.2 62.8 91.6 99.5
Data sourceRelative performance Grade, 𝐺9
Gas Lift 30.3
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
G9
with Gomez Enhanced
BB AGF GREGHasan-Kabir
Ansari GomezGomez
EnhOLGAS
BHR 2002 16.2 48.9 95.8 66.1 50.9 82.6 88.6 87.8
SPE-13279 8.5 61.8 79.6 84.9 63.0 88.9 91.9 94.3
SMFD 58.4 80.2 82.1 0.0 82.3 80.9 90.7 89.9
Gas lift 57.1 45.5 59.2 43.7 80.1 30.3 79.0 86.1
TOTAL 9.8 68.4 93.2 64.9 62.6 91.2 96.7 99.1
Data source
Relative performance Grade, 𝐺9
Gas Lift
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
G9
with Gomez Enhanced
BB AGF GREGHasan-Kabir
Ansari GomezGomez
EnhOLGAS
BHR 2002 16.2 48.9 95.8 66.1 50.9 82.6 88.6 87.8
SPE-13279 8.5 61.8 79.6 84.9 63.0 88.9 91.9 94.3
SMFD 58.4 80.2 82.1 0.0 82.3 80.9 90.7 89.9
Gas lift 57.1 45.5 59.2 43.7 80.1 30.3 79.0 86.1
TOTAL 9.8 68.4 93.2 64.9 62.6 91.2 96.7 99.1
Data source
Relative performance Grade, 𝐺9
Gas Lift
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
G9
with Gomez Enhanced
BB AGF GREGHasan-Kabir
Ansari GomezGomez
EnhOLGAS
BHR 2002 16.2 48.9 95.8 66.1 50.9 82.6 88.6 87.8
SPE-13279 8.5 61.8 79.6 84.9 63.0 88.9 91.9 94.3
SMFD 58.4 80.2 82.1 0.0 82.3 80.9 90.7 89.9
Gas lift 57.1 45.5 59.2 43.7 80.1 30.3 79.0 86.1
TOTAL 9.8 68.4 93.2 64.9 62.6 91.2 96.7 99.1
Data source
Relative performance Grade, 𝐺9
Gas Lift
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
What changed?
One closure relation
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Liquid entrainment
Wallis, 1969
FE = 1− e−0.125(φ−1.5)
φ = 104vsgµg
√ρgρl
σgl
Oliemans, 1986
FE =FEF
1 + FEF
FEF = 0.003We1.8sg Fr−.92
sg ×Re.7
sl Re−1.4sg ×(
ρl
ρg
).38(µl
µg
).97
Wesg =ρgv2
sgdσgl
, …
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Gas lift case UT-888 from SMFD
0
500
1000
1500
2000
2500
0 10 20 30 40 50 60
Dep
th, m
Pressure, bar
Gomez
Gomex Enhanced
Gas injection
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Gas lift case UT-888 from SMFD
0
500
1000
1500
2000
2500
0 10 20 30 40 50 60
Dep
th, m
Pressure, bar
Gomez
Gomex Enhanced
Gas injection
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
The flow pattern map
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
The flow pattern map
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
UT888 with Gomez et al.
0
500
1000
1500
2000
2500
0 10 20 30 40 50 60
Dep
th,
m
Pressure, bar
GomezGas injection
Pressure profile Flow pattern
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
UT888 with Gomez et al.
0
500
1000
1500
2000
2500
0 10 20 30 40 50 60
Dep
th,
m
Pressure, bar
GomezGas injection
Pressure profile Flow pattern
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
UT888 with Gomez et al.
0
500
1000
1500
2000
2500
0 10 20 30 40 50 60
Dep
th,
m
Pressure, bar
GomezGas injection
Pressure profile Flow pattern
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Flow pattern, Gomez et al.
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Flow pattern, Gomez Enhanced
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
The flow patterns, a closer look
Gomez et al. Gomez Enhanced
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Table of Contents
Introduction
Objectives
Methodology
Results
Conclusions
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Conclusions
1 The grade is an easier to read indicator ofrelative model performance
2 The newer mechanistic models do show animprovement in overall grade
3 With some modifications the Gomez model canbe very reliable
4 Changes in a closure relation can impactpredictions substantially
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Thank you
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Comparing pressure gradients
This graph shows theregions where there arelarge differences inpressure gradient betweenGomez and GomezEnhanced for an examplefluid flowing vertically up.
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Errors per case
Type Case error
Error e i = ∆p i,calc −∆p i,meas
Abs. error |e i | = |∆p i,calc −∆p i,meas|
Rel. error e r,i =∆pi,calc−∆pi,meas
∆pi,meas
Abs. rel. error |e r,i | = |∆pi,calc−∆pi,meas
∆pi,meas|
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Model statistical variables
Type Model avg error Model std. dev
Error e = 1n∑
e i σe =
√∑ni=1 (ei−e)2
n−1
Abs. error |e| = 1n∑
|e i | σ|er | =∑√
(|ei |−|e|)2n−1
Rel. error e r = 1n∑
e r,i σ er =∑√
(er,i−er )2
n−1
Abs. rel. error |e r | = 1n∑
|e r,i | σ|er | =∑√
(|er,i |−|er |)2n−1
Eight statistical variables in total,x j = e, |e|, e r , |e r |, σe, σ|er |, σ er , σ|er |
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
A compound performance index
To compare amongst models using q = 1, . . . ,Qvariableslet’s construct a relative performance index for thek model:
Irp,k =Q∑
q=1
indexxq,k
Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
An index per statistical variable
Each statistical variable x q provides one index permodel:
indexxk =x k − min x j
max x j − min x j
With j = 1, . . . , J models.