Comparison vertical flow models BHR Cannes June14 2013

Comparison of mechanistic models
in gas-liquid ﬂow in vertical and
deviated wells
Pablo Adames, SPT Group Canada
PAdames@slb.com
Brent Young, The University of Auckland
b.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

Landmarks in the development
of comprehensive gas-liquid ﬂow models
Models became more complex…
more interconnected and using more closures

About using published
comprehensive mechanistic models
Are the results of the more recent
models better?
Can they work in a wellbore simulator
without modiﬁcations?
How do they perform against
industry-accepted models?

The criteria for selection
among flow models
Connection between flow pattern
prediction and hydrodynamic calculation
uses predecessor’s logic
uses similar models for both
After Ansari, it uses a unit cell model for
slug flow
Better results against a similar data set
as the predecessor’s

The model implementations
SeqMMFLO, C++ library
Hasan and Kabir: SPE Production &
Facilities, 3(2):263–272, 1988 and SPE
Production & 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

The well cases
456 in total
BHR 2002: 119 gas-water and
gas-condensate wells
SPE 13297: 68 deep, high rate, high water
cut wells from Germany
SMFDB: 269 wells from the Stanford
Multiphase Flow Data Bank

Description of the well cases
Data
Source
di Angle MD Oil
rate
Gas
rate
WGR Oil
den-
sity
BHPf
mm ◦ %
data
m
sm3
d
e3sm3
d
m3
106m3
◦API kPaa
BHR 2002 50.8
to
101.6
90 97.3 1,120
to
3,680
1 to
254
3 to
776
0 to
823
17
to
112
4,502
to
28,034
SPE-13279 60
to
152
90
to
80
94.0 3,073
to
4,940
0 12
to
1,205
4 to
780
8,100
to
48,200
SMFDB 44
to
179
90
to
80
80.4 908
to
4,000
9.5
to
3,657
1.1
to
4,974
0 to
42.4
11
to
96
2,309
to
45,479

Solved cases
as relative performance index
The total number of wells solved by a model,
nk, by setting the bottom hole pressure
and computing the well head pressure,
can be used to construct an additional index:
indexnk =
max nj − nk
max nj − min nj

Relative performance index
Irp,k =
|¯erk
| − min |¯erj
|
max |¯erj
| − min |¯erj
|
+
σ¯er k − min σ¯er j
max σ¯er j − min σ¯er j
+
|¯er |k − min |¯er |j
max |¯er |j − min |¯er |j
+
σ|¯er |k − min σ|¯er |j
max σ|¯er |j − min σ|¯er |j
+
|¯ek| − min |¯ej|
max |¯ej| − min |¯ej|
+
σ¯ek − min σ¯ej
max σ¯ej − min σ¯ej
+
|¯e|k − min |¯e|j
max |¯e|j − min |¯e|j
+
σ|¯e|k − min σ|¯e|j
max σ|¯e|j − min σ|¯e|j
+
max nj − nk
max nj − min nj

Irp
with the original model implementations
BB AGF GREG
Hasan-
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

G9
with the original model implementations
BB AGF GREG
Hasan-
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

G9
with the Gas-lift subgroup
BB AGF GREG
Hasan-
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 source
Relative performance Grade, 𝐺9

G9
with the Gas-lift subgroup
BB AGF GREG
Hasan-
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 source
Gas Lift 30.3

G9
with Gomez Enhanced
BB AGF GREG
Hasan-
Kabir
Ansari Gomez
Gomez
Enh
OLGAS
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

G9
with Gomez Enhanced
BB AGF GREG
Hasan-
Kabir
Ansari Gomez
Gomez
Enh
OLGAS
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
Gas Lift

What changed?
One closure relation

Liquid entrainment
Wallis, 1969
FE = 1 − e−0.125(φ−1.5)
φ = 104
vsg µg
ρg
ρl
σgl
Oliemans, 1986
FE =
FEF
1 + FEF
FEF = 0.003We1.8
sg Fr−.92
sg ×
Re.7
sl Re−1.4
sg ×
ρl
ρg
.38
µl
µg
.97
Wesg =
ρg v2
sg d
σgl
, …

Gas lift case UT-888 from SMFD
0
500
1000
1500
2000
2500
0 10 20 30 40 50 60
Depth,m
Pressure, bar
Gomez
Gomex Enhanced
Gas injection

The ﬂow pattern map

UT888 with Gomez et al.
0
500
1000
1500
2000
2500
0 10 20 30 40 50 60
Depth,m
Pressure, bar
Gomez
Gas injection
Pressure proﬁle Flow pattern
100.010.01.00.10.0
10.0
1.0
0.1
0.0
0.0
Flow pattern map
vSG, m/s
vSL,m/s

Flow pattern, Gomez et al.
100.010.01.00.10.0
10.0
1.0
0.1
0.0
0.0
Flow pattern map
vSG, m/s
vSL,m/s

Flow pattern, Gomez Enhanced
100.010.01.00.10.0
10.0
1.0
0.1
0.0
0.0
Flow pattern map
vSG, m/s
vSL,m/s

The ﬂow patterns, a closer look
Gomez et al. Gomez Enhanced
5.04.03.02.01.00.5
0.5
0.4
0.3
0.2
0.1
Flow pattern map
vSG, m/s
vSL,m/s
5.04.03.02.01.00.5
0.5
0.4
0.3
0.2
0.1
Flow pattern map
vSG, m/s
vSL,m/s

Conclusions
1 The grade is an easier to read indicator of
relative model performance
2 The newer mechanistic models do show an
improvement in overall grade
3 With some modiﬁcations the Gomez model can
be very reliable
4 Changes in a closure relation can impact
predictions substantially

Thank you

Comparing pressure gradients
This graph shows the
regions where there are
large differences in
pressure gradient between
Gomez and Gomez
Enhanced for an example
fluid flowing vertically up.

Errors per case
Type Case error
Error ei = ∆pi,calc − ∆pi,meas
Abs. error |ei | = |∆pi,calc − ∆pi,meas|
Rel. error er,i =
∆pi,calc−∆pi,meas
∆pi,meas
Abs. rel. error |er,i | = |
∆pi,calc−∆pi,meas
∆pi,meas
|

Model statistical variables
Type Model avg error Model std. dev
Error ¯e = 1
n
ei σe =
n
i=1 (ei −e)2
n−1
Abs. error |¯e| = 1
n
|ei | σ|¯er | = (|¯ei |−|¯e|)2
n−1
Rel. error ¯er = 1
n
er,i σ¯er =
(er,i −er )2
n−1
Abs. rel. error |¯er | = 1
n
|er,i | σ|¯er | =
(|er,i |−|¯er |)2
n−1
Eight statistical variables in total,
xj = ¯e, |¯e|, ¯er , |¯er |, σe, σ|¯er |, σ¯er , σ|¯er |

A compound performance index
To compare amongst models using q = 1, . . . , Q
variables
let’s construct a relative performance index for the
k model:
Irp,k =
Q
q=1
indexxq,k

An index per statistical variable
Each statistical variable xq provides one index per
model:
indexxk =
xk − min xj
max xj − min xj
With j = 1, . . . , J models.

Comparison vertical flow models BHR Cannes June14 2013

Recommended

Recommended

More Related Content

What's hot

What's hot (19)

Viewers also liked

Viewers also liked (17)

Similar to Comparison vertical flow models BHR Cannes June14 2013

Similar to Comparison vertical flow models BHR Cannes June14 2013 (20)

Recently uploaded

Recently uploaded (20)

Comparison vertical flow models BHR Cannes June14 2013