Comparison vertical flow models BHR Cannes June14 2013

Comparison of mechanistic modelsin gas-liquid flow in vertical and

deviated wells

Pablo Adames, SPT Group [email protected]

Brent Young, The University of [email protected]

mailto:[email protected]

mailto:[email protected]

Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells

Table of Contents

Introduction

Objectives

Methodology

Results

Conclusions


Landmarks in the developmentof comprehensive gas-liquid flow models

Models became more complex…more interconnected and using more closures


Table of Contents

Introduction

Objectives

Methodology

Results

Conclusions


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?


Table of Contents

Introduction

Objectives

Methodology

Results

Conclusions


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


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


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


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


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


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


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


Table of Contents

Introduction

Objectives

Methodology

Results

Conclusions


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


I rp



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


Data source

𝐼𝑟𝑝

Irp,k =Q∑

q=1

indexxq,k


I rp



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


Data source

𝐼𝑟𝑝

Irp,k =Q∑

q=1

indexxq,k


G9



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



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


Data source

𝐺9

GQ,k = (1− Irp,k

Q )× 100


G9



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


Data source

𝐺9

GQ,k = (1− Irp,k

Q )× 100


G9

with the Gas-lift subgroup


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


G9

with the Gas-lift subgroup


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


G9

with Gomez Enhanced


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


G9

with Gomez Enhanced


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


Gas Lift


G9

with Gomez Enhanced


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


Gas Lift


What changed?

One closure relation


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

, …


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


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


The flow pattern map


The flow pattern map


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



0

500

1000

1500

2000

2500

0 10 20 30 40 50 60

Dep

th,

m

Pressure, bar

GomezGas injection




0

500

1000

1500

2000

2500

0 10 20 30 40 50 60

Dep

th,

m

Pressure, bar

GomezGas injection



Flow pattern, Gomez et al.


Flow pattern, Gomez Enhanced


The flow patterns, a closer look

Gomez et al. Gomez Enhanced


Table of Contents

Introduction

Objectives

Methodology

Results

Conclusions


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


Thank you


Comparing pressure gradients

This graph shows theregions where there arelarge differences inpressure gradient betweenGomez and GomezEnhanced for an examplefluid flowing vertically up.


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|


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 |


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


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.

Technology

Comparison vertical flow models BHR Cannes June14 2013