The document compares several mechanistic models for gas-liquid flow in vertical and deviated wells. It evaluates the models based on their ability to predict pressure and flow rate data from 456 wells. The models include those developed by Hasan-Kabir, Ansari, Gomez, and OLGAS. The Gomez model is also enhanced for the comparison. Based on a relative performance index calculation, the enhanced Gomez model and OLGAS model perform the best overall, with the enhanced Gomez performing particularly well on gas lift wells.
Presentation Acme engineering- Two Stage Turbo Shaft Engine- Pratt and WhittneySiddharth Salkar
Design and Analysis of Two Stage Turbofan Gas Turbine Engine-Pratt and Whitney
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Optimization of performance and emission characteristics of dual flow diesel ...eSAT Journals
Abstract
Depleting sources of fossil fuels coupled with after effects of exhaust gases on environment i.e. global warming and climate change has necessitated the need for development and use of alternate biodegradable fuels. In this present study optimization of performance and emission characteristics has been carried out using dual flow of CNG and Diesel with varying EGR under varying load by Taguchi method. Optimum values of output response parameters have been calculated with the help of regression equation and influence of various factors on output response has carried out with the help of analysis of variance.
Keywords: Taguchi method, CNG, EGR, biodegradable fuels
Presentation Acme engineering- Two Stage Turbo Shaft Engine- Pratt and WhittneySiddharth Salkar
Design and Analysis of Two Stage Turbofan Gas Turbine Engine-Pratt and Whitney
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-Presented to delegates of Pratt and Whitney Canada
Optimization of performance and emission characteristics of dual flow diesel ...eSAT Journals
Abstract
Depleting sources of fossil fuels coupled with after effects of exhaust gases on environment i.e. global warming and climate change has necessitated the need for development and use of alternate biodegradable fuels. In this present study optimization of performance and emission characteristics has been carried out using dual flow of CNG and Diesel with varying EGR under varying load by Taguchi method. Optimum values of output response parameters have been calculated with the help of regression equation and influence of various factors on output response has carried out with the help of analysis of variance.
Keywords: Taguchi method, CNG, EGR, biodegradable fuels
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economically optimal solution. So, in this project, a new shell and tube heat exchanger
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algorithms Genetic algorithm, Simulated Annealing, Pattern search and fmincon
algorithm. In this study all the four optimization algorithms are applied to minimize the
total cost of equipment including capital investment and the sum of discounted annual
energy expenditures related to pumping of shell and tube heat exchanger by varying
various design variables such as length, tube outer diameter, pitch size, baffle spacing,
etc. Based on proposed methods, a full computer code was developed for optimal design
of shell and tube heat exchanger. Finally the results are compared
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Tractor-trailers are used all across America to transport cargo, but are not designed with fuel efficiency in mind. Therefor, there is an incentive for companies to invest in making their tractor-trailers more aerodynamic in order to save on fuel costs. I go into the testing and methodology of how my team and I decided to tackle the problem of reducing the coefficient of drag on tractor-trailers by implementing air channeling devices (ACDs). Then, I cover the results from our experiments and our ACD recommendation.
COST MINIMIZATION OF SHELL AND TUBE HEAT EXCHANGER USING NON-TRADITIONAL OPTI...IAEME Publication
Cost minimization of shell and tube heat exchanger is the key objective. Traditional
design approaches besides being time consuming, do not guarantee the reach of an
economically optimal solution. So, in this project, a new shell and tube heat exchanger
optimization design approach is developed based on four nontraditional optimization
algorithms Genetic algorithm, Simulated Annealing, Pattern search and fmincon
algorithm. In this study all the four optimization algorithms are applied to minimize the
total cost of equipment including capital investment and the sum of discounted annual
energy expenditures related to pumping of shell and tube heat exchanger by varying
various design variables such as length, tube outer diameter, pitch size, baffle spacing,
etc. Based on proposed methods, a full computer code was developed for optimal design
of shell and tube heat exchanger. Finally the results are compared
• Created a conceptual aircraft that can use wing in ground effect to fly at low altitude to achieve fuel efficiency and high payload carrying capacity.
An Aerodynamic Study of Bulk Commodity Tractor TrailersBrandon Hilliard
My capstone project was with Western Trailers, where my team and I had to create scale models of various trailers, gather aerodynamic data using wind tunnel procedures, and then predict emissions output and fuel consumption rates for each trailer model.
PRODUCTION OPTIMIZATION ASSESSMENT USING THAI, AND VAPEX EOR METHODS BY USING...Mahmood Ajabbar
Nowadays the energy sources generation is getting more difficult by using the enhanced and advanced level of technology around the world and as non-renewable energy oil and gas industries have become the largest and most demanded supplements of energy generation.
In brief, this project utilizes two types of EOR methods which use to produce heavy oil. The first method is the TAHI method which use steam to reduce the viscosity. The second method is the VAPEX method which use solvent to produce the heavy oil with economical way and friendly environment. It has bee got the RF for VAPEX IS around 62%, and for THAI is 71%. After comparing the both results in term of ability, now will compared it in terms of economics, the THAI method has profit which is 211.96×10^6 Dollars, and the VAPEX method is around 184.04×10^6$. So, the best method for this reservoir is the THAI method.
This paper calculates optimal drafting distances in a NASCAR race, specifically in cornering scenarios. A NASCAR model was placed inside a wind tunnel and the data was interpolated to accurately represent a life-size stock car.
Tractor-trailers are used all across America to transport cargo, but are not designed with fuel efficiency in mind. Therefor, there is an incentive for companies to invest in making their tractor-trailers more aerodynamic in order to save on fuel costs. I go into the testing and methodology of how my team and I decided to tackle the problem of reducing the coefficient of drag on tractor-trailers by implementing air channeling devices (ACDs). Then, I cover the results from our experiments and our ACD recommendation.
An exclusive in-depth look at the latest technology trends on natural refrigerants CO2, ammonia and hydrocarbons by Prof. Jiangping Chen, Shanghai Jiaotong University.
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Presentation of the final event for the three GV04 projects: ReFreeDrive, ModulED and Drivemode. Recordings available at https://www.youtube.com/playlist?list=PLUFRNkTrB5O-38psbMgeWAvzXQ5QWzNsk.
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The 2013 EPA Draft SO2 NAAQS Designations Modeling Technical Assistance Document states that an accurate characterization of the modeled facility is critical. The document also says that that if the building information is not accurate, downwash will not be accurately accounted for in AERMOD. This presentation will discuss two generic facilities, one with a 31 m high long narrow solid building and a single stack that is 1.5 times the building height. The second facility has two 50 m high porous structures located near a single stack of the same height. Accurate building information was assembled for these two facilities and input into BPIP. The BPIP AERMOD input file was analyzed and the following problems were found: 1) building widths and/or lengths outside the range of AERMOD theory; and 2) the porous structures were assumed to be solid. In spite of inputting accurate site information, BPIP generated building dimensions for AERMOD input will not result in accurate predictions. Consequently, an EPA “Source Characterization” study was conducted where “Equivalent Building Dimensions” were defined that more accurately model the dispersion for these two sites. AERMOD was then run using the original BPIP determined inputs and the refined inputs based on a more accurate “Source Characterization.” With refined BPIP inputs, the maximum 1-hr concentrations decreased by factors of 2 to 3.5 Due to the stringent nature of the 1-hr NAAQS, clearly a more accurate source characterization study should be high on the list of refined modeling options.
Isothermal Methanol Converter (IMC) UA Distribution AnalysisGerard B. Hawkins
Isothermal Methanol Converter (IMC) UA Distribution Analysis - Case Study: #0630416GB/H; ACME Co. 9,000 MTD MeOH
This converter uses plates instead of tubes to remove the heat from the reaction gas. The use of the plates and the orientation allow the heat transfer within the converter to be more accurately controlled to follow the maximum rate line.
This case study examines the Radial Flow – Isothermal Methanol Converter (IMC) for ACME Co. 9,000 MTD, based on the Casale Isothermal Methanol Converter (IMC) design.
Develop a simple equation to calculate the heat loss due to flue gases in boilerSalah Salem
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Voidage Replacement And Production Balancing Strategy To Optimize The Increm...EnasAlJamal
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A zero dimensional model has been used as a model to investigate the combustion performance of a single cylinder direct injection diesel engine fuelled by high speed diesel. The numerical simulation was performed at different speeds and compression ratios. The pressure, temperature diagrams vs crank angle are plotted. The simulation model includes sub models for various frictional pressure losses, fuel inflow rate with crank angle.
A solution procedure is developed for solving the available equations using numerical methods. An appropriate C++ code is written for brake power, friction power, indicated power, brake thermal efficiency are simulated. Experiment was conducted on available four stroke diesel engine and the model is validated.
KEYWORDS: Simulation model, combustion performance, zero dimensional model, numerical simulation, indicated power, brake power, brake thermal efficiency, friction power.
Le nuove frontiere dell'AI nell'RPA con UiPath Autopilot™UiPathCommunity
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1. 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
2. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Table of Contents
Introduction
Objectives
Methodology
Results
Conclusions
3. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Landmarks in the development
of comprehensive gas-liquid flow models
Models became more complex…
more interconnected and using more closures
4. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Table of Contents
Introduction
Objectives
Methodology
Results
Conclusions
5. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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?
6. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Table of Contents
Introduction
Objectives
Methodology
Results
Conclusions
7. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
8. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
9. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
10. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
11. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
12. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
13. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
14. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Table of Contents
Introduction
Objectives
Methodology
Results
Conclusions
15. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
16. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
17. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
18. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
19. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
20. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
21. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
22. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
Gas Lift 30.3
23. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
Relative performance Grade, 𝐺9
24. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
Relative performance Grade, 𝐺9
Gas Lift
25. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
Relative performance Grade, 𝐺9
26. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
What changed?
One closure relation
27. 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 = 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
, …
28. 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
Depth,m
Pressure, bar
Gomez
Gomex Enhanced
Gas injection
29. 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
Depth,m
Pressure, bar
Gomez
Gomex Enhanced
Gas injection
30. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
The flow pattern map
31. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
The flow pattern map
32. 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
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
33. 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
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
34. 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
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
35. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
36. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
37. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
38. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
Table of Contents
Introduction
Objectives
Methodology
Results
Conclusions
39. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
41. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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.
42. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
|
43. 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 = 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 |
44. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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
45. Comparison of mechanistic models in gas-liquid flow in vertical and deviated wells
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.