Abstract

Natural gas is one of the main fossil energy resources, and its density is an effective thermodynamic property, which is required in almost every pressure–volume–temperature (PVT) calculation. Conventionally, the density of natural gas is determined from the gas deviation (Z-) factor using an equation of states (EOS). Several models have been developed to estimate the Z-factor utilizing the EOS approach, however, most of these models involve complex calculations and require many input parameters. In this study, an improved natural gas density prediction model is presented using robust machine learning techniques such as artificial neural networks and functional networks. A total of 3800 data points were collected from different published sources covering a wide range of input parameters. Moreover, explicit empirical correlations are also derived that can be used explicitly without the need for any machine learning-based software. The proposed correlations are a function of molecular weight (Mw) of natural gas, pseudo-reduced pressure (Ppr), and pseudo-reduced temperature (Tpr). The proposed correlations can be applied for the gases having Mw between 16 and 129.7 g, Ppr range of 0.02–29.3, and Tpr range 0.of 5–2.7. The prediction of the new correlation was compared against the most common methods for determining the natural gas density. The developed correlation showed better estimation than the common prediction models. The estimation error was reduced by 2% on average using the new correlations, and the coefficient of determination (R2) was 0.98 using the developed correlation.

References

1.
British Petroleum Company
,
2019
, “
BP Statistical Review of World Energy
,”
London
:
British Petroleum Co
.
2.
Danesh
,
A.
,
1998
,
PVT and Phase Behaviour of Petroleum Reservoir Fluids
,
Elsevier
,
New York
.
3.
Ahmed
,
T.
,
2018
,
Reservoir Engineering Handbook
,
Elsevier/Gulf Professional
.
4.
El-Banbi
,
A.
,
Alzahabi
,
A.
, and
El-Maraghi
,
A.
,
2018
,
PVT Property Correlations: Selection and Estimation
,
Gulf Professional Publishing
.
5.
Sutton
,
R. P.
,
2005
, “
Fundamental PVT Calculations for Associated and Gas/Condensate Natural-Gas Systems
,”
SPE Annual Technical Conference and Exhibition
,
Dallas, TX
,
October
,
Society of Petroleum Engineers
, pp.
270
284
.
6.
Dodson
,
C. R.
,
Goodwill
,
D.
, and
Mayer
,
E. H.
,
1953
, “
Application of Laboratory PVT Data to Reservoir Engineering Problems
,”
J. Pet. Technol.
,
5
(
12
), pp.
287
298
.
7.
Beggs
,
H. D.
, and
Brill
,
J. R.
,
1973
, “
Study of Two-Phase Flow in Inclined Pipes
,”
J. Pet. Technol.
,
25
(
5
), pp.
607
617
.
8.
Ahmed
,
T.
,
2016
,
Equations of State and PVT Analysis: Applications for Improved Reservoir Modeling: Second Edition
,
Gulf Professional Publishing
.
9.
Benedict
,
M.
,
Webb
,
G. B.
, and
Rubin
,
L. C.
,
1942
, “
An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures II. Mixtures of Methane, Ethane, Propane, and N-Butane
,”
J. Chem. Phys.
,
10
(
12
), pp.
747
758
.
10.
Londono
,
F. E.
,
Archer
,
R. A.
, and
Blasingame
,
T. A.
,
2002
, “
Simplified Correlations for Hydrocarbon Gas Viscosity and Gas Density—Validation and Correlation of Behavior Using a Large-Scale Database
,”
SPE Gas Technology Symposium
,
Calgary, Alberta, Canada
,
April
.
11.
AlQuraishi
,
A.
, and
Shokir
,
E. M.
,
2009
, “
Viscosity and Density Correlations for Hydrocarbon Gases and Pure and Impure Gas Mixtures
,”
Pet. Sci. Technol.
,
27
(
15
), pp.
1674
1689
.
12.
Sage
,
B. H.
,
Budenholzer
,
R. A.
, and
Lacey
,
W. N.
,
1940
, “
Phase Equilibria in Hydrocarbon Systems Methane–n-Butane System in the Gaseous and Liquid Regions
,”
Ind. Eng. Chem.
,
32
(
9
), pp.
1262
1277
.
13.
Cengel
,
Y. A.
, and
Boles
,
M. A.
,
2015
,
Thermodynamics: An Engineering Approach
, 8th ed.,
McGraw-Hill
,
New York
.
14.
Yang
,
X.
,
Zhang
,
S.
, and
Zhu
,
W.
,
2017
, “
A New Model for the Accurate Calculation of Natural Gas Viscosity
,”
Nat. Gas Ind. B
,
4
(
2
), pp.
100
105
.
15.
Wu
,
R.
, and
Rosenegger
,
L.
,
2000
, “
Comparison of PVT Properties From Equation of State Analysis and PVT Correlations for Reservoir Studies
,”
J. Can. Pet. Technol.
,
39
(
7
).
16.
Standing
,
M. B.
, and
Katz
,
D. L.
,
1942
, “
Density of Natural Gases
,”
Trans. AIME
,
146
(
1
), pp.
140
149
.
17.
Dranchuk
,
P. M.
, and
Abou-Kassem
,
J. H.
,
1975
, “
Calculation of Z Factors for Natural Gases Using Equations of State
,”
J. Can. Pet. Technol.
,
14
(
3
), pp.
34
36
.
18.
Hall
,
K. R.
, and
Yarborough
,
L.
,
1973
, “
New Equation of State For Z-Factor Calculations
,”
Oil Gas J.
,
71
(
25
), p.
82
.
19.
Kontogeorgis
,
G. M.
,
Michelsen
,
M. L.
,
Folas
,
G. K.
,
Derawi
,
S.
,
von Solms
,
N.
, and
Stenby
,
E. H.
,
2006
, “
Ten Years With the CPA (Cubic-Plus-Association) Equation of State. Part 1. Pure Compounds and Self-associating Systems
,”
Ind. Eng. Chem. Res.
,
45
(
14
), pp.
4855
4868
.
20.
Kontogeorgis
,
G. M.
,
Voutsas
,
E. C.
,
Yakoumis
,
I. V.
, and
Tassios
,
D. P.
,
1996
, “
An Equation of State for Associating Fluids
,”
Ind. Eng. Chem. Res.
,
35
(
11
), pp.
4310
4318
.
21.
Nath
,
S. K.
,
2003
, “
Molecular Simulation of Vapor−Liquid Phase Equilibria of Hydrogen Sulfide and Its Mixtures With Alkanes
,”
J. Phys. Chem. B
,
107
(
35
), pp.
9498
9504
.
22.
Moiseeva
,
E. F.
, and
Malyshev
,
V. L.
,
2019
, “
Compressibility Factor of Natural Gas Determination by Means of Molecular Dynamics Simulations
,”
AIP Adv.
,
9
(
5
), p.
055108
.
23.
Jin
,
L.
,
He
,
Y.
,
Zhou
,
G.
,
Chang
,
Q.
,
Huang
,
L.
, and
Wu
,
X.
,
2020
, “
Natural Gas Density Under Extremely High Pressure and High Temperature: Comparison of Molecular Dynamics Simulation With Corresponding State Model
,”
Chin. J. Chem. Eng.
,
31
, pp.
2
9
.
24.
Kareem
,
L. A.
,
Iwalewa
,
T. M.
, and
Al-Marhoun
,
M.
,
2016
, “
New Explicit Correlation for the Compressibility Factor of Natural Gas: Linearized z-Factor Isotherms
,”
J. Pet. Explor. Prod. Technol.
,
6
(
3
), pp.
481
492
.
25.
Choubineh
,
A.
,
Khalafi
,
E.
,
Kharrat
,
R.
,
Bahreini
,
A.
, and
Hosseini
,
A. H.
,
2017
, “
Forecasting Gas Density Using Artificial Intelligence
,”
Pet. Sci. Technol.
,
35
(
9
), pp.
903
909
.
26.
Khosravi
,
A.
,
Machado
,
L.
, and
Nunes
,
R. O.
,
2018
, “
Estimation of Density and Compressibility Factor of Natural Gas Using Artificial Intelligence Approach
,”
J. Pet. Sci. Eng.
,
168
, pp.
201
216
.
27.
Ghorbani
,
H.
,
Wood
,
D. A.
,
Choubineh
,
A.
,
Mohamadian
,
N.
,
Tatar
,
A.
,
Farhangian
,
H.
, and
Nikooey
,
A.
,
2020
, “
Performance Comparison of Bubble Point Pressure From Oil PVT Data: Several Neurocomputing Techniques Compared
,”
Exp. Comput. Multiphase Flow
,
2
(
4
), pp.
225
246
.
28.
Schmidhuber
,
J.
,
2015
, “
Deep Learning in Neural Networks: An Overview
,”
Neural Networks
,
61
, pp.
85
117
.
29.
Elsharkawy
,
A. M.
,
2004
, “
Efficient Methods for Calculations of Compressibility, Density and Viscosity of Natural Gases
,”
Fluid Phase Equilib.
,
218
(
1
), pp.
1
13
.
30.
Izadmehr
,
M.
,
Shams
,
R.
, and
Ghazanfari
,
M. H.
,
2016
, “
New Correlations for Predicting Pure and Impure Natural Gas Viscosity
,”
J. Nat. Gas Sci. Eng.
,
30
, pp.
364
378
.
31.
Choubineh
,
A.
,
Ghorbani
,
H.
,
Wood
,
D. A.
,
Robab Moosavi
,
S.
,
Khalafi
,
E.
, and
Sadatshojaei
,
E.
,
2017
, “
Improved Predictions of Wellhead Choke Liquid Critical-Flow Rates: Modelling Based on Hybrid Neural Network Training Learning Based Optimization
,”
Fuel
,
207
, pp.
547
560
.
32.
Mir
,
M.
,
Kamyab
,
M.
,
Lariche
,
M. J.
,
Bemani
,
A.
, and
Baghban
,
A.
,
2018
, “
Applying ANFIS-PSO Algorithm as a Novel Accurate Approach for Prediction of Gas Density
,”
Pet. Sci. Technol.
,
36
(
12
), pp.
820
826
.
33.
Razavi
,
R.
,
Kardani
,
M. N.
,
Ghanbari
,
A.
,
Lariche
,
M. J.
, and
Baghban
,
A.
,
2018
, “
Utilization of LSSVM Algorithm for Estimating Synthetic Natural Gas Density
,”
Pet. Sci. Technol.
,
36
(
11
), pp.
807
812
.
34.
Gysling
,
D. L.
,
2007
, “
An Aeroelastic Model of Coriolis Mass and Density Meters Operating on Aerated Mixtures
,”
Flow Meas. Instrum.
,
18
(
2
), pp.
69
77
.
35.
Farzaneh-Gord
,
M.
, and
Rahbari
,
H.
,
2011
, “
Developing Novel Correlations for Calculating Natural Gas Thermodynamic Properties
,”
Chem. Process Eng.
,
32
(
4
), pp.
435
452
.
36.
AlQuraishi
,
A. A.
, and
Shokir
,
E. M.
,
2011
, “
Artificial Neural Networks Modeling for Hydrocarbon Gas Viscosity and Density Estimation
,”
J. King Saud Univ.—Eng. Sci.
,
23
(
2
), pp.
123
129
.
37.
Wood
,
D. A.
, and
Choubineh
,
A.
,
2020
, “
Transparent Machine Learning Provides Insightful Estimates of Natural Gas Density Based on Pressure, Temperature and Compositional Variables
,”
J. Nat. Gas Geosci.
,
5
(
1
), pp.
33
43
.
38.
Schley
,
P.
,
Jaeschke
,
M.
,
Küchenmeister
,
C.
, and
Vogel
,
E.
,
2004
, “
Viscosity Measurements and Predictions for Natural Gas
,”
Int. J. Thermophys.
,
25
(
6
), pp.
1623
1652
.
39.
Langelandsvik
,
L. I.
,
Solvang
,
S.
,
Rousselet
,
M.
,
Metaxa
,
I. N.
, and
Assael
,
M. J.
,
2007
, “
Dynamic Viscosity Measurements of Three Natural Gas Mixtures—Comparison Against Prediction Models
,”
Int. J. Thermophys.
,
28
(
4
), pp.
1120
1130
.
40.
Atilhan
,
M.
,
Aparicio
,
S.
,
Karadas
,
F.
,
Hall
,
K. R.
, and
Alcalde
,
R.
,
2012
, “
Isothermal PρT Measurements on Qatar’s North Field Type Synthetic Natural Gas Mixtures Using a Vibrating-Tube Densimeter
,”
J. Chem. Thermodyn.
,
53
, pp.
1
8
.
41.
Abdulraheem
,
A.
,
Sabakhi
,
E.
,
Ahmed
,
M.
,
Vantala
,
A.
,
Raharja
,
I.
, and
Korvin
,
G.
,
2007
, “
Estimation of Permeability From Wireline Logs in a Middle Eastern Carbonate Reservoir Using Fuzzy Logic
,”
Proceedings of SPE Middle East Oil and Gas Show and Conference, MEOS
,
Manama, Bahrain
,
March
,
Society of Petroleum Engineers
, pp.
944
954
.
42.
Nooruddin
,
H. A.
,
Anifowose
,
F.
, and
Abdulraheem
,
A.
,
2013
, “
Applying Artificial Intelligence Techniques to Develop Permeability Predictive Models Using Mercury Injection Capillary-Pressure Data
,”
SPE Saudi Arabia Section Technical Symposium and Exhibition 2013
,
Al-Khobar, Saudi Arabia
,
May
,
Society of Petroleum Engineers
, pp.
554
569
.
43.
Anifowose
,
F.
,
Labadin
,
J.
, and
Abdulraheem
,
A.
,
2013
, “
A Least-Square-Driven Functional Networks Type-2 Fuzzy Logic Hybrid Model for Efficient Petroleum Reservoir Properties Prediction
,”
Neural Comput. Appl.
,
23
(
Suppl 1
), pp.
179
190
.
44.
Helmy
,
T.
,
Rahman
,
S. M.
,
Hossain
,
M. I.
, and
Abdelraheem
,
A.
,
2013
, “
Non-linear Heterogeneous Ensemble Model for Permeability Prediction of Oil Reservoirs
,”
Arab. J. Sci. Eng.
,
38
(
6
), pp.
1379
1395
.
45.
Anifowose
,
F.
,
Adeniye
,
S.
, and
Abdulraheem
,
A.
,
2014
, “
Recent Advances in the Application of Computational Intelligence Techniques in Oil and Gas Reservoir Characterisation: A Comparative Study
,”
J. Exp. Theor. Artif. Intell.
,
26
(
4
), pp.
551
570
.
46.
Anifowose
,
F.
,
Khoukhi
,
A.
, and
Abdulraheem
,
A.
,
2017
, “
Investigating the Effect of Training–Testing Data Stratification on the Performance of Soft Computing Techniques: An Experimental Study
,”
J. Exp. Theor. Artif. Intell.
,
29
(
3
), pp.
517
535
.
47.
El-Sebakhy
,
E. A.
,
Asparouhov
,
O.
,
Abdulraheem
,
A. A.
,
Al-Majed
,
A. A.
,
Wu
,
D.
,
Latinski
,
K.
, and
Raharja
,
I.
,
2012
, “
Functional Networks as a New Data Mining Predictive Paradigm to Predict Permeability in a Carbonate Reservoir
,”
Expert Syst. Appl.
,
39
(
12
), pp.
10359
10375
.
48.
Abdulraheem
,
A.
,
Ahmed
,
M.
,
Vantala
,
A.
, and
Parvez
,
T.
,
2009
, “
Prediction of Rock Mechanical Parameters for Hydrocarbon Reservoirs Using Different Artificial Intelligence Techniques
,”
SPE Saudi Arabia Section Technical Symposium 2009
,
Al-Khobar, Saudi Arabia
,
May
,
Society of Petroleum Engineers
.
49.
Yang
,
Y.
, and
Rosenbaum
,
M. S.
,
2002
, “
The Artificial Neural Network as a Tool for Assessing Geotechnical Properties
,”
Geotech. Geol. Eng.
,
20
(
2
), pp.
149
168
.
50.
Sonmez
,
H.
,
Tuncay
,
E.
, and
Gokceoglu
,
C.
,
2004
, “
Models to Predict the Uniaxial Compressive Strength and the Modulus of Elasticity for Ankara Agglomerate
,”
Int. J. Rock Mech. Min. Sci.
,
41
(
5
), pp.
717
729
.
51.
Cevik
,
A.
,
Sezer
,
E. A.
,
Cabalar
,
A. F.
, and
Gokceoglu
,
C.
,
2011
, “
Modeling of the Uniaxial Compressive Strength of Some Clay-Bearing Rocks Using Neural Network
,”
Appl. Soft Comput. J.
,
11
(
2
), pp.
2587
2594
.
52.
Tariq
,
Z.
,
Abdulraheem
,
A.
,
Mahmoud
,
M.
, and
Ahmed
,
A.
,
2018
, “
A Rigorous Data-Driven Approach to Predict Poisson’s Ratio of Carbonate Rocks Using a Functional Network
,”
Petrophysics
,
59
(
6
), pp.
761
777
.
53.
Ali
,
S. S.
,
Hossain
,
M. E.
,
Hassan
,
M. R.
, and
Abdulraheem
,
A.
,
2013
, “
Hydraulic Unit Estimation From Predicted Permeability and Porosity Using Artificial Intelligence Techniques
,”
North Africa Technical Conference and Exhibition 2013, NATC 2013
,
Cairo, Egypt
,
April
,
Society of Petroleum Engineers
, pp.
1217
1225
.
54.
Tariq
,
Z.
,
Mahmoud
,
M.
, and
Abdulraheem
,
A.
,
2019
, “
Core Log Integration: A Hybrid Intelligent Data-Driven Solution to Improve Elastic Parameter Prediction
,”
Neural Comput. Appl.
,
31
(
12
), pp.
8561
8581
.
55.
Bazargan
,
H.
, and
Adibifard
,
M.
,
2019
, “
A Stochastic Well-Test Analysis on Transient Pressure Data Using Iterative Ensemble Kalman Filter
,”
Neural Comput. Appl.
,
31
(
8
), pp.
3227
3243
.
56.
Artun
,
E.
,
2017
, “
Characterizing Interwell Connectivity in Waterflooded Reservoirs Using Data-Driven and Reduced-Physics Models: A Comparative Study
,”
Neural Comput. Appl.
,
28
(
7
), pp.
1729
1743
.
57.
Fattahi
,
H.
,
Gholami
,
A.
,
Amiribakhtiar
,
M. S.
, and
Moradi
,
S.
,
2015
, “
Estimation of Asphaltene Precipitation From Titration Data: A Hybrid Support Vector Regression With Harmony Search
,”
Neural Comput. Appl.
,
26
(
4
), pp.
789
798
.
58.
Alimohammadi
,
S.
,
Sayyad Amin
,
J.
, and
Nikooee
,
E.
,
2017
, “
Estimation of Asphaltene Precipitation in Light, Medium and Heavy Oils: Experimental Study and Neural Network Modeling
,”
Neural Comput. Appl.
,
28
(
4
), pp.
679
694
.
59.
Adeyemi
,
B. J.
, and
Sulaimon
,
A. A.
,
2012
, “
Predicting Wax Formation Using Artificial Neural Network
,”
Proceedings of the 36th Nigeria Annual International Conference and Exhibition 2012, NAICE 2012 on Future of Oil and Gas: Right Balance with the Environment and Sustainable Stakeholders’ Participation
,
Lagos, Nigeria
,
August
,
Society of Petroleum Engineers
, pp.
975
982
.
60.
Rezaian
,
A.
,
Kordestany
,
A.
, and
Haghighat
,
S. M.
,
2010
, “
An Artificial Neural Network Approach to Formation Damage Prediction Due to Asphaltene Deposition
,”
Nigeria Annual International Conference and Exhibition 2010, NAICE
,
Tinapa – Calabar, Nigeria
,
July
,
Society of Petroleum Engineers
, pp.
891
898
.
61.
Adebayo
,
A. R.
,
Abdulraheem
,
A.
, and
Olatunji
,
S. O.
,
2015
, “
Artificial Intelligence Based Estimation of Water Saturation in Complex Reservoir Systems
,”
J. Porous Media
,
18
(
9
), pp.
893
906
.
62.
Baziar
,
S.
,
Shahripour
,
H. B.
,
Tadayoni
,
M.
, and
Nabi-Bidhendi
,
M.
,
2018
, “
Prediction of Water Saturation in a Tight Gas Sandstone Reservoir by Using Four Intelligent Methods: A Comparative Study
,”
Neural Comput. Appl.
,
30
(
4
), pp.
1171
1185
.
63.
Bageri
,
B. S.
,
Anifowose
,
F. A.
, and
Abdulraheem
,
A.
,
2015
, “
Artificial Intelligence Based Estimation of Water Saturation Using Electrical Measurements Data in a Carbonate Reservoir
,”
SPE Middle East Oil and Gas Show and Conference, MEOS, Proceedings
,
Manama, Bahrain
,
March
,
Society of Petroleum Engineers
, pp.
499
515
.
64.
Khan
,
M. R.
,
Tariq
,
Z.
, and
Abdulraheem
,
A.
,
2018
, “
Machine Learning Derived Correlation to Determine Water Saturation in Complex Lithologies
,”
SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition
,
Dammam, Saudi Arabia
,
April
,
Society of Petroleum Engineers
.
65.
Mohagheghian
,
E.
,
Zafarian-Rigaki
,
H.
,
Motamedi-Ghahfarrokhi
,
Y.
, and
Hemmati-Sarapardeh
,
A.
,
2015
, “
Using an Artificial Neural Network to Predict Carbon Dioxide Compressibility Factor at High Pressure and Temperature
,”
Korean J. Chem. Eng.
,
32
(
10
), pp.
2087
2096
.
66.
Tariq
,
Z.
, and
Mahmoud
,
M.
,
2019
, “
New Correlation for the Gas Deviation Factor for High-Temperature and High-Pressure Gas Reservoirs Using Neural Networks
,”
Energy Fuels
,
33
(
3
), pp.
2426
2436
.
67.
Gidh
,
Y.
,
Purwanto
,
A.
, and
Ibrahim
,
H.
,
2012
, “
Artificial Neural Network Drilling Parameter Optimization System Improves ROP by Predicting/Managing Bit Wear
,”
SPE Intelligent Energy International 2012
,
Utrecht, The Netherlands
,
March
,
Society of Petroleum Engineers
, pp.
195
207
.
68.
Jahanandish
,
I.
,
Salimifard
,
B.
, and
Jalalifar
,
H.
,
2011
, “
Predicting Bottomhole Pressure in Vertical Multiphase Flowing Wells Using Artificial Neural Networks
,”
J. Pet. Sci. Eng.
,
75
(
3–4
), pp.
336
342
.
69.
Asoodeh
,
M.
,
2013
, “
Prediction of Poisson’s Ratio From Conventional Well Log Data: A Committee Machine With Intelligent Systems Approach
,”
Energy Sources Part A Recover. Util. Environ. Eff.
,
35
(
10
), pp.
962
975
.
70.
Ashena
,
R.
,
Moghadasi
,
J.
,
Ghalambor
,
A.
,
Bataee
,
M.
,
Ashena
,
R.
, and
Feghhi
,
A.
,
2010
, “
Neural Networks in BHCP Prediction Performed Much Better Than Mechanistic Models
,”
International Oil and Gas Conference and Exhibition in China 2010, IOGCEC
,
China
,
June 8–10
,
Society of Petroleum Engineers
, pp.
187
193
.
71.
Rammay
,
M. H.
, and
Abdulraheem
,
A.
,
2017
, “
PVT Correlations for Pakistani Crude Oils Using Artificial Neural Network
,”
J. Pet. Explor. Prod. Technol.
,
7
(
1
), pp.
217
233
.
72.
Castillo
,
E.
,
1998
, “
Functional Networks
,”
Neural Process. Lett.
,
7
(
3
), pp.
151
159
.
73.
Castillo
,
E.
,
Cobo
,
A.
,
Gutiérrez
,
J. M.
, and
Pruneda
,
E.
,
2000
, “
Functional Networks: A New Network-Based Methodology
,”
Comput. Civ. Infrastruct. Eng.
,
15
(
2
), pp.
90
106
.
74.
Castillo
,
E.
,
Gutiérrez
,
J. M.
,
Hadi
,
A. S.
, and
Lacruz
,
B.
,
2001
, “
Some Applications of Functional Networks in Statistics and Engineering
,”
Technometrics
,
43
(
1
), pp.
10
24
.
75.
Korany
,
M. A.
,
Mahgoub
,
H.
,
Fahmy
,
O. T.
, and
Maher
,
H. M.
,
2012
, “
Application of Artificial Neural Networks for Response Surface Modelling in HPLC Method Development
,”
J. Adv. Res.
,
3
(
1
), pp.
53
63
.
76.
Vasumathi
,
B.
, and
Moorthi
,
S.
,
2012
, “
Implementation of Hybrid ANNPSO Algorithm on FPGA for Harmonic Estimation
,”
Eng. Appl. Artif. Intell.
,
25
(
3
), pp.
476
483
.
77.
Wang
,
J.
,
Zhou
,
Q.
,
Jiang
,
H.
, and
Hou
,
R.
,
2015
, “
Short-Term Wind Speed Forecasting Using Support Vector Regression Optimized by Cuckoo Optimization Algorithm
,”
Math. Probl. Eng.
,
2015
, pp.
1
13
.
78.
Chatterjee
,
S.
,
Sarkar
,
S.
,
Hore
,
S.
,
Dey
,
N.
,
Ashour
,
A. S.
, and
Balas
,
V. E.
,
2017
, “
Particle Swarm Optimization Trained Neural Network for Structural Failure Prediction of Multistoried RC Buildings
,”
Neural Comput. Appl.
,
28
(
8
), pp.
2005
2016
.
79.
Catalão
,
J. P. S.
,
Pousinho
,
H. M. I.
, and
Mendes
,
V. M. F.
,
2011
, “
Hybrid Wavelet-PSO-ANFIS Approach for Short-Term Wind Power Forecasting in Portugal
,”
IEEE Trans. Sustainable Energy
,
2
(
1
), pp.
50
59
.
80.
Ethaib
,
S.
,
Omar
,
R.
,
Mazlina
,
M. K. S.
,
Radiah
,
A. B. D.
, and
Syafiie
,
S.
,
2018
, “
Development of a Hybrid PSO–ANN Model for Estimating Glucose and Xylose Yields for Microwave-Assisted Pretreatment and the Enzymatic Hydrolysis of Lignocellulosic Biomass
,”
Neural Comput. Appl.
,
30
(
4
), pp.
1111
1121
.
81.
Abido
,
M. A.
,
2002
, “
Optimal Design of Power-System Stabilizers Using Particle Swarm Optimization
,”
IEEE Trans. Energy Convers.
,
17
(
3
), pp.
406
413
.
82.
Mahmoud
,
M. A.
,
2013
, “
Development of a New Correlation of Gas Compressibility Factor (Z-Factor) for High Pressure Gas Reservoirs
,”
Society of Petroleum Engineering—North Africa Technical Conference and Exhibition 2013, NATC 2013
,
Apr. 15–17
, vol. 1, p.
74
86
.
83.
Poettmann
,
F. H.
, and
Carpenter
,
P. G.
,
1952
, “
The Multiphase Flow of Gas, Oil, and Water Through Vertical Flow Strings With Application to the Design of Gas-Lift Installations
,”
Drilling and Production Practice
,
New York
,
January
,
API
, pp.
257
317
.
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