Abstract

Conventional hydrocarbon reservoirs, from an engineering and economic standpoint, are the easiest and most cost-efficient deposits to develop and produce. However, as economic deposits of conventional oil/gas become scarce, hydrocarbon recovered from tight sands and shale deposits will likely fill the void created by diminished conventional oil and gas sources. The purpose of this paper is to review the numerical methods available for simulating multiphase flow in highly fractured reservoirs and present a concise method to implement a fully implicit, two-phase numerical model for simulating multiphase flow, and predicting fluid recovery in highly fractured tight gas and shale gas reservoirs. The paper covers the five primary numerical modeling categories. It addresses the physical and theoretical concepts that support the development of numerical reservoir models and sequentially presents the stages of model development starting with mass balance fundamentals, Darcy’s law and the continuity equations. The paper shows how to develop and reduce the fluid transport equations. It also addresses equation discretization and linearization, model validation and typical model outputs. More advanced topics such as compositional models, reactive transport models, and artificial neural network models are also briefly discussed. The paper concludes with a discussion of field-scale model implementation challenges and constraints. The paper focuses on concisely and clearly presenting fundamental methods available to the novice petroleum engineer with the goal of improving their understanding of the inner workings of commercially available black box reservoir simulators. The paper assumes the reader has a working understanding of flow a porous media, Darcy’s law, and reservoir rock and fluid properties such as porosity, permeability, saturation, formation volume factor, viscosity, and capillary pressure. The paper does not explain these physical concepts neither are the laboratory tests needed to quantify these physical phenomena addressed. However, the paper briefly addresses these concepts in the context of sampling, uncertainty, upscaling, field-scale distribution, and the impact they have on field-scale numerical models.

References

References
1.
Singh
,
K.
,
Holditch
,
S. A.
, and
Ayers
,
W. B.
,
2008
, “
Basin Analog Investigations Answer Characterization Challenges of Unconventional Gas Potential in Frontier Basins
,”
ASME J. Energy Resour. Technol.
,
130
(
4
), p.
043202
. 10.1115/1.3000104
2.
Polischuk
,
A. V.
, and
Lebedev
,
M. V.
,
2019
, “
Oil and Gas Accumulation Zones Based on 3D Basin Modeling, Solimoes Basin, Jurua Sub-Basin, Brazil
,”
Oil Ind. J.
,
2019
(
10
), pp.
19
23
.
3.
Elmahdy
,
M.
,
Farag
,
A. E.
,
Tarabees
,
E.
, and
Bakr
,
A.
,
2018
, “
Pore Pressure Prediction in Unconventional Carbonate Reservoir
,”
SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition
,
Dammam, Saudi Arabia
,
Apr. 23–26
, SPE Paper No. 194224-MS.
4.
Waltrich
,
P. J.
,
Capovilla
,
M. S.
,
Lee
,
W.
,
Zulqarnain
,
M.
,
de Sousa
,
P. C.
,
Zulqarnain
,
M.
,
Hughes
,
R.
,
Tyagi
,
M.
,
Williams
,
W.
,
Kam
,
S.
,
Archer
,
A.
,
Singh
,
J.
,
Nguyen
,
H.
,
Duhon
,
J.
, and
Griffith
,
C.
,
2019
, “
Experimental Evaluation of Wellbore Flow Models Applied to Worst-Case-Discharge Calculations for Oil Wells
,”
SPE Drill. Completion
,
34
(
3
), pp.
315
333
. 10.2118/184444-PA
5.
Abbas
,
A. K.
,
Flori
,
R. E.
, and
Alsaba
,
M.
,
2019
, “
Stability Analysis of Highly Deviated Boreholes to Minimize Drilling Risks and Nonproductive Time
,”
ASME J. Energy Resour. Technol.
,
141
(
8
), p.
082904
. 10.1115/1.4042733
6.
Chuanliang
,
Y.
,
Jingen
,
D.
,
Xiangdong
,
L.
,
Xiaorong
,
L.
, and
Yongcun
,
F.
,
2015
, “
Borehole Stability Analysis in Deepwater Shallow Sediments
,”
ASME J. Energy Resour. Technol.
,
137
(
1
), p.
012901
. 10.1115/1.4027564
7.
Chen
,
X.
,
Gao
,
D.
,
Yang
,
J.
,
Luo
,
M.
,
Feng
,
Y.
, and
Li
,
X.
,
2018
, “
A Comprehensive Wellbore Stability Model Considering Poroelastic and Thermal Effects for Inclined Wellbores in Deepwater Drilling
,”
ASME J. Energy Resour. Technol.
,
140
(
9
), p.
092903
. 10.1115/1.4039983
8.
Nogueira Araújo
,
J. P.
,
Pereira de Gouveia
,
L.
,
Toledo Lima Junior
,
E.
,
Barbosa Silva
,
T.
,
Lopes Rodrigues dos Anjos
,
J.
,
Lima Oliveira
,
F.
,
Lima Santos
,
J. P.
,
2019
, “
On the Ultimate Limit State Strength Models and Its Application for Casing Design
,”
Offshore Technology Conference
,
Rio de Janeiro, Brazil
,
Oct. 29–31
, SPE Paper No. 29866-MS.
9.
Shi
,
H.
,
Song
,
H.
,
Zhao
,
H.
, and
Chen
,
Z.
,
2019
, “
Numerical Study of a Flow Field Near the Bit for a Coiled-Tubing Partial Underbalanced Drilling Method
,”
ASME J. Energy Resour. Technol.
,
141
(
10
), p.
102902
. 10.1115/1.4043388
10.
Al-AbdulJabbar
,
A.
,
Elkatatny
,
S.
,
Mahmoud
,
M.
,
Abdelgawad
,
K.
, and
Al-Majed
,
A.
,
2019
, “
A Robust Rate of Penetration Model for Carbonate Formation
,”
ASME J. Energy Resour. Technol.
,
141
(
4
), p.
042903
. 10.1115/1.4041840
11.
Siavashi
,
M.
,
Tehrani
,
M. R.
, and
Nakhaee
,
A.
,
2016
, “
Efficient Particle Swarm Optimization of Well Placement to Enhance oil Recovery Using a Novel Streamline-Based Objective Function
,”
ASME J. Energy Resour. Technol.
,
138
(
5
), p.
052903
. 10.1115/1.4032547
12.
Yang
,
J.
,
Wang
,
X.
,
Yang
,
Y.
,
Peng
,
X.
, and
Zeng
,
F.
,
2019
, “
An Empirical Model to Estimate Sweep Efficiency of a Surfactant-Alternating-Gas Foam Process in Heterogeneous Reservoirs
,”
ASME J. Energy Resour. Technol.
,
141
(
12
), p.
122902
. 10.1115/1.4043861
13.
Wang
,
S.
,
Cheng
,
L.
,
Huang
,
S.
,
Xue
,
Y.
,
Bai
,
M.
,
Wu
,
Y.
,
Jia
,
P.
,
Sun
,
Z.
, and
Wang
,
J.
,
2019
, “
A Semi-Analytical Method for Modeling Two-Phase Flow Behavior in Fractured Carbonate Oil Reservoirs
,”
ASME J. Energy Resour. Technol.
,
141
(
7
), p.
072902
. 10.1115/1.4042237
14.
Obinna
,
E. D.
, and
Hassan
,
D.
,
2016
, “
Characterizing Tight Oil Reservoirs With Dual-and Triple-Porosity Models
,”
ASME J. Energy Resour. Technol.
,
138
(
3
), p.
032801
. 10.1115/1.4032520
15.
Christman
,
P. G.
,
1995
, “
Modeling the Effects of Infill Drilling and Pattern Modification in Discontinuous Reservoirs
,”
SPE Reservoir Eng.
,
10
(
1
), pp.
4
9
. 10.2118/27747-PA
16.
Acs
,
G.
,
Doleschall
,
S.
, and
Farkas
,
E.
,
1985
, “
General Purpose Compositional Model
,”
SPE J.
,
25
(
4
), pp.
543
553
.
17.
Forouzanfar
,
F.
,
Pires
,
A. P.
, and
Reynolds
,
A. C.
,
2015
, “
Formulation of a Transient Multi-Phase Thermal Compositional Wellbore Model and Its Coupling With a Thermal Compositional Reservoir Simulator
,”
SPE Annual Technical Conference and Exhibition
,
Houston, TX
,
Sept. 28–30
, SPE Paper No. 174749-MS.
18.
Van
,
S. L.
, and
Chon
,
B. H.
,
2018
, “
Effective Prediction and Management of a CO2 Flooding Process for Enhancing Oil Recovery Using Artificial Neural Networks
,”
ASME J. Energy Resour. Technol.
,
140
(
3
), p.
032906
. 10.1115/1.4038054
19.
Yuan
,
T.
, and
Qin
,
G.
,
2020
, “
Numerical Investigation of Wormhole Formation During Matrix Acidizing of Carbonate Rocks by Coupling Stokes-Brinkman Equation With Reactive Transport Model Under Radial Flow Conditions
,”
SPE International Conference and Exhibition on Formation Damage Control
,
Lafayette, LA
,
Feb. 19–21
, SPE Paper No. 199262-MS.
20.
Denney
,
D.
,
2000
, “
Artificial Neural Networks Identify Restimulation Candidates
,”
J. Pet. Technol.
,
52
(
2
), pp.
44
45
. 10.2118/0200-0044-JPT
21.
Enyioha
,
C.
, and
Ertekin
,
T.
,
2014
, “
Advanced Well Structures: An Artificial Intelligence Approach to Field Deployment and Performance Prediction
,”
SPE Intelligent Energy Conference & Exhibition
,
Utrecht, The Netherlands
,
Apr. 1–3
, SPE Paper No. 167870-MS.
22.
Enyioha
,
C.
, and
Ertekin
,
T.
,
2017
, “
Performance Prediction for Advanced Well Structures in Unconventional Oil and Gas Reservoirs Using Artificial Intelligent Expert Systems
,”
SPE Annual Technical Conference and Exhibition
,
San Antonio, TX
,
Oct. 9–11
, SPE Paper No. 187037-MS.
23.
Dandekar
,
A. Y.
,
2013
,
Petroleum Reservoir Rock and Fluid Properties
,
CRC Press
,
Boca Raton, FL
.
24.
Ertekin
,
T.
,
Abou-Kassem
,
J. H.
, and
King
,
G. R.
,
2001
,
Basic Applied Reservoir Simulation. SPE Textbook Series
,
Society of Petroleum Engineers
,
Richardson, TX
.
25.
Coats
,
K. H.
,
Thomas
,
L. K.
, and
Pierson
,
R. G.
,
1998
, “
Compositional and Black oil Reservoir Simulation
,”
SPE Reservoir Eval. Eng.
,
1
(
4
), pp.
372
379
. 10.2118/50990-PA
26.
Fevang
,
Ø
,
Singh
,
K.
, and
Whitson
,
C. H.
,
2000
, “
Guidelines for Choosing Compositional and Black-Oil Models for Volatile Oil and Gas-Condensate Reservoirs
,”
SPE Annual Technical Conference and Exhibition
,
Dallas, TX
,
Oct. 1–4
, SPE Paper No. 63087-MS.
27.
U.S. Energy Information Administration
,
2011
,
Review of Emerging Resources: U.S. Shale Gas and Shale Oil Plays
,
U.S. Department of Energy
,
Washington, DC
.
28.
U.S. Energy Information Administration
,
2014
,
Annual Energy Outlook 2014
,
U.S. Department of Energy
,
Washington, DC
.
29.
National Petroleum Council
,
2011
,
Prudent Development: Realizing the Potential of North America’s Abundant Natural Gas and Oil Resources
,
U.S. Department of Energy
,
Washington, DC
.
30.
Ahn
,
C. H.
,
Dilmore
,
R.
, and
Wang
,
J. Y.
,
2017
, “
Modeling of Hydraulic Fracture Propagation in Shale Gas Reservoirs: A Three-Dimensional, Two-Phase Model
,”
ASME J. Energy Resour. Technol.
,
139
(
1
), p.
012903
. 10.1115/1.4033856
31.
Zhou
,
Q.
,
Kleit
,
A.
,
Wang
,
J. Y.
, and
Dilmore
,
R.
,
2014
, “
Evaluating Gas Production Performances in Marcellus Using Data Mining Technologies
,”
J. Nat. Gas Sci. Eng.
,
20
, pp.
109
120
. 10.1016/j.jngse.2014.06.014
32.
Seales
,
M. B.
,
Dilmore
,
R.
,
Ertekin
,
T.
, and
Wang
,
J. Y.
,
2017
, “
A Numerical Study of Factors Affecting Fracture-Fluid Cleanup and Produced Gas/Water in Marcellus Shale: Part II
,”
SPE J.
,
22
(
2
), pp.
596
614
. 10.2118/183632-PA
33.
Barenblatt
,
G. I.
,
Zheltov
,
I. P.
, and
Kochina
,
I. N.
,
1960
, “
Basic Concepts in the Theory of Seepage of Homogeneous Liquids in Fissured Rocks [Strata]
,”
J. Appl. Math. Mech.
,
24
(
5
), pp.
1286
1303
. 10.1016/0021-8928(60)90107-6
34.
Warren
,
J. E.
, and
Root
,
P. J.
,
1963
, “
The Behavior of Naturally Fractured Reservoirs
,”
SPE J.
,
3
(
3
), pp.
245
255
.
35.
Kazemi
,
H.
,
Merrill
,
L. S.
,
Porterfield
,
K. L.
, and
Zeman
,
R. R.
,
1976
, “
Numerical Simulation of Water–Oil Flow in Naturally Fractured Reservoirs
,”
SPE J.
,
16
(
6
), pp.
317
326
.
36.
Thomas
,
L. K.
,
Dixon
,
T. N.
, and
Pierson
,
R. G.
,
1983
, “
Fractured Reservoir Simulation
,”
SPE J.
,
23
(
1
), pp.
42
54
.
37.
De Swaan
,
O. A.
,
1976
, “
Analytic Solutions for Determining Naturally Fractured Reservoir Properties by Well Testing
,”
SPE J.
,
16
(
3
), pp.
117
122
.
38.
Saidi
,
A. M.
,
1983
, “
Simulation of Naturally Fractured Reservoirs
,”
SPE Reservoir Simulation Symposium
,
San Francisco, CA
,
Nov. 15–18
, SPE Paper No. 12270-MS.
39.
Gilman
,
J. R.
,
1986
, “
An Efficient Finite-Difference Method for Simulating Phase Segregation in the Matrix Blocks in Double-Porosity Reservoirs
,”
SPE Reservoir Eng.
,
1
(
4
), pp.
403
413
. 10.2118/12271-PA
40.
Wu
,
Y.
, and
Pruess
,
K.
,
1988
, “
A Multiple-Porosity Method for Simulation of Naturally Fractured Petroleum Reservoirs
,”
SPE Reservoir Eng.
,
3
(
1
), pp.
327
336
. 10.2118/15129-PA
41.
Beckner
,
B. L.
,
Chan
,
H. M.
,
McDonald
,
A. E.
,
Wooten
,
S. O.
, and
Jones
,
T. A.
,
1991
, “
Simulating Naturally Fractured Reservoirs Using a Subdomain Method
,”
SPE Symposium on Reservoir Simulation
,
Anaheim, CA
,
Feb. 17–20
, SPE Paper No. 21241.
42.
Zhang
,
X.
,
Du
,
C.
,
Deimbacher
,
F.
,
Crick
,
M.
, and
Harikesavanallur
,
A.
,
2009
, “
Sensitivity Studies of Horizontal Wells With Hydraulic Fractures in Shale Gas Reservoirs
,”
International Petroleum Technology Conference
,
Doha, Qatar
,
Dec. 7–9
, SPE Paper No. 13338-MS.
43.
Carlson
,
E. S.
, and
Latham
,
G. V.
,
1993
, “
Discrete Network Modeling for Tight Gas Fractured Reservoirs
,”
Society of Petroleum Engineers
, SPE Paper No. 26122-MS.
44.
Dershowitz
,
W.
,
Shuttle
,
D.
, and
Parney
,
R.
,
2002
, “
Improved Oil Sweep Through Discrete Fracture Network Modeling of Gel Injections in the South Oregon Basin Field, Wyoming
,”
SPE/DOE Improved Oil Recovery Symposium
,
Tulsa, OK
,
Apr. 13–17
, SPE Paper No. 75162-MS.
45.
Shiqian
,
X.
,
Yuyao
,
L.
,
Yu
,
Z.
,
Sen
,
W.
, and
Qihong
,
F.
,
2020
, “
A History Matching Framework to Characterize Fracture Network and Reservoir Properties in Tight Oil
,”
ASME J. Energy Resour. Technol.
,
142
(
4
), p.
042902
. 10.1115/1.4044767
46.
Hofmann
,
H.
,
Babadagli
,
T.
, and
Zimmermann
,
G.
,
2014
, “
Numerical Simulation of Complex Fracture Network Development by Hydraulic Fracturing in Naturally Fractured Ultratight Formations
,”
ASME J. Energy Resour. Technol.
,
136
(
4
), p.
042905
. 10.1115/1.4028690
47.
Gilman
,
J. R.
, and
Kazemi
,
H.
,
1983
, “
Improvements in Simulation of Naturally Fractured Reservoirs
,”
SPE J.
,
23
(
4
), pp.
695
707
.
48.
Al-Shaalan
,
T. M.
,
Fung
,
L.
, and
Dogru
,
A. H.
,
2003
, “
A Scalable Massively Parallel Dual-Porosity Dual-Permeability Simulator for Fractured Reservoirs With Super-k Permeability
,”
SPE Annual Technical Conference and Exhibition
,
Denver, CO
,
Oct. 5–8
, SPE Paper No. 84371-MS.
49.
DeGraff
,
J. M.
,
Meurer
,
M. E.
,
Landis
,
L. H.
, and
Lyons
,
S. L.
,
2005
, “
Fracture Network Modeling and Dual Permeability Simulation of Carbonate Reservoirs
,”
International Petroleum Technology Conference
,
Doha, Qatar
,
Nov. 21–23
, SPE Paper No. 10954-MS.
50.
Chawathe
,
A.
,
Ertekin
,
T.
, and
Grader
,
A.
,
1996
, “
Numerical Simulation of Multimechanistic Gas-Water Flow in Fractured Reservoirs
,”
Permian Basin Oil and Gas Recovery Conference
,
Midland, TX
,
Mar. 27–29
, SPE Paper No. 35186-MS.
51.
Sonier
,
F.
, and
Eymard
,
R.
,
1987
, “
A New Simulator for Naturally Fractured Reservoirs
,”
SPE Symposium on Reservoir Simulation
,
San Antonio, TX
,
Feb. 1–1
, SPE Paper No. 16006-MS.
52.
Dean
,
R. H.
, and
Lo
,
L. L.
,
1988
, “
Simulations of Naturally Fractured Reservoirs
,”
SPE Reservoir Eng.
,
3
(
2
), pp.
638
648
. 10.2118/14110-PA
53.
Marcus
,
H.
,
1962
, “
The Permeability of a Sample of an Anisotropic Porous Medium
,”
J. Geophys. Res.
,
67
(
13
), pp.
5215
5225
. 10.1029/JZ067i013p05215
54.
Parsons
,
R. W.
,
1966
, “
Permeability of Idealized Fractured Rock
,”
SPE J.
,
6
(
2
), pp.
126
136
.
55.
Khaleel
,
R.
,
1989
, “
Scale Dependence of Continuum Models for Fractured Basalts
,”
Water Resour. Res.
,
25
(
8
), pp.
1847
1855
. 10.1029/WR025i008p01847
56.
Fussell
,
L. T.
, and
Fussell
,
D. D.
,
1979
, “
An Iterative Technique for Compositional Reservoir Models
,”
SPE J.
,
19
(
4
), pp.
211
220
.
57.
Coats
,
K. H.
,
1980
, “
An Equation of State Compositional Model
,”
SPE J.
,
20
(
5
), pp.
363
376
.
58.
Crane
,
M.
,
Bratvedt
,
F.
,
Bratvedt
,
K.
,
Childs
,
P.
, and
Olufsen
,
R.
,
2000
, “
A Fully Compositional Streamline Simulator
,”
SPE Annual Technical Conference and Exhibition
,
Dallas, TX
,
Oct. 1–4
, SPE Paper No. 63156-MS.
59.
Schmall
,
L.
,
Varavei
,
A.
, and
Sepehrnoori
,
K.
,
2013
, “
A Comparison of Various Formulations for Compositional Reservoir Simulation
,”
SPE Reservoir Simulation Symposium
,
Woodlands, TX
,
Feb. 18–20
, SPE Paper No. 163630-MS.
60.
Wu
,
S.
,
Dong
,
J.
,
Wang
,
B.
,
Fan
,
T.
, and
Li
,
H.
,
2018
, “
A General Purpose Model for Multiphase Compositional Flow Simulation
,”
SPE Asia Pacific Oil and Gas Conference and Exhibition
,
Brisbane, Australia
,
Oct. 23–25
, SPE Paper No. 191996-MS.
61.
Steefel
,
C. I
.,
2008
, “Geochemical Kinetics and Transport,”
Kinetics of Water-Rock Interaction
,
S. L.
Brantley
,
J. D.
Kubicki
and
A. F.
White
, eds.,
Springer
,
New York, NY
, pp.
545
589
.
62.
Steefel
,
C. I.
,
DePaolo
,
D. J.
, and
Lichtner
,
P. C.
,
2005
, “
Reactive Transport Modeling: An Essential Tool and a New Research Approach for the Earth Sciences
,”
Earth Planet. Sci. Lett.
,
240
(
3–4
), pp.
539
558
. 10.1016/j.epsl.2005.09.017
63.
Li
,
L.
,
Maher
,
K.
,
Navarre-Sitchler
,
A.
,
Druhan
,
J.
,
Meile
,
C.
,
Lawrence
,
C.
,
Moore
,
J.
,
Perdrial
,
J.
,
Sullivan
,
P.
,
Thompson
,
A.
,
Jin
,
L.
,
Bolton
,
E. W.
,
Brantley
,
S. L.
,
Dietrich
,
W. E.
,
Mayer
,
K. U.
,
Steefel
,
C. I.
,
Valocchi
,
A.
,
Zachara
,
J.
,
Kocar
,
B.
,
Mcintosh
,
J.
,
Tutolo
,
B. M.
,
Kumar
,
M.
,
Sonnenthal
,
E.
,
Bao
,
C.
, and
Beisman
,
J.
,
2017
, “
Expanding the Role of Reactive Transport Models in Critical Zone Processes
,”
Earth Sci. Rev.
,
165
, pp.
280
301
. 10.1016/j.earscirev.2016.09.001
64.
Rolle
,
M.
,
Maier
,
U.
, and
Grathwohl
,
P
.,
2011
, “Contaminant Fate and Reactive Transport in Groundwater,”
Dealing With Contaminated Sites: From Theory Towards Practical Application
,
F. A.
Swartjes
, ed,
Springer
,
Dordrecht
, pp.
851
885
.
65.
Prommer
,
H.
,
Sun
,
J.
, and
Kocar
,
B. D.
,
2019
, “
Using Reactive Transport Models to Quantify and Predict Groundwater Quality
,”
Elements
,
15
(
2
), pp.
87
92
.
66.
Meakin
,
P.
, and
Tartakovsky
,
A. M.
,
2009
, “
Modeling and Simulation of Pore-Scale Multiphase Fluid Flow and Reactive Transport in Fractured and Porous Media
,”
Rev. Geophys.
,
47
(
3
), pp.
1
47
. 10.1029/2008RG000263
67.
Fan
,
Y.
,
Durlofsky
,
L. J.
, and
Tchelepi
,
H. A.
,
2012
, “
A Fully-Coupled Flow-Reactive-Transport Formulation Based on Element Conservation, With Application to CO2 Storage Simulations
,”
Adv. Water Res.
,
42
, pp.
47
61
. 10.1016/j.advwatres.2012.03.012
68.
Xiao
,
Y.
,
Xu
,
T.
, and
Pruess
,
K.
,
2009
, “
The Effects of Gas-Fluid-Rock Interactions on CO2 Injection and Storage: Insights From Reactive Transport Modeling
,”
Energy Procedia
,
1
(
1
), pp.
1783
1790
. 10.1016/j.egypro.2009.01.233
69.
Sevougian
,
S. D.
,
Lake
,
L. W.
, and
Schechter
,
R. S.
,
1995
, “
A new Geochemical Simulator To Design More Effective Sandstone Acidizing Treatments
,”
SPE Prod. Facil.
,
10
(
1
), pp.
13
19
. SPE Paper No. 24780-PA. 10.2118/24780-PA
70.
Maheshwari
,
P.
,
Gharbi
,
O.
,
Thirion
,
A.
,
Ali
,
N. S.
,
Peyrony
,
V.
,
Aubry
,
E.
,
Benquet
,
J. C.
,
2016
, “
Development of a Reactive Transport Simulator for Carbonates Acid Stimulation
,”
SPE Annual Technical Conference and Exhibition
,
Dubai, UAE
,
Sept. 26–28
, SPE Paper No. 181603-MS.
71.
Dagan
,
G.
, and
Cvetkovic
,
V.
,
1996
, “
Reactive Transport and Immiscible Flow in Geological Media. I. General Theory
,”
Proc. R. Soc. London, Ser. A
,
452
(
1945
), pp.
285
301
. 10.1098/rspa.1996.0016
72.
Bhuyan
,
D.
,
Lake
,
L. W.
, and
Pope
,
G. A.
,
1990
, “
Mathematical Modeling of High-pH Chemical Flooding
,”
SPE Reservoir Eng.
,
5
(
2
), pp.
213
220
. 10.2118/17398-PA
73.
Shelley
,
R. F.
,
1999
, “
Artificial Neural Networks Identify Restimulation Candidates in the Red Oak Field
,”
SPE Mid-Continent Operations Symposium
,
Oklahoma City, OK
,
Mar. 28–31
, SPE Paper No. 52190-MS.
74.
Alarifi
,
S.
,
AlNuaim
,
S.
, and
Abdulraheem
,
A.
,
2015
, “
Productivity Index Prediction for oil Horizontal Wells Using Different Artificial Intelligence Techniques
,”
SPE Middle East Oil & Gas Show and Conference
,
Manama, Bahrain
,
Mar. 8–11
, SPE Paper No. 172729-MS.
75.
Hassan
,
A.
,
Al-Majed
,
A.
,
Mahmoud
,
M.
,
Elkatatny
,
S.
, and
Abdulraheem
,
A.
,
2019
, “
Improved Predictions in Oil Operations Using Artificial Intelligent Techniques
,”
SPE Middle East Oil and Gas Show and Conference
,
Manama, Bahrain
,
Mar. 18–2
, SPE Paper No. 194994-MS.
76.
AlAjmi
,
M. D.
,
Alarifi
,
S. A.
, and
Mahsoon
,
A. H.
,
2015
, “
Improving Multiphase Choke Performance Prediction and Well Production Test Validation Using Artificial Intelligence: A New Milestone
,”
SPE Digital Energy Conference and Exhibition
,
Woodlands, TX
,
Mar. 3–5
, SPE Paper No. 173394-MS.
77.
Haykin
,
S.
,
1998
,
Neural Networks: A Comprehensive Foundation
, 2nd ed.,
Prentice Hall
,
New Jersey, USA
.
78.
Haykin
,
S.
,
2008
,
Neural Networks and Learning Machines
, 3rd ed.,
Pearson
,
New Jersey, USA
.
79.
Seales
,
M. B.
,
Dilmore
,
R.
,
Ertekin
,
T.
, and
Wang
,
J. Y.
,
2016
, “
Development of a Halite Dissolution Numerical Model for Hydraulically Fractured Shale Formations (Part I)
,”
J. Unconv. Oil Gas Resour.
,
15
, pp.
66
78
. 10.1016/j.juogr.2016.05.002
80.
Seales
,
M. B.
,
2015
, “
Analysis of Fracture Fluid Cleanup and Long-Term Recovery in Shale Gas Reservoirs
,”
Ph.D. dissertation
,
The Pennsylvania State University
,
University Park, PA
.
81.
Ertekin
,
T. G.
,
King
,
G.
, and
Schwerer
,
F. C.
,
1986
, “
Dynamic Gas Slippage: A Unique Dual-Mechanism Approach to the Flow of Gas in Tight Formations
,”
SPE Form. Eval.
,
1
(
1
), pp.
43
52
. 10.2118/12045-PA
82.
Chao
,
G.
,
Lee
,
W. J.
,
Spivey
,
J. P.
, and
Semmelbeck
,
M. E.
,
1994
, “
Modeling Multilayer Gas Reservoirs Including Sorption Effects
,”
SPE Eastern Regional Meeting
,
Charleston, WV
,
Nov. 8–10
, SPE Paper No. 29173-MS.
83.
Laurie
,
D. P
.,
1983
, “Basic Principles of Discretization Methods,”
Numerical Solution of Partial Differential Equations: Theory, Tools and Case Studies
,
D. P.
Laurie
, ed.,
Birkhäuser
,
Basel
, pp.
52
75
.
84.
Peaceman
,
D. W.
,
1983
, “
Interpretation of Well-Block Pressures in Numerical Reservoir Simulation With Nonsquare Grid Blocks and Anisotropic Permeability
,”
SPE J.
,
23
(
3
), pp.
531
543
.
85.
King
,
G.
,
1985
, “
Numerical Simulation of the Simultaneous Flow of Methane and Water Through Dual Porosity Coal Seams During the Degasification Process
,”
Ph.D. dissertation
,
The Pennsylvania State University
,
University Park, PA
.
86.
Barrera
,
A. E.
, and
Srinivasan
,
S.
,
2009
, “
History Matching by Simultaneous Calibration of Reservoir Geological Models at Pore Level and Field Scales
,”
SPE Annual Technical Conference and Exhibition
,
New Orleans, LA
,
Oct. 4–7
, SPE Paper No. 124939-MS.
87.
Monsen
,
E.
,
Randen
,
T.
, and
Sonneland
,
L.
,
2005
, “
Multi-Scale Volume Model Building
,”
Society of Exploration Geophysicists
, SEG Technical Program Expanded Abstracts, pp.
798
801
.
88.
Ahammad
,
M. J.
,
Rahman
,
M. A.
,
Alam
,
J.
, and
Butt
,
S.
,
2019
, “
A Computational Fluid Dynamics Investigation of the Flow Behavior Near a Wellbore Using Three-Dimensional Navier–Stokes Equations
,”
Adv. Mech. Eng.
,
11
(
9
), p.
1687814019873250
. 10.1177/1687814019873250
89.
Al-Mohannadi
,
N. S.
,
Ozkan
,
E.
, and
Kazemi
,
H.
,
2007
, “
Grid-System Requirements in Numerical Modeling of Pressure-Transient Tests in Horizontal Wells
,”
SPE Reservoir Eval. Eng.
,
10
(
2
), pp.
122
131
. 10.2118/92041-PA
90.
Abdou
,
M. K.
,
Pham
,
H. D.
, and
Al-Aqeell
,
A. S.
,
1993
, “
Impact of Grid Selection on Reservoir Simulation
,”
J. Pet. Technol.
,
45
(
7
), pp.
664
669
. 10.2118/21391-PA
91.
Aziz
,
K.
,
1993
, “
Reservoir Simulation Grids: Opportunities and Problems
,”
J. Pet. Technol.
,
45
(
7
), pp.
658
663
. 10.2118/25233-PA
92.
Gholami
,
V.
, and
Mohaghegh
,
S. D.
,
2009
, “
Intelligent Upscaling of Static and Dynamic Reservoir Properties
,”
SPE Annual Technical Conference and Exhibition
,
New Orleans, LA
,
Oct. 4–7
, SPE Paper No. 124477.
93.
Salazar
,
M. O.
, and
Villa Piamo
,
J. R.
,
2007
, “
Permeability Upscaling Techniques for Reservoir Simulation
,”
Latin American & Caribbean Petroleum Engineering Conference
,
Buenos Aires, AR
,
Apr. 15–18
, SPE Paper No. 106679.
94.
Deutsch
,
C. V.
, and
Hewett
,
T. A.
,
1996
, “
Challenges in Reservoir Forecasting
,”
Math. Geol.
,
28
(
7
), pp.
829
842
. 10.1007/BF02066003
95.
Johnson
,
A.
,
2018
, “
Upscaling of Saturation Height Functions
,”
SPWLA 59th Annual Logging Symposium
,
London, UK
,
June 2–6
.
96.
Yao
,
J.
,
Wang
,
C.
,
Yang
,
Y.
, and
Yan
,
X.
,
2013
, “
A Stochastic Upscaling Analysis for Carbonate Media
,”
ASME J. Energy Resour. Technol.
,
135
(
2
), p.
022901
. 10.1115/1.4023005
97.
Jansen
,
F. E.
, and
Kelkar
,
M. G.
,
1998
, “
Upscaling of Reservoir Properties Using Wavelets.” SPE India Oil and Gas Conference and Exhibition
,
New Delhi, India
,
Feb. 17–19
, SPE Paper No. 39495-MS.
98.
Partyka
,
G. A.
,
Thomas
,
J. B.
,
Turco
,
K. P.
, and
Hartmann
,
D. J.
,
2000
, “
Upscaling Petrophysical Properties to the Seismic Scale
,”
Society of Exploration Geophysicists
, SEG Technical Program Expanded Abstracts, pp.
1636
1638
.
99.
Chu
,
L.
,
Schatzinger
,
R. A.
, and
Tham
,
M. K.
,
1998
, “
Application of Wavelet Analysis to Upscaling of Rock Properties
,”
SPE Reservoir Eval. Eng.
,
1
(
1
), pp.
75
81
. 10.2118/36517-PA
100.
Moreno
,
J. E.
, and
Flew
,
S.
,
2011
, “
EOR: Challenges of Translating Fine Scale Displacement Into Full Field Models
,”
SPE Enhanced Oil Recovery Conference
,
Kuala Lumpur, Malaysia
,
July 19–21
, SPE Paper No. 143568-MS.
101.
Rwechungura
,
R. W.
,
Dadashpour
,
M.
, and
Kleppe
,
J.
,
2011
, “
Advanced History Matching Techniques Reviewed
,”
SPE Middle East Oil and Gas Show and Conference
,
Manama, Bahrain
,
Sept. 25–28
, SPE Paper No. 142497-MS.
102.
Kang
,
B.
, and
Choe
,
J.
,
2017
, “
Regeneration of Initial Ensembles With Facies Analysis for Efficient History Matching
,”
ASME J. Energy Resour. Technol.
,
139
(
4
), p.
042903
. 10.1115/1.4036382
103.
Tavassoli
,
Z.
,
Carter
,
J. N.
, and
King
,
P. R.
,
2004
, “
Errors in History Matching
,”
SPE J.
,
9
(
3
), pp.
352
361
. 10.2118/86883-PA
104.
Matveev
,
I.
,
Shishaev
,
G.
,
Eremyan
,
G.
,
Demyanov
,
V.
,
Popova
,
O.
,
Kaygorodov
,
S.
, and
Korovin
,
M.
,
2019
, “
Geology Driven History Matching
,”
SPE Russian Petroleum Technology Conference
,
Moscow, Russia
,
Oct. 22–24
, SPE Paper No. 196881-MS.
105.
Denney
,
D.
,
2003
, “
Experiences with Automated History Matching
,”
J. Pet. Technol.
,
55
(
4
), pp.
73
74
. 10.2118/0403-0073-JPT
You do not currently have access to this content.