Abstract
In this paper, pragmatic and robust techniques have been developed to simultaneously interpret absolute permeability and relative permeability together with capillary pressure in a naturally fractured carbonate formation from wireline formation testing (WFT) measurements. By using two sets of pressure and flow rate field data collected by a dual-packer tool, two high-resolution cylindrical near-wellbore numerical models are developed for each dataset on the basis of single- and dual-porosity concepts. Then, simulations and history matchings are performed for both the measured pressure drawdown and buildup profiles, while absolute permeability is determined and relative permeability is interpreted with and without considering capillary pressure. Compared to the experimentally measured relative permeability curves for the same formation collected from the literature, relative permeability interpreted with consideration of capillary pressure has a better match than those without considering capillary pressure. Also, relative permeability obtained from dual-porosity models has similar characteristics to those from single-porosity models especially in the region away from the endpoints, though the computational expenses with dual-porosity models are much larger. Absolute permeabilities in the vertical and the horizontal directions of the upper layer are determined to be 201.0 mD and 86.4 mD, respectively, while those of the lower layer are found to be 342.9 mD and 1.8 mD, respectively. Such a large vertical permeability of the lower layer reflects the contribution of the extensively distributed natural fractures in the vertical direction.
References
1.
Wiener
, J. M.
, Rogers
, J. A.
, Rogers
, J. R.
, and Moll
, R. F.
, 1991
, “Predicting Carbonate Permeabilities From Wireline Logs Using a Back-Propagation Neural Network
,” SEG Technical Program Expanded Abstracts, pp. 285
–288
.2.
Heller
, R.
, Vermylen
, J.
, and Zoback
, M.
, 2014
, “Experimental Investigation of Matrix Permeability of Gas Shales
,” AAPG Bull.
, 98
(5
), pp. 975
–995
. 10.1306/092313130233.
Li
, K.
, and Horne
, R. N.
, 2004
, “Steam-Water and Air-Water Capillary Pressures: Measurement and Comparison
,” J. Can. Pet. Technol.
, 43
(7
), pp. 24
–30
. 10.2118/04-07-014.
Hou
, J.
, Luo
, F.
, Wang
, D.
, Li
, Z.
, and Bing
, S.
, 2012
, “Estimation of the Water–Oil Relative Permeability Curve From Radial Displacement Experiments. Part 2: Reasonable Experimental Parameters
,” Energy Fuels
, 26
(7
), pp. 4300
–4309
. 10.1021/ef30058665.
Shafer
, J.
, 2013
, “Recent Advances in Core Analysis
,” Petrophysics
, 54
(6
), pp. 554
–579
.6.
Chen
, S.
, Li
, G.
, Peres
, A. M.
, and Reynolds
, A. C.
, 2008
, “A Well Test for In-Situ Determination of Relative Permeability Curves
,” SPE Reservoir Eval. Eng.
, 11
(1
), pp. 95
–107
. 10.2118/96414-PA7.
Green
, A. J.
, Gringarten
, A. C.
, and Whittle
, T. M.
, 2012
, “Multi-Phase Well Testing to Calibrate Relative Permeability Measurements for Reservoir Simulation
,” SPE Europec/EAGE Annual Conference
, Copenhagen, Denmark
, June 4–7
, SPE Paper No. SPE 154851.8.
Li
, H.
, Chen
, S.
, Yang
, D.
, and Tontiwachwuthikul
, P.
, 2010
, “Ensemble-Based Relative Permeability Estimation Using B-Spline Model
,” Transp. Porous Media
, 85
(3
), pp. 703
–721
. 10.1007/s11242-010-9587-79.
Li
, H.
, and Yang
, D.
, 2012
, “Estimation of Multiple Petrophysical Parameters for Hydrocarbon Reservoirs With the Ensemble-Based Technique
,” Adv. Pet. Explor. Dev.
, 4
(2
), pp. 1
–17
.10.
Yang
, D.
, Song
, C.
, Zhang
, J.
, Zhang
, G.
, Ji
, Y.
, and Gao
, J.
, 2015
, “Performance Evaluation of Injectivity for Water-Alternating-CO2 Processes in Tight Oil Formations
,” Fuel
, 139
, pp. 292
–300
. 10.1016/j.fuel.2014.08.03311.
Al-Harbi
, A.
, Gringarten
, A.
, and Akkurt
, R.
, 2007
, “A Practical Approach to Determine Permeability From Wireline Measurements
,” SPE Saudi Arabia Section Technical Symposium
, Dhahran, Saudi Arabia
, May 7–8
, SPE Paper No. SPE 111221.12.
Shabani
, B.
, Kazemzadeh
, E.
, Entezari
, A.
, Aladaghloo
, J.
, and Mohammadi
, S.
, 2014
, “The Calculation of Oil–Water Relative Permeability From Capillary Pressure Data in an Oil-Wet Porous Media: Case Study in a Dolomite Reservoir
,” Pet. Sci. Technol.
, 32
(1
), pp. 38
–50
. 10.1080/10916466.2011.58206613.
Fan
, Z.
, Zhang
, Y.
, and Yang
, D.
, 2016
, “Estimation of Three-Phase Relative Permeabilities for a Water-Alternating-Gas Process by Use of an Improved Ensemble Randomized Maximum-Likelihood Algorithm
,” SPE Reservoir Eval. Eng.
, 19
(4
), pp. 683
–693
. 10.2118/180931-PA14.
Fan
, Z.
, Yang
, D.
, Chai
, D.
, and Li
, X.
, 2019
, “Estimation of Relative Permeability and Capillary Pressure for PUNQ-S3 Model Using a Modified Iterative Ensemble Smoother
,” ASME J. Energy Resour. Technol.
, 141
(2
), p. 022901
. 10.1115/1.404140615.
Thomas
, E. C.
, 2017
, “Tutorial: Preparing Your Digital Well Logs for Computer-Based Interpretation
,” Petrophysics
, 58
(6
), pp. 559
–563
.16.
Zhang
, Y.
, Fan
, Z.
, Yang
, D.
, Li
, H.
, and Patil
, S.
, 2017
, “Simultaneous Estimation of Relative Permeability and Capillary Pressure for PUNQ-S3 Model With a Damped Iterative-Ensemble-Kalman-Filter Technique
,” SPE J.
, 22
(3
), pp. 971
–984
. 10.2118/177846-PA17.
Earlougher
, R. C.
, 1977
, Advances in Well Test Analysis
, Henry L. Doherty Memorial Fund of AIME
, New York
.18.
Kamal
, M. M.
, and Pan
, Y.
, 2010
, “Use of Transient Data to Calculate Absolute Permeability and Average Fluid Saturations
,” SPE Reservoir Eval. Eng.
, 13
(2
), pp. 306
–312
. 10.2118/113903-PA19.
Spivey
, J. P.
, and Lee
, J. W.
, 2013
, Applied Well Test Interpretation
, SPE
, Richardson, TX
.20.
Lenormand
, R.
, Touboul
, E.
, and Zarcone
, C.
, 1988
, “Numerical Models and Experiments on Immiscible Displacements in Porous Media
,” J. Fluid Mech.
, 189
, pp. 165
–187
. 10.1017/S002211208800095321.
Ferrand
, L. A.
, and Celia
, M. A.
, 1992
, “The Effect of Heterogeneity on the Drainage Capillary Pressure-Saturation Relation
,” Water Resour. Res.
, 28
(3
), pp. 859
–870
. 10.1029/91WR0267922.
Li
, H.
, Chen
, S.
, Yang
, D.
, and Tontiwachwuthikul
, P.
, 2012
, “Estimation of Relative Permeability by Assisted History Matching Using the Ensemble Kalman Filter Method
,” J. Can. Pet. Technol.
, 51
(2
), pp. 205
–214
. 10.2118/156027-PA23.
Lee
, C. H.
, and Karpyn
, Z. T.
, 2012
, “Numerical Analysis of Imbibition Front Evolution in Fractured Sandstone Under Capillary-Dominated Conditions
,” Transp. Porous Media
, 94
(1
), pp. 359
–383
. 10.1007/s11242-012-0009-x24.
Zhang
, Y.
, Li
, H.
, and Yang
, D.
, 2012
, “Simultaneous Estimation of Relative Permeability and Capillary Pressure Using Ensemble-Based History Matching Techniques
,” Transp. Porous Media
, 94
(1
), pp. 259
–276
. 10.1007/s11242-012-0003-325.
Zhang
, Y.
, Song
, C.
, and Yang
, D.
, 2016
, “A Damped Iterative EnKF Method to Estimate Relative Permeability and Capillary Pressure for Tight Formations From Displacement Experiments
,” Fuel
, 167
, pp. 306
–315
. 10.1016/j.fuel.2015.11.04026.
Zhang
, Y.
, and Yang
, D.
, 2013
, “Simultaneous Estimation of Relative Permeability and Capillary Pressure for Tight Formations Using Ensemble-Based History Matching Method
,” Comput. Fluids
, 71
, pp. 446
–460
. 10.1016/j.compfluid.2012.11.01327.
Ucan
, S.
, Civan
, F.
, and Evans
, R. D.
, 1997
, “Uniqueness and Simultaneous Predictability of Relative Permeability and Capillary Pressure by Discrete and Continuous Means
,” J. Can. Pet. Technol.
, 36
(4
), pp. 52
–61
. 10.2118/97-04-0528.
Zhang
, Y.
, and Yang
, D.
, 2014
, “Estimation of Relative Permeability and Capillary Pressure for Tight Formations by Assimilating Field Production Data
,” Inverse Probl. Sci. Eng.
, 22
(7
), pp. 1150
–1175
. 10.1080/17415977.2013.85689929.
Frimann-Dahl
, C.
, Irvine-Fortescue
, J.
, Rokke
, E.
, Vik
, S.
, and Wahl
, O.
, 1998
, “Formation Testers vs. DST—The Cost Effective Use of Transient Analysis to Get Reservoir Parameters
,” SPE Annual Technical Conference and Exhibition
, New Orleans, LA
, Sep. 27–30
, SPE Paper No. SPE 48962.30.
Cantini
, S.
, Baldini
, D.
, Beretta
, E.
, Loi
, D.
, and Mazzoni
, S.
, 2013
, “Reservoir Permeability From Wireline Formation Testers
,” EAGE Annual Conference & Exhibition Incorporating SPE Europec
, London
, June 10–13
, SPE Paper No. SPE 164924.31.
Yang
, M.
, and Yang
, D.
, 2016
, “Permeability Interpretation From Wireline Formation Testing Measurements With Consideration of Effective Thickness
,” Petrophysics
, 57
(3
), pp. 251
–269
.32.
Yznaga
, R. J. A.
, Quintero
, L. F.
, Negm
, E.
, Arevalo
, F.
, and Soleiman
, W.
, 2017
, “Uncertainties Associated With the Interpretation and Estimation of Relative Permeabilities Using In-Situ Formation Tester Measurements
,” SPE Reservoir Characterisation and Simulation Conference and Exhibition
, Abu Dhabi, UAE
, May 8–10
, SPE Paper No. SPE 186084. 10.2118/186084-ms33.
Ramaswami
, S. R.
, Cornelisse
, P. W.
, Elshahawi
, H.
, Hows
, M.
, and Dong
, C. L.
, 2016
, “Extracting More From Wireline Formation Testing: Better Permeability Estimation
,” International Petroleum Technology Conference
, Bangkok, Thailand
, Nov. 14–16
, IPTC Paper No. IPTC 18914.34.
Brochure
, S.
, 2002
, “MDT Modular Formation Dynamics Tester, Quality Fluid Samples and Highly Accurate Reservoir Pressures
,” SMP-5124 Copyright, June
.35.
Reid
, L.
, Harrigan
, E.
, and Brennan
, W. E.
, III, 2007
, “Downhole Formation Testing Tool
,” Patent US7191831B2, Schlumberger Technology Corp.
36.
Moran
, J. H.
, and Finklea
, E. E.
, 1962
, “Theoretical Analysis of Pressure Phenomena Associated With the Wireline Formation Tester
,” J. Pet. Technol.
, 14
(8
), pp. 899
–908
. 10.2118/177-PA37.
Proett
, M. A.
, Chin
, W. C.
, Manohar
, M.
, Sigal
, R.
, and Wu
, J.
, 2001
, “Multiple Factors That Influence Wireline Formation Tester Pressure Measurements and Fluid Contacts Estimates
,” SPE Annual Technical Conference and Exhibition
, New Orleans, LA
, Sep. 30–Oct. 3
, SPE Paper No. SPE 71566.38.
Decnop Coelho
, A. C.
, de Camargo
, C.
, Kato
, E. T.
, and Legrand
, V. M.
, 2005
, “Utilizing Mini-DST for Formation Evaluation
,” SPE Latin American and Caribbean Petroleum Engineering Conference
, Rio de Janeiro, Brazil
, June 20–23
, SPE Paper No. SPE 94963.39.
Yang
, M.
, Yang
, D.
, and Chen
, A.
, 2018
, “Interpretation of Formation Permeability and Pressure Responses From Wireline Formation Testing With Consideration of Interlayer
,” Interpretation
, 6
(4
), pp. T835
–T847
. 10.1190/INT-2017-0087.140.
Ramaswami
, S. R.
, Elshahawi
, H.
, and El-Battawy
, A.
, 2012
, “Integration of Wireline Formation Testing and Well Testing Evaluation—An Example From the Caspian
,” SPE Reservoir Eval. Eng.
, 15
(3
), pp. 300
–313
. 10.2118/139837-PA41.
Goode
, P. A.
, and Thambynayagam
, R. K. M.
, 1996
, “Influence of an Invaded Zone on a Multiprobe Formation Tester
,” SPE Form. Eval.
, 11
(1
), pp. 31
–40
. 10.2118/23030-PA42.
Gok
, I. M.
, Onur
, M.
, Hegeman
, P. S.
, and Kuchuk
, F. J.
, 2006
, “Effect of an Invaded Zone on Pressure-Transient Data From Multiprobe and Packer-Probe Wireline Formation Testers
,” SPE Reservoir Eval. Eng.
, 9
(1
), pp. 39
–49
. 10.2118/84093-PA43.
Alpak
, F. O.
, Elshahawi
, H.
, Hashem
, M. N.
, and Mullins
, O. C.
, 2008
, “Compositional Modeling of Oil-Based-Mud-Filtrate Cleanup During Wireline Formation Tester Sampling
,” SPE Reservoir Eval. Eng.
, 11
(2
), pp. 219
–232
. 10.2118/100393-PA44.
Malik
, M.
, Dindoruk
, B.
, Elshahawi
, H.
, and Torres-Verdin
, C.
, 2010
, “Numerical Investigation of Oil-Base Mud Contamination in Condensates: From Cleanup to Sample Quality
,” J. Nat. Gas Sci. Eng.
, 2
(2
), pp. 69
–78
. 10.1016/j.jngse.2010.03.00145.
Al-Harthi
, M.
, Kelly
, F.
, Alenezi
, F. N.
, and Soleiman
, W.
, 2014
, “Differentiating Between Oil-Base Mud Filtrate and Multiphase Formation Fluids Using Wireline Formation Testing Techniques: Case Studies From Saudi Arabia
,” International Petroleum Technology Conference
, Doha, Qatar
, Jan. 19–22
, IPTC Paper No. IPTC 17391.46.
Cig
, K.
, Ayan
, C.
, Kristensen
, M.
, and Mackay
, E.
, 2015
, “Numerical Modeling of In-Situ Relative Permeability and Capillary Pressure From Inversion of Wireline Formation Tester Data
,” 2015 SPE/EUROPEC 2015
, Madrid, Spain
, June 1–4
, SPE Paper No. SPE 174381.47.
Proett
, M. A.
, and Chin
, W. C.
, 1998
, “New Exact Spherical Flow Solution With Storage and Skin for Early-Time Interpretation With Applications to Wireline Formation and Early-Evaluation Drillstem Testing
,” SPE Annual Technical Conference and Exhibition
, New Orleans, LA
, Sep. 27–30
, SPE Paper No. SPE 49140.48.
Akram
, A. H.
, Fitzpatrick
, A. J.
, and Halford
, F. R.
, 1999
, “A Model to Predict Wireline Formation Tester Sample Contamination
,” SPE Reservoir Eval. Eng.
, 2
(6
), pp. 499
–505
. 10.2118/59559-PA49.
Wu
, J.
, Torres-Verdin
, C.
, Sepehrnoori
, K.
, and Delshad
, M.
, 2001
, “Numerical Simulation of Mud Filtrate Invasion in Deviated Wells
,” SPE Annual Technical Conference and Exhibition
, New Orleans, LA
, Sep. 30–Oct. 3
, SPE Paper No. SPE 71739.50.
Angeles
, R.
, Torres-Verdín
, C.
, Sepehrnoori
, K.
, and Malik
, M.
, 2009
, “Prediction of Formation-Tester Fluid-Sample Quality in Highly-Deviated Wells
,” Petrophysics
, 50
(1
), pp. 32
–48
.51.
Waid
, M. C.
, Proett
, M. A.
, Chen
, C. C.
, and Ford
, W. T.
, 1991
, “Improved Models for Interpreting the Pressure Response of Formation Testers
,” SPE Annual Technical Conference and Exhibition
, Dallas, TX
, Oct. 6–9
, SPE Paper No. SPE 22754.52.
Samaha
, A.
, Huang
, K.
, Kasap
, E.
, Shwe
, T.
, and Georgi
, D.
, 1996
, “Near Wellbore Permeability and Damage Measurements: Experiments and Numerical Simulations for Interpretation of WFT Data
,” SPE Formation Damage Control Symposium
, Lafayette, LA
, Feb. 14–15
, SPE Paper No. SPE 35150.53.
Liu
, W.
, Hildebrand
, M. A.
, Lee
, J.
, and Sheng
, J.
, 2004
, “High-Resolution Near-Wellbore Modeling and Its Applications in Formation Testing
,” SPE Annual Technical Conference and Exhibition
, Houston, TX
, Sep. 26–29
, SPE Paper No. SPE 90767.54.
Zeybek
, M.
, Ramakrishnan
, T. S.
, Al-Otaibi
, S. S.
, Salamy
, S. P.
, and Kuchuk
, F. J.
, 2001
, “Estimating Multiphase Flow Properties Using Pressure and Flowline Water-Cut Data From Dual Packer Formation Tester Interval Tests and Openhole Array Resistivity Measurements
,” SPE Annual Technical Conference and Exhibition
, New Orleans, LA
, Sep. 30–Oct. 3
, SPE Paper No. SPE 71568.55.
Wu
, J.
, Torres-Verdin
, C.
, Proett
, M. A.
, Sepehrnoori
, K.
, and Belanger
, D.
, 2002
, “Inversion of Multi-Phase Petrophysical Properties Using Pumpout Sampling Data Acquired With a Wireline Formation Tester
,” SPE Annual Technical Conference and Exhibition
, San Antonio, TX
, Sep. 29–Oct. 2
, SPE Paper No. SPE 77345.56.
Angeles
, R.
, Torres-Verdín
, C.
, Lee
, H.
, Alpak
, F. O.
, and Sheng
, J. J.
, 2007
, “Estimation of Permeability and Permeability Anisotropy From Straddle-Packer Formation-Tester Measurements Based on the Physics of Two-Phase Immiscible Flow and Invasion
,” SPE J.
, 12
(3
), pp. 339
–354
. 10.2118/95897-PA57.
Lane
, H. S.
, 1993
, “Numerical Simulation of Mud Filtrate Invasion and Dissipation
,” SPWLA 34th Annual Logging Symposium
, Calgary, AB
, June 13–16
, SPWLA Paper No. SPWLA-1993-D.58.
Chin
, W. C.
, and Proett
, M. A.
, 2005
, “Formation Tester Immiscible and Miscible Flow Modeling for Job Planning Applications
,” SPWLA 46th Annual Logging Symposium
, New Orleans, LA
, June 26–29
, SPWLA Paper No. SPWLA 2005.59.
Tian
, L.
, Feng
, B.
, Zheng
, S.
, Gu
, D.
, Ren
, X.
, and Yang
, D.
, 2019
, “Performance Evaluation of Gas Production With Consideration of Dynamic Capillary Pressure in Tight Sandstone Reservoirs
,” ASME J. Energy Resour. Technol.
, 141
(2
), p. 022902
. 10.1115/1.404141060.
Schroeder
, C.
, Torres-Verdin
, C.
, and Elshahawi
, H.
, 2017
, “Influence of Mud-Filtrate Invasion Effects on Pressure Gradients Estimated From Wireline Formation Tester Measurements
,” SPWLA 58th Annual Logging Symposium
, Oklahoma, OK
, June 17–21
, SPWLA Paper No. SPWLA 2017.61.
Elshahawi
, H.
, Fathy
, K.
, and Hiekal
, S.
, 1999
, “Capillary Pressure and Rock Wettability Effects on Wireline Formation Tester Measurements
,” SPE Annual Technical Conference and Exhibition
, Houston, TX
, Oct. 3–6
, SPE Paper No. SPE 56712.62.
Elshahawi
, H.
, Samir
, M.
, and Fathy
, K.
, 2000
, “Correcting for Wettability and Capillary Pressure Effects on Formation Tester Measurements
,” SPE Annual Technical Conference and Exhibition
, Dallas, TX
, Oct. 1–4
, SPE Paper No. SPE 63075.63.
Harmawan
, I.
, Kabir
, C. S.
, Habib
, S. M.
, Kennedy
, J.
, Henson
, J.
, and Minhas
, H. N.
, 2012
, “Integrating Mini-DST-Derived Permeability With Other Sources: A Case Study
,” SPE Reservoir Eval. Eng.
, 15
(3
), pp. 361
–369
. 10.2118/145764-PA64.
Treiber
, L. E.
, and Owens
, W. W.
, 1972
, “A Laboratory Evaluation of the Wettability of Fifty Oil-Producing Reservoirs
,” SPE J.
, 12
(6
), pp. 531
–540
. 10.2118/3526-pa65.
Chilingar
, G. V.
, and Yen
, T. F.
, 1983
, “Some Notes on Wettability and Relative Permeabilities of Carbonate Reservoir Rocks, II
,” Energy Sources
, 7
(1
), pp. 67
–75
. 10.1080/0090831830890807666.
Grover
, G. A.
, Jr., 1993
, “Abqaiq Hajifa Reservoir: Geologic Attributes Controlling Hydrocarbon Production and Water Injection
,” SPE Middle East Oil Show
, Bahrain
, Apr. 3–6
, SPE Paper No. SPE 25607.67.
Alsharhan
, A. S.
, and Magara
, K.
, 1995
, “Nature and Distribution of Porosity and Permeability in Jurassic Carbonate Reservoirs of the Arabian Gulf Basin
,” Facies
, 32
(1
), pp. 237
–253
. 10.1007/BF0253687268.
Olarewaju
, J. S.
, 1997
, “Pressure Transient Analysis of Naturally Fractured Reservoirs: A Case Study
,” SPE Middle East Oil Show and Conference
, Bahrain
, Mar. 15–18
, SPE Paper No. SPE 37801.69.
Al-Garni
, S. A.
, Yuen
, B. B. W.
, Najjar
, N. F.
, Lyngra
, S.
, and Al-Shammari
, M.
, 2005
, “Optimizing Production/Injection and Accelerating Recovery of Mature Field Through Fracture Simulation Model
,” International Petroleum Technology Conference
, Doha, Qatar
, Nov. 21–23
, IPTC Paper No. IPTC 10433.70.
Malinowski
, R.
, 1961
, “Water Injection, Arab-D Member, Abqaiq Field, Saudi Arabia
,” SPE Middle East Regional Meeting
, Dhahran, Saudi Arabia
, Mar. 27–29
, SPE Paper No. SPE 85.71.
Zhang
, F.
, and Yang
, D.
, 2018
, “Effects of Non-Darcy Flow and Penetrating Ratio on Performance of Horizontal Wells With Multiple Fractures in a Tight Formation
,” ASME J. Energy Resour. Technol.
, 140
(3
), p. 032903
. 10.1115/1.403790372.
Zhou
, D.
, and Yang
, D.
, 2017
, “Scaling Criteria for Waterflooding and Immiscible CO2 Flooding in Heavy Oil Reservoirs
,” ASME J. Energy Resour. Technol.
, 139
(2
), p. 022909
. 10.1115/1.403551373.
Phelps
, R. E.
, 1993
, “Practical Aspects of Constructing a Large 3D Simulation Model of a Complex Reservoir
,” SPE Middle East Oil Show
, Bahrain
, Apr. 3–6
, SPE Paper No. SPE 25602.74.
Heiba
, A. A.
, Davis
, H. T.
, and Scriven
, L. E.
, 1983
, “Effect of Wettability on Two-Phase Relative Permeabilities and Capillary Pressures
,” SPE Annual Technical Conference and Exhibition
, San Francisco, CA
, Oct. 5–8
, SPE Paper No. SPE 12172.75.
Heiba
, A. A.
, Sahimi
, M.
, Scriven
, L. E.
, and Davis
, H. T.
, 1992
, “Percolation Theory of Two-Phase Relative Permeability
,” SPE Reservoir Eng.
, 7
(1
), pp. 123
–132
. 10.2118/11015-PA76.
Dixit
, A. B.
, McDougall
, S. R.
, and Sorbie
, K. S.
, 1998
, “A Pore-Level Investigation of Relative Permeability Hysteresis in Water-Wet Systems
,” SPE J.
, 3
(2
), pp. 115
–123
. 10.2118/37233-PA77.
Liu
, G.
, Meng
, Z.
, Li
, X.
, Gu
, D.
, Yang
, D.
, and Yin
, H.
, 2019
, “Experimental and Numerical Evaluation of Water Control and Production Increase in a Tight Gas Formation With Polymer
,” ASME J. Energy Resour. Technol.
, 141
(10
), p. 102903
. 10.1115/1.404339278.
Kamath
, J.
, de Zabala
, E. F.
, and Boyer
, R. E.
, 1995
, “Water/Oil Relative Permeability Endpoints of Intermediate-Wet, Low-Permeability Rocks
,” SPE Form. Eval.
, 10
(1
), pp. 4
–10
. 10.2118/26092-PA79.
Wang
, J. X.
, and Buckley
, J. S.
, 1999
, “Wettability and Rate Effects on End-Point Relative Permeability to Water
,” International Symposium of the Society of Core Analysts
, Golden, CO
, Aug.
, SCA Paper No. SCA 9937.80.
Nguyen
, V. H.
, Sheppard
, A. P.
, Knackstedt
, M. A.
, and Pinczewski
, W. V.
, 2006
, “The Effect of Displacement Rate on Imbibition Relative Permeability and Residual Saturation
,” SPE J.
, 52
(1–4
), pp. 54
–70
. 10.1016/j.petrol.2006.03.02081.
Liu
, G.
, Bai
, Y.
, Gu
, D.
, Lu
, Y.
, and Yang
, D.
, 2018
, “Determination of Static and Dynamic Characteristics of Microscopic Pore-Throat Structure in a Tight Oil-Bearing Sandstone Formation
,” AAPG Bull.
, 102
(9
), pp. 1867
–1892
. 10.1306/010818161321706182.
Gates
, J. I.
, and Lietz
, W. T.
, 1950
, Relative Permeabilities of California Cores by the Capillary-Pressure Method, Drilling and Production Practice
, American Petroleum Institute
, New York
.83.
Masalmeh
, S. K.
, 2003
, “The Effect of Wettability Heterogeneity on Capillary Pressure and Relative Permeability
,” J. Pet. Sci. Eng.
, 39
(3–4
), pp. 399
–408
. 10.1016/S0920-4105(03)00078-084.
Kalaydjian
, F. J.-M.
, 1992
, “Dynamic Capillary Pressure Curve for Water/Oil Displacement in Porous Media: Theory vs. Experiment
,” SPE Annual Technical Conference and Exhibition
, Washington, DC
, Oct. 4–7
, SPE Paper No. SPE 24813.85.
Masalmeh
, S. K.
, 2002
, “The Effect of Wettability on Saturation Functions and Impact on Carbonate Reservoirs in the Middle East
,” SPE Abu Dhabi International Petroleum Exhibition and Conference
, Abu Dhabi, United Arab Emirates
, Oct. 13–16
, SPE Paper No. SPE 78515.86.
Zhao
, J.
, Kang
, Q.
, Yao
, J.
, Viswanathan
, H.
, Pawar
, R.
, Zhang
, L.
, and Sun
, H.
, 2018
, “The Effect of Wettability Heterogeneity on Relative Permeability of Two-Phase Flow in Porous Media: A Lattice Boltzmann Study
,” Water Resour. Res.
, 54
(2
), pp. 1295
–1311
. 10.1002/2017WR02144387.
Lee
, C. C.
, Lee
, C. H.
, Yeh
, H. F.
, and Lin
, H. I.
, 2011
, “Modeling Spatial Fracture Intensity as a Control on Flow in Fractured Rock
,” Environ. Earth Sci.
, 63
(6
), pp. 1199
–1211
. 10.1007/s12665-010-0794-x88.
Wang
, J.
, Dong
, M.
, and Asghari
, K.
, 2006
, “Effect of Oil Viscosity on Heavy Oil–Water Relative Permeability Curves
,” SPE/DOE Symposium on Improved Oil Recovery
, Tulsa, OK
, Apr. 22–26
, SPE Paper No. SPE 99763.Copyright © 2019 by ASME
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