Abstract

In this research, experimental and mathematical modeling were carried out to estimate the permeability of tight sandstones. The pore structure parameters such as the number of pores, pore cross-sectional area, and pore radius were obtained by microcomputed tomography (micro-CT) scanning and image processing. A mathematical model was developed to predict the permeability of tight sandstones using the pore structure parameters. In the model, hydraulic radius was used to estimate the pore hydraulic conductance, where the pore diameter variation in a sinusoidal manner was observed. The stereological correction factor was used to characterize the arbitrary angle between the pore axis and the cross-sectional area. The tortuosity model was applied to characterize the behavior of non-Darcy flow inside the tight formations. Finally, the permeability prediction model was developed based on the effective medium theory. The proposed model was validated by 21 tight sandstone samples, with the relative errors within ±20%. In addition, due to the presence of small pores in tight sandstone with little contribution to overall permeability, the permeability shows inversely proportional behavior against the number of small pores.

References

1.
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
. 10.1115/1.4037903
2.
Carpenter
,
C.
,
2018
, “
A Review of Improved-Oil-Recovery Methods in North American Unconventional Reservoirs
,”
J. Pet. Technol.
,
70
(
1
), pp.
42
44
. 10.2118/0118-0042-jpt
3.
Burrows
,
L. C.
,
Haeri
,
F.
,
Cvetic
,
P.
,
Sanguinito
,
S.
,
Shi
,
F.
,
Tapriyal
,
D.
,
Goodman
,
A.
, and
Enick
,
R. M.
,
2020
, “
A Literature Review of CO2, Natural Gas, and Water-Based Fluids for Enhanced Oil Recovery in Unconventional Reservoirs
,”
Energy Fuels
,
34
(
5
), pp.
5331
5380
. 10.1021/acs.energyfuels.9b03658
4.
Lan
,
Y.
,
Yang
,
Z.
,
Wang
,
P.
,
Yan
,
Y.
,
Zhang
,
L.
, and
Ran
,
J.
,
2019
, “
A Review of Microscopic Seepage Mechanism for Shale Gas Extracted by Supercritical CO2 Flooding
,”
Fuel
,
238
, pp.
412
424
. 10.1016/j.fuel.2018.10.130
5.
Gao
,
H.
, and
Li
,
H. A.
,
2016
, “
Pore Structure Characterization, Permeability Evaluation and Enhanced Gas Recovery Techniques of Tight Gas Sandstones
,”
J. Nat. Gas Sci. Eng.
,
28
, pp.
536
547
. 10.1016/j.jngse.2015.12.018
6.
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
,”
Am. Assoc. Pet. Geol. Bull.
,
102
(
9
), pp.
1867
1892
. 10.1306/0108181613217061
7.
Liu
,
G.
,
Yin
,
H.
,
Lan
,
Y.
,
Fei
,
S.
, and
Yang
,
D.
,
2020
, “
Experimental Determination of Dynamic Pore-Throat Structure Characteristics in a Tight Gas Sandstone Formation With Consideration of Effective Stress
,”
Mar. Pet. Geol.
,
113
, p.
104170
. 10.1016/j.marpetgeo.2019.104170
8.
Aminpour
,
M.
,
Galindo-Torres
,
S. A.
,
Scheuermann
,
A.
, and
Li
,
L.
,
2018
, “
Pore-Scale Behavior of Darcy Flow in Static and Dynamic Porous Media
,”
Phys. Rev. Appl.
,
9
(
6
), pp.
1
15
. 10.1103/PhysRevApplied.9.064025
9.
Feng
,
R.
,
Chen
,
S.
,
Bryant
,
S.
, and
Liu
,
J.
,
2019
, “
Stress-Dependent Permeability Measurement Techniques for Unconventional Gas Reservoirs: Review, Evaluation, and Application
,”
Fuel
,
256
, p.
115987
. 10.1016/j.fuel.2019.115987
10.
Alfi
,
M.
,
Hosseini
,
S. A.
,
Enriquez
,
D.
, and
Zhang
,
T.
,
2019
, “
A New Technique for Permeability Calculation of Core Samples From Unconventional Gas Reservoirs
,”
Fuel
,
235
, pp.
301
305
. 10.1016/j.fuel.2018.07.114
11.
Behrang
,
A.
,
Mohammadmoradi
,
P.
,
Taheri
,
S.
, and
Kantzas
,
A.
,
2016
, “
A Theoretical Study on the Permeability of Tight Media; Effects of Slippage and Condensation
,”
Fuel
,
181
, pp.
610
617
. 10.1016/j.fuel.2016.05.048
12.
Abbasi
,
S.
,
Singh
,
T. N.
, and
Pritchard
,
T.
,
2016
, “
Error and Impact of Porosity-Permeability Transform in Tight Reservoir
,”
J. Nat. Gas Sci. Eng.
,
35
, pp.
354
361
. 10.1016/j.jngse.2016.08.055
13.
Moussa
,
T.
,
Elkatatny
,
S.
,
Mahmoud
,
M.
, and
Abdulraheem
,
A.
,
2018
, “
Development of New Permeability Formulation From Well Log Data Using Artificial Intelligence Approaches
,”
ASME J. Energy Resour. Technol.
,
140
(
7
), p.
037101
. 10.1115/1.4039270
14.
Azari
,
M.
,
Hamza
,
F.
,
Hadibeik
,
H.
, and
Ramakrishna
,
S.
,
2019
, “
Well-Testing Challenges in Unconventional and Tight-Gas-Formation Reservoirs
,”
SPE Reserv. Eval. Eng.
,
22
(
4
), pp.
1371
1384
. 10.2118/190025-PA
15.
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
981
. 10.2118/177846-pa
16.
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
. 10.1115/1.4041406
17.
Rezaee
,
R.
,
Saeedi
,
A.
, and
Clennell
,
B.
,
2012
, “
Tight Gas Sands Permeability Estimation From Mercury Injection Capillary Pressure and Nuclear Magnetic Resonance Data
,”
J. Pet. Sci. Eng.
,
88–89
, pp.
92
99
. 10.1016/j.petrol.2011.12.014
18.
Xiao
,
L.
,
Liu
,
X. P.
,
Zou
,
C. C.
,
Hu
,
X. X.
,
Mao
,
Z. Q.
,
Shi
,
Y. J.
,
Guo
,
H. P.
, and
Li
,
G. R.
,
2014
, “
Comparative Study of Models for Predicting Permeability From Nuclear Magnetic Resonance (NMR) Logs in Two Chinese Tight Sandstone Reservoirs
,”
Acta Geophys.
,
62
(
1
), pp.
116
141
. 10.2478/s11600-013-0165-6
19.
Gao
,
H.
,
Wang
,
C.
,
Cao
,
J.
,
He
,
M.
, and
Dou
,
L.
,
2019
, “
Quantitative Study on the Stress Sensitivity of Pores in Tight Sandstone Reservoirs of Ordos Basin Using NMR Technique
,”
J. Pet. Sci. Eng.
,
172
, pp.
401
410
. 10.1016/j.petrol.2018.09.083
20.
Zhao
,
X.
,
Yang
,
Z.
,
Lin
,
W.
,
Xiong
,
S.
,
Luo
,
Y.
,
Wang
,
Z.
,
Chen
,
T.
,
Xia
,
D.
, and
Wu
,
Z.
,
2019
, “
Study on Pore Structures of Tight Sandstone Reservoirs Based on Nitrogen Adsorption, High-Pressure Mercury Intrusion, and Rate-Controlled Mercury Intrusion
,”
ASME J. Energy Resour. Technol.
,
141
(
11
), p.
112903
. 10.1115/1.4043695
21.
Valvatne
,
P. H.
,
Piri
,
M.
,
Lopez
,
X.
, and
Blunt
,
M. J.
,
2005
, “
Predictive Pore-Scale Modeling of Single and Multiphase Flow
,”
Transp. Porous Media
,
58
(
1–2
), pp.
23
41
. 10.1007/s11242-004-5468-2
22.
Dong
,
H.
,
2007
, “
Micro-CT Imaging and Pore Network Extraction
,”
Ph.D. thesis
,
Imperial College
,
London
.
23.
Chen
,
L.
,
Kang
,
Q.
,
Pawar
,
R.
,
He
,
Y. L.
, and
Tao
,
W. Q.
,
2015
, “
Pore-Scale Prediction of Transport Properties in Reconstructed Nanostructures of Organic Matter in Shales
,”
Fuel
,
158
, pp.
650
658
. 10.1016/j.fuel.2015.06.022
24.
Lin
,
W.
,
Li
,
X.
,
Yang
,
Z.
,
Manga
,
M.
,
Fu
,
X.
,
Xiong
,
S.
,
Gong
,
A.
,
Chen
,
G.
,
Li
,
H.
,
Pei
,
L.
,
Li
,
S.
,
Zhao
,
X.
, and
Wang
,
X.
,
2019
, “
Multiscale Digital Porous Rock Reconstruction Using Template Matching
,”
Water Resour. Res.
,
55
(
8
), pp.
6911
6922
. 10.1029/2019WR025219
25.
Lin
,
W.
,
Li
,
X.
,
Yang
,
Z.
,
Xiong
,
S.
,
Luo
,
Y.
, and
Zhao
,
X.
,
2020
, “
Modeling of 3D Rock Porous Media by Combining X-Ray CT and Markov Chain Monte Carlo
,”
ASME J. Energy Resour. Technol.
,
142
(
1
), p.
013001
. 10.1115/1.4045461
26.
Yang
,
Y.
,
Yang
,
H.
,
Tao
,
L.
,
Yao
,
J.
,
Wang
,
W.
,
Zhang
,
K.
, and
Luquot
,
L.
,
2019
, “
Microscopic Determination of Remaining Oil Distribution in Sandstones With Different Permeability Scales Using Computed Tomography Scanning
,”
ASME J. Energy Resour. Technol.
,
141
(
9
), p.
092903
. 10.1115/1.4043131
27.
Behrang
,
A.
, and
Kantzas
,
A.
,
2017
, “
A Hybrid Methodology to Predict Gas Permeability in Nanoscale Organic Materials; A Combination of Fractal Theory, Kinetic Theory of Gases and Boltzmann Transport Equation
,”
Fuel
,
188
, pp.
239
245
. 10.1016/j.fuel.2016.10.014
28.
Ho
,
M. T.
,
Zhu
,
L.
,
Wu
,
L.
,
Wang
,
P.
,
Guo
,
Z.
,
Ma
,
J.
, and
Zhang
,
Y.
,
2019
, “
Pore-Scale Simulations of Rarefied Gas Flows in Ultra-Tight Porous Media
,”
Fuel
,
249
, pp.
341
351
. 10.1016/j.fuel.2019.03.106
29.
Zimmerman
,
R. W.
,
Kumar
,
S.
, and
Bodvarsson
,
G. S.
,
1991
, “
Lubrication Theory Analysis of the Permeability of Rough-Walled Fractures
,”
High Lev. Radioact. Waste Manag.
,
28
(
1
), pp.
535
541
. 10.1016/0148-9062(92)91194-a
30.
Schlueter
,
E. M.
,
1990
, “
Predicting the Transport Properties of Sedimentary Rocks From Microstructure
,”
Ph.D. thesis
,
University of California Berkeley
,
California
.
31.
Lock
,
P. A.
,
Jing
,
X.
,
Zimmerman
,
R. W.
, and
Schlueter
,
E. M.
,
2002
, “
Predicting the Permeability of Sandstone From Image Analysis of Pore Structure
,”
J. Appl. Phys.
,
92
(
10
), pp.
6311
6319
. 10.1063/1.1516271
32.
Wong
,
H. S.
,
Zimmerman
,
R. W.
, and
Buenfeld
,
N. R.
,
2012
, “
Estimating the Permeability of Cement Pastes and Mortars Using Image Analysis and Effective Medium Theory
,”
Cem. Concr. Res.
,
42
(
2
), pp.
476
483
. 10.1016/j.cemconres.2011.11.018
33.
Ghanbarian
,
B.
,
Liang
,
F.
, and
Liu
,
H. H.
,
2020
, “
Modeling Gas Relative Permeability in Shales and Tight Porous Rocks
,”
Fuel
,
272
, pp.
117686
. 10.1016/j.fuel.2020.117686
34.
Lock
,
P.
,
2001
, “
Imperial College of Science, Technology and Medicine University of London Department of Earth Science and Engineering Centre for Petroleum Studies Estimating the Permeability of Reservoir
,”
Ph.D. thesis
,
Imperial College
,
London
.
35.
Nabovati
,
A.
,
Llewellin
,
E. W.
, and
Sousa
,
A. C. M.
,
2009
, “
A General Model for the Permeability of Fibrous Porous Media Based on Fluid Flow Simulations Using the Lattice Boltzmann Method
,”
Composites, Part A
,
40
(
6–7
), pp.
860
869
. 10.1016/j.compositesa.2009.04.009
36.
Carman
,
P. C.
,
1997
, “
Fluid Flow Through Granular Beds
,”
Process Saf. Environ. Prot.
,
75
, pp.
S32
S48
. 10.1016/s0263-8762(97)80003-2
37.
Ebrahimi Khabbazi
,
A.
,
Hinebaugh
,
J.
, and
Bazylak
,
A.
,
2015
, “
Analytical Tortuosity-Porosity Correlations for Sierpinski Carpet Fractal Geometries, Chaos
,”
Solitons Fractals
,
78
, pp.
124
133
. 10.1016/j.chaos.2015.07.019
38.
Feranie
,
S.
, and
Latief
,
F. D. E.
,
2013
, “
Tortuosity-Porosity Relationship in Two-Dimensional Fractal Model of Porous Media
,”
Fractals
,
21
(
02
), pp.
1
7
. 10.1142/S0218348X13500138
39.
Ghanbarian
,
B.
,
Hunt
,
A. G.
,
Ewing
,
R. P.
, and
Sahimi
,
M.
,
2013
, “
Tortuosity in Porous Media: A Critical Review
,”
Soil Sci. Soc. Am. J.
,
77
(
5
), pp.
1461
1477
. 10.2136/sssaj2012.0435
40.
Saomoto
,
H.
, and
Katagiri
,
J.
,
2015
, “
Direct Comparison of Hydraulic Tortuosity and Electric Tortuosity Based on Finite Element Analysis
,”
Theor. Appl. Mech. Lett.
,
5
(
5
), pp.
177
180
. 10.1016/j.taml.2015.07.001
41.
Rabbani
,
A.
, and
Jamshidi
,
S.
,
2014
, “
Specific Surface and Porosity Relationship for Sandstones for Prediction of Permeability
,”
Int. J. Rock Mech. Min. Sci.
,
71
, pp.
25
32
. 10.1016/j.ijrmms.2014.06.013
42.
Jurgawczynski
,
M.
,
2007
, “
Predicting Absolute and Relative Permeabilities of Carbonate Rocks Using Image Analysis and Effective Medium Theory
,”
Ph.D. thesis
,
Imperial College
,
London
.
43.
Su
,
N.
,
Duan
,
Y.
,
Chen
,
W.
, and
Yu
,
C.
,
2010
, “
Three-Dimensional Reconstruction of Micro Pore Structure
,”
International Conference on Computational and Information Sciences
,
Chengdu, China
.
44.
Goh
,
T. Y.
,
Basah
,
S. N.
,
Yazid
,
H.
,
Aziz Safar
,
M. J.
, and
Ahmad Saad
,
F. S.
,
2018
, “
Performance Analysis of Image Thresholding: Otsu Technique
,”
Meas. J. Int. Meas. Confed.
,
114
, pp.
298
307
. 10.1016/j.measurement.2017.09.052
45.
Peng
,
S.
,
Marone
,
F.
, and
Dultz
,
S.
,
2014
, “
Resolution Effect in X-ray Microcomputed Tomography Imaging and Small Pore’s Contribution to Permeability for a Berea Sandstone
,”
J. Hydrol.
,
510
, pp.
403
411
. 10.1016/j.jhydrol.2013.12.028
46.
Goral
,
J.
,
Walton
,
I.
,
Andrew
,
M.
, and
Deo
,
M.
,
2019
, “
Pore System Characterization of Organic-Rich Shales Using Nanoscale-Resolution 3D Imaging
,”
Fuel
,
258
, p.
116049
. 10.1016/j.fuel.2019.116049
47.
Lai
,
J.
,
Wang
,
G.
,
Meng
,
C.
,
Guan
,
B.
,
Zheng
,
X.
,
Zhou
,
L.
,
Xin
,
Y.
, and
Han
,
C.
,
2015
, “
Pore Structure Characteristics and Formation Mechanisms Analysis of Tight Gas Sandstones
,”
Prog. Geophys.
,
30
, pp.
0217
0227
. 10.6038/pg20150133
You do not currently have access to this content.