Pore-scale modeling is becoming a hot topic in overall reservoir characterization process. It is an important approach for revealing the flow behaviors in porous media and exploring unknown flow patterns at pore scale. Over the past few decades, many reconstruction methods have been proposed, and among them the simulated annealing method (SAM) is extensively tested and easier to program. However, SAM is usually based on the two-point probability function or linear-path function, which fails to capture much more information on the multipoint connectivity of various shapes. For this reason, a new reconstruction method is proposed to reproduce the characteristics of a two-dimensional (2D) thin section based on the multipoint histogram. First, the two-point correlation coefficient matrix will be introduced to determine an optimal unit configuration of a multipoint histogram. Second, five different types of seven-point unit configurations will be used to test the unit configuration selection algorithm. Third, the multipoint histogram technology is used for generating the porous space reconstruction based on the prior unit configuration with a different calculation of the objective function. Finally, the spatial connectivity, patterns reproduction, the local percolation theory (LPT), and hydraulic connectivity are used to compare with those of the reference models. The results show that the multipoint histogram technology can produce better multipoint connectivity information than SAM. The reconstructed system matches the training image very well, which reveals that the reconstruction captures the geometry and topology information of the training image, for instance, the shape and distribution of pore space. The seven-point unit configuration is enough to get the spatial characters of the training image. The quality of pattern reproduction of the reconstruction is assessed by computing the multipoint histogram, and the similarity is around 97.3%. Based on the LPT analysis, the multipoint histogram can describe the anticipated patterns of geological heterogeneities and reproduce the connectivity of pore media with a high degree of accuracy. The two-point correlation coefficient matrix and a new construction theory are proposed. The new construction theory provides a stable theory and technology guidance for the study of pore space development and multiphase fluid flow rule in the digital rock.

References

1.
Yue
,
W.
, and
Wang
,
J. Y.
,
2015
, “
Feasibility of Waterflooding for a Carbonate Oil Field Through Whole-Field Simulation Studies
,”
ASME J. Energy Resour. Technol.
,
137
(
6
), p.
064501
.
2.
Wang
,
W. D.
,
Shahvali
,
M.
, and
Su
,
Y. L.
,
2017
, “
Analytical Solutions for a Quad-Linear Flow Model Derived for Multistage Fractured Horizontal Wells in Tight Oil Reservoirs
,”
ASME J. Energy Resour. Technol.
,
139
(
1
), p.
012905
.
3.
Shirman
,
E.
,
Wojtanowicz
,
A. K.
, and
Kurban
,
H.
,
2014
, “
Enhancing Oil Recovery With Bottom Water Drainage Completion
,”
ASME J. Energy Resour. Technol.
,
136
(
4
), p.
042906
.
4.
Zhou
,
D. Y.
, and
Yang
,
D. Y.
,
2017
, “
Scaling Criteria for Waterflooding and Immiscible CO2 Flooding in Heavy Oil Reservoirs
,”
ASME J. Energy Resour. Technol.
,
139
(2), p.
022909
.
5.
Caers
,
J.
,
2001
, “
Geostatistical Reservoir Modelling Using Statistical Pattern Recognition
,”
J. Pet. Sci. Eng.
,
29
(3–4), pp.
177
188
.
6.
Yu
,
J.
,
Armstrong
,
R. T.
,
Ramandi
,
H. L.
, and
Mostaghimi
,
P.
,
2016
, “
Coal Cleat Reconstruction Using Micro-Computed Tomography Imaging
,”
Fuel
,
181
, pp.
286
299
.
7.
Liu
,
X. F.
,
Sun
,
J. M.
,
Wang
,
H. T.
, and
Yu
,
H. W.
,
2009
, “
The Accuracy Evaluation on 3D Digital Cores Reconstructed by Sequence Indicator Simulation
,”
Acta Pet. Sin.
,
30
, pp.
391
395
.http://en.cnki.com.cn/Article_en/CJFDTOTAL-SYXB200903014.htm
8.
Zhao
,
X. C.
,
Yao
,
J.
, and
Yi
,
Y. J.
,
2007
, “
A New Stochastic Method of Reconstructing Porous Media
,”
Transp. Porous Media
,
69
(1), pp.
1
11
.
9.
Okabe
,
H.
, and
Blunt
,
M. J.
,
2007
, “
Pore Space Reconstruction of Vuggy Carbonates Using Microtomography and Multiple-Point Statistics
,”
Water Resour. Res.
,
43
(12), p.
W12S02
.
10.
Jing
,
Y.
,
Armstrong
,
R. T.
, and
Mostaghimi
,
P.
,
2017
, “
Rough-Walled Discrete Fracture Network Modelling for Coal Characterisation
,”
Fuel
,
191
, pp.
442
453
.
11.
Xu
,
Z.
,
Teng
,
Q. Z.
,
He
,
X. H.
, and
Li
,
Z. J.
,
2013
, “
A Reconstruction Method for Three-Dimensional Pore Space Using Multiple-Point Geology Statistic Based on Statistical Pattern Recognition and Microstructure Characterization
,”
Int. J. Numer. Anal Methods Geomech.
,
37
(1), pp.
97
110
.
12.
Liu
,
X. H.
,
Srinivasan
,
S.
, and
Wong
,
D.
,
2002
, “
Geological Characterization of Naturally Fractured Reservoirs Using Multiple Point Geostatistics
,” SPE/DOE Improved Oil Recovery Symposium, Tulsa, OK, Apr. 13–17,
SPE
Paper No. SPE-75246-MS.
13.
Yao
,
J.
,
Wang
,
C. C.
,
Yang
,
Y. F.
, and
Yan
,
X.
,
2012
, “
A Stochastic Upscaling Analysis for Carbonate Media
,”
ASME J. Energy Resour. Technol.
,
135
(
2
), p.
022901
.
14.
Bryant
,
S.
, and
Blunt
,
M.
,
1992
, “
Prediction of Relative Permeability in Simple Porous Media
,”
Phys. Rev. A
,
46
, pp.
2004
2011
.
15.
Safavisohi
,
S. R. F. B.
, and
Sharbati
,
E.
,
2007
, “
Porosity and Permeability Effects on Centerline Temperature Distributions, Peak Flame Temperature, Flame Structure, and Preheating Mechanism for Combustion in Porous Media
,”
ASME J. Energy Resour. Technol.
,
129
(
1
), pp.
54
65
.
16.
Strebelle
,
S.
,
2002
, “
Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics
,”
Math. Geol.
,
34
(1), pp.
1
21
.
17.
Yeong
,
C. L. Y.
, and
Torquato
,
S.
,
1998
, “
Reconstructing Random Media—II: Three-Dimensional Media From Two-Dimensional Cuts
,”
Phys. Rev. E
,
58
, pp.
224
233
.
18.
Joshi
,
M. Y.
,
1974
, “
A Class of Stochastic Models for Porous Media
,” Ph.D. dissertation, University of Kansas, Lawrence, KS.
19.
Keehm
,
Y.
,
Mukerji
,
T.
, and
Nur
,
A.
,
2004
, “
Permeability Prediction From Thin Sections: 3D Reconstruction and Lattice-Boltzmann Flow Simulation
,”
Geophys. Res. Lett.
,
31
(4), p.
L04606
.
20.
Guardiano
,
F.
, and
Srivastava
,
R. M.
,
1993
,
Multivariate Geostatistics: Beyond Bivariate Moments
, Vol.
1
,
Kluwer
,
Dordrecht, The Netherlands
, pp.
133
144
.
21.
Strebelle
,
S.
, and
Cavelius
,
C.
,
2014
, “
Solving Speed and Memory Issues in Multiple-Point Statistics Simulation Program SNESIM
,”
Math. Geosci.
,
46
, pp.
171
186
.
22.
Hajizadeh
,
A.
,
Safekordi
,
A.
, and
Farhadpour
,
F. A.
,
2011
, “
A Multiple-Point Statistics Algorithm for 3D Pore Space Reconstruction From 2D Images
,”
Adv. Water Resour.
,
34
(10), pp.
1256
1267
.
23.
Okabe
,
H.
, and
Blunt
,
M. J.
,
2004
, “
Prediction of Permeability for Porous Media Reconstructed Using Multiple-Point Statistics
,”
Phys. Rev. E
,
70
(6), p.
066135
.
24.
Tahmasebi
,
P.
, and
Sahimi
,
M.
,
2012
, “
Reconstruction of Three-Dimensional Porous Media Using a Single Thin Section
,”
Phys. Rev. E
,
85
(6), p.
066709
.
25.
Hajizadeh
,
A.
, and
Farhadpour
,
Z.
,
2012
, “
An Algorithm for 3D Pore Space Reconstruction From a 2D Image Using Sequential Simulation and Gradual Deformation With the Probability Perturbation Sampler
,”
Transp. Porous Media
,
94
(3), pp.
859
881
.
26.
Naraghi
,
M. E.
,
Spikes
,
K.
, and
Srinivasan
,
S.
,
2016
, “
3-D Reconstruction of Porous Media From a 2-D Section and Comparisons of Transport and Elastic Properties
,”
SPE Western Regional Meeting, Anchorage
, AK, May 23–26,
SPE
Paper No. SPE-180489-MS.
27.
Farmer
,
C. L.
,
1989
, “
The Mathematical Generation of Reservoir Geology
,”
Joint IMA/SPE European Conference on the Mathematics of Oil Recovery
, Cambridge, UK, July 25–27, pp. 1–12.
28.
Qiu
,
W. Y.
, and
Kelkar
,
M. G.
,
1995
, “
Simulation of Geological Models Using Multipoint Histogram
,” SPE Annual Technical Conference & Exhibition, Dallas, TX, Oct. 22–25,
SPE
Paper No. SPE-30601-MS.
29.
Metropolis
,
N.
,
Rosenbluth
,
A. W.
,
Rosenbluth
,
M. N.
,
Teller
,
A. H.
, and
Teller
,
E.
,
1953
, “
Equation of State Calculations by Fast Computing Machines
,”
J. Chem. Phys.
,
21
, pp.
1087
1092
.
30.
Honarkhah
,
M.
, and
Caers
,
J.
,
2010
, “
Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling
,”
Math. Geosci.
,
42
(5), pp.
487
517
.
31.
Hilfer
,
R.
,
1992
, “
Local-Porosity Theory for Flow in Porous Media
,”
Phys. Rev. E
,
45
, pp.
7115
7121
.
32.
Hilfer
,
R.
,
2002
, “
Review on Scale Dependent Characterization of the Microstructure of Porous Media
,”
Transp. Porous Media
,
46
(2–3), pp.
373
390
.
33.
Mei
,
R. W.
,
Luo
,
L. S.
, and
Shyy
,
W.
,
1999
, “
An Accurate Curved Boundary Treatment in the Lattice Boltzmann Method
,”
J. Comput. Phys.
,
155
(2), pp.
307
330
.
34.
Okabe
,
H.
, and
Blunt
,
M. J.
,
2005
, “
Pore Space Reconstruction Using Multiple-Point Statistics
,”
J. Pet. Sci. Eng.
,
46
(1–2), pp.
121
137
.
35.
Liang
,
Z. R.
,
Fernandes
,
C. P.
,
Magnani
,
F. S.
, and
Philippi
,
P. C.
,
1998
, “
A Reconstruction Technique for Three-Dimensional Porous Media Using Image Analysis and Fourier Transforms
,”
J. Pet. Sci. Eng.
,
21
(3–4), pp.
273
283
.
36.
Hu
,
J.
, and
Stroeven
,
P.
,
2005
, “
Local Porosity Analysis of Pore Structure in Cement Paste
,”
Cem. Concr. Res.
,
35
(2), pp.
233
242
.
You do not currently have access to this content.