Research ArticleMicro- and Nanoscale Pore Structure Characterization ofCarbonates from the Xiaoerbulake Formation in the Tarim Basin,Northwest China

Jingyi Wang ,1 Qinhong Hu ,2 Mengdi Sun ,1 Zhongxian Cai,1 Cong Zhang,3,4

and Tao Zhang5

1Key Laboratory of Tectonics and Petroleum Resources, Ministry of Education, China University of Geosciences,Wuhan 430074, China2Department of Earth and Environment Sciences, University of Texas at Arlington, Arlington, TX 76019, USA3Oil & Gas Survey Center, China Geological Survey, Beijing 100029, China4Key Laboratory of Unconventional Oil & Gas Geology, China Geological Survey, Beijing 100029, China5Key Laboratory of Deep Oil and Gas, China University of Petroleum (East China), Qingdao 266580, China

Correspondence should be addressed to Qinhong Hu; maxhu@uta.edu and Mengdi Sun; sunmd@cug.edu.cn

Received 30 October 2020; Revised 23 November 2020; Accepted 12 April 2021; Published 29 April 2021

Academic Editor: Andrea Brogi

Copyright © 2021 Jingyi Wang et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The evaluation of pore structure is an essential part in the assessment of carbonate reservoirs. The structures (geometry andconnectivity) of nm to μm-scale pore networks in outcrop samples of carbonates from Xiaoerbulake Formation in Tarim Basinof China were studied by using optical microscopy, field emission-scanning electron microscopy (FE-SEM), as well as mercuryintrusion porosimetry (MIP) with fractal analyses of the data, and spontaneous imbibition tests (distilled water). The resultsdemonstrate that the lithologies are micritic dolomites, fine-to-medium-to-coarse crystalline dolomites, microbial dolomites,and dolarenite. At micro- to nanoscales in size, pore types are dominated by intergranular, intercrystalline, and intragranular(e.g., dissolution) pores. These pore networks have pore-throat diameters from 0.01 to >10μm. Compared with a nanoscalepore network, the μm-scale pore networks are relatively well connected and serve as the most important permeability pathways.Although the pore volume accounts for most of the total porosity, the permeability of nanoscale pore networks is low. Theexistence of micro-nano-fractures could improve connectivity, especially for the nanoscale pore networks, by linking theintragranular (dissolution) pores which are mostly in the range of nm-scale.

1. Introduction

Carbonate reservoirs have a considerable exploration andexploitation significance as they contain a significant propor-tion of the world’s hydrocarbon resources [1]. China has avast area of carbonate rock, mostly located in the Tarimand Sichuan Basins. Cambrian-aged carbonates are widelydeveloped in the Tarim Basin with a thickness of over2100m covering an area of 41 × 104 km2, and they form partof well-developed source-reservoir-seal petroleum system.Since commercial hydrocarbon production started in 2013from the Xiaoerbulake Formation in Well ZS 1 drilled in

the central uplift of the Tarim Basin [2], Cambrian carbon-ates have become an exploration target in the Tarim Basin.However, for the experiences of more than 100 million yearsof geological history, also multistage tectonic movements anddiagenetic transformations, a pattern of multiple media wasformed in Cambrian carbonate reservoirs, which cause theextremely high heterogeneity [3].

Previous studies of Cambrian carbonates in the Xiaoer-bulake Formation have mostly focused on the provenanceof the carbonates, their sedimentary characteristics, and poreformation [4]. For example, Li et al. [5] studied the origin anddevelopment of porosity. Bai et al. [6] investigated the

HindawiGeofluidsVolume 2021, Article ID 6667496, 20 pageshttps://doi.org/10.1155/2021/6667496

geological characteristics and major controlling factors ofplatform margin microbial reef reservoirs in the formation.However, less attention has been paid to the pore structure(both geometry and connectivity [7] of the carbonates),which is an essential part of reservoir characterizationincluding reservoir quality, hydrocarbon storage capabilitiesand transport properties.

The pore structure in carbonates is more complex andheterogeneous, compared with conventional reservoirs suchas sandstones, due to the diverse pore types caused by sedi-mentation and diagenesis [8–10]. Recent studies indicate thatthe Xiaoerbulake Formation is characterized by low porosity,low permeability, and strong heterogeneity [6, 11]. As aresult, a number of complementary methods are needed toevaluate and characterize the structure and connectivity ofpore networks at the microscale in these carbonate reservoirs.

In recent years, fractal theory has been widely used todescribe the irregularity and roughness of natural structures[12]. Pfeifer et al. [13] suggested that the microstructure ofrock pores is fractal. Krohn [14] proposed that in a certainpore size range, carbonate rocks, sandstone, and shale showtypical fractal characteristics, while Muller [15] first character-ized the multifractal behavior of pore spaces in sedimentaryrocks. And according to Xie et al. [16], the pore structure ofcarbonates is multifractal using the box-counting methodapplied to images from environmental scanning electronmicroscopy (ESEM). Therefore, the pore heterogeneity of car-bonate rocks can be defined by fractal dimensions [16], and asa result, the heterogeneity of pore structures was quantitativelyassessed in a single parameter.

The purpose of this research is to qualitatively and quanti-tatively characterize the micro- and nanoscale pore structureof carbonate reservoir carbonates from the Xiaoerbulake For-mation in the Tarim Basin, Northwest China, classify the porenetwork types of carbonate in the study area, and investigatethe connectivity for various pore network types. In this study,the pore structure of outcrop carbonate samples from theXiaoerbulake Formation was observed directly in photomi-crographs (optical microscopy and field emission-SEM), theporosity was measured by different methods including vac-uum saturation and routine core analysis, and the pore-throat size distributions were obtained by mercury intrusionporosimetry (MIP). Subsequently, the micro- and nanoscalepore network was classified into three types based on theanalysis of MIP data and curves. The fractal dimensions ofdifferent pore networks were derived from the MIP results.Moreover, the connectivity of pore networks was evaluatedby spontaneous imbibition and the relationships betweenpore structure (pore-throat diameter and tortuosity) andconnectivity have been investigated.

2. Geological Setting

The Tarim Basin is located in northwest part of China, cov-ering an area of about 560,000 km2, and is the largest basinwith hydrocarbon production in China. Keping uplift islocated in the northwest margin of the Tarim Basin, WushiCounty, Akesu Prefecture, with an area of nearly 20,000km2

(Figure 1). Keping uplift is a thrust belt formed by thrust nap-

ping since the Neogene and is divided into three areas (Akesu,Keping, and Xiker, from east to west) by two large strike slipfaults, Yingan fault and Pieqiang fault [17]. The study area ofKeping belongs to the secondary tectonic unit of the Kepingfault uplift and was situated in a passive continental marginenvironment during the Cambrian and Early Ordovician [5,18]. The Cambrian system in the Tarim Basin is made of tidalplatforms, platform-marginal marls, mudstones, carbonates,and evaporate rocks [19], which are well exposed continuouslyin the Keping area, and is easy to follow laterally. The Sugaite-bulake and Shihuiyao sections in the Keping area were selectedas the study areas, due to their relatively easy sampling condi-tions and because they have been used previously as typicaloutcrop sections in studies on the Cambrian dolomite reser-voirs of the northwestern Tarim Basin [5, 20].

The exposed Cambrian in the Keping area can be dividedinto three subsequences, namely, the Lower Cambrian Yuer-tusi, Xiaoerbulake, and Wusonger Formations (Figure 2); theMiddle Cambrian Shayike and Awatage Formations; and theUpper Cambrian Lower Qiulitage Formation. The YuertusiFormation is the oldest section, and it mainly consists of darkshale and siliceous shale, and these contain the dominantsource rock [21]. The overlying Wusonger Formation is theyoungest section in the Lower Cambrian and includes argilla-ceous dolomite, micritic, and fine-grained dolomite [17, 22].It forms the cap rock. The primary target of this study is theXiaoerbulake Formation, which can be divided into twomembers. The upper member is composed of light grayfine-grained dolomites, dolarenite, and microbial dolomiteswith a thickness of 90m. The lower member is more densethan the upper member and is composed of dark micriticdolomites with a thickness of 50m [5]. These members makeup the reservoir section.

3. Samples and Analyses

3.1. Samples. The field outcrop of the Xiaoerbulake Forma-tion is characterized by a darker overall color in the lowermember, which is mainly composed of dark gray-to-graythin-layer micrite-to-silty dolomite, and a lighter color in theupper member, mainly consisting of light gray thick-layermicrobial dolomite and residual granular dolomite. In thiswork, eighteen outcrop samples were collected from Sugaite-bulake (seven sample names starting with SGT) and Shihuiyao(eleven starting with SHY) sections (Table 1). It should benoted that there are no visible vugs and fractures in any ofthe outcrop samples.

Helium porosity and permeability were obtained by rou-tine core analyses on cored and plug-sized samples, with thediameter of 2.54 cm and the height of 4-6 cm. Impregnatedwith blue-dyed resin under vacuum conditions [23], thin sec-tions were prepared from these samples for microtexture andpore structure determination at submillimeter scales, andunder the polarizing microscope, the reservoir spaces wereobserved as blue color [24].

3.2. Mercury Intrusion Porosimetry (MIP) and Calculationof Pore Structure Properties. Pore structure includingpore-throat size distributions of carbonate samples was

2 Geofluids

characterized by the MIP technique. Samples were preparedas 1 cm3 cubes, and for removing the moisture in connectedpore spaces, cubic samples were drying in a 60°C oven formore than 48 hours, then left to cool at room temperature.The MIP analyses were carried out using the MicromeriticsAutoPore 9520. Mercury which has the molecular size of0.31 nm is nonwetting to most porous materials and has highinterfacial tension with air. When the intrusion pressure isincreasing, mercury is pressed into the connected pore net-works, and is controlled by the small pore throats of the sam-ples, and the pore radius can be calculated from theWashburn equation [25]:

Pc =2 × σ × cos θ

r, ð1Þ

where Pc is the mercury intrusion capillary pressure, r is poreradius, σ is the interfacial tension between mercury and air,and θ is the contact angle through the mercury phase. In thisstudy, the pressure range used was from 5psi (0.034MPa) to60000 psi (413MPa), connected pore spaces with pore-throatdiameters ranging from 2.8 nm to 50μm could be measured,and the published physical constant values used weresurface tension = 485mN/m and contact angle = 140° [26].

The permeability of a connected pore network can bederived from MIP data using the method of Thompson[26] and Katz [27]:

K =189

L3maxLt

∅SLmax, ð2Þ

5 km0

240 km0Study area

Shihuiyao

Akesu

Ayinker

Tarim Basin

Kuerla

Keping uplift

Keping area

Nanhuan Sinian Fault River

Tarim BasinChina

Beijing

AkesuGroup

LowerCambrian

MiddleCambrian

UpperCambrian

MiddleOrdovician

-LowerPermian

Highway Studysection

Sugaitebulake Village

Sugaitebulake Qiaoenbulake Village

Youermeinake Village

Qigebulake Village

Kelatieke Mount

WushiAkeya

Figure 1: Location of study area and sampling sections.

3Geofluids

in which k (μD) is absolute permeability, Lmax (μm) is thepore-throat diameter at which hydraulic conductance ismaximum, Lt (μm) is the characteristic length representingthe pore-throat diameter corresponding to the critical(threshold) pressure Pt (psia), ∅ is porosity, and SLmax

repre-sents the fraction of connected pore space composed of porediameter of size Lmax and larger.

FromMIP data, an important topological parameter, effec-tive tortuosity τ, can also be derived via Equation (3) [28, 29]:

τ =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ρ

24k 1 + ρV totð Þðη=rc ,max

η=rc ,minη2 f v ηð Þdη

s

, ð3Þ

where ρ is mercury density (g/cm3), V tot is total pore volume(mL/g), k is permeability (Darcy), and

Ð η=rc ,maxη=rc ,minη

2 f vðηÞdη is

the pore throat volume probability density function [7].Equation (4) relates the effective tortuosity τ to the effec-

tive diffusion coefficient and travel distance of mercury mol-ecules [30–32]:

τ =D0De

=1ϕ

LeL

� �2, ð4Þ

with Le/L is defined as the geometrical tortuosity[7].

Previous studies have confirmed that the pore structurecomplexity, which indicates the heterogeneity condition ofthe pore structure (e.g., pore-throat diameter, pore shape,and pore size distribution), can be quantitatively analyzedby fractal dimensions [1, 14, 33]. Several models have beenused to derive fractal dimensions from MIP data, such asthe tubular model, spherical model [34, 35], and the thermo-dynamic model reported by Zhang and Li [36]. In this work,the tubular model derived from MIP data was adopted toobtain the fractal dimensions of carbonate samples, becauseof negative results occurred by using the spherical modelwhich are irrational.

Based on the fractal geometry theory, if pore structure isfractal, it will satisfy a specific power-law function [12]:

N >rð Þ∝ r−Df , ð5Þ

where r is the pores radius (or characteristic length), Nð>rÞ isthe number of pore with radius larger than r, and Df is thefractal dimension.

When assuming a tubular model, pore networks of sam-ples are a bundle of tortuous capillary tubes [37]. Accordingto Li [38], the number of units required to fill the entire

Si

Si

Xiao

erbu

lake

Wus

ongg

er

Cap

rock

Rese

rvoi

r

Age Formation LithologyReservoir-source

assemblageDescription

Dominated by siliceous shaleand shale

Argillaceousdolomite Dolomite Microbial

dolomite Doloarenite

Granulardolomite Limestone

Si

Siliceous shale Shale

Argillaceousdolomiteinterbeddedwith micritedolomite

Characterizedby micritedolomite,granulardolomite andmicrobialdolomite

Sour

ce ro

ck

Yuer

tus

Low

er ca

mbr

ian

Figure 2: Stratigraphic column of the Lower Cambrian in the Keping area (modified after Wang et al. [22] and Jiang et al. [17]).

4 Geofluids

Table1:Porestructureprop

erties

from

routinecore

andMIP

tests.

Sampleno

.Medianpo

re-throat

diam

eter

(nm)

Volum

ea

Average

pore-throat

diam

eter

(nm)

4V/A

a

Effective

tortuo

sity

D0/De

Geometrical

tortuo

sity

L e/L

Porosity∗

(%)

Porosity#

(%)

Permeability∗

(mD)

10-100

nm>1

00nm

10-100

nm>1

00nm

SGT1-4-3

988

40.3

599

121.37

0.51

0.98

0.84

0.0545

SGT1-7-A

89.4

105

233

90.71

0.15

1.35

1.19

0.00233

SGT4-28-F

7967

37.1

5351

54.22

0.14

3.61

1.82

0.00505

SGT4-30-E

277

149

8323

2.21

1.20

5.16

2.78

0.0248

SGT5-47-A

2246

178

436

92.19

0.35

3.45

6.71

0.140

SGT6-49-A

66.3

63.1

589

83.05

0.77

0.49

2.30

0.00122

SGT6-56-2

12.0

12.6

1951

42.90

0.83

2.48

1.85

0.463

SHY1-002-3

456

34.1

989

82.07

0.50

1.24

2.08

0.00135

SHY1-008-2

304

14.5

167

471.46

0.78

2.04

1.52

1.14

SHY1-011-2

92.7

78.6

365

151.27

0.37

0.71

3.23

0.0758

SHY1-018-1

529

84.3

814

92.42

0.45

1.09

2.90

0.00448

SHY3-030-3

4143

403

433

101.54

0.23

2.37

1.83

0.00341

SHY3-041-3

3712

719

489

61.46

0.17

1.83

1.27

0.296

SHY3-098

2644

181

1427

82.55

0.23

2.13

2.63

0.0649

SHY4-091-D

87.3

82.2

167

221.61

0.70

2.06

3.02

0.00333

SHY5-107-3

22.1

120

167

92.22

0.57

1.06

2.79

0.0998

SHY5-108-D

221

205

234

371.92

0.77

1.07

1.50

0.0154

SHY6-133-1

486

234

233

191.57

0.45

2.44

2.55

0.00545

Avg

±stn

ddev

1352

±2107

152±

171

818±

1231

15±12

2:04

±0:81

0:51

±0:29

1:98

±1:18

2:38

±1:29

0:133±0:279

a Whenpo

re-throatd

iameter

correspo

ndsto

50%of

totalcum

ulativeintrusionvolume(byvolume);V

=totalporev

olum

e;A=surfa

cearea.∗Porosityandperm

eabilityobtained

from

gas(helium)measurements.

# Porosityobtained

from

vacuum

saturation

(DIwater).

5Geofluids

capillary tube NðrÞ can be calculated by the cumulative vol-ume of mercury intrusion VHgðrÞ, which can be expressed by

N rð Þ = VHg rð Þπr2l

, ð6Þ

where l is the length of a capillary tube. Then substitutingEquation (6) into Equation (4) yields

VHg rð Þπr2l

∝ r−Df : ð7Þ

As the length of capillary tube is a constant, thus, Equa-tion (7) is simply expressed as

VHg rð Þ∝ r2−Df , ð8Þ

and VHg can be substituted by the mercury saturation SHg;moreover, according to Equation (1), pore radius r could beassociated with capillary pressure Pc; thus, the followingequation can be obtained:

SHg rð Þ∝ Pc− 2−Dfð Þ: ð9Þ

As revealed by Equation (9), the value of fractal dimen-sion Df can be obtained from the slope of the linear regres-sion of log SHg versus log Pc in a log-log plot.

3.3. Field Emission-Scanning Electron Microscopy (FE-SEM).The FE-SEM imaging method provides information aboutthe morphology of micro- to nanoscale pores and throats inthe samples. Both backscattered electron (BSE) and second-ary electron (SE) modes were used to observe cross-sectionsof six representative carbonate samples at magnificationscales from 200 to 20000. Before imaging with FE-SEM (ZeissMerlin Compact), the sample was firstly cut at right angles tothe bedding plane. To obtain an extremely flat plane for bet-ter observation, fine grinding was carried out using a LeicaEM TXP with a sequence of 9μm, 2μm, and 0.5μm abrasivepapers and finally ion milled by Ion Beam Milling System(Leica EM TIC 3X) for two hours [39]. During the millingprocess, two accelerating voltages of 5.5 kV and 2.0 kV wereselected alternately for 4 rounds of milling [40]. The edgeof each sample was coated with a conductive carbon adhesiveto improve electrical conductivity.

3.4. Vacuum Saturation. The open porosity of carbonatescore samples was obtained by vacuum saturation of DI water.The first sample chamber was vacuumed to 0.05Torr(1 Torr = 1mmHg = 133:3 Pa), equivalent to a 99.993% vac-uum [41] and keeping this pressure for 6 h. Then, a saturat-ing fluid (DI water) was injected into the vacuumedchamber under the pressure of 10-15MPa, until the samplewas immersed, and the fluid would occupy the evacuatedopen porosity. After 12h, the sample was removed from thechamber and the open porosity could be obtained by thechanges of samples weight.

3.5. Contact Angle Measurement. The contact angle refers tothe angle between the liquid-solid interface and the solid-liquid interface when the tangent line of the gas-liquid inter-face is made at the intersection of the three phases. The mea-surement of contact angle is a quick and quantitativetechnology to evaluate the wettability of rock, which has clearmechanical and thermodynamic properties [42]. In thisstudy, the contact angle between deionized (DI) water andcarbonate samples was measured by using a droplet of 2μLfluid on a flat surface (polished with 200 grit sandpaper) ofa 1 cm × 1 cm sample piece and a contact angle meter andan interface tensiometer (Model SL200KB, USA Kino Indus-try Co.), and the wettability was quantitatively evaluated. Inorder to obtain correct contact angle, the focus should beadjusted to make the clear image of the injection needle dur-ing the measurement process, and the needle should bemoved to the center of the view field through the fine-tuning knob. When the liquid drops on the sample, capturethe shape picture of the liquid drop, select the measurementreference line, and then identify the outline of the liquid dropto directly measure the contact angle. The measurementmethod used in this study is circular fitting, and the accuracyof the measurement result is ±1°.

3.6. Spontaneous Imbibition. Spontaneous fluid imbibitiontests were carried out on six representative carbonate sam-ples, and distilled (DI) water was used as the displacementfluid to replace the air in the pore space. For the purpose ofminimizing the effect of vapor absorption, four sides of eachcubic sample were coated with quick-cure epoxy before thetest. The top and bottom surfaces were left untreated, soimbibition could take place. The same with the MIP tests,the samples were drying in a 60°C oven for 48 hours andcooled to 23°C (room temperature). The experimental proce-dure of imbibition tests, as well as the data processing, hasbeen described in detail by Hu et al. [43]. In brief, for theimbibition test, the bottom surface of the cubic sample wassubmerged in DI water to a depth of about 1mm. Severalbeakers of water were placed inside the test chamber to main-tain the environment with high and constant relative humid-ity [44, 45]. The imbibed mass of DI water over time wasrecorded by a high-precision microbalance with a readabilityof 0.01mg (Shimazu, Model AUW220WD) connected to acomputer for periodic recording of the balance weights.

4. Results and Discussion

4.1. Petrography of Carbonate Samples and Reservoir Quality.The original characteristics of the pores in the XiaoerbulakeFormation have almost been completely destroyed due toits deep burial and multistage diagenetic modifications, andthe reservoir pore space is now mainly composed of compos-ite genetic pores (secondary transformed primary pores) andsecondary pores and fractures [17]. From directly observa-tions of outcrop samples and thin sections, we found thatthe samples in this study are mainly fine-medium grainedcrystalline dolomites (Figure 3(a)) and micritic dolomites(Figure 3(d)); in addition, dolarenite (Figure 3(b)) and micro-bial dolomites (Figure 3(c)) are occasionally observed. Two

6 Geofluids

dolomite textures are also observed in these samples, namely,matrix dolomites and dolomite cements (Figure 3(i)) [21].Using the porosity type classification of Choquette and Lloyd[46] and the sample observation of thin sections by opticalmicroscope and FE-SEM images, the pore systems of theXiaoerbulake Formation samples are dominated by threetypes of pores, ranging in size from nanometers to microns:intergranular pores, intragranular pores, and intercrystallinepores (Figures 3(g)–3(i) and 4); also micro- and nanoscalefractures are observed (Figures 5 and 6). Additionally, two ormore pore types could be observed in adjacent areas, which

indicate the different types of pores are developed togetherin the Xiaoerbulake Formation carbonates.

Typical FE-SEM images of carbonate samples fromXiaoerbulake Formation are presented in Figure 4. Itshows the presence of intergranular pores in Figures 4(a)and 4(b), intercrystalline pores in Figures 4(c) and 4(d),and intragranular pores in Figures 4(e) and 4(f). Inter-granular pores in samples are heterogeneous and irregularwith pore sizes > 10 μm (Figures 4(a) and 4(b)). The poresize distribution of intercrystalline pores ranges from100 nm to 10μm (Figures 4(c) and 4(d)). Intragranular pores

500 𝜇m

(a)

500 𝜇m

(b)

500 𝜇m

(c)

500 𝜇m

(d)

500 𝜇m

(e)

500 𝜇m

(f)

500 𝜇m

(g)

500 𝜇m

(h)

500 𝜇m

(i)

Figure 3: Thin sections of outcrop samples from different sections of the Xiaoerbulake Formation, Tarim Basin; observed by opticalmicroscopy under a polarized light: (a) fine-medium grained dolomite, no evidence of pores, SHY 5-107-3; (b) doloarenite, fine-graineddolomite cementing the space between grains, SGT 6-56-2; (c) microbial dolomite (spongy layered dolomite), multigeneration, andmultistage dolomite filling the dissolution pores, SHY 6-133-1; (d) micritic dolomite, bitumen filling some dissolution pores, SGT 4-30-E;(e) micritic dolomite, calcite filling the microfracture, SHY 3-041-3; (f) fine grained dolomite, few fabric dissolution pores filled bybitumen, SHY 3-041-3; (g) fine-medium grained dolomite, intragranular pores and microfractures (red arrows) in the grain, intergranularpores in the matrix dolomite (yellow arrow), SGT 5-47-A; (h) intergranular pores in the dissolved dolomite (yellow arrow) andintercrystalline pores (green arrow), SHY 4-091-D; (i) intercrystalline dissolution pores (green arrow) in the filling dolomite, SHY 5-108-3.

7Geofluids

are mostly circular, linear, and angular (Figures 4(e) and 4(f)), and the pore shapes of the well-developed intragranulardissolution pores vary from nearly circular to irregular(Figures 4(g)–4(i)). Generally, the pore size distribution ofintragranular and dissolution pores ranges from 10nm to1μm. Microfractures with apertures ranging from nm- toμm-scale are developed in several samples, but they are filledwith various types of cements including dolomite, quartz,and calcite (Figure 3(e)). The various pore types and micro-lithologies in our samples give rise to variable and heteroge-neous pore systems, and these will be described in Section4.3.

4.2. Porosity Obtained by Different Methods. The heliumporosity and permeability results of outcrop samples indicaterelatively poor reservoir quality of the Xiaoerbulake Forma-tion. The porosity is in the range of 0.49%–5.16%, with anaverage of 1.98%, and the permeability is from 0.001mD to1.140mD, and the average permeability is 0.133mD.

The open porosity of outcrop samples was measuredby vacuum saturation (DI water), and the results are listed

in Table 1. Generally, the vacuum saturation porosity islower than gas porosity considering the unconnectedpores. However, the average vacuum saturation porosityof samples is 2.38%, which is higher than the averagegas porosity (1.98%). The wettability of samples hasimpact on the vacuum saturation porosity results. Thecontact angle measurements of these samples with DI watershow 47 degrees on average (from 34 to 82 degrees, Figure 7),indicative of their water-wet nature (in the air). Thus, the sat-uration porosity could be overestimated. In addition, the wellsdrilled in Xiaoerbulake Formation are mainly producing gas;we believe the gas porosity results of study samples are morereliable.

4.3. Pore Structure Characterization. Through the MIP testsand data analysis, the pore structure and pore size distribu-tions of 18 carbonate samples were investigated. As shownin Table 1, both nm- and μm-sized pores are developed inthe carbonate samples, with the median pore-throat diame-ters ranging from 12nm to 7967 nm, which indicates a widespectrum of pore-throat sizes. On average, pores with throat

InterG pore10 𝜇m

(a)

InterG pore

20 𝜇m

(b)

InterC pore

20 𝜇m

(c)

InterC pore

20 𝜇m

(d)

IntraG pore

200 nm

(e)

IntraG pore

200 nm

(f)

IntraG dissolution pore1 𝜇m

(g)

IntraG dissolution pore

2 𝜇m

(h)

IntraG dissolution pore

1 𝜇m

(i)

Figure 4: Typical FE-SEM images of pores in dolomites from the Xiaoerbulake Formation: (a) intergranular pores (SE mode); (b)intergranular pores (BSE mode); (c, d) intercrystalline pores (BSE mode); (e, f) intragranular pores (SE mode); (g–i) intragranulardissolution pores (SE mode).

8 Geofluids

sizes of >10μm account for 18.2% of the total pore volume,throat sizes of 1-10μm for 25.1%, throat sizes of 0.1-1μmfor 28.4%, and throat sizes of 10-100 nm for 27.9%(Table 2). Carbonate samples have different pore-throat sizedistributions in μm-nm ranges, and as we referred above, thepore systems of these samples are various.

As described in the study of Gao and Hu [47], the critical(threshold) pressure Pt of each of multiple connected porenetworks can be obtained from the inflection point, the max-imal location between the difference of intrusion volume wasdivided by the difference of logarithmical pore-throat diame-ter for two neighboring data points [48], and the values ofLmax and permeability can then be obtained.

Inflection points can be observed from the plot of logdifferential intrusion vs. intrusion pressure (numbered onthe Figures 8(a), 8(c), and 8(e)), which indicates differentconnected pore networks [48]. In general, four inflectionpoints are observed in μm- and nm-scales for all carbon-ate samples, which suggests four connected pore networks.The average corresponding critical pore-throat diameter ofthe 1st to 4th inflection points is 22.8μm, 5.39μm,0.500μm, and 50.5 nm, from the pore networks locatedat the intervals of 10μm–45μm, 1–10μm, 0.1–1μm, and10–100 nm, respectively (Table 1). Based on inflectionpoints and pore-throat size distributions, the pore systemsof carbonate samples can be divided into three types

(Table 2). For samples belonging to Type I, the pore net-works are dominated by pore diameters at the nm-scale(10 nm < pore‐throat diameter < 1 μm) with an averagemedian pore-throat diameter of 180 nm, and the poresare dominated by intragranular (dissolution) pores.Figures 8(a) and 8(b) show plots of incremental intrusionand pore volume percentage distribution from MIP of atypical Type I sample (SGT 4-30-E). This sample has agas porosity of 5.16% and a median pore-throat diameterof 277 nm, with nearly 95% of the pore-throat sizeslocated in the 100 nm to 1μm range. This result alsoexplains why there are no evident pores in the thin sectionof this sample (Figure 9(a)), but the porosity is relativelyhigh, which could be due to nm-size intragranular poresobservable by FE-SEM (Figures 9(b)–9(d)).

Type II samples have a pore system dominated by bothμm-scale (pore‐throat diameter > 1 μm) and nm-scale(10 nm < pore‐throat diameter < 1 μm) pore diameter net-works, with an average median pore-throat diameter of341 nm, and the pore system is a mix of different pore types.As shown in Figures 8(c) and 8(d), the gas porosity of theType II sample (SGT 6-49-A) is mainly composed of poreswith pore-throat diameters of >1μm and 10nm-100nm,with the proportion of about 40% and 50% of the total porevolume, respectively. The porosity of this sample is 0.49%with the median pore-throat diameter of 66.3 nm (Table 1).

500 𝜇m

Sample No.17

Microfracture

SHY 3-030-3

Microfracture

500 𝜇m

SHY 3-041-3

Microfracture

500 𝜇m

Figure 5: Observed microfractures by optical microscopy from thin sections under a polarized light.

IntraG dissolution pore

Microfracture

InterG pore IntraG dissolution pore

4 𝜇m

InterG pore

IntraG pore

4 𝜇m

Figure 6: FE-SEM photomicrographs (SE mode) for sample SHY 1-002-3: intergranular pores and intragranular (dissolution) pores aredeveloped and connected by fractures at micro- and nanoscale.

9Geofluids

The photomicrographs also illustrate the mixed pore system.From the thin section of this Type II sample, some intergran-ular pores and intercrystalline pores ranging from 5μm to50μm are observed (Figure 9(e)), and intragranular and dis-solution pores in the range from 10nm to 100nm are found(Figures 9(f)–9(h)).

Type III samples have pore systems dominated by μm-scale pore networks, with pore-throat diameters > 1 μm andan average median pore-throat diameter of 4.14μm; the pore

types are dominated by intergranular and intercrystallinepores. Plots of incremental intrusion and pore volume per-centage distribution of the typical Type III sample (SGT5-47-A) are shown in Figures 8(e) and 8(f); pores withpore-throat diameters of >1μm account for nearly 70% ofthe total pore volume. The observations of the thin sectionand FE-SEM are consistent with the MIP results. Intragra-nular (dissolution) pores with pore-throat diameters < 1 μmrarely are found, while the intergranular pores ranging

CA_L = 54.048° CA_R = 54.048° CA_AV = 54.048°

SGT 4-30-EContact angle: 54°

(a)

CA_L = 33.927° CA_R = 33.927° CA_AV = 33.927°

SGT 5-47-AContact angle: 34°

(b)

CA_L = 34.157° CA_R = 34.157° CA_AV = 34.157°

SGT 6-49-AContact angle: 34°

(c)

CA_L = 67.292° CA_R = 67.292° CA_AV = 67.292°

SGT 6-56-2Contact angle: 67°

(d)

CA_L = 81.804° CA_R = 81.804° CA_AV = 81.804°

SHY 1-002-3Contact angle: 82°

(e)

CA_L = 68.770° CA_R = 68.770° CA_AV = 68.770°

SHY 3-098Contact angle: 69°

(f)

Figure 7: Contact angle (in degrees) measurements (at 30 s after droplet contact).

10 Geofluids

from 10μm to 50μm and intercrystalline pores ranging from1μm to 10μm are more frequently observed (Figures 9(i)and 9(j)).

4.3. Permeability of Multiple Connected Pore Networks.According to Equation (2) and inflection points and thresholdpressures from MIP data, the permeability of each con-nected pore network with pore-throats covering differentranges (micro- to nanoscale) can be obtained. Table 3 dis-plays the calculated permeability values for four pore diameterranges for carbonate samples, the corresponding thresholdpressures, and the critical pore-throat diameters. The valuesof calculated permeability and corresponding critical pore-throat diameter decrease over several orders of magnitudewith increasing threshold pressure. The calculated permeabil-ity of pore networks with pore-throat diameters > 10μm is inthe range of 0.14–12.5mD, which is comparable to the air per-meability of carbonates dominated by intergranular pores (inthe range of 0.002–11.0mD) [17, 49]. In addition, the calcu-lated permeability of pore networks with pore-throat diame-ters of 1μm to 10μm is in the range of 0.034–1.14mD,which is in line with the air permeability of carbonates domi-nated by intercrystalline pores [17, 49]. While pore throatdiameters of 0.1–1μm and 10–100nm have relatively low cal-culated permeability ranging from 0.0003mD to 0.0507mDand 10-5mD to 0.00317mD, respectively. These results aresimilar to the permeability (0.001-0.008mD) of carbonates

dominated by intragranular and dissolution pores on thenm-scale [17, 49].

These results suggest that μm-scale pore networks domi-nated by interganular or intercrystalline pores can providesignificant permeability, which may in turn make a contribu-tion to the ability of oil to move, or migrate, within carbonatereservoirs.

In this work, the permeability contribution values of mul-tiple pore networks were obtained by the equation proposedby Purcell [50]:

ΔKci =ΔKmi

∑ni=1ΔKmi

,

ΔKmi =12

1P2ci

+1

P2ci+1

� �

ΔSi+1,ð10Þ

where ΔKci is the permeability contribution value of porenetwork with different ranges of pore-throat diameters, i rep-resents the interval number of pore network, ΔSi+1 is thecumulative volume of intruded mercury at different intervals,and Pci is the capillary pressure at different intervals. Theintervals were obtained by the inflection points shown inFigure 8, and the Pci is equal to the threshold pressure.

The distributions of pore volume and corresponding per-meability contributions were calculated and are shown inTable 2. It shows that even though pore-throat diameter >

Table 2: Total pore volume and permeability contribution of the four pore networks to each sample.

Pore networktype

SamplePore volume

(%)ΔKc1(%)

Pore volume(%)

ΔKc2(%)

Pore volume(%)

ΔKc3(%)

Pore volume(%)

ΔKc4(%)

>10 μm 1 μm-10 μm 0.1 μm-1μm 10nm-100 nm

II SGT 1-4-3 6.3 87.4 29.5 12.51 14.5 0.060 49.8 0.0003

II SGT 1-7-A 9.0 92.9 28.1 6.53 21.3 0.617 41.5 0.0020

III SGT 4-28-F 50.9 97.5 29.3 2.44 7.6 0.022 4.3 0.0000

I SGT 4-30-E 2.0 16.8 2.6 82.87 85 0.353 10.3 0.0060

III SGT 5-47-A 35.2 96.1 24.5 3.39 21.9 0.475 18.5 0.0010

II SGT 6-49-A 23.4 96.0 15.0 3.97 9.3 0.020 52.3 0.0005

I SGT 6-56-2 17.9 97.5 7.9 2.57 2.2 0.034 72.1 0.0004

II SHY 1-002-3 11.7 90.9 34.7 9.06 9.6 0.035 44.0 0.0001

I SHY 1-008-2 9.0 96.0 24.7 4.01 43.7 0.015 22.6 0.0020

II SHY 1-011-2 17.0 96.7 20.5 3.00 16.9 0.279 45.6 0.0010

II SHY 1-018-1 15.8 88.1 29.2 11.79 23.5 0.067 31.4 0.0001

III SHY 3-030-3 32.6 93.6 41.8 6.41 20.1 0.000 5.5 0.0000

III SHY 3-041-3 36.2 88.2 44.3 11.81 17.5 0.005 2.0 0.0000

III SHY 3-098 36.7 95.0 29.4 4.94 17.9 0.049 16.0 0.0000

I SHY 4-091-D 3.9 93.6 22.4 5.81 27.6 0.580 46.1 0.0160

II SHY 5-107-3 2.9 71.2 32.6 25.77 35.8 3.000 28.7 0.0040

I SHY 5-108-D 5.9 78.4 10.3 21.69 79.2 0.014 4.6 0.0000

II SHY 6-133-1 10.7 87.1 25.7 12.47 57.3 0.388 6.3 0.0010

Average 18.2 86.8 25.1 12.84 28.4 0.334 27.9 0.0019

ΔK : the permeability contribution of each pore network.

11Geofluids

10 μmmakes up only 18.2% on average of total pore volume,their average contribution to the permeability is 86.8%, sug-gesting that for carbonates from Xiaoerbulake Formation,the pore networks with pore-throat diameter > 10 μm are

the main reservoir permeability channel. Therefore, the rela-tively highly interconnected intercrystalline pores and inter-granular pores are the main contributors to the overallpermeability. On the other hand, the proportion of nanoscale

101 100 1000Intrusion pressure (psia)

Log

diffe

rent

ial i

ntru

sion

(mm

3 /g)

100000

10 InterGLt = 24.691 𝜇mk = 3.834 md

InterCLt = 8.218 𝜇mk = 0.3479 md

InterG (dissolved)Lt = 0.449 𝜇mk = 3.448 × 10−2 md

InterG (dissolved)Lt = 0.122 𝜇mk = 3.166 × 10−3 md

20

30

40100 𝜇m 10 𝜇m 1 𝜇m 100 nm 10 nm

3

4

1 2

(a)

Pore-throat diameter (𝜇m)

Pore

vol

ume d

istrib

utio

n (%

)

Pore

vol

ume (

mm

3 /g)

00.0028−0.005 0.005−0.01 0.01−0.05 0.05−0.1 0.1−1 1−10 10−50

0

20

40

60

80

5

10

15

20

(b)

101 100 1000Intrusion pressure (psia)

Log

diffe

rent

ial i

ntru

sion

(mm

3 /g)

100000

3

InterGLt = 24.691 𝜇mk = 6.206 md

InterCLt = 6.380 𝜇mk = 1.137 md

InterG (dissolved)Lt = 0.273 𝜇mk = 2.417 × 10−3md

6

9100 𝜇m 10 𝜇m 1 𝜇m 100 nm 10 nm

3

4

1

2

InterG (dissolved)Lt = 0.0469 𝜇mk = 1.315 × 10−4 md

(c)

Pore-throat diameter (𝜇m)

Pore

vol

ume d

istrib

utio

n (%

)

Pore

vol

ume (

mm

3 /g)

00.0028−0.005 0.005−0.01 0.01−0.05 0.05−0.1 0.1−1 1−10 10−50

0

6

12

18

24

30

0.3

0.9

0.6

1.5

1.2

(d)

101 100 1000

Intrusion pressure (psia)

Log

diffe

rent

ial i

ntru

sion

(mm

3 /g)

100000

1.2

0.6

InterGLt = 41.164 𝜇mk = 12.48 md

InterG (dissolved)Lt = 0.886 𝜇mk = 9.912 × 10−3md InterG (dissolved)

Lt = 0.0315 𝜇mk = 2.433 × 10−5 md

2.4

1.8

3.0100 𝜇m 10 𝜇m 1 𝜇m 100 nm 10 nm

3

4

1

InterCLt = 8.502 𝜇mk = 0.487 md

2

(e)

Pore-throat diameter (𝜇m)

Pore

vol

ume d

istrib

utio

n (%

)

Pore

vol

ume (

mm

3 /g)

0.000.0028−0.005 0.005−0.01 0.01−0.05 0.05−0.1 0.1−1 1−10 10−50

0

7

14

21

28

35

0.30

0.15

0.60

0.45

(f)

Figure 8: Three typical samples with different types of PSD ((a, b) SGT 4-30-E, Type I; (c, d) SGT 6-49-A, Type II: (e, f) SHY 3-098, Type III)(see Section 4.2 and Table 2 for description of the “Types”). (a), (c) and (e): log differential intrusion vs. intrusion pressure, with eachinflection point corresponding to a connected pore network. (b), (d) and (f): volume and percentage of different intervals of pore-throat sizes.

12 Geofluids

pores is 56.7%, which becomes the main reservoir storagespace, even though its contribution to permeability is limited.The poor connectivity of the pore networks at the nanoscalemay explain the phenomenon of high porosity with low per-meability, which is in keeping with the observation results ofthe FE-SEM (Figures 4(e) and 4(f)). It can be concluded thatthe permeability is mainly controlled by a small number ofμm-size pores for most of the samples.

4.4. Fractal Dimension of Pore Networks. The curve of mer-cury saturation vs. the capillary pressure can be used todetermine whether samples conform to the fractal charac-teristics. If it is a straight line on a log-log plot, the porestructure can be characterized by fractal dimensions [51].However, the statistical results of studied samples showthat there is no linear relationship between log mercuryinjection capillary pressure and log mercury saturation.Considering the multiple connected pore networks in car-bonate samples discussed before, we divide the fractaldimensions into a four-segment pattern basing on theinflection points, and good linear relationships are found,respectively, for each pore network (Figure 10). This find-ing indicates the heterogeneity and complexity of the poresurfaces and distribution within different pore-size rangesand pore types.

According to Equation (8), fractal dimensions of mul-tiple pore networks can be calculated from the slope ofeach fitted line (Figure 10). The calculated fractal dimen-sions of multiple pore networks are expressed as Dt1, Dt2

, Dt3, and Dt4, respectively. Generally, the correlation coef-ficient of each segment is higher than 0.9, which is good(Table 4). Because each segment was decided by an inflec-tion point (with corresponding characteristic length andthreshold pressure), the fractal dimension of each segmentcan be correlated loosely to the pore networks located atthe intervals of >10μm, 1-10μm, 0.1-1μm, and 0.01-0.1μm, respectively. The results suggest that the values offractal dimension for the pores with larger pore-throatdiameters are greater than those of pores with smallerpore-throat diameters. It may indicate that the larger poreshave more complex structure (such as rough surface andirregular size), whereas the pore networks with smallerpore-throat diameters are relatively homogenous. The pho-tomicrographs (Figures 4 and 9) show comparable results:the intragranular pores are mostly circular, linear, andangular, while the intergranular pores and intercrystallinepores are more heterogeneous and irregular.

However, fractal dimensions greater than three arefound in a few samples (SGT 1-7-1, SHY 3-030-3, andSHY 3-041-3). According to fractal theory, the fractaldimensions should be less than the physical dimensionof three. The invalid value may be due to the oversimpli-fication of the assumption that micro-scale pores are cylin-drical. Song et al. reported a similar result (>3) which maybe related to the existence of microfractures with the morecomplex and rough structure in the sample [52]. From thethin section images, microfractures are actually developedin the three samples with D1 > 3 (Figure 5). Furthermore,

Type I:SGT 4-30-E

Type II:SGT 6-49-A

Type III:SHY 3-098

500 𝜇m 2 𝜇m 1 𝜇m 1 𝜇m

500 𝜇m 10 𝜇m 1 𝜇m 1 𝜇m

500 𝜇m 20 𝜇m 10 𝜇m 1 𝜇m

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

Figure 9: Photomicrographs of typical samples from Type I, Type II, and Type III ((a), (e), and (i) obtained from optical microscopy; theothers from FE-SEM); red arrows: intragranular (dissolution) pores; green arrows: intercrystalline pores; yellow arrows: intergranular pores.

13Geofluids

Table3:Porenetworkdiam

eter

ranges

andassociated

parametersfrom

MIP

tests.

Sample

Pt(M

Pa)

L t1(μm)

Calculated

perm

eability(m

D)

Pt(M

Pa)

L t2(μm)

Calculated

perm

eability(m

D)

Pt(M

Pa)

L t3(μm)

Calculated

perm

eability(m

D)

Pt(M

Pa)

L t4(μm)

Calculated

perm

eability(m

D)

>10μm

1μm–10μm

0.1μm–1

μm

10nm

–100

nm

SGT1-4-3

0.117

12.8

0.14

0.406

3.68

0.092

6.89

0.217

0.0006

68.9

0.021

0.00001

SGT1-7-A

0.069

21.9

0.32

0.271

5.54

0.092

1.37

1.100

0.0071

20.7

0.071

0.00007

SGT4-28-F

0.083

18.2

2.50

0.406

3.68

0.191

2.75

0.547

0.0046

68.9

0.021

0.00001

SGT4-30-E

0.069

24.7

3.83

0.207

8.22

0.348

3.78

0.449

0.0345

14.4

0.123

0.00317

SGT5-47-A

0.138

10.9

3.83

0.548

2.76

0.324

2.20

0.684

0.0170

26.2

0.056

0.00019

SGT6-49-A

0.069

24.7

6.21

0.270

6.39

1.137

6.20

0.273

0.0024

35.1

0.047

0.00013

SGT6-56-2

0.069

21.9

1.37

0.241

6.35

0.377

2.47

0.607

0.0017

68.9

0.021

0.00000

SHY1-002-3

0.055

27.4

1.62

0.239

6.35

0.219

3.43

0.437

0.0023

68.9

0.021

0.00001

SHY1-008-2

0.165

9.2

0.89

1.235

1.22

0.034

14.47

0.102

0.0004

24.8

0.059

0.00034

SHY1-011-2

0.138

10.9

0.61

0.615

2.45

0.054

4.13

0.363

0.0008

35.1

0.041

0.00005

SHY1-018-1

0.048

31.3

4.30

0.207

7.28

0.862

2.75

0.547

0.0089

48.2

0.030

0.00004

SHY3-030-3

0.055

27.4

3.18

0.238

6.35

0.775

14.46

0.102

0.0003

30.3

0.048

0.00012

SHY3-041-3

0.048

31.3

2.52

0.165

9.20

0.891

3.44

0.437

0.0040

35.1

0.041

0.00009

SHY3-098

0.041

41.2

12.48

0.200

8.50

0.487

1.92

0.886

0.0099

51.6

0.032

0.00002

SHY4-091-D

0.179

8.4

0.72

0.955

1.58

0.057

4.13

0.363

0.0048

23.4

0.063

0.00034

SHY5-107-3

0.200

7.5

0.54

0.407

3.68

0.824

1.93

0.783

0.0507

26.2

0.056

0.00062

SHY5-108-D

0.041

39.9

2.19

0.231

6.35

0.375

6.89

0.217

0.0049

26.2

0.056

0.00029

SHY6-133-1

0.041

39.9

4.55

0.200

7.49

0.526

1.72

0.879

0.0190

14.5

0.102

0.00060

Average

0.090

22.8

2.88

0.391

5.39

0.426

4.72

0.500

0.0097

38.2

0.051

0.00034

L t:the

characteristiclength

isthepo

re-throatdiam

eter

correspo

ndingto

thecritical(thresho

ld)pressure

Pt.

14 Geofluids

Liu et al. suggested the upper value 3 indicates a totallyirregular or rough surface [53]. Thus, the values between3 and 4 obtained in this study are considered the resultof microfractures and physically reasonable.

4.5. Connectivity of Pore Networks. Spontaneous imbibitionis the invasion of wetting fluid into a porous medium bycapillary forces [54, 55]. For unconventional reservoirs,spontaneous imbibition is the primary mechanism respon-sible for enhanced oil production and an effective oilrecovery method [56–58]. Previous studies have concludedthat the spontaneous imbibition process is primarily con-trolled by the pore structure of the porous media, as wellas the physical properties of fluids and interactions

between them [55, 57]. Thus, the pore structure and thehydrocarbon production behavior can be better under-stood by studying the spontaneous imbibition process.Handy [59] proposed that plotting cumulative imbibitionheight against imbibition time on a log-log scale wouldin theory give a slope of 1/2 for porous media with well-connected pore networks [60]. However, a 1/2 slope isnot always obtained for natural rocks. Based on the perco-lation theory [61, 62], a lower slope value (<1/2) may sug-gest poorer pore connectivity [60, 63]. Hu et al. [63]observed a 1/2 slope for Berea sandstone indicative of awell-connected pore space and an imbibition slope of 1/4for well-cemented Indiana sandstone of low pore connec-tivity. According to Hu et al. [63] and Yang et al. [64],

0.0

0.5

1.0Lg S

Hg

1.5

2.0

−1.0−1.5 −0.5 0.0 0.5 1.0 1.5 2.0

Lg PcSHY 1-018-1

Dt1 = 2.70, R2 = 0.90Dt2 = 2.40, R2 = 0.98

Dt3 = 2.14, R2 = 0.97Dt4 = 2.29, R2 = 0.96

1.0

1.5Lg S

Hg

2.0

−1.0 −0.5 0.0 0.5 1.0 1.5 2.0

Lg PcSHY 1-011-2

Dt1 = 2.47, R2 = 0.96Dt2 = 2.13, R2 = 0.94

Dt3 = 2.35, R2 = 0.91Dt4 = 2.23, R2 = 0.92

1.0

Lg S

Hg

1.5

2.0

−1.0−1.5 −0.5 0.0 0.5 1.0 1.5 2.0

Lg PcSGT 6-49-A

Dt1 = 2.81, R2 = 0.92Dt2 = 2.11, R2 = 0.94

Dt3 = 2.30, R2 = 0.84Dt4 = 2.41, R2 = 0.98

0.0

0.5

1.0Lg S

Hg

1.5

2.0

−1.0 −0.5 0.0 0.5 1.0 1.5 2.0

Lg PcSHY 4-30-E

Dt1 = 2.34, R2 = 0.99Dt2 = 2.78, R2 = 0.73

Dt3 = 2.62, R2 = 0.92Dt4 = 2.06, R2 = 0.96

Figure 10: Fractal dimension calculation with a tubular pore model (D = 2 + slope) using four-straight-line fitting.

15Geofluids

the imbibition rate can be indicated by the slope of thestraight lines, and afterward, the connectivity of pore net-works could be qualitatively assessed by it.

Spontaneous imbibition tests using DI water were con-ducted on six representative samples. The plots of DI waterimbibition behavior are shown in Figure 11. The imbibitioncurves are generally composed of two stages: rapid increasingstage at the beginning and stably increasing stage. At thebeginning of the test (1-2 minutes), with increasing imbibi-tion time, the log cumulative imbibition increases rapidlyand some fluctuations may occur (e.g., Figure 11(d)), whichmay be caused by unstable sample and the boundary effects.After that, the log cumulative imbibition increases stably andlinear relationships which have different slopes can beobserved. When the sample is saturated with imbibitionfluid, the straight line paralleled to the x-axis will appear(the green line, Figure 11(c)). Except for sample SGT 6-56-2 and SHY 1-002-3 (Figures 11(e) and 11(f)), only one slopeis evident in the stably increasing stage for three other sam-ples (the blue line). These results are at first sight in contrastwith the MIP results; namely, that there are different con-nected pore networks in all six samples.

A second stable slope is observed after a long time periodof imbibition in the curves of samples SGT 6-56-2 and SHY1-002-3 (the green line in Figures 11(e) and 11(f)). Basedon the FE-SEM images, micro- to nanoscale fractures wereobserved in these two samples. As shown in Figure 6, frac-tures at nm-scales are developed in sample SHY 1-002-3which connect the intragranular (dissolution) pores andintergranular pores. Moreover, dissolution pores associated

with the fractures are observed. From the fractal dimensionof these six samples (Table 4), it can be found that the fractaldimension values of pores ranging in 10 nm-100 nm (D4) ofsamples SGT 6-56-2 and SHY 1-002-3 are higher than theaverage value, especially for sample SGT 6-56-2, whose frac-tal dimension is as high as 2.95. As we mentioned in Section4.4, because of its more complex shape and rough edge, thefractal dimension of fracture will be higher, even more than3. This is consistent with observation of FE-SEM. Addition-ally, the MIP result shows that for sample SHY 1-002-3,44% of the whole pores are in the 10-100 nm range, and35% are in the 1-10μm range; and for sample SGT 6-56-2,17.9% of the whole pores have pore-throat diameter > 10μm,and 72.1% are ranging in 10-100nm. Therefore, the occur-rence of two different slopes could be explained by two rela-tively developed well-connected pore networks and theexistence of fractures at micro- to nanoscale. However,according to Hu et al. [63], spontaneous imbibition of a wet-ting fluid into a well-connected porous material produces alate-time imbibition slope (d log ðmass imbibedÞ/log ðtimeÞ) of approximately 0.5; an imbibition slope of 0.25 indicatesthat the sample has a relatively poor connectivity. The imbibi-tion slopes of selected samples are all around 0.30 or evenlower than 0.25, which may indicate the poor to moderatepore connectivity of pore networks in these carbonate samplesfromXiaoerbulake Formation. The intragranular (dissolution)pores account nearly half of the total pore volume, while thepores are well-developed in the granular, the poor pore con-nectivity limits the permeability, and thus the fractures madeby an oil recovery method may significantly improve the res-ervoir quality.

As shown in Figure 12, the relationship between spon-taneous imbibition slope with the proportion of pores ofpore-throat diameter > 10 μm shows a positive correlation(R2 = 0:8). Combined with the permeability contributionof different pore networks, it is obvious that pore networkslocated at μm-scale are the most important permeability chan-nel for samples from Xiaoerbulake Formation, even though itspore volume is not predominant in the total porosity. Further-more, pore types in samples from Xiaoerbulake Formationwere identified before; it could be concluded that unless thereis micro-nano-fracture development, the pore networks dom-inated by intergranular pores have the best connectivity, whilethose predominated by intragranular and dissolution poreshave the relatively low pore connectivity.

Additionally, the effective tortuosity can be calculated byEquation (3) (Table 1). The value of tortuosity for pore net-works ranging from 10nm to 100 nm is as high as 818 ±1231. Put another way, the effective diffusion coefficient fornonsorbing gas and oil molecules in carbonates will be inthe order of 10-8 and 10-12. These relatively large values oftortuosity imply that, in order to migrate from one locationto another, fluid within the nano-scale pore network willneed to make its way through some tortuous pathways. Thegeometrical tortuosity Le/L of 2:04 ± 0:81 means that fluidhas to actually travel 2:04 ± 0:81 cm to reach a point 1 cmaway. This is consistent with the imbibition results that thepore networks ranging in nm-scale of the carbonates are

Table 4: Fractal dimensions of the carbonate samples.

Sample Dt1 R21 Dt2 R2

2 Dt3 R23 Dt4 R2

4

SGT 1-4-3 2.98 0.96 2.29 0.95 2.18 0.59 2.51 1.00

SGT 1-7-A 3.03 0.97 2.28 0.88 2.19 0.81 2.45 0.90

SGT 4-28-F 2.33 0.99 2.12 0.98 2.03 0.97 2.06 1.00

SGT 4-30-E 2.34 0.99 2.78 0.73 2.62 0.91 2.06 0.96

SGT 5-47-A 2.25 0.96 2.15 1.00 2.15 0.97 2.09 0.92

SGT 6-49-A 2.81 0.92 2.11 0.94 2.30 0.84 2.41 0.98

SGT 6-56-2 2.63 0.94 2.01 0.98 2.00 0.58 2.95 1.00

SHY 1-002-3 2.66 0.94 2.35 0.96 2.08 0.68 2.28 0.97

SHY 1-008-2 2.46 0.97 2.39 0.99 2.39 1.00 2.17 0.88

SHY 1-011-2 2.47 0.96 2.13 0.94 2.35 0.91 2.23 0.92

SHY 1-018-1 2.70 0.90 2.40 0.98 2.14 0.97 2.29 0.96

SHY 3-030-3 3.21 0.98 2.16 0.91 2.09 0.97 2.04 0.99

SHY 3-041-3 3.39 0.95 2.30 0.95 2.04 0.81 2.12 0.88

SHY 3-098 2.32 0.92 2.25 0.99 2.09 0.97 2.10 0.99

SHY 4-091-D 2.43 0.99 2.46 0.98 2.34 0.93 2.31 0.88

SHY 5-107-3 2.95 0.99 2.52 0.92 2.31 0.98 2.11 0.83

SHY 5-108-D 2.94 0.94 2.58 0.94 2.24 0.83 2.02 0.88

SHY 6-133-1 2.39 0.98 2.40 0.99 2.39 0.98 2.10 0.90

Average 2.68 0.96 2.32 0.95 2.22 0.87 2.24 0.94

D: the fractal dimension derived from a tubular pore model.

16 Geofluids

0.530 sec 60 min 24 hr

0.0

−0.5

−1.0

−1.5

SGT 4−30−ERectangular bar(1.146 cm long × 1.1345 cm wide × 1.0895 cm tall)

Slope 0.220

Log

cum

ulat

ive i

mbi

bitio

n (m

m)

−1 0 1

Log time (min)2 3

(a)

−1 0 1

Log time (min)2 3

0.530 sec 60 min 24 hr

0.0

−0.5

−1.5

−2.5

SGT 5−47−ARectangular bar(1.140 cm long × 1.0855 cm wide × 1.145 cm tall)

Slope 0.303

Log

cum

ulat

ive i

mbi

bitio

n (m

m)

−1.0

(b)

130 sec 60 min 24 hr

0

−1 SGT 6−49−ARectangular bar(1.030 cm long × 0.9845 cm wide × 1.045 cm tall)

Slope 0.285

Log

cum

ulat

ive i

mbi

bitio

n (m

m)

−1 0 1

Log time (min)2 3

(c)

−1 0 1

Log time (min)2 3

130 sec 60 min 24 hr

0

−1 SHY 5−108−DRectangular bar(1.041 cm long × 0.8505 cm wide × 1.0595 cm tall)

Slope 0.171

Log

cum

ulat

ive i

mbi

bitio

n (m

m)

(d)

130 sec 60 min 24 hr

0

−1−1 0 1

Log time (min)2 3

SGT 6−56−2Rectangular bar(1.007 cm long × 1.021 cm wide × 1.1425 cm tall)

Slope 0.081

Slope 0.230

Log

cum

ulat

ive i

mbi

bitio

n (m

m)

(e)

130 sec 60 min 24 hr

−1

−3

−2

−1 0 1

Log time (min)2 3

SHY 1-002-3Rectangular bar(0.946 cm long × 0.9065 cm wide × 1.043 cm tall)

Slope 0.435

Slope 0.174

Log

cum

ulat

ive i

mbi

bitio

n (m

m) 0

(f)

Figure 11: Spontaneous imbibition results for six representative carbonate samples from the Xiaoerbulake Formation.

17Geofluids

poorly connected; therefore, much time is required for fluidto find connected pathways to travel a limited distance [44].This section may be divided by subheadings. It should pro-vide a concise and precise description of the experimentalresults, their interpretation as well as the experimental con-clusions that can be drawn.

5. Conclusions

In the present work, the nature and connectivity of pore net-works in 18 carbonate samples from two outcrop locations ofthe Xiaoerbulake Formation have been characterized bycombining the methods of MIP, FE-SEM, spontaneous imbi-bition, and fractal dimensions analyses. The following con-clusions can be drawn:

(1) The lithologies are dominated by micritic dolomites,finely to medium to coarsely crystalline dolomites,microbial dolomites, and dolarenite. Three main typesof pores within micro-nano-scale were identified bycombining MIP analyses with photomicrographicobservations (both optical microscope and FE-SEM),namely, intergranular pores, intercrystalline pores,and intragranular pores (dissolution pores)

(2) The Xiaoerbulake Formation carbonates are charac-terized by complex multiscale pore networks. Fourdifferent pore networks ranging in nm-μm spectrumare identified by MIP. Based on the pore volume dis-tributions of the four different pore-throat diameterranges, three types of pore network patterns wereidentified. Multiple fractal characteristics show porenetworks with larger pore throat diameter have morecomplex structure (more irregular shape and roughsurface)

(3) The permeability is controlled by pore networks inmicroscale, which means the interparticle pores and

intercrystalline pores make a considerable strongercontribution to permeability. Even though pore-throat diameter > 1 μm makes up only 43.3% onaverage of total pore volume, their average contribu-tion to the permeability is 99.64%

(4) The spontaneous imbibition tests show that the con-nectivity of pore networks is controlled by pore type;the Type III pattern pore networks dominated by μmsize pores are better connected. Generally, the porenetworks in Xiaoerbulake samples exhibit poor tomoderate pore connectivity. Nevertheless, the devel-opment of fractures ranging from μm to nm is benefi-cial for the connectivity greatly by connecting differentpore types, such as among intragranular (dissolution)pores as well as between intragranular (dissolution)and intergranular or intercrystalline pores

Data Availability

The laboratory data used to support the findings of this studyare included within the article.

Conflicts of Interest

The authors declare no conflict of interest.

Authors’ Contributions

Qinhong Hu, Jingyi Wang, and Mengdi Sun are responsiblefor the conceptualization. Jingyi Wang curated the data. Jin-gyi Wang, Mengdi Sun, and Tao Zhang did the formal anal-ysis. Mengdi Sun, Zhongxian Cai, and Cong Zhang acquiredfunding. Qinhong Hu, Cong Zhang, and Tao Zhang areassigned to the methodology. Zhongxian Cai is involved inthe project administration. Zhongxian Cai is responsible forthe resources. Qinhong Hu performed the supervision. JingyiWang wrote the original draft. Qinhong Hu, Mengdi Sun,Zhongxian Cai, Cong Chang, and Tao Zhang wrote,reviewed, and edited the manuscript.

Acknowledgments

The authors sincerely thank the Strategic Priority ResearchProgram of the Chinese Academy of Science (Grant No.XDA14010302), the National Natural Science Foundationof China (Grant Nos. 41802146, 41830431, and 41572134),and the Key Laboratory of Unconventional Oil and GasGeology, China Geological Survey (No. 30200018-19-ZC0613-0065) for the financial support.

References

[1] K. Zhang, X. Pang, Z. Zhao et al., “Pore structure and fractalanalysis of Lower Carboniferous carbonate reservoirs in theMarsel area, Chu-Sarysu basin,” Marine and Petroleum Geol-ogy, vol. 93, pp. 451–467, 2018.

[2] J. Peng, X. Wang, H. Han, S. Yin, Q. Xia, and B. Li, “Simulationfor the dissolution mechanism of Cambrian carbonate rocks in

0 5 10 15 20 25 30 35 40

0.20

0.25

0.30

Proportion of pores with pore-throat diameter > 10 𝜇m

R2 = 0.8

Spon

tane

ous i

mbi

bitio

n slo

pe

Figure 12: Relationship between spontaneous imbibition slope with(a) proportion of pores with pore-throat diameter > 10μm(excluding the two-slope spontaneous imbibition).

18 Geofluids

Tarim Basin, NWChina,” Petroleum Exploration and Develop-ment, vol. 45, no. 3, pp. 431–441, 2018.

[3] L. Wang, Y. He, X. Peng, H. Deng, Y. Liu, and W. Xu, “Porestructure characteristics of an ultradeep carbonate gas reser-voir and their effects on gas storage and percolation capacitiesin the Deng IV member, Gaoshiti-Moxi Area, Sichuan Basin,SW China,” Marine and Petroleum Geology, vol. 111, pp. 44–65, 2020.

[4] W. Zhao, A. Shen, Z. Qiao, L. Pan, A. Hu, and J. Zhang,“Genetic types and distinguished characteristics of dolomiteand the origin of dolomite reservoirs,” Petroleum Explorationand Development, vol. 45, no. 6, pp. 983–997, 2018.

[5] Q. Li, Z. Jiang, W. Hu et al., “Origin of dolomites in the LowerCambrian Xiaoerbulak Formation in the Tarim Basin, NWChina: implications for porosity development,” Journal ofAsian Earth Sciences, vol. 115, pp. 557–570, 2016.

[6] Y. Bai, P. Luo, S. Wang et al., “Structure characteristics andmajor controlling factors of platform margin microbial reef res-ervoirs: a case study of Xiaoerbulak Formation, Lower Cam-brian, Aksu area, Tarim Basin, NW China,” PetroleumExploration and Development, vol. 44, no. 3, pp. 377–386, 2017.

[7] Q.-H. Hu, X.-G. Liu, Z.-Y. Gao, S.-G. Liu, W. Zhou, and W.-X. Hu, “Pore structure and tracer migration behavior of typicalAmerican and Chinese shales,” Petroleum Science, vol. 12,no. 4, pp. 651–663, 2015.

[8] A. S. Gundogar, C. M. Ross, S. Akin, and A. R. Kovscek, “Mul-tiscale pore structure characterization of Middle East carbon-ates,” Journal of Petroleum Science and Engineering, vol. 146,pp. 570–583, 2016.

[9] P. Sun, H. Xu, Q. Dou et al., “Investigation of pore-type hetero-geneity and its inherent genetic mechanisms in deeply buriedcarbonate reservoirs based on some analytical methods of rockphysics,” Journal of Natural Gas Science and Engineering,vol. 27, pp. 385–398, 2015.

[10] D. Wei, Z. Gao, C. Zhang, T. Fan, G. M. Karubandika, andM. Meng, “Pore characteristics of the carbonate shoal fromfractal perspective,” Journal of Petroleum Science and Engi-neering, vol. 174, pp. 1249–1260, 2019.

[11] A. Shen, J. Zheng, Y. Chen, X. Ni, and L. Huang, “Characteris-tics, origin and distribution of dolomite reservoirs in Lower-Middle Cambrian, Tarim Basin, NWChina,” Petroleum Explo-ration and Development, vol. 43, no. 3, pp. 375–385, 2016.

[12] B. B. Mandelbrot, D. E. Passoja, and A. J. Paullay, “Fractalcharacter of fracture surfaces of metals,” Nature, vol. 308,no. 5961, pp. 721-722, 1984.

[13] P. Pfeifer, D. Avnir, and D. Farin, “Ideally irregular surfaces, ofdimension greater than two, in theory and practice,” SurfaceScience, vol. 126, no. 1-3, pp. 569–572, 1983.

[14] C. Krohn, “Fractal measurements of sandstones, shales, andcarbonates,” Journal of Geophysical Research, vol. 93, no. B4,pp. 3297–3305, 1988.

[15] J. Muller, “Multifractal characterization of petrophysical data,”Physica A: Statistical Mechanics and its Applications, vol. 191,no. 1-4, pp. 284–288, 1992.

[16] S. Xie, Q. Cheng, Q. Ling, B. Li, Z. Bao, and P. Fan, “Fractal andmultifractal analysis of carbonate pore-scale digital images ofpetroleum reservoirs,” Marine and Petroleum Geology,vol. 27, no. 2, pp. 476–485, 2010.

[17] W. Jiang, B. Liu, K. Shi, and X. Gao, Microfacies and Charac-teristics of Carbonate Reservoir in Xiaoerbulake Formation ofKeping Area, Tarim Basin, Xinjiang Petroleum Geology, 2019.

[18] C. Jia, Tectonic Characteristics and Petroleum, PetroleumIndustry Press, Tarim basin, China, 1997.

[19] G. Zhu, H. Huang, and H.Wang, “Geochemical significance ofdiscovery in Cambrian reservoirs at well ZS1 of the TarimBasin, Northwest China,” Energy & Fuels, vol. 29, no. 3,pp. 1332–1344, 2015.

[20] X. Wang, W. Hu, S. Yao, Q. Chen, and X. Xie, “Carbon andstrontium isotopes and global correlation of Cambrian Series2-Series 3 carbonate rocks in the Keping area of the northwest-ern Tarim Basin, NW China,”Marine and Petroleum Geology,vol. 28, no. 5, pp. 992–1002, 2011.

[21] J. Lai, S. Wang, C. Zhang et al., “Spectrum of pore types andnetworks in the deep Cambrian to Lower Ordovician dolos-tones in Tarim Basin, China,”Marine and Petroleum Geology,vol. 112, article 104081, 2020.

[22] S. Wang, Y. Cao, and D. Du, “The characteristics and maincontrolling factors of dolostone reservoir in Lower CambrianXiaoerbulak Formation in Keping-Bachu area, Tarim Basin,NW China,” Natural Gas Geoscience, vol. 29, pp. 784–795,2018.

[23] H. Liu, Z. Tian, B. Liu et al., “Pore types, origins and control onreservoir heterogeneity of carbonate rocks in Middle Creta-ceous Mishrif Formation of the West Qurna oilfield, Iraq,”Journal of Petroleum Science and Engineering, vol. 171,pp. 1338–1349, 2018.

[24] B. Liu, Y. Song, K. Zhu, P. Su, X. Ye, andW. Zhao, “Mineralogyand element geochemistry of salinized lacustrine organic-richshale in the Middle Permian Santanghu Basin: implicationsfor paleoenvironment, provenance, tectonic setting and shaleoil potential,” Marine and Petroleum Geology, vol. 120, article104569, 2020.

[25] E. W. Washburn, “The dynamics of capillary flow,” PhysicalReview, vol. 17, no. 3, pp. 273–283, 1921.

[26] A. J. Katz and A. H. Thompson, “Quantitative prediction ofpermeability in porous rock,” Physical Review B: CondensedMatter, vol. 34, no. 11, pp. 8179–8181, 1986.

[27] A. J. Katz and A. H. Thompson, “Prediction of rock electricalconductivity from mercury injection measurements,” Journalof Geophysical Research, vol. 92, no. B1, p. 599, 1987.

[28] J. Hager, Steam Drying of Porous Media, [M.S. thesis], LundUniversity, Sweden, 1998.

[29] P. Webb, An Introduction to the Physical Characterization ofMaterials by Mercury Intrusion Porosimetry with Emphasison Reduction And Presentation of Experimental Data, Micro-meritics Instrument Corp, Norcross, Georgia, 2001.

[30] C. J. Gommes, A.-J. Bons, S. Blacher, J. H. Dunsmuir, andA. H. Tsou, “Practical methods for measuring the tortuosityof porous materials from binary or gray-tone tomographicreconstructions,” AIChE Journal, vol. 55, no. 8, pp. 2000–2012, 2009.

[31] N. Epstein, “On tortuosity and the tortuosity factor in flow anddiffusion through porous media,” Chemical Engineering Sci-ence, vol. 44, no. 3, pp. 777–779, 1989.

[32] Q.-H. Hu and J. Wang, “Aqueous-phase diffusion in unsatu-rated geologic media: a review,” Critical Reviews in Environ-mental Science and Technology, vol. 33, no. 3, pp. 275–297,2003.

[33] K. Liu and M. Ostadhassan, “Quantification of the microstruc-tures of Bakken shale reservoirs using multi- fractal and lacu-narity analysis,” Journal of Natural Gas Science andEngineering, vol. 39, pp. 62–71, 2017.

19Geofluids

[34] J. Lai and G. Wang, “Fractal analysis of tight gas sandstonesusing high-pressure mercury intrusion techniques,” Journal ofNatural Gas Science and Engineering, vol. 24, pp. 185–196, 2015.

[35] J. Lai, G. Wang, Z. Fan et al., “Insight into the pore structure oftight sandstones using NMR and HPMI measurements,”Energy & Fuels, vol. 30, no. 12, pp. 10200–10214, 2016.

[36] B. Zhang and S. Li, “Determination of the surface fractaldimension for porous media by mercury porosimetry,” Indus-trial & Engineering Chemistry Research, vol. 34, no. 4,pp. 1383–1386, 1995.

[37] F. Wang, K. Yang, J. You, and X. Lei, “Analysis of pore size dis-tribution and fractal dimension in tight sandstone with mer-cury intrusion porosimetry,” Results in Physics, vol. 13,article 102283, 2019.

[38] K. Li, “Analytical derivation of Brooks-Corey type capillarypressure models using fractal geometry and evaluation of rockheterogeneity,” Journal of Petroleum Science and Engineering,vol. 73, no. 1-2, pp. 20–26, 2010.

[39] B. Liu, Y. Yang, J. Li, Y. Chi, J. Li, and X. Fu, “Stress sensitivityof tight reservoirs and its effect on oil saturation: a case studyof Lower Cretaceous tight clastic reservoirs in the Hailar Basin,Northeast China,” Journal of Petroleum Science and Engineer-ing, vol. 184, article 106484, 2020.

[40] M. Bai, X. Xia, and C. Zhang, “Study on shale organic porosityin the Longmaxi Formation, AnYe - 1 well using fieldemission-scanning electron microscopy and PerGeos system,”Rock and Mineral Analysis, vol. 37, pp. 225–234, 2018.

[41] M. G. Kibria, Q. Hu, H. Liu, Y. Zhang, and J. Kang, “Porestructure, wettability, and spontaneous imbibition of Wood-ford Shale, Permian Basin, West Texas,” Marine and Petro-leum Geology, vol. 91, pp. 735–748, 2018.

[42] M. Xu and H. Dehghanpour, “Advances in understanding wet-tability of gas shales,” Energy & Fuels, vol. 28, no. 7, pp. 4362–4375, 2014.

[43] M. Q. Hu, P. Persoff, and J. S. Y. Wang, “Laboratory measure-ment of water imbibition into low-permeability welded tuff,”Journal of Hydrology, vol. 242, no. 1-2, pp. 64–78, 2001.

[44] Q. Hu, R. P. Ewing, and H. D. Rowe, “Low nanopore connec-tivity limits gas production in Barnett formation,” Journal ofGeophysical Research: Solid Earth, vol. 120, no. 12, pp. 8073–8087, 2015.

[45] M. Meng, H. Ge, Y. Shen et al., “The effect of clay-swellinginduced cracks on imbibition behavior of marine shale reser-voirs,” Journal of Natural Gas Science and Engineering,vol. 83, article 103525, 2020.

[46] P. W. Choquette and C. P. Lloyd, “Geologic nomenclature andclassification of porosity in sedimentary carbonates,” AAPGBulletin, vol. 54, 1970.

[47] Z. Gao and Q. Hu, “Estimating permeability using medianpore-throat radius obtained from mercury intrusion porosi-metry,” Journal of Geophysics and Engineering, vol. 10, no. 2,article 025014, 2013.

[48] Q. Hu, Y. Zhang, X. Meng, Z. Li, Z. Xie, and M. Li, “Character-ization of micro-nano pore networks in shale oil reservoirs ofPaleogene Shahejie Formation in Dongying Sag of Bohai BayBasin, East China,” Petroleum Exploration and Development,vol. 44, no. 5, pp. 720–730, 2017.

[49] W. Yan, J. Zheng, Y. Chen, L. Huang, P. Zhou, and Y. Zhu,“Characteristics and genesis of dolomite reservoir in the lowerCambrian Xiaoerblak formation Tarim basin,” Marine OriginPetroleum Geology, vol. 22, no. 4, pp. 35–43, 2017.

[50] W. R. Purcell, “Capillary pressures - their measurement usingmercury and the calculation of permeability therefrom,” Jour-nal of Petroleum Technology, vol. 1, no. 2, pp. 39–48, 1949.

[51] J. Li, S. Lu, L. Xie et al., “Modeling of hydrocarbon adsorptionon continental oil shale: a case study on _n_ -alkane,” Fuel,vol. 206, pp. 603–613, 2017.

[52] Z. Song, G. Liu, W. Yang, H. Zou, M. Sun, and X. Wang,“Multi-fractal distribution analysis for pore structure charac-terization of tight sandstone–a case study of the Upper Paleo-zoic tight formations in the Longdong District, Ordos Basin,”Marine and Petroleum Geology, vol. 92, pp. 842–854, 2018.

[53] X. Liu, J. Xiong, and L. Liang, “Investigation of pore structureand fractal characteristics of organic-rich Yanchang formationshale in Central China by nitrogen adsorption/desorptionanalysis,” Journal of Natural Gas Science and Engineering,vol. 22, pp. 62–72, 2015.

[54] N. Alyafei and M. J. Blunt, “Estimation of relative permeabilityand capillary pressure from mass imbibition experiments,”Advances in Water Resources, vol. 115, pp. 88–94, 2018.

[55] N. R. Morrow and G. Mason, “Recovery of oil by spontaneousimbibition,” Current Opinion in Colloid & Interface Science,vol. 6, no. 4, pp. 321–337, 2001.

[56] Z. Cheng, Z. Ning, X. Yu, Q. Wang, and W. Zhang, “Newinsights into spontaneous imbibition in tight oil sandstoneswith NMR,” Journal of Petroleum Science and Engineering,vol. 179, pp. 455–464, 2019.

[57] Z. Gao and Q. Hu, “Wettability of Mississippian Barnett Shalesamples at different depths: investigations from directionalspontaneous imbibition,” AAPG Bulletin, vol. 100, no. 1,pp. 101–114, 2016.

[58] M. Meng, H. Ge, Y. Shen, L. Li, T. Tian, and J. Chao, “Theeffect of clay-swelling induced cracks on shale permeabilityduring liquid imbibition and diffusion,” Journal of NaturalGas Science and Engineering, vol. 83, article 103514, 2020.

[59] L. Handy, “Determination of effective capillary pressures forporous media from imbibition data,” Transactions of theAIME, vol. 219, no. 1, pp. 75–80, 1960.

[60] Z. Gao, S. Yang, Z. Jiang, K. Zhang, and L. Chen, “Investigatingthe spontaneous imbibition characteristics of continentalJurassic Ziliujing Formation shale from the northeasternSichuan Basin and correlations to pore structure and composi-tion,” Marine and Petroleum Geology, vol. 98, pp. 697–705,2018.

[61] A. Hunt and R. Ewing, “Percolation theory for flow in porousmedia,” in Lecture Notes in Physics, p. 880, Springer, 2nd edi-tion, 2009.

[62] M. Sahini and M. Sahimi, Applications of Percolation Theory,Taylor & Francis, 1994.

[63] Q. Hu, R. P. Ewing, and S. Dultz, “Low pore connectivity innatural rock,” Journal of Contaminant Hydrology, vol. 133,pp. 76–83, 2012.

[64] R. Yang, X. Guo, J. Yi, Z. Fang, Q. Hu, and S. He, “Spontaneousimbibition of three leading shale formations in the middleYangtze Platform, South China,” Energy & Fuels, vol. 31,no. 7, pp. 6903–6916, 2017.

[65] A. J. Katz and A. H. Thompson, “Prediction of rock electricalconductivity from mercury injection measurements,” Journalof Geophysical Research, vol. 92, no. B1, p. 599, 1987.

20 Geofluids