Scale-Dependent Pore and Hydraulic Connectivity of Shale Matrix

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Scale Dependent Pore and Hydraulic Connectivity of Shale Matrix Davud Davudov, and Rouzbeh Ghanbarnezhad Moghanloo Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b02619 • Publication Date (Web): 04 Dec 2017 Downloaded from http://pubs.acs.org on December 4, 2017

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Scale Dependent Pore and Hydraulic Connectivity of Shale Matrix Davud Davudov a *, Rouzbeh Ghanbarnezhad Moghanloo a a

Mewbourne School of Petroleum & Geological Engineering, The University of Oklahoma, Norman, OK, USA * Correspondence author. Email: [email protected] Abstract Shale resources have distinctive characteristics compared to conventional reservoirs, including micro size pores (IUPAC definition), ultra-low permeability, several gas storage mechanisms, and complex fluid flow behavior. Prediction of productivity and deliverability of shale systems requires knowledge about in-situ porosity and permeability. In this study, we evaluate pore and hydraulic connectivity of matrix for Barnett and Haynesville shale plays based on mercury injection capillary pressure (MICP) data and percolation theory. Using MICP porosity values measured at the laboratory for different sample size, accessible porosity and permeability for Barnett and Haynesville shale samples are reported. Next, pore and hydraulic connectivity for both Barnett and Haynesville samples are evaluated based on percolation theory. Moreover, permeability values calculated based on MICP data is used to estimate average coordination number as a function of sample size. Our results indicate that accessible porosity and matrix permeability decreases with increasing sample size, which predicts lower connectivity for shale matrix in large-scale. Consistent with percolation theory, results suggest that accessible porosity decreases with increasing sample size following a power law function. Furthermore, results show that sample size has significant impact on estimated coordination number; this is expected as interconnected porosity is strong function of average coordination number. The main contribution of this work is the evaluation of accessible porosity and pore connectivity for different sample sizes from two shale plays. The new insight about scale-dependent pore 1

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connectivity and interconnected porosity may lead to improved predictions of production performance and project economics. Keywords: accessible porosity; scale dependent; pore connectivity; hydraulic connectivity; coordination number 1. Introduction As production from shale plays maintain its role as one of the main energy resources in the U.S., prediction of formation deliverability during the production life becomes a decision-making factor for future investments. The complexity of shale gas reservoirs can, in part, be attributed to the geological and petrophysical heterogeneity of the reservoir rocks themselves. Shales are comprised of common minerals such as silica dioxide, but also include considerable amounts of clays and organic matter; wherein, the latter is an essential constituent of a productive shale gas reservoir.33 Shales with 50% of grains smaller than 62.5 µm in diameter fall into a category of mudrocks.28 These small grains combined with the clay minerals generate multifarious pore geometry. Pores are observed at various locations inside the shale matrix; the porosity in the Barnett is dominantly within the organic matter.29, 30 However, Curtis et al.7 and Chalmers et al.2 reported that the porosity in the Haynesville shale is most prevalent in the inorganic part. By analyzing 3D shale microstructure, constructed based on scanning electron microscope (SEM) images, Curtis et al.8 noted that only 19% of total porosity is connected. Hu et al.20 examined pore connectivity with three experimental approaches (imbibition, tracer concentration profiles, and imaging) which they have also reported very low connectivity in shale matrix. Davudov et al.12, 14 also studied connectivity in shale formations based on mercury injection capillary pressure (MICP) data, which they have concluded that the percentage of accessible pores in Barnett and Haynesville shale fields is around 30%.


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In this study, we investigate MICP porosity for different sample sizes and evaluate accessible/interconnected porosity and hydraulic connectivity based on experimental data coupled with percolation theory. Previously, Comisky et al.5 and Tinni et al.40 investigated shale porosity based on MICP test for different sample sizes and concluded that mercury porosity is decreasing with increasing sample size and suggested that this is due to the effect of restricted pore connectivity. This paper is organized as follows: (1) description of experimental procedures and chosen samples; (2) accessible porosity and permeability estimation for Barnett and Haynesville samples based on MICP test; and (3) evaluation of results based on percolation theory. 2. Experimental Procedures To analyze accessible and interconnected porosity, samples from Barnett, and Haynesville formations with several different sizes are selected, and mercury injection is carried out on all the sample size ranges. After 1-inch core plug samples are crushed, and series of mesh size are used to break out several sample sizes from the same depth interval. Particle sizes of core plug (25.4mm), 5.7mm, 3.5mm, 1.6mm, and 0.7mm are selected for MICP tests (Figure 1). The properties of the selected shale samples are summarized in Table 1. Table 1: Summary of sample properties obtained with FTIR method. Sample

Quartz + Feldspars (wt %)

Clays (wt %)

Carbonates (wt %)

TOC (wt %)

Others (wt %)

Barnett

21

65

4

5

5

Haynesville

5 42 43 2 8 The measurements are conducted with an Autopore IV Mercury Porosimeter which is a 60000 psi porosimeter and can measure pore diameter range from 360 μm to 3 nm. For MICP test all samples are first dried at 100 C for 48 hours and cooled in a desiccator for 30 minutes before mercury


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injection. Then all samples undergo a vacuum stage to ensure all in-situ fluids are cleaned before mercury is introduced into the testing cell. b)

a)

Figure 1. Mercury injection capillary pressure experimental setup a) Autopore IV Mercury Porosimeter b) Sampling of material from each particle size

During the mercury injection test, the volume of mercury introduced into the sample is quantified by measuring the capacitance change of the penetrometer stem. To account for the temperature and the mercury compressibility effects, MICP experiment is conducted in an empty penetrometer and the apparent intrusion is subtracted from the intrusion data of the samples, which is a normal blank correction. Additionally, conformance which is the amount of mercury that is needed to envelope rock surface has been recognized as another source of error when calculating petrophysical properties from mercury injection data13, 43 and it should be also considered when porosity values are calculated and in this study. Porosity from MICP measurements is determined once the mercury injection has concluded at a pressure of around 60,000 psia following:

MICP 

VHg Vb

,

(1)

where 𝑉𝐻𝑔 is the pore volume or the total volume of mercury injected at 60,000 psia, and 𝑉𝑏 is bulk volume of sample.


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To evaluate fraction of accessible pore volume, ratio of porosity calculated from MICP test to absolute total porosity, (ϕ𝐿𝑃𝑃 ) are calculated. Total porosity values are estimated from crushed sample low-pressure pycnometer (LPP) test. 1-inch samples with average weight of 9 to 12 grams were selected for LPP porosity measurements and all samples were obtained from the same depths as the samples used for MICP. Chosen samples are cooled in a humidity controlled desiccator after they are dried in an oven at 100° C for 8 hours. Mass and bulk volume of the sample is calculated using mercury immersion technique. The samples are then crushed to average particle size of 0.4 mm. The crushed samples are dried again at 100°C and cooled back. Next, the grain volume of sample is measured using LPP apparatus and absolute porosity is calculated from the measured bulk and grain volumes. In case difference in sample mass before and after crushing is more than 0.5 %, the sample is discarded and procedure is repeated. 3. Accessible Porosity and Permeability The basis for this study is to measure and compare accessible porosity and permeability values based on MICP test on a variety of sample sizes for Barnett and Haynesville shale samples. By addressing this we would understand impact of sample size on accessible porosity and hydraulic connectivity for different shale formations. 3.1. Porosity We define MICP porosity values as accessible pore volume (ϕ𝑎 ), where absolute total porosity (ϕ𝐿𝑃𝑃 ) is determined based on crushed sample LPP test and fraction of accessible porosity (ϕ𝑎 /ϕ𝐿𝑃𝑃 ) is analyzed to determine impact of sample size on accessible porosity. Incremental and cumulative mercury volume measured in milliliters per gram (ml/g) for all sample sizes are illustrated in Figure 2 & 3 for Barnett and Haynesville samples respectively. As it can be seen for the both samples, as sample size increases cumulative mercury volume and porosity decreases.


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a) Incremental volume 0.7 mm

1.6 mm

3.5 mm

5.7 mm

25.4 mm

Incremental Hg Volume (ml/g)

0.0007 0.0006 0.0005 0.0004 0.0003 0.0002 0.0001 0 10

100

1000

10000

100000

Capillary Pressure, psi

b) Cumulative volume 0.7 mm

1.6 mm

3.5 mm

5.7 mm

25.4 mm

0.016

Cumulative Hg Volume (ml/g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.014 0.012 0.01 0.008 0.006 0.004 0.002 0 10

100

1000

10000

100000


Figure 2. Mercury injection capillary pressure data for Barnett samples a) Incremental volume b) Cumulative volume


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a) Incremental volume 0.7 mm

1.6 mm

3.5 mm

5.7 mm

25.4 mm

Incremental Hg Volume (ml/g)

0.0004 0.00035

0.0003 0.00025 0.0002 0.00015 0.0001 0.00005 0 10

100

1000

10000

100000


b) Cumulative volume 0.7 mm

1.6 mm

3.5 mm

5.7 mm

25.4 mm

0.014

Cumulative Hg Volume (ml/g)

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0.012 0.01 0.008 0.006 0.004 0.002 0 1

10

100

1000

10000

100000


Figure 3. Mercury injection capillary pressure data for Haynesville samples a) Incremental volume b) Cumulative volume


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The fraction of accessible porosity values, (ϕ𝑎 /ϕ𝐿𝑃𝑃 ) plotted as a function of sample size is illustrated in Figure 4 & 5 for raw and conformance corrected values respectively. Results show a dramatic difference between porosity values measured from MICP as a function of particle size for any given sample as illustrated in Figure 4. Even after conformance correction, we still observe a strong dependence of sample size on the measured MICP porosity (Figure 5). It can be observed that, in all cases, accessible porosity is smallest for the core plug and largest for finest particle size range. This can be explained through diminishing of the pore connectivity as sample size increases which results in less amount of mercury gets intruded, consistent with reduction in accessible porosity for larger samples. In addition, results indicate that for all sample sizes, accessible pore fraction for Barnett is higher than Haynesville. Based on results, around 30 % of pores are saturated and accessible in Barnett shale sample, where this value is around 15% for Haynesville. 1.0 0.9 Accessible Porosity Fraction

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0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0

5

10

15

20

25

Sample Size, mm Barnett Sample

Haynesville Sample

Figure 4. Fraction of accessible porosity (ϕ𝑀𝐼𝐶𝑃 /ϕ𝐿𝑃𝑃 ) as a function of sample size (without conformance corrected)


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Barnett

Haynesville

Accessible Porosity Fraction

0.7 0.6 0.5

y = 0.5268x-0.181 R² = 0.8438

0.4 0.3

y = 0.3696x-0.345 R² = 0.8227

0.2 0.1 0.0 0

5

10

15

20

25

30

Sample Size, mm

Figure 5. Fraction of accessible porosity after conformance correction as a function of sample size Further, we chose 45 core plug (1-inch) samples from each shale play with MICP and LPP measured porosity values and calculated accessible pore fraction (ϕ𝑎 /ϕ𝐿𝑃𝑃 ) as shown in Figure 6a and 6b. Results show that average accessible pore for Barnett samples is around 53%, which this value is around 43% for Haynesville samples. Additionally, results show that the lowest value in Barnett samples is 30% but this number can be as low as 5 % in Haynesville. 9 8 7 6 5 4 3 2 1 0

12 10 Frequency

Frequency

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8 6 4 2

0 Accessible Porosity Ratio

Accessible Porosity Ratio

Figure 6. Histogram of the MICP porosity fraction (ϕ𝑎 /ϕ𝐿𝑃𝑃 ) from 45 samples in plug size for the a) Barnett and b) Haynesville


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It is worth mentioning that pore accessibility is dynamic and depends on the pore network as well as fluid saturation; thus, the estimated accessible pore fractions is likely different for various fluids. Which is why, with MICP test, only connectivity of the rock that partially saturated with mercury can be measured; pores smaller than 3 nm which mercury cannot intrude will not be evaluated using the methodology discussed here. However, as King et al.27 mentioned, MICP measurements is one of the best techniques and they give direct information about pore throats which is the key parameter for connectivity/conductivity. Thus, while acknowledging the limitations of MICP test, we still believe that, current study provides important evaluation to understand pore connectivity in shale formations studied.

Permeability Hu et al.20 studied impact of connectivity in Barnett shale and they have mentioned that due to low-connectivity, an increase in the size of the sample results in decreases in permeability, diffusivity, and an increase in tortuosity. For further evaluation of matrix hydraulic connectivity, intrinsic permeability values for different sample sizes based on MICP data are calculated and analyzed. There have been many developed models to estimate absolute permeability values based on basic rock properties. The most widespread ones of those models incorporate pore dimensions and length characteristics, which can be quantified from MICP measurements.11, 21, 25, 26, 32, 37 Comisky et al.6 evaluated 63 core samples obtained from tight formations and compared absolute permeability values calculated based on 13 different MICP based models. They have concluded that Swanson is one of the best permeability estimation methods among 13 techniques that they have analyzed. Swanson37 used the apex of bulk volume mercury saturation, (𝑆𝑏 ) to capillary pressure ratio,


10

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(𝑆𝑏 /𝑝𝑐 )𝐴 to represent the critical point at which major connected pore volumes contributing to permeability have been intruded with mercury. Based on 319 samples studied, Swanson37 suggested that permeability can be determined as a function of (𝑆𝑏 /𝑝𝑐 )𝐴 : 1.691

S  k  399  b  ,  pc  A

(2)

Table 2 and Figure 7 summarizes results of predicted permeability values using MICP data for different sample sizes for both Barnett and Haynesville. Results indicate that permeability also is strong dependent of sample size, which with increasing size permeability values decrease. This is an anticipated result since permeability is a strong function of interconnected porosity and as discussed before accessible porosity values decrease with increasing sample size. Although permeability values for Haynesville is slightly higher than Barnett for small sample size ranges, but at the same time decline rate with increasing sample size is much higher than Barnett. For core plug size samples, calculated permeability value for Barnett is 2.9×10-4 md, where this number is around 1.4×10-5 md for Haynesville. Our permeability results at core-scale from both formations are similar to that measured by Kang et al.24, Vermylen41 and Bhandari et al.1 for Barnett samples and by Tinni et al.39 and Dewers et al.15 for Haynesville samples Table 2: Summary porosity and permeability values for different sample sizes Barnett Shale Sample Sample Size

Haynesville Shale Sample

0.7

MICP Porosity, % 3.62

K (Swanson), µd 38.1

MICP Porosity, % 2.96

K (Swanson), µd 58.9

1.6

2.91

16.6

1.53

11.7

3.5

2.48

3.90

0.98

12.9

5.7

1.94

1.72

1.20

4.31

25.4

1.95

0.29

0.76

0.0114


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Barnett

Haynesville

10

15

1.E-01

1.E-02

Permeability, md

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1.E-03

1.E-04

1.E-05 0

5

20

25

30

Sample Size, mm

Figure 7. Predicted permeability as a function of sample size

Connected Porosity and Hydraulic Connectivity - Percolation Theory Percolation theory, which is the study of pathways in disordered media such as rock matrices is one of the best approaches to model a system of pores that have low connectivity. 16, 17, 18, 35, 36 Moreover, application of fractal and percolation theories to shale formations has been widely reported in the literature. 23, 31, 45 In this section, both accessible porosity and hydraulic connectivity values predicted from experimental data are evaluated based on percolation theory. 3.2. Connected Porosity Percolation theory predicts that in a 3-D material with constant total porosity and low connectivity, the portion of porosity that is accessible will decrease with distance from the exterior in proportion to 𝑙 −𝑚 , until distance exceeds some crossover distance χ. 16, 17, 18, 19, 20 Beyond this crossover distance, the accessible porosity either reaches to stable value if pore connectivity is above the critical percolation threshold, 𝑝𝑐 or gets zero if connectivity is below the threshold, which it means


12

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fluid will not be able to percolate from that rock sample. Rock samples with high connectivity may have χ on the order of a single pore and accessible porosity will be close to the total porosity, but as pore connectivity decreases, this crossover distance χ is increasing and it becomes close to half the thickness of the sample, when connectivity is close to percolation threshold. Following Ewing et al.17, accessible porosity change with intragranular distance 𝑙 to the grain’s exterior and it can be formulized as:  p l  m  (l , p)   a

for l  x

(3)

for l  x

, where p represents the probability of accessible pore, 𝑙 is the sample size, χ is correlation length beyond which value of accessible pore becomes constant, and m is power law function exponent. If experimental data is fitted to power law function (Eq. 3), exponent 𝑚 is 0.18 for Barnett and 0.35 for Haynesville, which indicates that accessible porosity in Haynesville decreases faster with increasing sample size when compared with Barnett results (Figure 5). 3.3. Hydraulic Conductivity and Coordination Number To capture and include connectivity effect in their permeability models several equations have been proposed. Civan

3, 4

modified Karmen-Kozeny permeability model and proposed the

following equation for fractal porous media: 2

   k      1  ,

(4)

where β is exponent usually equal to 1, and Γ is interconnectivity parameter which is a measure of the pore space connectivity.4 The number of the pore throats is generally expressed by average coordination number denoted as z. The values z = 0 and z = 1 represent isolated pores and dead end pores, respectively and the lowest value of the coordination number for a conductive pore


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body is z = 2. Thus, the interconnectivity parameter, Γ is strong function of average coordination number and it becomes zero when all the pore throats are blocked due to mechanisms like fine migration, deposition of precipitates and collapse of pore throats under mechanical stresses. Recently Daigle 9, 10 developed permeability model based on percolation and fractal theories as:

r 2   1  pc   k  max   8  1   pc 

2

2

  pc  3 D , 1    

(5)

where ϕ is porosity; 𝑟𝑚𝑎𝑥 is the largest accessible pore size in the medium; 𝜃 is the ratio of pore volume to the sum of the pore and solid volumes in the fractal model (in the limit where number of replications in fractal model approaches to infinity, then 𝜃 ≈ 𝜙); D is fractal dimension which is 2 ≤ 𝐷 < 3; and, 𝑝𝑐 is the critical percolation threshold. Following Revil

34

, it is assumed that in clay-bearing rocks, 1 − 𝜙𝑝𝑐 ≈ 1, and also 𝜃 ≈ 𝜙 for

infinite number of replications, then Eq. 5 can be written as:

k

2 2 rmax 2  2 1  pc  3 D , 8

(6)

Moreover, critical percolation threshold, 𝑝𝑐 can be expressed in terms of coordination number as 𝑝𝑐 = 1.5/𝑧 22, 42: 2

r2  z  1.5  3 D k  max  2   8  z 

2

(7)

2 When Eq. 7 is compared with Civan model (Eq. 4), it is clear that 𝑟𝑚𝑎𝑥 𝜙 2 ⁄8 is maximum 2

achievable permeability and

𝑧−1.5 3−𝐷+2 ( ) 𝑧

represents interconnectivity term (Γ).

To analyze impact of sample size on pore connectivity/average coordination number, permeability results obtained from MICP are evaluated based on Eq. 7. 𝑟𝑚𝑎𝑥 is estimated as 2.24 μm and 1.96 μm for Barnett and Haynesville samples respectively based on first intrusion pressure of mercury.


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Furthermore, following Yu and Li 44, fractal dimension is estimated as a function of porosity, and pore throat radius as: D  3

ln  

(8)

ln  rmin rmax 

Using Eq. 8, fractal dimension is calculated as 2.6; next, coordination number as a function of sample size is estimated using Eq. 7 as shown in Figure 8. Results indicate that for smallest sample size if average coordination number is estimated as 4 for Barnett and 4.5 for Haynesville, then these values reduce to 2.3 and 2 when samples are at plug size. Although permeability reduction is two to three orders of magnitude with increasing sample size (Table 2), this is can be explained with 50% reduction in average coordination. In previous studies, this has been explained with high tortuosity values, which based on Hu et al. 20 and Sun et al. 38 tortuosity in shale formations can be as high as 7000. Barnett

Haynesville

5.0

Average Coordination Number

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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4.5 4.0 3.5 3.0

y = 3.6554x-0.154 R² = 0.9565

2.5 2.0

y = 4.1054x-0.21 R² = 0.9437

1.5 0

5

10

15

20

25

30

Sample Size, mm

Figure 8. Average coordination number as a function of sample size for the Barnett and Haynesville shale samples


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4. Conclusions We evaluated accessible/interconnected porosity and hydraulic connectivity as a function of sample size for Barnett and Haynesville shale formations. Also, we estimated coordination number for both formations using percolation theory. The main contributions of this work are as follows: • MICP measured accessible porosity values and matrix permeability strongly depends on the sample size; both of them decrease with increasing sample size. • Accessible porosity and permeability reduction with sample size is more pronounced in Haynesville than Barnett for the samples we studied here. • The estimated average coordination number for both shale plays decreases with the sample size: it decreases from 4 (for the smallest sample) to 2 for the plug-size sample. Acknowledgments Acknowledgment is made to the donors of the American Chemical Society Petroleum Research Fund for support (or partial support) of this research (PRF 56929-DN19). We also thank Unconventional Shale Gas Consortium and specifically Dr. Ali Tinni for providing the experimental data. Nomenclature D: fractal dimension k: permeability l : distance from exterior or size of rock sample

m: power law function exponent in Eq. 3 p: connection probability of accessible pores 𝑝𝑐 : the critical percolation threshold


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𝑟𝑚𝑎𝑥 : the largest accessible pore size 𝑟𝑚𝑖𝑛 : the smallest accessible pore size (𝑆𝑏 /𝑝𝑐 )𝐴 : apex of bulk volume mercury saturation to capillary pressure ratio Vb: sample bulk volume VHg: total volume of mercury injected z: coordination number

β: exponent in Eq. 4 Γ: interconnectivity parameter ϕ: porosity χ: correlation length beyond with accessible pores become constant 𝜃: the ratio of pore volume to the sum of the pore and solid volumes in the fractal model

References 1. Bhandari, A. R., Flemings, P. B., Polito, P. J., Cronin, M. B., & Bryant, S. L. (2015). Anisotropy and stress dependence of permeability in the Barnett shale. Transport in porous media, 108(2), 393-411.

2. Chalmers, R.C., Bustin, R.M., and Power, I.M., 2012. Characterization of Shale Gas Pore Systems by Porosimetry, Pycnometry, Surface Area, and Field Emission Scanning Electron Microscopy/Transmission Electron Microscopy Image Analyses: Examples from the Barnett, Woodford, Haynesville, Marcellus, and Doig Units. AAPG Bull. 96 (6), 1099-1119.


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3. Civan, F., 2001. Scale effect on porosity and permeability: kinetics, model and correlation. AIChE J. 47, 271–287.

4. Civan, F., 2011. Porous Media Transport Phenomena. Wiley, pp. 15

5. Comisky, J. T., Santiago, M., McCollom, B., Buddhala, A., & Newsham, K. E. (2011, January 1). Sample Size Effects on the Application of Mercury Injection Capillary Pressure for Determining the Storage Capacity of Tight Gas and Oil Shales. Society of Petroleum Engineers. doi:10.2118/149432-MS

6. Comisky, J. T., Newsham, K., Rushing, J. A., & Blasingame, T. A. (2007, January). A comparative study of capillary-pressure-based empirical models for estimating absolute permeability in tight gas sands. In SPE Annual Technical Conference and Exhibition. 7. Curtis, M. E., Ambrose, R. J.&Sondergeld, C. H. Investigating the Microstructure of Gas Shales by FIB/SEM Tomography & STEM Imaging

8. Curtis, M.E., Cardott, B.J., Sondergeld, C.H., and Rai, C.S., 2012. Development of Organic Porosity in The Woodford Shale with Increasing Thermal maturity. International Journal of Coal Geology. 103, 26–31.

9. Daigle, H., 2016. Application of critical path analysis for permeability prediction in natural porous media. Adv. Water Resour. 96, 43-54


18

Page 19 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

10. Daigle, H., Johnson, A., 2016. Combining mercury intrusion and nuclear magnetic resonance measurements using percolation theory. Transp. Porous Media 111, 669-679

11. Dastidar, R., Sondergeld, C.H., and Rai, C.S.: "An Improved Empirical Permeability Estimator from Mercury Injection for Tight Clastic Rocks," Petrophysics, Vol. 48, No. 3, (June, 2007) 186-187.

12. Davudov, D., Ghanbarnezhad Moghanloo, R., Dadmohammadi, Y., Curtis, M., Javadpour, F., 2016. Impact of Pore Topology on Gas Diffusion and Productivity in Barnett and Haynesville Shale Plays, ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering

13. Davudov, D., Moghanloo, R. G., Lan, Y. et al. 2017. Investigation of Shale Pore Compressibility Impact on Production with Reservoir Simulation. Presented at the SPE Unconventional Resources Conference, Calgary, 15–16 February. SPE-185059-MS. https://doi.org/10.2118/185059-MS.

14. Davudov, D., Moghanloo, R. G., and Yuan, B. 2016. Impact of Pore Connectivity and Topology on Gas Productivity in Barnett and Haynesville Shale Plays. Presented at the Unconventional Resources Technology Conference, San Antonio, Texas, 1–3 August. URTEC-2461331-MS. https://doi.org/10.15530/URTEC-2016-2461331.


19

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 24

15. Dewers, T. A., Heath, J., Ewy, R., & Duranti, L. (2012). Three-dimensional pore networks and transport properties of a shale gas formation determined from focused ion beam serial imaging. International Journal of Oil, Gas and Coal Technology, 5(2-3), 229-248.

16. Ewing, R.P., Horton, R., 2002. Diffusion in sparsely connected pore spaces: temporal and spatial scaling. Water Resources Research 38 (12), 1285. doi:10.1029/2002WR001412.

17. Ewing, R. P., Q. H. Hu, and C. X. Liu (2010), Scale dependence of intra-granular porosity, diffusivity, and tortuosity, Water Resour. Res., 46, W06513, doi:10.1029/2009WR008183.

18. Ewing, R. P., C. X. Liu, and Q. H. Hu (2012), Modeling intragranular diffusion in low connectivity granular media, Water Resour. Res., 48, W03518, doi:10.1029/2011WR011407.

19. Hu, Q., Ewing, R.P., Dultz, S., 2012. Low pore connectivity in natural rock. J. Contaminant Hydrol. 133, 76–83.

20. Hu, Q., Ewing, R. P., & Rowe, H. D. (2015). Low nanopore connectivity limits gas production in Barnett formation. Journal of Geophysical Research: Solid Earth, 120(12), 8073-8087.

21. Huet, C. C., Rushing, J. A., Newsham, K. E., & Blasingame, T. A. (2005, January). A modified Purcell/Burdine model for estimating absolute permeability from mercury-injection capillary pressure data. In International Petroleum Technology Conference. International Petroleum Technology Conference.


20

Page 21 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

22. Hunt, A., Ewing, R., & Ghanbarian, B. (2014). Percolation theory for flow in porous media (Vol. 880). Springer.

23. Jin, Y., Li, X., Zhao, M., Liu, X., & Li, H. (2017). A mathematical model of fluid flow in tight porous media based on fractal assumptions. International Journal of Heat and Mass Transfer, 108, 1078-1088.

24. Kang, S.M., Fathi, E., Ambrose,R.J., Akkutlu, I.Y., Sigal, R.F.:Carbon dioxide storage capacity of organic-rich shales. SPE J. 16(4), 842–855 (2011). doi:10.2118/134583-PA. SPE 134583 25. Katz, A.J. and Thompson, A.H.: "Quantitative Prediction of Permeability in Porous Rock," Physical Review B, Vol. 34, No. 11, (December 1986) 8179-8181 26. Katz, A.J. and Thompson, A.H.: "Prediction of Rock Electrical Conductivity from Mercury Injection Measurements," Journal of Geophysical Research, Vol. 92, No. B1 (Jan. 1987), 599607.

27. King Jr, H. E., Eberle, A. P., Walters, C. C., Kliewer, C. E., Ertas, D., & Huynh, C. (2015). Pore architecture and connectivity in gas shale. Energy & Fuels, 29(3), 1375-1390.

28. Kuila, U., Prasad, M., Derkowski, A., & McCarty, D. K. (2012, January). Compositional controls on mudrock pore-size distribution: an example from Niobrara formation. In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers.


21

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 24

29. Loucks, R.G., Reed, R.M., Ruppel, S.C., and Jarvie, D.M., 2009. Morphology, Genesis, and Distribution of Nanometer-Scale Pores in Siliceous Mudstones of the Mississippian Barnett Shale. Journal of Sedimentary Research 79: 848-861.

30. Loucks, R.G., Reed, R.M., Ruppel, S.C., and Hammes, U., 2012. Spectrum of Pore Types and Networks in Mudrocks and a Descriptive Classification for Matrix-Related Mudrock Pores. AAPG Bulletin 96 (6): 1071–1098.

31. Ojha, S. P., Misra, S., Tinni, A., Sondergeld, C., & Rai, C. (2017). Relative permeability estimates for Wolfcamp and Eagle Ford shale samples from oil, gas and condensate windows using adsorption-desorption measurements. Fuel, 208, 52-64.

32. Pittman, E. D. (1992). Relationship of porosity and permeability to various parameters derived from mercury injection-capillary pressure curves for sandstone (1). AAPG bulletin, 76(2), 191198.

33. Potter, P.E., Maynard, J.B., and Depetris, P.J., 2005. Mud and Mudstones: Introduction and Overview. Berlin: Springer-Verlag.

34. Revil, A., 2002. The hydroelectric problem of porous rocks: thermodynamic approach and introduction of a percolation threshold. Geophys. J. Int. 151, 944–949


22

Page 23 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

35. Sahimi, M. (1994), Applications of Percolation Theory, Taylor and Francis, London.

36. Stauffer, D., and A. Aharony (1994), Introduction to Percolation Theory, 2nd ed., Taylor and Francis, London.

37. Swanson, B. F. (1981). A simple correlation between permeabilities and mercury capillary pressures. Journal of Petroleum Technology, 33(12), 2-498.

38. Sun, M., Yu, B., Hu, Q., Yang, R., Zhang, Y., & Li, B. (2017). Pore connectivity and tracer migration of typical shales in south China. Fuel, 203, 32-46.

39. Tinni, A., Fathi, E., Agarwal, R., Sondergeld, C. H., Akkutlu, I. Y., & Rai, C. S. (2012, January). Shale permeability measurements on plugs and crushed samples. In SPE Canadian Unconventional Resources Conference. Society of Petroleum Engineers.

40. Tinni, A., Sondergeld, C. H., and Rai, C. S., "Particle size effect on porosity and specific surface area measurements of shales." International symposium of the society of core analysts, Avignon, France, September 8–11, 2014. 2014.

41. Vermylen, J.P.: Geomechanical Studies of the Barnett Shale, Texas, USA. PhD Thesis, Stanford University, Palo Alto, California, pp. 143 (2011)


23

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 24

42. Vyssotsky, V. A., Gordon, S. B., Frisch, H. L., & Hammersley, J. M. (1961). Critical percolation probabilities (bond problem). Physical review, 123(5), 1566.

43. Webb, P.A. 2001. An introduction to the physical characterization of materials by mercury intrusion porosimetry with emphasis on reduction and presentation of experimental data. Micromeritics Instrument Corporation

44. Yu, B., Li, J.: Some fractal characters of porous media. Fractals 9(03), 365–372 (2001)

45. Yuan, Y., Doonechaly, N. G., & Rahman, S. (2016). An analytical model of apparent gas permeability for tight porous media. Transport in porous media, 111(1), 193-214.


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Scale-Dependent Pore and Hydraulic Connectivity of Shale Matrix

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