Gas permeability tests on core plugs from unconventional reservoir rocks under controlled stress: A comparison of different transient methods

Accepted Manuscript Gas permeability tests on core plugs from unconventional reservoir rocks under controlled stress: a comparison of different transient methods Garri Gaus, Alexandra Amann-Hildenbrand, Bernhard M. Krooss, Reinhard Fink PII:

S1875-5100(19)30051-4

DOI:

https://doi.org/10.1016/j.jngse.2019.03.003

Reference:

JNGSE 2836

To appear in:

Journal of Natural Gas Science and Engineering

Received Date: 24 November 2018 Revised Date:

1 March 2019

Accepted Date: 2 March 2019

Please cite this article as: Gaus, G., Amann-Hildenbrand, A., Krooss, B.M., Fink, R., Gas permeability tests on core plugs from unconventional reservoir rocks under controlled stress: a comparison of different transient methods, Journal of Natural Gas Science & Engineering, https://doi.org/10.1016/ j.jngse.2019.03.003. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT 1

Gas permeability tests on core plugs from unconventional reservoir rocks under

2

controlled stress: a comparison of different transient methods

3

Garri Gaus1*, Alexandra Amann-Hildenbrand1, Bernhard M. Krooss1, Reinhard Fink1

4

1

5

Resources Group (EMR), Lochnerstr. 4-20, RWTH Aachen University, D-52062 Aachen,

6

Germany

7

* Corresponding author: [email protected]

8

Abstract

RI PT

SC

EP

TE D

M AN U

Accurate and routinely applicable methods to determine porosities and permeability coefficients are needed in order to ensure effective hydrocarbon recovery in shale and tight sandstone plays. In this study 129 gas uptake measurements (“GRI method”, “inflow” experiments) were performed on core plugs from three unconventional reservoir lithotypes (oil shales, gas shales and tight gas sandstones) under elevated effective stress conditions. The results were compared to those from “flow-through” tests (standard pulse decay) under similar experimental conditions, e.g. the same gas type and pore pressure range. The samples covered a porosity range from 1.3% to 12%. Equilibration times ranged from 102 s to 104 s and permeability coefficients from 10-18 to 10-21 m2. In order to successfully determine apparent gas permeability coefficients and porosities and to reliably interpret fluid dynamic effects from gas uptake data it is necessary to ensure a sufficiently high excess pressure drop during the uptake tests. This can be controlled by adjustment of the reservoir to pore volume ratio and initial differential pressure. Permeability coefficients derived from uptake tests on all six samples do not show any systematic deviations from those obtained from flow-through measurements. Best results were achieved for a core plug from the Lower Palaeozoic Alum Shale (Djupvik, Öland, Sweden), where Klinkenberg regressions of inflow and flow-through differ only by 4% (slope) and 10% (y-axis intercept). Here, the gas storage capacity ratio was ≈ 2.5 and excess pressure drops ranged from 0.1 to 1.2 MPa. Generally the measurement errors were lowest when the excess pressure drops during uptake were at least 0.05 MPa for all samples. Excess pressure drops of less than 0.05 MPa resulted in coefficients of variance of single apparent gas permeabilities of ≈ 10% to 100%, whereas excess pressure drops of > 0.05 MPa resulted in coefficients of variance of ≈ 2% to 15%. We show that it is possible to adjust the initial conditions of inflow measurements such that Klinkenberg-corrected permeability coefficients and gas slippage factors can be readily determined. This will contribute significantly to a better understanding of the effects of anisotropy and/or the pore structure on the transport properties of unconventional lithotypes under elevated stress conditions. However, standard deviations of single apparent permeability coefficients derived from inflow experiments are higher by up to one order of magnitude than for those obtained from flow-through tests under all tested conditions.

AC C

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

Institute of Geology and Geochemistry of Petroleum and Coal, Energy and Mineral

1

ACCEPTED MANUSCRIPT 38 39

Keywords: Gas permeability; Pressure transient analysis; Klinkenberg effect; Porosity; Unconventional reservoir

40

1 Introduction

42 43 44 45 46 47 48 49 50

The study of transport processes in low-permeable porous rocks has received increasing attention in research over the past four decades. This is due to their relevance in geotechnical applications such as carbon dioxide storage, nuclear & water waste disposal, and mining (Gensterblum et al., 2015) but also in the exploitation of conventional and unconventional hydrocarbon resources (gas shales and tight sandstones). The economical exploitation of unconventional reservoirs often requires horizontal drilling and hydraulic fracturing. Due to the high costs of these technologies an optimal reservoir assessment is essential. Therefore, accurate and routinely applicable methods to determine the pore volume and permeability are needed.

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73

Different laboratory methods, typically using cylindrical core or plugs, are used to determine permeability coefficients and porosity of porous rocks. These can be subdivided into steady state and non-steady state tests. The latter can be designed either as flow-through or as inflow experiments. A classical “flow-through” type measurement is the pressure pulse decay (PPD) technique (Brace et al., 1968; Dicker & Smits, 1988; Jones, 1997). This method is less time consuming than a typical steady state flow test and, within a well-calibrated system, of high accuracy and reproducibility. The experimental PPD protocol consists of the creation of a pressure difference across the faces of a cylindrical sample plug separating two closed reservoirs (upstream and downstream reservoir) of known volume, and continuous monitoring of the successive pressure transient. Permeability coefficients are obtained by solving the diffusion equation, which is derived by combining the differential form of Darcy’s law and the continuity equation (Jones, 1997; Ghanizadeh et al., 2014). An “inflow” type of experiment analyses the gas uptake rate into a sample, which is placed between two or one calibrated reservoir(s) (plane-parallel sheet, Crank, 1975; Cui and Bustin 2010; Yang et al., 2016; Peng & Loucks 2016). This approach is comparable to the “Gas Research Institute” (GRI) method usually applied to crushed rocks (cuttings; assuming spherical particle geometry) when cores or plugs are not available. Here the pressure drop observed after initial pressurisation is recorded and the permeability coefficient is obtained from the combined endmember solution for the diffusion in a plane sheet and effective gas diffusivity equation as given in Crank (1975). As a by-product, the porosity can be determined from these experiments. A detailed review of methods to measure low permeability rocks is given in Sander et al. (2017).

74 75 76

Publications on inflow tests with rock cuttings are relatively abundant (e.g. Luffel & Guidry, 1992; Guidry et al., 1996; Cui & Bustin, 2009; Heller et al., 2014; Ghanizadeh et al., 2015; Peng & Loucks, 2016; Blount et al., 2017; Fisher et al., 2017; Fink et al., 2017b).

AC C

EP

TE D

M AN U

SC

RI PT

41

2

ACCEPTED MANUSCRIPT Usage of crushed rock samples may offer advantages over intact core measurements with respect to the time needed to perform a measurement and the costs. However, so far it was not clearly demonstrated that crushed rock permeability is reproducible using different apparatuses and evaluations (Fisher et al., 2017). Additionally, fluid dynamic effects (slip flow) usually are not accounted for and measurements are performed at relatively small pore pressures and ambient conditions (Peng & Loucks, 2016). Comparisons with conventional core analysis methods often reveal large gaps, which is not surprising due to severe differences in boundary conditions. Only a few authors have addressed the inflow tests on intact cores (Cui and Bustin, 2010; Yang et al., 2016; Peng & Loucks 2016) and a detailed methodological study was either not possible due to the limited amount of experimental data or because of non-comparable measurement conditions (e.g. gas type, pore pressure range). Accordingly, the primary aim of this study was to compare the results obtained by these two different types of experiments (flow-through vs. inflow). For flow-through and inflow measurements, the same apparatus and gas type was used, and experiments were performed successively on the same sample and within the same pressure (effective stress) regime to yield best comparability. Key-parameters for comparison are the apparent and Klinkenbergcorrected permeability coefficients.

95

2 Theory and evaluation procedures

96

2.1 Transient flow-through test

SC

M AN U

TE D

k

= −

EP

Brace et al. (1968) describe a transient procedure to determine gas permeability coefficients on low-permeable rocks. This method was later modified by Dicker & Smits (1988) and Jones (1997). A pressure pulse is imposed across rock sample placed between two reservoirs of known volume. The evaluation is based on the mass balance equation and Darcy´s law (Dicker & Smits 1988; Jones, 1997; Ghanizadeh et al. 2014). The pressure transient is evaluated to obtain the apparent gas permeability coefficient:

(

AC C

97 98 99 100 101 102

RI PT

77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94



(1)

)

103

Here, µ is the dynamic gas viscosity [Pa s], L and A are the sample length and cross-

104

) and

105 106 107 108 109 110

sectional area [m], P

is the mean pressure of the gas [Pa] (P

=

V !" and V#! are the upstream and downstream compartments [m³]. The value of s% is the slope of the plot of the logarithm of the pressure difference between the reservoirs (log(ΔP)) versus time (t). The correction factor f% takes into account the time delay resulting from the filling of the pore system of the sample (inflow effect). It depends on the gas-storage capacity ratios of the sample pore volume V"!+ and the upstream and downstream compartment:

3

ACCEPTED MANUSCRIPT f% = 111

,-





#

(2) (

#),

Here, θ% is the first solution of tan(θ) = ,- 2 # , with a and b being gas storage ratios of 3

3

112

the sample and upstream or downstream compartments (a =

113 114

reservoir volumes are much larger than the sample pore volume, then the contribution of f% becomes negligible.

; b =

3

4

). If the

RI PT

4

can be determined by opening the downstream reservoir or keeping Alternatively, k it at constant pressure by appropriate measures. As a result, the compressive storage of the downstream reservoir is effectively infinite and equation 1 becomes: k



= − ,-



(



)

(3)

where f% ≈

119

2.2 Inflow method – modified GRI method

120 121 122 123 124 125 126 127

Cui et al. (2009) describe an approach to determine the gas uptake rate into rock samples placed in a defined volume by monitoring the decline of a gas pressure pulse. The permeability coefficients are computed under the assumption of a defined sample size and geometry (e.g. spherical particles with identical diameters). In the present study, the gas phase was allowed to enter cylindrical samples from the two faces while the sides of the cylinder were sealed. The gas uptake was interpreted in terms of (pressure) diffusion into a plane sheet from a stirred solution of limited volume (Crank, 1975; Yang et al., 2016).

130

TE D

Here L is the sample length [m], ϕ the porosity, c the gas compressibility [Pa-1] and α% the first positive root of tan(α ) = −K @ α . K @ is the ratio of the system void volume (V+ , 3

V !" & V#! ) and the pore volume (K @ = 3 A

BC

4

). The parameter s is the slope of the plot of

131

the logarithm of the fractional gas uptake (Fr = 1 −

132

(

133 134 135 136

(3)

EP

α%

AC C

128 129

= −

L (2) ϕμc s

M AN U

118

k

as b → 0.

SC

115 116 117

3

∆M! (N+) O

). Here, ρ

Q

(GH %)∗(J J

K 2J

K 2J B

)

) versus time

is the average initial gas density in the void volume (V+ , V !" &

V#! ) after expansion from Vref to Vtop and Vbot, ρ R denotes the initial gas density in V !" , V#! and V"!+ prior to expansion and ρ is the density of the gas at experimental time (t). A detailed explanation of the balance equations is given in Cui et al. (2009) and Yang et al. (2016).

4

ACCEPTED MANUSCRIPT 2.3 Klinkenberg effect

138 139 140 141 142 143 144 145 146 147 148 149 150

Deviations of the apparent permeability coefficient from the intrinsic permeability coefficient in fine-grained porous media are mainly due to slip flow (“Klinkenberg effect”). Slip flow occurs when molecule–wall collisions become more frequent as compared to molecule-molecule collisions. This is the case when the mean free path length of the gas molecules (distance travelled between two intermolecular collisions) is in the order of the pore diameters as will typically occur at low gas pressures and/or gas flow in very narrow (sub-µm) transport pores (Kundt & Warburg 1875, Klinkenberg, 1941). Therefore, the phenomenon becomes increasingly relevant for low-permeable rocks with gas transport in micro- and meso-pores (Ghanizadeh et al., 2014). Under these conditions the gas can no longer be considered as a uniform fluid phase in terms of continuum fluid mechanics (with defined viscosity or density). The “apparent” permeability (k ) can be related to the “intrinsic” or “liquid phase” gas permeability (k S ) according to the Klinkenberg equation: = k S (1 +

UVM +

) = k S W1 +

#

X

M AN U

k

SC

RI PT

137

(4)

Here, b is the gas slippage factor [MPa], P the mean pore pressure [Pa], C the dimensionless Adzumi constant (0.9) and r the mean effective transport pore radius [m]. The additional velocity component (slip factor b) is thus related to the mean free path of

154 155 156

the gas molecules (l) and the transport pore radius. The intrinsic permeability coefficient k S is determined from the y-axis intercept of the regression line of k -1. versus P

157

2.4 Stressed and unstressed pore volume measurements

158 159

The pore volumes (V"!+ ) of the dry cylindrical plugs under defined axial and confining stress conditions were determined using the following mass balance equation:

160 161 162 163 164 165 166 167 168 169

J4 Y 2J Z V J Z 2JK +

− V[

AC C

V"!+ =

EP

TE D

151 152 153

[





(5)

Here, ρ+ and ρQ are the gas densities [kg/m³] in the reference volume Vref and the dead volume of the set-up (V[ [ = V !" + V#! ) before pressure equilibration and ρ ] is the gas density in the entire system (V+ + V[ [ ) after pressure equilibration. Helium densities were calculated from the pressure and temperature readings using the

equation of state (ρ =

^

_`

) within the GERG-2004 software (Kunz et al., 2007).

In addition to the pore volume measurements under controlled stress, He-pycnometry measurements were performed on the unconfined plugs. The apparatus and procedure have been described in detail previously (Ghanizadeh et al., 2014). Briefly, the skeletal (“solid”) volume of the rock samples is determined by helium expansion from a calibrated reference volume into a sample cell of known volume under isothermal 5

ACCEPTED MANUSCRIPT 170 171

conditions. The mass balance equation yields the following expression for the skeletal volume V a : Va =V@−b

ρ+ − ρ ρ ]−ρ

]

@

(6)

V+ c

Here, V+ and V @ are the volumes of the reference cell and the sample cell, respectively, ρ+ and ρ @ are the gas densities in the corresponding cells prior to expansion, and ρ ] is the gas density after pressure equilibration between the two volumes.

176

In both procedures, the porosity ϕ and the specific pore volume V " are obtained by:

V " =

3de 3

V" V# − V a ϕ = = m m (1 − ϕ)ρ a

SC

ϕ=1−

RI PT

172 173 174 175

(7) (8)

With ρ a denoting the skeletal density. In both cases a separate determination of the bulk sample volume V# is required.

179

3 Samples

180 181 182 183 184 185 186 187 188 189

In this study, three unconventional lithotypes were investigated: oil shale samples from the Eagle Ford and Kimmeridge formations, potential gas shale samples from the Lower Palaeozoic carbonaceous Alum Shale (Djupvik, Öland, Sweden; Schovsbo & Buchardt, 1994), Lower Cretaceous Garau (Iran), the Upper Jurassic Bossier formations (USA) and an Upper Carboniferous tight gas sandstone from Germany (Pennsylvanian, Westphalian D). Porosity data, total organic carbon (TOC) contents, vitrinite reflectance and mineral compositions of the samples are listed in Table 1. Cylindrical cores with a diameter of 38 mm were drilled perpendicular to bedding from each sample set, except for the Bossier shale (parallel to bedding). All sample plugs were dried at 105 °C until weight constancy was reached, but for at least 24 hours.

190 191

Table 1: Porosity, specific pore volume, total organic carbon content (TOC), vitrinite reflectance (VRr) and mineral composition (XRD meas.) for the samples used in this study.

AC C

EP

TE D

M AN U

177 178

Porosity*

Specific pore volume*

[%]

[cm³g-1]

Alum Shale 1

11.5

0.052

8.2

0.5

57

33

0.2

Bossier Shale2

7.7

0.031

2.2

2.2

30

56

10

Sample

6

TOC

VRr Q+F Clays Carbonates

[wt.%] [%]

[wt.%]

ACCEPTED MANUSCRIPT 11.2

0.050

4.5

0.9

26

8

62

Carbonaceous Shale, Garau Formation4

2.0

0.007

0.9

1.1

12

3

82

Kimmeridge Shale5

7.0

0.045

45

0.5

8

40

10

Westphalian D sandstone

2.3

0.009

-

-

70

27

3

RI PT

Eagle Ford Shale3

*measured by He-pycnometry on unconfined sample plugs. Geochemical and mineralogical data from 1Ghanizadeh et al., 2014, 2Fink et al., 2017b, 3Gasparik et al., 2013, 4Shabani et al., 2018, 5Li et al., 2017. [Q+F]: quartz + feldspar.

195

4 Experimental set-up and testing procedure

196 197 198 199 200 201 202

Single-phase gas permeability and pore volume measurements were performed in a triaxial flow cell, which enabled loading of the cylindrical sample plugs with axial and confining pressure of up to 40 MPa (Figure 1). In the experimental set-up the samples are placed between stainless steel pistons. Porous steel discs between the pistons and the sample are used to distribute the fluid over the sample surface. A double-layered sleeve system (inner sleeve: 0.15 mm lead foil; 0.1 mm outer sleeve aluminium tube) separates the sample from the confining pressure chamber and prevents by-passing.

203 204 205 206 207

As shown in Figure 1, V+ (reference volume) is the volume between valves V1, V2 and V3, whereas V !" and V#! are the volumes between V3 and the sample surface and V2 and the sample surface, respectively. Prior to the experiments, V+ , V !" and V#! were calibrated by helium expansion at experimental pressure conditions. For this purpose, a stainless-steel cylinder was installed in place of the rock sample.

208 209 210 211 212 213 214

In the present study permeabilities and pore volumes were measured at 30 °C while unloading the samples from 40 to 10 MPa confining pressure. After loading of the sample to the respective confining pressure, a leak test was performed with helium at the maximum pore pressure. At a given confining pressure, alternating cycles of flowthrough and inflow experiments were run with successively increasing pore pressures to reduce stress effects. Alternatively, flow-through tests with constant downstream pressure and inflow measurements were performed successively.

AC C

EP

TE D

M AN U

SC

192 193 194

7

ACCEPTED MANUSCRIPT

Vtop Axial load

Vbot

V3

Ptop

Vref

V1

Sample

Pref

RI PT

Helium connection

Vacuum pump

Pbot V2 215

V0

Methane connection

SC

Confining pressure

Porous steel disc

Figure 1: Thermostated (30°C +/-0.3°C) experimental set-up for specific pore volume (hij ) and apparent gas permeability measurements under controlled effective stress. Permeability experiments can be performed with the inflow or flow-through method. Enclosed volumes hklm , hnlk and hopq , (volume between valves V1,V2 and V3) are calibrated by helium expansion.

220

5 Results and Discussion

221

5.1 Inflow measurements

222 223 224 225 226 227 228 229 230 231 232 233

Inflow permeability measurements utilize data that are recorded during porosity determination at experimentally induced overburden conditions. Therefore, they provide a simple means for determining the stress-dependence of gas permeability in low-permeable rocks. In this study, 129 apparent permeability coefficients were obtained from inflow measurements at increasing mean fluid pressures (up to 18 MPa) and defined initial pressure pulses (up to 5 MPa). Equilibration times ranged from 10² to 104 s. The flow tests were started at the maximum confining pressures. Confining pressures were then decreased stepwise from 40 to 10 MPa. Experimental results reported here are therefore representative of the first unloading cycle. The first loading path is known to be dominated by initial compaction of structures, which result from drilling, unloading to surface conditions, plug preparation and storage (McKernan et al., 2014).

234

Selected experimental results are shown in Figure 2 in terms of the normalized pressure

235 236 237 238 239

AC C

EP

TE D

M AN U

216 217 218 219

decline curves (Fr; 1 −

(GH %)∗(J J

K 2J

K 2J B

)

) as a function of time. All data show a reasonably

linear relationship between log10(Fr) and time in the late stage, which is a prerequisite to calculate permeability coefficients. The slope of log10(Fr) vs. time increases with pore pressure. Scattering of the data increases as the pressures approach the equilibrium values, particularly for samples with small pore volumes (Figure 2 d & f, Table 1, 8

ACCEPTED MANUSCRIPT porosity of ~2%), because the limit of the resolution of the pressure transducer is reached. For the Westphalian D sample (Figure 2f) more than 50% of the total gas uptake occurred during the first few seconds. This phenomenon was not observed for other samples.

244 245 246 247 248 249 250 251 252 253 254 255 256 257

The apparent gas permeability coefficients and specific pore volumes obtained from these measurements are shown in Figure 3. Apparent permeability coefficients range from 1600 nD to 1 nD and decrease significantly with increasing pore pressure. Specific pore volumes range from 0.005 to 0.045 cm³g-1 (equivalent to 0.013 and 0.1 fractional porosity) and generally increase slightly with increasing pore pressure and decreasing confining pressure. Similar observations are reported in numerous publications and are attributed to a combination of fluid-dynamic and poro-mechanic effects (e.g. Fink et al., 2017a). For two samples the experimental data deviate from the general trend at higher fluid pressures. Here both, apparent permeability and the specific pore volume, increase for the Garau shale at pore pressures > 5 MPa (P@! = 10 MPa) and for the Kimmeridge clay at pore pressures > 10 MPa (P@! = 40 MPa, Figure 3d & e). This is a clear indication of poro-elastic pore widening, superimposing the fluid dynamic effect of gas slippage (Fink et al., 2017a). Therefore, these values had to be excluded when determining the Klinkenberg-corrected permeability coefficients.

AC C

EP

TE D

M AN U

SC

RI PT

240 241 242 243

9

ACCEPTED MANUSCRIPT 0

100

200

300

Time [s] 400 500

600

700

800

0

1.000

100

200

300

Time [s] 400 500

600

700

800

1.000 Pmean: 0.5 MPa Pmean: 1.0 MPa Pmean: 1.3 MPa

0.100

0.100

Pmean: 1.6 MPa

Fr [-]

Fr [-]

Pmean: 2.6 MPa

Pmean: 0.4 MPa Pmean: 0.9 MPa Pmean: 1.7 MPa

0.010

Pmean: 4.8 MPa

0.010

a

Pmean: 10.5 MPa

0.001

0

500

Time [s] 1000

1500

0.001

2000

0 1.000

0.100

0.100

Fr [-]

Fr [-]

1.000

15000

Pmean: 2.5 MPa Pmean: 4.6 MPa Pmean: 9 MPa Pmean: 13 MPa Pmean: 18 MPa

TE D

Fr [-]

Pmean: 1.3 MPa

Fr [-]

0.100

Pmean: 6.5 MPa

e

100

200

300

Time [s] 400 500

600

700

800

Pmean: 0.6 MPa Pmean: 1.2 MPa Pmean: 1.7 MPa Pmean: 3 MPa Pmean: 5 MPa Pmean: 7.7 MPa

0.010

0.001

f

EP

Figure 2: Log-linear plot of normalized gas uptake (Fr) from inflow measurements for different mean pore pressures and constant confining pressures: (a) Bossier Shale at 40 MPa confining pressure, (b) Eagle Ford Shale at 10 MPa confining pressure, (c) Alum Shale at 30 MPa confining pressure, (d) Garau Shale at 10 MPa confining pressure, (e) Kimmeridge Shale at 40 MPa confining pressure and (f) Westphalian D sandstone at 30 MPa confining pressure.

AC C

259 260 261 262 263

0

20000

d

Pmean: 7.8 MPa

0.001

1.000

Pmean: 3.3 MPa

258

800

Pmean: 3.0 MPa

M AN U

Time [s] 10000

0.100

0.001

700

Pmean: 6.4 MPa

c

1.000

0.010

600

Pmean: 5.0 MPa

Pmean: 12 MPa Pmean: 15.6 MPa

5000

Time [s] 400 500

Pmean: 4.0 MPa

Pmean: 5.5 MPa Pmean: 9.2 MPa

0

300

Pmean: 2.0 MPa

0.010

Pmean: 2.4 MPa

0.001

200

Pmean: 1.0 MPa

Pmean: 0.4 MPa

0.010

100

b

SC

Pmean: 5.1 MPa Pmean: 8.9 MPa

RI PT

Pmean: 3.0 MPa

10

ACCEPTED MANUSCRIPT 0.030

Apparent permeability at 40 MPa Specific pore volume at 40 MPa

0.010

200

0.005

a

0.000 8

10

0.040 0.030

150

0.020

100

0.010

4

6 8 pmean [MPa]

10

12

5.0

0.030

0.020

1.0

0.010

100

50

d

0.000

5

10 pmean [MPa]

15

5

20

0.004

2

0.003 0.002

Apparent permeability at 10 MPa Specific pore volume at 10 MPa

0.001 0.000

4

400

6 pmean [MPa]

8

10

0.007

Apparent permeability at 30 MPa Specific pore volume at 30 MPa

0.006

300

0.005 0.004

200

0.003 0.002

100

Apparent permeability at 40 MPa Specific pore volume at 40 MPa

e

4

0.005

150

0

TE D

2.0

3 pmean [MPa]

0.006

0

0.040

3.0

200

14

0.050

4.0

2

0.008

M AN U 0.000

2

0.000

1

0.007

Apparent permeability [nD]

Apparent permeability [nD]

b

0

250

200

c

Apparent permeability at 10 MPa Specific pore volume at 10 MPa

0.050

50

Apparent permeability [nD]

0.010

0

250

264

400

12

Apparent permeability at 30 MPa Specific pore volume at 30 MPa

0

0.020

600

SC

6 pmean [MPa]

Apparent permeability [nD]

4

Specific pore volume [cm³g-1]

2

300

0.0

800

200

0

0

0.030

1000

Specific pore volume [cm³g-1]

400

1200

0.001

f

0 0

Specific pore volume [cm³g-1]

0.015

0.040

1400

Specific pore volume [cm³g-1]

600

1600

RI PT

0.020

Apparent permeability [nD]

800

Specific pore volume [cm³g-1]

0.025

0

0.050

1800

1000

0

2000

Specific pore volume [cm³g-1]

Apparent permeability [nD]

1200

0.000 2

4

6 pmean [MPa]

8

10

Figure 3: Specific pore volume and apparent permeability from inflow measurements for different pore pressure ranges and constant confining pressure: (a) Bossier Shale at 40 MPa confining pressure, (b) Eagle Ford Shale at 10 MPa confining pressure, (c) Alum Shale at 30 MPa confining pressure, (d) Garau Shale at 10 MPa confining pressure, (e) Kimmeridge Shale at 40 MPa confining pressure and (f) Westphalian D sandstone at 30 MPa confining pressure.

270 271 272 273 274 275 276 277 278 279 280

A major source of error when determining apparent permeability coefficients from inflow measurements lies in the determination of absolute porosity and its stressdependence. Figure 4 shows apparent permeability coefficients as a function of the mean fluid pressure using values of the porosity measured under stress (Figure 3) and at ambient conditions (unstressed porosity from He pycnometry). The error bars indicate deviations assuming an uncertainty of ±0.5% (abs.) for porosity values, which is a reasonable assumption. Figure 4 clearly shows that an overestimation of the pore volume (unstressed conditions), will lead to an underestimation of the gas storage capacity ratio and, in consequence, of the apparent permeability coefficient. Largest deviations were 52%, 70%, 176% and 63% for the Alum, Bossier, Kimmeridge and Garau samples. A dependence of these deviations on the gas storage capacity ratio, K @ , is

AC C

EP

265 266 267 268 269

11

ACCEPTED MANUSCRIPT not apparent for this data set. It should be noted that these are purely theoretical error/uncertainty considerations that do not necessarily imply the same level of uncertainty for the experimental data. For the Garau sample (Figure 4d), however, the determination of the pore volume yielded somewhat ambigious results: here the unstressed pore volume values were sometimes smaller than those measured under controlled stress. This is certainly due to the small pore volume of the sample (i.e. a large K @ ) and the fact that the accuracy limit of the experimental apparatus was reached.

RI PT

281 282 283 284 285 286 287 288

Stressed pore volume = 3.35 cm3

175

Unstressed pore volume = 3.07 cm3

Apparent permeability [nD]

Kc = 2.73

150 125

Kc = 2.58

100 75

Kc = 2.45

50

Kc = 2.10

25

2.0

4.0

10

6.0 8.0 Pmean [MPa]

10.0

12.0

b

2.0

350

4.0

Kc = 3.51

6.0 Pmean [MPa]

8.0

10.0

12.0

Stressed pore volume = 0.31 - 0.40 cm3 Unstressed pore volume = 0.34 cm3

Kc = 87.52

6

Kc = 6.45

4 Kc = 6.25

2

c

5.0

10.0 Pmean [MPa]

15.0

Apparent permeability [nD]

300

Kc = 7.84 Kc = 7.07

TE D

Apparent permeability [nD]

8

0.0

20.0

Kc = 60.57

250 200

Kc = 54.65

150

Kc = 46.42

Kc = 46.31

100 50

d

0 0.0

2.0

4.0

6.0

8.0

10.0

pmean [MPa]

EP

Figure 4: Uncertainties of apparent permeability coefficients by pore volume determination for (a) Alum, (b) Bossier, (c) Kimmeridge and (d) Garau shale. Red error bars describe deviation from measured apparent permeability when pore volumes are changed to an equivalent of ±0.5% porosity (abs.).

AC C

293

500

0.0

Stressed pore volume = 0.69 - 0.78 cm3

Kc = 5.56

290 291 292

Kc = 2.82

750

14.0

Unstressed pore volume = 0.88 cm3

289

Kc = 3.52 Kc = 3.25

1000

0

0.0

0

1250

250

Kc = 2.58

a

0

Stressed pore volume ~ 2.46 cm3

Kc = 3.82

M AN U

Apparent permeability [nD]

1500

Unstressed pore volume = 4.13 cm3

SC

200

294 295 296 297 298 299 300 301

Plotting single apparent permeability coefficients from each expansion over the linear segment of log10(Fr), gives a measure of the quality of each measurement in terms of the absolute standard deviation (SD). This is exemplary shown for selected inflow experiments at given ∆p, Pmean, and Pconf conditions in Figure 5. Ideally, there should not be a variation of apparent permeability coefficients for the chosen intervals, but standard deviations are one to two orders of magnitude lower than the mean apparent permeability coefficients. Standard deviations were analyzed for all expansion series and are shown as error bars in Figures 7 & 10.

302

Normalizing the standard deviation to the corresponding mean permeability, yields the

303

coefficient of variance (

uv

" +

#RMR w

∗ 100). Low coefficients of variance indicate high 12

ACCEPTED MANUSCRIPT precision of permeability coefficients. In this study the coefficient increases in the order Alum ≤ Kimmeridge ≤ Bossier << Eagle Ford ≈ Garau ≈ Westphalian D. This can be either related to the gas storage capacity ratio and/or the differential pressure, both of which control the excess pressure drop (theoretical system pressure after expansion from reference cell minus equilibrium pressure). In order to investigate this in more detail, Figure 6 shows the specific variance coefficient as function of the excess pressure drop for each uptake series measured in this study. It is shown, that below a critical uptake pressure of 0.05 MPa the specific variance coefficient increases dramatically to values of up to 100%, indicating a large permeability uncertainty. Above total pressure uptakes of > 0.05 MPa the specific variance coefficients are only 2% to 15%. From Figure 6 it is clear that measurements performed on the Westphalian D sandstone, Garau and Eagle Ford shale all fall into the region of high uncertainty, where apparent permeabilities may be grossly over or underestimated. A comparision to other measuring techniques should therefore be done with caution for these samples.

318

It is often implied in the literature that large K @ ( A 3

SC

3

BC

4

) ratios should be preferred for

inflow measurements because the dependence of K @ on Fr decreases (e.g. Cui et al., 2009, Yang et al., 2016). However, it was found in this study that a large K @ is counterproductive as larger uncertainties of pressure recordings and larger influences of temperature fluctuations will strongly affect the data accuracy and reproducibility (Figure 6).

M AN U

319 320 321 322 323

RI PT

304 305 306 307 308 309 310 311 312 313 314 315 316 317

AC C

EP

TE D

324

13

ACCEPTED MANUSCRIPT 2500

Apparent permeability [nD]

1200

y = -305x + 1344 SD = 97

400

1500

1000

a

Bossier, Pmean: 0.37 MPa, Dp: 0.45 MPa, Pconf: 40 MPa 0 0

2000

0.2 0.4 0.6 0.8 Fractional interval of total linear interval [-]

Eagle Ford, Pmean: 0.6 MPa, Dp: 0.1 MPa, Pconf: 10 MPa 0

1

0

250

350

y = -19x + 302 SD = 13

200 150 100

Alum, Pmean: 0.4 MPa, Dp: 0.6 MPa, Pconf: 30 MPa 0 0.2 0.4 0.6 0.8 Fractional interval of total linear interval [-]

y = -74x + 203 SD = 35

200

150

100

50

c

Garau, Pmean: 1.9 MPa, Dp: 0.6 MPa, Pconf: 10 MPa

1

0

500

4.0 3.5 3.0 2.5

y = -0.38x + 3.33 SD = 0.27

2.0 1.5 1.0 0.5

TE D

Apparent permeability [nD]

1

d

0

0

Kimmeridge, Pmean: 2.5 MPa, Dp: 1.1 MPa, Pconf: 40 MPa 0.0

0.2 0.4 0.6 0.8 Fractional interval of total linear interval [-]

e

1

EP

0

0.2 0.4 0.6 0.8 Fractional interval of total linear interval [-]

1

y = -158x + 440 SD = 116

400

300

200

100 Westphalian D, Pmean: 0.7 MPa, Dp: 0.1 MPa, Pconf: 30 MPa 0 0

0.2 0.4 0.6 0.8 Fractional interval of total linear interval [-]

f 1

Figure 5: Single apparent permeability coefficients over fractional intervals of the total linear interval for (a) Bossier, (b) Eagle Ford, (c) Alum (d) Garau, (e) Kimmeridge and (f) Westphalian D samples (standard deviation: SD).

AC C

329

b

0.2 0.4 0.6 0.8 Fractional interval of total linear interval [-]

M AN U

50

326 327 328

Apparent permeability [nD]

250

Apparent permeability [nD]

Apparent permeability [nD]

300

325

500

RI PT

800

y = -51x + 1650 SD = 223

SC

Apparent permeability [nD]

1600

14

ACCEPTED MANUSCRIPT 100

Westphalian D N=26 Garau N=31

90

Eagle Ford N=26

Critical pressure

70 60

Bossier N=16 Kimmeridge N=8 Alum N=22

50 40

Increasing gas storage capacity ratio Decreasing initial differential pressure

30 20 10 0.0

0.2

330

SC

0

RI PT

Coefficient of variance [%]

80

0.4 0.6 0.8 Excess pressure drop [MPa]

1.0

1.2

Figure 6: Variance coefficient versus excess pressure drop for all inflow measurements performed in this study. [N]: number of inflow measurements performed for the respective sample.

333 334 335 336 337 338 339

The Klinkenberg formulation (Klinkenberg, 1941) is commonly applied to investigate the dependence of flow regimes on apparent permeability coefficients in tight rocks. A linear relationship of apparent permeability coefficients and the reciprocal mean pore pressure is consistent with the slip flow theory. In contrast to uptake experiments with crushed or powdered samples the inflow measurements on the confined cylindrical rock samples yield realistic apparent permeability trends that provide information on the transport pore diameters in (axial) flow direction.

340 341 342 343 344 345 346

Figure 7 shows Klinkenberg plots obtained for samples derived from data of Figure 2. A summary of all inflow measurements performed is given in Table 2, whereas all Klinkenberg plots are visualized in Appendix A. Linear relationships were obtained for all samples, indicating gas transport in the slip-flow regime. Klinkenberg-corrected permeabilities ranged from 345 nD to 1.8 nD. At pressures > 5 MPa and > 10 MPa for the Garau and Kimmeridge samples (Figure 7d & e), respectively, pore-widening is more dominant than gas slippage, leading to a distinct apparent permeability minimum.

TE D

EP

AC C

347

M AN U

331 332

15

ACCEPTED MANUSCRIPT 2000

1400

Inflow at 40 MPa

Inflow at 10 MPa

y = 392x + 90.9 R² = 0.99

Apparent permeability [nD]

1000 800 600 400 200

1600

1200

1.0

1.5 1/pmean [MPa-1]

2.0

2.5

0.0

3.0

Inflow at 30 MPa

300

y = 116x + 17.1 R² = 0.99

100

Apparent permeability [nD]

Apparent permeability [nD]

125

0.5

75

50

25

200

1.0 1/Pmean [MPa-1]

150 100

M AN U

0

Inflow at 10 MPa

250

50

c

0.5

RI PT

b 0

0.0

1.5

2.0

y = 148x + 97.8 R² = 0.99

d

0

0.2

0.4 0.6 1/pmean [MPa-1]

0.8

6 Inflow at 40 MPa

1.0

0.0

4

TE D

3 2 1

e

0 0.2

0.4 0.6 1/Pmean [MPa-1]

0.8

1.0

Inflow at 30 MPa

y = 3.59x + 1.77 R² = 0.99

0.0

0.2

800

5

Apparent permeability [nD]

0.0

Apparent permeability [nD]

400

a

0

348

y = 706x + 373.9 R² = 0.99 800

SC

Apparent permeability [nD]

1200

0.4 1/pmean [MPa-1]

0.6

0.8

600

y = 200x + 109 R² = 0.91

400

200

f

0 0.0

0.3

0.5

0.8 1.0 1/Pmean [MPa-1]

1.3

1.5

Figure 7: Selected Klinkenberg plots from inflow measurements: (a) Bossier at 40 MPa confining pressure, (b) Eagle Ford at 10 MPa confining pressure, (c) Alum at 30 MPa confining pressure, (d) Garau at 10 MPa confining pressure, (e) Kimmerdige at 40 MPa confining pressure and (f) Westphalian D at 30 MPa confining pressure. Red error bars indicate standard deviations calculated as shown in Figure 5.

353 354 355

Table 2: Summary of inflow derived Klinkenberg-corrected permeabilities (xS ), gas slippage factors (b), average specific pore volumes (Avg. hij ) and coefficients of variance (Avg. CV) for different confining pressures.

AC C

EP

349 350 351 352

Sample

Bossier Shale Eagle Ford Shale

Confining pressure

yS

b

Avg. z{|

Avg. CV

[MPa]

[nD]

[MPa]

[cm³g-1]

[%]

40

74.9

4.5

0.025

11

30

96.5

5.5

0.025

10

40

116.4

5.6

0.044

26

30

204.0

2.9

0.044

44

16

ACCEPTED MANUSCRIPT

Westphalian D sandstone

0.044

33

10

373.9

1.9

0.045

25

40

20.0

6.6

0.043

4

30

17.1

6.8

0.044

6

20

17.9

6.6

0.044

5

40

23.8

3.6

0.007

33

30

43.3

1.7

0.007

37

20

56.9

1.7

0.007

35

10

97.8

1.5

0.007

27

40

1.8

2.0

0.036

8

40

80.7

2.3

0.005

50

30

109.1

1.8

0.005

64

20

135.9

1.8

0.006

45

10

218.8

1.3

0.006

77

356

RI PT

Kimmeridge Clay

3.2

SC

Carbonaceous shale, Garau Formation

234.4

M AN U

Alum Shale

20

5.2 Flow-through measurements

358 359 360 361 362 363

Permeability coefficients measured by flow-through (pulse-decay with two closed reservoirs or constant downstream volume) were performed under the same experimental conditions (gas type, pore pressure and confining pressure range) as the inflow experiments. Flow-through (mostly with two reservoirs) is a common and established method to measure permeability coefficients of low-permeable rocks (e.g. Brace et al., 1968; Dicker & Smits; 1988, Jones, 1997; Ghanizadeh et al., 2014).

364 365 366 367 368 369 370 371 372 373 374

Similar to Figure 5, apparent permeability coefficients from each measurement step plotted over dimensonless time give a measure of quality and can be used to determine the precision in terms of the absolute standard deviation (SD). This is shown here for the Eagle Ford (Figure 8a) and Garau shale (Figure 8b). Generally, the standard deviations are two to three orders of magnitude lower than average apparent permeability coefficients. Coefficients of variance are 0.93% and 0.36% for the Garau and Eagle Ford shale, respectively. The Garau shale revealed the largest variance coefficient of all flowthrough measurements with two closed reservoirs, which is still much better than for all inflow measurements. In fact, standard deviations are very small and negligible in flowthrough experiments and will therefore not be further reported explicitly in the following sections.

AC C

EP

TE D

357

375

17

ACCEPTED MANUSCRIPT 250

y = -12x + 2338 SD = 8.5

1500

1000

500 Eagle Ford, Pmean: 0.46 MPa, Dp: 0.7 MPa, Pconf: 10 MPa 0 0

0.2 0.4 0.6 0.8 Fractional interval of total linear interval [-]

376

a

200 y = 1.2x + 212 SD = 2.0 150

100

50

b

Garau, Pmean: 1.3 MPa, Dp: 0.65 MPa, Pconf: 10 MPa 0 1

0

RI PT

2000

Apparent permeability [nD]

Apparent permeability [nD]

2500

0.2 0.4 0.6 0.8 Fractional interval of total linear interval [-]

1

Figure 8: Single apparent permeability coefficients over dimensionless time for flow-through measurements for (a) Eagle Ford shale and (b) Garau shale.

379 380 381 382 383 384 385 386 387 388 389 390 391

Another source of error already discussed in the previous chapter is the volume error resulting from the gas-storage capacity ratio. Depending on the gas-storage capacity ratios, the permeability change for flow-through measurements may be negligible or not, as shown in Figure 9 for the Eagle Ford and Garau shales. Here, apparent gas permeabilities were calculated using the zero pore volume assumption (f% =1, equivalent to the solution given by Brace et al., 1968) as well as corrections based on pore volumes of the unstressed samples (equivalent to the solution given by Jones, 1997) and the pore volumes under stress. The unstressed pore volume correction uses pore volumes obtained from He-pycnometry, whereas stressed pore volume correction is performed by using a fitting function and extrapolating the pore volume measurements from inflow data to the effective stress at which the particular measurement was performed (Figure 2). Error bars (in red) show the permeability fluctuations upon stressed porosity variations of ± 0.5% (abs.).

392 393 394

The unstressed pore volume of the Eagle Ford sample (~3.4 cm³) exceeded the volume of the two reservoirs (~3 cm³ on average), which corresponds to a volumetric error of 18%. The calculation is shown exemplary in equations 9 to 12:

395

a =

3

4

=

396

b =

3

4

= }.€• @ ³ = 0.93

397

tan(θ% ) = ,- 2%.U„∗„.…} ; (θ% = 1.38)

398

f% = %.U„

399 400 401 402 403 404

This resulted in an apparent permeability increase of 418 nD after correction at lowest mean gas pressures of 0.5 MPa (Figure 9a). In contrast, the Garau shale has a much smaller pore volume of 0.3 cm³. The corresponding volume error is 3% and led to apparent permeability underestimations of 3 nD at lowest mean gas pressures of 1.2 MPa (Figure 9b). Using the pore volumes of the stressed samples for volume error calculations, the calculated volume errors decreased to 16% and 1% for the Eagle Ford

}.U @ ³

= 1.40

(9)

.U @ ³

}.U @ ³

(10)

(%.U„ „.…}),

(11)

AC C

3

EP

TE D

M AN U

SC

377 378

3

%.}‡²

„.…}

= 0.82

(12)

18

ACCEPTED MANUSCRIPT

f1= 0.836 - 0.839

2000

f1= 1

1600 1200 800 Unstressed pore volume correction Stressed pore volume correction Zero pore volume assumption

400 0

b

f1 = 0.97 - 1

75 60 45 30 15

Unstressed pore volume correction Stressed pore volume correction Zero pore volume assumption

0

0.0

414

90

f1= 0.82

SC

a

Apparent gas permeability [nD]

Apparent gas permeability [nD]

2400

RI PT

and Garau samples, respectively. A summary of average volume errors for each confining pressure step is provided in Table 3 together with Klinkenberg-corrected permeabilities and gas slippage factors. Additionally all Klinkenberg plots are displayed in Appendix A. Varying the value for the stressed pore volume by an equivalent of ± 0.5% (abs.) porosity for each sample resulted in a volume error change <1.5% for both samples, thus a negligible apparent permeability change. A similar uncertainty analysis was performed for flow-through measurements with one closed reservoir. However, as in this case the downstream reservoir is infinitely large, only one gas storage ratio needs to be accounted for.

M AN U

405 406 407 408 409 410 411 412 413

0.5

1.0 1.5 1/Pmean [MPa-1]

2.0

2.5

0.0

0.2

0.4 0.6 1/Pmean [MPa-1]

0.8

1.0

Figure 9: Errors in permeability determination based on gas storage capacity ratios for (a) Eagle Ford shale and (b) Garau shale.

417 418

Table 3: Summary of flow-through derived Klinkenberg-corrected permeabilities (xS ), gas slippage factors (b), and average volume errors of gas storage capacities (Avg. ‰% ) for different confining pressures.

Sample

TE D

415 416

yS

b

Avg. Š‹

[MPa]

[nD]

[MPa]

[-]

40

10985.3

0.2

0.88

30

11647.6

0.2

40

216.3

2.4

0.85

30

215.3

2.6

0.84

20

220.8

2.6

0.84

10

424.7

2.1

0.84

40

15.1

6.4

0.86

30

15.4

7.7

0.85

20

16.1

7.2

0.85

10

16.4

8.0

-

40

29.1

2.0

0.98

30

34.9

2.0

0.98

20

52.7

1.8

0.98

AC C

EP

Bossier Shale

Confining pressure

Eagle Ford Shale

Alum Shale

Carbonaceous shale, Garau Formation

19

ACCEPTED MANUSCRIPT

Westphalian D sandstone

111.2

1.3

0.98

40

1.5

1.7

0.93

40

21.5

4.1

0.96

30

27.4

3.4

0.96

20

33.1

3.17

0.95

10

58.8

2.5

419

RI PT

Kimmeridge Clay

10

0.95

5.3 Comparison of permeability coefficients from inflow and flow-through

421 422 423 424 425 426 427 428 429 430 431

Figure 10 shows the comparison of flow-through and inflow-derived permeabilities for all data sets using pore volumes determined under stress as input parameters. Standard deviations as determined in Figure 5 for inflow measurements were included for each data point. Generally, inflow permeabilities do not show any systematic deviations from flow-through derived permeabilities. However, sample-specific trends were observed: For the Bossier Shale flow-through permeabilities are consistently two orders of magnitude higher than inflow permeability coefficients (Figure 10a). For the Eagle Ford, Alum, Garau and Kimmeridge samples results are equal or similar (Figures 10b - e). For the Westphalian D sample, the permeability coefficients determined from inflow experiments are larger by 52% (slope) and 74% (y-axis intercept) than those determined from flow-through tests (Figure 10f).

432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447

Since the specific variance coefficients (uncertainty) for the Eagle Ford, Garau and Westphalian D samples are very large, these data sets cannot be readily compared with the results from flow-through measurements. Thus, the only meaningful interpretation at this point is that the results of the (more reliable) flow-through measurements lie within the range of variance of the inflow measurements for all three samples. A better agreement is likely to be achievable if measuring procedures for inflow tests can be improved. Averaging of apparent permeability coefficients for the Garau shale, as reported in Figure 5, gave approximately the same permeability coefficients as obtained with flow-through. Interestingly, the previously interpreted poro-elastic permeability increase (Figure 7d) was apparent in the flow-through data, too, thus confirming that not only fluid-dynamic but also poro-mechanic effects can be analyzed and quantified from inflow data. As for the Kimmeridge and Alum samples, based on the linear regressions (Figure 10c & e), the slopes and y-axis intercepts of the Klinkenberg trends differed by 29% and 14% as well as 4% and 10%, respectively, indicating that by improving the measuring procedure for inflow tests, permeability coefficients obtained from both methods will show better agreement.

448 449 450

The large deviation observed for the Bossier sample (Figure 10a) by approximately two orders of magnitude could be explained after detailed data analysis. Klinkenbergcorrected permeabilities were 91 nD from inflow measurements and 11000 nD from

AC C

EP

TE D

M AN U

SC

420

20

ACCEPTED MANUSCRIPT

EP

TE D

M AN U

SC

RI PT

flow-through measurements at 40 MPa confining pressure. Flow-through raw data (with two closed reservoirs) are shown in Figure 11a and it is evident that gas transport can be divided into two phases: i) flow through the sample from upstream to downstream reservoir until pressure equilibration is achieved in the reservoirs and ii) a slow subsequent pressure drop until finally reaching a minimum equilbration pressure. Comparison of the normalized pressure decay curves (Figure 11b) showed that pressure equilibration during inflow experiments is consistently longer. It is very likely, that this sample has a strong pore network anisotropy, e.g. parallel and perpendicular bedding flow, or a dual porosity system, e.g. fracture and matrix porosity. The Bossier sample was drilled parallel to bedding, but bedding-parallel fractures were observed, too. This implies that the two methods might have different effective transport pore accessibilities. It is reasonable to assume that flow-through favours more easily accessible and therefore larger pores (e.g. micro-fractures). As for inflow, infilling of larger pores occurs first for the same reasons, but as soon as infilling of all accessible larger pores has taken place, the gas will enter smaller pores at a lower rate yielding lower apparent permeability coefficients. This is well reflected in the gas slippage factors obtained from inflow (b = 4.0 MPa, Table 2) and flow-through (b = 0.2 MPa, Table 3) for this sample set at 40 MPa confining pressure. As thoroughly discussed by Klinkenberg (1941), Randolph et al. (1984) or Letham et al. (2015) the gas slippage factor is inversely proportional to the average transport pore diameter (Klinkenberg, 1941) or average transport slit width (Randolph et al., 1984). Thus, the combination of both methods shows, whether a dual porosity system or anisotropy are present or not and to what extent they may affect the permeability coefficient. Cui & Bustin (2010) reported that permeabilities differed by two orders of magnitude when flow-through and inflow (ISPP: In-Situ Permeability and Porosity) was measured on intact cores orientated parallel to the bedding. They argued that flow-through prefers high permeability zones, since it is based on differential pressures between the up- and downstream reservoirs, and solely gives information on largest pathways (e.g. fractures) in longitudinal direction (c-axis) of the samples. Since shales likely develop hierarchical and anisotropic structures and hence permeability pathways, inflow most likely gives information on permeability coefficients of smaller scaled pathways. This agrees with the findings made for the Bossier sample in this study and explains the difference of permeability coefficients from inflow and flow-through although the variance coefficient for inflow was relatively small (Figure 6). It should be noted that when performing flowthrough measurements with two closed reservoirs, flow perpendicular and parallel to bedding are competing throughout the measurement, probably leading to an underestimation of the maximum flow-through controlled permeability coefficients for the Bossier sample.

AC C

451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489

21

ACCEPTED MANUSCRIPT 2000

20000

Flow-through at 10 MPa

Inflow at 40 MPa

y = 891x + 424.7 R² = 0.99

Inflow at 10 MPa

y = 2064x + 10985 R² = 0.99 10000

y = 392x + 90.9 R² = 0.99

5000

1600

1200 y = 706x + 373.9 R² = 0.99 800

400

a

0 0.0

250

0.5

1.0

1.5 1/pmean [MPa-1]

2.0

2.5

b

0

3.0

0.0

300

Flow-through at 30 MPa

100

M AN U

c

0.5

1.0

5

y = 3.59x + 1.77 R² = 0.99

Flow-through at 40 MPa Inflow at 40 MPa

3

800

y = 2.56x + 1.53 R² = 0.99 2

1

TE D

Apparent permeability [nD]

4

e

0 0.0

490

0.0

0.2

0.4 1/pmean [MPa-1]

0.6

0.2

2.0

y = 148x + 98 R² = 0.99

d

0

1.5

1/pmean [MPa-1]

0.4 0.6 1/Pmean [MPa-1]

0.8

1.0

Flow-through at 30 MPa Inflow at 30 MPa

600

y = 200x + 109 R² = 0.91

400

y = 92x + 27.4 R² = 0.99

200

f

0 0.0

0.8

0.5

1.0 1/Pmean [MPa-1]

1.5

2.0

EP

Figure 10: Comparison of Klinkenberg plots from inflow and flow-through measurements: (a) Bossier Shale at 40 MPa confining pressure, (b) Eagle Ford Shale at 10 MPa confining pressure, (c) Alum Shale at 30 MPa confining pressure, (d) Garau Shale at 10 MPa confining pressure, (e) Kimmerdige Shale at 40 MPa confining pressure and (f) Westphalian D sandstone at 30 MPa confining pressure.

AC C

495

4.5

Time [s] 0

0

1000 Time [s]

800

1000

Inflow; Pmean: 3.0 MPa Flow-through; Pmean: 0.5 Mpa Flow-through; Pmean: 1.1 MPa

0.100

1500

2000

Flow-through; Pmean: 3.0 MPa

0.010

b

Downstream compartment 500

600

Inflow; Pmean: 0.9 MPa

Upstream compartment

a

400

Inflow; Pmean: 0.4 MPa

4

3.5

200

1.000

Normalized pressure decay [-]

Pressure [MPa]

5

497 498

100 50

0.0

496

150

50

0

491 492 493 494

200

1.5

y = 139x + 111 R² = 0.99

SC

y = 117x + 17.1 R² = 0.99

Apparent permeability [nD]

y = 122x + 15.4 R² = 0.99

250

Apparent permeability [nD]

Apparent permeability [nD]

150

1.0 1/Pmean [MPa-1]

Flow-through 10 MPa Inflow at 10 MPa

Inflow at 30 MPa 200

0.5

RI PT

Apparent permeability [nD]

Apparent permeability [nD]

Flow-through at 40 MPa 15000

0.001

Figure 11: (a) Raw data for flow-through measurement with two closed reservoirs and (b) comparison of normalized pressure decay for inflow and flow-through for the Bossier sample.

22

ACCEPTED MANUSCRIPT Yang et al. (2016) compared three flow-through and three inflow (OCPPD: One-Chamber Pressure Pulse Decay) measurements at equal differential and mean pore pressures as well as confining pressures. Main results were that inflow-derived permeability coefficients are smaller than flow-through derived permeability coefficients by ~ 10% for three apparent permeabilities. Data from our study do not support their conclusions as apparent inflow permeabilities were not consistently smaller than flow-through permeabilities. It should be noted that Yang et al. (2016) did not account for stressdependent porosity changes, but rather used unstressed (constant) porosity as input, and thus, permeability evaluations for both methods are questionable if stressdependent change is relevant for their sample set. Zheng et al. (2015) and Fink et al. (2017a) have shown that the largest decrease in specific pore volume occurs upon loading the sample at low effective stress (up to ~ 5 MPa). Using unstressed pore volumes instead of stressed pore volumes will always result in smaller apparent permeability coefficients because gas storage capacity ratios (K @ ) will be underestimated as shown in Figure 4 for the sample set of this study.

514 515 516 517 518 519 520 521 522 523

Peng & Loucks (2016) compared Klinkenberg-corrected helium permeabilities from inflow (MGE: Modified Gas Expansion) with apparent argon permeabilities from flowthrough (at 14 MPa for an Eagle Ford and 7 MPa for a Barnett sample) at varying confining pressures on intact cores. They found inflow-derived permeabilities 2 – 4 times larger than flow-through derived permeability coefficients. It is possible that this difference is due to the use of different gases (inflow – He, flow-through – Ar), even though fluid dynamic effects were accounted for. Fink et al. (2017b) showed that Klinkenberg-corrected permeability coefficients of fine-grained rocks decrease in the order of He >> Ar ≥ N2 ≥ CH4 ≥ CO2. Therefore, methodological comparisons of permeability data measured with different gases are problematic.

524

6 Conclusions

525 526 527 528 529

The primary objective of this study was to analyse whether inflow-derived permeability coefficients give reasonable results by comparing them to other commonly used and well-established methods (flow-through, standard pulse decay). This was achieved by performing a series of measurements on six different unconventional lithotypes from the Eagle Ford, Kimmeridge, Alum, Westphalian D, Garau and Bossier Formations.

530 531 532 533 534 535 536 537 538

Results indicate that in order to successfully use inflow data it is necessary to ensure a sufficient excess pressure drop during gas uptake by the sample. This can be controlled by adjustment of the gas storage capacity ratio (sample size/quantity and measuring cell volumes), the initial differential pressure and sensitivity of the pressure transducers. For inflow measurements, the excess pressure drop should be at least 0.05 MPa. Comparison of coefficients of variance of the two methods used in this study showed that flow-through accuracy is generally better by one order of magnitude at optimal conditions for inflow. Thus, inflow measurements should not be used to replace flowthrough measurements. However, comparing both methods can give information on

AC C

EP

TE D

M AN U

SC

RI PT

499 500 501 502 503 504 505 506 507 508 509 510 511 512 513

23

ACCEPTED MANUSCRIPT whether flow is controlled by anisotropy, either induced by bedding orientation or matrix/fracture porosity.

541 542 543 544 545 546 547 548 549 550 551 552

Based on a large data set, it was possible for the first time to show that inflow measurements on intact cores can be used to interpret fluid dynamic effects and, therefore can be reliably used to obtain Klinkenberg-corrected permeabilities. The question arises whether formulations used for crushed rock permeability are useful since basic fluid dynamic effects and stress-dependence, are absent or not detectable. Reasons for being absent or not detectable might be wrong initial boundary conditions chosen for the experiments and evaluations or experimental conditions that do not cover these effects. The results presented in this study may now be used to investigate whether inflow on intact cores at ambient conditions can be utilized - as a spin-off of porosity measurements - to give fast and cheap estimations of permeability on rock volumes that can be considered representative in terms of matrix pore structure and rock fabric.

553 554 555 556

It is important to note that the mathematical formulation used in this study requires radial sealing of the intact cores, which typically is the case in triaxial flow cells with overburden but is not in pycnometry vessels at ambient conditions. Therefore, materials capable of sealing the rocks while not invading the pore space need to be utilized.

557

Acknowledgements

558 559

We thank our anonymous reviewers for their constructive comments to improve this paper.

562 563 564 565 566

SC

M AN U

TE D

EP

561

AC C

560

RI PT

539 540

567 568 569 570 24

ACCEPTED MANUSCRIPT 571 572

Appendix A. Apparent permeability coefficients from all inflow and flow-through experiments.

573 574

Shown in Figures A-1.1 and A-1.2 are the Klinkenberg plots of all inflow and flowthrough tests, as requested by the reviewers.

575

250

800 600 400

0.0

1.5

300

140

80 60

0 0.0

0.5

1.0

150 100

c

d

0

1.5

0.0

0.5

2

1

40 MPa confining pressure y = 3.6x + 1.8

0

576 577 578

0.0

0.5

1.0

1.0

1.5

1/pmean [MPa-1]

800

10 MPa confining pressure y = 277x + 218.8 20 MPa confining pressure y = 243x + 135.9

700

Apparent permeability [nD]

EP

3

AC C

Apparent permeability [nD]

4

1.5

200

1/pmean [MPa-1]

5

1.0

1/pmean [MPa-1]

50

TE D

20 MPa confining pressure y = 119x + 17.9 30 MPa confining pressure y = 117x + 17.1 40 MPa confining pressure y = 131x + 20.0

20

Apparent permeability [nD]

100

b

10 MPa confining pressure y = 149x + 97.8 20 MPa confining pressure y = 94x + 56.9 30 MPa confining pressure y = 72x + 43.3 40 MPa confining pressure y = 86x + 23.8

250

120

40

0.5

M AN U

160

Apparent permeability [nD]

40 MPa confining pressure y = 662x + 116.4

1000

0

0 1.0

30 MPa confining pressure y = 593x + 204.0

1200

200

a 1/pmean [MPa-1]

20 MPa confining pressure y = 755x + 234.4

SC

500

0.5

10 MPa confining pressure y = 706x + 373.9

1400

750

0.0

RI PT

1600

30 MPa confining pressure y = 416x + 74.9 40 MPa confining pressure y = 432x + 96.5

Apparent permeability [nD]

Apparent permeability [nD]

1000

30 MPa confining pressure y = 200x + 109.1 600

40 MPa confining pressure y = 182x + 80.7

500 400 300 200 100

e

f

0

1.5

0.0

1/pmean [MPa-1]

0.5

1.0

1.5

1/pmean [MPa-1]

Figure A-1.1: Summary of all inflow-derived Klinkenberg plots for (a) Bossier Shale, (b) Eagle Ford Shale, (c) Alum Shale, (d) Garau Shale, (e) Kimmeridge Clay and (f) Westphalian D sandstone.

25

16000

1600

14000

1400

Apparent permeability [nD]

12000 10000 8000 6000 4000 30 MPa confining pressure y = 2454x + 11647.6

2000 0 0.0

0.5

1.0

1000 800 600 10 MPa confining pressure y = 891x + 424.7 400

20 MPa confining pressure y = 569x + 220.8 30 MPa confining pressure y = 552x + 215.3

200

a

40 MPa confining pressure y = 2064x + 10985.3

1200

40 MPa confining pressure y = 525x + 216.3 0 0.0

1.5

RI PT

Apparent permeability [nD]

ACCEPTED MANUSCRIPT

0.5

1/pmean [MPa-1]

30 MPa confining pressure y = 68x + 34.9 40 MPa confining pressure y = 59x + 29.1

100 80 60 10 MPa confining pressure 20 MPa confining pressure 30 MPa confining pressure 40 MPa confining pressure

40 20 0 0.0

0.5

1.0 1/pmean [MPa-1]

5

y = 131x + 16.4 y = 116x + 16.1 y = 118x + 15.4 y = 97x + 15.1

200 150

SC

Apparent permeability [nD]

250

120

100 50

c

M AN U

Apparent permeability [nD]

140

1.5

0

0.0

0.5

400

2

1

Apparent permeability [nD]

3

TE D

Apparent permeability [nD]

350

4

40 MPa confining pressure y = 2.6x + 1.53 0

579

0.0

0.5

1.0

1/pmean

1.5

e

[MPa-1]

b

1.5

1/pmean [MPa-1] 10 MPa confining pressure y = 139x + 111.2 20 MPa confining pressure y = 93x + 52.7

300

160

1.0

300

1.0

1.5

d

1/pmean [MPa-1] 10 MPa confining pressure y = 147x + 58.8 20 MPa confining pressure y = 105x + 33.1 30 MPa confining pressure y = 92x + 27.4 40 MPa confining pressure y = 87x + 21.5

250 200 150 100

50 0 0.0

0.5

1.0

1.5

f

1/pmean [MPa-1]

Figure A-1.2: Summary of all flow-through derived Klinkenberg plots for (a) Bossier Shale, (b) Eagle Ford Shale, (c) Alum Shale, (d) Garau Shale, (e) Kimmeridge Clay and (f) Westphalian D sandstone.

582

Appendix B. Stress-dependence of Klinkenberg-corrected permeability coefficients

583 584 585 586 587 588 589 590 591 592 593 594 595

Investigations of the stress-dependence of permeability coefficients of shales are important to estimate transport properties at in-situ conditions and to predict permeability changes during hydrocarbon production (e.g. Dong et al., 2010; Clarkson et al., 2012; Ghanizadeh et al., 2014; Zheng et al., 2015; Fink et al., 2017b). Stress-induced permeability changes determined in laboratory measurements on cylindrical sample plugs of a few cm thickness were typically reported to follow linear, exponential or power law trends. In this study both non-steady state methods were used to investigate the stress-dependence of permeability coefficients; we used solely exponential fitting functions to express the permeability decrease. The results are plotted in Figures B-1.1 and B-1.2 and the numerical data reported in Table B-1. Permeability values from flowthrough tests generally had a better accuracy by one order of magnitude than those from inflow tests. Therefore, permeability stress-dependence analysis based on inflow tests should be viewed with caution.

AC C

EP

580 581

26

ACCEPTED MANUSCRIPT 596 597

The exponential function used to describe the stress-dependence of the Klinkenbergcorrected permeability coefficient, k∞, is: k S = k S,„ e•e Ž

•

Here k S,„ is the “intrinsic” permeability coefficient at zero effective stress (σ‘ ) and αa is the stress sensitivity coefficient.

600 601 602 603 604 605 606

The Bossier Shale and Kimmeridge Clay were excluded from the stress-dependence interpretation due the limited database. Stress-dependence of permeability coefficients, as derived from flow-through tests decreased in the order Garau Shale > Westphalian D sandstone > Eagle Ford Shale > Alum Shale. Permeability coefficients derived from inflow tests indicated the strongest stress-dependence for the Eagle Ford Shale (αa : 0.086 MPa-1) with decreasing stress-dependence in the order Garau Shale > Westphalian D sandstone > Alum Shale (Figure B-1.1, B-1.2, Table B-1).

607 608 609 610 611 612 613 614 615 616 617 618

It is evident from Figure B-1 that Klinkenberg-corrected flow-through permeabilities of the Eagle Ford Shale did not change as the confining pressure decreased from 40 to 20 MPa. However, the permeability coefficient doubled (from 221 to 424 nD) upon further pressure decrease from 20 to 10 MPa. The inflow tests showed a more gradual change (from 204 to 374 nD) as the confining pressure was reduced from 40 to 10 MPa. The smallest stress sensitivity was observed for the Alum Shale in both methods (flowthrough: αa : -0.008 MPa-1, inflow: αa : 0.006 MPa-1. The positive αa value (0.006 MPa-1), and the low coefficient of determination (0.47) indicate that the Klinkenberg-corrected permeability coefficient does not depend on effective stress or that this dependence is below the detection limit of the inflow method. The best match of the results from the two methods was observed for the Garau Shale with αa : -0.045 MPa-1and k S,„: 151 nD for the inflow and αa : -0.044 MPa-1and k S,„: 149 nD for the flow-through test.

AC C

EP

TE D

M AN U

SC

RI PT

598 599

27

ACCEPTED MANUSCRIPT Eagle Ford Shale Westphalian D sandstone Bossier Shale Garau Shale Alum Shale Kimmeridge Clay y = 429e-0.020x

y = 13884e-0.006x

R² = 0.62

100

RI PT

y = 145e-0.044x R² = 0.92

73e-0.032x

y= R² = 0.93

y = 17e-0.003x R² = 0.97

SC

Klinkenberg-corrected permeability [nD]

10000

1 0

10

620 621

50

TE D

100

y = 206e-0.025x

y = 151e-0.045x R² = 0.98

Eagle Ford Shale Westphalian D sandstone Bossier Shale Garau Shale Alum Shale Kimmeridge Clay

10

y = 16e0.006x R² = 0.47

EP

Klinkenberg-corrected permeability [nD]

y = 531e-0.036x R² = 0.96

y = 284e-0.032x R² = 0.98

AC C

1

0

623 624

40

Figure 12B-1.1: Stress-dependence of Klinkenberg-corrected permeability coefficients derived from flowthrough measurements.

1000

622

20 30 Confining pressure [MPa]

M AN U

619

10

20 30 Confining pressure [MPa]

40

50

Figure B-1.2: Stress-dependence of Klinkenberg-corrected permeability coefficients derived from inflow measurements.

625 626 627

Table B-1: Summary of stress sensitivity parameters ’“ (stress-sensitivity coefficient) and xS,„ (intrinsic permeability at zero effective stress).

Sample

Eagle Ford Shale

Inflow

Flow-through

k S,„

αa

k S,„

αa

531

-0.086

429

-0.02

28

ACCEPTED MANUSCRIPT Westphalian D sandstone

284

-0.032

73

-0.032

Bossier Shale

206

-0.025

13884

-0.006

Garau Shale

151

-0.045

145

-0.044

Alum shale

15

0.006

17

-0.008

-

-

-

-

Kimmeridge Clay

RI PT

628 Appendix C. Comparison of permeability coefficients measured with helium and methane

631 632 633 634 635

One of the reviewers raised the question whether gas effects in low-permeable rocks affect transport properties and which implications are to be expected for reservoir gases. Several inflow and flow-through experiments have indeed been performed during this study with methane as test gas. We take this opportunity to summarize the most important results

636 637 638 639 640 641 642 643

Gas permeability measurements on conventional reservoir rocks are generally insensitive to the gas type. For convenience and safety, gases such as air, nitrogen and helium are used for permeability measurements and a slip flow (“Klinkenberg") correction is performed to obtain “intrinsic” permeability coefficients. For lowpermeable shales, however, these “intrinsic” permeabilities were found to depend on the measuring gas used (e.g. Sinha et al., 2013, Ghanizadeh et al., 2014; Fink et al., 2017b). These observations are attributed to fluid dynamic effects, molecular sieving, adsorption, and possibly pore size reduction as well as sorption-induced swelling.

644 645 646 647 648 649 650 651 652 653 654

In this study a set of inflow and flow-through permeability tests with methane was performed on the Alum Shale. This sample was chosen because the helium tests with both methods had shown good agreement and practically no stress-dependence of the permeability coefficients. It is evident from Figure C-1 that the apparent permeability coefficients measured with methane were significantly lower than those measured with helium. Similarly, the Klinkenberg-corrected permeability coefficients measured with methane in flow-through and inflow tests were lower by 50% and 62% (flow-through: 8.0 nD, inflow: 6.3 nD), respectively, than the helium (flow-through: 16.1 nD, inflow: 16.7 nD) data. In conclusion, (i) the effect of gas type on permeability coefficients of shales could be confirmed and (ii) both non-steady state methods yielded very similar results.

AC C

EP

TE D

M AN U

SC

629 630

29

ACCEPTED MANUSCRIPT He, 30 MPa confining pressure, inflow He, 30 MPa confining pressure, flow-through CH4, 30 MPa confining pressure, inflow CH4. 30 MPa confining pressure, flow-through

200

150 y = 119x + 16.1

RI PT

Apparent permeability [nD]

250

100 y = 117x + 16.7

y = 47x + 6.3 50

y = 25x + 8.0 0.0

SC

0 0.5

1.0

1.5

1/pmean [MPa-1]

655

Figure C-1: Comparison of inflow and flow-through derived helium and methane permeability coefficients for the Alum Shale at 30 MPa confining pressure.

658

References

659 660

Brace, W. F., Walsh, J. B., Frangos, W. T., 1968. Permeability of granite under high pressure. Journal of geophysical research 73, John Wiley & Sons Ltd., pp. 2225-2236.

661 662 663

Blount, A., Croft, T., Driskill, B., Tepper, B., 2017. Lessons learned in Permian core analysis: comparison between retort, GRI, and routine methodologies, Petrophysics 58 (5). pp. 517-527.

664 665 666

Clarkson, C.R., Jensen, J.L., Pedersen, P.K. & Freeman, M. 2012. Innovative methods for flowunit and pore-structure analyses in a tight siltstone and shale gas reservoir. American Association of Petroleum Geologists Bulletin, 96, pp. 355 – 374.

667 668 669

Cui, X., Bustin, A.M.M., Bustin, R.M., 2009. Measurements of gas permeability and diffusivity of tight reservoir rocks. Different approaches and their applications. Geofluids, John Wiley & Sons Ltd, pp. 208-223.

670 671 672 673

Cui, X. & Bustin, R.M., 2010. A new method to simultaneously measure in-situ permeability and porosity under reservoir conditions: Implications for characterization of unconventional gas reservoirs. Petroleum conference, Calgary, Canada, 19-21 October.

674

Crank, J., 1975. The mathematics of diffusion. Clarendon Press, pp.56-59.

675 676 677

Dicker, A. I. & Smits, R. M., 1988. A practical approach for determining permeability from laboratory pressure-pulse decay measurements. SPE paper 17578, presented at the 1988 international meeting on petroleum engineering, Tianjin, China, pp. 285-292.

AC C

EP

TE D

M AN U

656 657

30

ACCEPTED MANUSCRIPT Dong, J.-J., Hsu, J.-Y. et al. 2010. Stress-dependence of the permeability and porosity of sandstone and shale from TCDP Hole-A. International Journal of Rock Mechanics and Mining Sciences,47, pp. 1141 – 1157.

681 682 683

Fink, R., Krooss, B. M., Gensterblum, Y., Amann, A., 2017a. Apparent permeability of gas shales – Superposition of fluid-dynamic and poro-elastic effects. Fuel 199, pp. 532550.

684 685 686

Fink, R., Krooss, B. M., Amann, A., 2017b. Stress-dependence of porosity and permeability of the Upper Jurassic Bossier shale: An experimental study. Geological Society London Special publications 454(1).

687 688 689 690

Fisher, Q., Lorinczi, P., Grattoni, C., Rybalcenko, K., Crook, A. J., Allshorn, S., Burns, A. D. Shafagh, I., 2017. Laboratory characterization of the porosity and permeability of gas shales using the crushed shale method: Insights from experiments and numerical modelling. Marine and Petroleum Geology 86, Elsevier, pp. 95-110.

691 692 693

Gasparik, M., Bertier, P., Gensterblum, Y., Ghanizadeh, A., Krooss, B. M., Littke, R., 2013. Geological controls on the methane storage capacity in organic-rich shales. International Journal of Coal Geology 123, pp.34-51.

694 695 696 697

Ghanizadeh, A., Gasparik, M., Amann-Hildenbrand, A., Gensterblum, Y, Krooss, B. M., 2014. Experimental study of fluid transport processes in the matrix system of the European organic-rich shales: I. Scandinavian Alum Shale. Marine and Petroleum Geology 51, Elsevier, pp. 79-99.

698 699 700 701

Ghanizadeh, A., Bhowmik, S., Haeri-Ardakani, O., Sanei, H., Clarkson, C. R., 2015. A comparison of shale permeability coefficients derived using multiple non-steady-state measurement techniques: Examples from the Duvernay Formation, Alberta (Canada). Fuel 140, pp. 371-387.

702 703 704 705

Gensterblum, Y., Ghanizadeh, A., Cuss, R. J., Amann-Hildenbrand, A., Krooss, B.M., Clarkson, C. R., Harrington, J. F., Zoback, M. D., 2015. Gas transport and storage capacity in shale gas reservoirs – a review. Part A: Transport processes. Journal of unconventional oil and gas resources 12, Elsevier , pp. 87-122.

706 707 708

Guidry, K., Luffel, D., & Curtis, J. Development of laboratory and petrophysical techniques for evaluating shale reservoirs. Final technical report, October 1986-September 1993. United States.

709 710

Heller, R., Vermylen, J., Zoback, M. (2014) Experimental investigation of matrix permeability of gas shales. AAPG Bulletin 98 (5), pp. 975–995.

711 712

Jones, S.C., 1997. A technique for faster pulse-decay permeability measurements in tight rocks. SPE formation evaluation 12, pp. 19-25.

713 714

Klinkenberg, L. J., 1941. The permeability of porous media to liquids and gases. Drilling and production practics, American Petroleum Institute, pp. 200-213.

715 716

Kundt, A. & Warburg, E., 1875. Ueber Reibung und Wärmeleitung verdünnter Gase. Annalen der Physik und Chemie 7, VEB Johann Ambrosius Barth, pp. 337-365.

AC C

EP

TE D

M AN U

SC

RI PT

678 679 680

31

ACCEPTED MANUSCRIPT Kunz, O., Klimeck, R., Wagner, W., Jaeschke, M., 2007. The GERG-2004 wide-range equation of state for natural gases and other mixtures. Publishing House of the Association of German Engineers.

720 721 722

Letham, E. A. & Bustin, R. M., 2015. Klinkenberg gas slippage measurements as a means for shale pore structure chracterization. Geofluids, John Wiley & Sons Ltd., pp. 264278.

723 724 725

Li, X. & Krooss, B. M., 2017. Influence of grain size and moisture content on the highpressure methane sorption capacity of Kimmeridge Clay. Energy Fuels 31, pp. 1154811557.

726 727 728

Luffel, D.L. and Guidry, F.K., 1992. New Core Analysis Methods for Measuring Rock Properties of Devonian Shale. Journal of Petroleum Technology 44 (11), Paper SPE20571-PA, Society of Petroleum Engineers., pp. 1184-1190.

729 730 731 732

McKernan, R. E. et al. (2014) ‘SPE 14UNCV-167762-MS Influence of Effective Pressure on Mudstone Matrix Permeability: Implications for Shale Gas Production’, SPE/EAGE European Unconventional Conference and Exhibition held Vienna, p. 13. doi: 10.2118/167762-MS.

733 734 735

Peng, S. & Loucks, B., 2016. Permeability measurements in mudrocks using gasexpansion methods on plug and crushed-rock samples. Marine and Petroleum Geology 73, Elsevier, pp. 299-310.

736 737 738

Randolph, P. L., Soeder, D. J., Chowdiah, P., 1984. Porosity and permeability of tight sands. SPE paper 12836, presented at the SPE/DOE/GRI unconventional gas recovery symposium, 13-15 May, Pittburgh, USA, pp. 57-62.

739 740 741

Sander, R., Pan, Z., Connell, L. D., 2017. Laboratory measurment of low permeability unconventional gas reservoir rocks: A review of experimental methods. Journal of Natural Gas Science and Engineering 37, pp. 248-279.

742 743 744 745 746

Schovsbo, N. and Buchardt, B., 1994. Djupvik - 1 and Djupvik – 2 completion report, BMFT-project 032 66686 B: Pre-Westphalian source rocks in Northern Europe,

747 748 749 750

Shabani, M., Moallemi, S. A., Krooss, B. M., Amann-Hildenbrand, A., Zamani-Pozveh, Z., Ghalavand, H., Littke, R., 2018. Methane sorption and storage characteristics of organic-rich carboaceous rocks, Lurestan provincs, southwest Iran. International Journal of Coal Geology 186, pp. 51-64.

751 752 753 754

Sinha, S., Braun, E.M. et al. 2013. Steady-state permeability measurements on intact shale samples at reservoir conditions – effect of stress, temperature, pressure, and type of gas. Paper presented at the SPE Middle East Oil and Gas Show and Conference, 10 – 13 March 2013, Manama, Bahrain.

755 756 757

Yang, Z., Sang, Q., Dong, M., Zhang, S., Li, Y., Gong, H., 2016. A modified pressure-pulse decay method for determining permeabilities of tight reservoir cores. Journal of Natural Gas Science and Engineering, Elsevier, pp. 1-11. 32

EP

TE D

M AN U

SC

RI PT

717 718 719

AC C

https://www.researchgate.net/profile/Niels_Schovsbo/publication/299597690_Djupvik1_and_Djupvik-2_completion_report/links/57020c5a08ae1408e15eada0/Djupvik-1-andDjupvik-2-completion-report.pdf

ACCEPTED MANUSCRIPT

EP

TE D

M AN U

SC

RI PT

Zheng, J., Zheng, L., Liu, H.H., Ju, Y., 2015. Relationships between permeability, porosity and effective stress for low-permeability sedimentary rock. International Journal of Rock Mechanics & Mining Sciences 78, Elsevier, pp. 304-318.

AC C

758 759 760

33

ACCEPTED MANUSCRIPT Highlights Detailed comparative study of transient permeability methods on core samples Insights on effect of anisotropy on transport properties by coupling of methods Interpretation of fluid dynamic effects by modified GRI permeability method

AC C

EP

TE D

M AN U

SC

RI PT

Optimal experimental conditions for modified GRI method presented