Subscriber access provided by Olson Library | Northern Michigan University
Article
Shale pore characterization using NMR Cryoporometry with octamethylcyclotetrasiloxane as the probe liquid Qian Zhang, Yanhui Dong, Shimin Liu, Derek Elsworth, and Yixin Zhao Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b00880 • Publication Date (Web): 21 Jun 2017 Downloaded from http://pubs.acs.org on July 2, 2017
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Energy & Fuels is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 30
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
1
Shale pore characterization using NMR
2
Cryoporometry with octamethylcyclotetrasiloxane as
3
the probe liquid
4
Qian Zhang1,2, Yanhui Dong*,1,2,3, Shimin Liu3, Derek Elsworth3, Yixin Zhao4 1
5
Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics,
6
Chinese Academy of Sciences, Beijing 100029, China 2
7 8
3
Department of Energy and Mineral Engineering, G3 Center and EMS Energy Institute, The
9 10
University of Chinese Academy of Sciences, Beijing 100049, China
Pennsylvania State University, University Park, PA-16802, USA 4
College of Resources & Safety Engineering, China University of Mining and Technology,
11
Beijing 100083, China
12
13
ABSTRACT
14
Fluid flow and chemical transport within shale are determined by the pore size distribution and
15
its connectivity. Due to both low porosity and small (nanometer) pore size, common
16
characterization methods, such as Mercury Injection Capillary Pressure (MICP) and Nitrogen
ACS Paragon Plus Environment
1
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 2 of 30
17
Adsorption Method (NAM), have limited resolution and applicability. Nuclear Magnetic
18
Resonance Cryoporometry (NMR-C) is a novel characterization method that exploits the Gibbs-
19
Thomson effect and provides a complementary method of characterizing aggregate pore
20
structure at fine resolution. We use water and octamethylcyclotetrasiloxane (OMCTS) as probe
21
liquids for NMR-C on controlled-porosity samples of SBA, CPG and shale. The analysis
22
accommodates the influence of melting temperature, KGT, and surface layer thickness, ε, on the
23
pore size distribution (PSD). Calibration experiments permeated with the two fluids demonstrate
24
that OMCTS has a larger KGT and that the PSD for different cryoporometric materials is not
25
subject to different surface curvature of pores. Furthermore, the PSDs for shale are characterized
26
by MICP, NAM and NMR-C which give comparable results. Shale samples have heterogeneous
27
pore distributions with peak pore diameters at ~3 nm and mesopores diameters 2-50 nm
28
comprising the main storage volume. Due to its larger molecular size and corresponding large
29
KGT, NMR-C-OMCTS is able to characterize pores to 2 microns but misses pores smaller than 5
30
nm. Meanwhile, NMR-C using OMCTS images a broader PSD than that by NMR-C-Water due
31
to the propensity of OMCTS to imbibe into the organic matter, relative to water. NMR-C-
32
OMCTS shows the superiority and potential due to the higher signal/noise (S/N) ratio and wider
33
measurement range up to 2 microns. With regard to shales, an insight is that 115 Knm is an
34
appropriate KGT value for measurements with the surface layer thickness of 2 nm. Moreover, the
35
applications of NMR-C-OMCTS will come down to other rocks through further research.
36
KEYWORDS
37
Shale; Pore size distribution; NMR Cryoporometry; Octamethylcyclotetrasiloxane
ACS Paragon Plus Environment
2
Page 3 of 30
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
38
Energy & Fuels
1. Introduction
39
Porous rocks that are structurally and chemically heterogeneous have important uses1 as
40
reservoirs for water and hydrocarbons and as barriers to flow. Transport and storage properties of
41
such media are controlled by the pore size distribution (PSD) as this influences strength,
42
compressibility, permeability and development of fracture plane2,3.
43
Compared to conventional reservoir rocks, pores in shales vary in size from microns to
44
angstroms in both and typically have low porosities (5–10%) and permeabilities (nano-Darcy to
45
micro-Darcy)4. Pore characterization techniques applied to shales demonstrate that the pore size
46
distribution is sensitive to both the measurement technique and experimental conditions5. Some
47
measurements are applied directly on the pores while others effectively measure pore throat
48
diameters. Mercury Injection Capillary Pressure (MICP) and Nitrogen Adsorption Method
49
(NAM) measurements are commonly applied for PSD characterization for gas shales. These
50
methods are invasive and involve intrusion of a fluid by either high pressure mercury (MICP) or
51
low pressure nitrogen (NAM)6. Non-invasive imaging is possible through Small Angle Neutron
52
Scattering (SANS), Neutron Diffraction Cryoporometry (NDC), Differential Scanning
53
Calorimetry (DSC) and Nuclear Magnetic Resonance (NMR) – also to determine PSDs.
54
However, most methods above have limitations in covering a broad distribution of pore sizes -
55
from microspores to macrospores with high precision7,8. In order to cover an extended range of
56
PSDs, different techniques are frequently used in combination. For example, NMR and X-ray
57
small angle scattering may be combined to characterize pore system and flow characteristics9, as
58
may be NMR and micro-CT scanning to define pore network models10, and MICP and scanning
59
electron microscopy11 combined for petro-physical characterization of shale.
ACS Paragon Plus Environment
3
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 4 of 30
60
NMR Cryoporometry (NMR-C) has been used in pore characterization of various micro and
61
mesoporous materials12. This technique involves freezing a liquid in the liquid-saturated pores
62
and measuring the volume of liquid as the sample is incrementally warmed until all the liquid is
63
melted. Since the melting point is depressed for pores/crystals of small size, this melting point
64
depression gives a measurement of pore sizes. Since NMR distinguishes between solid and
65
liquid, quantifying only liquid mass, then NMR Cryoporometry obtains clear transitions with
66
high signal-to-noise ratio. Compared to other existing techniques, the major advantage of NMR-
67
C is the ability to perform spatial imaging of samples in a natural hydrated state13.
68 69 70
The NMR-C method relies on a pore-size-dependent melting temperature depression of a porefilling material, given by the Gibbs-Thomson equation14, ∆Tm ( x ) = Tm∞ − Tm ( x ) =
4σ slTm ， x∆H f ρ s
(1)
71
where, Tm∞ and Tm ( x ) are the bulk and the pore melting temperatures, σ sl is the solid-liquid
72
surface free energy, ∆H f is the latent heat of melting, ρ s is the density of the solid, and x is the
73
pore diameter. For arbitrarily shaped pores, Tm ( x ) depends on the average curvature of the pore
74
wall rather than on a uniform size parameter such as x. We may rewrite equation 1 as,
75
∆Tm =
K GT x ,
(2)
76
where, KGT is the melting point depression constant. In a typical experimental protocol, the NMR
77
signal intensity I(T) from the molten fraction of the pore-filling material is measured as the
78
initially frozen sample is incrementally-warmed. To separate this signal from that of the frozen
79
fraction, a difference between transverse relaxation times T2 in the respective states is exploited.
80
The PSD is then calculated by numerical differentiation of I(T). If the NMR signal intensity is
81
properly calibrated in terms of the mass of the sample, the PSD can be estimated.
ACS Paragon Plus Environment
4
Page 5 of 30
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
82
In NMR-C, the melting point depression constant KGT defines, in combination with
83
instrumental parameters such as temperature spread in the sample and temperature step size, the
84
achievable resolution and the detectable upper pore size15. Hence, choosing a probe material with
85
a greater KGT is preferable. Computing the probe material constant KGT from thermodynamic
86
properties requires knowledge of the solid-liquid surface tension, which is typically difficult to
87
measure and is rarely available from independent experiments. Instead, KGT is often calibrated
88
from the temperature shifts for phase transitions observed in some well-defined porous materials
89
with different pore sizes.
90
Water is the predominant liquid used in NMR-C measurements, which is easily imbibed into
91
hydrophilic pores and has a low melting point depression constant. There has been a wide range
92
of NMR-C-Water relying on the properties of water/ice systems in a confined geometry. NMR-
93
C-Water has been widely used to image cement, wood, fuel cells and rocks16-18. In low iron and
94
paramagnetic content materials, NMR-C-Water works well using 2τ echo sampling times of 2
95
ms or greater19. If the metallic and paramagnetic contents are high, the measurements should be
96
taken at intervals of 500 µs or less - essentially probing the brittle-plastic phase transition rather
97
than the brittle-liquid phase transition. This yields spuriously low pore-size magnitudes and
98
degrades accuracy. In addition, the expansion of water when freezing may damage porous media
99
and influence the results of pore size distribution19,20. Thus the further investigate commenced to
100
focus on the suitability of a-polar liquids to NMR-C measurements21. Cyclohexane has a long
101
and successful history as an NMR-C probe liquid with a greater KGT. Cyclohexane is an organic
102
compound, comprising a ring molecule with a six-fold symmetrical structure. The spin–spin
103
relaxation time, T2 of liquid for cyclohexane is easily distinguishable from that of solid – the
104
liquid T2 is of the order of milliseconds to seconds and the solid T2 of the order of microseconds.
ACS Paragon Plus Environment
5
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 6 of 30
105
However, this probe fluid exhibits a bulk-phase plastic state between the solid and liquid phases
106
and the transverse relaxation time does not change sufficiently sharply. Thus, it is well known
107
that measurements need to be performed with a 2τ echo time of ~20 ms.
108
Recently, octamethylcyclotetrasiloxane (OMCTS) has been observed to have a larger melting
109
point depression constant than cyclohexane, potentially allowing access to pores >1 µm in
110
diameter15. OMCTS also has the advantage of a short T2 (~20 µs) and a sharp at phase transition
111
thus providing a clear discrimination between liquid and solid 1H NMR signals. Additionally,
112
OMCTS is chemically inert, non-volatile, non-toxic, with a bulk melting point near 290 K22,23
113
and appears capable of wetting both hydrophilic and hydrophobic surfaces15,24. NMR-C-OMCTS
114
could be an effective method for characterizing nanopores in shales25, but there are still questions
115
left unanswered such as the value of KGT.
116
The following explores the characterization of pore size distributions for shales via NMR-C
117
using both water and OMCTS as probe fluids. The NMR-C results are compared with data from
118
MICP and NAM. With the calibration of OMCTS as the probe fluid, it is found that OMCTS not
119
only improves signal/noise (S/N) ratio, but also has the potential for yielding PSDs for µm-size
120
pores while simultaneously imbibing into both organic and inorganic components. Moreover, the
121
effects of melting point depression constant and surface layer thickness on PSD measurement are
122
discussed, which were rarely considered in previous studies using NMR-C.
123
2. Experimental Investigation
124
2.1 Sample preparation
125
The response of natural shale is compared with manufactured calibration samples of known
126
topology and morphology. Calibration samples were prepared from regular templated SBA-15
127
porous silica consisting of cylindrical pores ~7-9 nm and from controlled pore glass (CPG) with
ACS Paragon Plus Environment
6
Page 7 of 30
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
128
a nominal average pore size of 24 nm (shown in Figure 1). According to TEM/SEM images of
129
SBA and CPG, they were with an average pore diameter of 8.2 nm (SBA-15) and 23.9 nm
130
(CPG). Additionally, shale samples were collected from the Longmaxi Formation (Xiliao,
131
Shizhu County, China) and used in comparison. The shale samples were pulverized to sizes in
132
the range ~1-2 mm for use in the NMR-C experiments with mineral compositions measured
133
using SEM-EDS. Results were listed in Table 1. After drying at 105 ℃ for 24 h, the standard and
134
shale samples were immersed in the probe liquids for ~10 h and then centrifuged at 5000 rpm for
135
3 h in 5mm diameter thin-walled high-resolution NMR sample tubes. The containing tubes were
136
2 cm in length and capped and sealed at the top. The permeating fluids were distilled water and
137
anhydrous OMCTS.
138 139
Figure 1. (a) TEM images of SBA and (b) of CPG12 used for this study
140 141
Table 1. Mineral components of the shale sample measured by SEM-EDS
Sample
Quartz (%)
Pyrite (%)
Feldspa r (%)
Chlorite (%)
Apatite (%)
Calcite (%)
Dolomit e(%)
Illite (%)
Rutile (%)
Shale
37.5
6.37
35.10
1.87
0.08
2.22
0.81
8.09
0.80
ACS Paragon Plus Environment
7
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
142
Page 8 of 30
2.2 Experimental protocol
143
The cryoporometric 1H NMR measurements were conducted on a Niumag with a resonant
144
frequency of 21 MHz and equipped with a 10 mm probe. The temperature control system
145
comprises a compressor and a cooling bath with a low temperature limit of -65 ℃. During the
146
experiments, the temperature was incremented in 0.1-2 K steps and left to equilibrate for 10 mins
147
to allow for thermal equilibrium at each temperature. Temperatures are incremented in the range
148
240-283 K for water and 245-298 K for OMCTS (based on their bulk melting points). NMR-C
149
measurements were performed using the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence.
150
The spin-echo amplitude was measured with a time interval τ of 2 ms for water and 0.4 ms for
151
OMCTS to suppress the signature of the solid and to ensure that the signal was entirely from the
152
liquid phase. The amplitude of signal intensity at the first echo (T=2τ), representing the amount
153
of hydrogen protons, was transformed to the volume of liquids. Before the NMR signal intensity
154
could be converted into pore volumes, the measured intensity was corrected by calibration using
155
a MnCl2 solution (concentration ∼ 0.25%) with T2 of ~1 ms and then transformed into water
156
mass. The OMCTS mass was measured through the ratio of unit volume signal between water
157
and OMCTS. The cryoporometric calibration measurements were repeated at least three times
158
for each sample. Shale samples were also characterized by MICP and NAM, and the results were
159
then compared to measurements by scanning electron microscopy (SEM) to support pore
160
structure interpretations. MICP measurements were performed using a Micromeritics Autopore
161
IV 9500 instrument, and run to a pressure of 0.10 psia, defined as a plateau toward the maximum
162
pressure of injection at 60000 psi. NAM measurements were completed using a 3H-2000PS2
163
Instrument at 77.4 K with an outgas temperature at 473 K. The experiments of NMR-C and SEM
ACS Paragon Plus Environment
8
Page 9 of 30
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
164
are completed in the Key Laboratory of Shale Gas and Geoengineering of the Chinese Academy
165
of Sciences.
166
3. Results
167
3.1 Experimental calibration of KGT for water and OMCTS
168
Although the melting point depression constant (KGT) is a material parameter, its value usually
169
cannot be independently estimated due to the limited accuracy of determining σ sl . The KGT for a
170
given liquid must be calibrated using known pore sizes. As standard calibration samples, SBA-
171
15 and CPG were used to calibrate the KGT of both water and OMCTS in the NMR-C
172
measurements.
173
As to NMR-C-Water, with the temperature increasing for the standard samples (Figure
174
2(a),2(c)), the liquid in the pores begins to melt (Figure 2(b), 2(d) : from B to C) with cumulative
175
pore volume reaching a plateau when all the liquid in the pores has melted (Figure 2(b), 2(d):
176
from C to D). The difference in temperature between B and C gives the melting point depression
177
in the pores. The KGT were calibrated by SBA-15 and CPG, which have an average pore diameter
178
of 8.2 nm (SBA-15) and 23.9 nm (CPG) respectively. As a result, they obtained the best fit when
179
KGT=116±2 Knm (SBA-15) and 59±1 Knm (CPG) according to eq 2. The PSDs of SBA-15 and
180
CPG from NMR-C-Water are both of the Gaussian type NMR-C-Water, having a full width at
181
half maximum (FWHM) of 1.9 nm and 15 nm. From NMR-C-Water calibration experiments, the
182
ratio of KGT for CPG and KGT for SBA is close to 1/2, which is similar to the results reported for
183
sol-gel silicas and SBA-1526.
184
ACS Paragon Plus Environment
9
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 10 of 30
185
186
Figure 2. Data of NMR-C-Water measurements for standard samples. (a) Echo amplitude at 4ms
187
as a function of temperature for SBA-15; (b) Echo amplitude at 4ms as a function of temperature
188
for CPG; (c) The PSD of SBA-15 (with KGT=116±2 Knm) ; (d) The PSD of CPG (with
189
KGT=59±1 Knm).
190
The melting curves measured by NMR-C-OMCTS have a similar form to those for NMR-C-
191
Water. However, when considering organic liquids such as OMCTS, the influence of the liquid-
192
like surface layer to the signal has to be considered. Non-linearity in the Gibbs-Thomson
193
equation has been observed in previous work with the modified Gibbs-Thomson equation
194
proposed as:
ACS Paragon Plus Environment
10
Page 11 of 30
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
195
Energy & Fuels
∆Tm =
K GT , x − 2ε
(3)
196
where ε is the width of the liquid-like layer. At a particular temperature, the thickness, ε, of the
197
layer minimizes the interfacial interaction. Some studies have concluded that the surface layer
198
can be approximated as approximately two-monolayers thick27-29 and this assumption simplifies
199
the problem to one of defining a single-parameter. For OMCTS, with a monolayer width of 0.7-
200
1.1 nm30, ε=2 nm is adopted in this work. The KGT calibrated by SBA-15 is 122±3 Knm with a
201
FWHM of 1.8 nm. As for CPG, the KGT is 115±3 Knm with a FWHM of 4 nm (see Figure 3).
202
Comparing the PSDs of SBA and CPG using NMR-C-Water, the data detected by NMR-C-
203
OMCTS have the more similar data to the results calculated by TEM/SEM images with smaller
204
FWHMs. In addition, according to the eq 2, with the same gradient of temperature, the NMR-C
205
measurements using the liquid with a larger KGT , such as OMCTS, could obtain more diameter
206
data. It means that the results measured by NMR-C-OMCTS have a significantly higher S/N than
207
NMR-C-Water.
208
ACS Paragon Plus Environment
11
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 12 of 30
209 210
Figure 3. Data of NMR-C-OMCTS measurements for standard samples. (a) Echo amplitude at
211
0.8 ms as a function of temperature for SBA-15; (b) Echo amplitude at 0.8 ms as a function of
212
temperature for CPG; (c) The PSD of SBA-15 (with KGT=122±3 Knm) ; (d) The PSD of CPG
213
(with KGT=115±3 Knm)
214 215
3.2 Comparison of PSDs of shales measured by different techniques
216
Shales have unique pore structures as a result of their complex evolution31 comprising multi-
217
scale pore architectures spanning nanoscale to macroscale. Longmaxi shale comprises clay
218
minerals, quartz, feldspar, calcite, dolomite and pyrite32. With these complex compositional
219
components, the pore structure of Longmaxi shale comprises multiple pore types, including
ACS Paragon Plus Environment
12
Page 13 of 30
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
220
organic, inter-crystalline, framework, dissolution and biological pores and micro-factures.
221
Typical SEM images are shown in Fig. 4 with various minerals and pores labeled.
222 223
Figure 4. SEM images of contrasting pore types. (a) Organic pores, Dissolved pores, Framework
224
pores; (b) Inter-crystalline pores, Micro-fractures, Organic pores.
225
In this study, PSDs were characterized by three different techniques (MICP, NAM and NMR-
226
C). MICP is a widely accepted technique to characterize pore throat diameters in a porous
227
medium by recording the volume of mercury injected at each step of incremented fluid pressure.
228
Unfortunately, MICP is incapable of quantifying the volume of the pore or the volumetric
229
properties of those pores. The maximum injection pressure is 60,000 psi (413 MPa), representing
230
a pore throat diameter of ~3 nm. NAM determines the amount of gas occupying the internal
231
surface of a porous material and estimates the PSD for pore sizes 100 nm.
257 258
Figure 6. Comparison of pore size distributions evaluated by MICP, NAM, NMR-C (KGT=59
259
Knm for water and KGT=115 Knm for OMCTS)
260
The PSDs derived from the melting behavior by NMR-C are also compared with MICP and
261
NAM. According to the hysteresis loop obtained by NAM and the SEM images, the shale pores
262
are closer to CPG than SBA, and the PSDs detected by NMR-C-Water (Figure 6), as calculated
263
by KGT =59 Knm, are the same as the value calibrated by CPG, while the influence on OMCTS is
264
less. The PSDs determined from using water as the probe liquid contain details of pores below 2
265
nm while OMCTS excludes pores below a 5 nm threshold (when KGT =115 Knm and ε=2 nm).
ACS Paragon Plus Environment
15
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 16 of 30
266
The magnitude of the PSD obtained by OMCTS is larger than that recovered from using water,
267
especially on macropores (see Figure 7). This is also larger than recovered by MICP and NAM.
268
OMCTS is again superior to previous probe materials due to its ability to access large pores with
269
pore sizes up to 2 µm.
270 271
Figure 7. Comparison of bar graphs using NMR-C-Water (with KGT =59 Knm) and NMR-C-
272
OMCTS (with KGT =115 Knm)
273
4. Discussion
274
4.1 The KGT of water and OMCTS for different samples
275
The melting temperature of liquids is related to the surface energy and dependents on the
276
geometry of the interface between the crystal and liquid. For convenience eq 2 can be expressed
277
in the following form37
ACS Paragon Plus Environment
16
Page 17 of 30
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
278
Energy & Fuels
∆Tm =
K GT k g ⋅ k s ⋅ ki , = x x
(4)
279
where kg is a structural geometric factor depending on the interfacial shape, ks is a constant
280
describing the crystalline solid of the solid–liquid system, and ki is an interfacial energy term.
281
The term kg/x is related to the surface-to-volume (S/V) ratio for different media. SBA-15 is a
282
highly regular material containing cylindrical pores on a hexagonal lattice and with a very
283
narrow pore distribution38. Conversely, CPG is fabricated via spinoidal decomposition with
284
ligaments of a complex non-cylindrical geometry24,39. The shape indicator value of CPG falls
285
between cylinders and spheres, due to the random and interconnected tubular shape of the pores.
286
Thus, KGT evaluated by eq 2 and modeled for cylindrical pores may provide the main difference
287
between the different samples. It is noteworthy that the relative magnitude of KGT for OMCTS,
288
for different cryoporometric materials, is not subject to this limitation15. In addition, the property
289
of liquids may be the main factor contributing to the different behavior of KGT. The values of KGT
290
in earlier studies were summarized in Table 2. Actually, water is a liquid most strongly subject to
291
thermodynamic fluctuations, especially coupling with porous media of disordered pore structure
292
40
293
of water.
.Because of this, the evident variation of KGT is occurred in different porous materials in terms
294
Table 2. Cryoporometrically relevant physical properties of OMCTS (ε is the thickness of
295
surface layer)
Probe liquid
KGT calibrated by different samples (Knm) Sol-gel 1
Water OMCTS
57.3 , 58.2 5341 -
16
SBA
MCM
CPG
14026, 116.4±0.538
51.942, 52±243
48±0.815, 5044
-
-
113±3 (ε=2)15, 160±4 (ε=0)15
ACS Paragon Plus Environment
17
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 18 of 30
296 297
Due to various pore formation mechanisms, each type of pore is distinguished by its pore size,
298
shape and environment. For example, organic pores are predominantly round or oval in shape
299
and are relatively small in size; and dissolution usually occurs in carbonates and feldspars with
300
micro-factures zigzagged in shape and with high tortuosity – all of which influence the
301
magnitude of the KGT in term of surface curvature and may introduce a large error to the
302
interpreted PSD. For shales, with a broad range of structural features (size and form), OMCTS
303
with its broad operating range will be superior compared to other cryoporometric materials.
304
Actually, the KGT=115 Knm of OMCTS is a reference value for shale measurements considering
305
the existence of surface layers, which will be discussed in Section 4.2.
306
4.2 The effect of a surface layer for OMCTS
307
Stapf and Kimmich (1995)45 suggested that fluid-mineral surface layers may interfere with the
308
interpretation of NMR Cryoporometry by providing a signal even at very low temperatures -
309
misinterpreted as indicating the presence of very small pores. The effect of the surface layer may
310
be diminished by lengthening the total echo time. The signal of water in pores is not highly
311
sensitive to ε within the time interval, 2τ, of 4 ms. However, to some extent, the signal and the
312
width of a surface layer may influence the results of PSDs when using OMCTS in pore diameters
313
