Shale Pore Characterization Using NMR Cryoporometry with

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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

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Energy & Fuels

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Shale pore characterization using NMR

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Cryoporometry with octamethylcyclotetrasiloxane as

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the probe liquid

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Qian Zhang1,2, Yanhui Dong*,1,2,3, Shimin Liu3, Derek Elsworth3, Yixin Zhao4 1

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Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics,

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Chinese Academy of Sciences, Beijing 100029, China 2

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3

Department of Energy and Mineral Engineering, G3 Center and EMS Energy Institute, The

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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,

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Beijing 100083, China

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ABSTRACT

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Fluid flow and chemical transport within shale are determined by the pore size distribution and

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its connectivity. Due to both low porosity and small (nanometer) pore size, common

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characterization methods, such as Mercury Injection Capillary Pressure (MICP) and Nitrogen

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Adsorption Method (NAM), have limited resolution and applicability. Nuclear Magnetic

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Resonance Cryoporometry (NMR-C) is a novel characterization method that exploits the Gibbs-

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Thomson effect and provides a complementary method of characterizing aggregate pore

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structure at fine resolution. We use water and octamethylcyclotetrasiloxane (OMCTS) as probe

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liquids for NMR-C on controlled-porosity samples of SBA, CPG and shale. The analysis

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accommodates the influence of melting temperature, KGT, and surface layer thickness, ε, on the

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pore size distribution (PSD). Calibration experiments permeated with the two fluids demonstrate

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that OMCTS has a larger KGT and that the PSD for different cryoporometric materials is not

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subject to different surface curvature of pores. Furthermore, the PSDs for shale are characterized

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by MICP, NAM and NMR-C which give comparable results. Shale samples have heterogeneous

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pore distributions with peak pore diameters at ~3 nm and mesopores diameters 2-50 nm

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comprising the main storage volume. Due to its larger molecular size and corresponding large

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KGT, NMR-C-OMCTS is able to characterize pores to 2 microns but misses pores smaller than 5

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nm. Meanwhile, NMR-C using OMCTS images a broader PSD than that by NMR-C-Water due

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to the propensity of OMCTS to imbibe into the organic matter, relative to water. NMR-C-

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OMCTS shows the superiority and potential due to the higher signal/noise (S/N) ratio and wider

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measurement range up to 2 microns. With regard to shales, an insight is that 115 Knm is an

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appropriate KGT value for measurements with the surface layer thickness of 2 nm. Moreover, the

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applications of NMR-C-OMCTS will come down to other rocks through further research.

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KEYWORDS

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Shale; Pore size distribution; NMR Cryoporometry; Octamethylcyclotetrasiloxane


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Energy & Fuels

1. Introduction

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Porous rocks that are structurally and chemically heterogeneous have important uses1 as

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reservoirs for water and hydrocarbons and as barriers to flow. Transport and storage properties of

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such media are controlled by the pore size distribution (PSD) as this influences strength,

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compressibility, permeability and development of fracture plane2,3.

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Compared to conventional reservoir rocks, pores in shales vary in size from microns to

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angstroms in both and typically have low porosities (5–10%) and permeabilities (nano-Darcy to

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micro-Darcy)4. Pore characterization techniques applied to shales demonstrate that the pore size

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distribution is sensitive to both the measurement technique and experimental conditions5. Some

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measurements are applied directly on the pores while others effectively measure pore throat

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diameters. Mercury Injection Capillary Pressure (MICP) and Nitrogen Adsorption Method

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(NAM) measurements are commonly applied for PSD characterization for gas shales. These

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methods are invasive and involve intrusion of a fluid by either high pressure mercury (MICP) or

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low pressure nitrogen (NAM)6. Non-invasive imaging is possible through Small Angle Neutron

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Scattering (SANS), Neutron Diffraction Cryoporometry (NDC), Differential Scanning

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Calorimetry (DSC) and Nuclear Magnetic Resonance (NMR) – also to determine PSDs.

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However, most methods above have limitations in covering a broad distribution of pore sizes -

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from microspores to macrospores with high precision7,8. In order to cover an extended range of

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PSDs, different techniques are frequently used in combination. For example, NMR and X-ray

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small angle scattering may be combined to characterize pore system and flow characteristics9, as

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may be NMR and micro-CT scanning to define pore network models10, and MICP and scanning

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electron microscopy11 combined for petro-physical characterization of shale.


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NMR Cryoporometry (NMR-C) has been used in pore characterization of various micro and

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mesoporous materials12. This technique involves freezing a liquid in the liquid-saturated pores

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and measuring the volume of liquid as the sample is incrementally warmed until all the liquid is

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melted. Since the melting point is depressed for pores/crystals of small size, this melting point

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depression gives a measurement of pore sizes. Since NMR distinguishes between solid and

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liquid, quantifying only liquid mass, then NMR Cryoporometry obtains clear transitions with

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high signal-to-noise ratio. Compared to other existing techniques, the major advantage of NMR-

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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)

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where, Tm∞ and Tm ( x ) are the bulk and the pore melting temperatures, σ sl is the solid-liquid

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surface free energy, ∆H f is the latent heat of melting, ρ s is the density of the solid, and x is the

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pore diameter. For arbitrarily shaped pores, Tm ( x ) depends on the average curvature of the pore

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wall rather than on a uniform size parameter such as x. We may rewrite equation 1 as,

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∆Tm =

K GT x ,

(2)

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where, KGT is the melting point depression constant. In a typical experimental protocol, the NMR

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signal intensity I(T) from the molten fraction of the pore-filling material is measured as the

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initially frozen sample is incrementally-warmed. To separate this signal from that of the frozen

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fraction, a difference between transverse relaxation times T2 in the respective states is exploited.

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The PSD is then calculated by numerical differentiation of I(T). If the NMR signal intensity is

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properly calibrated in terms of the mass of the sample, the PSD can be estimated.


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In NMR-C, the melting point depression constant KGT defines, in combination with

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instrumental parameters such as temperature spread in the sample and temperature step size, the

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achievable resolution and the detectable upper pore size15. Hence, choosing a probe material with

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a greater KGT is preferable. Computing the probe material constant KGT from thermodynamic

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properties requires knowledge of the solid-liquid surface tension, which is typically difficult to

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measure and is rarely available from independent experiments. Instead, KGT is often calibrated

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from the temperature shifts for phase transitions observed in some well-defined porous materials

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with different pore sizes.

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Water is the predominant liquid used in NMR-C measurements, which is easily imbibed into

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hydrophilic pores and has a low melting point depression constant. There has been a wide range

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of NMR-C-Water relying on the properties of water/ice systems in a confined geometry. NMR-

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C-Water has been widely used to image cement, wood, fuel cells and rocks16-18. In low iron and

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paramagnetic content materials, NMR-C-Water works well using 2τ echo sampling times of 2

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ms or greater19. If the metallic and paramagnetic contents are high, the measurements should be

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taken at intervals of 500 µs or less - essentially probing the brittle-plastic phase transition rather

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than the brittle-liquid phase transition. This yields spuriously low pore-size magnitudes and

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degrades accuracy. In addition, the expansion of water when freezing may damage porous media

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and influence the results of pore size distribution19,20. Thus the further investigate commenced to

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focus on the suitability of a-polar liquids to NMR-C measurements21. Cyclohexane has a long

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and successful history as an NMR-C probe liquid with a greater KGT. Cyclohexane is an organic

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compound, comprising a ring molecule with a six-fold symmetrical structure. The spin–spin

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relaxation time, T2 of liquid for cyclohexane is easily distinguishable from that of solid – the

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liquid T2 is of the order of milliseconds to seconds and the solid T2 of the order of microseconds.


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However, this probe fluid exhibits a bulk-phase plastic state between the solid and liquid phases

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and the transverse relaxation time does not change sufficiently sharply. Thus, it is well known

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that measurements need to be performed with a 2τ echo time of ~20 ms.

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Recently, octamethylcyclotetrasiloxane (OMCTS) has been observed to have a larger melting

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point depression constant than cyclohexane, potentially allowing access to pores >1 µm in

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diameter15. OMCTS also has the advantage of a short T2 (~20 µs) and a sharp at phase transition

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thus providing a clear discrimination between liquid and solid 1H NMR signals. Additionally,

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OMCTS is chemically inert, non-volatile, non-toxic, with a bulk melting point near 290 K22,23

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and appears capable of wetting both hydrophilic and hydrophobic surfaces15,24. NMR-C-OMCTS

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could be an effective method for characterizing nanopores in shales25, but there are still questions

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left unanswered such as the value of KGT.

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The following explores the characterization of pore size distributions for shales via NMR-C

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using both water and OMCTS as probe fluids. The NMR-C results are compared with data from

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MICP and NAM. With the calibration of OMCTS as the probe fluid, it is found that OMCTS not

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only improves signal/noise (S/N) ratio, but also has the potential for yielding PSDs for µm-size

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pores while simultaneously imbibing into both organic and inorganic components. Moreover, the

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effects of melting point depression constant and surface layer thickness on PSD measurement are

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discussed, which were rarely considered in previous studies using NMR-C.

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2. Experimental Investigation

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2.1 Sample preparation

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The response of natural shale is compared with manufactured calibration samples of known

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topology and morphology. Calibration samples were prepared from regular templated SBA-15

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porous silica consisting of cylindrical pores ~7-9 nm and from controlled pore glass (CPG) with


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a nominal average pore size of 24 nm (shown in Figure 1). According to TEM/SEM images of

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SBA and CPG, they were with an average pore diameter of 8.2 nm (SBA-15) and 23.9 nm

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(CPG). Additionally, shale samples were collected from the Longmaxi Formation (Xiliao,

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Shizhu County, China) and used in comparison. The shale samples were pulverized to sizes in

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the range ~1-2 mm for use in the NMR-C experiments with mineral compositions measured

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using SEM-EDS. Results were listed in Table 1. After drying at 105 ℃ for 24 h, the standard and

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shale samples were immersed in the probe liquids for ~10 h and then centrifuged at 5000 rpm for

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3 h in 5mm diameter thin-walled high-resolution NMR sample tubes. The containing tubes were

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2 cm in length and capped and sealed at the top. The permeating fluids were distilled water and

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anhydrous OMCTS.

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Figure 1. (a) TEM images of SBA and (b) of CPG12 used for this study

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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


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2.2 Experimental protocol

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The cryoporometric 1H NMR measurements were conducted on a Niumag with a resonant

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frequency of 21 MHz and equipped with a 10 mm probe. The temperature control system

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comprises a compressor and a cooling bath with a low temperature limit of -65 ℃. During the

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experiments, the temperature was incremented in 0.1-2 K steps and left to equilibrate for 10 mins

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to allow for thermal equilibrium at each temperature. Temperatures are incremented in the range

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240-283 K for water and 245-298 K for OMCTS (based on their bulk melting points). NMR-C

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measurements were performed using the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence.

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The spin-echo amplitude was measured with a time interval τ of 2 ms for water and 0.4 ms for

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OMCTS to suppress the signature of the solid and to ensure that the signal was entirely from the

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liquid phase. The amplitude of signal intensity at the first echo (T=2τ), representing the amount

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of hydrogen protons, was transformed to the volume of liquids. Before the NMR signal intensity

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could be converted into pore volumes, the measured intensity was corrected by calibration using

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a MnCl2 solution (concentration ∼ 0.25%) with T2 of ~1 ms and then transformed into water

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mass. The OMCTS mass was measured through the ratio of unit volume signal between water

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and OMCTS. The cryoporometric calibration measurements were repeated at least three times

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for each sample. Shale samples were also characterized by MICP and NAM, and the results were

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then compared to measurements by scanning electron microscopy (SEM) to support pore

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structure interpretations. MICP measurements were performed using a Micromeritics Autopore

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IV 9500 instrument, and run to a pressure of 0.10 psia, defined as a plateau toward the maximum

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pressure of injection at 60000 psi. NAM measurements were completed using a 3H-2000PS2

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Instrument at 77.4 K with an outgas temperature at 473 K. The experiments of NMR-C and SEM


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Energy & Fuels

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are completed in the Key Laboratory of Shale Gas and Geoengineering of the Chinese Academy

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of Sciences.

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3. Results

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3.1 Experimental calibration of KGT for water and OMCTS

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Although the melting point depression constant (KGT) is a material parameter, its value usually

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cannot be independently estimated due to the limited accuracy of determining σ sl . The KGT for a

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given liquid must be calibrated using known pore sizes. As standard calibration samples, SBA-

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15 and CPG were used to calibrate the KGT of both water and OMCTS in the NMR-C

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measurements.

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As to NMR-C-Water, with the temperature increasing for the standard samples (Figure

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2(a),2(c)), the liquid in the pores begins to melt (Figure 2(b), 2(d) : from B to C) with cumulative

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pore volume reaching a plateau when all the liquid in the pores has melted (Figure 2(b), 2(d):

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from C to D). The difference in temperature between B and C gives the melting point depression

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in the pores. The KGT were calibrated by SBA-15 and CPG, which have an average pore diameter

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of 8.2 nm (SBA-15) and 23.9 nm (CPG) respectively. As a result, they obtained the best fit when

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KGT=116±2 Knm (SBA-15) and 59±1 Knm (CPG) according to eq 2. The PSDs of SBA-15 and

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CPG from NMR-C-Water are both of the Gaussian type NMR-C-Water, having a full width at

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half maximum (FWHM) of 1.9 nm and 15 nm. From NMR-C-Water calibration experiments, the

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ratio of KGT for CPG and KGT for SBA is close to 1/2, which is similar to the results reported for

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sol-gel silicas and SBA-1526.

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Figure 2. Data of NMR-C-Water measurements for standard samples. (a) Echo amplitude at 4ms

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as a function of temperature for SBA-15; (b) Echo amplitude at 4ms as a function of temperature

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for CPG; (c) The PSD of SBA-15 (with KGT=116±2 Knm) ; (d) The PSD of CPG (with

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KGT=59±1 Knm).

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The melting curves measured by NMR-C-OMCTS have a similar form to those for NMR-C-

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Water. However, when considering organic liquids such as OMCTS, the influence of the liquid-

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like surface layer to the signal has to be considered. Non-linearity in the Gibbs-Thomson

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equation has been observed in previous work with the modified Gibbs-Thomson equation

194

proposed as:


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Energy & Fuels

∆Tm =

K GT , x − 2ε

(3)

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where ε is the width of the liquid-like layer. At a particular temperature, the thickness, ε, of the

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layer minimizes the interfacial interaction. Some studies have concluded that the surface layer

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can be approximated as approximately two-monolayers thick27-29 and this assumption simplifies

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the problem to one of defining a single-parameter. For OMCTS, with a monolayer width of 0.7-

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1.1 nm30, ε=2 nm is adopted in this work. The KGT calibrated by SBA-15 is 122±3 Knm with a

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FWHM of 1.8 nm. As for CPG, the KGT is 115±3 Knm with a FWHM of 4 nm (see Figure 3).

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Comparing the PSDs of SBA and CPG using NMR-C-Water, the data detected by NMR-C-

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OMCTS have the more similar data to the results calculated by TEM/SEM images with smaller

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FWHMs. In addition, according to the eq 2, with the same gradient of temperature, the NMR-C

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measurements using the liquid with a larger KGT , such as OMCTS, could obtain more diameter

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data. It means that the results measured by NMR-C-OMCTS have a significantly higher S/N than

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NMR-C-Water.

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Figure 3. Data of NMR-C-OMCTS measurements for standard samples. (a) Echo amplitude at

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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

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(with KGT=115±3 Knm)

214 215

3.2 Comparison of PSDs of shales measured by different techniques

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Shales have unique pore structures as a result of their complex evolution31 comprising multi-

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scale pore architectures spanning nanoscale to macroscale. Longmaxi shale comprises clay

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minerals, quartz, feldspar, calcite, dolomite and pyrite32. With these complex compositional

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components, the pore structure of Longmaxi shale comprises multiple pore types, including


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organic, inter-crystalline, framework, dissolution and biological pores and micro-factures.

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Typical SEM images are shown in Fig. 4 with various minerals and pores labeled.

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Figure 4. SEM images of contrasting pore types. (a) Organic pores, Dissolved pores, Framework

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pores; (b) Inter-crystalline pores, Micro-fractures, Organic pores.

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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).


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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


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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


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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

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magnitude of the KGT in term of surface curvature and may introduce a large error to the

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interpreted PSD. For shales, with a broad range of structural features (size and form), OMCTS

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with its broad operating range will be superior compared to other cryoporometric materials.

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Actually, the KGT=115 Knm of OMCTS is a reference value for shale measurements considering

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the existence of surface layers, which will be discussed in Section 4.2.

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4.2 The effect of a surface layer for OMCTS

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Stapf and Kimmich (1995)45 suggested that fluid-mineral surface layers may interfere with the

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interpretation of NMR Cryoporometry by providing a signal even at very low temperatures -

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misinterpreted as indicating the presence of very small pores. The effect of the surface layer may

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be diminished by lengthening the total echo time. The signal of water in pores is not highly

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sensitive to ε within the time interval, 2τ, of 4 ms. However, to some extent, the signal and the

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width of a surface layer may influence the results of PSDs when using OMCTS in pore diameters

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Shale Pore Characterization Using NMR Cryoporometry with

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