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The applications of NMR Relaxometry, NMR Cryoporometry and FFC NMR to nanoporous structures and dynamics in shale at low magnetic fields Bing Zhou Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b01603 • Publication Date (Web): 27 Aug 2018 Downloaded from http://pubs.acs.org on August 30, 2018
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Energy & Fuels
The applications of NMR Relaxometry, NMR Cryoporometry and FFC NMR to nanoporous structures and dynamics in shale at low magnetic fields
Bing Zhou
School of Materials Science and Engineering, Tongji University, Shanghai 210000, China
[email protected] 0086-18721759096
Key words: shale, NMR Relaxometry, NMR Cryoporometry, FFC NMR, nanopores, microwettability, surface dynamics, applicability
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ABSTRACT
Shale gas and oil have increasingly become a very important unconventional energy resource. As such, it is critical to characterize the porous structure and surface dynamics such as micro-wettability and diffusion, for the estimation and recovery of these unconventional resources. Due to the salient nanoporous structures present in shales, nuclear magnetic resonance (NMR) may currently be the only efficient and powerful tool for investigating and characterizing the nanoporous structures and dynamics in shales. This review discusses various NMR methods including NMR Relaxometry, NMR Cryoporometry and Fast Field Cycling (FFC) NMR and identifies the merits and limitations of these approaches. The review also identifies fallacies associated with such applications often seen in the literature. The potential of NMR can be exploited further as the methods used here for unconventional energy resources can also be applied to other intriguing porous media.
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INTRODUCTION The past decades have witnessed shale gas and oil as an increasingly important source of unconventional energy, owing to the shale gas revolution in the USA.1-4 The most salient feature of gas/oil shales is their nanoporous structures, which result in low porosity and ultralow permeability compared with the conventional reservoirs. Therefore, measurements and characterizations of nanoporous structures and dynamics in shales play an essential role in evaluating and developing shale gas reservoirs. 4-6 However, nanopores in such shales make traditional laboratory characterization methods such as gas sorption, mercury intrusion porosimetry (MIP), scanning electron microscopy (SEM) and transmission electron microscopy (TEM), difficult to apply. 7,8 Nuclear magnetic resonance (NMR), however, is very sensitive to local structural environments and dynamic processes at the atomic/molecular level and is, therefore, an ideal approach for characterizing the nanoporous structures and dynamics in shales. Because low field NMR (LF NMR) can suppress the adverse NMR effects from the strong heterogeneities in porous media, in contrast to high field NMR. LF NMR experiments, such as NMR Relaxometry, NMR Cryoporometry and Fast Field Cycling (FFC) NMR, have been gaining momentum in characterizing nanopores and dynamics for strongly heterogeneous shale rocks. 8-15 NMR relaxation measurements are the cornerstone for all of these LF NMR methods for the study of porous media. Shales are characterized by ultralow permeability and very low porosity, dominated by nanometer-scale pores, unlike conventional reservoir rocks where 1H NMR signals are mainly associated with the fluids inside micro- and macroscopic pores within the rocks. The majority of the NMR signal decay in shale is produced by magnetic interactions on and near pore surfaces within shale, since very high surface-to-volume ratios in nanopores
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significantly enhance surface relaxation.
4,16-17
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The BPP and surface relaxation theories are
briefly described in the following section.
BRIEF DESCRIPTION OF RELAXATION THEORY FOR POROUS MEDIA After polarization of total sample magnetization, by orientation of 1H nuclei in the sample along the direction of an external magnetic field, and excitation of a detectable signal, by the application of a radiofrequency magnetic field, NMR experiments measure the decay of detectable sample magnetization. The total initial magnetization (M0) is proportional to the total number of 1H nuclei (informally “spins”) in the sample under ideal conditions. Both the longitudinal relaxation time constant (T1) and the transverse relaxation time constant (T2) can be obtained from the measured magnetization decay, depending on the form of the measurement, which give different characteristic information about the samples. The T1 values are affected by the collisions between the liquid-state molecules and the walls of the pore boundaries, particularly dominated by the presence of strong relaxation sinks at the pore surface for porous media. On the other hand, T2 is associated with the spin dephasing (exchange of energy between spins) during an NMR measurement sequence. 1. BPP Relaxation Theory T1 and T2 can be modeled by the classical BPP theory, 18 which relates the relaxation times to the correlation time τ of the dipolar interaction as stated by Eq. (1): 1 T1
= 2C [
2τ 1+ω2 τ2
+
8τ ] 1+4ω2 τ2
1 T2
= C [6τ + 1+ω2 τ2 + 1+4ω2 τ2]
10τ
4τ
where ω is the Larmor frequency and C is a constant.
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(1)
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2.
Surface relaxation theory for porous media Unlike the bulk state, relaxation for the confined liquid in pores will be promoted by
surface interactions, which result in the dipolar NMR interactions between molecular 1H and electronic spins (paramagnetic sinks) on the pore walls. Assuming fast molecular exchange or diffusion between the liquid within the pore and the liquid layer adsorbed on the pore surface, the measured relaxation rates are the weighted average of the bulk (TB) and surface relaxation (TS) rates governed by Eq. (2): 19-21 Sp S p εS 1 𝑓S 𝑓b 1 1 = + ≈ + = + ρ1 Vp T1 T1S T1B T1B Vp T1S T1B
1 T2
𝑓
𝑓
= TS + Tb + 1S
2B
𝐷𝛾 2 𝐺 2 𝑇𝐸2 12
1
≈T
2B
+
S p εS Vp T2S
+
𝐷𝛾 2 𝐺 2 𝑇𝐸2 12
1
=T
2B
Sp
+ ρ2 V + p
𝐷𝛾 2 𝐺 2 𝑇𝐸2 12
(2)
where fb and fs are the volume fraction for bulk and surface layer of the pore respectively with fb+fs=1; ρ1 (=εS/T1S) and ρ2 (=εS/T2S) are the surface relaxivity for surface relaxation times of T1S and T2S which express the strength of surface relaxation; εS is the thickness of adsorbed liquid layer on the pore surface; Sp and Vp are the pore surface area and volume, respectively; D and G are the diffusion coefficient and magnetic field gradient strength, respectively; while TE is the experimental inter-echo time for 180º pulses. Therefore, based on Eq. (2), measured relaxation times cannot be shorter than the corresponding surface relaxations. Even though the measured 1/T2 rate is the weighted average between bulk (1/T2B) and surface (1/T2S) relaxation rates based on the surface relaxation theory, the bulk T2B in Eq. (2) can be neglected if it is long enough compared with surface relaxation T2S for sake of approximations and simplifications.
16-17
More importantly, Eq. (2) yields the
well-known dependence of relaxation times on the surface to volume ratio (Sp/Vp) of a pore, thus, relates pore size to measured relaxation times.
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LF NMR EXPERIMENTS AND INSTRUMENTATIONS T1 is usually measured using the inversion recovery (IR) or saturation recovery method, while T2 is measured with the Carr Purcell Meiboom Gill (CPMG) sequence or from a series of spin echoes with different echo times. 7 The measurement of diffusion coefficient (D) in porous media is usually facilitated by external magnetic field gradients. An inversion method will be adopted to obtain the distribution of exponential decay time constants from the NMR data, which will be the basis of all succeeding interpretation methods. 21 The distributions of relaxation times are considered as an indication of pore size distribution (PSD) under ideal conditions and T2 is most commonly used for NMR Relaxometry measurements. Almost all LF NMR spectrometers in a very wide frequency range are capable of such measurements. In appropriately equipped spectrometers, T2 may be correlated with T1 or D in two-dimensional (2D) experiments at low fields, which can provide further dispersion and enhance phase discrimination in porous media (Mitchell et al. 2014).
22
Depending on the LF
NMR spectrometer and the main purpose for LF NMR experiments, the sizes for NMR probe and sample vary from 5 mm to 1 inch, while the sample can be in powder or in a cylindrical shape. Generally, Inverse Laplace Transformation (1D and 2D) is employed to process experimental NMR data in order to determine the distribution of relaxation times in porous media. The 1H Larmor frequency at various magnetic fields for LF NMR Cryoporometry spectrometers usually varies from 2 to 22 MHz and typically the CPMG sequence has been employed for measuring M0 and T2 distributions. As an example, commercial LF NMR Cryoporometry spectrometers, MicroMR12-025V with 1H resonance frequencies of 12 or 21
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MHz and a lowest temperature of -60ºC, had been developed specifically for NMR Cryoporometry measurements on shale by the Suzhou Niumag Analytical Instrument Co. in China. The validity and accuracy of PSD in porous media obtained by NMR Cryoporometry rely heavily on the temperature resolution of the instrumentation, and various apparatuses have been designed and developed to achieve such temperature resolution within the sample inside the probe. 23-25 In order to avoid possible supercooling effects, usually the shale samples are initially cooled to the lowest temperature and then incrementally warmed up to bulk melting temperature in suitable steps for NMR Cryoporometry measurements. 8 The 1H Larmor frequency of commercially available spectrometers for FFC NMR experiments ranges from 10 kHz to 40 MHz. As an example, such FFC NMR instruments from Stelar s.r.l., based in Mede in Italy, which were designed to obtain a T1 profile at each magnetic field, were really a breakthrough in this field. In order to improve the NMR signal to noise ratio at low Larmor frequencies between 10 kHz and 3 MHz, the so-called pre-polarized (PP) NMR sequence can be used to firstly pre-polarize the spins at a relatively high magnetic field Bp (with a Larmor frequency generally ~9 MHz for 1H) in Stelar instruments. The complementary nonpolarized (NP) NMR sequence can then be used for the higher frequency range (4~40 MHz for 1H). As the result of FFC NMR experiments, the NMR dispersion profile, which consists of the average T1 at each field, can provide an unique perspective and micro-dynamic parameters in porous media. 16,17
SOME SPECIFIC CONSIDERATIONS FOR SHALE LF NMR As shale is dominated by very small pores with possible diffusional couplings between the nanopores, the length scale of the diffusion displacements is comparable to pore size
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during a period comparable to T2. The conventional surface relaxivity concept may not hold for such a nanoporous system, so the measured relaxation times may not be valid for characterizing and calibrating pore sizes any more.
21
Due to such dominant small pore sizes, shales often
contain less fluid content but significant amounts of restricted hydrogen in organic solids or hydrated minerals,
20
which poses another challenge for the NMR characterizations of shales
although NMR relaxation techniques could be well suited for detecting and quantifying water or other liquids in nanopores. 21 As a result, there exists disagreement about whether T2 in shale is significantly affected by the internal field gradients (local field heterogeneity). Josh et al. (2012) 4 claimed that T2 decay is affected at least as much by local magnetic field gradients within the pore space as by the surface relaxation, however, the effects of local field heterogeneity on NMR signal appeared negligible in almost all situations due to the small sizes of the nanopores, where the effect of such field heterogeneity on NMR signals is expected to be very small at low magnetic fields, specifically using CPMG pulse sequences. 7 Furthermore, surface relaxation usually is assumed to be the main NMR relaxation mechanism in porous media samples, however, other relaxation mechanisms, such as residual dipolar couplings, rapid exchange and transfer of magnetization between mobile and immobile phases, 7,21 may also exert certain influences on T2 relaxation in shales.7,8 Of course, the possible NMR interactions between 1H and the almost ubiquitous paramagnetic impurities in shale such as iron oxides and pyrite, should not be ignored either. It is also worth emphasizing that homonuclear dipolar coupling among the significant amount of 1H spins in forms with restricted motion (especially within organic materials), which cannot be effectively refocused by the usual spin echo method, may also significantly affect T2 and so its interpretations for organic shales.
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14,20
Additionally, in such heterogeneous porous systems as the inorganic and organic pores in
shale, it is challenging to decide whether the peaks of the T2 distribution result from different PSD or are caused by different fluids in the different pores.
21
For T2 NMR Relaxometry
experiments on shales, although only the free and adsorbed H2O in nanopores are the main targets, structural H, such as OH in clay minerals and H in organic materials, may also interfere with the NMR measurements and should be distinguished or filtered out. Similarly, relaxation and diffusion properties of gas in shales are controlled by the combined effects of adsorption, spin rotation of gas molecules, enhanced surface relaxation, restricted diffusion and molecular exchange between the adsorbed and free phases. 26,27 According to Eq. (2), nevertheless, and different from T2 with the dephasing of 1H spin coherence, molecular diffusion does not affect T1. Thus, diffusion coupling among pores and so the internal field gradients do not affect the interpretation of measured T1, especially for PSD. Furthermore, as T1 is always longer than T2, T1 appears more robust and more feasible for shale. Few T1 NMR Relaxometry studies have been done for shale so far, 20 although some researchers have made use of the dependence of T1 on external magnetic field strengths, such as FFC NMR, to probe the dynamics and identify components in nanopores within shales. 16,17 In summary, the assumptions and approximations for surface NMR relaxation theory should not be taken for granted for every porous media sample. The T2 relaxation mechanism in shale is very complicated and only the apparent T2 can be measured. Therefore, cautions and discretions are advised during the application of surface NMR methodology and theory to the study of shale samples. Based on the NMR relaxations and other NMR characteristics caused by the unique properties of shales, this review tries to sort out the NMR tools for characterizing the nanopores such as PSD and surface dynamics in shales, and also list the merits as well as the
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limits for such NMR tools. Additionally, the review points to a few fallacies associated with such NMR applications by some researchers. By presenting this review, the author hopes that the advantages and potential of NMR can be fully exploited for this important unconventional energy resource, while being appropriately aware of and cautious about the limitations of such techniques. Some possible developments in applying NMR to shale studies in the future are also speculated about in this review.
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THE APPLICATIONS OF LF NMR TO SHALE 1. NMR Relaxometry for shale PSD and logging (1) Applying NMR Relaxometry characterizing PSD within shales Assuming the general biphasic fast exchange model, where the exchange time between protons in liquid transiently belonging to the surface and the bulk in pores is much shorter than their respective relaxation times, NMR Relaxometry is the most widely used family of methods which provide limited but valuable information on geological samples. In particular, information about fluid saturation and pore structure can be obtained by taking advantage of the two principal relaxation mechanisms of T1 and T2, and usually 1H T2 NMR Relaxometry is used to infer the distribution of pore sizes.
20
Josh et al. (2012)
4
found that the T1 and T2 can be
readily measured for water within most shale samples and deduced that NMR is very sensitive to 1
H spin diffusion and surface relaxation in the shales, including 1H NMR signals from surface
bound water, confined water within the pore space and water in tiny cracks or in silty patches (i.e., larger pores). Josh et al. (2012) 4 and Daigle et al. (2017) 28 also correlated T2 distributions with PSD down to pores as small as 3 nm for shale samples, which were compared with PSD measured by other techniques such as MIP or gas sorption. NMR Relaxometry is typically unable to detect pores smaller than ~2 nm due to the extremely fast relaxation of 1H in such small pores,
8,28
and it does not work either for large pores such as multiple μm where surface
relaxation theory does not hold well any more. Taking advantage of the wettability contrast among inorganic pores, organic pores and mixed pores located at the interfaces between clays and organic matter, using water and dodecane as well as 65% MnCl2 aqueous solution as the probe liquids, Gannaway (2014)
29
exploited the T2 NMR Relaxometry spectra to characterize and quantify each of the three pore
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systems in 5 Barnett shale samples. These measurements allowed for the quantification of the total effective porosity, inorganic porosity, organic porosity, and porosity at the inorganic-organic interface, as well as the clay-bound water. Due to the homonuclear dipolar couplings between 1H with restricted relative motion within organic-rich shales, which cannot be refocused by usual spin echo methods such as CPMG, Birdwell and Washburn (2015)
20
applied the solid-echo approach to measure T2
distributions. Because of the dominant nanopores (in both organic and inorganic matrices) within shales, diffusion measurements for gas are usually hindered in shale because of such extremely small pore sizes,
26
although researchers have obtained some successes.
20
By studying shale core
samples in the laboratory using NMR Relaxometry at 2 MHz with elevated pressures up to 5 kP, Kausik et al. (2011) 26 tried to devise novel NMR logging techniques to determine the quantity of free and adsorbed gas based on NMR measurements. Similarly, Sigal and Odusina (2010) 6 also suggested that NMR logging possesses the potential to accurately estimate the total free gas stored in both the organic and inorganic pores, providing a reservoir-dependent correlation to the amount of adsorbed gas. (2) The limitations for NMR Relaxometry The PSD obtained by NMR Relaxometry, however, sometimes appear to be independent of the samples, rendering it unusable for the purpose of fingerprinting shales and other porous media. This effect is caused by the dependence of T2 NMR Relaxometry on surface relaxation, which is governed by the diffusion and exchange rates of probing solutions and the pore geometry and is further complicated by other factors, such as paramagnetic impurities, strong anisotropic properties, defects in crystals, local internal field gradients inside the shale and
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interactions between the probing solution and the matrix, such as magnetization exchanges and transfers.
7
Thus, the lack of the expected fingerprinting for NMR Relaxometry results from
some improper assumptions in the surface relaxation theory as well as very complicated relaxation mechanisms in shale. 7,20 Furthermore, small pore sizes coupled with the presence of a large number of hydrogen-bearing organic constituents in shales, can result in the surface relaxation in organic matter being dominated by the homonuclear dipolar couplings between the significant quantity of 1H present in immobile forms,
7,14,20
thus will seriously affect T2 and
so any derived PSD. Such homonuclear dipolar couplings may give rise to anomalously short T2 and weak overall signal intensity. Of course, Zhou et al. (2016) 8 and other researchers such as Li et al. (2017)
14
indicated that T2 is almost temperature-independent for some shale samples,
14,17
i.e., interactions between 1H and paramagnetic impurities such as iron oxides and pyrite dominate the T2 relaxation, at least for some shales. However, the most serious problem for NMR Relaxometry lies in the fact that during a period comparable to T2 the molecules of the probe liquid may stretch, displace and diffuse over multiple pores due to the couplings between nanopores, such that only the average value of T2 can be measured. Josh et al (2012)
4
had already noticed that such couplings over ms scales in the
standard CPMG experiment leads to a single, homogenized T2 population for shales. In contrast, the T1 distribution can differentiate the nano-scale pores, because T1 relaxation is dominated by the interactions at short-range, such as interactions between the water on the pore surface and the thermodynamically stable bulk water inside the pore space.
4
Similarly, Fleury et al. (2015)
30
already definitely demonstrated that the T2 distribution did not necessarily represent PSD, due to such fatal shortcomings. They commented upon the inability of T2 NMR Relaxometry to characterize nano-porous structures in shales, since all pore sizes below the diffusion length will
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be averaged around a single T2 relaxation time, which only represents an average ratio of volume to surface. Washburn (2014)
7
was also seriously concerned that not only such diffusional couplings
between pores, but also the rapid exchange of magnetization between mobile and immobile phases in the samples, may shed more doubts on interpreting the T2 response in terms of PSD. Another shortcoming of T2 NMR Relaxometry is due to the non-stable nature of the Inverse Laplace Transformation (ILT) universally employed by NMR Relaxometry, which is very sensitive to S/N of NMR signals, and so may result in multiple possible solutions especially for low S/N. The ILT may also, therefore, contribute to the lack of fingerprinting significance of a T2 distribution, through arbitrariness and ambiguities in the number of assigned T2 peaks, in the pattern for the T2 distribution and, thus, in its PSD interpretation for many media samples. 8,20,26 In summary, although surface relaxation and NMR Relaxometry may be held to be valid for a medium with larger pore sizes for example, Zhao et al. (2017b)
13
indicated the PSD
similarity between Micro-CT and NMR Relaxometry for pore sizes >60 μm (or T2 >100ms) in artificial core samples it is seriously doubtful that T2 NMR Relaxometry can work as well as expected in characterizing the nanopores in complex media such as shale.
2. NMR Cryoporometry (1) Applying NMR Cryoporometry to PSD of shales The limitations of NMR Relaxometry for PSD determination provide motivation for the development of NMR Cryoporometry for shale. It is well known that nanometer scale structure changes the Gibbs free enthalpy of a liquid since surface tension is directly equivalent to the volumetric energy.
25
Based on the differences in the Helmholtz free energy for fluids on the
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surface and in the center of a pore, the melting point depression (MPD) can be calculated via Eq. (3): 24 ∆T = −
vl γsl T0 Ss ∆H
Vs
S
= −𝐾𝐺𝑇 Vs
(3)
s
where T0 is the bulk solid-liquid transition temperature, ΔH is the bulk enthalpy of fusion, ɤsl is liquid-solid surface energy, vl is molar volume for the liquid, KGT stands for the Gibbs-Thomsen coefficient which can be empirically calibrated and determined, while Ss and Vs denote the surface and volume of the pore, respectively. Such freezing/melting phase transitions can be detected by measuring the NMR signals from the probe liquid, since the frozen phase and the structural OH are nonobservable or can be filtered out because of their faster relaxation times (Zhou et al. 2016). 8 Assuming spherical pores with radius D, the liquid-solid equilibrium from Eq. (3) can be readily transformed into the Gibbs-Thomson Eq. (4): 23,24,31,32 ΔT=-KGT/D
(4)
Thus, as indicated by Eq. (4), the MPD is directly related to the pore size. NMR Cryoporometry has significant advantages over NMR Relaxometry for shale PSD measurements, particularly in that the diffusion of NMR probe liquids in nanoporous shales is limited by the confinement in very small pore spaces as well as being occluded by the frozen phase (i.e., pore blocking on freezing). Also, NMR Cryoporometry is applicable even when liquids and volatile components already exist in the pores.
24
Additionally, compared with the
ILT method for NMR Relaxometry, the data processing method of differential treatment for NMR Cryoporometry measurements of shale is simple and straightforward and does not incur new errors, additional distortions or artifacts,
7,8,19
i.e., incrementally increasing NMR intensity
caused by increasing temperature can be directly and quantitatively converted to each portion of the PSD. Since magnetization magnitude is temperature-dependent, data processing for NMR
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Cryoporometry also includes calibration of experimental NMR signals, for example, M0 measured at each temperature has to be corrected according to Curie’s law. 8 Therefore, recently a few NMR Cryoporometry studies have attempted to analyze the PSD in shales using water and some organic solvents such as octamethylcyclotetrasiloxane (OMCTS) as the probe liquid.
8-10, 23-24
In order to extend the upper limit of detectable pore sizes (up to ~1
µm), according to Eqs. (3) and (4), NMR probe liquids with larger KGT such as OMCTS are preferably employed for NMR Cryoporometry measurements. 19,33-34 In contrast to the fact that the T2 distribution obtained by NMR Relaxometry is log-normal and relatively narrow, the PSD obtained by NMR Cryoporometry is quasi-uniform from 2 nm up to 100 nm for the shale samples (Fig. 1). Although such disagreement between the two methods was attributed to the couplings between pores by some authors, such as Fleury et al. (2015),
30
it actually may be
inherently caused by the different physical principles behind the methodologies, i.e., classical thermodynamics for NMR Cryoporometry vs. a pure NMR mechanism for NMR Relaxometry. Although NMR Cryoporometry is not in itself “an imaging method”, it can be readily combined with NMR imaging methods. 35-37 Of course, the conventional T2 distribution at each temperature during NMR Cryoporometry measurements can also be obtained, which may be used to correlate temperature (T) with T2 distribution for a new kind of 2D spectrum such as T-T2. 8 Since NMR Cryoporometry is a thermodynamic method in essence, the resolution and accuracy of PSD obtained by NMR Cryoporometry depends critically on the experimental temperature resolution and stability (with due care paid to the possibility of developing a temperature gradient within the sample), and the temperature increment should be as small as possible, especially for temperatures close to the bulk transition point, since the increment sets the ultimate upper limit of detectable pore sizes and so the PSD resolution. With 25 years of
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continuing development, the probe used by Webber for NMR Cryoporometry experiments can reach a temperature resolution and repeatability better than 10 mK, thus can measure pore size up to 10 μm,
24,25
although normally a commercial NMR spectrometer does not have a similar
measurement resolution. For the lower limit, considering surface relaxivity (ρ) from 1 to 10 μm/s, T2 for H2O in 1 nm nanopores will be ~0.1 ms which can be detected by most commercial NMR instruments, 23 thus the lower pore size limit as small as ~1 nm may be achieved by NMR Cryoporometry in principle. In practice nanopores
