Characterization of shale pore size distribution by NMR considering

Jun 11, 2019 - As a non-destructive method, proton nuclear magnetic resonance (1H NMR) technique with low echo time (TE, e.g., 0.07 ms) has been ...
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Cite This: Energy Fuels 2019, 33, 6361−6372

Characterization of Shale Pore Size Distribution by NMR Considering the Influence of Shale Skeleton Signals Jinbu Li,†,‡,§ Shuangfang Lu,*,†,‡ Chunqing Jiang,§ Min Wang,*,†,‡ Zhuoheng Chen,§ Guohui Chen,†,‡ Jijun Li,†,‡ and Shudong Lu∥ Key Laboratory of Deep Oil and Gas and ‡School of Geosciences, China University of Petroleum (East China), Qingdao 266580, Shandong, PR China § Geological Survey of Canada, Calgary, Alberta T2L 2A7, Canada ∥ Richfit Information Technology Co., Ltd. CNPC, Beijing 100000, PR China Downloaded via NOTTINGHAM TRENT UNIV on August 14, 2019 at 01:28:43 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

†

ABSTRACT: As a non-destructive method, the proton nuclear magnetic resonance (1H NMR) technique with low echo time (TE, e.g., 0.07 ms) has been increasingly used for characterizing full pore size distribution (PSD) of shales. However, hydrogen contained in some components of the shale skeleton (e.g., kerogen and structural water) also can be detected by NMR in the case of low TE, resulting in a questionable PSD derived directly from the T2 spectra of oil-saturated shale. In this study, eight shale samples with different organic and mineralogical components from the Jiyang Depression, China were investigated with regular NMR, low-temperature nitrogen adsorption (LTNA), NMR cryoporometry (NMRC), and mercury injection capillary pressure (MICP) techniques to propose a corrected NMR approach for characterizing shale PSD by considering the influence of the shale skeleton signals. The NMR relaxation characteristics (e.g., T2 spectra and T1−T2 map) of as-received shale, solventextracted and dried shale (EX), and oil-saturated shale (OS) were discussed to reveal the NMR response from the shale skeleton itself at T2 below 1 ms on the T2 spectra. With the new approach, the NMR T2 spectra of oil occurring in the OS shale were first obtained through inversion of the differentiated T2 decay curves between the T2 decay curves of the EX shale and OS shale and were then converted to PSD by combination of LTNA, NMRC, and MICP results. For pores with T2 less than 1 ms, the PSD obtained from NMR T2 spectra of the oil signals only compared well with the results of LTNA and NMRC, with a relative error of less than 15% in pore volume. In contrast, the relative errors of PSD obtained directly from the NMR T2 spectra of oil-saturated shales were up to 134%. It was found that the higher total organic carbon shale contained, the larger errors in the PSD profiles, pore volume, and porosity that were calculated directly from the oil-saturated shale’s NMR T2 spectra. Compared with the traditional NMR methods, the corrected approach can provide a more accurate PSD for shales, especially for those organic-rich ones.

1. INTRODUCTION

information on pore types, pore shapes, and 3D spatial distribution. As a nondestructive method, NMR has been widely used for characterizing full pore size distribution (i.e., nanoscale to macroscale) of both conventional and unconventional reservoirs.16,21−23 There are two NMR relaxation mechanisms for the dipole moment time evolution of protons present in the rocks: longitudinal relaxation (T1) and transverse relaxation (T2). Generally, the NMR relaxation rate of a rock saturated with a single low-viscosity fluid is related to the rock’s pore sizes: the larger the pore size, the slower the fluid relaxation rate and the longer the relaxation time.16,22,23 These are the principles of the NMR method for characterizing a rock’s PSD using a low-viscosity fluid such as water or light oil. In contrast, for high-viscosity fluids or pseudo-solid protons (e.g., kerogen and structural water) present in the rocks, their relaxation mechanism is determined by intramolecular dipole coupling interactions with the electronic spins24,25 and is not related to the PSD.

As one of the key parameters of shale reservoir properties, pore size distribution (PSD) directly determines the fluid storage and transport mechanisms.1−3 Consequently, accurate characterization of shale PSD plays a critical role in shale reservoir property evaluation and favorable area delineation for shale oil and gas production.2,4,5 The current experimental methods for evaluating shale PSD include low-temperature nitrogen adsorption (LTNA),6−9 mercury injection capillary pressure (MICP),10−12 microscopy observation,13−15 and proton nuclear magnetic resonance (1H NMR).16−19 Although these methods have their own advantages, some limitations exist with each method. For example, LTNA is not suitable for detecting pores larger than 200 nm.2,20 Pore volume determined by the MICP method is controlled by the sizes of pore throats and therefore is not a true reflection of the PSD. In addition, matrix compression and damage may result from the high pressure associated with MICP.10,12 For the methods of microscopy observation such as X-ray computed tomography (CT), field emission scanning electron microscopy (FE-SEM), and focused ion beam emission (FIB) SEM, they all have an issue of sample and data representativeness and spatial resolution5,13,14 although they can provide © 2019 American Chemical Society

Received: April 29, 2019 Revised: June 4, 2019 Published: June 11, 2019 6361

DOI: 10.1021/acs.energyfuels.9b01317 Energy Fuels 2019, 33, 6361−6372

Article

Energy & Fuels For the PSD characterization of conventional reservoirs with low contents of clay minerals and high porosity, the echo time (TE) of an NMR test is usually set as 0.2 ms, and the NMR T2 distribution of water-saturated rocks is directly used to derive the PSD by combining with other measurements (e.g., MICP, LTNA, and SEM).26,27 By contrast, shales generally develop large amounts of micro- and nanopores and are rich in clay minerals and kerogen. In order to obtain the full PSD for shales, a lower TE (e.g., 0.1 or 0.07 ms) has to be used to generate NMR signals from the hydrogen of fluids occurring in as small pores as possible that usually has very short relaxation.28−30 However, some recent studies suggested that hydrogen in the shale skeleton (e.g., kerogen and structural water) may also make a significant contribution to the total NMR signal of oil-saturated shales in the case of low TE,28,31 and this can result in an overestimate of the porosity.29,32 Therefore, shale PSD obtained directly from the T2 spectra of an oil-saturated shale is questionable in the case of low TE. Some researchers elected to use different NMR test parameters according to the porosity values in order to minimize the interference of the shale skeleton in PSD characterization;33 this, however, appears to be too cumbersome for analyzing samples with different lithologies and characteristics. As such, traditional NMR methods cannot be readily applied to predict the PSD of shales, especially for those organic-rich ones. This study aims to establish a corrected method for characterizing shale PSD with 1H NMR by considering the influence of the shale skeleton signals. The NMR relaxation characteristics (e.g., T2 spectra and T1−T2 map) of as-received shale (AR), solvent-extracted and dried shale (EX), and oilsaturated shale (OS) were compared to reveal the T2 distributions of the shale skeleton. The NMR T2 spectra of oil occurring in the OS shale were inverted from the difference of T2 decay curves between EX shale and OS shale and then calibrated with a combination of LTNA, NMR cryoporometry (NMRC), and MICP to characterize the shale PSD. Pore volume, porosity, and fractal dimension comparisons among different methods were also discussed to verify the reliability of the corrected NMR method.

Figure 1. Sampling well locations and geological characteristics of the research area. and the inversion recovery (IR) CPMG sequence were used for acquiring T2 spectra and the T1−T2 map, respectively. The NMR test parameters were set as follows: number of echoes (NECH) at 6000; waiting time (TW) at 1000 ms; number of scans (NS) at 32. The inverse time number (ITN) of 31 was used for the T1−T2 map tests. In order to get the full PSD of shales, the echo time (TE) was set at 0.07 ms to ensure the detection of proton signals from fluids in the smallest pores that can be possibly measured. In this case, the NMR signals of the shale skeleton (e.g., kerogen and structural water) could also be detected using the above testing parameters.31,32 The NMR T2 spectra and T1−T2 map were produced for the studied shale samples in three states: as-received (AR), solventextracted (EX), and oil saturated (OS). All samples used in NMR experiments are fragmental shales with irregular shapes due to a lack of standard core plugs. n-Dodecane (nC12) has been used as the fluid medium for oil-saturated shale experiments, and NMR tests on pure n-dodecane of different volumes were conducted to obtain the calibration equation between oil volume and its NMR response, which was reported in our previous study.29 2.2.2. LTNA Tests. LTNA experiments were carried out on a Micromeritics ASAP 2460 surface area analyzer. Before the LTNA experiments, samples were crushed to 100−120 mesh size, subjected to extraction using chloroform as the solvent for 7 days, and then dried at 110 °C (283.15 K) for 24 h to remove residual oil and water. The same solvent extraction and drying procedures have also been used on the samples for other experiments in this study. Such prepared shale samples (∼2 g) were then placed into a glass tube and tested under a relative pressure (P/P0) varying from 0.01 to 0.995 at −196.15 °C (77 K) to obtain the adsorption/desorption isotherms. Specific surface area, PSD, and pore volume of the shale samples were derived from the adsorption isotherms. Specifically, the specific surface area was calculated using the BET model, and the PSD was obtained using the DFT model. In this study, the LTNA tests were utilized for revealing the PSD in the range from 1.71 to 100 nm. 2.2.3. NMRC Tests. As with normal NMR measurements, NMRC tests were also carried out on a MicroMR23-060H-1 instrument, and the same testing sequence (CPMG) was used in the NMRC tests. Unlike the regular NMR experiments, the NMRC instrument was connected to a temperature control system with precision of 0.1 K. Before the NMRC tests, samples were crushed to 40−60 mesh size36 and then extracted and dried to remove residual oil and water. Thereafter, samples were saturated with octamethylcyclotetrasiloxane (OMCTS) because of its amphiphilic wetting nature and its large Gibbs−Thomson constant (KGT). Samples were then placed into a glass tube (diameter of 1 cm) and sealed immediately. The sealed samples were initially cooled to 244.15 K (−29 °C), then warmed slowly to 290.45 K (17.3 °C) at increments between 0.1 and 2 K, and held at each temperature point for 20 min to ensure that the samples

2. SAMPLES AND METHODS 2.1. Samples. The Jiyang Depression is located in the southeast of Bohai Bay Basin, China. It consists of four sags (i.e., Dongying, Zhanhua, Huimin, and Minfeng) and has developed with thick source rocks in the lower part of the third member (Es3L) and the upper part of the fourth member (Es4U) of the Tertiary Shahejie Formation. The Dongying and Zhanhua Sags are located in the southern and northern parts of the Jiyang Depression, respectively (Figure 1), and they are the main targets of shale oil exploration and development in the Jiyang Depression.34,35 A total of eight shale core samples were selected from the Paleogene Shahejie Formation of four wells: one sample (#1) from well XYS 9, four (#2, #4, #5, and #6) from well LY1, one (#3) from well NY1, and two (#7 and #8) from well FY1. Well XYS 9 is located in the Zhanhua Sag, and the other three wells are in the Dongying Sag (Figure 1). Before the analyses, each shale core sample was cleaned and divided into six aliquots for complete components and petrophysical property characterization including total organic carbon (TOC) contents, X-ray diffraction (XRD), LTNA, MICP, NMRC, and NMR measurements. 2.2. Experiments and Methods. 2.2.1. 1H NMR Measurements. NMR experiments were carried out on a MicroMR23-060H-1 instrument (Suzhou Niumag, China). The instrument was operated at 32 °C with a magnetic field strength of 0.28 T and frequency of 21.36 MHz. The Carr−Purcell−Meiboom−Gill (CPMG) sequence 6362

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Figure 2. Shale PSD by NMR cryoporometry (NMRC) experiments: (a) variation of NMR signal intensity with increasing temperature during NMRC tests and (b) PSD calculated from the Gibbs−Thomson equation for each shale sample.

Table 1. TOC and Mineralogical Characteristics of the Studied Samples mineral composition (%) sample number

well name

depth (m)

lithology

TOC (wt %)

clay

quartz

feldspar

dolomite

calcite

othersa

#1 #2 #3 #4 #5 #6 #7 #8

XYS9 LY1 NY1 LY1 LY1 LY1 FY1 FY1

3382 3812.3 3472.97 3672.86 3769.3 3833.78 3139.04 3201.9

shale shale shale shale shale shale shale shale

3.15 1.78 0.29 1.44 5.39 5.12 1.98 2.6

38.9 21.3 53.6 36 31.9 31.6 25.1 20.1

25.8 10.1 12.8 17.8 13.3 16.3 17.1 9.6

6.4 2.9 3.6 3.6 2.5 4.2 1.5 1.5

10.8 26.3 4.7 21.2 35.6 22.7 40.2 55.6

14.8 31.3 13.8 14.3 13.9 21.2 13.4 10.6

3.3 8.1 11.5 7.1 2.8 4 2.7 2.6

a

Note: others include pyrite, hematite, and siderite. 2.2.4. MICP Tests. MICP experiments were carried out on a Micromeritics AutoPore 9520 porosimeter. Before the MICP experiments, samples were prepared in cylindrical plugs with a diameter of 1 cm and height of 1 cm and then subjected to solvent extraction and drying as described above. Mercury injection pressure from 0.001 to 200 MPa was applied to the tests for calculating the volume of pores with a throat size larger than 7 nm based on the

had reached thermal equilibrium. NMR signals were acquired at the end of each temperature increment (Figure 2a). The NMRC tests were only performed on three shale samples (#1, #2, and #3) in this study due to sample availability issues and the extremely timeconsuming nature of this experiment. PSD was generated from the NMRC tests based on the Gibbs−Thomson equation,37 which revealed the pores in the range of 3−1000 nm (Figure 2b). 6363

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Figure 3. Pore size distribution of shales obtained by different methods: (a) LTNA method and (b) MICP method.

Table 2. Microstructure Parameters Obtained from LTNA Tests and Porosity Results Measured with Various Techniquesa microstructure parameters obtained from LTNA tests

porosity (%) by various methods

sample number

surface area (m2/g)

pore volume (cm3/g)

average pore size (nm)

MICP

NMRC

fluid saturation

NMR-OS

NMR-O

#1 #2 #3 #4 #5 #6 #7 #8

8.11 7.75 41.64 11.62 6.74 16.49 4.46 3.23

0.025 0.019 0.067 0.03 0.023 0.031 0.013 0.013

12.12 9.94 6.46 10.21 13.38 7.47 11.51 15.53

8.9 6.78 13.72 12.33 5.74 3.93 3.63 2.84

10.41 5.36 12.92 − − − − −

9.84 8.53 13.77 14.2 7.13 5.77 3.91 4.32

11.38 10.83 17.5 18.39 8.64 7.22 6 7.08

9.43 8.62 14.15 15.98 6.63 5.72 3.78 4.96

a

Note: NMR-O for the NMR method based on the oil signals of oil-saturated shale; NMR-OS for the NMR method based on the oil-saturated shale; − for no data.

Washburn equation.38 In addition, shale porosity was obtained by a combination of the shale bulk volume and the mercury injection volume at 200 MPa. 2.2.5. Other Experiments. 2.2.5.1. TOC and XRD Experiments. TOC contents were obtained on powdered ( 50 nm, with the contributions from the 50 nm pores to the total pore volume. However, the PSD of sample #3 shows a bimodal distribution, with the two peaks having maxima at diameters of 5 and 80 nm. The amplitude of the front peak is larger than that of the rear peak, indicating that this sample had a large number of small pores, which is also illustrated by the LTNA tests. The pore throat distributions of the eight shales obtained by MICP tests are shown in Figure 3b. The MICP methods revealed a large peak at the pore size smaller than 100 nm. Because the pore volume detected by MICP tests consists of not only small pores but also those large pores that have small

3. RESULTS AND DISCUSSION 3.1. Component Characteristics. Table 1 presents the TOC contents and mineralogy compositions of the eight shale samples used in this study. The shale samples have a TOC content ranging from 0.29 to 5.39 wt %, with a mean value of 2.72 wt %, indicating fair to good source rock potential. The mineralogical compositions were mainly dominated by clay minerals, quartz, dolomite, and calcite. Specifically, their clay mineral contents range from 20.1 to 53.6%, with an average value of 32.31%, showing the clay-rich character typical of continental shale. The calcareous minerals (dolomite plus calcite) are in the range 18.5 to 66.2%, with an average value of 43.8%. Content of feldspar is low in all samples 7 nm pores under an intrusion pressure of 200 MPa. Therefore, MICP tests have not been used to calibrate PSD profiles from NMR T2 spectra in this study but only used for verifying porosity results from fluid saturation experiments and NMR tests. The parameters of pore structure and porosity are listed in Table 2 for the studied samples. According to the LTNA experiments, their specific surface area (obtained by the BET method) ranges from 3.23 to 16.49 m2/g (except for #3), with a mean value of 8.34 m2/g. The micropores of lacustrine shales at the oil generation stage are mainly contributed by inorganic pores since no significant amount of organic pores was generated yet.9,40 Compared with other samples, sample #3 with the lowest TOC and highest clay content (Table 1) has the largest specific surface area and pore volume and lowest

average pore size, indicating the existence of a large number of small pores associated with clay minerals, which makes a great contribution to its total porosity. 3.3. NMR Relaxation Characteristics of AR, EX, and OS Shales. Figure 4 shows the NMR T2 spectra and T1−T2 maps for shale sample #1 as-received (AR), after solvent extraction and drying (EX), and when the extracted sample was saturated with dodecane (OS). The NMR T2 spectra of AR shale have a bimodal distribution (blue line in Figure 4a) with the two peaks separated around T2 of 1 ms (peak 1, 0.01−1 ms; peak 2, 1−10 ms), and the amplitude of peak 1 is larger than that of peak 2. In terms of the NMR T1−T2 map of the AR shale (Figure 4b), the signals under peak 1 are composed of kerogen (region 2), structural and adsorbed water (regions 4 and 5), and some adsorbed oil or oil stored in the organic pores (left part of region 3 with T2 less than 1 ms).31 NMR signals at the highest T1 and lowest T2 (region 1 in Figure 4b) may correspond to the strong paramagnetic impurities in the 6365

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Figure 5. NMR T2 spectra of other shale samples in this study in the forms of as-received (AR: blue), solvent-extracted and dried (EX: black), and oil-saturated (OS: red).

sample. Peak 2 on the AR shale’s T2 spectra represents free oil or oil occurring in the inorganic pores.31,41 After solvent extraction and drying, the NMR T2 spectra of EX shale showed a unimodal distribution (black line in Figure 4a). Compared with the AR shale, the amplitude of peak 1 decreased, and that of peak 2 largely disappeared in the EX shale. As shown in Figure 4c, peak 1 of the EX shale is a reflection of kerogen and structural water and corresponds to regions 2 and 4 on the T1−T2 map. Response of peak 2 on T2 spectra and region 3 on the T1−T2 map was almost reduced to

the baseline for the EX shale after solvent extraction as a result of the removal of free oil from the inorganic pores. After saturation with n-dodecane, the intensities of NMR signals of OS shale increased significantly, and the shape of T2 spectra became trimodal (red line in Figure 4a). Unlike the T2 spectra of AR shale with two major peaks of similar amplitudes, peak 2 of OS shale predominates over peak 1 on the T2 spectra in both peak height and width. In addition, a third peak (peak 3) appears at >100 ms on the T2 spectra of OS shale, likely a reflection of the presence of larger pores, microfractures, or 6366

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Figure 6. (a) NMR T2 decay curves and (b) NMR T2 spectra for shale sample #1. Black curves represent solvent-extracted and dried shale (EX), red curves represent oil-saturated shale (OS), and blue curve represents the saturating oil in the oil-saturated shale (Oil).

laminae in shale.42 Peak 1 of OS shale in Figure 4a divided obviously into two subpeaks in terms of the OS shale’s T1−T2 map (Figure 4d). Specifically, the first peak with the shortest T2 relaxation (T2 < 0.22 ms) comprises signals of kerogen (region 2), structural water (region 4), and the strong paramagnetic impurities (region 1), and it cannot be used for evaluating PSD since it is not the signal from pore fluids. The second peak (0.22 ms < T2 < 1 ms) is likely composed of adsorbed oil and adsorbed water (region 5). NMR T2 spectra of other samples (#2 to #8) are shown in Figure 5. Similar to sample #1, the NMR T2 spectra of AR shales were bimodal with front peaks being lager than the rear peaks, while the EX shales all displayed unimodal T2 spectra with only the front peaks at T2 < 1 ms. After being saturated with oil, their rear peaks increased significantly and became dominant over other peaks, with a third peak appearing after 100 ms T2 for shales developed with large pores or laminae. It is worth noting that sample #3 has different T2 spectra from all other samples, with its front peak being lager than the rear peak even when it is saturated with oil. The shapes of T2 spectra were related to the shale pore structure, and their amplitude was a reflection of the number of pores at a particular pore size.20,43 The NMR T2 spectra of sample #3 indicate relatively small pore size characteristics, which was consistent with the results from LTNA and NMRC (Figures 3a and 2b). 3.4. PSD Characterization by NMR. 3.4.1. Construction of T2 Spectra of Oil Occurring in the OS Shale. For T2 relaxation of low-viscosity fluids in shale pores that are dominated by surface relaxation (T2S), the larger the pore size, the longer the T2 time.16,22,23 Generally, it can be expressed as follows 1 1 F ≈ = ρ2 T2 T2S d

intramolecular dipolar coupling with the solid or semisolid, which can be expressed by the Bloembergen−Purcell−Pound (BPP) model as follows44 ÄÅ ÉÑ Å ÑÑ 1 10τ 4τ ÑÑ = AÅÅÅÅ6τ + + 2 2 2 2 ÅÅÇ T2 1+ωτ 1 + 4ω τ ÑÑÑÖ (3) where A is a constant, τ is the correlation time, and ω is the Larmor frequency. Generally, ωτ values of those immobile protons are much larger than 1.32 This relaxation mechanism is not related to the pore size, and this has been illustrated by a study on the relaxation time of water in smectite interlayers.45 Obviously, the NMR T2 spectra obtained for oil-saturated shale include the signals of both pore fluids and the shale skeleton (kerogen and structural water) and thus cannot be used to characterize the shale PSD directly. This is evident from the porosity data listed in Table 2. Porosity calculated from the NMR T2 signal intensity (the integrated area under the curves of T2 spectra) of OS shales ranges from 6 to 18.39%, with an average value of 10.88% for the studied shale samples. They are consistently higher than the results obtained from the saturation experiments and MICP technique (Table 2), and this has also been reported in our previous study.29 Therefore, the signals of the shale skeleton must be removed from the total signals to afford pore-fluid-only signals for characterizing the shale PSD. The NMR T2 spectra are usually obtained by inversion of the T2 decay curve.23 Figure 6 shows the NMR T2 decay curves and the inverted T2 spectra of the EX shale and OS shale for sample #1. Generally, the amplitude of the first echo in the spin echo train plays the most important role in the mathematical inversion of NMR T2 spectra. The amplitude at the first echo time of the EX shale was 108.92 a.u., while that of the OS shale was 667.81 a.u., indicating that approximately 16% of the OS shale NMR signals originated from the shale skeleton. The T2 decay curves of the oil present in the pores of the OS shale (ΔN(t,oil)) were calculated based on the difference between the T2 decay curves of the OS shale (N(t,os)) and the EX shale (N(t,ex)). This can be expressed as follows46

(1)

where ρ2 is the transverse surface relaxivity in nm/ms, F is the pore geometry morphologic factor, and d is the pore width in nm. Equation 1 can be rewritten as d = ρ2 FT2 = C × T2

(2)

where C is the calibrated coefficient, which is theoretically equal to the product of ρ2 and F. However, for the T2 of pseudosolid materials (such as kerogen and structural water) and fluids with a high viscosity in shales, the relaxation behavior is heavily influenced by

N (t , ex) =

i

6367

i t yz zz zz k T2i {

∑ Mi expjjjjj

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Figure 7. The dV/dlog D plots (a) and cumulative pore volume (b) of three shale samples (#1 to #3) by different methods. Pink lines represent the PSD of LTNA tests, green lines represent the PSD of NMRC tests, blue lines (NMR-O) represent the PSD of the NMR method based on the oil signals of oil-saturated shale, and red dotted lines (NMR-OS) represent the PSD of the NMR method based on the signals of oil-saturated shale.

N (t , os) =

ij t yz zz z T2j zz k {

∑ Mj expjjjjj j

ΔN (t , oil) = N (t , os) − N (t , ex) =

part of which represents the signals of the shale skeleton. In practice, the T2 spectra of saturating oil also could be calculated by subtracting the T2 spectra of EX shale from those of OS shale, but this would introduce larger errors from the two mathematical inversions of T2 decay curves, one for the OS shale and the other for the EX shale. Thus, in this study, we obtained the T2 decay curve of saturating oil first, which was then converted into T2 spectra, involving only one mathematical inversion and thus introducing smaller errors. 3.4.2. PSD Characterization. In this study, the T2 spectra of saturating oil present in the pores of OS shale as obtained above were used to characterize the shale PSD by combining with results from LTNA and NMRC. Porosity calculated from the NMR method based on the oil signals of OS shale (NMRO in Table 2) is slightly larger than the porosity from both MICP and NMRC methods, indicating that the saturating fluid has likely filled in some small pores that could not be measured by MICP and NMRC methods with a detection limit of 7 and

(5)

i t yz zz zz k T2k {

∑ ΔMk expjjjjj k

(6)

where n is the echo number, t = n × TE, Mi and Mj are the amplitude of EX shale at T2i and the amplitude of OS shale at T2j, respectively, and ΔMk is the amplitude of oil at T2k of OS shale. By solving the above eqs 4−6, the T2 spectra of oil present in the OS shale were then able to be obtained by a mathematical inversion of the T2 decay curve of oil represented by ΔN(t, oil), and this is displayed in Figure 6b for sample #1. The T2 spectra of the saturating oil (blue line) and OS shale (red line) are different in the amplitudes of their front peak (T2 < 1 ms), 6368

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Energy & Fuels Table 3. Comparison of Pore Volume between Different Methods in the Pores with NMR T2 Less than 1 msa pore volume* (cm3/g)

relative error (%)

sample number

LTNA

NMRC

NMR-O

NMR-OS

NMR-O

NMR-OS

#1 #2 #3 #4 #5 #6 #7 #8

0.0041 0.0072 0.0406 0.0115 0.0083 0.0047 0.0026 0.0057

0.0042 0.0061 0.0314

0.0036 0.0065 0.0414 0.0101 0.0087 0.0046 0.0022 0.006

0.0096 0.0141 0.044 0.0191 0.016 0.0106 0.0054 0.0125

−13.04 −8.89 2.06 −12.2 4.3 −0.93 −13.56 5.9

134.15 95.83 8.37 66.09 92.77 125.53 107.69 119.3

a

Note: pore volume* represents the pore volume with T2 less than 1 ms; NMR-O represents the NMR method based on the oil signals of oilsaturated shale; NMR-OS represents the NMR method based on the oil-saturated shale; d = (PV-PVLTNA)/PVLTNA × 100% where d is the relative errors (%) and PVLTNA is the pore volume of LTNA tests (cm3/g).

3 nm, respectively. This seems to further indicate that the shale samples have been saturated completely to produce full-size PSD profiles from the NMR tests. The PSDs from LTNA and NMRC tests were used for calibrating T2 spectra, and the calibration method for T2 spectra was based on the linear method (eq 2) reported in our previous study.9 Figure 7 presents the PSD profiles derived from (1) the T2 spectra of OS shales (NMR-OS), (2) the T2 spectra of saturating oil in the OS shales (NMR-O), (3) the LTNA tests, and (4) the NMRC tests for shale samples #1 to #3 in this study. Particularly, the same dV/dlog D coordinate scales were used here for the PSD profiles from different methods to make it convenient for revealing the quantity of pores at different pore size ranges and their contributions to the total pore volume. Previous studies mainly focused on the shapes of the PSD profiles and the differences among various methods and paid little attention to the dV/dlog D values due to the limitations of each method.9,18 It is clear from Figure 7a that for small pores