Advances in Characterizing Gas Hydrate Formation in Sediments with NMR Transverse Relaxation Time

Abstract

The formation process, structure, and distribution of gas hydrate in sediments have become focal points in exploring and exploiting natural gas hydrate. To better understand the dynamic behavior of gas hydrate formation in sediments, transverse relaxation time (T₂) of nuclear magnetic resonance (NMR) is widely used to quantitatively characterize the formation process of gas hydrate and the change in pore characteristics of sediments. NMR T₂ has been considered as a rapid and non-destructive method to distinguish the phase states of water, gas, and gas hydrate, estimate the saturations of water and gas hydrate, and analyze the kinetics of gas hydrate formation in sediments. NMR T₂ is also widely employed to specify the pore structure in sediments in terms of pore size distribution, porosity, and permeability. For the recognition of the advantages and shortage of NMR T₂ method, comparisons with other methods as X-ray CT, cryo-SEM, etc., are made regarding the application characteristics including resolution, phase recognition, and scanning time. As a future perspective, combining NMR T₂ with other techniques can more effectively characterize the dynamic behavior of gas hydrate formation and pore structure in sediments.

1. Introduction

Gas hydrate is a cage-type crystalline compound formed by water and gas molecules (methane, carbon dioxide, and hydrogen) at low temperature and high pressure, in which water molecules interact with each other through hydrogen bonds to form cavities and encase gas molecules in a cage-like structure [1,2]. Gas hydrate is a solid crystal with an extremely high capacity for gas storage and a unit volume of gas hydrate can store 160–180 unit volumes of gas at standard temperature and pressure [3,4,5,6,7]. Gas hydrate has wide application in many fields, such as energy storage, gas transportation, gas separation, carbon dioxide storage, and seawater desalination [2,8,9,10,11]. In addition, gas hydrate is also a crucial unconventional energy source with huge reserves, and the total amount of natural gas contained in hydrate reservoirs currently distributed on the seabed and permafrost is 1–120 × 10¹⁵ m³ [3,12,13]. In conclusion, natural gas hydrate is one of the clean energy sources with the most potential to replace coal, oil, and conventional natural gas [5,14].

The fundamentals of gas hydrate application are closely related to the formation process of gas hydrate [2,15,16,17]. Natural gas hydrate occurs in continental margin sediments [4,12,13,18]. The hydrate-bearing sediment has complex pore structures, unique interfacial properties, and various mineral compositions, prompting huge contrasts between the formation of gas hydrates in the confined space and that in the free space [19,20,21,22,23]. The formation process, structure, and distribution of natural gas hydrates in sediments have become focal points of exploring natural gas hydrates [24,25,26]. Therefore, it is essential to understand the physical and chemical properties of natural gas hydrate in sediments [27,28,29]. At present, previous literature mainly focuses on two major types of hydrate-bearing sediments: drilled hydrate sediment samples and synthesis of gas hydrate in the pore space of sediments such as quartz sand or clay minerals [22,23,30,31]. Most scholars use the latter sediment due to the difficulty of obtaining natural samples [32].

NMR T₂ method provides a fast, easy, and non-destructive way of detecting hydrogen-bearing fluids [33,34,35,36]. The NMR T₂ method is used to determine the petrophysical characteristics of conventional and unconventional porous media in oil and gas fields, such as porosity, pore geometry, pore connectivity, permeability, and even the fluid saturation in reservoirs [37,38,39,40,41,42,43,44]. Therefore, the NMR T₂ method is also widely used for monitoring the pore structure and the formation process of gas hydrate in sediments [45,46,47,48,49,50,51,52,53]. NMR T₂ is an effective method for microscopic detection of hydrate-bearing sediments with considerable advantages (e.g., fast response, high resolution, and no damage) in the quantitative analysis of gas hydrate in sediments by low-field NMR (LF-NMR) [54,55,56]. For instance, Minagawa et al. [57] calculated the pore-size distribution of hydrate-bearing sediments using the transverse relaxation time (T₂). Ma et al. [49] investigated the characteristics of methane hydrate formation under different driving forces using the T₂. Ji et al. [47] studied the effects of heterogeneous distribution of methane hydrate on the permeability of porous media by LF-NMR during hydrate formation.

Although this review is not exhaustive, it summarizes recent advances in the literature relating to the application of NMR T₂ in in situ quantitative characterization of gas hydrate formation in sediments, evaluates the current developments, and considers future advances in this promising experimental technique. This review is presented in four parts: (1) overview of the principles of NMR T₂ and LF-NMR equipment; (2) brief review of quantitative characterization of gas hydrate formation in sediments; (3) analysis of the differences and similarities between NMR T₂ method and other technologies; (4) discussion on the research trends and potential future development of the application of NMR T₂ in quantitative characterization of gas hydrate formation in sediments.

2. Basics of NMR T₂ Method

2.1. Principle of NMR T₂

The objects of interest in NMR measurement are the nuclei with non-zero magnetic moments, such as hydrogen nuclei (¹H), carbon nuclei (¹³C), and fluorine (¹⁹F) [58,59]. However, for most of the nuclei found in the sediment, the nuclear magnetic signal responding to external magnetic fields is too small to be detected with low-field NMR (

Table 1. NMR properties of some nuclei [58,59].

Nucleus	Natural Abundance (%)	Spin Quantum Number (I)	Gyromagnetic Ratio (γ) (107 rad s−1 T−1)	Sensitivity Relative to 1H
1H	99.98	1/2	26.75	100
2H	0.02	1	4.11	1.45 × 10−6
11B	80.42	3/2	8.58	0.13
13C	1.11	1/2	6.73	1.76 × 10−4
14N	99.63	1	1.93	1.00 × 10−3
19F	100	1/2	25.18	0.83
31P	100	1/2	10.84	0.07
17O	0.04	5/2	−3.63	1.08 × 10−5

) [58,59]. Different from other nuclei, ¹H, which is consisted of one proton but no neutrons and is abundant in water and gas hydrate, have a relatively large magnetic moment and produce a strong signal. Therefore, the study of gas hydrate formation in sediments using NMR T₂ method is based on responses of the ¹H.

Figure 1 shows the schematic diagram of the NMR T₂ method. The spin of a positively charged ¹H will form the net magnetic moments which are random (Figure 1a) [33,58,59]. When there is an external magnetic field ($B_0$), the ¹H will precess around the direction of $B_0$ (Figure 1b) [33,58,59]. The precession frequency ($f$), called the Larmor frequency, is determined by the following equation:

$$f=\frac{\gamma B_0}{2\pi }$$

(1)

where $\gamma$ is the gyromagnetic ratio (Table 1).

When a lot of ¹H are precessing about $B_0$, more spins are precessing parallel than anti-parallel to $B_0$ [33,58,59]. The differences between the number of ¹H aligned parallel and anti-parallel to the $B_0$ field form the bulk magnetization $M_0$ that provides the signal measured by NMR spectrometer (Figure 1c), in which $M_0$ is given by Curie’s Law as:

$$M_0=N\frac{r^2{h}^2\left(I+1\right)}{3\left(4{\pi }^2\right)kT}{B}_o$$

(2)

where $k$ is Boltzman’s constant, $T$ is temperature, $h$ is Planck’s constant, and $I$ is the spin quantum number of ¹H (Table 1) [33,58,59].

After that, the magnetic moments of ¹H can be deflected to the perpendicular transverse plane of the magnetic field $B_0$ under the influence of the radio frequency (RF) pulse at the Carr–Purcell–Meiboom–Gill (CPMG) sequences (Figure 1d) [33,58,59,60,61]. It is worth noting that the frequency of RF pulse is the same as the $f$ of ¹H in $B_0$, namely, the resonance phenomenon [33]. Therefore, ¹H transits from a low energy state to a high energy state by the energy provided by the RF pulse. Subsequently, as shown in Figure 1e, the magnetic moment of ¹H returns to the original direction in the form of precession after the RF pulse is turned off. In other words, these ¹H fall back to a low energy state and this process is called “relaxation” [6,58,59]. Meanwhile, a time-dependent NMR signal generated by the transverse magnetization decay can be measured (Figure 1e). The following formula gives T₂:

$$M_x\left(t\right)=M_o{\mathrm{e}}^{\frac{-t}{T_2}}$$

(3)

where $t$ is the time, and $M_x\left(t\right)$ is the magnitude of transverse magnetization at the time $t$ [33]. The decay amplitude of the spin-echo train can be accurately fitted by the sum of a set of exponential decay curves. The inverse Laplace transform algorithm (ILTA) was used to obtain the T₂ spectrum by fitting the relaxation echo signal (Figure 1f) [35,62,63]. Each exponential curve has a different decay constant and the collection of all the attenuation constants forms the T₂ spectra.

The relaxation of ¹H in pores of sediments includes bulk relaxation, surface relaxation, and diffuse relaxation [33,64,65]. Bulk relaxation is an intrinsic property of the fluid and is controlled by the physical properties (e.g., viscosity and chemical composition) of the fluid. Surface relaxation occurs at the fluid–solid interface depending on how frequently protons can collide with the surface. Diffuse relaxation is phasing incoherency that only affects T₂ as the proton spins diffuse across strong internal field gradients generated by the susceptibility contrast between grain surfaces and pore fluids. In general, the relaxation behavior of hydrogen fluid in sediments can be quantified by the T₂, which can be expressed as:

$$\frac{1}{T_2}=\frac{1}{T_{2s}}+\frac{1}{T_{2B}}+\frac{1}{T_{2D}}$$

(4)

where $T_{2B}$ is the bulk relaxation time, $T_{2s}$ is the surface relaxation time, and $T_{2D}$ is the diffuse relaxation time [33,64,65].

2.2. Low-Field NMR Equipment

The measurement of NMR T₂ is mainly realized by LF-NMR equipment which mainly consists of a powerful magnet (<1 T) and radio frequency pulse. Figure 2 shows the schematic diagram of a real-time monitoring apparatus of LF-NMR, which mainly consists of a hydrate crystallizer and an analysis system of LF-NMR. The temperature of radio frequency coil is constant. To achieve the conditions of the hydrate crystallization, a temperature control unit circulating hydrogen-free liquid was installed surrounding the reactor chamber to control the surrounding pressure and temperature of the reactor.

Based on previous literature, CPMG pulse sequences are employed by LF-NMR to obtain the decay signal of transverse magnetization [60,61]. As shown in Figure 3, the CPMG sequence involves applying not a single 90-degree RF pulse (P1) to the sample, but many 180-degree pulses (P2). The main parameters of the CPMG pulse sequence are the radio frequency delay (RFD), the waiting time (TW), the echo time (TE), the number of echoes (NECH), and the number of scans (

Table 2. CPMG parameters.

Year	Hydrate	P1 (μs)	P2 (μs)	TW (s)	TE (ms)	NECH	Scan Time	References
2017	CO2 hydrate	/	/	/	0.24	10,000	/	[45]
2017	CO2 hydrate	/	/	/	0.24	10,000	/	[52]
2018	CH4 hydrate	/	/	6.00	0.1	10,000	4	[30]
2019	CH4 hydrate	/	/	/	0.17	18,000	/	[66]
2020	CH4 hydrate	/	/	/	0.17	18,000	/	[47]
2020	CO2-CH4 hydrate	14.4	29.5	15	2.00	4096	16	[67]
2020	CH4 hydrate	/	/	1.5	/	9259	2	[55]
2021	Xenon hydrate	/	/	5	0.4	10,000	8	[56,68]

).

3. NMR T₂ Application

NMR T₂ test provides a fast, easy, and non-destructive way of detecting hydrogen-bearing fluids, which is widely used to monitor the dynamic behavior of gas hydrate formation and pore structure in sediments [30,45,46,47,48,49,50,51,52,53,56,66,68,69,70]. Figure 4 shows the schematic diagram of the NMR T₂ method applied to quantitative characterization of gas hydrate formation in sediments.

3.1. Gas Hydrate Formation Process

3.1.1. NMR T₂ Relaxation of Hydrate, Water, and Gas

To study the formation process of gas hydrates in sediments, identifying phase states, particularly the hydrate and water phases, is the first task. The basic principle of using NMR T₂ spectrum to distinguish phase states is based on different relaxation responses of NMR corresponding to different contents of protons and lattice states in substances [33,71].

In the course of gas hydrate formation, three possible phases are generally considered, including the water phase, gas phase, and hydrate phase [1].

Table 3. NMR T₂ relaxation of hydrate, water, and gas in porous media.

Porous Media	Pore Size (μm)	Gas	Hydrate	T2 (ms)						References
				Water		Gas			Hydrate
				Porous Confined Water	Bulk Water	Absorbed Gas	Porous Confined Gas	Bulk Gas
Berea sandstone	20	CH4	CH4 hydrate	460	2000	/	/	1000–2000	0.02	[73]
Coal	/	CH4	/	/	/	/	240–2000	<240	/	[31]
Shale	/	CH4	/	/	/	0.1–11	11–270	270–2500	/	[75]
Shale	/	C2H6	/	/	/	0.1–11	11–270	270–2500	/
Shale	0.002–0.2	CH4	/	/	/	0.1–1	1–50	50–2000	/	[76]
Sandstone	/	CH4	CH4 hydrate	0.2–1000	/	/	/	/	/	[47]
Unconsolidated sandstone	/	CH4	CH4 hydrate	10–2000	/	/	/	/	/	[30]
Brea sandstone	/	CH4	CH4 hydrate	0.1–500	/	/	/	/	/
Consolidated sandstone	/	CH4	CH4 hydrate	1–2000	/	/	/	/	/
Tight sandstone	/	CH4	CH4 hydrate	0.2–200	/	/	/	/	/
Mineral powders	0–110	/	THF hydrate	100–800	/	/	/	/	0.1–1	[77]

shows NMR T₂ relaxation of hydrate, water, and gas in porous media according to previous studies. Specifically, water in pore space shows a longer T₂ (Figure 5a). The NMR signal of water can be detected during the entire CPMG sequence. There are three states of gas in the sediment, including adsorbed gas, gas confined in pores, and bulk gas (Figure 5b). However, the content of adsorbed gas and gas confined in pores is very limited in water-saturated sediments. The signal intensity of methane gas is smaller than that of water [66,72]. The gas hydrate showing a short T₂ cannot be identified because complete relaxation occurs before the first echo is detected [73]. Therefore, it is assumed that the NMR signals of hydrate and gas can be ignored by the LF-NMR [49,52,54,55,56,66,69,70,74]. That is, the effective signals in the NMR T₂ measurement of gas hydrates are all from the water. Specifically, Ge et al. [30] studied the formation process of methane hydrate in the porous rocks using LF-NMR. The changes in the characteristics of the gas hydrate phase could be inferred by the area differences between the measured spectrum and the full water-saturated spectrum in Figure 5a.

In addition to methane hydrate, tetrahydrofuran (THF) hydrate consists of the THF hydrate phase and the remaining solution phase during its formation. In the NMR T₂ measurement, the T₂ reaching the peak position of the THF solution is about 1351.01 ms and the T₂ spectrum around 0.1–1 ms is from the THF hydrate phase [77,78]. Gao et al. [79] demonstrated that the T₂ distribution of THF-deuterium oxide (D₂O) hydrate centered 2–3 ms at atmospheric pressure and the T₂ spectrum of THF-D₂O solution is about 2000 ms in Figure 6. The T₂ spectra of THF hydrate and coexisting THF solution could be easily distinguished as three orders of magnitude (Table 3). Therefore, the THF hydrate phase and the THF solution phase can be detected by LF-NMR.

3.1.2. Saturation of Water and Gas Hydrate

Hydrate saturation in sediments refers to the percentage of the volume of hydrates in the total pore volume of sediments. To determine the degree of hydrate saturation using NMR T₂, the relationship between the water content and the T₂ spectral area should firstly be determined. The water content in the sediment follows a linear relationship with the T₂ area [47,66,80]. The water mass ($m_w$) in pores of sediments can be calculated by:

$$m_w=a·I_w$$

(5)

where $I_w$ is the T₂ spectral area of water in the pore of sediments and $a$ is a coefficient related to experimental equipment parameters; $a$ is obtained by a simple linear regression model relating to the T₂ spectral area and the water mass in sediments (Figure 7) [40,47,66,81].

The water volume ($v_w$) can be computed by:

$$v_w=\frac{m_w}{{\rho }_w}$$

(6)

where ${\rho }_w$ is the water density and $m_w$ is calculated by Equation (5).

In most studies, the effect of gas on the T₂ spectrum is negligible compared with the signal of water [30,52,55,66,70]. The gas hydrate is undetectable by LF-NMR [73]. Accordingly, the mass of gas hydrate ($m_h$) can be calculated by:

$$m_h=\frac{a\left(I_o-I_w\right)\times \left(M_c+n·M_w\right)}{n·M_w}$$

(7)

where $I_o$ is the T₂ spectral area of the water in the saturated sample before the hydrate formation, $M_c$ is the relative molecular mass of gas, $M_w$ is the relative molecular mass of water, and $n$ is the hydration number. The chemical formula of methane hydrate is CH₄·nH₂O [1] in which $n$ is taken as 5.78–6.1 in the process of saturation calculation [47,52,66,69,74].

The volume of gas hydrate ($v_h$) can be calculated by:

$$v_h=\frac{m_h}{{\rho }_h}$$

(8)

where ${\rho }_h$ is the density of gas hydrate.

The hydrate saturation ($S_h$) can be calculated by:

$$S_h=\frac{v_h}{v_o}$$

(9)

where $v_o$ is the pore volume of the sediment. The water mass in the pore of sediments before the hydrate formation ($m_o$) can be calculated by Equation (5). $v_o$ can be calculated by Equation (6). The water saturation ($S_w$) can be calculated by:

$$S_w=\frac{v_w}{v_o}$$

(10)

Therefore, based on the changes in the characteristics of the T₂ spectrum in the hydrate formation process, the hydrate and water saturations in the pore of sediments can be obtained. For example, Ge et al. [30] investigated the formation process of methane hydrate in sedimentary rocks by T₂ spectrum. They found that there was no significant relationship between the gas hydrate saturation and the porosity of the sedimentary rock. Zhan et al. [52] studied the methane hydrate formation in porous media based on the T₂ spectrum and discussed the relationship between the hydrate saturation, the water content, and the particle size of sediments. Ji et al. [66] conducted the experimental study on a partially saturated sandstone to analyze the formation process of methane hydrates and calculated the saturation changes of various substances (hydrates, methane gas, and water) by using the T₂ spectrum.

3.1.3. Kinetics of Gas Hydrate Formation

Kinetic parameters (e.g., the induction time, the water consumption, and the formation rate of gas hydrate) are determined from the NMR T₂ spectrum.

The elapsed time between the beginning of nucleation and the occurrence of a large number of stable hydrate nucleates with the critical size is called the induction time [1]. In other words, the induction time is the time elapsed until the appearance of a certain detectable volume of hydrate nuclei judged by turbidity, pressure fluctuations, and temperature fluctuations in previous studies. However, the judgment of hydrate nuclei in previous studies lacks accuracy if considering the randomness and heterogeneity of hydrate nucleation [82,83,84,85]. In hydrate-bearing sediments, the working principles of LF-NMR are based on the phenomenon that the NMR responses of ¹H residing in various phases are quite different [33,71]. Therefore, the analysis of T₂ spectrum in the formation process of gas hydrate provides a new way to measure the induction time.

According to the T₂ spectral area at different times, the gas hydrate mass in the formation process of gas hydrate can be obtained by Equation (7). Thus, the formation rate ($r_i$) of gas hydrate at the time step number i can be approximated by:

$$r_i=\frac{m_{i+1}-m_i}{T_{i+1}-T_i}$$

(11)

where m_i+1 and m_i are the gas hydrate masses at the time step numbers i + 1 and i, respectively, and T_i+1 and T_i are the times at the time step numbers i + 1 and i, respectively.

3.2. Pore Structure in Sediments

3.2.1. Pore Size Distribution

The pore structure in the sediments determines the space in which gas hydrates can grow and the permeability of gas hydrate-bearing sediments, necessitating the measurement of the pore size distribution of sediments with great significance for studying the formation process of gas hydrate [86].

Previous research demonstrated that $T_{2B}$ is generally above 3000 ms, resulting in a very small $1/T_{2B}$[44]. For a uniform magnetic field, $1/T_{2B}$ and $1/T_{2D}$ are small enough to be neglected in Equation (4) [33,87], resulting in:

$$\frac{1}{T_2}\approx \frac{1}{T_{2s}}$$

(12)

For the evaluation of the pore sizes, T₂ is commonly expressed as [31,33,88,89]:

$$\frac{1}{T_2}\approx \frac{1}{T_{2s}}=\rho \frac{S}{V}=\rho \frac{F_S}{r}$$

(13)

where $\frac{S}{V}$ is the surface-to-volume ratio of the pore, $\rho$ is the transverse surface relaxivity, $F_S$ stands for the geometric shape factor of pores (3 for spherical, 2 for cylindrical, and 1 for grooved), and $r$ is the pore radius [90,91].

The determination of $\rho$ is an important step for pore structure characterization with NMR T₂ spectra. The value of $\rho$, which is highly dependent on the solid surface, limits the accuracy of the pore size measurements. Even though the surface properties of minerals in sediments are different, an equivalent $\rho$ is commonly applied to convert T₂ spectrum to pore sizes based on Equation (13). The $\rho$ value is anticipated to vary (

Table 4. Transverse surface relaxivity of different material.

Material	Transverse Surface Relaxivity (μm/s)	References
Quartz	5–55	[56,95]
Calcite	0–5	[95]
Illite	0.5–2.5	[96]
Clay minerals	0.06–0.3	[97]
Pyrite	1.2–1.8	[97,98]
Shale	0.11–0.39	[97,98]
Sandstone	21–187	[53,99]
Berea sand	135.9	[53]
Quartzitic sand	27.3	[68]

) when the mineralogy and morphology in sediments change at the water–solid interface [68,92,93]. In addition, the $\rho$ value of hydrate-bearing sediments is assumed to be constant in the process of hydrate formation [51,86]. Since the water relaxation at the water-sand interface mainly occurs at the sand particle surface while the proton spin is relaxed dominantly by intra-dipole–dipole interaction at the water–hydrate interface, the $\rho$ value must be changed by the variations of the fluid–solid interface mineralogy and morphology in the hydrate formation process [53,68,70,79]. It suggests that further studies are required to understand the water–hydrate interface properties and $\rho$ in hydrate-bearing sediments in the formation process of gas hydrate [94].

According to Equation (13), the relation between T₂ distribution and pore size distribution is that the smallest pore has the shortest relaxation time and the largest pore has the longest relaxation time.

NMR T₂ has been widely used to characterize the pore size distribution characteristics of oil and gas reservoir rocks. For example, Yao et al. [89] characterized the pore size distribution of coal from 100 nm to 1 mm by NMR T₂ and found that NMR T₂ is an efficient tool for quantifying the pore size distribution of coal in a non-destructive way. Li et al. [100] studied the pore structure and fractal characteristics of shale based on NMR T₂. Li et al. [101] conducted research on quantitative analysis for nanopore structure characteristics of shale based on LF-NMR. Xiao et al. [102] combined rate-controlled porosimetry and NMR T₂ to probe full-range pore throat structures and their evolution features in tight sands. In summary, LF-NMR shows excellent advantages for obtaining pore size distribution of oil and gas reservoir rocks, such as rapid measurement, non-destructive test, and wide testing range.

The lithology of the hydrate reservoir is clayey silt, and the main minerals are quartz, feldspar, carbonate, and clay [4]. The mean grain size of sediments is tens of microns [4,103]. The pore diameter of hydrate-bearing sediments in the Shenhu area of the South China Sea ranges from 500 nm to 20 μm. Due to the nano-micron pores and high water content of the unconsolidated sediments, it is difficult to measure the pore size distribution characteristics of hydrate-bearing sediments using conventional experimental methods. Therefore, many researchers use NMR T₂ to study the pore size distribution of sediments. For instance, Minagawa et al. [86] used NMR T₂ to characterize the pore size distribution of hydrate-bearing sediments. Zhang et al. [104] used LF-NMR to monitor the formation process of xenon hydrate in different sand samples. The NMR T₂ spectrum was used to analyze the microscopic pore structure and the evolution law of water permeability in the process of gas hydrate formation.

3.2.2. Permeability

Gas permeability and water permeability in the gas hydrate sediments are important factors for estimating the efficiency of gas production [86]. The permeability of the hydrate formation process can be calculated by the T₂ spectrum. In oilfield NMR loggings, the permeability of sediments is obtained by the Schlumberger Doll Research model [56,70,105]. The permeability $k$ can be calculated by:

$$k=A{\left({\varphi }_{NMR}\right)}^4{\left(T_{2LM}\right)}^2$$

(14)

where $A$ is an empirical constant proportional to the square of $\rho$, ${\varphi }_{NMR}$ is the porosity of sediments in the hydrate formation process, and $T_{2LM}$ is the logarithmic mean of T₂ spectrum. The porosity of sediments before the hydrate formation (${\varphi }_o$) can be calculated by:

$${\varphi }_o=\frac{v_0}{v}$$

(15)

where $v$ is the volume of sediments, and ${\varphi }_0$ is constant.

The porosity in the process of gas hydrate formation (${\varphi }_{NMR}$) is defined as:

$${\varphi }_{NMR}=\frac{v_w}{v}=\frac{v_w}{v_O}·\frac{v_0}{v}=s_w·{\varphi }_0$$

(16)

According to Equations (13) and (14), $k$ can be expressed by Equation (16) [56,68,70]:

$$k={\rho }^2{\left(s_w·{\varphi }_0\right)}^4{\left(\frac{T_{2LM}}{T_{2LM}{}^{\prime }}\right)}^2$$

(17)

where $T_{2LM}{}^{\prime }$ is the logarithmic mean of the T₂ spectrum before the hydrate formation.

The T₂ spectrum estimates the permeability based on the theoretical models, indicating that the permeability increases with both increasing porosity and pore size [106]. Kuang et al. [48] determinated that the permeability of the hydrate-bearing sediments was predicted under different hydrate saturation conditions by T₂ spectrum. Zhang et al. [56] used Schlumberger Doll Research model to predict the permeability in the hydrate dissociation based on the NMR T₂ spectra and found that the water permeability is not sensitive to the changes in pore structure characteristics in the hydrate dissociation.

4. Comparison of NMR T₂ Method with Other Technologies

Given the advances in modern technology, many non-destructive detection techniques (e.g., X-ray computed tomography (CT), magnetic resonance imaging (MRI), Cryogenic scanning electron microscopy (Cryo-SEM), ¹³C solid-state NMR, and NMR T₂) are used to acquire in situ quantitative and real-time characterization of gas hydrate formation process [47,50,51,68,69,70,107,108,109,110,111,112,113,114,115,116]. This study compares their application characteristics in the fields of resolution, phase recognition, scanning time, advantages, and drawbacks.

CT technology distinguishes materials by their different electron densities and attenuation coefficients [107]. The CT images the habits of hydrate pore with a resolution of tens of microns to sub microns in Figure 8a,b [103,107,108,110,111,112]. The scanning time is inversely proportional to the resolution and can reach dozens of hours at a resolution of 1 micron [107,108,110]. According to the different gray values of different phases in CT images, the identification of sediments, hydrates, water, and gas can be realized, and then the phase change characteristics can be reconstructed in the hydrate formation process as shown in Figure 8a,b. According to the 3D image, the distributions of the pore size and saturation can be calculated. The permeability can be predicted using Lattice Boltzmann modeling, pore network model, or other predictive permeability models [103,110,117]. However, in CT measurement, the attenuation coefficients of methane hydrates and water (due to their minuscule density difference) are too close to identify methane hydrate segmentation. Two techniques have been commonly utilized to separate hydrate from pore water: (a) adding the dissolved salts (e.g., KI) into pore water as an enhancing agent in Figure 8b [107,118] and (b) forming hydrate with xenon or krypton as the guest molecule [119,120]. Both approaches use high atomic number elements to enhance the attenuation coefficients of the host materials. However, xenon and krypton have a much higher solubility in water than methane, leading to different morphologies of the resulting hydrates. Additionally, dissolved salts in water may affect the formation process of methane hydrate. Although the spatial resolution is improved, the similar attenuation coefficient between methane hydrate and water is still a challenge for CT in the field of methane hydrate development.

MRI is an effective tool for investigations in physical, chemical, life, and clinical sciences as it noninvasively maps the liquid water protons with high spatial resolution in three dimensions [122,123,124,125]. MRI technique has been vastly used to observe the dynamic process of hydrate formation and decomposition in hydrate-bearing sediments due to its immediacy of image acquisition (Figure 8c–f). A standard spin echo multi-slice sequence is applied to detect the ¹H contained in the liquid water phase only [115,116,126,127,128,129,130]. It should be noted that the ¹H in the gaseous or solid phase is hard to be imaged in the MRI due to much shorter T₂. The resolution of MRI is at a scale of several hundred microns or even smaller [126,128]. The acquisition time of the image is about 2 min–1 h [126,130,131]. The signal intensity on the image is related to water saturation. The hydrate saturation, phase distinction, and pore size distribution in the formation process of gas hydrate are calculated using MRI mean intensity of water. Although MRI has been applied to study hydrate formation in synthetic sediment matrices, the limited resolution of MRI at a scale of several hundred microns or even smaller does not allow more accurate observation of the microstructure of gas hydrates.

Cryogenic scanning electron microscopy (Cryo-SEM) refers to the combination of cryogenic sample chamber and SEM. The sample chamber of Cryo-SEM is taken at about 90 K and about 0.1 Pa [114,121,132,133]. Cryo-SEM was used to observe the microscopic morphology of the hydrate samples in Figure 8g,h [114,121,132,133]. Cryo-SEM enables more detailed access to hydrate surface properties down to the nanometer scale on the samples [132], which has been extremely helpful to observe gas hydrates in pore spaces. However, the practicability of this method is largely hampered by the difficulty of distinguishing ice from gas hydrate with the same gray in the secondary electron image [121]. In addition, the hydrate phase sublimates rapidly in a high vacuum environment, which brings about changes in microscopic morphology [132]. Despite the technical challenges imposed by rapid sublimation of the hydrate phase in the high-vacuum conditions of SEM column and electron beam damage of the imaging area, Cryo-SEM offers an excellent means of obtaining textural information of hydrate-bearing sediments at the grain-level scale.

Since the NMR parameters are sensitive to the environment in which a molecule experiences, ¹³C solid-state NMR can be used to experimentally identify the types of crystalline phases, distinguish the kinds of hydrocarbon molecules, cage occupancies, and hydration number, and monitor formation processes and structural transformations [134,135,136,137,138]. ¹³C solid-state NMR recognizes different types of gas hydrates relying on chemical shifts in the hydrate structure (the resolution is molecular level) [137,138]. ¹³C solid-state NMR has been mainly used in high-static magnetic fields of 1–20T [115,116,126,128,139,140,141]. The high magnetic field strength is extremely sensitive to the inhomogeneity of the magnetic field. Such high magnetic fields lead to unfavorable quantitative NMR measurements [142]. Nevertheless, quantitative measurements of fluids in sediments are important for understanding how much fluid is present and how those fluids move throughout the pore spaces during the formation process of methane hydrate [115]. It has been indicated that a low magnetic field has the advantage of minimizing the magnetic susceptibility contrast. Additionally, the pure phase encoding MRI method allows quantitative measurement of the static fluid content and dynamic transport process in porous media, which is not influenced by $B_0$ inhomogeneity, susceptibility effects, or chemical properties.

These methods, characterized by high resolution and non-destructive tests, have different advantages and drawbacks in the application process (

Table 5. Comparison of key information of several methods.

Method	Parameter for Phase Distinction	Resolution	Measurement Range	Scan Time	2D/3D
NMR T2	Relaxation time	10 nm	10 nm–1 mm	About 1 minute	2D data
CT	Attenuation coefficient	1–40 μm [103,107,108,110,111,112]	1 μm–centimeter	Few seconds–76 h [107,108,110] *	3D image
MRI	Relaxation time	55–234 μm [126,128]	55 μm–1 mm	About 3 min [126,130]	3D image
Cryo-SEM	Gray scale	Nanoscale [114,121,132,133]	Nanometer–centimeter	Few seconds	2D image
13C solid-state NMR	Chemical shift	Molecular-level	Molecular-level	Few minutes	2D data

* The resolution of CT is proportional to the scanning times.

). X-ray CT and MRI provide a non-destructive 3D method for the internal observation and quantitative analysis of hydrate [143,144,145,146]. The drawback of X-ray CT is barely distinguishing ice from the hydrate in the hydrate formation process by the reason of their marginal density differences [111]. The resolution of X-ray CT and MRI depends on the optical system of the device. If the optical system is the same, the longer the measurement time, the more contrast improvement can be obtained. To obtain higher quality images, CT and MRI tests take more time. However, hydrate formation is a continuous process, requiring the observation of the time scale of a second or even shorter [1]. Consequently, X-ray CT and MRI tests are not suitable for observing the continuous process of hydrate formation in sediments. Cryo-SEM enables a more detailed access to hydrate surface properties down to the nanometer scale on the sediment. However, the practicability of this method is largely hampered by the difficulty in distinguishing ice from gas hydrate and changes in microscopic morphology of hydrate in the vacuum environment. ¹³C solid-state NMR can provide information on the crystal structure of gas hydrates, but the experimental operation process is complicated and impossible to obtain information on the formation process of gas hydrates in sediments. Compared with other technologies, NMR T₂ can obtain the real-time continuous formation process of gas hydrates in sediments, but not the spatial distribution characteristics of hydrates in sediments. Considering its fast, non-destructive, and convenient characteristics, and its capability of obtaining overall information of the process of gas hydrate formation, LF-NMR has been applied to monitor the dynamic behavior of phase change in the hydrate formation process and pore structure in sediments.

5. Potential Research Trends and Improvements

NMR T₂ method is used widely to determine the formation process of gas hydrate and the pore structure in sediments. However, because NMR T₂ is a bulk measurement that provides no information about spatial hydrate and water distributions, the literatures using NMR T₂ did not consider the effects of hydrate pore occurrences on the pore structure parameters and permeability of sediments [56].

The limitations of applying a single method indicate that the evolution of the gas hydrate formation in sediments is yet to be understood comprehensively. The need for pore-scale tests makes it urgent to advance the present technology beyond mere identification, develop a combined method of characterizing the formation process of gas hydrate, and investigate the pore characteristics of hydrate-bearing sediments.

Although there have been a lot of excellent studies on the gas hydrate formation in sediments using NMR T₂ method, a few of them combined NMR T₂ with other methods to characterize the formation process of gas hydrate and the pore structure in sediments in a more effective way [30,45,50,51,52,53,56,66,67,68,69,70,74,147,148,149]. The combined use of these techniques can provide more information about the gas hydrate formation in sediments than any single technique.

6. Conclusions

In this review, the Basics of NMR T₂ method and its application in quantitative characterization of gas hydrate formation in sediments are summarized based on recent advances, and the differences and complements between NMR T₂ method and other hydrate quantitative characterization methods are also compared. The following conclusions are drawn:

(1) NMR T₂ has been considered as a rapid and non-destructive method to distinguish the phase states of water, gas, and gas hydrate, estimate the saturations of water and gas hydrate, and analyze the kinetics of gas hydrate formation in sediments.

(2) NMR T₂ is widely used to measure the pore information on the pore structure in sediments, including pore size distribution, porosity, and permeability.

(3) Many non-destructive detection techniques (e.g., CT, MRI, Cryo-SEM, ¹³C solid-state NMR, and NMR T₂) are used to acquire in situ quantitative and real-time characterization of gas hydrate formation process. This study compares their application characteristics in terms of resolution, phase recognition, scanning time, advantages, and drawbacks. Compared with other technologies, NMR T₂ can obtain the real-time continuous formation process of gas hydrates in sediments, rather than the spatial distribution characteristics of hydrates in sediments.

(4) To overcome the limitations of NMR T₂ in capturing the spatial distributions of hydrate and water, combining NMR T₂ with other techniques can more effectively characterize the dynamic behavior of gas hydrate formation and pore structure in sediments.