Microscopic Characterization and Fractal Analysis of Pore Systems for Unconventional Reservoirs

Abstract

The complex pore structure of unconventional oil and gas reservoirs is one of the reasons for the difficulties in resource evaluation and development. Therefore, it is crucial to comprehensively characterize the pore structure, understand reservoir heterogeneity from multiple perspectives, and gain an in-depth understanding of fluid migration and accumulation mechanisms. This review outlines the methods and basic principles for characterizing microporous systems in unconventional reservoirs, summarizes the fractal analysis corresponding to the different methods, sorts out the relationship between the fractals and reservoir macroscopic physical properties (porosity, permeability, etc.) with the reservoir microscopic pore structures (pore structure parameters, pore connectivity, etc.). The research focuses on cutting-edge applications of characterization techniques, such as improved characterization accuracy, calibration of PSD ranges, and identification of different hydrogen compositions in pore systems for dynamic assessment of unconventional reservoirs. Fractal dimension analysis can effectively identify the quality level of the reservoir; complex pore-throat structures reduce permeability and destroy free fluid storage space, and the saturation of removable fluids is negatively correlated with D_f. As for the mineral composition, the fractal dimension is positively correlated with quartz, negatively correlated with feldspar, and weakly correlated with clay mineral content. In future qualitative characterization studies, the application and combination of contrast agents, molecular dynamics simulations, artificial intelligence techniques, and 4D imaging techniques can effectively improve the spatial resolution of the images and explore the adsorption/desorption of gases within the pores, and also help to reduce the computational cost of these processes; these could also attempt to link reservoir characterization to research on supercritical carbon dioxide-enhanced integrated shale gas recovery, carbon geological sequestration, and advanced underground hydrogen storage.

1. Introduction

1.1. Unconventional Reservoirs

The microscopic pore system, which is the main control parameter for fluid movement, controls the reservoir’s macroscopic properties (porosity and permeability) [1,2]. Depositional environment and diagenetic alteration resulted in a diverse range of pore sizes, pore types, developed nanoscale pores, complex structures and massive nonhomogeneity. Exploration and exploitation of unconventional resources need a comprehensive understanding of the characteristics of the pore system since all of these factors impact the reservoirs’ storage performance [3,4,5].

Unconventional resource types come in different varieties (

Table 1. Types of Petroleum Resources.

Resource Type	Distribution Characteristics	Accumulation Type
conventional hydrocarbon	discrete-type	structural pool
	clustered-type	stratigraphic pool
		lithologic pool
unconventional hydrocarbon	continuous hydrocarbon accumulation	tight (sandstone) oil, gas
		tight (carbonates) oil, gas
		hydrate
		shale oil, gas
		coal bed methane

). The primary types of unconventional oil resources are tight oil, shale oil, thick oil, oil sands, and oil shale. Meanwhile, the main types of unconventional natural gas resources are tight sandstone [6,7], shale gas [2,8], coal bed methane [9], natural gas hydrate [10], etc.

Reservoirs are generally divided into clastic reservoir (sandstone, mudstone, shale), igneous reservoir and metamorphic reservoir. Originally loose and deposited in low-lying areas, the reservoir sediments were mainly caused by the damaging effects of weathering and erosion of primary rocks. After extended periods of sedimentary evolution, the overlying sediments gradually thickened, while the lower sediments were buried deeper, and eventually solidified into rocks as a result of compression, dehydration and cementation effects.

1.2. Pore System

The microscopic structure of pores or throats refers to the width, size distribution, geometric, topological properties and connectivity of pores, which affects the storage performance of reservoirs (Figure 1). The features of unconventional reservoir pore systems are loss of primary porosity, mainly developing secondary (dissolved) pores and micropores, and the existence of slits [11]. When characterizing micropores, it is necessary to select appropriate methods for joint characterization [12,13].

Currently, the most extensively used pore size classification systems are the Hodot pore size classification (micropore < 10 nm; micropore 10–100 nm; mesopore 100–1000 nm; macropore > 1000 nm) and the IUPAC pore classification (micropore < 2 nm; mesopore 2–50 nm; macropore > 50 nm) [11]. Furthermore, pores can be classified as intergranular pores, intragranular pores and microcracks, etc. (Figure 1) according to the pore morphology, the pores can also be classified into brittle mineral pores, clay mineral pores and other mineral pores based on the mineral components, spatial position and genesis (

Table 2. Classification of Sediment Pore System.

Classification	Mineral Component	Developmental Genesis Spatial Location	Development Scale	Morphological Characteristics
pores	clay mineral pores	intercrystalline pores	large size (>1000 nm) medium size (100–1000 nm) small size (10–100 nm) micro size (2–10 nm) ultra-micro size (<2 nm)	round, slit, flat, and zigzag
		aggregates (stacks) circumferential pores
		clay minerals or aggregates circumferential pores
	brittle mineral pores	circumferential pores
		dissolution pores
		intragranular pores (non-solviferous genesis)
		intergranular pores
		fracture pores
	other mineral pores	other mineral-related pores
microcrack	microfractures, inter-mineral microfractures, etc., caused by sedimentary tectonic genesis		sub-micron, micron	slit, flat, zigzag

).

As the channel connecting pores, the size and shape of the throat and the way it connects with pores control the seepage capacity of the reservoir.

Table 3. Throat Types.

Throat Types	Examples	Features
necking		pore throats vary greatly in size, and this variability is common in rocks with grain-supported textures, point contacts and contact cementation.
laminar		pore-throat widths are generally less than 1 mm; pore-throat ratios are moderately high, common in contact cemented, line-contact, and concave-contact rocks.
curved laminar
tube		the diameter of tube is generally smaller than 0.5 μm; the ratios of pore to throat is 1:1, which are very common in rocks with matrix support, suture contact and pore cementation.

[14] lists the four different forms of throat.

For the purpose of identifying and evaluating reservoirs, estimating oil and gas capacity, and enhancing oil and gas recovery, pore system characterization is crucial [2,15,16]. Pore structure, quantitative parameter characterization, reservoir classification, and evaluation are the key areas of research. The geometry, size, pore size distribution, interconnection, and composition of pores and throats are all regarded as parts of pore structure. These characteristics may reflect the combination or interaction of various kinds of pores [3,17,18].

1.3. Methods for Reservoir Characterization

The reservoir micropore system can be qualitatively and quantitatively analyzed using a variety of techniques.

Qualitative methods include optical microscope (OM), casting thin section (CTS) [19], field emission scanning electron microscopy (FESEM) [2,16,20,21,22,23,24], transmission electron microscope (TEM) [25,26,27,28,29], focused ion beam scanning electron microscopy (FIBSEM) [30,31,32,33,34,35,36,37], focused ion beam helium ion microscope (FIBHIM) [38,39], atomic force microscope (AFM) [40,41,42,43,44,45,46], X-ray computed tomography (X-CT) [12,47,48,49,50,51,52,53,54]; the quantitative methods can be divided into mercury injection capillary pressure (MICP) [5,55,56,57], constant-rate mercury injection (CRMI) [58,59,60,61], nuclear magnetic resonance (NMR) [59,62,63,64,65,66,67,68,69], small angle X-ray scattering (SAXS), small-angle neutron scattering (SANS) [30,70,71,72,73,74], and gas adsorption techniques such as CO₂ gas adsorption and N₂ gas adsorption (CO₂GA, N₂GA) [17,75,76].

Researchers have used various methods to characterize sediment pores in different reservoirs (Figure 2). This paper summarizes the mainstream viewpoints on reservoir pores delineation in recent years and compiles them through the comprehensive application of the listed methods; it also briefly discusses the development trend and key points.

This paper summarizes the innovative applications of various techniques for reservoir characterization, focusing on data correction, image processing, and reservoir fluid discrimination. In addition, although there are many research works on fractals, there are fewer systematic discussions; this paper summarizes the principles and formulas of fractals of various characterization methods, which can be used as a reference for future characterization studies.

2. Materials and Methods Multi-Scale Characterization of Pores of Unconventional Reservoirs

2.1. Methods for Quantitative Characterization

2.1.1. Nuclear Magnetic Resonance (NMR)

In recent decades, NMR methods have been widely used in geological research, particularly for the characterization of pore structures, evaluation of wettability, fluid discrimination and prediction of porosity and permeability [77].

The $T_2$ of the fluid can be expressed by:

$$\frac{1}{T_2}=\frac{1}{T_{2b}}+\frac{1}{T_{2s}}+\frac{1}{T_{2d}}$$

(1)

where $T_2$ is the relaxation time of the hydrogen-containing fluid in the pore; $T_{2b}$ is the bulk relaxation time; $T_{2s}$ is the surface relaxation time; $T_{2d}$ is the diffusion relaxation time [78]. $T_{2b}$ is higher for distilled water, so that the term 1/$T_{2b}$ can be neglected, and diffusion relaxation can be reduced when a low and uniform magnetic field and shorter pulse intervals are used. Hence, for the evaluation of the pore sizes, the $T_2$ can be simplified as:

$$\frac{1}{T_2}\approx \frac{1}{T_{2S}}=\rho {\left(\frac{S}{V}\right)}_{pore}$$

(2)

where $\rho$ is the surface relaxivity, ${\left(\frac{S}{V}\right)}_{pore}$ is the surface-to-volume ratio of pores.

Since ${\left(\frac{S}{V}\right)}_{pore}$ of the pore is a function of the pore radius ($r$) and the pore geometry morphologic factor ($F_s$), the $T_2$ can also be expressed as:

$$\frac{1}{T_2}=\rho \frac{F_s}{r}$$

(3)

The constant value $F_s$ is influenced by the geometry of the pores, with 1, 2 and 3 corresponding to slit, cylindrical and spherical pores, respectively [79].

The $T_2$ curve distribution, which is derived through mathematical fitting of the NMR signal, provides an indirect representation of the sample’s pore size and distribution.

Bound water and bulk water represent the two categories of enriched water in the pore; NMR can be utilized to identify the borders between these two liquid types, enhancing the estimation of pore permeability. There are differences in the relaxation times of the free state, pore-confined, and adsorbed water, and a cut-off value (T_2cutoff) is generally used to distinguish the different states [59].

The T_2cutoff value (Figure 3) can separate bound water from bulk water; the T_2cutoff value obtained from centrifugal tests divides the T₂ spectrum into two parts, bound water pore volume is represented by the sum of T₂ distributions smaller than the T_2cutoff value and bulk water pore volume is represented by the sum of T₂ distributions larger than the T_2cutoff value [59,80].

The Coates model (Figure 4) is a frequently used model for permeability estimation. It can be used to estimate formations that include hydrocarbons and water:

$$K={\left[{\left(\frac{\varnothing }{C}\right)}^2\left(\frac{FFI}{BVI}\right)\right]}^2$$

(4)

where $\varnothing$ is porosity; $K$ is permeability; the constant C reflects the correlation between the pore throat and pore size as a function of pore geometry.

Different hydrogen fractions in complex pore structures can be more accurately identified by 2D NMR T₁–T₂ correlation maps and T₁–T₂ ratios (Figure 5). Furthermore, these identify a variety of fluids in different pore types, such as organic pores (OP) and inorganic pores (IP), including inter- and intra-particle pores, as well as detecting the geochemistry of organic pores.

The PSD of NMR can be calibrated by N₂GA and SEM. To obtain a quantitative relationship between T₂ and PSD, the two peaks of the T₂ spectrum are combined with N₂GA (microporous PSD) and SEM (mesoporous PSD), respectively. From this, linear and power index fitting equations were established to derive a linear model and a power index model to calibrate the PSD (Figure 6).

2.1.2. Nuclear Magnetic Resonance Cryoporometry

Nuclear magnetic resonance cryoporometry (NMRC) is an emerging method to analyze the PSD of nanoscale porous materials. The Gibbs–Thompson equation, which forms the basis of NMRC theory, determines the relationship between the melting temperature ($T_m$) of a solid and pore size (x):

$$∆T_m=T_m-T_m\left(x\right)=\frac{K_{GT}}{x}$$

(5)

where $T_m$ is the melting temperature of the solid, $∆T_m$ is the decrease in melting temperature, $T_m\left(x\right)$ is the melting temperature of a crystal with pore diameter x, K_GT is the Gibbs–Thompson constant [81,82].

PSD is the pore volume differential coefficient of pore size (x), and is expressed as dV/dx. Since K_GT is an experimental empirical value, the increase in pore diameter x corresponds to $∆T_m$.

The pore volume can be detected through NMRC by using the following expression:

$$\frac{dV}{dx}\propto \frac{dI}{dx}=\frac{K_{GT}}{X^2}\times \frac{dI}{d{T}_m\left(x\right)}$$

(6)

The choice of probe material to characterize a geological sample can have a significant impact on the accuracy of the measurements. Probe materials with varying K_GT values have a direct effect on the accuracy of pore size analysis at the same temperature control; the main probe materials currently used in the NMRC characterization technique include water, OMTCS, cyclohexane, and calcium chloride hexahydrate (

Table 4. Properties of the Four Different Probe Materials.

Probe Material	Melting Point (K)	KGT (K·nm)	Liquid Density (g/cm3)	Enthalpy of Fusion (kJ/mol)	Molecular Size (nm)
Water [83]	273.1	57.3	0.997	6.01	0.4
Cyclohexane [84]	279.9	148	0.779	2.72	0.67
Octamethyl cyclotetrasiloxane [85]	290.5	160	0.955	19.7	0.9–1.0
CaCl2·6H2O [86]	303.15	-	1.352	37.24	-

).

2.1.3. Mercury Intrusion Capillary Pressure

The basic principle of MICP is based on the non-wetting property of mercury towards most solid interfaces.

Mercury enters the capillary without wetting the surface and overcomes the capillary pressure while expanding in the pores and throats, where the capillary pressure $P_c$ can be expressed as:

$$P_c=\frac{2\sigma \cos \theta }{R}$$

(7)

where R is pore radius, σ is interfacial tension, θ is static contact angle. The pore or throat radius distribution curve can be calculated by the equation, while the capillary pressure curve is generated from the entering mercury volume and the corresponding pressure obtained in the mercury pressure experiment [87].

This method has both advantages and limitations. One of the advantages is the wide range of experimental pressures, as shown in Equation (7), where different pressure values correspond to pores of a certain pore size; secondly, experimental capillary pressure curves for mercury rejection can be obtained to analyze the samples’ surface wettability; lastly, batch experiments can be easily conducted owing to the speed of the experiment.

The following are the limitations: (1) For samples with low porosity and low permeability, the resulting high pressure can create artificial cracks that introduce inaccuracies, which are especially noticeable in block samples; (2) The Washburn equation assumes that the sample pores are smooth cylindrical connected pores, but the pores of unconventional reservoirs have complex morphology and rough pore surfaces, which will cause errors in actual measurements; (3) R in Equation (7) is the maximum pore diameter to be measured, the existence of pore throats causes the measured PSD to deviate from the true value.

Nowadays, a good match between MICP-N₂GA integrated porosity and helium porosity of the same sample validates some new data calibration methods, and an adequate correlation between the PSD curves recorded by these methods in their overlapping pore size range [5].

2.1.4. Constant-Rate Mercury Injection

Yuan and Swanson were the first to perform the RCMI experiments on the APEX (pore inspection equipment) pore analyzer.

The RCMI method injects mercury into pores at a very low velocity, obtains information about pore structure based on fluctuation of pressure controlled by the throat, and sequentially goes from one throat to another, thus distinguishing the pores and throats within the samples. The results can be visualized and quantitatively analyzed for parameters such as pore size, PSD, pore-throat radius ratio and throat channels.

As the mercury enters the main throat 1, the pressure gradually increases (Figure 7). Once it breaks through the throat, there is a sudden drop in pressure, known as the first pressure drop O(1); the mercury then fills the first hole gradually and moves on to the next throat, causing a second secondary pressure drop O(2); this process continues until all the holes controlled by the main throat are filled, and the pressure reaches the value of the main throat, completing the unit. The radius of the main throat is defined by the pressure at the breakthrough point, and the size of the orifice is determined by the volume of mercury feed. Hence, the size and number of throats can be distinctly observed in the typical intrusion and extrusion curve of RCMI.

Figure 6 depicts the experimental procedure. Initially, mercury enters throat I; once the pressure reaches a specific threshold, mercury breaks through the throat and enters pore 1, and the pressure drops; pore 1 then fills and the pressure rises. Mercury next breaks through throat II and enters pore 2, causing another drop in pressure; this cycle remains until the experiment ends. Compared with MICP, RCMI has a significantly lower maximum inlet pressure, leading to a higher minimum throat radius [58].

The MICP method is generally based on the capillary bundle model, which assumes that the porous media is composed of uniform capillary bundles of varying diameters. This method only provides information about the volume of pores controlled by the throat and is unable to measure the number of throats directly. In contrast, the RCMI method assumes that the porous media consists of throats and pores with different diameters, this method can simultaneously obtain information about both the pores and the throats (Figure 8). It is particularly suitable for low permeability and ultra-low permeability reservoirs with ranging properties of pore and throat. The completion of RCMI experiments usually takes 2–3 days due to the slow quasi-static mercury feed process. The contact angle θ closely approximates the static contact angle, thus in the experimentally obtained throat radius nearly equals the actual throat radius. Thereby, the RCMI method has the advantage of quantitatively characterizing the microscopic throat structure.

2.1.5. N₂ Gas Adsorption

Based on the physical adsorption principle of gas and capillary condensation theory, the N₂GA method can measure the pore volume (PV), specific surface area (SSA), pore structure, pore shape, and PSD of porous media. The PSD is usually calculated using the BJH (Barrett-Joiner-Halenda) model [88], which points out that the assumed hypotheses are the same as in the MICP technique: a bundle of capillary tubes (cylindrical) connected to the sample’s borders. For SSA calculations, the BET (Brunauer-Emmett-Teller) method is generally used [1,16,75,89].

According to the principle, the sample is placed in a nitrogen-helium gas mixture environment at liquid nitrogen temperature (77 K), and part of the nitrogen molecules are adsorbed on the samples’ pore surface. As the relative pressure increases, the thickness of the nitrogen adsorption layer rises until the pressure matches the corresponding pressure within the pores, then capillary condensation occurs, allowing the samples’ adsorption-desorption isotherms and nitrogen adsorption capacity at various pressures to be determined. When relative pressures (P/P₀) are close to 1.0, coalescence occurs on all surfaces [9].

Adsorption or desorption isotherms are obtained by measuring the amount of adsorbed nitrogen and the equilibrium pressure. These are then divided into five categories (Figure 9: from I to V).

Types A, B, C and D hysteresis curves correspond to cylindrical pores, slit-like pores, t wedge-shaped pores, and bottle neck pores, respectively.

The advantages and limitations of the above quantitative characterization techniques are summarized in

Table 5. Comparison of quantitative characterization techniques.

Method	Advantages	Limitations
Low-Field NMR	Non-intrusive, does not destroy the sample	May be interfered with by magnetic impurities in the sample
	Fast measurement for a large number of samples	Limited resolution, may not detect very small pores
	Provides pore size and distribution information
NMR Cryoporometry (NMRC)	Directly reveals the relationship between melting point and pore volume	Special sample preparation and handling required
	Suitable for complex pore structures	May be interfered with by other components in the sample
	Provides a relatively complete pore size distribution
Mercury Intrusion Capillary Pressure (MICP)	Measures a wide range of pore size distributions	High pressure may alter the pore structure
	Suitable for large pore measurements	The pore limit values measured by this method are related to the maximum mercury pressure of the device
	Provides pore volume and specific surface area information	Calculated PSD overestimates the volume of large pores to the detriment of tiny pores
Constant-Rate Mercury Injection (CRMI)	Distinguishes between pores and throats	Longer experiment time
	Provides pore and throat radii and quantities	Limited maximum mercury intrusion pressure
	Obtains three capillary pressure curves
Nitrogen Adsorption (N2GA)	Suitable for micropore and mesopore measurements	Underestimate the content of larger mesopores and macropores
	Provides specific surface area and pore size distribution information	Requires a longer adsorption equilibration time
	Non-intrusive method, does not destroy the sample

.

2.2. Qualitative Characterization Methods

2.2.1. Field Emission Scanning Electron Microscopy

FESEM’s ultra-high resolution of 0.5–2 nm enables image processing for surface morphology analysis of samples. With its X-ray spectrometer, the FESEM is one of the most useful tools for observing morphology and analyzing micro- and nanoscale pore structure (Figure 10). It can assess micro-area elements on sample surfaces both qualitatively and quantitatively; further, it can analyze the chemical composition and morphology of the samples.

2.2.2. Laser Scanning Confocal Microscopy

Laser scanning confocal microscopy (LSCM) utilizes a laser spot as a fluorescence excitation light for continuous scanning of samples, blocking the out-of-focus plane light through spatially conjugated diaphragms (pinholes) and imaging [91]. LSCM offers a high level of detail, with the ability to magnify up to 10,000 times and achieve an ultimate resolution of 0.15 μm. By employing LSCM, it is possible to rebuild 3D pictures and achieve both 3D imaging and structural reconstruction of the pore throat [92] (Figure 11).

2.2.3. Focused Ion Beam–Scanning Electron Microscopy

Seliger et al. pioneered the development of the world’s inaugural focused ion beam (FIB) system in 1978 at Hughes Research Labs (Malibu, CA, USA), utilizing liquid metal gallium (Ga) ions as the emission source. FEI subsequently manufactured the initial focused ion beam system in 1982 and the first electrostatic field-focused electron in 1988. Subsequently, the initial FIB-SEM system was effectively created by integrating a standard scanning electron microscope with the FIB system, positioning the ion beam at a specific angle relative to the electron beam. The FIB-SEM imaging principle is similar to that of SEM, as both use the detector to capture the excitation of the secondary electron imaging; the main difference is that FIB uses an ion beam as the irradiation source, which possesses greater power and mass compared to electrons.

FIB-SEM can analyze and simulate microscopic pores and perform nanoscale 3D reconstruction of unconventional reservoirs to gain insight into the microscopic pore structure inside the reservoir (Figure 12). Specifically, it can characterize the structure, orientation, grain morphology, size, distribution and other information of samples.

2.2.4. Transmission Electron Microscopy

Roska invented the transmission electron microscope (TEM) in 1932, which uses electron beams as the light source. The principle of TEM is to project an electron beam onto a very thin sample. When the electrons collide with the atoms in the sample, the trajectory of the electrons changes, resulting in solid angle scattering. The magnitude of the scattering angle is associated with the density and thickness of the sample; this relationship allows for the formation of bright and dark pictures, which may be viewed on imaging devices after being magnified and focused (Figure 13).

The resolution of TEM surpasses that of OM, achieving a range of 0.1~0.2 nm with magnifications ranging from tens of thousands to millions of times. Therefore, TEM can be used to observe the intricate morphology of samples, including the arrangement of just one column of atoms.

TEM contains three levels of lenses. The lenses include a focusing lens, an objective lens, and a projection lens. The focusing lens is used to mold the initial electron beam, while the objective lens is utilized to focus the electron beam as it traverses the sample, ensuring it passes through the samples. The magnification of TEM is determined by the ratio of the image plane distance of the sample to the objective lens. Cryo-microscopy typically involves integrating a sample freezing device into a conventional transmission electron microscope to cool the sample to liquid nitrogen temperature (77 K). This process minimizes electron beam damage and sample distortion, allowing for a more accurate representation of the sample’s shape.

2.2.5. Atomic Force Microscopy

Atomic force microscopy (AFM) is employed for studying the surface structure of porous media. By detecting the interatomic contact force between the sample surface and the micro force-sensitive components, the surface structure and characteristics of porous media are examined. The force modifies the state of the micro-cantilever, which is fixed at one end and has a micro-tip near the other end that interacts with the samples. With nanoscale resolution, the sensor will identify the change and determine the force distribution, providing information on the surface morphological structure and surface roughness [94,95,96,97].

Recently, AFM has been widely used for on the situ imaging in nanoscale and direct measurement of oil–rock interaction [98,99]. By using quantitative force curve data, it can be utilized to confirm the in situ wettability of the reservoirs and validate the adsorption of nanoparticles on the solid surfaces [99,100,101,102]. By measuring the thickness of the oil–water film directly on the sample surface, the force between the sample and the liquid film, and the roughness of the solid surface, an AFM probe may investigate changes in the wettability of the solid surface. Deng et al. [103] evaluated the wettability of reservoir rock mineral particles based on AFM; the study utilized AFM to measure micrometer-sized water droplets on the surface of quartz minerals of sandstone reservoir to calculate the water–quartz contact angle. Most studies evaluate the wettability-changing ability of wetting agents based on macroscopic phenomena such as contact angle. Three types of operating modes are distinguished according to how the tip interacts with the sample (

Table 6. Three Operation Modes of AFM.

Operation Mode	Contact Mode	Non-Contact Mode	Tapping Mode
advantages	yielding stable, high-resolution images.	no force applied to the sample surface.	eliminates the effect of lateral forces; reduces of forces caused by adsorbed liquid layers; high image resolution; suitable for soft, fragile or sticky samples without damaging its surface.
disadvantages	lateral forces may affect image quality; the capillary effect of the adsorbed liquid layer on surface results in high adhesion forces between the needle tip and the sample; the combined force of the lateral force and the adhesion force reduces the spatial resolution of the image, the tip of the needle crossing the sample can damage soft samples.	low scanning speed; needle tip separates from the sample, resulting in low lateral resolution; can only be used for hydrophobic samples; the adsorption layer must be very thin.	slower scanning speed than contact mode.

).

The advantages are that the sample does not require pretreatment and AFM can directly image the surface morphology of nanoscale pores or pore throats. During the experiment, it is not easy to damage the sample and it can provide three-dimensional images of the surface. The main disadvantages include the image ranging limitation, its slow imaging speed and the probe’s substantial impact on the measurement results.

In previous studies, shale samples from the Longmaxi Formation in the Sichuan Basin were selected for AFM and N₂GA experiments. The study proposes a new method to quantify shale porosity and a dual-threshold discrete integration method to estimate the pore contribution of major materials [44].

The advantages and limitations of the above qualitative characterization techniques are summarized in

Table 7. Comparison of qualitative characterization methods.

Method	Advantages	Limitations
Atomic Force Microscope (AFM)	Provides true three-dimensional surface images	Limited field of view, only small areas can be observed
	High resolution up to the atomic level	May be affected by interactions between the probe and the sample
	Suitable for conductors and non-conductors
Field Emission Scanning Electron Microscope (FE-SEM)	High-resolution imaging	Special sample preparation (e.g., metal coating) required
	Direct observation of pore morphology and structure	Potential damage to the sample by the electron beam
	Suitable for various material types
Transmission Electron Microscope (TEM)	High-resolution imaging, observes internal structures	Sample needs to be sliced, which may alter the pore structure
	Suitable for various material types	Limited field of view, only small areas can be observed
	Direct observation of pore morphology and structure
Focused Ion Beam–Scanning Electron Microscope (FIB–SEM)	Combines high resolution of SEM with precise cutting of FIB	Expensive equipment and operational costs
	Enables 3D reconstruction and quantitative analysis	Complex sample preparation, may introduce artifacts
	Suitable for various material types
Laser Scanning Confocal Microscope (LSCM)	Enables 3D imaging and quantitative analysis	Lower resolution compared to electron microscopes
	Suitable for fluorescently labeled samples	May be affected by fluorescent dyes
	Non-intrusive, does not destroy the sample

.

2.3. X-ray Radiation Method

2.3.1. Small Angle X-ray Scattering

The development of the SAXS technique is based on the idea that a porous medium consists of two phases (pore matrix), which has been consistently investigated by Guinier, Fournet and Porod. X-ray scattering is caused by the difference in electron density between the pore space and the reservoir rock matrix. The parameters of the pore structure in an ideal two-phase system are ascertained as follows:

$$I\left(q\right)=4\pi ·{\left({\rho }_m-{\rho }_p\right)}^2·\phi ·\left(1-\phi \right)·V·{\int }_0^{\infty }{r}^2{\gamma }_0\left(r\right)\frac{\sin \left(qr\right)}{qr}dr$$

(8)

$$R_g=\sqrt{\frac{3}{5}}·R$$

(9)

$$q=4\pi \sin \frac{\theta }{\lambda }$$

(10)

$$D=\frac{2\pi }{q}$$

(11)

where ${\gamma }_0$: normal correlation function of the reservoir sample; $I\left(q\right)$: scattering intensity; q: scattering vector; ${\left({\rho }_m-{\rho }_p\right)}^2$: electron density difference between the sample matrix (${\rho }_m$) and the air in the pores (${\rho }_p$), proportional to the pore density); φ: volume fraction of the pores in the sample (total porosity); V: volume of the sample; R: pore radius; R_g: radius of gyration of the pores; λ: the wavelength of the X-rays; 2θ: scattering angle; D: pore diameter.

Based on Porod’s theory, the scattering intensity of SAXS is given by the following equation:

$$I\left(q\to \infty \right)=2\pi I_e·{\left({\rho }_m-{\rho }_p\right)}^2·\frac{S}{q^4}$$

(12)

$$\lim \left[q^4·I\left(q\right)\right]=K$$

(13)

where K: Porod constant; S: surface area; I_e: scattering intensity of electrons. When there are electron density fluctuations at the pore boundary, the Porod curve shows a positive deviation; when there is a fuzzy phase boundary in the pore, the Porod curve shows a negative deviation.

$$Q={\int }_0^{\infty }I·q^{2}dq=I_e·V·2{\pi }^2\phi ·\left(1-\phi \right)·{\left({\rho }_m-{\rho }_p\right)}^2$$

(14)

Based on Equations (12) and (14), the SSA can be expressed as:

where S_v: specific surface area; Q: an integral invariant. The 2D scattering images can be converted to 1D scattering data by FIT2D software V12. Equation (13) determines the I(q)–q curve, and then the structural information such as R_g, pore size, fractal dimension, and thickness of the interfacial layer are calculated by post-processing.

2.3.2. X-ray Computed Tomography

Because of the considerable non-homogeneity of reservoir pores, it is important to precisely figure out how pores and fractures are developing to formulate a development program that would maximize returns from exploitation. In the 1980s, medical CT scanning technology was brought to the field of core analysis; as science and technology advanced and research methods were refined, this technology became widely applied in a variety of fields, including saturation and porosity measurement, core inhomogeneity characterization, and more.

The basis of CT imaging is the concept that CT involves using an X-ray beam to scan a sample via layers of a specific thickness; the X-ray attenuation difference is used to create two-dimensional slices. The computer system uses the “filtered-back projection” algorithm to rebuild the two-dimensional slices after converting the attenuation coefficients into CT numbers, which show up as gray values in the grayscale image. CT is equipped with an X-ray microscope, sample stage and slice reconstruction processing software, enabling non-destructive three-dimensional imaging of samples in their original state, and for determining the PSD, size, and connectivity of nano-submicron pores and throats in the reservoirs.

Equation (15) expresses how the X-ray beam attenuates during the scanning process:

$$I=I_{0}exp\left(-\mu D\right)$$

(15)

where I: the residual intensity of the ray after it passes through the sample, is the initial intensity of the ray; μ: ray attenuation coefficient, is related to the sample density and atomic coefficient. The larger the μ, the closer the point; μ represents the distribution of the density of the substance; the attenuation coefficient is usually converted to the CT number. D: thickness of the substance.

Currently, CT analysis methods are mainly divided into image direct observation, CT number analysis, and 3D reconstruction model methods (Table 8).

Table 8. Three Analysis Methods of XCT.

Method	Image Direct Observation	CT Number Analysis	3D Reconstruction Model Method
principle	the internal structural features of the core can be directly observed; in the scanned section, there are 256 levels of grayscale, with 0 representing the darkest (all black) and 255 representing the brightest (all white); lower density material appears as black and higher density material appears as white (Figure 14).	CT values correlate with the attenuation coefficient and indirectly reflect the density of the substance; for scanned samples, the larger mean CT value indicates a denser, more inhomogeneous substance.	threshold segmentation is performed by recognizing material with different densities and pores according to their respective CT number distribution intervals; none standardized criteria for setting the threshold.

Table 8. Three Analysis Methods of XCT.

Method	Image Direct Observation	CT Number Analysis	3D Reconstruction Model Method
principle	the internal structural features of the core can be directly observed; in the scanned section, there are 256 levels of grayscale, with 0 representing the darkest (all black) and 255 representing the brightest (all white); lower density material appears as black and higher density material appears as white (Figure 14).	CT values correlate with the attenuation coefficient and indirectly reflect the density of the substance; for scanned samples, the larger mean CT value indicates a denser, more inhomogeneous substance.	threshold segmentation is performed by recognizing material with different densities and pores according to their respective CT number distribution intervals; none standardized criteria for setting the threshold.

Figure 14. Porosity calculated from AFM-calculated values and N₂GA-converted values, respectively [44].

Figure 14. Porosity calculated from AFM-calculated values and N₂GA-converted values, respectively [44].

In image visualization, the white part of grayscale represents mineral grains or high-density cement, such as silica; the black part represents micropores and microfractures; and the gray part represents the matrix components.

Mimics 21 software is used for processing CT statistics, Avizo 9.2 software performs 3D model reconstruction, and the researcher establishes the thresholds relying on their subjective judgment, which may lead to limited and inaccurate reconstruction outcomes (Figure 14, Figure 15, Figure 16 and Figure 17).

The advantages and limitations of the above X-ray characterization methods are summarized in

Table 9. Comparison of radiation methods for characterizing pores in reservoirs.

Method	Advantages	Limitations
Small-Angle X-ray Scattering (SAXS)	Measures a wide range of pore size distributions	Complex data analysis requiring specialized software support
	Non-destructive to the sample, suitable for various materials	Limited sensitivity to small pores
	Provides pore shape and structure information
X-ray Computed Tomography (XCT)	Provides non-destructive testing, maintaining sample integrity.	Limited detection capability for large-volume samples using XCT.
	High resolution and contrast, clearly showing pore structure.	Potential radiation safety concerns, requiring strict operational guidelines.
	Applicable to a variety of materials and morphologies.	Relatively high equipment and maintenance costs.

:

2.4. Comprehensive Characterization PSD of Reservoir

Comprehending and defining the pore structure of reservoirs is vital for efficient hydrocarbon exploration. Reservoirs exhibit unique pore features, prompting the development of numerous methodologies to evaluate intricate pore systems. Table 7 outlines the benefits and constraints of these techniques; choosing the most suitable approach for characterizing reservoir pores is crucial for accurately evaluating reservoir potential and optimizing extraction procedures. The current challenge and primary focus of research in this field is how to harmonize multiple scales of PSD produced through several approaches onto a unified coordinate scale. Existing studies focus on quantitative characterization by stitching PSDs acquired by various methods (Figure 18, Figure 19, Figure 20, Figure 21, Figure 22 and Figure 23); however, there is still work to be done on the problems of image scale extension and feature point selection for quali–tative characterization methodologies [4,15,16,58,66,72,104,105,106].

The PSDs derived by the two SAXS models (Gaussian distribution model and maxi–mum entropy model) are different. The PSD obtained from the Gaussian distribution model for the range of 0–15 nm and the PSD obtained from the maximum entropy theory for the range of 15–48 nm were similar to the PSDs acquired from the NMRC.

The calculations between pore volume and pore size are different; while NMRC tests open pores, SAXS tests both open and closed pores, resulting in larger pore volumes. During NMRC experience, the interaction between water and the sample itself can cause pore dilatation and mineral dissolution. Specifically, the expansion of clay minerals owing to water interaction may increase the number of micropores. The bigger pore volume is correlated with the larger pore SSA, as shown by the strong positive association between TPV and SSA (Figure 18).

The combined analysis of CTS, SEM and HPMI contributed to a comprehensive study of the unconventional pore system (Figure 19).

Research in imaging is also innovating; for example, Du combines FESEM and XCT to establish three parameter categories, i.e., size, direction and morphology, through which the pore evolution characteristics of unconventional reservoirs at microscale depths can be investigated [109].

Based on the non-homogeneous nature of unconventional reservoirs, fluid flow in nanoscale microscopic pores has also become a major challenge in characterization [13], such as the nature of the initial interface between two miscible fluids and the control by peripheral magnetism on the convection of Casson fluids formed by the internal temperature variations in the microscopic pores [110,111,112,113].

2.5. Method Limitations and Challenges

The characterization of microporous structures in unconventional reservoirs still faces many challenges in both qualitative description and quantitative analysis, which need to be studied in depth.

In terms of qualitative characterization, the current results for nanopores inevitably contain errors. In order to improve the accuracy of characterization, there is an urgent need to develop higher precision techniques. At present, it is difficult for image observation techniques to take into account the needs of high resolution and large field of view. Optical microscopes and scanning electron microscopes can cover a wider field of view but lose resolution, while high-precision techniques suffer from the problems of small observation range, poor representation of the samples, long time-consumption, and high cost. In the 3D reconstruction technique, the threshold segmentation of the image is controlled by human factors, which leads to inaccurate hole throat localization. Therefore, combining the application of machine learning and imaging technology, further updating and improving the pore network modeling method, reducing the influence of human factors, and improving the characterization accuracy to solve the research bottleneck of high resolution and large field of view is an important development direction of unconventional reservoir characterization technology.

In terms of quantitative characterization techniques, the joint characterization of the full pore size distribution is the mainstream direction. The data splicing part of different quantitative experimental results is often contradictory. In future research, we need to analyze and compare the experimental principles and accuracy of various testing techniques in depth, find the number of unified parameters that can connect various techniques in series, and correct the errors effectively. This will help to understand the pore structure of unconventional reservoirs more comprehensively and provide more accurate data support for oil and gas exploration and development.

3. Characterization of Reservoir Inhomogeneity by Fractal Dimension (D_f)

Previous studies defined fractals as self-similar objects independent of the level of magnification, characterized by the fractal dimension D_f [114]. Since Mandelbrot (1977) proposed fractal theory, it has been widely used in petroleum exploration and development. Fractal theory is used to quantitatively characterize the inhomogeneity of reservoirs, explaining irregular, unstable, and highly complex pore structure features, and helping to relate macroscopic petrophysical parameters (porosity, permeability) to microscopic pore structure (pore diameter, PSD and pore throat connectivity).

Within the same scale range, the smaller D_f represents a simpler reservoir pore structure, strong homogeneity, and the formation of the reservoir is conducive to the filling and enrichment of hydrocarbons [16,115,116]. The D_f of the reservoir pore structure ranges from 2.0 to 3.0 (not included). A low D_f (close to 2.0) indicates that the pore throat structure is regular and the pore surface is smooth; on the contrary, a D_f close to 3.0 indicates that the pore throat structure is rough and the pore structure is complex. The change in pore morphology from regular to complex, which lowers permeability and obstructs pore fluid movement, is reflected in the increase in D_f. Here are varies factors affecting the D_f in

Table 10. Factors affecting the fractal dimension D_f.

Influencing Factor	Features of Df	Impact on Reservoir Heterogeneity
Sedimentary environment	Range of Df values	Different sedimentary environments may lead to varying fractal characteristics of the reservoir, such as river, delta, and lake environments, which affect the structure, pore distribution, and connectivity of the reservoir, thereby influencing its heterogeneity.
Diagenesis	Pattern of Df value distribution	Diagenetic processes such as compaction, cementation, and dissolution can affect the petrophysical properties of the reservoir, such as porosity and permeability, thereby affecting the heterogeneity of the reservoir.
Tectonic activity	Anomalous regions in Df values	Tectonic activities like folding and faulting can lead to complex fracture and fault systems within the reservoir, which often exhibit higher heterogeneity, manifesting as anomalous values of the Df.
Scale effect	Scale-dependence of Df values	At different observation scales, the heterogeneity of the reservoir may exhibit different characteristics. Larger scales may mask local heterogeneity, while smaller scales may more accurately reveal the heterogeneous structure of the reservoir.
Measurement method	Accuracy of Df value calculation	Different measurement methods may yield varying fractal dimension values.

.

According to fractal theory, the number of pores with a radius greater than r, N(>r), is related to the power function of the pore radius as follows:

$$N\left(>r\right)={\int }_r^{r_{max}}P\left(r\right)dr\propto r^{-D_f}$$

(16)

where $r_{max}$: maximum pore radius; P(r): distribution density functions of pore radius.

MICP, N₂GA, NMR and NMRC methods can be used to infer the D_f of the reservoir.

3.1. Fractal Dimension (D_f) of Mercury Intrusion Capillary Pressure

In MICP analysis, assuming that the pores of the reservoir sample are cylindrical, the number of pores with a pore radius greater than r can be expressed by Equation (16). The complex pore throat structure is considered as a series of interconnected irregular capillary networks [59,79,117,118,119,120,121,122,123,124].

Assuming that the pores in the reservoir sample are tubular (tube model), N(>r) can be expressed as:

$$N\left(>r\right)=\frac{V_{Hg}}{\pi r^{2}l}\propto r^{-D_f}$$

(17)

where $V_{Hg}$: cumulative volume of mercury at a specific capillary pressure; l: the length of the capillary.

According to the Yang–Laplace equation, the pressure of mercury injection can be expressed as:

$$P_c=\frac{2\sigma \cos \theta }{r},V_{Hg}\propto P_c^{D_f-2}$$

(18)

The D_f relating the mercury saturation $S_{Hg}$ to the capillary pressure $P_c$ can be expressed by the following equation:

$$S_{Hg}=a{P}_c^{D_f-2}$$

(19)

where a is a constant. Slope “$D_f-2$” can be obtained from the plot of $\log S_{Hg}$ vs. $\log P_c$:

$$\log S_{Hg}=\left(D_f-2\right)\log P_c+\log a$$

(20)

This equation describes the linear relationship between $\log S_{Hg}$ and $\log P_c$. The D_f is calculated by D_f = S + 2.

In addition to the tubular model, the ball-and-stick model (l = r) is also widely adopted by many scholars. Considering r_min ≪ r_max, $S_v$ can be described as:

$$S_v=\frac{r^{3-D_f}-r_{min}^{3-D_f}}{r_{max}^{3-D_f}-r_{min}^{3-D_f}}={\left(\frac{r}{r_{mac}}\right)}^{3-D_f}$$

(21)

where $S_v$: accumulated pore volume corresponding to the total pore volume less than the pore radius of r, i.e., the saturation of the wetting phase during mercury injection. Thus:

$$S_v=1-S_{Hg}$$

(22)

By the formula

$$P_c=\frac{2\sigma \cos \theta }{r},V_{Hg}\propto P_c^{D-2}$$

(23)

Equation (24) can be expressed as follows:

$$S_v={\left(\frac{P_{min}}{P_c}\right)}^{3-D_f}$$

(24)

The logarithm of both sides of the equation yields:

$$\log S_v=\left(D_f-3\right)\log P_c-\left(D_f-3\right)\log P_{min}$$

(25)

$$D_f=S+3$$

(26)

3.2. Fractal Dimension (D_f) of N₂ Gas Adsorption

Qi et al. proposed that the Frenkel–Halsey–Hill equation (FHH model) can be used to calculate $D_f$ from N₂GA data, which is described by the following equation:

$$\ln \frac{V}{V_0}=A\ln \left(\ln \frac{P}{P_0}\right)+C$$

(27)

where C is a constant; A is derived from the slope of the $\ln \frac{V}{V_0}$ vs. $\ln \frac{P}{P_0}$ curve [16,108,109,125,126,127,128].

Figure 21. $\ln V$ vs. $\ln \left(\ln \frac{P_0}{P}\right)$ curves [115].

Figure 21. $\ln V$ vs. $\ln \left(\ln \frac{P_0}{P}\right)$ curves [115].

The FHH plot of the coal samples is shown in the figure, indicating that there are different fractal regions on the coal surface. Based on the fitting coefficient R greater than 0.95, the “average” D_f was used to describe the overall roughness of the coal surface.

3.3. Fractal Dimension (D_f) of Nuclear Magnetic Resonance

In the fractal model, the number of pores N(r) with dimensions greater than r is calculated from the total fractal equation above. In NMR measurements, the cumulative porosity $V_p$ can be expressed by Equation (32) [19,78,79,129,130,131,132,133,134].

$$V_p=\frac{{\left(\frac{r}{r_{max}}\right)}^{3-D_f}-{\left(\frac{r_{min}}{r_{max}}\right)}^{3-D_f}}{1-{\left(\frac{r_{min}}{r_{max}}\right)}^{3-D_f}}$$

(28)

where $r_{max}$ is the maximum pore size; $r_{min}$ is the minimum pore size. These two parameters correspond to the maximum and minimum T₂ values, respectively.

Equation (28) describes the mass fractal model of the PSD in NMR measurements. The pore size r is directly related to the $T_2$ value; thus, Equation (29) can be obtained:

$$V_p=\frac{{\left(\frac{T_2}{{T_2}_{max}}\right)}^{3-D_f}-{\left(\frac{{T_2}_{min}}{{T_2}_{max}}\right)}^{3-D_f}}{1-{\left(\frac{{T_2}_{min}}{{T_2}_{max}}\right)}^{3-D_f}}$$

(29)

where ${T_2}_{max}$ and ${T_2}_{min}$ are the maximum and minimum T₂ values. Equation (29) quantifies the relationship between the T₂ relaxation time distribution and the D_f of the pore system.

Since the minimum value of the T₂ (${T_2}_{min}$) is small enough compared to the associated measured T₂, Equation (30) is obtained:

$$V_p={\left(\frac{T_2}{{T_2}_{max}}\right)}^{3-D_f}$$

(30)

where $V_p$ is the accumulative pore volume at T₂ values; ${T_2}_{max}$ is the maximum T₂ value in the NMR T₂ spectrum.

D_f can be calculated from the slope $\left(3-D_f\right)$:

$$\log V_p=\left(3-D_f\right)\log T_2+\left(D_f-3\right)\log {T_2}_{max}$$

(31)

where ${T_2}_{max}$ is the maximum relaxation time, ms; $V_p$ is the cumulative volume.

Equation (31) describes the linear relationship between $\log V_p$ and $\log T_2$; D_f can be calculated from the slope “$3-D_f$” of the $\log V_p$ vs. $\log T_2$ plot.

The research also needs to determine the demarcation line between capillary bound water and movable water—the T_2cutoff value, T_2c. The part of T₂ smaller than T_2c or larger than T_2c characterizes the fractal features of bound and movable water, respectively.

Figure 22. The double-logarithm coordination showing the relationship between $V_p$ and T₂ [134].

Figure 22. The double-logarithm coordination showing the relationship between $V_p$ and T₂ [134].

3.4. Fractal Dimension (D_f) of Nuclear Magnetic Resonance Cryoporometry

Combining the principles of D_f calculation with the NMRC results, it is found that NMRC data can also be used for the estimation of D_f of unconventional reservoirs:

$$∆T_m=T_m-T_m\left(x\right)=\frac{K_{GT}}{x}$$

(32)

The following expression can be derived:

$$∆{T_m}_{min}=\frac{K_{GT}}{x_{max}}$$

(33)

And then can be expressed as:

$$S_v={\left(\frac{∆{T_m}_{min}}{∆T_m}\right)}^{3-D_f}$$

(34)

where $S_v$ is the cumulative volume of the pore with radius less than r; $∆T_m$ is calculated using raw NMR signal intensities at different temperature points. Taking the logarithm of the above equation [85,88].

$$\log S_v=\left(D_f-3\right)\log ∆T_m+\left(3-D_f\right)\log {∆T_m}_{min}$$

(35)

Figure 23. D_f curves obtained from NMRC [93]. The fractal dimension ranges from 2.8063 to 2.9847 for segment I, and from 1.4181 to 2.3621 for segment II.

Figure 23. D_f curves obtained from NMRC [93]. The fractal dimension ranges from 2.8063 to 2.9847 for segment I, and from 1.4181 to 2.3621 for segment II.

3.5. Relationship between Df and Physical Properties of Reservoirs

D_f has no obvious correlation with porosity, but is negatively correlated with permeability. When D_f is larger, the pore structure is more complex, making it difficult for fluids to pass through and resulting in a decrease in permeability.

As shown in Figure 24, both D_g-s and D_g-b are negatively correlated with porosity and permeability. In terms of porosity, the coefficient of determination between D_g-b and D_g-s, shows that the porosity is mainly affected by the D_f of large pore throats with regular shapes and smooth surfaces, while small pore throats only affect porosity to a certain extent. Regarding permeability aspects, the coefficient of determination between D_g-s, D_g-b and permeability are similar, which means that D_f of both large and small pore throats has an impact on the permeability.

4. Conclusions and Future Research

This review outlines the methods and fundamentals of characterizing microporous systems in unconventional reservoirs, summarizes the fractal analysis methods corresponding to the different methods, and sorts out the relationship between the fractals and reservoir macroscopic physical properties (porosity, permeability, etc.) with the reservoir microscopic pore structures (pore structure parameters, pore connectivity, etc.). The conclusions are drawn as follows:

The scale of the pores in unconventional reservoirs varies greatly, ranging from nanometers to microns. When the characterization study of the reservoir focuses on the range of less than 10 nm, it is recommended to combine TEM, FIB-SEM, AFM and SAXS methods. For pores smaller than 100 nm, N₂GA, NMRC and FESEM methods can be mainly used, and for the characterization of the range of hundreds of nanometers and micrometers, CTS, OM, MICP, CRMI, and NMR methods can be effectively combined. XCT (threshold segmentation) and CRMI techniques can be used to effectively differentiate between pores and throats, and the connectivity of pores can be combined with the pore connectivity analysis of XCT and the MICP technique; when the study involves the information of minerals and bioclastic debris, the OM and XCT techniques are the most intuitive, and the details can be further investigated by the FIBSEM and FESEM techniques; when obtaining pore diameter characterization while focusing on the information of fluids within the pore, it is recommended to use the NMR (T₁, T₁–T₂) and NMRC techniques.

The techniques and ideas for characterizing the pores are constantly advancing. This is mainly demonstrated through improvements reflected in the accuracy of characterization (the integrated approach of FIB-HIM and FIB-SEM extends organic pore imaging and quantitative analysis to less than 10 nm), calibration of the range of PSD (converting T₂ spectra of NMR to full-scale PSD by using linear and power exponential models in combination with N₂GA and SEM), identification of different hydrogen components in the pore system (T₁/T₂), and dynamic assessment of unconventional reservoirs (estimation of seepage resistance during water displacement based on pore throat size and distribution characteristics using a capillary bundle model, and modeling to dynamically monitor and evaluate the coproduction behavior of multilayer reservoirs).

The issue of balancing spatial resolution with the field of view remains unresolved. Destructive characterization approaches yield data with some inaccuracies, to ensure the reliability of the results, it is necessary to compare them with those obtained by non-destructive techniques.

The analysis of fractal dimension can effectively identify the quality level of reservoirs. Research on macroscopic petrophysical parameters shows that the saturation of movable fluid is negatively correlated with D_f due to the complex pore-throat structure that reduces the permeability and destroys the storage space of free fluid. The mineral composition analysis reveals that the fractal dimension is positively correlated with quartz, negatively correlated with feldspar, and weakly correlated with clay mineral content, which needs to be analyzed specifically for each individual reservoir.

In future qualitative characterization research, the injection of contrast agents can be used as a new approach to study the pore structure and enhance the quality of imaging; moreover, the combination with molecular dynamics simulation and artificial intelligence techniques can effectively improve the spatial resolution of images and explore the adsorption/desorption of gases within the pores. This combination also helps in reducing the computational cost of these processes. Furthermore, the utilization of 4D imaging, which combines three-dimensional visualization with real-time monitoring, allows for the observation of the dynamic alterations in microstructure at the pore-scale level, this capability is of utmost importance for future research endeavors.

Regarding quantitative characterization, there are several emerging research areas that can be explored, such as supercritical CO₂-enhanced integrated shale gas recovery, carbon geological sequestration, and advanced underground hydrogen storage; these areas aim to achieve the goals of long-term energy supply and net-zero carbon emissions.