Multiscale Fractal Characterization of Pore Structure and Reservoir Quality Based on Deep-Learning-Assisted Pore Extraction in the Majiagou Tight Dolomite Gas Reservoir, Central Ordos Basin, China

Abstract

Tight dolomite gas reservoirs are promising exploration targets, yet their evaluation is complicated by multiscale pore-throat heterogeneity and poor seepage connectivity. Here, high-pressure mercury intrusion (HPMI), nuclear magnetic resonance (NMR), scanning electron microscopy (SEM), and deep-learning-assisted pore extraction were integrated to characterize the pore-throat structure and fractal features of the Middle Ordovician Majiagou Formation in the Ordos Basin. The reservoir is dominated by diagenetic-origin pores, mainly intercrystalline and intragranular dissolution pores, together with microfractures, and can be classified into three types with progressively poorer connectivity and flow capacity. Type I reservoirs contain more regular pores, larger pore-throat systems, and better storage and seepage capacity; Type II reservoirs are intermediate, whereas Type III reservoirs exhibit complex pore morphology, isolated pore networks, poor petrophysical properties, and limited gas-flow potential. The corresponding fractal dimensions are weakly correlated but complementary: D_SEM captures pore-boundary complexity, D_HPMI reflects pore-throat architecture and capillary-pressure-controlled seepage pathways, and D_NMR reflects multiscale movable-fluid distribution. Clay minerals, especially illite-rich mixed layers, further intensify pore-throat heterogeneity. Increasing fractal dimension is generally associated with higher displacement and median pressures, but poorer connectivity, porosity, permeability, movable-fluid content, and gas deliverability. These results provide a basis for the quantitative evaluation of multiscale pore systems and reservoir quality in tight dolomite gas reservoirs.

1. Introduction

Carbonate rocks host a large proportion of the world’s hydrocarbon reserves and remain important targets for hydrocarbon exploration and development [1,2,3]. Tight dolomite gas reservoir is a key type of carbonate reservoir. Due to the development of multi-scale pores and fractures, they are usually highly heterogeneous, and these pores and fractures are the result of the combined effects of sedimentary fabric, diagenesis, and tectonic deformation [4,5]. Pore structure strongly controls hydrocarbon storage and migration [6,7]. Robust pore-structure characterization is therefore essential for evaluating reservoir quality, improving exploration and development efficiency, and constraining diagenetic evolution [8,9].

Fractal geometry provides a quantitative framework for describing the complexity and heterogeneity of porous media [10,11,12]. In carbonate reservoirs, fractal analysis has been used to quantify pore morphology, pore-throat organization, and reservoir heterogeneity [13,14,15]. Previous studies generally report inverse relationships between fractal dimension (D) and porosity or permeability [14,16], although dissolution-generated pores and microfractures may locally increase both structural complexity and effective storage or flow capacity [17]. D has also been linked to pore-throat sorting, characteristic radius, and capillary-pressure behavior [15,18]. However, a single bulk D can obscure scale-dependent differences among pore domains and may show weak relationships with individual structural parameters [19].

Scanning electron microscopy (SEM), high-pressure mercury intrusion (HPMI), and nuclear magnetic resonance (NMR) provide complementary observations of heterogeneous pore systems. SEM directly resolves two-dimensional pore morphology and boundary complexity [20,21], HPMI constrains capillary-controlled throat accessibility and connectivity [15,19], and NMR characterizes pore-size and movable-fluid distributions through relaxation behavior [22,23,24]. Deep-learning-assisted image segmentation can reduce interpreter dependence and improve the reproducibility of pore-boundary extraction [21,25]. For example, deep-learning approaches have been used for CT-image reconstruction, shale-content prediction, coal-fracture extraction, rock-pore detection, and intelligent thin-section characterization [25,26,27,28,29,30,31]. Nevertheless, most studies either focus on image segmentation itself or use different pore-characterization methods as parallel descriptors. For example, fully convolutional network (FCN) and multiscale convolutional segmentation network (MCSN) perform well in coal-fracture identification [29,30], Mask region-based convolutional neural network (Mask R-CNN) has advantages in rock-pore detection [25], and U-Net has been widely applied to micropore extraction [31]. In addition, conventional NMR fractal models commonly assume a linear relationship between transverse relaxation time (T₂) and pore radius, despite evidence that the relationship may follow a power law [32].

Although combinations of SEM and NMR or mercury intrusion and NMR have been used to characterize heterogeneous reservoirs [22,23,24], direct same-sample comparison of SEM-, HPMI-, and NMR-derived fractal dimensions remains limited for tight dolomite systems. Consequently, it is still unclear whether image-based pore-boundary complexity, capillary-controlled pore-throat architecture, and relaxation-based fluid distribution represent equivalent or complementary aspects of pore-system heterogeneity. The applicability of a power-law-corrected NMR fractal model to heterogeneous carbonate pore systems also requires further evaluation [32].

Accordingly, this study investigates the tight dolomite gas reservoir in submember Ma₅⁴ of the Middle Ordovician Majiagou Formation in the central Ordos Basin. Petrophysical measurements, mineralogical data, HPMI, NMR, and deep-learning-assisted SEM image analysis are integrated to characterize pore geometry, pore-throat architecture, movable-fluid distribution, and multiscale fractal behavior. The principal advances are threefold. First, SEM-, HPMI-, and NMR-derived fractal dimensions are compared within a unified framework using the same sample dataset, allowing pore-boundary complexity, capillary-controlled pore-throat architecture, and relaxation-based movable-fluid distribution to be distinguished across scales. Second, a power-law-corrected NMR fractal model employing sample-specific T₂–pore-radius relationships is evaluated for carbonate pore systems, thereby reducing uncertainty associated with the conventional linear assumption. Third, mineral composition, pore geometry, and multiscale fractal parameters are linked to reservoir typing, pore-throat accessibility, movable-fluid behavior, and gas seepage capacity, providing an integrated basis for evaluating tight dolomite reservoir quality.

2. Geological Background

The Ordos Basin, located in the western part of the North China Plate, is a stable multicycle cratonic basin. It can be subdivided into six first-order tectonic units: the Yimeng Uplift, the Western Thrust Belt, the Tianhuan Depression, the western Shanxi flexural fold belt, the Yishan Slope, and the Weibei Uplift [33,34] (Figure 1a,b).

The study area is situated on the Yishan Slope in the central Ordos Basin (Figure 1a). Under the tectonic compression of the late Caledonian cycle, the basin as a whole was uplifted and subjected to 150 Ma of weathering and erosion, resulting in the absence of the Upper Ordovician, Silurian, Devonian, and Lower-Middle Carboniferous strata within the basin. The central paleo-uplift is located in the central–western part of the Ordos Basin and extends approximately from the Etuoke–Dingbian area in the north to the Huanxian–Qingyang–Zhenyuan area in the south (Figure 1a). During deposition of the Ordovician Majiagou Formation, this paleogeomorphic high reduced the available accommodation space and caused the strata to thin toward the uplift, with local non-deposition or erosion. It also influenced depositional-facies differentiation and the spatial distribution of carbonate and evaporite successions, whereas relatively thicker and more complete stratigraphic successions accumulated in the surrounding depressions. The Majiagou Formation is subdivided into six members (Ma₁–Ma₆), and the member Ma₅ is further divided into ten submembers (Ma₅¹–Ma₅¹⁰) [35]. The succession shows significant vertical lithologic variation controlled by multiple transgressive–regressive cycles (Figure 1d). The dominant lithologies include limestone, dolomite, dolomitic limestone, calcareous dolomite, argillaceous dolomite, argillaceous limestone, and mudstone [36,37]. A total of 33 core samples were collected from the tight dolomite gas reservoir of submember Ma₅⁴ of the Majiagou Formation (Figure 1c).

3. Materials and Methods

3.1. Experimental Measurements

To characterize pore-structure heterogeneity and its controlling factors, porosity and permeability were measured for all 33 core samples. Cylindrical plugs with a diameter of 25 mm were prepared, cleaned with dichloromethane to remove residual hydrocarbons and organic contaminants, and subsequently vacuum-dried at 120 °C for 24 h. Helium porosity and pulse-decay permeability were measured using an AP-608 automated porosimeter and permeameter (Coretest Systems Inc., Morgan Hill, CA, USA).

Based on the measured porosity and permeability, 28 representative samples covering the full range of petrophysical characteristics and reservoir types were selected for detailed petrographic, mineralogical, and pore-structure analyses. Blue-epoxy-impregnated cast thin sections (CTSs) were examined using an Olympuscx21 polarizing microscope (Olympus Corporation, Tokyo, Japan) to characterize rock fabrics, mineral relationships, and pore types. Microscopic pore morphology and mineral textures were further investigated using an FEI Quanta 400 FEG scanning electron microscope (SEM) (FEI Company, Hillsboro, OR, USA). Bulk mineralogical compositions were determined by X-ray diffraction (XRD) using a D8 DISCOVER diffractometer (Bruker AXS GmbH, Karlsruhe, Germany) under laboratory conditions of 24 °C and 35% relative humidity. Mineral phases were identified by comparing the positions and relative intensities of the measured diffraction peaks with standard reference diffraction patterns.

For nuclear magnetic resonance (NMR) and high-pressure mercury intrusion (HPMI) analyses, the 28 selected samples were dried at 100 °C for 24 h and subsequently evacuated for 12 h. Sample dimensions and dry masses were recorded before testing. Water-saturated NMR T₂ spectra were acquired using a RecCore-2500 low-field NMR spectrometer (Research Institute of Petroleum Exploration and Development, PetroChina, Beijing, China). The measurements were conducted at 25 °C with a resonance frequency of 2.38 MHz, 2048 echoes, a repetition time of 5000 ms, and an echo spacing of 0.6 ms. The samples were then centrifuged sequentially at 2500, 2900, 3500, 5000, 7900, and 9100 rpm for 2 h at each rotational speed. After each centrifugation step, the samples were weighed, and their T₂ spectra were remeasured. The T₂ cutoff separating bound and movable fluids was determined by comparing the T₂ distributions before and after centrifugation.

HPMI measurements were subsequently performed using an AutoPore IV 9505 mercury intrusion porosimeter (Micromeritics Instrument Corporation, Norcross, GA, USA) at 20–25 °C and a relative humidity of 80–85%. Cylindrical segments approximately 1 cm in length were cut from the core plugs, cleaned, dried to a constant mass, and placed in the sample chamber under vacuum. Mercury was progressively injected by stepwise increasing the applied pressure to the maximum experimental pressure, thereby accessing successively smaller pore throats. The pressure was then gradually reduced to obtain the mercury extrusion curve. Applied pressure, intruded mercury volume, mercury saturation, and experimental conditions were continuously recorded to construct capillary-pressure curves and derive the corresponding pore-throat structure parameters.

All experiments were conducted at the State Key Laboratory of Continental Evolution and Early Life, Northwest University.

3.2. Methods

3.2.1. Enhanced U-Net Model

This study adopted an enhanced U-Net model to segment pores in SEM images [21,38]. The convolutional blocks were redesigned, and regularization was introduced to make the model more stable during training. DropBlock was added to the convolutional layers, where continuous regions of neurons are masked rather than individual points, helping to reduce redundant feature connections and limit overfitting. Batch normalization (BN) was used to support faster convergence and improve the generalization of the network. The conventional skip connections in U-Net were further replaced by a feature pyramid network (FPN), which allowed shallow spatial information and deeper semantic features to be combined across multiple scales.

A total of 84 SEM images were obtained from 28 dolomite samples. From these images, 21 representative 512 × 512 pixel image blocks were prepared for model training and evaluation. All 21 selected patches were manually delineated in ImageJ 1.54 to generate pixel-level reference masks. In the representative SEM images used in this work, the magnification ranged from 3376× to 13,980×, corresponding to an approximate spatial resolution of 0.06–0.27 μm/pixel for the 512 × 512 input patches. During feature extraction, the network passed the input images through five downsampling stages. The number of feature channels started at 64 and doubled after each stage. The fused multiscale features were then progressively upsampled to produce the final segmentation maps.

The segmentation model was developed in PyTorch 3.12.0 and optimized using Adam. During training, the learning rate was set to 1 × 10⁻⁴, the batch size was 8, and the training process lasted for 100 epochs. Evaluation on the independent test set showed that the final model reached a precision of 0.928, a mean absolute error (MAE) of 0.128, and a Dice coefficient of 0.866. These results suggest that the model can extract pore structures from carbonate-rock SEM images with relatively stable accuracy, and may also be applicable to other materials that have complex microstructural features (Figure 2).

The workflow included four main stages: data preprocessing, backbone feature extraction, multiscale feature fusion, and pixel-level prediction. During preprocessing, the SEM images were first cropped into 512 × 512 pixel patches using Adobe Photoshop. The pore regions in these patches were then manually outlined in ImageJ, and the annotated masks were converted into grayscale label images. A consistent pore-identification criterion was applied throughout the annotation procedure, and ambiguous pore boundaries and obvious non-pore artifacts were re-examined and corrected before model training. The full dataset was divided into training, validation, and test sets at a ratio of 7:2:1. To expand the variability of the training samples and reduce the risk of overfitting, data augmentation was performed with the Imgaug library. The applied augmentation operations included elastic deformation, random shear, scaling, and rotation. Data augmentation was applied only to the training subset, and all augmented variants generated from an original training image remained within the training subset. No formal k-fold cross-validation was performed; therefore, the reported metrics represent a fixed holdout evaluation of the present labelled dataset.

For backbone feature extraction, each stage contained two 3 × 3 convolutional layers followed by a 2 × 2 max-pooling layer. With an initial channel number of 64, the network generated five effective feature levels through successive downsampling. These feature maps were then passed into the FPN module for multiscale fusion. The FPN combined bottom-up and top-down feature propagation with lateral connections and convolutional integration, enabling information from different depths to be merged. During the upsampling process, 2 × 2 convolutions were used, and the number of channels was gradually reduced by half.

Finally, the fused feature layers were used for pixel-wise classification to generate the segmentation results. After segmentation, isolated noise objects and non-pore artifacts were removed through manual inspection and size-based filtering. The retained pore masks were then used to calculate pore geometric parameters.

To further evaluate the practical effectiveness of the enhanced U-Net, a controlled comparison with conventional ImageJ-based segmentation was performed using the same SEM fields. The ImageJ results (Figure 3d–f) demonstrate that threshold-based segmentation is sensitive to grayscale variations caused by mineral surfaces and shadows. Consequently, several non-pore regions were incorrectly identified as pores, whereas numerous small, weak-contrast, and irregularly shaped pores were omitted. In contrast, the enhanced U-Net results (Figure 3g–i) provide more continuous pore-boundary delineation, retain small and elongated pores, and substantially reduce interference from non-pore artifacts across samples with different pore textures. This improvement is attributed to the combined use of DropBlock regularization and feature pyramid network-based multiscale feature fusion, which strengthens the distinction between true pore space and matrix-related grayscale variations.

The comparative results indicate that the enhanced U-Net provides more robust and reproducible pore segmentation than conventional ImageJ processing for heterogeneous tight-dolomite SEM images.

3.2.2. Fractal Dimension Based on SEM

SEM image analysis can be used to characterize the irregularity and complexity of pore structure. In two-dimensional space, the fractal dimension is constrained to values below 2 [11]. For micropores identified in SEM images, the relationship between pore perimeter and pore area is given by [39,40]:

$$\lg P={\displaystyle \frac{\mathrm{D}}{2}}\lg A+C$$

(1)

where P is the pore perimeter extracted from the SEM images (μm), A is the pore area (μm²), D is the fractal dimension describing pore morphology, and C is a constant.

In this study, deep learning was used to extract pore parameters from 28 dolomite samples, yielding 7258 valid pores. Based on Equation (1), log-transformed pore area and perimeter were fitted linearly, and the SEM area-perimeter fractal dimension was calculated as D_SEM = 2S_SEM, where S_SEM is the fitted slope.

3.2.3. Fractal Dimension Based on HPMI

HPMI characterizes pore-throat structure and pore-size distribution by applying external pressure to overcome the capillary entry pressure of mercury, which acts as the non-wetting phase. As the intrusion pressure increases, progressively smaller pore throats are accessed, and the mercury intrusion volume corresponds to the pore volume controlled by throats of equivalent radius. The pore-throat radius r is calculated as follows [41]:

$$r={\displaystyle \frac{2\sigma \cos \theta }{P_C}}$$

(2)

where P_C is the capillary pressure (MPa), S_Hg is mercury saturation, σ is the surface tension (dyne/cm), and θ is the contact angle, which was taken as 140°.

According to fractal theory, if the pore-throat system in a rock exhibits fractal behavior, the cumulative number of objects larger than a given scale, N(>r), follows a power-law relationship with the linear scale r:

$$N\left(>r\right)={\int }_r^{r_{\mathrm{m}\mathrm{a}\mathrm{x}}}P\left(r\right)\mathrm{d}r=a{r}^{-\mathrm{D}}$$

(3)

where r_max is the maximum pore-throat radius, P(r) is the pore-throat radius distribution density function, a is a proportionality constant, and D is the fractal dimension.

Differentiating with respect to r gives:

$$P\left(r\right)={\displaystyle \frac{\mathrm{d}N\left(>r\right)}{\mathrm{d}r}}=a^{\prime }{r}^{-\mathrm{D}-1}$$

(4)

where a′ is a proportionality constant equal to −Da.

The cumulative pore volume associated with pore throats smaller than r, V(<r), can be expressed as:

$$V={\int }_{r_s}^{r}P\left(r\right)a{r}^3\mathrm{d}r={\displaystyle \frac{{-\mathrm{a}}^2\mathrm{D}}{3-\mathrm{D}}}({\mathrm{r}}^{3-\mathrm{D}}-{\mathrm{r}}_{\mathrm{m}\mathrm{i}\mathrm{n}}^{3-\mathrm{D}})$$

(5)

The total pore volume V can be written as:

$$\mathrm{V}={\displaystyle \frac{{-a}^2\mathrm{D}}{3-\mathrm{D}}}(r^{3-\mathrm{D}}-r_{\mathrm{m}\mathrm{i}\mathrm{n}}^{3-\mathrm{D}})$$

(6)

Combining Equations (5) and (6) yields the cumulative volume fraction of pore throats with radii smaller than r:

$$S={\displaystyle \frac{V(<r)}{V}}={\displaystyle \frac{r^{3-\mathrm{D}}-r_{\mathrm{m}\mathrm{i}\mathrm{n}}^{3-\mathrm{D}}}{r_{\mathrm{m}\mathrm{a}\mathrm{x}}^{3-\mathrm{D}}-r_{\mathrm{m}\mathrm{i}\mathrm{n}}^{3-\mathrm{D}}}}$$

(7)

If r_min << r_max, Equation (7) can be simplified to:

$$S={\left({\displaystyle \frac{r}{r_{\mathrm{m}\mathrm{i}\mathrm{n}}}}\right)}^{3-\mathrm{D}}$$

(8)

Assuming that the contact angle remains constant with pore-throat size, substituting Equation (2) into Equation (8) gives:

$$S={1-S}_{\mathrm{H}\mathrm{g}}={\left({\displaystyle \frac{P_{\mathrm{c}\mathrm{m}\mathrm{i}\mathrm{n}}}{P_c}}\right)}^{3-\mathrm{D}}$$

(9)

where S is the wetting-phase saturation corresponding to capillary pressure P_C, expressed as a percentage.

Taking logarithms on both sides of Equation (9) yields:

$$\log S=\log (1-S_{\mathrm{H}\mathrm{g}})=\left(\mathrm{D}-3\right)\log {\mathrm{P}}_{\mathrm{C}}-(\mathrm{D}-3)\log P_{C\mathrm{m}\mathrm{i}\mathrm{n}}$$

(10)

In the HPMI experiment, air is treated as the wetting phase and mercury as the non-wetting phase. Therefore, logS can be expressed as log(1 − S_Hg), where S_Hg is mercury saturation. Segmented linear fits of log(1 − S_Hg) versus logP_C were performed for each sample, and the fitted slopes were used to calculate D_HPMI1–D_HPMI3. In this study, D_HPMI1, D_HPMI2, and D_HPMI3 represent the fractal dimensions of the macropore-, mesopore-, and micropore-dominated pore-throat domains, respectively.

3.2.4. Fractal Dimension Based on NMR

NMR experiments indirectly reflect pore-throat size distribution through the T₂ relaxation spectrum. Fractal analysis of the NMR T₂ spectrum can therefore be used to evaluate pore-throat structural complexity in different samples. Higher complexity corresponds to a larger fractal dimension [16,42].

According to NMR theory, the transverse relaxation time T₂ can be expressed as:

$$T_2={\displaystyle \frac{r}{F_S\rho }}$$

(11)

where T₂ is the transverse relaxation time (ms), ρ is the transverse surface relaxivity (μm/ms), r is the pore-throat radius (μm), and F_S is the shape factor, taken as 2 for cylindrical pores and 3 for spherical pores.

The cumulative pore-volume fraction associated with pore throats smaller than r can be expressed as:

$$S_V={\displaystyle \frac{V(<r)}{V_s}}={\displaystyle \frac{r^{3-\mathrm{D}}-{\mathrm{r}}_{\mathrm{m}\mathrm{i}\mathrm{n}}^{3-\mathrm{D}}}{r_{\mathrm{m}\mathrm{a}\mathrm{x}}^{3-\mathrm{D}}-r_{\mathrm{m}\mathrm{i}\mathrm{n}}^{3-\mathrm{D}}}}$$

(12)

Here, S_V is the percentage of cumulative pore-throat volume with relaxation times smaller than T₂ relative to the total pore volume, and D is the fractal dimension of the pore space in three dimensions. When r_min << r_max and r_min << r, Equation (12) can be simplified to:

$$S_V={\left({\displaystyle \frac{r}{r_{\mathrm{m}\mathrm{a}\mathrm{x}}}}\right)}^{3-\mathrm{D}}$$

(13)

Substituting Equation (11) into Equation (13) gives:

$${\mathrm{S}}_{\mathrm{V}}={\left({\displaystyle \frac{T_{2\mathrm{m}\mathrm{a}\mathrm{x}}}{{\mathrm{T}}_2}}\right)}^{\mathrm{D}-3}$$

(14)

where T_2max is the maximum relaxation time.

Taking logarithms on both sides yields:

$$\log {\mathrm{S}}_{\mathrm{V}}=\left(3-\mathrm{D}\right)\log T_2-(3-\mathrm{D})\mathrm{l}\mathrm{o}\mathrm{g}{T}_{2\mathrm{m}\mathrm{a}\mathrm{x}}$$

(15)

As shown in Equation (15), the fractal dimension can be calculated from the slope (S_NMR) of the logS_V − logT₂ plot according to D_NMR = 3 − S_NMR.

The above approach assumes a linear relationship between transverse relaxation time T₂ and pore-throat radius. However, many studies have shown that T₂ and pore-throat radius are related by a power law [32]:

$$T_2={\displaystyle \frac{r^n}{F_S\rho }}$$

(16)

where n is the exponent. Using core sample #18 as an example, the cumulative probability curve of the NMR T₂ spectrum and that of pore radius obtained from HPMI were plotted on the same graph. For a given cumulative pore-volume fraction, the corresponding transverse relaxation time T₂ and pore radius were determined (Figure 4a), and their relationship was then fitted with a power function (Figure 4b). The same procedure was applied to all samples with paired HPMI and NMR data to obtain sample-specific n values.

Substituting Equation (16) into Equation (15) gives:

$$S_V={\left({\displaystyle \frac{T_{2\mathrm{m}\mathrm{a}\mathrm{x}}}{T_2}}\right)}^{{\displaystyle \frac{D-3}{n}}}$$

(17)

Taking logarithms on both sides yields:

$$\log S_V={\displaystyle \frac{\left(3-\mathrm{D}\right)}{n}}\lg T_2-{\displaystyle \frac{\left(3-\mathrm{D}\right)}{n}}\mathrm{l}\mathrm{o}\mathrm{g}{T}_{2\mathrm{m}\mathrm{a}\mathrm{x}}$$

(18)

As shown in Equation (18), the fractal dimension corrected using the power-law relationship between T₂ and pore size can be calculated as D′_NMR = 3 − nS_NMR. Segmented linear fits of logS_V versus logT₂ were then used to calculate D_NMR1–D_NMR3 and D′_NMR1–D′_NMR3. In this study, D_NMR1/D′_NMR1, D_NMR2/D′_NMR2, and D_NMR3/D′_NMR3 represent the macropore, mesopore, and micropore domains, respectively.

4. Results

4.1. Reservoir Space Types

SEM and cast thin-section observations show that the reservoir space in the dolomite of the study area consists mainly of diagenetic-origin pores, with subordinate sedimentary-origin pores. The diagenetic-origin pores include intercrystalline pores, intercrystalline dissolution pores, intracrystalline dissolution pores, and intragranular dissolution pores, whereas the sedimentary-origin pores are mainly relict intergranular pores. Among them, dolomitization and dissolution-related pores constitute the main reservoir space. The pore spaces are preferentially distributed along intercrystalline contacts and dissolution-enlarged crystal margins, indicating that the arrangement of dolomite crystals strongly controls pore occurrence and connectivity.

Intercrystalline pores occur between rhombic dolomite crystals, are mostly 1–10 μm in size, and are relatively uniformly distributed, giving a sieve-like appearance. As the dominant pore type in these low-porosity dolomites, they contribute little to permeability because of their small size and only moderate connectivity (Figure 5a,b). Intercrystalline dissolution pores formed after dolomitization and were further enlarged by burial hydrothermal dissolution. They show embayed crystal margins and pore sizes of approximately 10–100 μm. These pores greatly improve connectivity and are a key control on relatively high permeability (Figure 5c,d). Intracrystalline dissolution pores are commonly distributed as isolated pores or discontinuous pore arrays preferentially aligned with the rhombohedral cleavage traces of dolomite crystals, and they contribute little to effective reservoir space when they remain isolated (Figure 5f,h).

Intergranular pores are relict sedimentary-origin pores formed during deposition. They are mainly triangular to polygonal and relatively large (10–50 μm). However, most were destroyed by later diagenesis, resulting in poor connectivity and a limited contribution to reservoir quality (Figure 5e–g). Intragranular dissolution pores are diagenetic-origin pores formed mainly through meteoric freshwater leaching and selective dissolution within grains. They are mostly isolated and therefore contribute little to permeability, even though they increase porosity (Figure 5e,g).

Microfractures are important post-diagenetic or tectonically related structures. They connect isolated pores and significantly enhance gas seepage capacity, thereby playing a critical role in the development of an effective pore-fracture reservoir system (Figure 5b,i).

4.2. Pore Structure Characterization

4.2.1. Pore Structure Characteristics Based on SEM

The enhanced U-Net model was applied to SEM images to automatically identify pores and extract geometric parameters, including perimeter, circularity, major axis, aspect ratio, and solidity (Table S1). Mean values of these parameters were calculated for each sample. Based on pore morphology, the extracted pores were classified into three types (Figure 3). Circular pores are relatively regular in shape, with high circularity (0.65–0.95), low to moderate aspect ratios (1.15–3.00), and high solidity (0.75–1.00). They mainly correspond to dissolution pores, especially intracrystalline and intragranular dissolution pores, and form an important part of the reservoir space in the dolomite. Irregular pores are triangular, polygonal, or mesh-like and are typical of intercrystalline pores, intercrystalline dissolution pores, intergranular pores, and intragranular dissolution pores. They are generally characterized by moderate solidity (0.40–0.60), relatively low circularity (0.30–0.75), and relatively high aspect ratios (1.60–1.75). Long-strip pores are narrow and slender, with the lowest circularity (0.10–0.30), the highest aspect ratios (>2.4), and generally high solidity (0.70–1.00). They are the typical morphology of microfractures, although they also occur between dolomite crystals.

Based on pore parameters and petrophysical characteristics, the samples were further divided into three reservoir types (Table S1). Type I samples (#1–#8) exhibit relatively regular pore morphologies, with short mean perimeters (2.56–5.99 μm), high mean circularity (0.65–0.81), relatively large major axes (1.18–2.18 μm), low aspect ratios (2.46–3.02), low solidity (0.25–0.46), and relatively large pore areas (0.49–3.80 μm²). These pores are closer to circular in shape and have larger sizes and better connectivity, which favor fluid storage and flow.

Type II samples (#9–#17) show slightly larger mean perimeters (3.20–6.76 μm), lower mean circularity (0.55–0.78), somewhat smaller major axes, higher aspect ratios (2.57–3.15), greater solidity (0.30–0.62), and pore areas of 0.60–4.65 μm². Their pore morphology is more elongated and concave, and the associated flow pathways are more tortuous. As a result, their storage and seepage capacities are poorer than those of Type I reservoirs.

Type III samples (#18–#28) display markedly irregular pore morphologies, with large mean perimeters (3.83–6.10 μm), low mean circularity (0.50–0.70), short major axes (0.39–1.99 μm), high aspect ratios (2.66–3.36), high solidity (0.41–0.78), and small pore areas (0.35–1.46 μm²). These pores are commonly narrow, concave, and geometrically complex, which leads to highly tortuous flow pathways and severely restricted storage space and permeability.

Comparison of the three reservoir types shows that circularity, major axis, and pore area decrease systematically from Type I to Type III, whereas perimeter, aspect ratio, and solidity increase. Higher circularity, a longer major axis, and a larger pore area are more favorable for gas seepage connectivity and storage space. In contrast, a larger perimeter, a higher aspect ratio, and greater solidity produce a more complex pore structure, poorer seepage pathways, and higher flow resistance. Overall, pore morphology and structural parameters jointly control the storage and flow capacities of tight dolomite gas reservoirs. Complex multitype and multiscale pore networks provide the main storage space for tight hydrocarbons and are therefore critical for reservoir-quality evaluation.

4.2.2. Pore Structure Characteristics Based on HPMI and NMR

The 28 samples from the study area yielded HPMI porosities of 0.293–5.024%, whereas NMR porosities range from 0.56% to 5.98%. These values are consistent with the measured porosity, with R² values of 0.781 and 0.845, respectively (Figure 6). Integrated analysis of the capillary-pressure curves and NMR T₂ spectra shows that the reservoirs in the study area can be classified into three types (Figure 7; Tables S2 and S3).

Reservoir typing was based on an integrated evaluation of petrophysical properties, SEM pore morphology, HPMI capillary-pressure parameters, and NMR movable-fluid characteristics rather than on a single manually selected threshold. Type I reservoirs are characterized by relatively low displacement pressure, larger connected pore-throat systems, higher movable-fluid saturation, and better porosity–permeability conditions; Type II reservoirs show intermediate values; Type III reservoirs are defined by high displacement pressure, low maximum mercury injection saturation, high bound-water saturation, and poor pore-throat connectivity.

Type I reservoirs are characterized by HPMI curves typical of potentially high-productivity intervals. The displacement pressure is usually below 1.0 MPa, indicating the presence of large to coarse pore throats and strong connectivity. The middle section of the mercury injection curve exhibits a wide, gradual plateau, suggesting the dominance of a specific pore-throat radius. The sorting coefficient ranges from 0.023 to 0.166 (average 0.098), and skewness varies between 2.174 and 4.815 (average 3.226), reflecting poor sorting and a prevalence of large pores. The NMR T₂ spectrum is generally bimodal, with the right peak being higher than the left, further confirming the predominance of large pores. The porosity contribution exceeds 0.2%, and the T₂ distribution is mainly concentrated between 10 and 1000 ms. The T₂ ranges from 5.15 to 165.11 ms and is mostly located to the left of the main peak. These samples also show relatively low bound-water saturation (25.33–57.23%) and high movable-fluid saturation (43.13–74.32%).

Type II reservoirs have displacement pressures lower than 10.0 MPa and are dominated by large to medium pore throats with relatively good connectivity. The capillary-pressure curve commonly exhibits a long plateau, indicating a favorable pore-throat structure. The sorting coefficient ranges from 0.05 to 0.186 (average 0.105), and skewness ranges from 2.377 to 9.594 (average 5.777), suggesting poor sorting but a predominance of relatively large pores. The NMR T₂ spectrum is also bimodal. The porosity contribution is lower than 0.3%, and the T₂ distribution is mainly concentrated between 1 and 1000 ms. The T₂ cutoff ranges from 0.14 to 10.14 ms and is generally located to the left of the peak, indicating a relatively concentrated pore-size distribution dominated by medium to large pores. Bound-water saturation remains relatively low (51.22–68.81%), whereas movable-fluid saturation is comparatively high (31.02–50.98%).

Type III reservoirs represent tight intervals. Their HPMI curves usually show displacement pressures greater than 10 MPa, steep slopes, and no obvious plateau, indicating the dominance of medium-small pores and fine throats. Maximum mercury saturation is only 7.6–29.9%, much lower than that of Types I and II. The sorting coefficient ranges from 0.112 to 0.328 (average 0.216), and skewness ranges from 3.077 to 22.113 (average 7.304), reflecting the absence of large pore throats and strong heterogeneity. The NMR T₂ spectrum is commonly unimodal or weakly bimodal, with the first peak higher than the following peak. The porosity contribution is only 0.1–0.2%. The T₂ distribution is mainly concentrated between 10 and 1000 ms, with a peak slightly below 10 ms. The T₂ cutoff ranges from 0.13 to 5.72 ms and lies to the right of the peak, indicating the dominance of medium pores and micropores. These samples are characterized by high bound-water saturation (50.41–75.05%) and low movable-fluid saturation (24.57–43.13%).

4.3. Fractal Characterization

4.3.1. Fractal Dimensions Obtained from SEM Data

According to fractal theory, the fractal dimension derived from SEM images should range from one to two. All calculated values fall within this interval, indicating consistency with fractal geometry. Using the deep-learning-extracted SEM pore data, log–log crossplots of pore area (A) versus perimeter (P) were constructed for 28 samples. These plots show strong linear relationships (R² > 0.9) (Figure 8a–c; Table S4). Overall, D_SEM ranges from 1.298 to 1.746, with an average of 1.504 (Figure 8j), indicating that pore morphology in the studied samples exhibits clear fractal characteristics.

For Type I samples (#1–#8), D_SEM ranges from 1.365 to 1.588, with an average of 1.485 (Figure 8a,j). For Type II samples (#9–#17), D_SEM ranges from 1.298 to 1.696, with an average of 1.496 (Figure 8b,j). For Type III samples (#18–#28), D_SEM ranges from 1.309 to 1.746, with an average of 1.525 (Figure 8c,j). These results show that D_SEM is lowest in Type I reservoirs, intermediate in Type II reservoirs, and highest in Type III reservoirs. This trend indicates that pore structure becomes more complex and pore morphology becomes more irregular as reservoir quality decreases.

4.3.2. Fractal Dimensions Obtained from HPMI Data

Based on pore-throat structural parameters derived from HPMI, segmented crossplots of log(1 − S_Hg) versus logP_C were constructed for each sample, and linear fitting was performed for each segment. The resulting R² values range from 0.900 to 0.999 (Table S4). The presence of three distinct segments indicates that the pore-throat system exhibits clear multifractal characteristics (Figure 8d–f). The total fractal dimension (D_HPMI) of each sample was obtained by weighting the fractal dimensions of different pore-throat classes according to their average porosity contributions. D_HPMI was calculated as follows [14]:

$$D_{HPMI}={\displaystyle \frac{{D_{HPMI1}{\phi }_{HPMI1}+D}_{HPMI2}{\phi }_{HPMI2}+D_{HPMI3}{\phi }_{HPMI3}}{{\phi }_{HPMI1}{+\phi }_{HPMI2}{+\phi }_{HPMI3}}}$$

(19)

Here, φ_HPMI1, φ_HPMI2, and φ_HPMI3 are the HPMI porosities of the macropore, mesopore, and micropore domains, respectively.

For Type I samples, the mean fractal dimensions of the macropore, mesopore, and micropore segments (D_HPMI1, D_HPMI2, and D_HPMI3) are 2.899, 2.766, and 2.540, respectively. The corresponding values for Type II samples are 2.965, 2.792, and 2.700, whereas those for Type III samples are 2.960, 2.858, and 2.615, respectively. Overall, macropores show the highest fractal dimensions, micropores the lowest, and mesopores intermediate values. These results suggest that macropore systems are geometrically more complex. This complexity may reflect more intricate connectivity between pores and throats within the macropore system, which is difficult to resolve explicitly.

Using Equation (19), D_HPMI values for the 28 samples were calculated to range from 2.558 to 2.847, indicating that the pore-throat systems exhibit well-developed fractal characteristics. Specifically, D_HPMI ranges from 2.690 to 2.838 for Type I samples, from 2.699 to 2.847 for Type II samples, and from 2.558 to 2.842 for Type III samples. The mean D_HPMI values of the three reservoir types are similar, indicating that the overall pore-throat network complexity differs only weakly among them.

For all three reservoir types, D_HPMI shows a clear positive correlation with D_HPMI3 (Figure 9), whereas correlations with the mesopore and macropore fractal dimensions are relatively weak. In addition, D_HPMI3 values (2.391–2.891) are consistently lower than those of the macropore and mesopore segments. This implies that within the pore-structure complexity defined by HPMI, the geometry and spatial arrangement of micropores play a key role in determining the overall complexity [16,43].

4.3.3. Fractal Dimensions Obtained from NMR Data

Based on NMR data, segmented crossplots of logS_V versus logT₂ were constructed for each sample, and the fitted correlations are high (R² > 0.898) (Figure 8g–i). The presence of three distinct segments indicates clear multifractal behavior, suggesting that the macropore, mesopore, and micropore domains have different structural characteristics.

For the linear relation between T₂ and pore radius Equation (15), fractal dimensions were calculated as D_NMRi = 3 − S, where D_NMR1, D_NMR2, and D_NMR3 correspond to the macropore, mesopore, and micropore segments, respectively. For the power-law relation between T₂ and pore radius Equation (18), fractal dimensions were calculated as D′_NMRi = 3 − nS, where D′_NMR1, D′_NMR2, and D′_NMR3 denote the corresponding macropore, mesopore, and micropore segments.

The exponent n obtained from power-law regression ranges from 0.527 to 0.887 for all core samples (Table S5). Because the fitted slope S is positive, the relationship 3 − nS > 3 − S holds, and fractal dimensions calculated from the power-law model are therefore larger. For all samples, D_NMR3 values calculated from the linear T₂-pore-radius relation are <2, whereas most D′_NMR3 values calculated from the power-law relation are >2. Because the theoretically reasonable range of fractal dimensions in three-dimensional pore systems is 2 < D < 3, the power-law model is more suitable for the studied tight dolomite gas reservoirs.

The total NMR fractal dimension (D′_NMR) is a porosity-weighted average of the fractal dimensions of the three pore classes and can be expressed as follows [14]:

$${D^{\prime }}_{NMR}={\displaystyle \frac{{D^{\prime }}_{NMR1}{{\phi }^{\prime }}_{NMR1}+{D\prime }_{NMR2}{\phi }_{NMR2}+{D\prime }_{NMR3}{\phi }_{NMR3}}{{\phi }_{NMR1}+{\phi }_{NMR2}+{\phi }_{NMR3}}}$$

(20)

Here, φ_NMR1, φ_NMR2, and φ_NMR3 are the NMR porosities of the macropore, mesopore, and micropore domains, respectively.

Using the power-law relation between T₂ and pore radius, the mean fractal dimensions of the macropore, mesopore, and micropore segments (D′_NMR1, D′_NMR2, and D′_NMR3) are 2.951, 2.611, and 1.904 for Type I samples; 2.984, 2.714, and 2.109 for Type II samples; and 2.983, 2.752, and 2.171 for Type III samples, respectively. Across all reservoir types, the segmental fractal dimensions increase from micropores to mesopores to macropores, indicating that larger pore domains exhibit higher structural complexity and heterogeneity in the NMR response.

According to Equation (20), D′_NMR was calculated for 28 samples, with an average value of 2.519. Specifically, D′_NMR ranges from 2.587 to 2.755 for Type I samples, from 2.417 to 2.725 for Type II samples, and from 2.326 to 2.537 for Type III samples. Unlike D_SEM, total D′_NMR does not show a simple monotonic increase from Type I to Type III reservoirs. Except for a moderate correlation of D′_NMR with D′_NMR2 and D′_NMR3 in Type II samples (Figure 9), no clear correlations are observed between D′_NMR and the segmental fractal dimensions. This shows that different pore-size classes work together to control D′_NMR, and reflects the combined effect of pore-size distribution and movable-fluid distribution, not the behavior of a single pore domain [44,45].

5. Discussion

5.1. Mineralogical Controls on Multiscale Fractal Behavior

Mineralogical control on pore-system heterogeneity is scale dependent (Figure 10). Among all measured components, clay minerals, especially illite and illite/smectite (I/S) mixed layers, show the strongest and most consistent positive correlations with fractal dimension [14,15,18], particularly with D′_NMR in Type III reservoirs. This indicates that clay enrichment promotes the development of micropore-dominated and surface-relaxation-sensitive pore systems and increases bound-fluid content, pore-surface roughness, and pore-throat segmentation. Mechanistically, pore-filling clay aggregates can roughen pore boundaries, subdivide pore throats, and generate micropore-dominated domains, thereby increasing fractal dimensions and reducing effective connectivity [14,16]. Calcite exerts a secondary but locally important influence on D_HPMI and D_SEM, suggesting that cementation and partial pore-throat occlusion increase capillary restriction and geometric complexity in moderate- to poor-quality reservoirs [15,16]. Pyrite and kaolinite occur locally, but their weak and inconsistent correlations indicate that they are secondary controls. Trace accessory heavy minerals may be present, but monazite, apatite, and Fe-Ti oxides were not sufficiently abundant and clearly identifiable in the representative SEM fields used for quantitative pore analysis.

The differences among methods further clarify the role of mineralogy at different observation scales. D_SEM mainly records boundary roughness and microscale geometric partitioning visible in pore images [21,46]. D_HPMI captures mineral controls on throat accessibility and capillary structure [15,47]. D′_NMR is more sensitive to movable-fluid distribution and small-pore heterogeneity [23,47]. Taken together, these relationships indicate that reservoir degradation from Type I to Type III is accompanied by stronger clay control, more intense micropore development, and poorer effective connectivity [14,15,21].

5.2. Relationships Between D_SEM and Pore Geometry

The relationships between D_SEM and pore geometry indicate that the D_SEM dimension is controlled by both pore-body size and boundary complexity (Figure 11). D_SEM decreases with increasing major axis, pore area, and mean circularity, but increases with perimeter, aspect ratio, and, in general, solidity. Thus, higher D_SEM corresponds to smaller pore bodies, longer boundaries, more elongated pore shapes, and stronger geometric partitioning of pore space, rather than to a single shape descriptor. These trends are consistent with progressive reservoir petrophysical properties during cementation and compaction [21,23].

The dominant control on D_SEM changes systematically with reservoir quality [14,15]. In Type I reservoirs, D_SEM is influenced mainly by pore size and regularity, implying that larger and more equant pores retain smoother boundaries and better connectivity [46]. In Type II reservoirs, the effects of pore-body reduction and boundary modification become comparable. This pattern reflects a transitional stage in which both the loss of effective pore volume and increasing irregularity contribute to heterogeneity [15,16]. In Type III reservoirs, D_SEM is controlled more strongly by perimeter, aspect ratio, and circularity than by pore size alone, indicating that microscale boundary complexity and pore-space subdivision are the main expressions of reservoir deterioration [13,20]. D_SEM is therefore a useful indicator of microscale pore-network degradation in tight dolomite gas reservoirs [13,21,46].

5.3. Relationships Between D_SEM and Pore Morphology

The pore morphology results suggest that D_SEM is influenced by both the average shape of individual pores and the variety of pore types in a sample (Figure 12) [21]. Previous digital-image and SEM-based studies have similarly shown that image-derived fractal dimensions reflect the combined effects of pore-boundary irregularity, pore-size distribution, and morphological diversity rather than any single geometric parameter [13,20,46]. In Type III reservoirs, the correlation is strongest, with samples showing higher D_SEM generally having more circular pores and fewer irregular ones. This seems to contrast with the negative relationship between D_SEM and mean circularity shown in Figure 11. However, the two observations describe different levels of organization.

In dolomites, many circular pores are small, isolated dissolution pores, whereas irregular pores more commonly represent larger intercrystalline pores or connected dissolution pores [6,18,46]. Therefore, an increase in the proportion of circular pores does not necessarily imply a better pore network [13,20]. Instead, it may indicate fragmentation of larger connected pores into many smaller isolated units. This explains why higher D_SEM can coexist with lower mean circularity at the pore level but higher circular-pore frequency at the sample level. From Type I to Type III reservoirs, D_SEM therefore increasingly records pore-system discretization, poorer effective connectivity, and stronger microscale heterogeneity rather than boundary irregularity alone [18,21].

5.4. Relationships Between D_HPMI and Pore-Throat Structure

D_HPMI shows clear relationships with capillary-controlled pore-throat parameters (Figure 13). Higher D_HPMI is associated with higher displacement and median pressures and with lower mercury withdrawal efficiency, maximum mercury injection saturation, maximum connected pore-throat radius, and sorting coefficient. This combination indicates a more capillary-restricted pore system, smaller effective throats, poorer accessibility, and weaker connectivity [15,21]. Thus, D_HPMI is a useful descriptor of pore-throat restriction and entry-pressure heterogeneity [47,48].

However, D_HPMI alone only weakly differentiates the three reservoir types because it is a weighted average of multiple pore-size domains [19,48]. The correlation between D_HPMI and D_HPMI3 suggests that micropores contribute strongly to the overall measured complexity of the pore-throat system. In contrast, the segmented analyses indicate that reservoir-quality differentiation is governed mainly by the larger pore-throat domains (Figure 14). In Type II reservoirs, D_HPMI1 shows the clearest relationships with capillary parameters, highlighting the importance of degradation within the large-pore framework during reservoir decline. In Type III reservoirs, DHPM_I1 and D_HPMI2 better capture the contrast between a few retained connected large throats and the much more abundant narrow throats. Therefore, micropores dominate the overall complexity signal, whereas macro- and mesopore throats exert the strongest control on storage accessibility and producibility [15,18].

5.5. Relationships Between D′_NMR and Movable-Fluid Distribution and Gas Seepage Capacity

D′_NMR provides the most direct link between fractal behavior and movable-fluid distribution. Across all reservoir types, D′_NMR decreases with increasing movable-fluid porosity, movable-fluid saturation, and T₂ cutoff, indicating that increasing heterogeneity and stronger confinement reduce the proportion of producible fluid (Figure 15) [47,49]. Compared with the segmented NMR fractal dimensions (Figure 16), D′_NMR shows a more stable relationship with flow-related parameters because it integrates the combined effects of different pore-size classes and fluid states [50].

The scale-dependent results further show that the physical meaning of D′_NMR varies among pore classes [23,32,45]. In Type I reservoirs, the weak correlations of D′_NMR1–D′_NMR3 with fluid-flow parameters suggest that no single pore-size domain controls fluid behavior in relatively well-connected networks. In Type II reservoirs, the large-pore fractal dimension is more closely related to movable-fluid saturation, whereas the small-pore fractal dimension shows the strongest negative relationship with T₂ cutoff. This indicates that larger pores mainly contribute to effective movable-fluid distribution, whereas increasing small-pore complexity enhances fluid confinement [51,52]. In Type III reservoirs, the correlations become weaker and less systematic because bound-fluid-dominated micropores, poorly connected intermediate pores, and a limited number of isolated large pores coexist [32,53]. Importantly, the lower D′_NMR values of many Type III reservoirs do not indicate a simpler pore system. Instead, they reflect the stronger weighting of small pores with lower segmental fractal dimensions in the NMR response. The NMR results therefore emphasize fluid-state heterogeneity rather than geometric complexity alone [23,45].

5.6. Relationships Between Fractal Dimension and Reservoir Quality

Fractal dimension is closely related to reservoir quality [14,15,22]. In carbonate rocks and tight reservoirs, the higher the fractal dimension, the greater the heterogeneity of pores and throats, the stronger the capillary resistance [16,19,49], and the poorer the reservoir quality, although the controlling mechanisms differ among methods and reservoir types (Figure 17 and Figure 18). Higher D_SEM and D_HPMI values generally correspond to lower porosity and permeability, showing that increasing boundary roughness, pore-throat tortuosity, and capillary heterogeneity reduce both effective storage space and gas seepage capacity. The petrophysical significance of D′_NMR is more nuanced. D′_NMR is negatively related to movable-fluid behavior and commonly to porosity and permeability, but its total value does not show a simple monotonic increase from Type I to Type III reservoirs. This is because D′_NMR is a porosity-weighted response that integrates different pore-size domains and fluid states. Its magnitude therefore reflects the combined contributions of macropores, mesopores, and micropores rather than reservoir quality alone [23,47,51].

The type-specific correlations show a progressive shift in the dominant control on storage and seepage [14,15]. In Type I reservoirs, permeability is more strongly associated with D_HPMI, suggesting that the connected pore-throat structure plays a key role in governing fluid flow in these relatively high-quality reservoirs [18,47]. For Type II reservoirs, stronger correlations are observed between D_SEM and D_HPMI1–D_HPMI2, which points to the combined effect of larger pore-throat system deterioration and increased microscale segmentation in the decline of reservoir quality [16,19]. In Type III reservoirs, D_SEM and D_HPMI continue to correlate with permeability, while D′_NMR is more closely related to ineffective pore volume and the occurrence of bound fluid [32,51]. These differences indicate that no single fractal parameter can fully characterize reservoir quality and that integrated multiscale evaluation is required [23].

5.7. Comparison of Multisource Fractal Dimensions and Their Geological Implications

D_HPMI, D′_NMR, and D_SEM collectively indicate that the studied tight dolomite gas reservoirs possess a multifractal pore system and marked heterogeneity across scales. These methods capture complementary aspects of pore structure. HPMI mainly characterizes the geometry and connectivity of the pore-throat network, NMR characterizes pore-size distribution and movable-fluid distribution through relaxation behavior, and deep-learning-assisted SEM quantifies two-dimensional pore morphology and pore-boundary complexity [14,16,18,21,47]. However, correlations among the different fractal dimensions are generally weak (Figure 19a–c), with R² values of 0.361 (p = 0.001) for D_HPMI versus D′_NMR, 0.353 (p = 0.001) for D_HPMI versus D_SEM, and 0.052 (p = 0.264) for D′_NMR versus D_SEM. Although the first two relationships are statistically significant, the D′_NMR–D_SEM correlation is not significant. This weak correspondence reflects both the strong heterogeneity of low-porosity and low-permeability tight dolomite gas reservoirs and the different physical meanings of each method. The discrepancy becomes more evident at the pore-size-class scale (Figure 19d–f), where the D_HPMI–D′_NMR relationship is strongest for macropores (R² = 0.223, p = 0.015), but not for mesopores (R² = 0.104, p = 0.107) or micropores (R² = 0.087, p = 0.145). Only the macropore relationship is statistically significant, whereas the mesopore and micropore relationships are not, suggesting the pattern indicates that direct comparison between pore-throat radius and relaxation-time-based pore classification is limited in poorly connected reservoirs [22,32].

Geologically, fractal dimensions are jointly controlled by depositional setting, diagenesis, and mineral composition [6,16,18]. Illite and illite/smectite mixed layers are the main mineralogical factors that enhance pore-surface roughness and microscopic heterogeneity, whereas calcite cementation exerts a secondary but locally important effect through pore-throat occlusion [16,18]. Compaction and cementation generally increase pore-system complexity and fractal dimension, whereas dissolution may reduce fractal dimension when it enlarges effective pore throats and improves connectivity [6,15,16]. The transition from Type I to Type III reservoirs therefore reflects progressive reduction of dissolution-enhanced intercrystalline pores, stronger compaction and cementation, greater clay-mineral influence, and poorer preservation of connected pore-throat pathways.

Accordingly, reservoir quality deterioration from Type I to Type III is characterized by higher D_SEM, limited variation in D_HPMI, and a non-monotonic D′_NMR response. This pattern reflects a transition from relatively homogeneous and better-connected pore systems to tighter, more segmented, and more isolated networks with weaker gas seepage capacity [5,6,15,17]. This reservoir-type dependence indicates that lower-quality reservoirs require stronger connectivity-enhancement measures during development, whereas reservoirs with larger effective pore-throat systems and better connectivity should be regarded as more favorable gas-bearing intervals and development targets. Practically, Type I reservoirs should be prioritized as sweet-spot targets because they preserve larger effective pore-throat systems and better movable-fluid conditions. Type II reservoirs may require connectivity-enhancement measures during development, whereas Type III reservoirs have limited gas-flow potential unless stimulation can effectively improve throat connectivity [5,17].

5.8. Methodological Challenges and Future Perspectives

The main methodological challenge of this study is to integrate pore characteristics measured by techniques with different physical meanings. SEM characterizes two-dimensional pore morphology, whereas HPMI and NMR describe capillary-controlled pore-throat accessibility and fluid distribution, respectively [15,22,23,24]. Although combining these methods provides a more comprehensive characterization of multiscale pore systems, differences in their physical principles inevitably introduce uncertainty into direct comparisons.

A second limitation arises from the strong heterogeneity of tight dolomite reservoirs and the relatively limited number of complete datasets. Porosity and permeability were measured for all 33 core samples, after which 28 representative samples covering the full petrophysical range and all reservoir types were selected for the integrated analyses. Although these samples capture the principal characteristics of the investigated Ma₅⁴ interval, additional samples from a wider range of wells are required to further evaluate the regional applicability of the observed relationships.

Another limitation concerns mineral identification. Mineralogical interpretation was primarily based on bulk XRD, cast thin sections, and secondary-electron SEM observations. While these methods reliably identify the dominant mineral assemblages, they do not provide in situ chemical identification of individual clay-mineral aggregates or trace accessory phases. Future resampling combined with systematic BSE-EDS mapping and EPMA analyses will allow more detailed mineral-chemical characterization and a better understanding of the influence of mineral chemistry on pore evolution and multiscale fractal behavior [18,46].

Finally, although the integrated SEM-HPMI-NMR framework improves the multiscale characterization of tight dolomite reservoirs, direct gas-flow experiments and three-dimensional digital-rock simulations remain necessary to further validate the relationships between fractal parameters, pore-network connectivity, and gas deliverability [26,27,38].

6. Conclusions

By integrating experimental measurements, deep-learning-assisted SEM analysis, and multiscale fractal modeling, this study quantitatively characterized the pore system of the Ma₅⁴ tight dolomite gas reservoir in the Majiagou Formation, central Ordos Basin. The main conclusions are as follows:

(1)

The Ma₅⁴ tight dolomite gas reservoir is dominated by secondary pores, with dissolution-related intercrystalline pores and microfractures providing the main gas storage space and seepage pathways. Enhanced U-Net SEM extraction, combined with HPMI and NMR data, identifies three gas-reservoir types. Type I reservoirs contain relatively regular pores, larger effective pore-throat systems, better connectivity, and the highest gas storage and seepage capacity. Type II reservoirs show intermediate quality and moderate gas-flow potential. Type III reservoirs have more complex pore morphology, poorer connectivity, weaker petrophysical properties, and limited gas-flow potential.

(2)

SEM, HPMI, and NMR reveal clear fractal or multifractal behavior with different implications. D_SEM increases from Type I to Type III reservoirs, indicating stronger pore-shape irregularity and microscale heterogeneity. D_HPMI characterize pore-throat architecture and capillary-pressure-controlled seepage pathways; macropores show the highest fractal dimensions, whereas micropores exert the strongest control on total pore-throat complexity. The power-law-derived D′_NMR is more reasonable than the linear model, and segmental D′_NMR increases from micropores to macropores. Total D′_NMR reflects a porosity-weighted response rather than a simple reservoir quality trend.

(3)

Fractal dimensions are systematically related to mineral composition, pore geometry, petrophysical properties, and gas seepage capacity. Clay minerals, especially illite and illite/smectite mixed layers, are the main positive controls on pore-throat heterogeneity. Higher fractal dimensions generally correspond to smaller and more complex pore systems, higher displacement and median pressures, poorer connectivity, lower porosity and permeability, weaker movable-fluid behavior, and reduced gas seepage capacity. Weak correlations among D_SEM, D_HPMI, and D′_NMR indicate that SEM, HPMI, and NMR capture complementary aspects of pore morphology, pore-throat architecture, and movable-fluid distribution, supporting integrated multiscale fractal evaluation of tight dolomite gas reservoirs.