Microscopic Pore Structure Heterogeneity on the Breakthrough Pressure and Sealing Capacity of Carbonate Rocks: Insight from Monofractal and Multifractal Investigation

Abstract

Reservoirs and caprocks overlap with each other in heterogeneous carbonate rocks. The sealing capacity of caprocks and their controlling factors are not clear, which restricts the prediction, exploration, and development of carbonate hydrocarbon reservoirs. We selected core samples from the Ordovician reservoirs and caprocks in the Tarim Basin, China, for scanning electron microscopy, thin section, breakthrough pressure (BP), high-pressure mercury intrusion porosimetry (HMIP), and nitrogen adsorption method (N₂GA). The experimental results show that the reservoir and caprock can be distinguished by BP. The BP of the reservoir is less than 3.0 MPa, and the BP of the caprock is less than 3.0 Mpa. We analyzed the heterogeneity characteristics and differences in reservoirs and caprocks with different lithologies from the perspectives of monofractal and multifractal. The results indicate that the differences in pore structure of grainstone, dolomite, and micrite/argillaceous limestone result in significant heterogeneity differences between samples. The correlation analysis between the fractal parameters and BP indicates that the characteristics of reservoir microporous structures have a decisive impact on BP (correlation coefficient > 0.7). The pore structure of the carbonate reservoir–caprock system exhibits self-similarity. The heterogeneity of the caprock has no significant control effect on BP (correlation coefficient < 0.3), while the higher the heterogeneity of the reservoir, the greater the BP. The sealing capacity of the caprock depends on the heterogeneity differences in pore types and pore structures between the reservoirs and caprocks. When both the reservoir and the caprock are grainstone, the micropores in the reservoirs and caprocks are dispersed but evenly distributed, and little heterogeneous differences can achieve sealing. When the lithology of reservoirs and caprocks is different, the enhancement of heterogeneity differences in micropores will improve the sealing capacity of the caprock. In summary, fractal dimension is an effective method for studying the heterogeneous structure and sealing capacity of pore–throat in carbonate caprocks. This study proposes a new perspective that the difference between the heterogeneity of micropore structures of reservoirs and caprocks affects the sealing capacity of carbonate rocks, and provides a new explanation and model for the sealing mode of carbonate rock caprocks.

1. Introduction

Carbonate rocks exhibit pronounced heterogeneity in pore structure, a consequence of complex interplay between primary sedimentary environments and subsequent diagenetic modifications [1,2,3,4]. This heterogeneity is macroscopically manifested as alternating reservoir–caprock configurations, a phenomenon observed globally in basins such as the Volga-Ural Basin in Russia [5], the Zagros Basin in Iraq [6], and the Tarim Basin in China [1,2,3,7,8]. In the Tarim Basin, the Ordovician carbonate system exemplifies such characteristics, where the Yingshan Formation reservoirs are vertically sealed by high-resistivity intraformational caprocks and the Lianglitage Formation’s regional caprocks [1,2,7]. Previous studies have identified the breakthrough pressure gradient between reservoirs and caprocks as a critical factor controlling hydrocarbon sealing efficiency [3,8]. Recent advances further highlight the role of microscale pore structure heterogeneity in modulating macroscopic breakthrough pressure, with diagenetic alterations and mineralogical compositions jointly shaping pore geometry and fluid migration behavior [9,10]. Consequently, deciphering the pore architecture of carbonate systems is fundamental to unraveling caprock sealing mechanisms, particularly their intricate small-scale pore–throat networks.

Conventional pore structure characterization techniques, including casting thin sections, scanning electron microscopy (SEM), high-pressure mercury intrusion porosimetry (HMIP), and gas adsorption analyses (N₂GA/CO₂GA), have been extensively applied to tight sandstones and shales [11,12,13,14,15,16,17,18]. However, the inherent multi-scale pore systems of carbonates—spanning crystalline microporosity to vuggy macropores—pose unique challenges [1,3,10]. While monofractal analysis has been widely adopted to quantify self-similarity in porous media [19,20,21,22,23], its reliance on a single fractal dimension fails to capture the multi-scale complexity of natural carbonates [24,25,26]. In contrast, multifractal theory provides a multidimensional method to characterize heterogeneity across distinct probability intervals of pore space distribution [24,25,26,27,28]. The multifractal theory describes the heterogeneity of different distribution probability intervals through parameters extracted from the generalized dimension spectrum and singularity spectrum [29,30,31]. Compared to monofractal theory, multifractal theory quantitatively characterizes the heterogeneity of porous media from another dimension. Fractal theory has been extensively applied to characterize pore structures and fluid activities in tight sandstones [13,22], shales [32,33,34,35], and coals [36,37,38]. However, monofractal and multifractal analyses of carbonate rock pore systems remain inadequately explored, warranting further comprehensive investigation.

In view of the control of the heterogeneity of the carbonate pore system on fluid flow dynamics and sealing ability, this study combined HMIP and N₂GA analysis with single-fractal and multifractal modeling to study the heterogeneity of the pore structure of Ordovician carbonate reservoirs and caprocks in the Tarim Basin. We aim to

• Establish links between fractal parameters and breakthrough pressure variations;
• Elucidate how multi-scale pore heterogeneity governs hydrocarbon sealing.

This study innovatively uses the method of comparing the heterogeneity of carbonate reservoirs and caprocks to analyze the sealing properties of caprocks. Our findings provide novel insights into the microscale controls on carbonate caprock sealing mechanisms, with implications for exploration strategies in heterogeneous carbonate systems.

2. Geological Setting

The study area of this research is between the Tazhong I fault zone and the Tazhong II fault zone in the northern slope belt of the Tazhong uplift in the Tarim Basin, western China (Figure 1A). The Tarim Basin constitutes a large composite geological structure formed by the superimposition of a Paleozoic craton basin and a Mesozoic–Cenozoic foreland basin over an Archean–Proterozoic metamorphic basement [39,40]. Positioned along the central uplift belt of this basin, the Tazhong uplift features three distinct structural zones: the north slope belt, central uplift belt, and south slope belt (Figure 1A). The Tazhong uplift is a long-term inherited paleo uplift. The superposition and transformation of multistage tectonic movements construct complex structural characteristics. During the Middle and Late Ordovician, a karst landform was formed that gradually decreased from southwest to northeast (Figure 1A). The Yingshan and Lianglitage Formations mainly comprise grainstone, micrite, dolomite, and bioclastic limestone deposited in the open platform (Figure 1B,C). The karst fracture–cavity and reef reservoirs are vertically overlapped with tight carbonate caprocks in these formations, forming good reservoir–caprock combinations [8]. In addition, they are distributed under the stable mudstone caprock in the Sangtamu Formation (Figure 1B,C). Consequently, these formations are identified as the primary production layers in the Tazhong area [41,42].

3. Samples and Methods

3.1. Samples

The selection of samples for this study is based on core observations and logging data from 13 wells. A total of 14 carbonate rock samples were taken from 6 wells. A total of 7 samples were collected from carbonate reservoir sections, while the other seven were taken from tight caprock sections. After making a 5 mm × 5 mm × 5 mm natural cross-section sample (Figure S1) and thin sections, all samples were cut into plunger samples with a diameter of 25 mm and a length of 50 mm. The experimental sequence for the plunger is nitrogen adsorption, breakthrough pressure, and mercury intrusion porosimetry.

3.2. Measurement Methods

3.2.1. Breakthrough Pressure

The breakthrough pressure (BP) measurements were performed following the Chinese petroleum industry standard SY/T 5748-2013 (Determination of Gas Breakthrough Pressure in Rock) [44] (https://std.samr.gov.cn/hb/search/stdHBDetailed?id=8B1827F21322BB19E05397BE0A0AB44A, accessed on 11 May 2020), with experimental apparatus comprising the TYL-II automated BP measurement system (Hai’an County Petroleum Research Instrument Company, Nantong, China), Fyks-III high-temperature/overburden porosity–permeability integrated analyzer (Hai’an County Petroleum Research Instrument Company, Nantong, China), and precision electronic balance from the Japanese Shimadzu Corp. (Kyoto, Japan). The measurement principle relies on displacing wetting-phase fluids from saturated core specimens using a non-wetting phase, where the capillary resistance inversely correlates with pore–throat radius—smaller radii demand higher breakthrough pressures. Operationally, the rock sample is pressurized in the core holder. The test terminated upon establishment of continuous gas flow through the sample, with BP defined as the equilibrium pressure differential (ΔP) between inlet and outlet.

3.2.2. Thin Section Analysis

A total of 20 thin sections were impregnated with epoxy mixed with blue dye. These sections were observed under an L150A polarizing light microscope produced by Nikon Corporation in Tokyo, Japan. Observation results were used to analyze lithology and pore characteristics.

3.2.3. Scanning Electron Microscopy

Observation and analysis were conducted on 14 carbon-sprayed samples using Crossbeam 540 scanning electron microscopy produced by Zeiss inJena, Germany. Focus on observing the morphology and structural characteristics of pores and throats in carbonate reservoirs and caprocks, as well as the surface roughness.

3.2.4. Porosity and Permeability Test

Porosity and permeability were determined via the unsteady-state method following the Chinese petroleum industry standard SY/T 6385-2016 (Measurement of Core Porosity and Permeability Under Net Confining Stress) [45] (https://std.samr.gov.cn/hb/search/stdHBDtailed?id=8B1827F20B9BBB19E05397BE0A0AB44A, accessed on 6 August 2023). All experiments were performed using the FYKS-III integrated system from Hai’an County Petroleum Research Instrument Company in Nantong, China. This system is designed to simulate reservoir conditions, with capabilities for simultaneous high-temperature and overburden stress applications during petrophysical property characterization.

3.2.5. High-Pressure Mercury Intrusion Porosimetry

High-pressure mercury intrusion porosimetry (HMIP) analyses were performed utilizing the Quantachrome Instruments Poremaster PM-33-13 system equipped with Type 113 porosimeter and Type 112 gas permeameter modules produced by Quantachrome Instruments Corporation in Boynton Beach, Florida, USA. The experiment was conducted in accordance with Chinese petroleum industry standards SY/T 5346-2005 (Rock Capillary Pressure Measurement) [46] (https://std.samr.gov.cn/hb/search/stdHBDetailed?id=8B1827F16495BB19E05397BE0A0AB44A, accessed on 6 September 2024) and SY/T5336-2006 (Core Analysis Methodology) [47] (https://std.samr.gov.cn/hb/search/stdHBDetailed?id=8B1827F18C2EBB19E05397BE0A0AB44A, accessed on 6 September 2024). Sample preparation involved oven-drying at 105 °C to constant mass prior to testing. The experimental protocol comprised two phases: (1) high-pressure mercury intrusion (0.1–80 MPa) to characterize pore–throat accessibility under non-wetting phase displacement, followed by (2) controlled depressurization to assess mercury withdrawal hysteresis.

3.2.6. Nitrogen Adsorption Method

Specific surface area (SSA) and pore size distribution (PSD) analyses were conducted using the ASAP 2460 device produced by Micromeritics Company in Norcross, Georgia, USA, following Chinese petroleum industry standard SY/T 6154-2019 [48] (https://std.samr.gov.cn/hb/search/stdHBDtailed?id=AAD678EA7665AE45E05397BE0A0AC5F7, accessed on 27 August 2024). The instrument’s operational range spanned 1.5–200 nm, covering physisorption-dominated pore regimes. Sample preparation involved sequential processing as follows:

(1)

Crushing and sieving bulk specimens to obtain 0.28–0.45 mm particles;

(2)

Oven-drying 5–10 g aliquots at 105 °C for 8 h to remove adsorbed moisture and volatiles;

(3)

Vacuum-degassing prepared samples prior to analysis.

3.3. Monofractal Method

The calculation formula flow for the monofractal method is shown in Figure 2A.

According to the monofractal method, the association between pore radius r and pore number can be characterized as follows [49]:

N(r) ∝ r − Df

(1)

where r corresponds to pore radius, N(r) indicates the number of pores with radii greater than r, and Df represents the fractal dimension. Through examination of the imbibition process, the saturation (the volumetric fraction of pore space attributable to pores smaller than r) can be derived as follows:

log(S(r)) = 3 − Df log(r/r_max)

(2)

Consequently, the fractal dimension (Df) can be determined by generating a log–log plot of S(r) versus r/r_max and measuring the slope of the regression line. Specifically, pore size distribution (PSD) data obtained via N₂GA measurements can be analyzed using the Frenkel–Halsey–Hill (FHH) model according to the following [21]:

log(V) = (Df − 3) log(log (P0/P)) + constant

(3)

where V (mL) is the N₂ adsorption volume at pressure P and P₀ (MPa) is the saturated vapor pressure.

According to Kelvin’s formula, when P₀/P = 0.5, the corresponding pore width is 2 nm. The boundary between micropores and mesopores is 2 nm. Therefore, the calculation results of nitrogen adsorption are divided into two sections based on P₀/P = 0.5 in this research, and the fractal dimensions of the two sections are calculated (D_n1 and D_n2) separately. The left fractal dimension (D_n1) characterizes the regularity and multi-layer adsorption characteristics of the pore system, and when its value approaches 3, it indicates that the pore space tends towards an ideal regular geometric shape; The right fractal dimension (D_n2) is used as a surface roughness index, and an increase in its value reflects an increase in the topological complexity of the pore wall surface. This dual fractal model can effectively decouple the differential control mechanism between the geometric characteristics of pore structure and surface properties, providing a theoretical basis for the characterization of multi-scale pore networks.

The fractal dimension based on HMIP is calculated with the tube model, which is consistent with the pore–throat radius model used in the Washburn equation [50]. The model can be described as follows [51]:

log S_Hg = (Df − 3) log P_c + (Df − 3) log P_min

(4)

where S_Hg is the mercury saturation and P_c (MPa) is the capillary pressure.

Based on fractal theory, when the pore structure is similar, the regression results of log S_Hg and log P_c are a straight line, indicating that the fractal dimensions are close and can be classified as single fractals. If the pore structure is different, the regression between log S_Hg and log P_c shows a curve trend with different turning points. The calculation results of high-pressure mercury injection are segmented according to the trend of the curve. Therefore, this study segmented the calculation curve based on the trend of calculation results of HMIP, and calculated the fractal dimension (D_m1 and D_m2).

The fractal dimension ranges from 2 to 3, and its value is positively correlated with the complexity of pore–throat structure. That is, the larger the fractal dimension, the more significant the heterogeneity of pore–throat structure and the higher the surface roughness. On the contrary, it indicates that the pore–throat structure is relatively uniform and the surface is smooth.

After calculating the fractal dimensions of the segments, the total fractal dimensions (D_t) of the samples are calculated based on the weighted average of the pore volume fraction:

$$D_{t }= {\sum }_{i=1}^n{D}_i{\phi }_{i}i$$

(5)

where D_i and φ_i represent the fractal dimension and pore volume fraction of the ith segment.

The total fractal dimensions calculated by HMIP and N₂GA are represented by D_mt and D_nt, respectively.

3.4. Multifractal Method

As an advancement of monofractal analysis, multifractal theory quantifies self-similarity through a continuous dimensional spectrum. Deriving multifractal metrics generally relies on the moment method. Here, we offer a brief exposition of the theory and process. The calculation formula flow for the multifractal method is shown in Figure 2B.

Commencing the analysis, the data were segmented into N(ε) = 2k intervals characterized by scale ε (ε = 20,21, …, 2k, where k is a positive integer). The probability distribution P_i(ε) (percentage content) of the specific constituent per interval was evaluated:

$$Pi \left(\epsilon \right) = {\displaystyle \frac{Ni\left(\epsilon \right)}{\sum _{i=1}^{ N\left(\epsilon \right)}Ni\left(\epsilon \right)}}$$

(6)

where Ni (ε) means the pore volume of the ith box. The Pi (ε) obeys an exponential function with scale ε [52], which can be expressed as follows:

$$Pi \left(\epsilon \right) ~ {\epsilon }^{{\alpha }_i}$$

(7)

where αi means the Lipschitz−Holder singularity strength.

The number of boxes with the same α was denoted as Nα (ε) [53]:

$$N\alpha (\epsilon ) ~{ \epsilon }^{-f(\alpha )}$$

(8)

where f (α) means the multifractal spectrum

The partition function X (q, ε) at the order q can be expressed as follows (q is in the range of −10~10):

$$\chi \left(q, \epsilon \right)={\sum }_{i=1}^{N(\epsilon )}{P}_i^q(\epsilon )$$

(9)

where Dq means the multifractal dimension, can be further expressed as follows [54]:

$$D_q={\displaystyle \frac{1}{q-1}}\underset{\epsilon \to 0}{lim}{\displaystyle \frac{log{\sum }_{i=1}^{N(\epsilon )}{P}_i^q(\epsilon )}{log \epsilon }}$$

(10)

When q = 1, Equation (10) does not make mathematical sense. D₁ can be determined by the L’Hôpital’s rules [55]:

$$D_1=\underset{\epsilon \to 0}{lim}{\displaystyle \frac{log\sum _{i=1}^{N(\epsilon )}{P}_i(\epsilon )log{P}_i(\epsilon )}{log \epsilon }}$$

(11)

The mass exponent τ (q) can be simplified and expressed as follows [56]:

$$\tau (q)=(q-1)D_q$$

(12)

Via a Legendre transformation, the singularity strength α (q) of order q can be simplified as follows [53]:

$$\alpha (q)={\displaystyle \frac{d\tau \left(q\right)}{dq}}={\displaystyle \frac{d}{dq}}(\underset{\epsilon \to 0}{lim}{\displaystyle \frac{logX \left(q, \epsilon \right)}{log\epsilon }})$$

(13)

$$f\left(\alpha \right)=q\alpha \left(q\right)-\alpha \left(q\right)$$

(14)

The value of ε in Equation (8) tends towards 0, and a (q) and f (a) can be solved by [52], with the following expressions:

$$\alpha (q)\propto {\displaystyle \frac{{\sum }_{i=1}^{N(\epsilon )}\left[u_i\left(q,\epsilon \right)lg\epsilon \right]}{lg\epsilon }}$$

(15)

$$f(a)\propto {\displaystyle \frac{{\sum }_{i=1}^{N(\epsilon )}\left[u_i\left(q,\epsilon \right)lg{u}_i\left(q,\epsilon \right)\right]}{lg\epsilon }}$$

(16)

In these two formulas:

$$u_i\left(q,\epsilon \right)={\displaystyle \frac{P_i^q(\epsilon )}{\chi \left(q, \epsilon \right)}}$$

(17)

Based on the results of multifractal calculations, many parameters representing heterogeneity can be calculated. For example, D₁, D₀ − D₁, D₋₁₀ − D₀, D₀ − D₊₁₀, D₋₁₀ − D₊₁₀, H, α₀, Δα, and R_d.

Among them,

H = (D₂ + 1)/2

(18)

Δα = α₋₁₀ − α₊₁₀

(19)

R_d = (α₀ − α₊₁₀) − (α₋₁₀ − α₀)

(20)

The definition and physical significance of the parameters are as follows:

(1)

The D₁ reflects the spatial clustering characteristics of the pore size distribution. When D₁ approaches D₀, it signifies that the pore size distribution tends toward homogeneity.

(2)

The dispersion index D₀ − D₁ quantifies the degree of heterogeneity in the pore size distribution. A smaller D₀ − D₁ value indicates a more homogeneous pore size distribution.

(3)

The value range of H characterizes the spatial autocorrelation and connectivity of the pore network. A higher H value indicates superior autocorrelation and connectivity within the sample.

(4)

The left and right spectral widths of the generalized fractal dimension spectrum are defined as D₋₁₀ − D₀ (low-probability region) and D₀ − D₊₁₀ (high-probability region), respectively. The magnitude of each width exhibits a positive correlation with the intensity of heterogeneity within its corresponding pore size range.

(5)

The singularity index (α₀) represents the most probable distribution state of the pore system. An increase in α₀ reflects an enhancement in the heterogeneity of the pore size distribution.

(6)

The singularity spectrum width (Δα) comprehensively characterizes the degree of heterogeneity across the entire pore size range. A larger Δα value corresponds to stronger heterogeneity in the pore size distribution.

(7)

The spectral symmetry parameter (R_d) quantitatively describes the differential contribution of high- and low-probability regions to the overall heterogeneity. When R_d > 0, the high-probability region dominates the heterogeneity, whereas when R_d < 0, the low-probability region plays the dominant role.

4. Results

4.1. Lithology and Pore Characteristics

The carbonate samples are composed of dolomite, micrite, argillaceous limestone, and grainstone (

Table 1. Basic information, porosity, permeability, and breakthrough pressure of the samples.

Types	Well	Sample ID	Formation	Lithology	Porosity (%)	Permeability (mD)	Breakthrough Pressure (Mpa)
Caprock	T3	Z1	Ying 1	dolomite	0.59	0.0013	3.92
	T4	Z5	Liang 3	micrite	0.68	0.0003	9.77
	T4	Z6	Liang 4 and 5	argillaceous limestone	0.60	0.00035	7.77
	T2	Z7	Liang 3	micrite	0.72	0.0007	7.56
	T2	Z8	Ying 2	grainstone	1.05	0.0024	7.2
	G4	Z9	Liang 4 and 5	grainstone	2.68	0.0008	4.36
	G3	Z14	Ying 1	dolomite	3.39	0.001	3.55
Reservoir	T1	Z2	Liang 3	grainstone	1.81	0.0012	2.51
	T1	Z3	Ying 2	grainstone	1.06	0.0005	1.48
	T1	Z4	Ying 2	grainstone	0.56	0.0016	0.51
	G4	Z10	Liang 4 and 5	grainstone	3.31	0.0015	1.47
	G4	Z11	Liang 4 and 5	grainstone	3.72	0.0038	0.58
	G4	Z12	Liang 4 and 5	grainstone	3.93	0.001	0.21
	G3	Z13	Ying 1	dolomite	22.00	2.7703	0.03

, Figure 3). After the few intergranular pores in the dolomite caprock are filled with bitumen, there is a small amount of residual pore space (Figure 3A). Almost no pores can be observed in the micrite and grainstone caprock samples, and the fractures and stylolites in these caprocks are filled with sparry calcite and residual bitumen (Figure 3B–E). The argillaceous limestone caprock samples are very tight (Figure 3F). Based on the observations of reservoir samples, two lithological types were identified: dolomite and grainstone (Figure 3G–I). Intergranular pores are the main pore space in the dolomite reservoirs (Figure 3G). The pore distribution in granular limestone is irregular, with some areas completely cemented by calcite between grains (Figure 3H), while others show residual intergranular pores between sparry calcite (Figure 3I).

Scanning electron microscopy images reveal diverse microscopic pore morphologies. Intergranular pores, intragranular pores, and intercrystalline pores are the main types of pores in carbonate rock samples, with occasional microcracks (Figure 4A–E). There are small intercrystalline pores in both reservoir and caprock samples, which are spaces between microcrystalline calcite (Figure 4A,B). The carbonate caprocks are dense and mainly consist of isolated pores [1,2,9]. We observed isolated pores in calcite grains of caprocksamples (Figure 4C). There are numerous intergranular pores in dolomite reservoirs (Figure 4D,E), and dispersed illite occasionally blocks these intergranular pores (Figure 4E). This phenomenon is similar to the sample characteristics observed by previous scholars in the Tabei area of the Tarim Basin [2]. The space between the layered illite is sheet-like (Figure 4F). Overall, the pore morphology in carbonate rocks is irregular, and the pore types in reservoirs and caprocks are similar, but the proportion and combination relationship of different types of pores are different. Scanning electron microscopy can also observe the roughness of the rock surface. The surface of carbonate rocks with smaller crystals is rougher than that of carbonate rocks with larger crystals (Figure 4).

4.2. Porosity and Permeability

Porosity and permeability of the 14 samples vary widely from 0.56% to 22.00% and from 0.0003 mD to 2.7703 mD, respectively (Table 1). The porosity values of caprock and reservoir samples are in the range of 0.59%–3.39% and 0.56%–3.93%, respectively (Table 1). The permeability values of these two types of samples are in the range of 0.0003 mD to 0.0024 mD and 0.0005 mD to 2.7703 mD, respectively (Table 1). There is considerable overlap between the variation ranges of caprock and reservoir in porosity and permeability. This implies that the distinction between reservoirs and caprocks is not solely based on physical properties.

4.3. Breakthrough Pressure Characteristic

The 10% sample selected for repeated experiments has an error of less than 10% between the two measurement results, indicating that the breakthrough pressure test value is reliable. The breakthrough pressure (BP) values of these 14 samples are in the range of 0.03–9.77 MPa (Table 1). The BP values of the caprock samples are higher than those of the reservoir samples. The measurement values of the caprock samples are distributed from 3.55 MPa to 9.77 MPa, averaging 6.301 MPa. The BP of reservoir samples ranges from 0.03 MPa to 2.51 MPa, with an average of 0.97 MPa. The micrite and argillaceous limestone samples are all caprock with high BP, and the BP of dolomite and grainstone samples has a great varying range. This indicates that BP may not be completely controlled by lithology.

4.4. Pore Size Distribution

Measurement ranges of pores by HMIP and N₂GA methods are different [57,58]. In general, the measurement results of the HMIP and N₂GA methods are considered to be the distribution of macropores and micropores, respectively. Due to the intersection of the detection ranges of the two methods, this study analyzed the PSD obtained by each method separately.

Except for the Z7 sample, there is only one obvious peak on the PSD of caprock samples based on HMIP, indicating that the pore distribution of the cover layer sample is concentrated (Figure 5A). The pore radii corresponding to the main peaks are concentrated within the range of 0.02–0.2 μm. The right peak area of sample 7 is larger than the left peak area (Figure 5A). The PSD (HMIP) of reservoir samples can be both multimodal and unimodal, with a wide range of radius distribution corresponding to the peak values (Figure 5B). The PSD (HMIP) curves of Z3, Z10, and Z12 samples have one peak, while the curves of Z2, Z4, Z11, and Z12 have two or multiple peaks (Figure 5B). The PSD (N₂GA) curves of the caprock sample can be divided into two types. One type has a peak pore radius of 2.9–3.2 nm, followed by a slow decrease (Z1, Z5, Z6, and Z7 samples; Figure 5C); the other type has a gentle curve without obvious peaks (Z7, Z8, and Z14 samples; Figure 5C). The PSD (N₂GA) curve of reservoir samples shows a similar trend, with no obvious peak (Figure 5D). The distribution of pore volume is relatively stable within the radius range of less than 10nm, and gradually decreases after the radius is greater than 10nm (Figure 5D). This indicates that within the range of less than 10 nm, the pore volume of small pores with different radii does not change significantly. Pores with a radius greater than 10 nm gradually decrease in volume as the pore radius increases. The PSD can only analyze the heterogeneity of pore structure qualitatively; thus, calculations for mono- and multifractal are also required.

4.5. Fractal Characteristics

4.5.1. Monofractal Characteristics

Based on the results of multifractal calculations, many parameters representing heterogeneity can be calculated, for example, D₁, D₀ − D₁, D₋₁₀ − D₀, D₀ − D₊₁₀, D₋₁₀ − D₊₁₀, H, α₀, Δα, and R_d. The curves show the relationships between log S_Hg and log P_c based on the HMIP (Figure 6A–D). These curves can be divided into two parts according to the trend of curve changes. The left segments represent a larger pore diameter with a low Pc value, while the right segments represent a smaller pore size with higher injection pressure. The two segments show a good linear correlation. The correlation coefficients of left and right segments are in the range of 0.8334–0.9959 and 0.8398–0.9859, respectively (

Table 2. Typical fractal dimensions calculated by the monofractal method from HMIP and N₂GA.

Types	Sample ID	HMIP					N2GA
		Left Segment		Right Segment		Dmt	Left Segment		Right Segment		Dnt
		Dm1	R2	Dm2	R2		Dn1	R2	Dn2	R2
Caprock	Z1	2.972	0.9954	2.9884	0.9789	2.9758	2.6882	0.9995	2.5266	0.9996	2.5707
	Z5	2.7621	0.9959	2.5534	0.9842	2.7087	2.7511	0.9946	2.5677	0.9998	2.6366
	Z6	2.9399	0.9029	2.6709	0.9783	2.8420	2.6419	0.9941	2.4748	0.9967	2.5164
	Z7	2.9955	0.8334	2.8902	0.9158	2.9071	2.5263	0.9987	2.464	0.9994	2.4738
	Z8	2.9753	0.9291	2.384	0.9026	2.4551	2.4558	0.9977	2.4809	0.9955	2.4780
	Z9	2.9696	0.9583	2.0126	0.9701	2.2774	2.5868	0.9898	2.4796	0.9945	2.5019
	Z14	2.8727	0.9271	2.8201	0.9781	2.8451	2.485	0.9978	1.821	0.9924	1.9037
Reservoir	Z2	2.8061	0.9946	2.9507	0.8719	2.8248	2.5991	0.9984	2.5191	0.9998	2.5363
	Z3	2.9333	0.9875	2.7897	0.9003	2.9082	2.5759	0.9966	2.4699	0.9997	2.4883
	Z4	2.9781	0.9951	2.9972	0.8398	2.9790	2.5597	0.9992	2.4649	0.9998	2.4822
	Z10	2.9732	0.9671	1.9526	0.9609	2.1903	2.5256	0.9951	2.4422	0.9978	2.4559
	Z11	2.9833	0.9295	2.9977	0.9674	2.9847	2.5325	0.9972	2.4421	0.998	2.4569
	Z12	2.8969	0.9835	2.9046	0.9851	2.8990	2.4967	0.9991	2.4644	0.9995	2.4691
	Z13	2.7291	0.9805	2.9605	0.9859	2.7542	2.5268	0.999	2.3651	0.9658	2.3903

).

The ln V vs. ln (ln (P₀/P)) relationships based on the N₂GA measurements of carbonate samples are shown in Figure 6E–H. The left sections reflect the smaller pore characteristic, and the right sections show the pore feature with a smaller size. The two segments show good linear correlation between ln V and ln (ln (P₀/P)), with correlation coefficients larger than 0.98.

4.5.2. Multifractal Characteristics

Figure 7 displays the double-logarithmic curves of X (q, ε) and ε based on N₂ GA and HMIP with different ranks. The log X (q, ε) and log (ε) showed a significant linear relationship, with the correlation coefficients R² > 0.94 for different moment orders. When q < 0, the log X (q, ε) values are negatively correlated with log (ε), whereas the relationship was positive when q > 0. The excellent power-law correlations of X (q, ε) and ε indicate that the PSD data of N₂GA and HMIP satisfy the multifractal characteristics.

Figure 8 shows the generalized fractal dimension spectra (Figure 8A,B) and multifractal singular spectra (Figure 8C,D) of caprock and reservoir samples based on N₂GA. The generalized fractal dimensions (D_q) decrease with the values of q, and the spectrogram presented an inverted S-shaped. When q is less than 0, the amplitudes of the curve change are more significant than when q is larger than 0 (Figure 8A,B). The f(α) vs. singularity strength α(q) relationships show a concave-down parabola (Figure 8C,D). When q < 0, the multifractal spectrum f(α) increases with increasing singularity strength α. In contrast, f(α) shows a decreasing trend with the increase in singularity strength α when q > 0. In addition, the f(α) curves of the samples based on N₂GA all exhibited left hook shapes (Figure 8C,D). Several unique parameters (N₂GA) that characterize the heterogeneity of pore structure were reported in

Table 3. Typical fractal dimensions calculated by the multifractal method from HMIP and N₂GA.

Types	Sample ID	Typical Fractal Dimensions						Fractal Parameters
		D1	D0 − D1	D−10 − D0	D0 − D+10	D−10 − D+10	H	α0	Δα	Rd
Caprock	Z1	1.47	0.32	2.67	1.79	0.88	1.39	0.23	2.94	−1.07
	Z5	1.30	0.55	3.61	2.37	1.24	1.43	0.24	2.90	−1.02
	Z6	1.50	0.39	3.16	2.02	1.14	1.45	0.24	2.91	−1.00
	Z7	1.52	0.27	2.37	1.40	0.97	1.39	0.23	2.99	−1.10
	Z8	1.68	0.08	1.43	0.94	0.49	1.38	0.23	2.96	−1.09
	Z9	1.58	0.19	2.49	1.85	0.64	1.38	0.23	2.87	−1.06
	Z14	1.91	0.11	1.47	0.93	0.54	1.51	0.23	2.50	−1.75
Reservoir	Z2	1.53	0.44	3.03	1.78	1.25	1.48	0.24	3.04	−1.04
	Z3	1.57	0.20	2.29	1.52	0.78	1.38	0.23	2.92	−1.06
	Z4	1.74	0.29	2.52	1.48	1.04	1.51	0.23	3.13	−1.07
	Z10	1.66	0.13	2.05	1.55	0.50	1.39	0.23	2.90	−1.07
	Z11	1.65	0.14	2.04	1.46	0.58	1.40	0.23	2.90	−1.05
	Z12	1.77	0.10	1.68	1.24	0.45	1.44	0.23	2.94	−1.01
	Z13	1.90	0.15	1.70	1.18	0.52	1.52	0.22	2.32	−2.06

.

Figure 9 displays the generalized fractal dimension spectra (Figure 9A,B) and multifractal singular spectra (Figure 9C,D) of caprock and reservoir samples based on HMIP. The generalized fractal dimensions (D_q) presented an inverted S-shaped curve. When q is less than 0, the amplitudes of the curve change are significant, and the curve tends to flatten out when q is larger than 0 (Figure 9A,B). The f(α) vs. singularity strength α_q relationships show two types of curve characteristics (Figure 9C,D). One type is a monotonic function that conforms to the characteristics of multifractal; the other type of curve is not a monotonic function and does not conform to the characteristics of multifractal (Figure 9C,D). The pore radius distribution obtained from HMIP for nine samples conforms to the multifractal characteristics, while five samples do not (Figure 9C,D). It is believed that samples with a unimodal shape do not exhibit the characteristics of multifractal based on the analysis of curve characteristics. The f(α) curves of the caprock samples in these nine samples all exhibited left hook shapes (Figure 9C). In the reservoir samples, Z13 exhibited a left hook shape (Figure 9C), and Z4, Z11, and Z12 exhibited right hook shapes (Figure 9D). Several unique parameters (HMIP) that characterize the heterogeneity of pore structure were reported in

Table 4. Typical fractal dimensions and fractal parameters calculated by the multifractal method from HMIP.

Types	Sample ID	Typical Fractal Dimensions						Fractal Parameters
		D1	D0 − D1	D−10 − D0	D0 − D+10	D−10 − D+10	H	a0	Δa	Rd
Caprock	Z1	2.01	0.44	3.16	0.86	4.03	1.72	−0.04	0.57	2.99
	Z5	2.09	0.47	2.00	0.86	2.87	1.78	−0.11	4.67	−1.02
	Z6	1.33	1.60	4.07	1.93	6.00	1.96	−0.56	6.70	0.03
	Z7	1.96	1.27	6.52	1.73	8.25	2.11	−1.58	6.73	−0.80
	Z8	1.56	1.61	5.62	1.97	7.59	2.08	−0.87	6.85	−0.71
	Z9	1.78	1.38	7.13	1.72	8.86	2.08	−0.86	0.34	5.47
	Z14	2.00	0.79	3.86	1.21	5.07	1.90	−0.38	5.54	−1.12
Reservoir	Z2	1.89	0.33	5.52	0.78	6.30	1.61	0.11	0.26	2.33
	Z3	1.59	1.57	5.95	2.14	8.09	2.08	−0.86	0.87	6.01
	Z4	2.10	0.94	2.55	1.97	4.52	2.02	−0.69	6.48	0.31
	Z10	1.91	1.24	6.66	1.66	8.32	2.08	−0.86	−0.22	4.91
	Z11	1.98	0.29	0.80	0.86	1.67	1.64	0.13	3.35	0.02
	Z12	1.89	0.50	1.58	0.89	2.47	1.69	0.07	3.74	−0.29
	Z13	2.38	0.41	2.71	0.96	3.67	1.90	−0.38	5.56	−1.18

.

5. Discussion

5.1. Monofractal and Multifractal Investigation on Pore Structure Heterogeneity

5.1.1. The Heterogeneous Differences in Pore Structure Between Reservoirs and Caprocks

Based on the fractal parameters described in Section 3.3 and Section 3.4, we compared the differences in reservoir and caprock heterogeneity. The fractal dimensions of reservoirs and caprocks vary in different pore size ranges, which is consistent with the results observed by previous researchers in studying the classification characteristics of carbonate caprocks [1,3,10]. We also found that the distribution ranges of most monofractal dimension parameters in the caprocks are larger than those in the reservoir, indicating that there are significant differences in heterogeneity between different caprock samples, while the similarity between reservoir samples is higher (Figure 10). The D_m2 of caprock generally is smaller than that of the reservoir (Figure 10A), indicating that the heterogeneity of pore distribution in the micropore section of the caprock is lower than that in the reservoir. The consistency between D_mt and D_m2 of reservoir and caprock (Figure 10A) indicates that the micropore segment plays a crucial role in the monofractal of HMIP. We observed significant differences in the N₂GA monofractal dimension of the caprock, while the monofractal dimension of the reservoir is concentrated (Figure 10B). This indicates that there are significant differences between caprock samples and similar heterogeneity between reservoir samples, within the detection range of N₂GA.

5.1.2. The Relationship Between Lithology, Pore Types, and Heterogeneity

Heterogeneity analysis of reservoirs and caprocks demonstrates certain disparities among their respective samples. Nevertheless, N₂GA multifractal parameters exhibit no significant differentiation between these two. Previous studies have confirmed that the pore–throat structure of carbonate caprock is influenced by lithology [1,9]. Consequently, heterogeneity analysis ought to be conducted based on lithological and pore type differentiation. We categorized the samples into three types: grainstone, dolomite, and micrite/argillaceous limestone.

There is no obvious boundary between the fractal dimension parameters of different rock types (Figure 11). The distribution ranges of fractal parameters obtained by HMIP, in descending order, are grainstone, micrite/argillaceous limestone, and dolomite (Figure 11A,C), while those obtained by N₂GA, in descending order, are dolomite, micrite/argillaceous limestone, and grainstone (Figure 11B,D). This indicates that the differences in macropores of grainstone samples are relatively significant, and the differences in micropores of dolomite samples are relatively notable. Combined with the observation results of pore types, it is considered that the existence of irregular intergranular pores in grainstone leads to differences in fractal parameters among different samples. Among the fractal dimension parameters obtained by N₂GA, D₀ − D₁, D₀ − D₊₁₀, D₋₁₀ − D₀, and D₋₁₀ − D₊₁₀ can distinguish micrite/argillaceous limestone from grainstone and dolomite (Figure 11D), indicating that the heterogeneity of micrite/argillaceous limestone is stronger than that of the other two lithologies within the N₂GA detection range.

In summary, we draw three inferences. The differences in intergranular pores between grainstone caprocks and reservoirs result in heterogeneity differences among different samples. Intergranular pores are generally developed in dolomites, so the differences within the detection range of HMIP are not significant. Micrite/argillaceous limestone is dominated by small intercrystalline pores. Therefore, the pore–throat structure of the sample is highly heterogeneous within the detection range of N₂GA.

5.2. Impact of Pore Structure Heterogeneity on Breakthrough Pressure

Porosity and permeability have been identified as crucial indicators for distinguishing caprocks from reservoirs and as parameters for investigating breakthrough pressure (BP) [1,7,8,9]. Consequently, this study examined BP in relation to monofractal parameters while also considering porosity and permeability. We use the Pearson correlation matrix to observe the relationship between all parameters intuitively (Figure 12, Figure 13 and Figure 14). The number at the center of the circular symbol is the correlation coefficient (R). When R is positive, the parameters are positively correlated, and when R is negative, the parameters are negatively correlated; the larger the circle, the darker the color, and the greater the absolute value of the correlation coefficient (R) [59]. The experimental results indicate that while BP is influenced by porosity and permeability, the correlation coefficients are not high. Therefore, it is necessary to investigate the impact of heterogeneity on BP.

5.2.1. Monofractal Investigation

Among the three monofractal parameters derived from HMIP, D_m1 exhibits the highest correlation with petrophysical properties (Figure 12), revealing that larger pore–throat segments exert a dominant control on porosity and permeability. The fractal dimension (D_mt) shows a negative correlation with both porosity and permeability (Figure 12), indicating that increased complexity within the larger pore segments leads to reduced porosity and permeability. It is noteworthy that the control exerted by macropore heterogeneity on porosity and permeability is more pronounced in reservoirs than in caprocks. Previous studies have shown a close relationship between coverage coefficient and fractal dimension, and have revealed the importance of pore structure fractal dimension in controlling rock sealing ability [9]. However, the correlations between HMIP parameters in this study and BP are weak (R < 0.3, Figure 12), suggesting that the macropore heterogeneity has a limited influence on BP. This suggests that the micropore segment may have a controlling effect on BP.

Nitrogen adsorption (N₂GA) experiments reveal the characteristics of micropore spaces. The correlations between monofractal parameters and porosity, permeability, and BP are significantly higher than those obtained from HMIP, yet remain relatively low in the total sample analysis (Figure 12A). After grouping and analyzing reservoirs and caprocks, the correlations between monofractal parameters and petrophysical properties are markedly enhanced. Specifically, D_n1 (an indicator of pore regularity) exhibits a negative correlation with porosity and permeability but a positive correlation with BP (Figure 11C and Figure 12B). This finding suggests that an increase in pore irregularity leads to a decrease in porosity and permeability, concurrent with an increase in BP. Similarly, D_n2 (an indicator of pore surface roughness) shows a negative correlation with porosity and permeability and a positive correlation with BP, suggesting that increased surface roughness elevates BP in reservoirs (Figure 11C and Figure 12B). The BP in reservoirs exhibits higher sensitivity to pore regularity (D_n1), whereas caprock petrophysical properties demonstrate more significant responses to D_n1 (Figure 11C and Figure 12B). The comprehensive fractal index D_nt displays the highest correlation coefficient, indicating that breakthrough pressure is synergistically controlled by pore regularity and surface roughness. It also proves that the rougher the pore surface, the more irregular the pore structure, and the greater the flow resistance of oil and gas fluids [57,60].

Based on the above analysis, we propose that petrophysical properties and breakthrough pressure (BP) in carbonate reservoir–caprock systems are differentially controlled by multi-scale pore structures. Macropore heterogeneity dominates porosity and permeability variations, while micropore structural characteristics (regularity, roughness) exert decisive control on BP.

5.2.2. Multifractal Investigation

This study reveals that differential control mechanisms of pore structure heterogeneity impact fluid sealing capacity in reservoir–caprock systems, as evidenced by the relationship between multifractal parameters and BP. The experimental findings demonstrate a substantially higher degree of correlation between multifractal parameters derived from N₂GA and physical properties and BP, in comparison to those obtained from HMIP (Figure 13 and Figure 14). This enhanced correlation is primarily attributed to the characterization sensitivity of N₂GA to micropores (<50 nm), where pore networks exert a decisive role in controlling BP. The phenomenon can be explained by the relatively micropore radius of the caprocks, which plays an important role in hindering the migration of petroleum fluids through the overlying strata [61,62]. It is important to note that, when differentiating reservoirs from caprocks, the correlation coefficients of multifractal parameters increase substantially. This observation serves to substantiate the inherent self-similarity that characterizes pore structures within reservoir–caprock systems, in addition to the presence of inter-group heterogeneity characteristics (Figure 13 and Figure 14).

The correlation analysis of HMIP parameters exhibits statistically insignificant results due to the limited validation sample size (five caprock samples and four reservoir samples). The overall low correlation coefficients are insufficient to demonstrate the influence of pore structure on breakthrough pressure (Figure 13).

Among the multifractal parameters for all samples, D₀ − D₁, D₋₁₀ − D₀, D₋₁₀ − D₊₁₀, and R_d demonstrate significant correlations with breakthrough pressure (BP) (R > 0.55, Figure 14), indicating that pore–throat size distribution dispersion, heterogeneity, and heterogeneous contributions across probability intervals collectively govern BP in carbonate caprocks. Specifically, the positive correlation between D₀ − D₁ and BP indicates that as the pore size distribution becomes more discrete, the BP will increase (Figure 14). The positive correlations of D₋₁₀ − D₀ and D₋₁₀ − D₊₁₀ with BP demonstrate that pore structure heterogeneity enhances BP, with low-probability intervals exerting significant influence (Figure 14). It is noteworthy that Rd demonstrates the most significant positive correlation with BP (R = 0.70, Figure 14), suggesting that increased heterogeneity contributions from high-probability intervals result in higher BP.

The correlation between the parameters of reservoir samples and BP and physical properties is approximately 20% to 30% higher than that of caprocks (Figure 14B,C), which is related to their more developed secondary pores and complex throat networks. Conversely, caprock BP demonstrates a reduced sensitivity to multifractal parameters, likely associated with the presence of finer grains and sparse, isolated pores in caprock samples. Among the parameters of caprock, D₁ and H exhibit relatively high correlations with permeability (R = 0.79 and 0.74, respectively; Figure 14B), indicating that greater pore concentration and improved connectivity enhance fluid flow capacity. It is noteworthy that BP is generally less influenced by the multifractal parameters of the caprock samples. The underlying cause of this phenomenon may be attributable to the presence of substantial variations in the pore structure of diverse lithology caprock samples. The multifractal parameters of reservoir samples (D₀ − D₁, D₀ − D₊₁₀, D₋₁₀ − D₊₁₀) and BP demonstrate substantial correlation (R > 0.6, Figure 14C). This finding suggests a direct correlation between the heterogeneity of the reservoir and the BP of the reservoir. The high probability zone has been shown to have a more significant control effect on BP (R = 0.75).

5.3. Sealing Mechanism of Carbonate Caprock

5.3.1. Impact of Heterogeneity Differences on Breakthrough Pressure

It has been posited by preceding studies on carbonate sealing capacity that if the breakthrough pressure (BP) difference between the reservoir and the caprock exceeds 3 MPa, the cap rock can effectively seal off hydrocarbon [7,8]. However, the analysis presented in Section 5.1 indicates the presence of overlapping ranges of fractal dimension parameters between reservoirs and caprocks, thereby suggesting an absence of any absolute heterogeneity distinction between these two types of geological formations. It is important to note that there is significant heterogeneity in samples of different lithologies. Consequently, we separately analyzed the correlations between fractal parameter differences and BP differences for reservoir and caprock of identical versus different lithologies.

In instances where both the reservoir and the caprock are composed of grainstone, the differences in the BP between the six groups of samples are found to exceed 3 MPa. The difference calculation data shows an interesting phenomenon: caprocks consistently show lower fractal parameter values than their paired reservoirs, indicating weaker heterogeneity in caprocks. The correlation analysis reveals close relationships between ΔD_n1, Δ (D₀ − D₁), Δ (D₀ − D₊₁₀), and ΔBP (R² = 0.5786, 0.4683, and 0.8446, respectively; Figure 15). This finding suggests that when both the reservoir and the caprock are composed of grainstone, the less the heterogeneity difference between the reservoir and the caprock in the micropore detected by N₂GA, the more significant the sealing effect of the caprock on the fluid in the reservoir.

In instances where the caprock is micrite or argillaceous limestone and the reservoir is grainstone, a total of 12 sets of valid data have been obtained. Subsequently, we analyzed the correlation between the differences in multifractal parameters and the differences in BP. The correlation between the difference in classification dimension and BP difference is generally high. The correlations between ΔD_n1, ΔD_n2, ΔD_nt, ΔD₁, Δ (D₋₁₀ − D₀), Δ (D₀ − D₊₁₀), and ΔBP are significant, and the correlation coefficient R² is distributed between 0.6004 and 0.9291 (Figure 16). The significant positive correlation between the difference in monofractal parameters obtained by N₂GA and the BP difference indicates that the greater the heterogeneity difference between the reservoir and the caprock in the micropore section, the greater the sealing capacity. The D₁ of multifractal parameters shows a negative correlation with BP, where lower D₁ values are observed in caprocks in comparison to reservoirs (Figure 16). This finding indicates that the pore size distribution of the micrite/argillaceous limestone caprocks is more concentrated, and that the greater the difference in concentration between the caprock and the reservoir, the better the sealing ability. The strong positive correlations between Δ (D₋₁₀ − D₀), Δ (D₀ − D₊₁₀), and ΔBP indicate that the heterogeneity of the caprock is higher than that of the reservoir in both high and low probability intervals. Furthermore, it has been demonstrated that the greater the difference, the better the sealing ability.

5.3.2. The Sealing Mode of Heterogeneous Carbonate Rocks

Strong anisotropy and poor connectivity of pore–throat structures in carbonates are key for the development of an effective seal [63]. However, based on the analysis of the impact of heterogeneity differences on BP in the previous section, we believe that the heterogeneity of pore–throat structures between reservoirs and caprocks is the key to controlling fluid flow in carbonate rocks. Different pore size distributions of carbonate caprock have varying impacts on their fractal behavior [64,65]. Based on this, we propose the following two sealing models.

In the instances when both the reservoir and the caprock are composed of grainstone, isolated large pores in the reservoir contribute mainly to the pore volume. Furthermore, the distribution of micropore segments in the reservoir and caprock is similar (Figure 17A). The small pores in the reservoir and caprock are the key to controlling BP. The micropores in the reservoir and caprock are dispersed but evenly distributed; the reduction in pore size does not affect the classification dimension value, but increases capillary force. Therefore, the little heterogeneity difference between them can make the caprock have sealing ability (Figure 17A). The increase in heterogeneity between the reservoir and caprock may be due to the concentrated distribution of pores within a certain pore size range in the sample. This will enhance the connectivity of pores in the reservoir, making it easier to break through the sealing of the caprock (Figure 17A).

When the caprock is micrite/argillaceous limestone and the reservoir is grainstone, there are significant differences in the pore types and pore size distribution between the reservoir and caprock. The caprock is primarily composed of micropores, which are defined as small, interconnected pores with narrow, strip-shaped throats. These characteristics contribute substantially to the enhancement of roughness and heterogeneity in the pore structure (Figure 17B). The pore types of reservoirs are mainly intergranular pores and intercrystalline pores. Within the detection range of small pore sizes, the heterogeneity is significantly lower than that of micrite/argillaceous limestone. The more significant the heterogeneity difference between the reservoir and the caprock, the greater the BP difference, which indicates that the heterogeneity of pore–throat structure enhances the capillary resistance of hydrocarbons, resulting in better sealing ability of the caprock (Figure 17B). In addition, the pore–throat surface of micrite/argillaceous limestone caprock is rough, while the pores of grainstone are relatively smooth. This difference can also lead to the pore system of caprock becoming a barrier for fluid flow [58,59,66].

6. Conclusions

The heterogeneity difference between caprocks is greater than that of reservoirs. The disparities in pore structure among grainstone, dolomite, and micrite/argillaceous limestone give rise to substantial heterogeneity among the samples. The presence of irregular intergranular pores in grainstone leads to substantial variations in the fractal parameters among samples of this category. Dolomite generally develops intergranular pores, thus resulting in minimal disparities between pore samples within the high-pressure mercury intrusion detection range. Micrite/argillaceous limestone is primarily distinguished by the presence of micropores between crystals, thereby exhibiting significant heterogeneity within the micropore size range of nitrogen adsorption.

The heterogeneity of macropores exerts a predominant influence on physical property alterations, exhibiting a marginal impact on breakthrough pressure. Conversely, the characteristics of microporous structures, such as regularity and roughness, have been demonstrated to exert a substantial influence on breakthrough pressure. The pore structure of the carbonate reservoir–caprock system exhibits self-similarity. The heterogeneity of the caprock exerts no significant control effect on BP, while the stronger the heterogeneity of the reservoir, the greater the BP.

The sealing capacity of the caprock depends on the heterogeneity differences in pore types and pore structures between the reservoirs and caprocks. When both the reservoir and caprock are grainstone, the distribution of micropore segments in the reservoir and caprock is similar. Consequently, the reduction in pore size does not affect the classification dimension value, but increases capillary force, and small heterogeneous changes can achieve sealing. When the lithology is different, there is a significant difference in the pore–throat types between the reservoir and caprock. The greater the difference in pore size distribution and roughness of the pore–throat surface, the better the sealing capacity.