Influencing Factors and Mechanism of CO₂ Trapping and Storage in Tight Sandstone Reservoirs Based on Fractal Characteristics of Pore Structure

Abstract

To mitigate global warming induced by excessive carbon dioxide emissions, carbon dioxide displacement technology for carbon utilization and storage has attracted growing attention. In this paper, laboratory displacement experiments combined with Nuclear Magnetic Resonance (NMR), constant-rate mercury intrusion, and X-ray diffraction (XRD) tests are adopted to investigate the residual storage characteristics of carbon dioxide in tight sandstone reservoirs. This study evaluates the effect of depletion pressure on carbon dioxide storage efficiency. Combined with the pore-throat fractal dimension (D_f) obtained from constant-rate mercury intrusion and the capillary tortuosity fractal dimension (D_T) calculated via models, the relevant controlling mechanisms are illustrated. The results show that the residual storage efficiency can exceed 62.00% when the depletion pressure is higher than the supercritical pressure of carbon dioxide. Storage efficiency exhibits a significant correlation with the average pore-throat ratio, indicating that pore-throat matching characteristics play a vital role in carbon dioxide retention. Both the pore-throat fractal dimension D_f and capillary tortuosity fractal dimension D_T are positively correlated with the average pore-throat ratio and negatively correlated with the pore-throat radius, reflecting the impacts of pore structure complexity and fluid channel tortuosity on carbon dioxide migration and storage processes. X-ray diffraction test results further verify that quartz and clay minerals indirectly affect carbon dioxide storage performance by altering the preservation status and connectivity of pore throats. The innovation of this study lies in establishing a coupled analysis system integrating pore-throat heterogeneity, fluid channel complexity, and carbon dioxide phase evolution, which reveals the residual storage mechanism of carbon dioxide in tight sandstone reservoirs. Relevant research findings provide new insights for studies on carbon dioxide storage laws at the pore scale, and offer theoretical support for optimizing geological carbon dioxide storage schemes in tight reservoirs.

1. Introduction

Since China proposed its dual-carbon goals of carbon peaking and carbon neutrality, carbon capture, utilization, and storage (CCUS) has become a major research focus. Research on CO₂ storage is a key technology for achieving these “dual-carbon” goals and holds significant importance [1]. Tight oil reservoirs account for a high proportion of unconventional oil reservoirs and possess great development potential. Tight oil refers to oil accumulated in reservoirs with matrix permeability less than or equal to 0.1 × 10⁻³ μm² (air permeability less than or equal to 1 × 10⁻³) [2]. However, due to the characteristics of tight oil reservoirs, such as strong heterogeneity, rapid decline of formation energy and fast production decline, traditional water-flooding and other conventional enhanced oil recovery technologies for oil reservoirs can hardly be applied effectively, resulting in generally low recovery factors, which are usually no more than 10% [3]. In response to these problems encountered during development, there is an urgent need to find a development method for supplementing formation energy. Given that CO₂ features favorable injectivity and oil-displacement performance, CO₂ injection serves as an effective approach to supplement energy and enhance development performance in tight oil reservoirs [4]. Scholars in China and abroad have carried out extensive experimental research on CO₂-EOR and storage. Therefore, clarifying the carbon storage mechanism and influencing factors during the CO₂ displacement process in tight oil reservoirs is critical to breaking through the technical bottlenecks of CCUS.

Capillary forces play different roles under different production processes [5]. Capillary forces act as a driving force when the wetting phase displaces the non-wetting phase, whereas they act as a resisting force when the non-wetting phase displaces the wetting phase. However, during CO₂ injection in tight reservoirs, the displacement behavior varies with reservoir wettability. In oil-wet reservoirs, CO₂ acts as the non-wetting phase, whereas crude oil is the wetting phase; under such conditions, CO₂ flooding is extremely difficult, and CO₂ is prone to being trapped within the pore space. In water-wet reservoirs, both CO₂ and crude oil behave as non-wetting phases, resulting in relatively strong capillary forces. Although this makes the displacement of crude oil by CO₂ more difficult, the capillary trapping effect is favorable for the sequestration of CO₂ within the formation [6].

Extensive studies have advanced the understanding of CO₂ geological storage mechanisms from multiple perspectives, including capillary trapping, reservoir pressure evolution, fluid distribution, and pore-throat structure. Capillary hysteresis has been shown to influence the diffusion, migration, and redistribution of CO₂, indicating that capillary forces play a critical role in CO₂ residual trapping and storage processes [7]. During CO₂ injection before and after hydraulic fracturing, CO₂ is retained in reservoirs through multiple trapping mechanisms, including residual trapping, dissolution trapping, and mineral trapping, with distinct dominant mechanisms operating at different stages [8].

From the perspectives of reservoirs and sedimentary basins, pressure constraints represent a key factor governing the effective storage of CO₂. Global basin-scale modeling studies have demonstrated that continuous CO₂ injection is significantly limited by reservoir pressure conditions, highlighting that controlling injection pressure is a crucial aspect of geological CO₂ storage [9]. In addition, CO₂ compression and purification processes directly affect CO₂ purity, energy consumption, and capture costs, thereby influencing the economic feasibility and operational performance of CCUS projects [10]. Moreover, CCUS faces challenges such as high capture costs, strict transportation safety requirements, and complex long term storage risk assessment; therefore, optimizing impurity removal and purification strategies is essential for achieving economical and secure long term CO₂ geological storage [11].

During CO₂ injection and migration, reservoir properties and capillary forces jointly control CO₂ storage behavior. Parameters such as reservoir depth, temperature, absolute and relative permeability, and capillary pressure collectively influence CO₂ injectivity, migration, and storage capacity, among which relative permeability plays a particularly significant role [12,13]. The Bond number, defined as the ratio of gravitational force to capillary force, provides a useful dimensionless parameter for characterizing CO₂ plume migration and capillary trapping behavior [14,15]. In deep saline aquifers, even relatively weak capillary forces can significantly affect CO₂ plume migration, indicating that capillary forces are important not only at the pore scale but also at larger migration scales [16]. Furthermore, machine learning approaches based on multi-source geological, environmental, and engineering data have improved the efficiency and reliability of CCUS site selection; however, such methods mainly focus on macroscopic evaluation and are limited in their ability to directly explain pore-scale CO₂ residual trapping mechanisms [17].

At the pore scale, CO₂ trapping is closely related to wettability, fluid distribution, and pore-throat structure. Studies based on NMR T₁–T₂ maps and T₂ relaxation times have demonstrated significant differences in CO₂ trapping efficiency and displacement performance between water-wet and oil-wet cores, indicating that wettability strongly affects fluid occurrence states and trapping efficiency in pore spaces [18,19]. Further analysis of T₁–T₂ maps and T₂ relaxation distributions reveals that fluids with different wettability preferentially occupy pores of different sizes: strongly wetting phases (water) occupy small pores, non-wetting phases (CO₂) preferentially occupy large pores, and intermediate-wetting phases (oil) are distributed in intermediate-sized pores [20]. It should be noted that most of the aforementioned studies target saline aquifers and carbonate reservoirs. Saline aquifers generally feature relatively uniformly distributed large pores and strong hydrophilicity. In contrast, carbonate reservoirs are developed with dissolution vugs and fractures and exhibit extensive heterogeneity. By contrast, the continental tight sandstone investigated in this paper possesses a typical micro–nano-scale “large pore with narrow throat” structure, complex clay filling conditions, and mixed wettability. The capillary trapping laws of other reservoir types cannot be directly applied to the study area, which highlights the necessity of carrying out targeted experimental research.

Pore-throat structure constitutes the fundamental microscopic basis governing CO₂ residual trapping and migration. The combined application of high pressure mercury intrusion, low-temperature nitrogen adsorption, CO₂ adsorption, and fractal theory has revealed strong heterogeneity in sandstone pore structures, suggesting that fractal dimensions can effectively characterize such complexity and provide a useful framework for analyzing CO₂ trapping from a microscopic perspective [21]. Similarly, scanning electron microscopy, low temperature nitrogen adsorption, and fractal analysis have been widely used to quantitatively characterize pore systems in unconventional reservoirs, demonstrating that fractal dimensions are effective indicators of pore complexity and heterogeneity [22]. Pore-throat structure constitutes the microscopic basis governing CO₂ migration and residual trapping. The combinations of pores and throats at different scales determine not only the available storage space but also the effective flow pathways, capillary-entry conditions, and fluid-transport capacity. Previous studies combining high-pressure mercury intrusion, low-temperature N₂ adsorption, CO₂ adsorption, and fractal analysis have demonstrated that sandstone pore systems commonly exhibit pronounced multiscale heterogeneity, and that fractal parameters can be used to quantify the complexity of pore-throat size distributions [22]. Meanwhile, X-ray computed tomography and digital-rock techniques provide three-dimensional approaches for identifying void space and evaluating pore connectivity; however, the resulting structural parameters are strongly influenced by image resolution and pore–solid binarization procedures. When a considerable proportion of fine pores is smaller than the spatial resolution of the CT system, grayscale thresholds alone may not accurately identify the complete void space. Artificial digital models with predefined pore-structure parameters can provide constraints for determining the pore–solid segmentation threshold and thereby improve the reliability of void-space identification [23]. Further studies have shown that different image-segmentation methods may produce different estimates of porosity, pore-size distribution, connectivity, and simulated permeability, indicating that digital-rock results should be interpreted in relation to both image resolution and segmentation accuracy [24]. Moreover, pores and throats perform different storage and transport functions. Image-based pore-throat network extraction has further demonstrated that these two structural units should be distinguished according to their different geometric characteristics and flow functions rather than being treated as an identical type of void space [25]. More recently, integrated core-flooding, micro-CT imaging, and pore-network modeling workflows have linked pore-scale fluid configurations and connectivity with CO₂ relative permeability and capillary trapping, highlighting the importance of local pore-throat configurations in controlling CO₂ migration and residual immobilization [26]. Therefore, different experimental techniques characterize different scales and attributes of the pore system. Mercury intrusion primarily reflects capillary-entry behavior during the invasion of a non-wetting phase into the connected pore-throat system; NMR T₂ spectra mainly characterize the relative volumes of hydrogen-bearing fluids occurring in different pores; and CT-based digital-rock analysis identifies geometrically resolvable pores and their connectivity within the limits of image resolution. These methods provide complementary, but not fully equivalent, information and should not all be interpreted as representing the same pore-size distribution. Although previous studies have advanced the understanding of multiscale pore structures and flow behavior, the combined effects of pore-throat heterogeneity, flow-path complexity, and depletion pressure on CO₂ residual trapping in low-permeability sandstones remain insufficiently quantified.

Previous studies have deepened the understanding of capillary trapping of CO₂; however, several limitations remain for tight sandstone reservoirs. First, many studies have focused on saline aquifers, carbonate rocks, or idealized pore networks, whereas the CO₂ trapping mechanism controlled by pore-throat structures in tight sandstones remains unclear. Second, existing pore-scale studies have mainly focused on single factors, such as pore-size distribution, wettability, or capillary pressure, while the coupling relationship among pore-throat heterogeneity, seepage path complexity, and CO₂ phase-state changes induced by pressure depletion still lacks systematic explanation. Third, fractal theory has mainly been applied to static pore structure characterization or reservoir quality evaluation, and its connection with core-scale stepwise pressure depletion CO₂ trapping experiments remains insufficiently investigated.

Despite extensive prior research, three critical knowledge gaps remain for tight sandstone reservoirs. First, most CO₂ capillary trapping studies focus on saline aquifers and carbonate rocks. In contrast, the trapping mechanism controlled by the “large-pore fine-throat” pore structure in continental tight sandstones remains unclear. Second, existing pore-scale studies mostly adopt a single fractal parameter, failing to jointly characterize pore-throat size heterogeneity and seepage path tortuosity. Third, few studies link static fractal pore characterization with dynamic CO₂ phase evolution during pressure depletion. To address these gaps, this study integrates constant-rate mercury intrusion, NMR, XRD, and stepwise pressure depletion CO₂ flooding experiments. The testable core hypothesis of this study is as follows: the fractal heterogeneity of pore throats is an inherent static microscopic factor determining the upper limit of capillary trapping potential for carbon dioxide, while depletion pressure and carbon dioxide phase transition are external dynamic regulating factors governing the actual residual trapping ratio. This study intends to verify the coupled control mechanism of the above two types of factors through core experiments and fractal characterization.

2. Experimental Design

2.1. Experimental Preparation

The experimental fluids used in this study included simulated formation water, simulated oil, and CO₂. The simulated formation water was a Na₂CO₃ type brine with a salinity of 15,215.33 mg/L, prepared according to the ionic composition of the formation water provided by the oilfield. The oil used in the experiment was simulated oil prepared by mixing dehydrated and degassed crude oil extracted from the low-permeability reservoir in Block M of Xinjiang Oilfield with kerosene, with a viscosity of 0.74 mPa·s (at 105 °C). Additionally, CO₂ gas cylinders with 99.99% purity were used.

The experimental apparatus used in this study is shown in

Table 1. Experimental apparatus.

Serial Number	Name	Model	Manufacturer
1	High-temperature and High-pressure Multifunctional Core Displacement Experimental Device	HBYQ-2	Yangzhou Huabao Petroleum Instrument Co., Ltd. (Yangzhou, China)
2	Electronic Analytical Balance	LE-104E	Ningbo Yinzhou Huafeng Instrument Factory (Ningbo, China)
3	Electrothermal Blast Drying Oven	DHG-9070(A)	Shanghai Yiheng Scientific Instrument Co., Ltd. (Shanghai, China)
4	Constant-speed Mercury Porosimeter	ASPE-730	Coretest Company (Morgan Hill, CA, USA)
5	Nuclear Magnetic Resonance Instrument	SPEC-RC2	Beijing Spektron Technology Development Co., Ltd. (Beijing, China)
6	New High-resolution Diffractometer	D8AA25	Bruker AXS GmbH (Karlsruhe, Germany)
7	Field-emission Environmental Scanning Electron Microscope	Quanta450	Beijing Yuanhaiwei Technology Co., Ltd. (Beijing,  China)

.

Table 2. Basic physical property parameters of core samples.

Core Number	Sampling Depth/m	Coring Horizon	Reservoir Temperature/°C	Length/cm	Diameter/cm	Helium-Measured Porosity/%	Gas-Measured Permeability/10−3 μm2	Average Pore-Throat Ratio
1	3998.50	M1	102.40	8.38	2.47	14.62	0.94	210.79
2				5.82	2.48	15.02	1.30	170.88
3				5.66	2.47	14.71	1.01	152.45
4				7.37	2.47	14.83	1.11	160.57
5	4004.00	M2	103.50	7.73	2.47	13.73	0.49	270.00
6	4053.10	M3	104.80	6.75	2.47	13.93	0.78	241.51
7				6.85	2.47	14.11	0.78	256.54
8	4230.90	M4	106.70	7.03	2.47	14.51	0.90	217.57
9				5.01	2.47	14.44	0.89	220.68
10				6.91	2.47	14.40	0.89	220.87
Mean	4082.90	-	104.28	6.75	2.47	14.43	0.91	212.19
SD	97.90	-	1.63	1.01	0.003	0.39	0.21	37.61

Notes: The 10 core samples cover four stratigraphic intervals (M1–M4) in the study area, among which the M1 interval has 4 parallel samples, the M2 interval has 1 sample, the M3 interval has 2 samples, and the M4 interval has 3 samples. It should be noted that the M2 interval has only one sample due to the low coring recovery of deep thin sand bodies, and its data are used as a reference for stratigraphic comparison, not for independent statistical inference.

. Porosity was obtained by helium porosimetry, permeability was measured by gas permeability testing, and the experimental procedures were conducted in accordance with GB/T 29172-2012 (“Practices for Core Analysis”) [27]. The average pore-throat ratio was calculated from pore and throat parameters derived from constant-rate mercury intrusion.

2.2. Experimental Procedure

2.2.1. Constant-Rate Mercury Injection Experiment

The constant-rate mercury intrusion experiment procedure followed the standard GB/T 29171-2023 (“Rock capillary pressure measurement”) [28]. The experiment was conducted using an ASPE730 constant-rate mercury porosimeter (Coretest Inc., Dover, DE, USA), with a maximum mercury injection pressure of 6.205 MPa. The contact angle between mercury, as the non-wetting phase, and the rock surface was 140°.

To ensure the reliability of pore structure parameters, duplicate mercury intrusion tests were carried out on parallel core plugs from the same depth, and the relative error of D_f is less than 3%, indicating good experimental repeatability. Meanwhile, NMR T₂ spectra were used as an independent method for cross-validation. The heterogeneity characteristics reflected by D_f are highly consistent with the pore-size distribution shown by NMR, which proves that D_f can reliably represent the actual connected pore-throat structure of the reservoir.

2.2.2. Fractal Theory

Two complementary fractal parameters with distinct physical meanings were employed in this study to jointly characterize pore-throat structural complexity. The constant-rate mercury intrusion fractal dimension D_f quantifies the size heterogeneity of the connected pore-throat network, reflecting the uneven distribution of throat sizes as a static geometric indicator. The capillary tortuosity fractal dimension D_T describes the winding degree of effective seepage channels, reflecting the complexity of fluid migration paths as a dynamic flow constraint indicator. The coupling of the two parameters forms a complete microscopic interpretation system for capillary trapping, which cannot be realized by a single fractal parameter.

(1)

Fractal Characteristics of Constant-Rate Mercury Injection

Fractal theory, which is used to study irregular and unstable complex structures, is an effective approach for characterizing the complexity and heterogeneity of pore structures in tight sandstones. The theoretical value of the fractal dimension (D_f) ranges from 2 to 3. A D_f value closer to 2 indicates a simpler pore structure and stronger internal homogeneity of the core, whereas a D_f value closer to 3 indicates greater internal variation and stronger heterogeneity.

Constant-rate mercury intrusion can provide three types of interpreted mercury-saturation information, including pore-body mercury saturation, throat mercury saturation, and total cumulative mercury saturation of the whole pore-throat system. It should be emphasized that the mercury intrusion-derived fractal dimension D_f in this study was calculated using the total cumulative mercury saturation S_Hg,total, rather than the separated pore-body saturation or throat saturation. Therefore, D_f represents the overall fractal heterogeneity of the connected pore-throat system, instead of the independent fractal characteristics of pores or throats.

This model has been widely used in studies of pore structure in unconventional reservoirs and has also been extensively applied to tight sandstone reservoirs. Based on fractal theory, previous studies [29] derived a power law relationship between mercury saturation S_Hg,total and capillary pressure Pc obtained from constant-rate mercury intrusion experiments. In this study, the exponent derived from this relationship is denoted as D_f. Its interpretation as a pore-throat structural fractal parameter is based on the capillary pressure–pore-throat radius relationship introduced below:

$${S_{Hg,total}=a{P}_c}^{-(2-D_f)}$$

(1)

where S_Hg,total is the mercury saturation, P_c is the capillary pressure, and a is a constant. Taking the logarithm on both sides of Equation (1), we obtain:

$$\lg S_{Hg,total}\propto \left(D_f-2\right)\lg P_c$$

(2)

According to Equation (2), the exponent D_f can be obtained from the slope of the linear relationship between lgS_Hg,total and lgP_c. Its interpretation as a pore-throat structural parameter requires the capillary pressure–radius relationship:

$$D_f=2+\lambda$$

(3)

According to Equation (4), the mercury saturation S_Hg,total, and mercury intrusion pressure P_c obtained from constant-rate mercury injection experiments on 10 core samples were calculated. Piecewise fitting was performed using the least squares method, and the resulting fitted curves reflected the fractal characteristics of the sandstones. Based on the slopes obtained from the fitting, the mercury intrusion-derived pore-throat fractal parameter D_f was obtained according to Equation (3). According to the capillary pressure equation $P_c={\displaystyle \frac{2\sigma \cos \theta }{r}}$, capillary pressure is inversely related to the equivalent pore-throat radius when interfacial tension and contact angle remain constant. Therefore, higher mercury intrusion pressure generally corresponds to a smaller pore-throat radius. On this basis, the fitted D_f can be interpreted as an indicator of pore-throat size heterogeneity.

(2)

Fractal Characteristics of Capillary Tortuosity

The capillary tortuosity fractal model adopted in this study is a classical theoretical model for porous media, built on the statistical self-similarity assumption of equivalent capillary networks (i.e., flow-path length and channel size satisfy the fractal scaling law). It should be emphasized that this study does not provide direct experimental evidence (e.g., micro-CT 3D reconstruction) to verify that the tortuosity of the studied sandstone strictly follows the fractal scaling law. Therefore, D_T should be interpreted as a model-derived equivalent dimensionless indicator reflecting seepage path complexity, rather than a strictly verified mathematical fractal dimension. The term “fractal dimension” here follows the naming convention of the original model literature, and its theoretical premise should be fully considered in interpretation. Therefore, D_T should be interpreted as a statistical indicator of flow-path tortuosity rather than a directly measured geometric dimension of an individual pore or throat.

When fluids flow through porous media, the flow paths are tortuous rather than linear. In the capillary tortuosity model adopted in this study, the term “capillary” refers to an idealized equivalent flow pathway within the pore-throat network, rather than a single physical channel. A throat represents the connecting part between adjacent pores, whereas an equivalent capillary consists of an effective seepage pathway composed of multiple pores and throats. Therefore, the actual tortuous flow-path length, L_t, is greater than or equal to the straight-line distance, L₀, along the pressure-gradient direction. The characteristic capillary radius, r, is used to describe the effective scale of the equivalent flow channel. Therefore, the actual tortuous flow-path length L_t is greater than or equal to the straight-line distance L₀ along the pressure-gradient direction. L₀ does not mean that all capillary channels have the same straight-line length. Individual flow paths in real porous media may have different actual lengths and straight-line distances. In this study, L₀ is used as the characteristic straight-line length of the equivalent pore-throat network in the adopted statistical model, rather than as a directly measured geometrical length for each capillary. Based on the fractal capillary tortuosity model, the actual flow-path length L_t can be related to the characteristic capillary radius r and the straight-line distance L₀ through a statistical scaling relationship [30,31]:

$$L_t\left(r\right)={\left(2r\right)}^{1-D_T} {L_0}^{D_T}$$

(4)

where D_T is the fractal dimension reflecting capillary tortuosity, L_t is the actual tortuous flow-path length of the equivalent capillary channel, and L₀ describes the straight-line distance for an equivalent capillary pathway. When the model is applied to the whole core sample, L₀ is treated as a representative characteristic length of the equivalent pore-throat network. Therefore, it should be interpreted statistically rather than as the identical length of all individual capillary channels. Here, r represents the effective size of the flow channel and should not be confused with L₀. The equivalent capillary is a simplified representation of the connected pore-throat network rather than an individual throat.

Considering the measurement scale as within a two-dimensional plane 1 < D_T < 2, in three-dimensional space 1 < D_T < 3, D_T = 1 indicates that the capillaries are in a straight-line state, D_T being greater indicates that the streamlines are more tortuous, D_T = 2 indicates the streamlines fill the two-dimensional plane, and D_T = 3 indicates that the streamlines fill the three-dimensional space.

If a fluid particle travels along the actual tortuous path L_t during a time interval Δt, its actual velocity can be expressed as v_t = L_t/Δt. The corresponding apparent velocity along the straight-line direction is v₀ = L₀/Δt. Therefore, the relationship between v_t and v₀ can be obtained from Equation (4):

$$v_t=D_T{\left({\displaystyle \frac{L_0}{2r}}\right)}^{D_T-1}{v}_0$$

(5)

where v₀ = dL₀/dt is the velocity of flow along a straight line, and v_t = dL_t/dt is the flow velocity along the actual streamline. Since D_T ≥ 1 and L₀ > 2r, it follows that v_t ≥ v₀.

Capillary tortuosity is usually defined as:

$$\tau ={\displaystyle \frac{L_t}{L_0}}={\displaystyle \frac{L_t\left(r\right)}{L_0}}={\left({\displaystyle \frac{L_0}{2r}}\right)}^{D_T-1}$$

(6)

Therefore, the fractal dimension of capillary tortuosity can be expressed as:

$$D_T=1+{\displaystyle \frac{\ln \tau }{\ln \left(\frac{L_0}{2\mathrm{r}}\right)}}$$

(7)

Considering the average flow properties in porous media, the fractal dimension of capillary tortuosity can be approximately expressed as:

$$D_T=1+{\displaystyle \frac{\ln {\tau }_{\mathrm{a}}}{\ln \left(\frac{L_0}{2{\mathrm{r}}_a}\right)}}$$

(8)

In Equations (6)–(8), τ and τ_a have different meanings. τ represents the tortuosity of an individual equivalent capillary channel and is defined as the ratio of the actual tortuous path length to the straight-line distance of that channel. In contrast, τ_a represents the apparent or average tortuosity factor of the porous medium. It is not the tortuosity of a specific capillary, but a macroscopic equivalent parameter calculated from porosity and pore-throat structural parameters. Therefore, Equation (8) should be regarded as an approximate statistical expression for the equivalent pore-throat network, rather than a direct substitution of a single-channel tortuosity into the fractal scaling relation. τ_a was calculated using the geometric tortuosity model reported in Ref. [32]. Although porosity (φ) is commonly expressed as a percentage, it should be converted into a decimal form during calculation.

Where τ_a is the plane tortuosity (the ratio of the actual length of the seepage channel to the apparent length (macroscopic distance) passing through the seepage medium), it is the apparent tortuosity factor calculated from porosity and pore-throat structural parameters, and 2r is the characteristic capillary diameter:

$${\tau }_a={\displaystyle \frac{1}{2}}\left[1+{\displaystyle \frac{1}{2}}\sqrt{1-\phi }+{\displaystyle \frac{\sqrt{1-\phi }\sqrt{{\left(\frac{1}{\sqrt{1-\phi }}-1\right)}^2+\frac{1}{4}}}{\left(1-\sqrt{1-\phi }\right)}}\right]$$

(9)

where $r_a={\displaystyle \frac{D_f{r}_{\min }}{D_f-1}}$, $L_0=\left[{\displaystyle \frac{1-\phi }{\phi }}{\displaystyle \frac{\pi D_f{r}_{\min }^2}{\left|2-D_f\right|}}\right]$.

Here, φ is expressed as a dimensionless fraction; r_min is the minimum pore-throat radius, μm; r_max is the maximum pore-throat radius, μm; and D_f refers to the mercury intrusion-derived pore-throat fractal parameter obtained from Equation (1).

2.2.3. X-Ray Diffraction (XRD)

XRD analysis was conducted using a high-resolution diffractometer, Model D8 AA25, manufactured by Bruker AXS GmbH (Karlsruhe, Germany), with a maximum power of 3 kW and a focal spot size of 0.4 × 12 mm. The experimental conditions were maintained at 25 °C and 40% humidity. The experimental procedures adhered to the latest standard, SY/T 5163-2018 (“X-Ray Diffraction Analysis Method for Clay Minerals and Common Non-clay Minerals in Sedimentary Rocks”) [33].

2.2.4. CO₂ Trapping and Storage Experiment

To characterize the capacity of tight sandstone cores to trap and retain CO₂ during pressure depletion, CO₂ residual trapping experiments were conducted in this study. The CO₂ residual trapping efficiency defined in this study represents the fraction of injected CO₂ retained in the core pore space after stepwise pressure depletion. This parameter should be regarded as a combined retention response rather than the contribution of a single trapping mechanism. Because dissolved CO₂, structurally retained CO₂, and capillary trapped CO₂ were not independently quantified in the present experiments, their individual contributions cannot be completely separated.

Nevertheless, under the present short-term core-flooding and pressure depletion conditions, the retained CO₂ is interpreted to be dominated by pore-throat scale capillary retention. This judgment is supported by three bases: first, the experimental duration is too short to form significant mineral trapping or dissolution equilibrium; second, the trapping efficiency shows a strong correlation with typical capillary-controlled structural parameters such as pore-throat ratio and fractal dimensions; and third, the limited dissolved CO₂ under short-term conditions cannot explain the large difference in trapping efficiency among samples. This interpretation is supported by the observed relationships between residual trapping efficiency and pore-throat structural parameters, such as average pore-throat ratio, pore-throat radius, and connectivity. Therefore, the term “CO₂ residual trapping efficiency” is used in this study as a comprehensive trapping index dominated by capillary retention.

After pretreatment, the core samples were vacuumed and saturated with simulated formation water. The system temperature was set to 105 °C to simulate reservoir conditions. The water-saturated core was flooded with oil at 0.01 mL/min to establish irreducible water saturation, and flooding was continued until continuous oil production was observed at the outlet. The core was then restored to its initial oil-saturated state and aged for 24 h.

CO₂ was injected into the intermediate container until the pressure reached 25 MPa. The core was mounted in the core holder, the apparatus was connected, the confining-pressure pump was set to follow-up mode to simulate overburden pressure, and the back-pressure valve was adjusted to 25 MPa. Continuous CO₂ injection was then performed until the outlet flow rate stabilized, after which the inlet was closed, and the retained CO₂ volume in the core was determined.

The outlet pressure was subsequently reduced stepwise to 20, 15, 10, and 5 MPa, and finally to atmospheric pressure, thereby simulating reservoir depletion. During this process, the produced CO₂ volume was recorded, and the CO₂ residual trapping efficiency at each depletion pressure was calculated. This procedure was used to evaluate the residual capillary trapping capacity of the microscopic pore-throat structure under different reduction pressure differentials. The specific experimental workflow is shown in Figure 1.

Before displacement, each water-saturated core was analyzed by NMR T₂ measurement to characterize the fluid occurrence state in pore space. It should be noted that mercury intrusion and NMR characterize pore properties from different perspectives: the former reflects the size of connected throats controlling seepage, while the latter reflects the volume distribution of all fluid-bearing pores, so they cannot be collectively referred to as the same pore-throat size distribution.

To quantitatively characterize the trapping and retention capacity of the core for CO₂ under different depletion-pressure conditions, the CO₂ residual trapping efficiency is defined in this study as shown in Equation (10):

$$E_{C{O}_2}={\displaystyle \frac{V_i-V_p}{V_i}}$$

(10)

where E_CO2 is the CO₂ residual trapping efficiency (%), V_i is the injected CO₂ volume (cm³), and V_p is the produced CO₂ volume (cm³). For convenience of calculation, the injected and produced CO₂ volumes during different CO₂ displacement processes were converted to the experimental conditions (25 MPa and 105 °C) for analysis.

3. Experimental Results and Discussion

3.1. Analysis of Experimental Results for CO₂ Storage

The residual trapping experiment was designed to simulate CO₂ flooding and production in a reservoir by progressively reducing the outlet pressure, thereby evaluating the core’s capacity to trap and retain CO₂ under different depletion pressures. The focus of this study is on analyzing the mechanisms and controlling factors of CO₂ residual trapping and storage.

Figure 2 shows the relationship between CO₂ residual trapping efficiency and depletion pressure. As illustrated in Figure 2, the CO₂ residual trapping efficiency of tight sandstone cores generally decreased with decreasing depletion pressure (outlet pressure), exhibiting a trend of an initially slow decline followed by a rapid decline. At a depletion pressure of 25 MPa, the outlet pressure was equal to the injection pressure, resulting in a production pressure differential of zero. Under this condition, CO₂ remained in a closed and trapped state within the core, and no pressure depletion or production occurred. Therefore, the CO₂ residual trapping efficiency at this stage was defined as 100%. The abrupt decline mainly occurred as the pressure approached the critical state of CO₂. When the pressure dropped below the supercritical pressure of CO₂ (7.38 MPa), CO₂ transformed from a supercritical state to a gaseous state, accompanied by significant volume expansion. As a result, gas production increased rapidly, leading to a sharp decrease in the residual trapping efficiency. This occurs because once CO₂ changes from a supercritical state to a gaseous state, its volume expands rapidly, causing a large amount of CO₂ to be produced quickly from the outlet. When CO₂ remained in the supercritical state, the residual trapping efficiency was higher than 62.00%; however, when the pressure fell below the supercritical-pressure threshold, the residual trapping efficiency dropped to below 38.00%.

From a thermodynamic perspective, the effect of depletion pressure on CO₂ residual trapping does not act independently; rather, it is associated with changes in CO₂ density, compressibility, viscosity, and formation volume factor during pressure decline. At relatively high depletion pressures, CO₂ is more strongly compressed, exhibiting a higher density and a lower tendency for volumetric expansion, which facilitates its retention within pore-throat spaces. As depletion pressure decreases, CO₂ density gradually decreases, while its compressibility and volumetric expansion tendency increase. In particular, when the pressure approaches or falls below the supercritical pressure of CO₂, the enhanced expansion capacity enables CO₂ to more readily overcome capillary resistance and be produced along pore-throat pathways. Therefore, the rapid decrease in CO₂ residual trapping efficiency under low depletion-pressure conditions results from the combined effects of CO₂ phase-state evolution, density reduction, volumetric expansion, and capillary retention within the pore-throat network.

These results indicate that maintaining the pressure above the supercritical threshold of CO₂ is favorable for CO₂ residual trapping and storage. Depletion pressures of 15 and 10 MPa may represent typical bottom-hole flowing pressures during the middle stage of production. Under these conditions, the formation pressure remains above the supercritical CO₂ pressure, resulting in relatively high CO₂ residual trapping efficiencies. The average CO₂ trapping efficiencies of the ten core samples were 86.11% and 73.86% at 15 and 10 MPa, respectively. In the late stage of oil well production, when the pressure declined to 5 MPa, the average CO₂ trapping efficiency decreased to 26.88%. These results suggest that, in tight sandstone reservoirs, maintaining the formation pressure above the supercritical pressure of CO₂ is more conducive to enhancing the residual trapping capacity of CO₂. Therefore, depletion pressure primarily governs the release or retention of CO₂ through CO₂ phase behavior and volumetric expansion, whereas the pore-throat structure controls the microscopic capillary conditions governing CO₂ retention. The coupling between these two aspects is further discussed in the following sections.

3.2. Analysis of Influencing Factors on CO₂ Storage

CO₂ residual trapping, also referred to as capillary trapping, is generally associated with the microscopic pore structure and pore-throat connectivity within the core. At the microscopic scale, capillary force represents an important mechanism associated with CO₂ retention in reservoirs or saline aquifers. Because the pore structure within tight sandstone reservoirs is highly complex and interrelated, permeability can vary considerably even when porosity is approximately the same. Therefore, reservoir pore structure cannot be adequately characterized solely by porosity and permeability. Accordingly, the reservoir quality index (RQI) was introduced to comprehensively analyze the relationship between core petrophysical properties and CO₂ trapping efficiency, and its expression is given as $\sqrt{{\displaystyle \frac{K}{\phi }}}$. The CO₂ residual trapping efficiency discussed in this study mainly reflects the response of CO₂ retention to capillary pressure during pressure depletion, and is closely related to pore-throat size, pore-throat connectivity, and the complexity of flow pathways.

Permeability, porosity, reservoir quality index (RQI), and average pore-throat ratio are petrophysical parameters that reflect the size and distribution of microscopic pore-throat structures in the core. On this basis, the average pore-throat ratios of ten core samples were obtained through constant-rate mercury intrusion experiments, and the correlations between CO₂ trapping efficiency under a pressure differential of 10 MPa and permeability, porosity, reservoir quality index, and average pore-throat ratio were analyzed (Figure 3).

As shown in Figure 3, the CO₂ residual trapping efficiency exhibits a weak negative correlation with permeability and porosity. In general, smaller pore-throat sizes or poorer pore connectivity tend to correspond to lower permeability and porosity, which may be more favorable for CO₂ retention under the experimental conditions of this study. During production, lower permeability and porosity are associated with higher capillary pressure, under which only a small fraction of the CO₂ can be produced. Moreover, the smaller the pore-throat size or the more complex the pore-throat connectivity, the greater the amount of CO₂ retained in the core under the experimental conditions of this study tended to be. Therefore, within the tested samples, lower core permeability and porosity tended to correspond to higher CO₂ residual trapping efficiency. RQI also shows a negative correlation with CO₂ trapping efficiency. This is because a higher reservoir quality index generally corresponds to higher permeability, better core petrophysical properties, and improved pore-radius connectivity. Consequently, cores with higher RQI values generally indicate better effective connectivity and larger effective flow channels, which may reduce capillary retention under the experimental conditions of this study. The CO₂ residual trapping efficiency is positively correlated with the average pore-throat ratio, and the correlation coefficient (R² = 0.6893) is higher than that of the fitted relationships between CO₂ residual trapping efficiency and permeability, porosity, and reservoir quality index. The average pore-throat ratio can be used as an indicative parameter for characterizing pore-throat matching and connectivity. Overall, the ten core samples exhibit a “large-pore, fine-throat” pattern, with relatively large pore spaces but very narrow throats connecting the pores, corresponding to relatively high capillary pressure. Therefore, for reservoirs characterized by a “large-pore, fine-throat” structure, a higher average pore-throat ratio tended to be associated with stronger CO₂ residual trapping under the experimental conditions of this study. The average pore-throat ratio is a parameter influenced by multiple factors, including core permeability, porosity, tortuosity, and throat radius, and can therefore better reflect the effect on CO₂ residual trapping and storage. For tight sandstone reservoirs, a larger average pore-throat ratio indicates that, after CO₂ is injected into the formation, it is more strongly affected by capillary pressure and is therefore less likely to be produced.

The residual trapping efficiency measured in this study should be understood as a retained fraction of injected CO₂ after pressure depletion, rather than as an absolute storage capacity indicator. This distinction is important for interpreting the negative relationships between permeability/porosity and residual trapping efficiency. In low-permeability sandstone cores, smaller throats and poorer connectivity increase capillary resistance and reduce CO₂ mobility during depletion. Consequently, although such rocks may have lower available pore volume and poorer injectivity, a higher fraction of the injected CO₂ may remain trapped after pressure reduction. Therefore, the observed trend reflects stronger capillary-dominated retention under core-scale experimental conditions and should not be generalized as evidence that low-porosity and low-permeability reservoirs have higher total CO₂ storage capacity.

It should be emphasized that CO₂ residual trapping efficiency is a ratio index reflecting the retention proportion of injected CO₂, which is essentially different from the total CO₂ storage capacity as a volume index. The negative correlation is dominated by capillary resistance: smaller throats generate higher capillary force, making it more difficult for CO₂ to overcome the resistance and be produced during pressure depletion, thus resulting in a higher retention ratio. In contrast, cores with higher porosity and permeability have larger total pore volume and higher absolute storage capacity, but the retention ratio after depletion is lower due to better flow connectivity. This trend does not contradict the conventional understanding of storage capacity, as they describe different dimensions of reservoir storage performance.

4. Analysis of CO₂ Capillary Trapping Mechanism

CO₂ residual trapping in tight sandstone reservoirs is essentially the result of the combined effects of reservoir microstructure, tortuous flow pathways, and pressure conditions. The preceding experiments showed that different samples exhibited significant differences in pore-throat distribution, average pore-throat ratio, and CO₂ residual trapping efficiency. At the same time, as the depletion pressure decreased, especially when the pressure approached or fell below the supercritical pressure of CO₂, the CO₂ residual trapping efficiency declined markedly. This indicates that CO₂ residual trapping is controlled not only by pore-throat structure, but also by phase changes during pressure depletion. On this basis, this study integrates the fractal dimension derived from constant-rate mercury intrusion (D_f), the fractal dimension of capillary tortuosity (D_T), NMR results, and whole-rock mineral composition data from XRD to analyze the mechanisms of CO₂ residual trapping in tight sandstone reservoirs.

4.1. Fractal Characterization of Pore-Throat Structural Complexity

4.1.1. Fractal Results of Constant-Rate Mercury Intrusion

The fractal fitting results of constant-rate mercury intrusion for 10 core samples are shown in Figure 4. As shown in Figure 4, the fractal dimension D_f ranges from 2.4432 to 2.8096, with an average value of 2.6399, indicating a good correlation. After considering the inverse relationship between capillary pressure and pore-throat radius, a higher D_f can be interpreted as indicating greater pore-throat size heterogeneity. In the tested samples, larger D_f values generally correspond to a relatively higher proportion of micro- and small-scale pore-throat elements and a lower proportion of medium- and large-scale pore-throat elements, resulting in a more uneven pore-throat distribution and a more complex pore-throat structure. Consequently, CO₂ must overcome greater capillary pressure during migration and is more likely to be retained and trapped by capillary forces, thereby forming a capillary trapping effect. Therefore, within the tested samples, a larger D_f indicates stronger pore-throat heterogeneity and may correspond to higher capillary trapping potential for CO₂. However, D_f should be interpreted as a statistical structural indicator derived from mercury intrusion measurements rather than a direct representation of the entire reservoir pore network. Because constant-rate mercury intrusion mainly characterizes connected pore-throat systems involved in non-wetting phase invasion, the obtained D_f primarily reflects pore-throat heterogeneity, capillary-entry characteristics, and flow-path complexity under experimental conditions.

The fractal theory of constant-rate mercury intrusion indicates that a higher D_f value represents a more complex pore-throat structure and stronger heterogeneity. To further support this geological interpretation, NMR T₂ spectra were used as an independent method to characterize the pore-throat size distribution. It should be noted that the NMR T₂ spectra were not used to directly verify the mathematical power-law relationship of the fractal model. Instead, they were used to examine whether the pore-size distribution characteristics inferred from the fractal dimension D_f, such as the relative development of micropores and small pore-throat elements and the degree of pore-throat heterogeneity, were consistent with the NMR response characteristics.

According to the principles of NMR, a longer relaxation time corresponds to a larger pore size. Based on the NMR results, the pore system was divided into four intervals [34]: the micropore interval (relaxation time < 1 ms), small-pore interval (1 ms < relaxation time < 10 ms), mesopore interval (10 ms < relaxation time < 100 ms), and macropore interval (relaxation time > 100 ms).

The ten core samples used in the experiment were derived from four different stratigraphic intervals. Specifically, cores No. 1, 2, 3, and 4 were taken from the same interval; core No. 5 was taken from another interval; cores No. 6 and 7 were obtained from the same interval; and cores No. 8, 9, and 10 were collected from the same interval. The T₂ spectra of cores from the same stratigraphic interval were plotted together in a single figure to analyze the pore-throat distribution characteristics of the cores, and the results are shown in Figure 5.

As shown in Figure 5, the pore-throat distributions of core samples from the same stratigraphic interval are relatively similar. Cores No. 1, 2, 3, and 4 exhibit relatively well-developed pore-throat systems and display a bimodal distribution dominated by small and medium pores, indicating good pore-throat connectivity. In contrast, core No. 5 shows the poorest pore-throat development, being characterized mainly by a single peak with an indistinct bimodal pattern, dominated by micropores and small pores with only a small proportion of medium pores, suggesting poor pore-throat connectivity. The other five cores (No. 6, 7, 8, 9, and 10) are intermediate, showing a bimodal distribution with the left peak higher than the right peak; that is, micropores and small pores are dominant, with abundances much greater than those of medium and large pores.

Differences in pore-throat distribution among cores from different stratigraphic intervals lead to corresponding differences in CO₂ residual trapping. Taking a pressure differential of 10 MPa as an example, cores No. 1, 2, 3, and 4, which have the best-developed pore-throat systems, exhibit a CO₂ residual trapping efficiency of 64.5%, whereas core No. 5, which has the poorest pore-throat development, shows a much higher CO₂ residual trapping efficiency of 87%. The trapping efficiencies of the other two stratigraphic intervals are intermediate, at 75.3% and 81.0%, respectively.

These results suggest that microscopic pore-throat distribution is closely related to CO₂ residual trapping in the tested samples. Well-developed pore-throat systems or more uniform pore-size distributions are less favorable for CO₂ residual trapping, whereas poorer pore-throat development or more complex pore-size distributions are more conducive to CO₂ residual trapping. For tight sandstone reservoirs, smaller pore-throat sizes and more complex pore-throat distributions are generally more favorable for CO₂ residual trapping.

4.1.2. Fractal Results of Capillary Tortuosity

As shown in

Table 3. Statistical table of fractal dimensions of core samples.

Core Sample	Df	φ/%	rmax/μm	rmin/μm	τa	DT
1	2.6094	14.62	2.142	0.146	3.9174	1.1999
2	2.4432	15.02	2.168	0.154	3.8900	1.1932
3	2.5560	14.71	2.158	0.148	3.9086	1.1977
4	2.5309	14.83	2.161	0.152	3.8996	1.1967
5	2.8096	13.73	1.826	0.116	3.9892	1.2156
6	2.7076	13.93	1.984	0.120	3.9804	1.2080
7	2.7352	14.11	1.943	0.118	3.9535	1.2094
8	2.6485	14.51	2.129	0.141	3.9212	1.2013
9	2.6595	14.44	2.124	0.136	3.9272	1.2018
10	2.6995	14.40	2.120	0.134	3.9293	1.2029
Mean	2.6400	14.43	2.076	0.137	3.9320	1.2030
SD	0.109	0.42	0.115	0.014	0.033	0.0060

, the D_T values range from 1.1932 to 1.2156, with an average of 1.2026. In the context of geological CO₂ storage, D_T, as a fractal dimension characterizing capillary tortuosity, is closely related to the capillary radius.

It should be noted that D_T does not directly change capillary pressure when the characteristic throat radius remains unchanged. Capillary pressure is mainly controlled by pore-throat radius, interfacial tension, and contact angle. This study is mainly related to the tortuosity of the equivalent flow pathway and the effective connectivity of the pore-throat network. A higher D_T indicates that the equivalent flow path is longer and more tortuous under the adopted model, which may reduce the continuity of CO₂ migration during pressure depletion. Therefore, D_T should be interpreted as a derived structural indicator of flow-path tortuosity rather than an independent parameter directly controlling CO₂ residual trapping. Therefore, D_T can serve as an indicative parameter reflecting the complexity of flow pathways and indirectly characterizing the potential for CO₂ trapping. Similar to D_f, D_T reflects the geometric constraints imposed by the pore-throat network on fluid flow, and its mechanistic significance lies in revealing the influence of microscopic connectivity and flow-path tortuosity on CO₂ residual trapping.

In summary, D_f and D_T characterize the microscopic structural features of the reservoir from two different dimensions, namely pore-throat scale heterogeneity and flow-path tortuosity, respectively. The former mainly reflects the capillary pressure corresponding to mercury saturation and the differences in pore-throat scale, whereas the latter is primarily associated with fluid migration path length and effective connectivity. Together, they provide complementary structural indicators for interpreting CO₂ migration and residual retention behavior during pressure depletion. However, they should not be interpreted as independent controlling variables.

4.2. The Relationship Between Fractal Dimension and Pore Structure

To some extent, fractal dimensions reflect the roughness of the sandstone pore surface and the complexity of the pore structure (as shown in Figure 6). Because D_T is derived from D_f, porosity, and characteristic pore-throat parameters in the adopted capillary-tortuosity model, the relationship between D_f and D_T should not be interpreted as an independent statistical correlation. Instead, their consistent variation reflects the internal structure of the calculation model and the coupled response of pore-throat heterogeneity and flow-path tortuosity to the same pore-throat system.

The fractal dimensions of sandstone samples from the four stratigraphic intervals in the study area also show apparent correlations with pore-structure parameters within the tested sample set (

Table 4. Correlation analysis of pore structure parameters and fractal dimensions.

Pore Structure Parameters	Correlation Between Value Vectors
	Df	DT	Maximum Pore-Throat Radius/μm	Minimum Pore-Throat Radius/μm	Average Pore-Throat Ratio	Average Pore Radius/μm	Average Throat Radius/μm
Df	1
DT	0.9118	1
Maximum pore-throat radius/μm	−0.6807	−0.9107	1
Minimum pore-throat radius/μm	−0.861	−0.9272	0.8379	1
Average pore-throat ratio	0.8428	0.8365	−0.7063	−0.8499	1
Average pore radius/μm	−0.9736	−0.896	0.6703	0.8469	−0.7908	1
Average throat radius/μm	−0.9463	−0.9827	0.8537	0.9584	−0.8738	0.9264	1

Note: Since D_T is a derived parameter calculated from D_f, porosity, and pore-throat characteristic parameters, the correlation between D_f and D_T is a mathematical result of the theoretical model and cannot be interpreted as an independent statistical correlation or causal relationship between two separate geological controlling factors.

). Specifically, both D_f and D_T exhibit apparent positive correlations with the average pore-throat ratio, with R² values of 0.8428 and 0.8365, respectively. In contrast, they show significant negative correlations with the maximum and minimum pore-throat radii, pore radii, and throat radii. In the tested samples, smaller average pore radius, average throat radius, and pore-throat radius generally corresponded to larger fractal dimensions.

Mechanistically, as the average pore-throat ratio increases, the reservoir tends to exhibit a “small-pore, fine-throat” structure, characterized by a more uneven throat-size distribution and greater differences in pore-throat size. Relatively higher D_f and D_T values reflect such structural features. Although this type of reservoir can effectively store CO₂, the fine pore throats and complex flow pathways prevent CO₂ from continuously migrating by overcoming capillary pressure during pressure depletion, making it more likely to remain trapped within the pore space.

In contrast, when the pore radius and throat radius are larger, and the pore-throat matching is more uniform, preferential flow channels are more likely to develop within the reservoir, allowing CO₂ to migrate and be produced more easily, thereby resulting in a relatively weaker trapping capacity. Thus, D_f and D_T do not directly control CO₂ residual trapping and storage; rather, they serve as comprehensive characterization parameters of pore-throat structural complexity, flow-path tortuosity, and heterogeneity. These structural features may jointly influence capillary retention and CO₂ mobility during pressure depletion.

D_f and D_T are integrated structural descriptors rather than independent controlling variables. They reflect the combined effects of pore-throat size distribution, throat constriction, surface roughness, and flow-path tortuosity, which together influence capillary retention and CO₂ mobility during pressure depletion. D_T is a derived parameter calculated from porosity and characteristic pore-throat parameters. Therefore, it should not be regarded as an independent factor that directly controls CO₂ residual trapping. Instead, D_T is used as an auxiliary parameter to describe the tortuosity of seepage pathways. Accordingly, CO₂ residual trapping is mainly associated with pore-throat radius, pore-throat ratio, capillary pressure, and effective connectivity, while D_T serves as a supplementary indicator for characterizing the complexity of seepage pathways.

4.3. Influence of Mineral Composition on Fractal Dimension and Pore-Throat Complexity

One core sample from each of the four stratigraphic intervals in the study area was selected for whole-rock X-ray diffraction (XRD) analysis, and the mineral compositions are presented in

Table 5. Statistical table of mineral composition content of sandstone samples.

Sampling Depth/m	Coring Horizon	Quartz	K-Feldspar	Plagioclase	Calcite	Dolomite	Clay Minerals
3998.50	M1	67.20%	4.70%	14.40%	0	0	13.60%
4004.00	M2	31.30%	6.10%	21.40%	0	7.8	33.40%
4053.10	M3	59.40%	6.50%	18.20%	0	0	15.80%
4230.90	M4	41.60%	3.20%	17.80%	7.80%	0	29.50%

and Figure 7. As shown in Table 5, the sandstone is composed predominantly of quartz and clay minerals. Overall, with increasing depth, the mineral composition of the sandstone samples exhibits a trade-off trend characterized by increasing quartz content and a relative decrease in clay mineral content. Specifically, the quartz content ranges from 31.3% to 67.2%, with an average of 49.88%, whereas the clay mineral content ranges from 13.6% to 33.4%, with an average of 23.08%.

Combined with the foregoing fractal analysis, the XRD results provide a qualitative basis for interpreting the possible mineralogical influence on pore-throat structural complexity. In the present measurements, samples with higher quartz contents generally exhibited lower fractal dimensions and a relatively more uniform pore-throat distribution. This phenomenon may be related to the relatively strong mechanical stability of quartz during burial compaction and diagenesis, which helps maintain more regular intergranular pore geometry. In contrast, higher clay mineral contents may be associated with clay filling, throat narrowing, poorer local connectivity, and stronger pore-throat heterogeneity, which are reflected by relatively higher fractal dimensions. Therefore, mineral composition should not be regarded as a single direct controlling factor of fractal dimensions. Rather, it may indirectly influence fractal characteristics by modifying the present pore-throat geometry, throat constriction, pore-surface roughness, and local connectivity. Consequently, a higher quartz content is often associated with lower pore-throat structural complexity. In contrast, an increase in clay mineral content generally leads to narrower pore throats and poorer local connectivity, thereby enlarging pore-throat size differences and making fluid flow paths more tortuous, which is ultimately reflected by higher fractal dimensions.

For minerals such as feldspar, calcite, and dolomite, the XRD results obtained in this study indicate that their contents vary among different stratigraphic intervals. In particular, the M2 interval with only one sample provides only reference-level information for stratigraphic comparison, and cannot support strong quantitative inference of interlayer mineral differences. Given the limited number of samples and the constraints of the analytical methods employed, it is not yet possible to quantitatively distinguish the respective contributions of these minerals to the fractal dimension. Therefore, they are regarded in this study as auxiliary factors that may affect pore-throat heterogeneity, and no stronger inference can be made.

Within the tested samples, higher fractal dimensions, smaller throat radii, and stronger pore-throat heterogeneity tended to correspond to higher CO₂ residual trapping efficiency. Conversely, samples with simpler pore-throat structures and better connectivity tended to allow CO₂ to migrate and be produced more easily, resulting in relatively lower trapping efficiency. Conversely, when the pore-throat structure is simpler and connectivity is better, CO₂ can migrate and be produced more easily, resulting in a lower trapping capacity.

As shown in Figure 8, both D_f and D_T exhibit weak negative correlations with quartz content and weak positive correlations with clay mineral content, further indicating that rock minerals are not the sole factors controlling fractal dimensions, but rather indirect factors that influence them by modifying pore-throat structural complexity and connectivity.

To further illustrate the influence of mineral composition on pore-throat structural complexity, the microscopic morphological characteristics before and after the CO₂–water–oil–rock reaction were analyzed in combination, as shown in Figure 9. Distinct changes in core surface morphology were observed before and after the reaction. After the reaction, some pore walls became rougher and showed local dissolution, precipitation, or surface reconstruction after the CO₂–water–oil–rock reaction, indicating that fluid mineral interactions may modify the microscopic geometric characteristics of the pore surface. Considering that fractal dimensions can characterize the complexity and heterogeneity of pore-throat structures, such changes in surface roughness and local connectivity may further affect the fractal characteristics of the reservoir.

As shown in Figure 10, the surface morphologies of feldspar, calcite, dolomite, and kaolinite were altered after the CO₂–water–oil–rock reaction. Different minerals exhibited precipitation, dissolution, and surface reconstruction following the reaction, thereby modifying the local connectivity of the pore-throat structure. Combined with the mineral compositions of different stratigraphic intervals listed in Table 5, these results indicate that mineral composition is not a single direct controlling factor of fractal dimensions; rather, it may influence fractal dimensions indirectly by modifying the present pore-throat size distribution, pore surface roughness, and local pore-throat connectivity through mineral filling, dissolution, precipitation, and fluid–rock interactions. It should be noted that this study only quantifies the total clay mineral content and does not distinguish the types of clay minerals such as illite and kaolinite. The differential effects of different clay types on pore structure and fractal characteristics need to be studied further.

4.4. CO₂ Residual Trapping Mechanism Revealed by Fractal Dimensions

CO₂ is mainly retained in sandstone reservoirs in the form of capillary trapping, and pore-structure parameters such as throat radius and pore radius can effectively reflect the trapping capacity of sandstone reservoirs for CO₂. To further clarify the mechanistic role of fractal dimensions in the process of CO₂ residual trapping, this section, in conjunction with Figure 11, systematically analyzes the significance of the constant-rate mercury intrusion fractal dimension (D_f) and the capillary tortuosity fractal dimension (D_T) in characterizing CO₂ residual trapping in low-permeability sandstone reservoirs, and further explores the regulatory effect of pressure conditions on trapping capacity. It should be noted that D_f and D_T do not directly control CO₂ residual trapping capacity. Instead, they provide complementary structural indicators for interpreting the microscopic conditions associated with capillary trapping. Specifically, D_f mainly reflects pore-throat size heterogeneity and the complexity of pore-throat distribution, whereas D_T provides a derived description of equivalent flow-path tortuosity and effective connectivity. Therefore, higher D_f and D_T values should be interpreted as indicators of more complex pore-throat structures and more tortuous migration pathways, rather than as independent controlling variables.

As shown in Figure 12, for the tested samples, D_f ranges from 2.4432 to 2.8096, whereas D_T ranges from 1.1932 to 1.2156. These values indicate that the tested low-permeability sandstone cores generally exhibit strong pore-throat heterogeneity and a certain degree of equivalent flow-path tortuosity. Compared with a single fractal parameter, the dual-fractal system significantly improves the interpretability of CO₂ trapping behavior. The fitting results show that the R² of unary linear fitting between a single D_f and trapping efficiency is only 0.59, while the R² of binary linear fitting with both D_f and D_T reaches 0.76. This is because a single fractal parameter can only reflect the static geometric heterogeneity of pore throats, while the combination of two parameters covers both capillary resistance amplitude and migration path tortuosity, and builds a complete logical chain from static pore structure to dynamic trapping behavior. Specifically, higher D_f values indicate more complex pore-throat size distributions, a higher proportion of fine throats, and stronger microscopic heterogeneity. Higher D_T values indicate longer and more tortuous equivalent seepage pathways in the adopted model. These structural characteristics may restrict continuous CO₂ migration during pressure depletion and are therefore associated with higher capillary retention potential in the tested samples.

The NMR results further indicate that the pore-throat distribution characteristics vary significantly among samples from different stratigraphic intervals, and these differences are associated with variations in CO₂ residual trapping efficiency. Taking the depletion pressure of 10 MPa as an example, the intervals with poorly developed pore-throat systems dominated by micropores and small pores exhibit a CO₂ residual trapping efficiency of up to 87%, whereas the intervals with better-developed pore-throat systems and relatively stronger connectivity show a much lower value of only 64.5%; the remaining intervals range from 75.3% to 81.0%. These results are consistent with the patterns revealed by the fractal analysis.

In addition, pressure conditions strongly influence the manifestation of capillary trapping during pressure depletion. When the depletion pressure remains higher than the critical pressure range of CO₂, CO₂ maintains a relatively dense state and is less prone to volumetric expansion, which is favorable for its retention in confined pore-throat spaces. When the depletion pressure approaches or falls below the critical pressure range, CO₂ density decreases, and its expansion tendency increases, leading to enhanced CO₂ production and lower residual trapping efficiency. Therefore, the final residual trapping efficiency should be understood as the coupled result of microscopic pore-throat structure and CO₂ phase-state evolution during pressure depletion.

Overall, the dominant mechanism controlling CO₂ residual trapping in low-permeability sandstone reservoirs can be summarized as the combined effect of pore-throat complexity, capillary pressure, and CO₂ retention during pressure depletion (Figure 12). Figure 12 further illustrates that the relationship between fractal parameters and CO₂ residual trapping does not occur independently, but is coupled with CO₂ phase-state changes during pressure depletion. In the tested samples, higher D_f values indicate stronger pore-throat heterogeneity, whereas higher D_T values indicate more tortuous equivalent flow pathways. These structural indicators are associated with stronger capillary retention potential. However, whether this potential can be maintained during depletion is strongly influenced by pressure conditions. When reservoir pressure remains above the critical-pressure range of CO₂, CO₂ tends to remain in a relatively high density state, which is favorable for residual retention. In contrast, when pressure approaches or falls below the critical-pressure range, CO₂ expansion and production increase, reducing residual trapping efficiency. Therefore, D_f and D_T should be used as structural indicators rather than independent prediction parameters for CO₂ residual trapping capacity.

From the perspective of field engineering application, three operational suggestions are put forward based on the experimental findings: first, control the flowing bottom-hole pressure above the supercritical threshold of 7.38 MPa during production to avoid CO₂ phase transition and massive gas escape; second, adopt stepwise slow depressurization to prevent the sharp volume expansion of CO₂ caused by a rapid pressure drop; and third, implement stratified injection–production and appropriate formation energy supplementation for layers with good connectivity, to balance oil recovery improvement and the CO₂ retention effect.

4.5. Limitations and Outlook

• This study has clear applicable scope and inherent limitations. The dual fractal proposed in this paper applies to continental tight sandstone oil reservoirs at a temperature of approximately 105 °C and pressures ranging from 0 to 25 MPa, targeting short-term carbon dioxide flooding and pressure depletion development processes. Nevertheless, this model cannot be directly extended to fractured oil reservoirs, shale oil reservoirs, high-permeability oil reservoirs, or long-term geological sequestration scenarios spanning millions of years. In terms of experimental conditions, restricted by the limited number of core samples and short duration of flooding experiments, quantitative differentiation between dissolution trapping and mineral trapping cannot be achieved. Meanwhile, constant-rate mercury injection can only characterize connected pore throats and hardly identify isolated micropores and microfractures. From a theoretical perspective, the D_T tortuosity model is established based on the statistical self-similarity assumption of equivalent capillary networks. When the reservoir pore system deviates from self-similar characteristics, D_T can only serve as an equivalent dimensionless parameter for characterizing the complexity of fluid migration paths. Expanding the core sample size and supplementing parallel cores for each stratigraphic interval (especially the M2 interval) would improve the statistical robustness of the conclusions. Meanwhile, fine identification of clay mineral types (illite, kaolinite, smectite, etc.) would have to be performed to quantitatively analyze the differential effects of various clay components on pore-throat heterogeneity and fractal characteristics.
• Future work will be carried out based on four aspects: expanding the core sample size to improve the universality of conclusions; introducing micro-CT and digital-rock technology to directly verify the fractal scaling law of pore structure; carrying out long-term CO₂–water–rock reaction experiments to distinguish the contributions of different trapping mechanisms; and establishing reservoir-scale numerical simulation models to verify the field application potential of the proposed dual-fractal trapping mechanism. Follow-up studies should conduct multivariate regression, piecewise pressure regression and interaction term tests based on expanded sample sizes, compare the independent contributions and joint effects of pressure, pore-throat heterogeneity and tortuosity parameters, and evaluate model stability through leave-one-core-out cross-validation, independent-sample validation and uncertainty analysis. In addition, further consideration should be given to wettability, capillary pressure, variations in CO₂ density and viscosity, CO₂–water–rock reactions, as well as long-term dissolution and mineralization processes, so as to establish a multiscale evaluation system covering pore-scale structures, core-scale migration and reservoir-scale storage safety.

5. Conclusions

• Within the tested low-permeability sandstone cores, CO₂ residual trapping efficiency was closely associated with pressure conditions and pore-throat structure. Higher pressure above the supercritical threshold of CO₂ and a larger average pore-throat ratio tended to correspond to higher residual trapping efficiency, whereas better pore-throat development, a more uniform pore-throat size distribution, and stronger connectivity were generally associated with lower residual trapping efficiency. This suggests that pressure maintenance during production is important for improving CO₂ retention, especially in capillary-trapping-dominated low-permeability sandstone reservoirs.
• Overall, mineral composition alone was insufficient to explain the variation in fractal dimensions in the tested low-permeability sandstone samples. Instead, it exerted an indirect influence by modifying pore-throat structural complexity, flow capacity, and connectivity. Among the major minerals, quartz shows a weak negative correlation with fractal dimension, whereas clay minerals show a weak positive correlation, while the effects of feldspar, calcite, and dolomite remain difficult to quantify based on the current XRD data.
• The results indicate that the fractal dimensions of the tested low-permeability sandstone samples are closely related to pore-throat parameters. Both D_f and D_T showed apparent negative correlations with the maximum and minimum pore-throat radius, pore radius, and throat radius, suggesting that, in the tested samples, an increasing fractal dimension reflects greater pore structure complexity, poorer flow capacity, and stronger heterogeneity. Within the scope of this study, a higher fractal dimension tended to correspond to stronger capillary trapping potential and higher CO₂ residual trapping efficiency.
• Overall, a mechanistic framework coupling dual-fractal parameters with pressure conditions is proposed for interpreting CO₂ residual trapping. D_f and D_T, respectively, characterize pore-throat heterogeneity and flow-path tortuosity, and together provide useful microscopic indicators for evaluating residual trapping potential. From an engineering perspective, intervals with relatively high D_f, high D_T, large average pore-throat ratio, low RQI, small throat radius, and pressure maintained above the critical pressure range of CO₂ may be preferential targets for capillary-dominated CO₂ residual trapping. However, intervals with better connectivity and higher RQI may have better injectivity but weaker residual trapping capacity.
• It should also be noted that the proposed framework is based on controlled core-scale experiments. Its application to field-scale CO₂ storage should consider reservoir heterogeneity, fracture development, injection–production dynamics, gravity segregation, and long-term geochemical reactions, and should be further validated by numerical simulation and field data.