Influence of Reservoir Pore-Throat Structure Heterogeneity on Water-Flooding Seepage: A Case Study of Yanchang Formation in Ordos Basin

Abstract

The microscopic pore-throat structure of low-porosity and ultralow permeability sandstone reservoirs controls the seepage characteristics, which directly affects the water injection development efficiency of oilfields. Different from typical tight sandstone reservoirs, macropores and mesopores are more developed in the pore-throat structure of this type of reservoir, which changes the dominance of micropores over seepage capacity. Based on the full-range pore-throat structure characterization method and fractal theory, many experimental methods are used to study the influence of the microscopic pore-throat structure over the seepage characteristics in the Chang 9 reservoir in the Yanchang Formation of the Ordos Basin. The results of 12 typical samples show that the pore-throat structure has multifractal characteristics, and the occurrence degree of movable fluid and seepage capacity vary greatly, showing strong microscopic heterogeneity. Following characterization of the full-range pore-throat structure, the relative proportion of macropores and mesopores determines the physical properties of the reservoir. The pore-throat scale and structural heterogeneity have a significant impact on porosity, while the pore-throat structure connectivity has a crucial impact on permeability. Quartz provides resistance to compaction and preserves more primary pores. Additionally, the relationship between clay minerals and physical properties is not significant. Only illite and I/S mixed layers have a slight effect on permeability reduction. Furthermore, laumontite cementation is the key factor in the destruction of the pore-throat structure. Porosity has a significant effect on movable fluid occurrence and is more closely related to the two-phase seepage. Permeability controls the oil displacement efficiency in the anhydrous period, and porosity controls the oil displacement efficiency in the final period. The fractal dimension has some significant controls on the pore-throat structure, which are reflected in the fact that the higher the homogeneity of macropores is and the higher the heterogeneity of mesopores and micropores is, the better the reservoir development will be. In particular, the degree of macropore development guarantees reservoir quality. The control of the fractal dimension on the seepage capacity is complex, especially for mesopores and micropores; the higher the degree of heterogeneity is, the stronger the seepage capacity will be. The occurrence of movable fluid is significantly affected by the scale and heterogeneity of the pore-throat structure, which is reflected as stronger heterogeneity of the pore-throat structure and poorer relative seepage capacity.

1. Introduction

As the second largest sedimentary basin in China, the Ordos Basin has attracted increasing attention due to its rich unconventional oil and gas resources [1]. During the depositional period of the Upper Triassic Yanchang Formation, a complete set of sandstone reservoirs with extremely low reservoir properties and tightness developed [2]. After years of exploration and development studies, it was confirmed that the microscopic pore structure is a key factor affecting the storage capacity and seepage capacity of tight reservoirs and directly determines oil and gas recovery [3]. The seepage mechanism evaluates the fluid flow ability in the pore medium of the reservoir, which directly affects the water-flooding development effect of the oilfield. Therefore, quantitative characterization of the pore-throat structure and its strong microscopic heterogeneity is an important means to explore the quality of unconventional reservoirs. For unconventional reservoirs with relatively poor reservoir quality, there is typically poor correspondence between storage capacity and seepage capacity [4], which is characterized by a poor correlation between porosity and permeability parameters. Therefore, the evaluation of seepage capacity is the key to reservoir productivity and evaluation [5,6].

In the accumulation or development stage of low-permeability reservoirs, the mutual displacement between multiple porous media needs to go through a series of alternately combined pores and throats [7], and this micropore structure is characterized by a curved pore system, small pore radius, poor connectivity and strong heterogeneity [8]. Therefore, the complex pore structure plays a major role in controlling reservoir characteristics and seepage mechanisms [9]. The geometric shape of the pore-throat structure affects the heterogeneity of pores [10]; the pore-throat size reflects the flow capacity of the fluid and the development degree of effective pores [11], and the distribution of pore throats reflects the difference in pore-throat sorting [12]. Pore-throat connectivity and matching relationships affect the connectivity among pore spaces [13].

At present, there are abundant experimental methods used in the study of reservoir pore-throat structures [14,15,16,17,18,19,20]. Among them, the mercury intrusion method is widely used to determine the pore-throat distribution of porous media by measuring the capillary pressure [21], and the detected pore throats have a wide range and high precision [22,23]. Since the critical value of the pore-throat size that can be detected by constant-rate mercury intrusion is 0.12 μm, nanoscale pores are ignored, and it is not suitable for low-porosity and ultralow permeability reservoirs with complex pore morphologies and structures [24]. Therefore, high-pressure mercury intrusion is mainly used to characterize these reservoirs [6].

The NMR T₂ spectrum reflects the transverse relaxation time, and the T_2cutoff defines the occurrence of the movable fluid. The range of pore-throat scales that can be characterized under a saturated water state is wider, which can supplement the differences and deficiencies in the characterization of pore-throat structures by mercury intrusion. Combined with mercury intrusion experiments, the characterization of reservoir pore-throat size distribution (PSD) can be more comprehensive [25,26,27]. Fractal theory can be used to calculate the quantitative fractal characteristic parameters of pore-throat structures [1,28], divide the pore-throat space into intervals according to the scale and extract the heterogeneous features [23].

Low- to ultralow-permeability reservoirs are characterized by small oil and gas seepage channels, obvious interactions at the fluid–rock interface and the two-phase fluid interface, large seepage resistance, and several influencing factors [2,29,30]. The oil–water relative permeability experiment reflects the linear seepage characteristics when oil and water coexist in rock pore throats [31] and represents the response results of the occurrence and flowability characteristics of movable fluids [32]. Combined with sandstone microscopic water-flooding experiments, the fluid migration state in the pore space of the reservoir rock can be observed directly [30].

Previous studies on the microscopic pore-throat structure of the Chang 9 oil-bearing formation in the Yanchang Formation in the Jiyuan area of the Ordos Basin mostly focused on macrosedimentary characteristics [33], sand body genesis [34], and oil and gas accumulation laws [3]. The microscopic aspect focuses on diagenesis studies [35] and qualitative analysis of pore space [34], and the quantitative characterization of microscopic pore-throat structures is seriously lacking. The correlation analysis of reservoir fluid seepage characteristics has not been carried out, and analysis of the factors influencing the seepage characteristics based on fractal dimension is still lacking. As a result, a series of theoretical barriers have arisen, resulting in the lack of effective guidance for oilfield development and production and hindering the process of enhanced oil recovery.

Therefore, this paper takes the low porosity and low permeability of the Chang 9 reservoir in the Yanchang Formation as the study object and uses many analytical and experimental methods to study the pore-throat structure and seepage characteristics. Through the combined characterization method of full-range pore-throat distribution and fractal theory, the causes and characteristic differences of the microscopic pore-throat structure of the reservoir are analysed, and the influencing factors of fluid seepage characteristics are summarized. Finally, the mechanism of the pore-throat structure fractal dimension that influences the seepage characteristics is innovatively proposed to provide new ideas for studying the influence of the pore-throat structure over seepage characteristics in unconventional reservoirs.

2. Materials and Methods

2.1. Geological Background and Samples

The Ordos Basin is in the western part of the North China platform and is a stable multicycle craton basin [36]. From the Early Paleozoic to the Mesozoic, the basin experienced the following three evolutionary stages: (1) Cambrian to Early Ordovician, when different discrete continental margins were developed; (2) Middle Ordovician to Middle Triassic, when a convergent continental margin was developed; and (3) Late Triassic to Early Cretaceous, which are the remnants of the cratonic basin [37]. The basin can be subdivided into six major tectonic units, including the Yimneg Uplift, the Weibei Uplift, the Western Overthrust Belt, the Tianhuan Depression, the Yishan Slope, and the Jinxi Flexure Belt, and the Jiyuan area crosses the Tianhuan depression and the Yishan slope (Figure 1A,B). In the Late Paleozoic, the Indosinian movement prompted the sedimentary facies to evolve from marine facies to marine–land transitional facies. In the early to middle Triassic, the basin was still not separated from the depression in the North China craton, and a river–lake sedimentary environment developed. In the middle and Late Triassic, foreland basins gradually formed due to regional tectonic collision and plate deformation [38], and during the depositional period of the Yanchang Formation in the Late Triassic, a river–lake–delta sedimentary system formed [36,39]. Following four uplifts and denudations, continental clastic rocks represented by multiperiod fluvial–lake sediments constituted the stratigraphic development framework of the Upper Triassic Yanchang Formation [40]. From bottom to top, it can be divided into Chang 10 to Chang 1 oil-bearing, which record the complete process of the formation, development, and decline of the lacustrine basin. Five mid-term cycles can be identified, with an overall thickness ranging from 1000–1400 m [39] (Figure 1C).

The research object is oil-bearing Chang 9, with a thickness range of 80–110 m. It receives the source rock at the bottom of Chang 7 in the upper part and belongs to an important replacement field for oil and gas exploration in the Jiyuan area. Sedimentary facies are distributed in the northwest and northeast directions, mainly delta-plain and delta-front subfacies. Distributary channels are the main sedimentary microfacies, and the horizontal and vertical continuity of the sand bodies is good. However, the differences in microscopic pore-throat structure and heterogeneity make the oil saturation of the Chang 9 reservoir relatively low.

The selected core samples are from drilling cores, and they are stored in the core library. The temperature during core observation and sampling was approximately 25– 30°C. Reservoir diagenesis is related to organic thermal metamorphism. The average reflectance of vitrinite in the Chang 8 Member of the Yanchang Formation is close to 1%, and the main high-temperature range of fluid inclusions is 115–125 °C [41]. The peak temperature of the long 9 segments will be between 130–140 degrees Celsius, and the vitrinite reflectance will be greater than 1% [42]. K-Ar dating of Permian–Triassic samples reveals distinct illitization at 170–160 Ma, during which a thermal event occurred due to subsurface magmatic intrusion related to the early Yanshanian movement. The mean vitrinite reflectance values (Ro) of the Triassic rocks range from 0.61 to 1.06%, giving a high coalification gradient of 0.36%/km and suggesting a high palaeothermal gradient of 57 °C/km [43]. Under the combined action of the burial depth and paleotemperature of the Yanchang Formation, the changes in pore fluid and permeability after compaction may, to a certain extent, cause differences in feldspar dissolution and turbidite formation [44,45]. For the Yanchang Formation sandstone reservoir, some primary intergranular pores can be retained after burial and compaction, and the development space of secondary pores can form.

2.2. Experimental Measurements

The dried core plugs were vacuumized for 24 h, and then their porosity and permeability were measured by a CMS-300 core analysis instrument. The porosity was measured using the gas expansion method with helium, and the permeability was measured by the pressure-transient method under a confining pressure of 1.5 MPa. In this paper, the porosity and permeability obtained by gas measurement are regarded as the effective porosity and absolute permeability, and the experimental standard conforms to the Chinese oil and gas industry standard (SY/T 5336-2006).

We divided the cut samples into several categories according to the experimental method and followed the principle of parallel experiments; that is, we tried to ensure that the same sample could participate in all experimental types so that the obtained test results had good correspondence. Among them, the 1 cm sheet sample was prepared for casting the thin section and scanning electron microscope observation, and the 5 cm plug sample was first subjected to NMR experiments and then to seepage experiments. Finally, the high-pressure mercury intrusion experiment was carried out, the 0.5 cm piece was ground for X-ray diffraction, and the 0.3 cm piece was prepared for the oil–water relative permeability and microscopic water-flooding oil seepage experiments.

2.2.1. Cast Thin Section and Scanning Electron Microscope Observations

A sample 1 cm in length and 2.5 cm in width was cut in half, half of which was used for the casting thin section experiments. After impregnating the samples with epoxy resin, they were ground to a 0.3-mm-thick, 25 mm × 25 mm flake size. Then, the sample was observed with a LEICA DM4500 polarizing microscope to analyse the pore type, mineral composition, and main diagenetic evolution, and the point-counting method was used to estimate the mineral content and proportion of different pore types on the micrographs. The other half of the sample was split into small pieces with a thickness of approximately 1 cm and a width of approximately 1 cm. The surface was polished and plated with gold and then placed in an FEI Quanta 400 SEM instrument for observation. A fine-focusing electron beam was used to perform a point-by-point scan on the surface of the sample to excite various electronic signals with different functions, and the detector selectively collected and processed the desired electronic signal and converted the signals into images. The experiment conforms to the Chinese standard SY/T5162-2014.

2.2.2. X-ray Diffraction

X-diffraction experiments were performed with a D8 DISCOVER X-ray diffractometer, the temperature was controlled at 24 °C, and the humidity was 35%. A monochromatic X-ray was used to illuminate the crystal surface. Under X-ray irradiation, the atoms surrounding each crystal exhibited periodic vibrations. The atomic electrons surrounding an electromagnetic wave superposition pattern vary depending on the atoms, thereby reflecting the atomic structure of the internal distribution. The composition of the sandstone sample can be determined by comparing the difference between the diffraction patterns of different samples and the standard diffraction patterns.

2.2.3. Nuclear Magnetic Resonance

The NMR experiment was carried out with a prepared plug sample with a length of approximately 2.5 cm. Before the start of the experiment, the vacuumed samples were weighed. First, the samples were saturated with formation water with the same salinity as the study area for 12 h and then weighed twice. After wiping the water off their surface and wrapping these samples in plastic, the T₂ relaxation time distribution of the saturated water samples was obtained by conducting NMR experiments with a RecCore-2500 low field magnetic resonance tester. The samples were centrifuged at different speeds (2500, 2900, 3500, 5000, 7900, and 9100 r/min) using a PC-1 petroleum core centrifuge. After reweighing the centrifuged samples, the NMR experiments were started. The temperature was controlled at 25 °C, the NMR frequency was 2.38 MHz, the number of echoes was 2048, the waiting time was 5000 ms, and the echo interval was 0.6 ms, which is suitable for measuring short T₂ components. The T₂ cut-offs were calculated according to the ratio of T₂ distributions before and after centrifugation and then applied to calculate the movable and irreducible water saturations according to the ratios of the coverage areas of T_2S to the left and the right of the T₂ cut-offs to the coverage area of the T_2S. The movable porosity can be calculated by multiplying the movable water saturation and NMR porosity. The experiment complies with the Chinese test standard SY-T6490-2007.

2.2.4. Oil–Water Relative Permeability Experiment

The oil–water relative permeability experiment, which can represent the wettability of the core and calculate the oil displacement efficiency, was performed after the NMR experiment, and the relative permeability experiment. First, the plunger sample was dried, and the simulated formation water was saturated after vacuum. Then, the HBXS-2 relative permeability tester was used for testing by the nonsteady state method according to the SY/T5345-2007 standard. Finally, the relative permeability curves of the core samples were obtained [46], including the relative permeability of oil and water under different water saturation states. The concept of the simultaneous vadose region area (SVRA) was proposed to better classify the complex microscopic pore-throat structure of tight sandstone reservoirs [47].

2.2.5. High-Pressure Mercury Injection

After the oil–water relative permeability experiment, the high-pressure mercury intrusion experiment was carried out, which was caused by the irreversibility of the damage of the sample by mercury intrusion. In this paper, the high-pressure mercury intrusion experiment method is abbreviated as HPMI, and a follow-up discussion is carried out. The basic assumption of this experiment is that the complex cross-sectional shape of all throats is equivalent to a circle with equal area, so the throat can be regarded as a capillary, and the pore-throat combination is equivalent to a combination of capillary bundles. The equivalent radius of the capillary bundle combination is defined as the pore-throat radius, so the mercury injection pressure in the mercury injection experiment is equivalent to the capillary pressure, and the relationship between the pore-throat radius and the capillary force is consistent with Equation (1) [21]:

$$Pc=\frac{2\sigma \cos \theta }{r}$$

(1)

where Pc is the capillary pressure, θ is the contact angle, σ is the surface tension, and r is the pore-throat radius. HPMI was conducted on a Corelab CMS300 mercury porosimeter following Chinese standard SY/T5346-2005. Since mercury is in a nonwetting phase, liquid mercury was not injected into the pores until a sufficient pressure level was reached. The maximum mercury injection pressure in this experiment was controlled at 200 MPa, and the corresponding minimum pore-throat scale was 1.6 nm. Both intrusion and extrusion curves were obtained from the HPMI experiment.

2.2.6. Microscopic Water-Flooding Oil Seepage

The pretreated sheet samples were further cut to form sandstone samples with lengths, widths, and thicknesses of 3.5 cm, 3.5 cm, and 0.08 cm, respectively. The grinding and cementation processes were used, and a block-shaped visualization model was formed. The pressure-bearing capacity of the sample was 0.35 MPa, and the temperature resistance was 100 °C. To simulate the water-flooding process in the study area to the greatest extent, the formation water type used in the experiment was CaCl₂, and the simulated oil with a viscosity of 0.98 mPa·s was configured. To facilitate the observation of the seepage characteristics of the fluid, methyl blue was added to the simulated water to make it blue, and oil red was added to the simulated oil [30].

After the experiment, first, the sandstone model was vacuumized and saturated with formation water, and the permeability of the model under the saturated water state was measured. Then, the simulated oil displacement of formation water, that is, the saturated oil process, was used to calculate the original oil saturation. Finally, the water-flooding experiment was started. The characteristics of fluid seepage and residual oil distribution in the process of water-flooding were observed through the microscope, and the oil displacement efficiency was calculated. When there was no change in water-flooding at constant pressure, the displacement pressure could be increased to observe the displacement effect of the remaining oil in the pore-throat structure. The entire experimental process was recorded by image acquisition, and data analysis and processing were performed simultaneously.

2.3. Methodology

2.3.1. Full-Range PSD Combined HPMI and NMR

Different microscopic pore structure experimental methods have limitations. Previous studies have found that due to the shielding effect of large pores, there are omissions in the characterization of relatively large pore spaces in HPMI experiments [48], resulting in inaccurate PSD characterization. Since the NMR T₂ spectrum distribution in the saturated water state can reflect the full-range pore-throat structure [1], the NMR T₂ spectrum can be converted into the pore-throat radius to realize the characterization of the full-range PSD.

According to NMR theory, the T₂ relaxation time can be expressed as Equation (2)

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

(2)

where $T_2$ is the transverse relaxation time, ms; $T_{2B}$ is the bulk relaxation time, ms; $T_{2D}$ is the diffusion relaxation time, ms; and $T_{2S}$ is the surface relaxation time, ms.

As $T_{2B}$ ranges from 1 to 3 s and is much longer than $T_{2S}$, 1/$T_{2B}$ can be ignored in Equation (2). $T_{2D}$ can also be ignored when the echo time is shorter than 0.6 ms and the magnetic field is uniform. Finally, $T_{2S}$ is used to approximate $T_2$.

The $T_2$ relaxation time in a single pore of saturated water in a uniform magnetic field can be expressed as Equation (3)

$$\frac{1}{T_2}=\frac{1}{T_{2s}}={\rho }_2\frac{S}{V}$$

(3)

where ${\rho }_2$ represents the surface relaxation strength, which depends on the properties of the pore surface, mineral composition, and properties of the saturated fluid, μm/ms, and $S/V$ is the specific surface, μm²/μm³. For the simplified spherical or cylindrical pore structure, the relationship between the specific surface area and the pore radius is shown in Equation (4)

$$\frac{S}{V}=\frac{F_S}{r_c}$$

(4)

Therefore, combining Equations (3) and (4), we can obtain Equation (5)

$$T_2=\frac{r_c}{{\rho }_2{F}_s}$$

(5)

where $F_S$ is the pore shape factor ($F_S$= 2 for tubular pores and $F_S$ = 3 for spherical pores), dimensionless, and $r_c$ is the pore radius, μm. The pore structure in the formation is complex. Based on experimental verification, it is believed that the following power function relationship exists between the $T_2$ distribution and the pore radius [25]

$$T_2=\frac{r_c^n}{{\rho }_2{F}_s}$$

(6)

where $n$ is the power exponent, dimensionless.

Since it is difficult to obtain ${\rho }_2$ and $F_S$ by the current experimental methods, it is necessary to use the principle of the mercury intrusion method to determine the capillary force curve to deduce and convert again. Given that the pore radius $r_c$ is equal to the product of the throat radius and pore-throat ratio, we have Equation (7)

$$T_2=\frac{{\left(C_1{r}_t\right)}^n}{{\rho }_2{F}_s}$$

(7)

where $C_1$ is the average pore-throat ratio, dimensionless, and $r_t$ is the throat radius, μm.

Then, we define a new constant $C$ as Equation (8)

$$C=\frac{{\left({\rho }_2{F}_s\right)}^{1/n}}{C_1}$$

(8)

The relationship between the throat radius and $T_2$ relaxation time is transformed into Equation (9)

$$r_t=C{T}_2^{1/n}$$

(9)

The values of $C$ and $n$ can be obtained to convert the $T_2$ distribution of the 100% saturated water core into the pore-throat radius distribution curve. By taking the logarithm of the left and right sides of Equation (9), we can transform the formula into Equation (10)

$$\ln r_t=\ln C+\frac{1}{n}\ln T_2$$

(10)

Equation (10) has a linear relationship, and $C$ and $n$ can be obtained by linear fitting. The parameter preparation and calculation methods need to use the interpolation method to correspond to the pore-throat radius of the HPMI and the cumulative distribution frequency curve of the NMR T₂ spectrum and use the linear least squares principle to obtain the fitting parameters $C$ and $n$ [1,25].

2.3.2. Fractal Methodology

To a certain extent, a fractal is a virtual geometric object that is completely independent and similar to the self-shape of the magnification. The microscopic pore structure of natural rocks with porous media has fractal characteristics, and the fractal dimension can be determined accordingly [49]. Usually, the fractal dimension of a three-dimensional fractal is between 2 and 3, which in a physical sense indicates the similarity between the partial and the overall pore-throat structure or the concentration of the pore size distribution. Therefore, it can be used to characterize the pore-throat structure and microscopic heterogeneity with complex features [50,51].

The rougher the pore-throat surface is, the worse the pore-throat sorting is, and the more complex the pore-throat distribution is, the stronger the microscopic heterogeneity of the corresponding reservoir is, and the closer to 3 the fractal dimension is [52]. Based on fractal geometry theory, a fractal object can be represented by the following power-law function [53]

$$N\left(r\right)\propto r^{-D_f}$$

(11)

where $N\left(r\right)$ is the number of a fractal object whose characteristic linear dimensions are larger than $r$, $r$ is the radius of a fractal object, and $D_f$ is the fractal dimension.

There are two main methods for calculating the fractal dimension based on mercury injection capillary pressure curves. In this paper, we chose the mercury saturation (nonwetting phase) method [54].

The derivation process of this method is given as follows

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

(12)

where $l$ is the length of the capillary, and $V_{Hg}$ is the cumulative volume of mercury flowing through the capillary with radius $r$. Then, after combining Equation (1) with Equations (11) and (12), we have

$$V_{Hg}\propto P_c{}^{-\left(2-D_f\right)}$$

(13)

According to the definition of mercury saturation in rock samples, we have

$$S_{Hg}=\frac{V_{Hg}}{V_p}$$

(14)

where $S_{Hg}$ is the mercury saturation and $V_p$ is the total pore volume of the sample.

Combining Equations (13) and (14), we have

$$S_{Hg}=\alpha P_c{}^{-\left(2-D_f\right)}$$

(15)

where α is a constant equal to $1/V_p$.

Finally, by taking logarithms on both sides of Equation (15) and making the following simple transformations, we have

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

(16)

Based on Equation (16), a correlation between $\log S_{Hg}$ and $\log P_c$ can be determined according to HPMI. If the slope $K$ of the trend line can be represented by a straight line, then the fractal dimension can be calculated from the slope of the trend line as follows

$$D_f=K+2$$

(17)

Equation (17) shows that the larger the slope is, the larger the fractal dimension is, and the higher the heterogeneity degree of the pore-throat structure is. Previous studies found the multifractal characteristics of tight sandstone reservoirs [28,55], and the fractal dimension calculation method produced a situation where the fractal dimension was greater than 3 [56], which was presumed to be related to the development of microfractures. This study does not use the water saturation calculation method to calculate the fractal dimension mainly because that method needs to remove the increments of the initial mercury injection and the final mercury injection in the linear fitting, which may cause unpredictable errors [51]. These errors are caused by the fact that mercury is a nonwetting phase [19], which will be supplemented in the following discussion.

3. Results and Interpretations

3.1. Petrology, Petrophysical Properties, and Pore Types

3.1.1. Mineral Compositions

Based on the results of 234 thin cast sections collected from the Chang 9 reservoir, a triangular figure of the framework mineral composition was created [57]. The rock types of the Chang 9 reservoir in the study area are lithic feldspar sandstone, feldspar lithic sandstone, and quartz sandstone (Figure 2), of which quartz accounts for 30.91%, feldspar accounts for 37.23%, and rock fragments account for 17.29% on average.

The XRD patterns of the 12 typical samples are shown in

Table 1. Mineral composition and content from the XRD tests for 12 samples.

Well	Depth (m)	Sample ID	Detrital Component Content from XRD (%)								Relative Content of Clay Minerals (%)
			Quartz	Feldspar	Calcite	Clay	Ferro-Calcite	Laumontite	Ferrodolomite	Siderite	Chlorite	Illite	I/S Mixed Layer	Smectite in I/S
C107	2863.5	J1	38.10	51.19	0.00	2.38	1.19	7.14	0.00	0.00	15.32	74.10	10.58	15
C123	2694.2	J2	26.60	57.45	0.00	7.45	0.00	8.51	0.00	0.00	38.54	47.87	13.59	20
C132	2666.7	J3	35.71	50.60	0.00	5.95	1.19	5.95	0.00	0.60	75.13	16.54	8.33	15
C139	2674.7	J4	34.44	45.00	0.00	7.78	1.11	11.11	0.00	0.56	66.83	22.15	11.02	10
C165	2640.5	J5	40.96	50.60	0.00	6.63	1.20	0.00	0.00	0.60	74.23	19.05	6.72	10
H337	2743.9	J6	44.29	42.86	0.00	5.71	1.43	5.71	0.00	0.00	47.25	43.1	9.65	15
H404	2889.0	J7	35.16	42.86	0.00	18.68	1.65	0.00	1.65	0.00	92.08	5.64	2.28	10
H435	2703.4	J8	46.75	46.75	0.00	5.19	0.00	1.30	0.00	0.00	79.76	9.54	10.7	20
H442	3003.3	J9	44.74	41.45	0.00	6.58	0.66	6.58	0.00	0.00	50.78	41.08	8.14	20
H61	2825.07	J10	53.89	38.32	0.00	2.99	0.00	4.79	0.00	0.00	58.75	15.23	26.02	20
H76	2696.0	J11	32.61	50.54	0.00	4.89	2.17	9.78	0.00	0.00	79.43	11.53	9.04	15
L100	2907.59	J12	45.98	45.98	1.15	4.60	0.00	2.30	0.00	0.00	23.16	66.48	10.36	10

.

The proportion of interstitials is 10.31%, and the composition maturity is medium to low. The rock fragments are dominated by metamorphic debris (11.37%), followed by igneous debris (5.78%), and a very small amount of sedimentary debris (0.14%). In the rock structure, the sorting is moderate, the rounding is mainly subangular, and the overall structural maturity is moderate to low. The content of interstitial materials accounts for an average of 13.1%, of which clay minerals and cement are the main materials. The chlorite content in the clay minerals is 58.44%, followed by illite (31.03%). In addition, the content of lamontite in cement is relatively high, with an average of 5.27%.

Since the Chang 8 depositional period of the Yanchang Formation, the linear relationship between sandstone porosity and depth has weakened, and individual samples are nonlinear in the secondary dissolution. Therefore, up to the Chang 9 Member of the Yanchang Formation, the porosity of some sandstone samples is not affected by the increase in burial depth and presents the characteristics of a lower pore structure. Especially for the samples from the secondary dissolution porosity section, the sandstone porosity evolution shows typical characteristics that are controlled by diagenesis [58].

3.1.2. Physical Properties

A total of 10,964 core physical property data were collected from 237 wells in the Chang 9 reservoir in the study area. According to the Chinese clastic reservoir physical property classification standard SY/T6285-2011, it is generally a low porosity and ultralow to ultralow permeability reservoir (Figure 3).

In this paper, 24 samples from 19 cored wells were tested for core physical property analysis, and a cross-plot of porosity and permeability was created (Figure 4). Notably, diagenetic, filamentous, illite clay in reservoir sandstones has an influence on fluid flow [45], which may be caused by the clay mineral content of rock. Especially under the condition of gas-measured porosity and permeability, since the samples were in the state of drying after being washed in a vacuum, the influence of some clay minerals on the pore connectivity will complicate the prediction of permeability. To some extent, the content of clay minerals obscures the true presentation of permeability.

As shown above, there is a predictive model for the porosity and permeability of samples from the study area (K = 0.0068e^0.4663φ). The correlation coefficient between porosity and permeability is 0.5047, reflecting the complex relationship between the pore-throat structure and seepage characteristics of the reservoir and the existence of strong microscopic heterogeneity. The relationship between permeability and porosity of unconventional sandstone reservoirs is not close, so it also reflects that the restriction of the pore-throat structure on seepage capacity is not absolute, but there are typical restrictions to a certain extent or in some respects. This is also the purpose of this article. Moreover, the complexity of the pore-throat structure of such reservoirs is related to various factors, and the relatively good pore size does not mean that the pore-throat structure is connected.

3.1.3. Pore-Throat Types

The 12 typical samples used in this study were dominated by intergranular pores and dissolution pores, with calcite cementation (Figure 5A) and necked throats (Figure 5B). The chlorite coating was wrapped around the grain edges (Figure 5C,D,I,J), which could retain more intergranular pores, and secondary enlargement of quartz and lamellar throats could be observed (Figure 5C,H). The dissolution of feldspar leaves mould pores and tube bundle throats (Figure 5E), and curved lamella throats are also common (Figure 5F). Authigenic quartz crystals (Figure 5F,H) and clay minerals are cemented to fill the particle size pores (Figure 5F), and bridge-like illite fills the pores, leaving only residual intercrystalline pores (Figure 5G). Microfractures are usually developed on the edge of feldspar dissolution (Figure 5J), and a large volume of laumontite cement plugs the pores (Figure 5K). Chlorite rim cementation and illite cover the surface of the grains, leaving authigenic quartz crystals in the intergranular pores, which means that chlorite can inhibit late-stage quartz cementation when present as a continuous coating, and it can protect pore space to some extent (Figure 5L). The edges of the intergranular pores are locally accompanied by feldspar dissolution. Especially in deeply buried sandstones, quartz cement can fill significant micropores within diagenetic chlorite coats, and the control mechanism may be affected by the depth and temperature of burial conditions [59].

The pore type and structural characteristics of the CTS of the 12 typical samples are described as follows (

Table 2. The CTS results of the 12 typical samples.

Sample ID	Intergranular Pore (%)	Interparticle Dissolution Pore (%)	Feldspar Dissolved Pore (%)	Debris Solution Pore (%)	Laumontite Dissolved Pore (%)	Plane Porosity (%)	Pore Type	Cement Form
J1	8		0.5		1	9.5	ITP	P
J2	1	/	2.5	/	/	3.5	ITP-DP	OP
J3	7	2	0.5	1	/	10.5	DP-ITP	FP
J4	4	/	0.5	1	/	5.5	DP-ITP	FP
J5	6	/	1	2	/	9	DP-ITP	FP
J6	4	/	1.5	1	/	6.5	DP-ITP	F
J7	2	/	0.5		/	2.5	ITP	FP
J8	7	/	1	0.5	/	8.5	DP-ITP	F
J9	5	/	2	1	/	8	DP-ITP	F
J10	8	/	2	0.3	/	10.3	DP-ITP	O
J11	4	/	0.6	/	/	4.6	DP-ITP	F
J12	1.5	1	/	/	/	14.5	DP-ITP	PF

Note: For pore types, the intergranular pore is abbreviated as ITP, and the dissolved pore is abbreviated as DP; DP-ITP means intergranular pores and some dissolved pores; porous cementation is abbreviated as P; secondary overgrowth-porous cementation is OP; secondary overgrowth cementation is abbreviated as O; film-porous cementation is abbreviated as FP; film cementation is abbreviated as F; porous-film is abbreviated as PF.

). The plane porosity was 7.74, and the results correspond to the thin sections of the cast and SEM images. The intergranular pores were the most developed in the pore space, followed by feldspar dissolution pores and a small number of rock fragment dissolution pores. Sorting was between medium and good. In addition, the rounding was mainly subangular, and the cementing type was mainly chlorite rim cementation and pore cementation.

3.2. HPMI Results and Fractal Features

3.2.1. HPMI Results

The average porosity of the 12 samples was 12.55% (7.6%–16.10%), and the average permeability was 5.47 mD (0.17–28.96 mD). Skewness indicates the symmetry of the PSD. When it is greater than 0, it has positive skewness (coarse skewness), and the curve shape of all samples was dominated by positive skewness (average 0.47). The sorting coefficient represents the uniformity of sorting, with an average of 2.73, and the coefficient of variation reflects the uniformity of the pore-throat structure. The smaller the pore-throat distribution is, the more uniform it is, with an average of 0.27. The median pressure was in the range of 0.18–8.46 MPa (average 3.14 MPa), while the displacement pressure was in the range of 0.02–1.16 MPa (average 0.38 MPa), reflecting the complex pore-throat structure and considerable changes in mercury injection pressure. The median radius was in the range of 0.09–4.1 μm (average 0.72 μm), reflecting the strong heterogeneity of the pore-throat size, and the mercury saturation range was 81.73%–96.43% (average 88.61%), indicating that the pore-throat space was generally large. The total amount of mercury input was large, but the efficiency of mercury ejection varied greatly, ranging from 19.05%–46.76% (average 28.30%), reflecting the complex relationship between pore-throat structure and the low mercury withdrawal degree (

Table 3. Parameters from the HPMI experiment.

Sample ID	Porosity (%)	Permeability (mD)	Skewness	Sorting Coefficient	Coefficient of Variation	Median Pressure (MPa)	Median Radius (μm)	Displacement Pressure (MPa)	Maximum Mercury Saturation (%)	Ejection Efficiency (%)	Radius at the Maximum Permeability Contribution (μm)	Maximum Permeability Contribution (mD)
J1	11.60	1.605	1.73	2.74	0.27	3.95	0.19	0.28	86.92	30.39	1.02	64.48%
J2	9.80	0.780	1.50	1.83	0.16	8.46	0.09	0.72	90.10	46.76	1.02	78.03%
J3	10.90	2.780	1.49	2.78	0.29	3.77	0.20	0.18	87.09	35.60	2.50	61.21%
J4	8.60	0.173	1.84	2.16	0.20	5.33	0.14	1.14	85.67	30.06	0.25	71.53%
J5	13.30	15.650	1.30	3.49	0.41	0.71	1.04	0.02	88.37	19.13	40.41	38.49%
J6	16.10	2.024	0.72	3.68	0.24	2.79	0.26	0.11	87.72	32.55	0.36	75.62%
J7	14.10	28.960	0.47	3.20	0.33	0.63	1.17	0.05	96.43	22.85	5.33	67.65%
J8	16.40	6.075	0.61	4.58	0.42	0.18	4.10	0.06	81.73	20.54	1.09	50.95%
J9	14.10	1.768	0.76	3.25	0.28	1.01	0.73	0.14	95.99	20.94	0.36	57.37%
J10	13.10	2.207	2.09	2.43	0.25	1.71	0.43	0.46	88.50	32.67	1.02	57.41%
J11	7.60	0.341	1.73	2.31	0.20	6.05	0.12	1.16	90.26	19.05	0.25	76.89%
J12	14.96	3.312	1.56	0.31	0.22	3.15	0.23	0.29	84.51	29.08	1.60	87.33%

).

The HPMI curves of the 12 typical samples (Figure 6) showed that the pore-throat structures of different samples were quite different. For example, in sample J8, the displacement pressure was extremely low (0.06 MPa), and the plateau period after mercury injection was long and flat, reflecting the large pore-throat structure and less difficulty in terms of mercury injection. However, the pressure rose rapidly after the plateau period, and the slope was very high between 45% and 80% of mercury saturation, indicating that the relatively small pore throats were more complex. The final mercury saturation was only 81.73%, indicating that the pore-throat space of the sample was very complex.

Sample J11 had extremely poor physical properties (porosity 7.6%; permeability 0.34 mD), an extremely high displacement pressure of 1.16 MPa, and an extremely small median radius (0.12 μm). Additionally, the efficiency of mercury ejection was low, and the pore-throat connectivity was poor. However, the final mercury saturation was higher (90.26%), far exceeding that of sample J8, indicating that the factors affecting the pore structure were comprehensive and complex. Due to the shielding effect on relatively large pores in HPMI [13], there were omissions when judging the pore-throat scale by only the high-pressure mercury intrusion.

Thomeer (1960) pointed out that the pore radius at the apex of the cross-plot of the log-logarithmic curve of mercury injection pressure and mercury saturation represents the main pore network capable of forming fluid flow [60], and the pore space under this pore-throat radius is efficient and interconnected. Pittman (1992) attempted to define this pore radius by constructing a cross-plot using two parameters [61], mercury saturation and mercury saturation, divided by mercury injection pressure. Finally, Pittman’s plot produces a sharp and easily defined apex [62]. The pore-throat radius at the vertex of the curve is the turning point between large pores with good connectivity and small pores with poor connectivity [4,27].

The pressure corresponding to the pore-throat radius at this location is Pc_apex. Taking sample J7 as an example, the cross-plot of its mercury saturation and mercury saturation divided by mercury injection pressure is shown (Figure 7A). The mercury saturation at the vertex is 30.41%, the corresponding capillary pressure Pc_apex is 0.2065 MPa, and the corresponding pore-throat radius is 3.561 μm. The Pittman intersection diagram of the 12 typical samples is shown (Figure 7B).

The r_apex parameter calculation of the 12 typical samples is shown in

Table 4. Parameters of the Pittman plot calculation for the 12 typical samples.

Sample ID	Porosity (%)	Permeability (mD)	SHgapex(%)	Pcapex(MPa)	rapex (μm)
J1	11.60	1.605	29.62	1.17	0.63
J2	9.80	0.780	24.43	2.91	0.25
J3	10.90	2.780	22.02	0.46	1.60
J4	8.60	0.173	46.73	4.56	0.16
J5	13.30	15.650	30.63	0.18	4.03
J6	16.10	2.024	18.85	0.27	2.76
J7	14.10	28.960	30.41	0.21	3.56
J8	16.40	6.075	43.12	0.11	6.66
J9	14.10	1.768	26.28	0.26	2.80
J10	13.10	2.207	40.91	1.16	0.63
J11	7.60	0.341	45.68	4.50	0.16
J12	14.96	3.312	24.91	0.46	1.60

.

The range of r_apex is 0.16–6.66 μm, with an average of 2.07 μm, indicating that when the pore-throat radius in the study area is greater than 2.07 μm, the pore structure is better, the pore space and pore-throat connectivity are stronger, and the fluid flow network is better. The distribution of SHg_apex ranges from 18.85% to 46.73%, with an average of 31.97%, reflecting that the pore-throat connectivity is relatively good before the mercury saturation reaches 31.97%. The range of Pc_apex is between 0.11–4.56 MPa, with an average of 1.35 MPa, reflecting that the pore-throat structure is better when the capillary pressure is lower than this value.

The relationship between r_apex and porosity and permeability is shown in Figure 8; r_apex has a strong correlation with porosity (R² = 0.7818) but a weaker correlation with permeability (R² = 0.2822).

3.2.2. Fractal Features

According to fractal theory, the double logarithmic distributions of capillary pressure and mercury injection saturation of the 12 typical samples were drawn (Figure 9). The figure shows that there are multifractal features in the study area. Samples J1/J5/J7/J10/J11/J12 have two-stage fractal characteristics, and samples J2/J3/J4/J6/J8/J9 have three-stage fractal characteristics. Because the physical properties of such unconventional reservoirs in the study area are still slightly higher than those of tight sandstone reservoirs and they have relatively large pore diameters, they are different from most tight sandstone reservoirs with two-stage fractal characteristics represented by micropores. There are still a certain number of large pores in the Chang 9 reservoir of the Yanchang Formation. According to the research idea of pore-throat structure heterogeneity, which is based on fractal theory, the heterogeneity difference between large and small pores is more significant than that of tight sandstone reservoirs, so this kind of three-stage fractal characteristic in the study area is generated. Specifically, each sample contained macropores, mesopores, and micropores, but the difference between the mesopores and micropores of some samples was not large, or the difference was extremely small, so the three-stage fractal becomes a two-stage fractal. This fractal difference reflects the complexity of the pore-throat structure of the samples in the study area. Especially for parameters, such as pore size, pore-throat heterogeneity, and pore-throat connectivity differences, although different samples had similar physical properties, differences in pore-throat structures will lead to differences in water-flooding seepage capabilities.

Through the slope of each fitted line segment, the analytical dimension of each sample was calculated by Equation (17), and the pore-throat radius at the inflection point was calculated (

Table 5. Fractal dimension calculation of HPMI.

Sample ID	Porosity (%)	Permeability (mD)	Df1	R2	Df2	R2	Df3	R2	rP1 (μm)	rP2 (μm)
J1	11.60	1.605	5.3278	0.9739	2.1606	0.9670	/	/	0.6310
J2	9.80	0.780	6.4484	0.9974	2.3524	0.9877	2.0458	0.9188	0.2525	0.0252
J3	10.90	2.780	6.1322	0.9091	2.2525	0.9844	2.0456	0.8999	1.6050	0.0404
J4	8.60	0.173	6.5820	0.9836	2.3016	0.9524	2.0587	0.9106	0.1613	0.0252
J5	13.30	15.650	3.5274	0.9940	2.1183	0.9787			2.5211	/
J6	16.10	2.024	2.3695	0.9591	3.0672	0.9702	2.1609	0.9349	5.3322	1.0909
J7	14.10	28.960	5.2395	0.9839	2.1294	0.9576	/	/	3.5613	/
J8	16.40	6.075	2.5183	0.9997	3.5903	0.8950	2.0666	0.9698	8.9108	5.3322
J9	14.10	1.768	2.3276	0.9792	2.5459	0.9836	2.1153	0.9581	5.3339	1.0900
J10	13.10	2.207	5.4908	0.9500	2.1053	0.9326	/	/	0.6316	/
J11	7.60	0.341	5.3406	0.9937	2.1763	0.9844	/	/	0.2532	/
J12	14.96	3.312	5.3640	0.9573	2.1630	0.9679	/	/	1.6008	/

Note: r_P1 and r_P2 in the table represent the pore radius at the turning point.

). The X-axis from small to large represents pores from large to small. The log(Pc) and log(SHg) of each segment on the scatterplot have a significant linear correlation, reflecting that pores of different scales have different fractal characteristics. For larger pores, Df1 is usually greater than three, which is due to the presence of pockmarks on the surface of relatively large pore throats during the low mercury injection pressure stage, and the mercury saturation does not increase with increasing pressure. This causes a certain degree of data distortion [54,63], so a fractal dimension greater than three is regarded as not having ideal fractal characteristics.

However, larger pores also have fractal characteristics [1]. In the study area, compared with small pores, the heterogeneity of large pores affects the differences in the pore-throat structure and petrophysical properties of reservoirs. Therefore, a fractal dimension greater than three is the embodiment of extreme differences in pore-throat structure. Df2 generally conforms to fractal characteristics; only individual samples were greater than three here, reflecting that the pores at this scale still have strong heterogeneity characteristics. Df3 is generally close to two, reflecting that relatively small pores have a weaker degree of heterogeneity and more, similar pore-throat structures.

Previously, the pore-throat structures of tight sandstone reservoirs were divided into three categories [64], namely, macropores (>1 μm in radius), mesopores (10 nm–1 μm), and micropores (<10 nm). The pore-throat radii of the samples in the study area at fractal turning point one were quite different. The pore types of the seven samples at the turning point of the analysis were macropores, the rest are mesopores, and the pore-throat radii of the three samples at turning point two of the analysis were macropores. Therefore, macropores and mesopores are the focus of this study.

3.3. NMR Results and Full-Range Pore Size Distribution

3.3.1. NMR Results

NMR can overcome this shortcoming but fails to directly obtain the PSD [65]. The distribution of the relaxation time T₂ spectra of the 12 typical samples in a saturated water state was obtained as follows (Figure 10). The pore-throat structure distribution of the Chang 9 reservoir in the study area is dominated by the right unimodal, reflecting that the pore-throat structure is dominated by larger pore throats, which is in line with the characteristics of positive skewness.

However, following further classification, there are pseudo double peaks (such as J1/J2/J3/J11/J12) with significant “left low and right high” samples, reflecting that the reservoir is dominated by large pores, and relatively small pores are also developed. The decrease in these pore scales will inevitably lead to larger differences in pore-throat scales, a decrease in the degree of connectivity of pore-throat structures, and an increase in the degree of reservoir heterogeneity. The figure shows that the distribution intervals of different samples on the T₂ spectrum are significantly different, reflecting that the pore size varies greatly.

The results of 12 NMR experiments are shown in

Table 6. Parameters of NMR results.

Sample ID	Helium Porosity (%)	Permeability (mD)	NMR Porosity (%)	Dead Porosity Content (%)	T2cutoff (ms)	Movable Fluid Saturation (%)	Irreducible Water Saturation (%)	Movable Fluid Porosity (%)
J1	11.60	1.605	13.47	1.87	16.58	53.21	46.79	7.17
J2	9.80	0.780	11.68	1.88	13.29	45.76	54.24	5.34
J3	10.90	2.780	12.78	1.88	16.84	54.65	45.35	6.98
J4	8.60	0.173	9.89	1.29	12.15	43.77	56.23	4.33
J5	13.30	15.650	15.76	2.46	19.21	58.12	41.88	9.16
J6	16.10	2.024	18.53	2.43	19.75	60.88	39.12	11.28
J7	14.10	28.960	16.36	2.26	21.23	63.87	36.13	10.45
J8	16.40	6.075	18.03	1.63	21.84	56.31	43.69	10.15
J9	14.10	1.768	17.29	3.19	20.93	57.22	42.78	9.89
J10	13.10	2.207	15.24	2.14	18.98	58.24	41.76	8.88
J11	7.60	0.341	8.73	1.13	10.35	40.13	59.87	3.50
J12	14.96	3.312	17.21	2.25	19.85	55.61	44.39	9.57

. The advantages of NMR are not only that they can measure the full-range pore-throat distribution range but also that they can characterize the flowability of fluids, considering the comprehensive evaluation of storage capacity and seepage capacity.

The NMR porosity is generally slightly larger than the gas measurement porosity because mercury intrusion can only measure the pore space connected to the throat, and there is an omission of unconnected pores. Therefore, the difference between the NMR porosity and the gas measurement porosity is the dead porosity content. T_2cutoff is distributed between 10.35–21.84 ms, with an average of 17.58 ms. The distribution of movable fluid saturation is 40.13%–63.87%, with an average of 53.98%. The movable fluid porosity is distributed between 3.5%–11.28%, with an average of 8.06%, reflecting the large difference in the distribution range of the parameters of the samples in the study area. The differences between samples were large. For example, samples J7 and J9 had similar gas-measured porosities but large differences in movable fluid saturation, reflecting the differences in throat connectivity in the pore-throat structure. The permeabilities of samples J6 and J10 were similar, but the porosity difference was large, which was directly reflected in the size difference of the pore space, and the larger pore space corresponds to the larger movable fluid porosity. Notably, the detrimental effect of chlorite on T₂ relaxation was demonstrated by a strong reduction in relaxation times for the longest T₂ components, which means that the estimate of T₂ may lead to deviations in porosity and permeability. Therefore, the content of chlorite may complicate those abovementioned parameters and cause some misunderstandings at scales of pore-throat structure [66].

3.3.2. Full-Range PSD Characteristics

Taking sample J9 as an example (Figure 11), the interpolation and fitting process in the combined characterization method of mercury intrusion and NMR is shown. Excluding the error of mercury saturation at the initial stage of mercury injection, there is a very significant linear relationship between ln(T₂) and ln(r).

According to the meaning of the parameters of the fitting formula, the values of C and n were obtained. The fitting parameters of the 12 typical samples in the study area are shown in

Table 7. Conversion factors between the NMR T₂ spectrum and pore–throat radius and the corresponding correlation index.

Sample ID	Max SHg (%)	Max Movable Fluid Saturation (%)	C	1/n	R2	Fitting Formula	rcutoff (μm)
J1	86.92	53.21	0.0097	1.2357	0.9516	r = 1.2357T2 − 4.6356	0.31
J2	90.10	45.76	0.0154	1.0526	0.9768	r = 1.0256T2 − 4.1734	0.23
J3	87.09	54.65	0.0068	1.3017	0.9449	r = 1.3017T2 − 4.9908	0.27
J4	85.67	43.77	0.0242	1.0139	0.9217	r = 1.0139T2 − 3.7214	0.30
J5	88.37	58.12	0.0114	1.1560	0.9834	r = 1.1560T2 − 4.4741	0.35
J6	87.72	60.88	0.0023	1.3943	0.9797	r = 1.3943T2 − 6.0737	0.15
J7	96.43	63.87	0.0103	1.2684	0.9856	r = 1.2684T2 − 4.5756	0.50
J8	81.73	56.31	0.0012	1.3875	0.9642	r = 1.3875T2 − 6.7254	0.09
J9	95.99	57.22	0.0119	1.1280	0.9906	r = 1.1280T2 − 4.4322	0.37
J10	88.50	58.24	0.0213	1.0427	0.9512	r = 1.0427T2 − 3.8490	0.46
J11	90.26	40.13	0.0083	1.0108	0.9429	r = 1.0108T2 − 4.7915	0.09
J12	84.51	55.61	0.0312	1.1143	0.9502	r = 1.1143T2 − 0.0312	0.87

. According to the conversion relationship between T₂ and the pore-throat radius, the r_cutoff corresponding to different T_2cutoff was obtained [67].

The fitted NMR pore-throat radius distribution of each sample is shown in Figure 12. The fitted NMR pore-throat distribution curve matches the mercury intrusion curve well, and the pore-throat radius at the maximum distribution frequency is relatively consistent. The coverage of saturated water NMR is generally larger than that of HPMI, especially for relatively small pores.

The characterization results of the full-range pore-throat structure distribution are shown in

Table 8. Contribution of pore size at different scales to porosity and permeability.

Sample ID	NMR Porosity%	Micropores (<0.01 μm)		Mesopores (0.01–1 μm)		Macropores (>1 μm)
		Frequency/%	Porosity/%	Frequency%	Porosity/%	Frequency/%	Porosity/%
J1	13.47	32.87%	4.43	55.77%	7.51	11.36%	1.53
J2	11.68	30.25%	3.53	69.37%	8.10	0.38%	0.04
J3	12.78	29.59%	3.78	48.93%	6.25	21.48%	2.75
J4	9.89	14.82%	1.47	84.15%	8.32	1.03%	0.10
J5	15.76	22.03%	3.47	45.35%	7.15	32.62%	5.14
J6	18.53	18.33%	3.40	53.05%	9.83	28.62%	5.30
J7	16.36	14.76%	2.41	42.36%	6.93	42.88%	7.02
J8	18.03	4.86%	0.88	43.76%	7.89	51.38%	9.26
J9	17.29	9.59%	1.66	51.69%	8.94	38.72%	6.70
J10	15.24	23.81%	3.63	66.76%	10.17	9.43%	1.44
J11	8.73	35.74%	3.12	61.89%	5.40	2.37%	0.21
J12	17.21	22.78%	3.92	55.63%	9.57	21.59%	3.72

. According to the classification criteria of macropores, mesopores, and micropores in this paper, the contribution of each pore size range to pore volume and permeability was calculated. The distribution frequency of micropores was between 4.86% and 35.74%, with an average of 21.62%; the distribution frequency of mesopores was between 42.36% and 84.15%, with an average of 56.56%; and the distribution frequency of macropores was between 0.38% and 51.38%, with an average of 21.82%. Therefore, compared with tight sandstone reservoirs, the Chang 9 reservoir in the study area has a higher proportion of mesopores and macropores, while the proportion of micropores is small. Thus, reservoir heterogeneity is mainly caused by the differential distribution of mesopores and macropores.

The macropores, mesopores, and micropores of each sample were distinguished, and the relationship between the proportion of different types of pores and physical properties was plotted (Figure 13). The distribution proportion of mesopores and micropores was weakly negatively correlated with porosity. That is, the more mesopores and micropores there were in the sample, the lower the porosity was, while the proportion of macropore distribution was positively correlated with porosity, reflecting that the contribution of macropores to porosity was the largest among the three types.

There was no correlation between micropores and permeability, reflecting that the proportion of these pores had no significant effect on permeability. The proportion of mesopore distribution had a good negative correlation with permeability, while the proportion of macropore distribution had an obvious positive correlation with permeability (Figure 13A–F). Macropores were positively correlated with movable fluid saturation, T₂ relaxation time, and movable fluid porosity, while mesopores and micropores were negatively correlated with these three parameters (Figure 13G–I). Therefore, the relative proportion of macropores and mesopores in the samples in the study area was an important factor in determining the physical properties of the reservoir.

3.4. Oil–Water Relative Permeability and Visualizing Seepage Experiments

3.4.1. Oil–Water Relative Permeability Experimental Results

The experimental curve of the oil–water relative permeability is shown in Figure 14. Overall, the samples in the study area were generally hydrophilic, the distribution area of each sample in the common seepage area was quite different, and the common seepage triangle area was distributed on the right side of the water saturation axis. The relative permeability of oil decreased slowly, while the relative permeability of water showed an accelerated upwards trend.

The parameters of the oil–water phase permeability experiment show (

Table 9. The oil–water relative permeability parameters for the 12 typical samples.

Sample ID	Irreducible Water Saturation (%)	Water Saturation at Isotonic Point (%)	Relative Permeability at Isotonic Point	Water Saturation at Residual oil	Relative Permeability at Residual Oil	Common Seepage Area (%)	Oil Displacement Efficiency (%)
J1	42.34	62.7	0.1384	72.58	0.2461	30.24	52.45
J2	51.39	65.13	0.0926	70.13	0.1683	18.74	38.55
J3	41.08	64.05	0.1207	74.51	0.2574	33.43	56.74
J4	55.27	67.12	0.091	71.1	0.1425	15.83	35.39
J5	39.63	69.07	0.1868	86.45	0.3651	46.82	77.56
J6	36.59	71.97	0.2281	88.23	0.4240	51.64	81.44
J7	34.2	68.31	0.2106	91.05	0.4522	56.85	86.40
J8	40.25	70.02	0.1794	87.54	0.3975	47.29	79.15
J9	40.56	69.18	0.1734	85.76	0.4257	45.20	76.04
J10	41.21	67.87	0.1426	79.56	0.2973	38.35	65.23
J11	57.59	68.73	0.094	72.13	0.1471	14.54	34.28
J12	41.25	69.81	0.2112	83.85	0.3970	42.60	72.51

) that the water saturation distribution at the irreducible water was 34.2%–57.59%, with an average of 43.45%, and the water saturation at the isotonic point was distributed in the range of 62.70%–71.97%, with an average of 67.83%. In addition, the distribution of water saturation in residual oil ranges from 70.13% to 91.05%, with an average of 80.24%, reflecting that the final water-flooding effect of each sample was quite different. The relative permeability values at the isotonic point ranged from 0.09 to 0.23, with an average of 0.16, indicating that the seepage capacity of the samples in the study area was strong. The range of the co-seepage area was between 14.54% and 56.85%, with an average of 36.79%, reflecting that the significant difference in the distribution range was composed of the difference in pore-throat structure and seepage capacity. The final oil displacement efficiency was distributed in the range of 34.28%–86.4%, with an average of 62.98%, which is very different. In the actual oilfield production stage, there are serious differences in the water-flooding effect.

3.4.2. Visualizing Water-Flooding Oil Seepage Experimental Results

The differences in pore-throat structure and seepage characteristics of different types of reservoirs directly affect the oil and water displacement effects. The visual microscopic water-flooding oil experiment can effectively analyse the accumulation process represented by “oil-flooding water” and the exploitation process represented by “water-flooding oil”, which is valuable for exploring the occurrence and distribution of the remaining oil and the characteristics of oil–water seepage. This paper focuses on the water-flooding process, and the experimental results are also a visual reflection of the seepage characteristics of samples with different pore-throat structures (

Table 10. Visualizing water-flooding oil characteristic parameters.

Sample ID	Porosity (%)	Permeability (mD)	Main Displacement Path	Oil Displacement Efficiency in Anhydrous Period (%)	Final Oil Displacement Efficiency (%)
J1	11.6	1.605	reticulate	20.8	42.7
J2	9.8	0.78	fingerlike-reticulate	12.5	27.5
J3	10.9	2.78	reticulate-homogeneous	22.4	45.9
J4	8.6	0.173	fingerlike-reticulate	12.9	24.9
J5	13.3	15.65	homogeneous	45.3	68.4
J6	16.1	2.024	reticulate-homogeneous	31.5	67.3
J7	14.1	28.96	homogeneous	54.9	80.2
J8	16.4	6.075	homogeneous	43.5	72.6
J9	14.101	1.768	reticulate	30.5	67.5
J10	13.1	2.207	reticulate	24.7	55.8
J11	7.6	0.341	fingerlike-reticulate	10.8	25.8
J12	14.96	3.3122	reticulate-homogeneous	36.9	63.5

).

In the selected samples, the distribution of different displacement paths was relatively scattered, and the four flooding forms of homogeneous, reticulate-homogeneous, reticulate, and fingerlike-reticulate were each represented by three samples (Figure 15). Oil displacement in the anhydrous period is usually the flooding stage between the occurrence of water at the other end of the visualization model. After water appears at the end of model flooding, a continuous channel has formed. Therefore, the simulated formation water entering the displacement front will be displaced along the existing path. After the displacement pressure increases, part of the capillary force breaks through, and new seepage channels are opened, so the displacement paths will be more abundant than in the anhydrous period. Since the seepage channel has been established, the final oil displacement efficiency of this experiment is lower than the oil displacement efficiency obtained by the relative permeability experiment.

The oil displacement efficiency in the anhydrous period was 10.8%–54.9%, with an average of 28.9%, reflecting the great difference in the difficulty of forming seepage channels in this period. Sample J7 could easily displace 54.9% of the simulated oil, which significantly exceeded half of the final oil displacement efficiency, while sample J11 could only displace 10.8% of the simulated oil, which was still far from half of the final oil displacement efficiency of this sample. The difference in the distribution of the final oil displacement efficiency in this experiment is also very significant, ranging from 24.9% to 80.2%, with an average of 53.5%, which is still closely related to the heterogeneity of the pore-throat structure.

4. Discussion

4.1. Influencing Factors of Reservoir Physical Properties

4.1.1. Control of Pore-Throat Structure on the Reservoir Quality

The skewness and the porosity–permeability parameter are negatively correlated, indicating that although the degree of positive skewness is higher, larger pores develop. However, the degree of heterogeneity between the large and small pores increases after excessive positive deviation, resulting in poor physical properties [1] (Figure 16A,B). There was a slight positive correlation between the sorting coefficient and porosity, indicating that the sorted samples were relatively homogeneous and had more connected pore throats in the gas measurement, and this parameter had little correlation with permeability (Figure 16C,D). The coefficient of variation reflects the uniformity of the pore-throat distribution and has a weak positive correlation with porosity and permeability. Therefore, for ultralow permeability reservoirs, when the coefficient of variation is large, relatively large pore throats can provide favourable reservoir physical properties (Figure 16E,F).

The median pressure and median radius reflect that the larger the pore-throat radius is, the stronger the physical properties are [23]. There is a difference in the correlation between porosity and permeability, so the effect of pore-throat radius on porosity is higher than that of permeability (Figure 16G–J). The displacement pressure also reflects that the size of the pore-throat radius has a significant influence on the physical properties [12], indicating that the larger the pore-throat radius is, the lower the displacement pressure is and the better the physical properties are (Figure 16K,L).

The maximum mercury saturation is not related to porosity, which is quite different from conventional understanding [67]. It is speculated that the highly heterogeneous pore-throat distribution pattern is caused by the extremely complex pore-throat structure of the reservoir and the large difference in connectivity. This parameter has a weak positive correlation with permeability, indicating that pore-throat connectivity is more important in the evaluation of seepage capacity (Figure 16M,N). The efficiency of mercury ejection is similar to the trend of the maximum mercury saturation [52], indicating that the complexity of the pore-throat structure cannot be screened by the physical properties (Figure 16O,P).

Both Pc_apex and r_apex represent the pore-throat scale at the turning point of the difference in pore-throat distribution, and the concept is consistent in this paper, so the correlation trends between these two parameters and physical properties are also consistent. Both have a good correlation with porosity but a poor correlation with permeability, which again shows that the influence of the pore-throat structure scale on porosity is significant, but the effect on seepage capacity is relatively weak [30] (Figure 16Q–T).

4.1.2. Effects of Mineral Composition on Physical Properties

Mineral components mainly include quartz, feldspar, clay minerals, and cement. Quartz content has an obvious positive correlation with porosity, and quartz resistance to compaction can retain primary pores but has no correlation with permeability (Figure 17A,B). Chlorite coatings usually inhibit the secondary growth of quartz, so the content of quartz is related to the continuity of chlorite rim cementation [59]. After excluding samples with high chlorite film development, the quartz content and permeability also had a certain positive correlation, which was related to the explanation of the anti-compaction protection of the connected throat [45].

Feldspar has a weak positive correlation with porosity. Since the study area is in middle diagenetic stage A, feldspar dissolution produces dissolution pores [29]. Therefore, the higher the degree of dissolution is, the greater the porosity is. However, similar to quartz, there is no correlation between feldspar dissolution and permeability, and it is speculated that the porosity-increasing effect produced by the dissolution of the samples in the study area does not significantly improve reservoir connectivity and permeability (Figure 17C,D). In addition, feldspar dissolution is often associated with precipitation. For example, the large mould pores produced by the I/S mixed layer and laumontite have a weak effect on the increase in physical properties [44]. The overall content of clay minerals is not correlated with porosity and is positively correlated with permeability; as seen here, the correlation is affected by an anomaly. This effect may be caused by the relatively high content of delicate clay minerals, which is related to the treatment method of drying the samples after vacuuming, which makes the physical properties of several high clay minerals more complex and masks the possible flaws [59]. According to the distribution of the remaining statistical points, the correlation trend between the total content of clay minerals and physical properties is not obvious (Figure 17E,F), and it is necessary to identify them separately.

Chlorite content does not correlate with porosity, which is different from the conclusion that many tight sandstone samples are protected by chlorite coatings and increased porosity. Especially for deeply buried reservoirs, the abovementioned situation requires that the chlorite coatings be continuous, which may not be totally the same as some selected samples in this study [59]. The increase in chlorite content increases the permeability due to the influence of abnormal points (Figure 17G,H). Illite has no significant effect on porosity, and the reason for the change is consistent with that of chlorite, while illite has a weak negative correlation with permeability, indicating that hairline illite blocks the throat and reduces the seepage capacity [8] (Figure 17I,J). In addition, the effects of I/S and illite on porosity and permeability are consistent (Figure 17K,L).

Ferro-calcite cementation has a certain positive correlation with porosity, which is significantly different from previous studies [56]. It is speculated that samples with larger pore throats can be intruded by more hydrothermal fluids during diagenesis and hydrocarbon charging [58], which increases the frequency of cementation. Therefore, carbonate cementation had a very weak destructive effect on the reservoir in this sample (Figure 17M,N). There was a good negative correlation between laumontite content and physical properties, so laumontite cementation in the Chang 9 reservoir is the key factor in destroying the pore-throat structure (Figure 17O,P).

4.1.3. Effects of Fluid Flowability and Seepage Capacity on Physical Properties

In the NMR results, the movable fluid saturation had a good correlation with both porosity and permeability, reflecting that the pore-throat structure is an important factor affecting fluid flowability (Figure 18A,B). The better the physical properties are, the higher the movable fluid content will be. The NMR relaxation time T₂ is the boundary between movable and immovable fluids, and there is a corresponding relationship between T₂ and the pore-throat radius. Therefore, the larger the value is, the larger the pore-throat radius is and the larger the porosity is, but T₂ is only weakly positively correlated with the permeability, again indicating that the seepage capacity is less affected by the pore-throat scale (Figure 18C,D). Furthermore, even though the pore spaces are relatively large, the pore spaces are not interconnected, and the permeability will not increase with increasing pore size [66].

The dead pore content had a good positive correlation with movable fluid saturation, which is inconsistent with previous knowledge. This finding shows that the samples in the study area were dominated by larger pore-throat scales, and the dead pores had little effect on the overall pore space and fluid flowability [27]. Therefore, the larger the overall pore space is, the higher the corresponding dead pore content is, but the higher the movable fluid porosity is, the larger the movable fluid saturation is. This is consistent with the relaxation time T₂ in the samples from the study area (Figure 18E,F). Dead pores restrict the flow of movable fluids. For the study area, the dead pore content does not have a good matching relationship with the transverse relaxation time, which may be due to the influence of clay minerals on the NMR experiment, resulting in a certain deviation of T₂ [66]. The T₂ relaxation time has a significant positive correlation with both the movable fluid saturation and the movable fluid porosity, which indicates that the pore-throat size of the samples in the study area has a great influence on the fluid flowability (Figure 18G,H).

In the results of the relative permeability experiments, irreducible water saturation and physical properties were significantly negatively correlated, but the correlation between irreducible water saturation and porosity was higher than that of permeability (Figure 18I,J). The water saturation at the isotonic point had a weak positive correlation with the porosity [30] but did not correlate with the permeability, reflecting that the pore structure has less influence on the isotonic point, while the seepage capacity does not correlate with the isotonic point (Figure 18K,L). This phenomenon may also be affected by the error in the experimental method for gas measurement of physical properties, resulting in inaccurate permeability measurement results for individual samples containing more clay minerals [59]. The water saturation at the residual oil was positively correlated with the physical properties, but the correlation with the porosity was higher than that with the permeability, reflecting that the two-phase seepage results were more closely related to the pore-throat structure (Figure 18M,N). After inspection and after excluding the influence of clay minerals, the value increased.

The relative permeability at the isotonic point and the residual oil were significantly positively correlated with porosity, and neither showed a significant negative correlation with permeability (Figure 18O–R). The relative permeability at the isotonic point was a turning point in the change in the oil–water seepage capacity difference, and it still showed a certain correlation with the overall permeability, but the correlation was not strong. It is speculated that the samples in the study area were mainly hydrophilic and were greatly affected by the content of clay minerals, which reduced the significance of the correlation. The positive correlation between the range of the common seepage area and the porosity was better than that of the permeability, indicating that the better the pore-throat structure is, the more favourable the oil–water two-phase seepage is [68,69] (Figure 18S,T).

In the results of water-flooding experiments, the correlation between oil displacement efficiency and permeability was better in the anhydrous period, which reflects that the oil displacement in the anhydrous period was less dependent on the pore structure. In the final stage, the oil displacement efficiency had a better correlation with porosity, indicating that even if the permeability of the samples in the study area was relatively poor, they can still achieve high final oil displacement efficiency after the pressurized effect (Figure 18U–X).

4.2. Evaluation of Microscopic Heterogeneity Based on the Multifractal Dimension

4.2.1. Effects of Physical Properties and Mineral Composition on the Multifractal Dimension

Df1 and porosity showed a negative correlation trend, while Df2 and Df3 showed a weak positive correlation with porosity, reflecting that the heterogeneity of larger pores was an important reason for the decrease in porosity [10] (Figure 19A). Df1 had a very weak negative correlation with permeability, so the larger pores were more uniformly developed, and the permeability was relatively higher, while Df2 and Df3 were not correlated with permeability (Figure 19B). The distribution frequency of macropores was significantly negatively correlated with Df1, reflecting that the more macropores there are, the higher the degree of homogeneity is (Figure 19C). The distribution frequency of mesopores was weakly positively correlated with Df1, so the more mesopores there are, the greater the heterogeneity effect on larger pores will be (Figure 19D). The distribution frequency of micropores had a weak positive correlation with Df1 and a weak negative correlation with Df2, With a higher number of small pores, relatively medium and small pores will become homogeneous, while relatively large pores will become more heterogeneous (Figure 19E). Therefore, the higher the proportion of macropores, the lower the heterogeneity of the larger pores will be in the reservoir, and the more favourable the reservoir is.

The quartz content had a weak negative correlation with Df1, indicating that quartz improves the compaction resistance of larger pores [1], and the larger pores composed of primary intergranular pores were retained. Quartz had a weak positive correlation with Df3, which is presumed to be due to the filling of dissolved pores by authigenic quartz crystals, resulting in more complex smaller pore spaces and increased fractal dimensions (Figure 19F). The feldspar content had a very weak positive correlation with Df1, indicating that the lower the degree of feldspar dissolution is, the greater the structural difference between larger pores is. The feldspar content was significantly negatively correlated with Df3, indicating that in the samples with higher feldspar content, the overall pore space is smaller, thus making such pores more homogeneous (Figure 19G).

Chlorite content only had a very weak negative correlation with Df3, indicating that the effect of chlorite clay on pore filling is mostly concentrated in relatively small pores, while the effect on large and medium pores is weak (Figure 19H). Similarly, the pore filling effect of illite is similar to that of chlorite (Figure 19I) [59]. The proportion of the I/S mixed layer in the study area is extremely low, so it has no significant effect on different pore types (Figure 19J). The content of ferro-calcite and laumontite is also lower, so the relationship with the three types of pores is weak. However, the increase in the laumontite content tends to intensify the heterogeneity of larger pores, which is an important factor in destroying reservoir development [70] (Figure 19K,L).

4.2.2. Evaluation of Pore-Throat Structure Heterogeneity Based on the Multifractal Dimension

Df1 was weakly positively correlated with skewness, while Df2 and Df3 were weakly negatively correlated with skewness, reflecting the more significant the positive skewness is, the more complex the distribution of larger pores is, and the more uniform the medium and smaller pores are (Figure 20A). The sorting coefficient had a weak negative correlation with Df1 and a weak positive correlation with Df2, reflecting that the poorer the sorting is, the larger the pores that develop will be and the more homogeneous the sample will be, but the structure of medium pores becomes more complex (Figure 20B). The coefficient of variation was weakly negatively correlated with Df1, so the greater the difference between particles is, the more dominant and homogeneous the distribution of larger pores is (Figure 20C).

The median pressure had a weak positive correlation with Df1 because the higher the median pressure is, the more difficult it is to inject mercury, and the stronger the heterogeneity of larger pores is. The median pressure was not correlated with Df2 and Df3, indicating that the degree of heterogeneity of medium and small pores was not affected by changes in median pressure (Figure 20D). The median radius had an obvious positive correlation with Df2 but a weak negative correlation with Df1, indicating that the increase in the pore size of the mesopores will increase the heterogeneity of the mesopores. The increase in the pore size of the macropores will reduce the heterogeneity of the macropores (Figure 20E). The displacement pressure had only a weak positive correlation with Df1, reflecting that the higher the displacement pressure is, the smaller the radius of the relatively small pores in the macropores, which widens the gap with the macropores, so the heterogeneity of the larger pores increases [19] (Figure 20F).

The maximum mercury saturation and efficiency of mercury ejection were both poorly correlated with the fractal dimension, reflecting that the connectivity of the pore-throat structure had little effect on the heterogeneity in general, and there was only a weak positive correlation between Df1 and the efficiency of mercury ejection. This finding shows that the development of larger pores in the samples in the study area had a positive effect on the connectivity of the pore-throat structure (Figure 20G,H).

The significance of the turning point of the pore-throat structure had a certain similarity with the fractal theory. It is observed in this paper that the larger the r_apex is, the more homogeneous the larger pores are, and the stronger the heterogeneity of the medium pores is. Therefore, the increase in r_apex is constructive for larger pores and opposite for medium pores (Figure 20I). There was no correlation between the pore-throat radius at which the permeability contribution is the largest and the fractal dimension, which indicates that the evaluation of seepage capacity is weakly affected by the heterogeneity of the pore structure (Figure 20J). The mercury saturation at the turning point is also a reflection of the connectivity of the pore-throat structure, so it has a very poor correlation with the fractal dimension (Figure 20K). However, the permeability contribution value at the turning point has a weak positive correlation with Df2 and Df3, indicating that the more complex the pore structure in the medium and smaller range is, the more favourable the permeability contribution is. However, Df1 had only a very weak negative correlation with the permeability contribution at the turning point, indicating that at larger pore scales, the lower the degree of heterogeneity is, the more favourable the permeability contribution is (Figure 20L).

4.2.3. Evaluation of the Heterogeneity of Reservoir Seepage Capability Based on the Multifractal Dimension

The movable fluid saturation had a weak negative correlation with Df1 and a weak positive correlation with Df3, reflecting that the larger the pore is, the more homogeneous it is for the movable fluid. In contrast, the smaller pores are more complex and the higher the degree of heterogeneity is, the easier it is to improve the flow capacity of the movable fluid (Figure 21A). The relaxation time T₂ had a weak negative correlation with Df1 and only a weak positive correlation with Df2 and Df3, reflecting that the larger the pore scale is, the more complex the medium and small pores are and the more homogeneous the distribution of larger pores is [1] (Figure 21B). The movable fluid porosity was negatively correlated with Df1 and positively correlated with Df3, indicating that the larger the pore throat is, the higher the degree of homogeneous fluid flow is, while the greater the difference between the smaller pore throats is, the more favourable the flow of movable fluid is (Figure 21C). The content of dead pores is weakly negatively correlated with Df1 because when the proportion of larger pores is larger, the content of dead pores is correspondingly larger, but in general, the pore structure of large pores is better, so the degree of heterogeneity is reduced. The dead pore content was weakly positively correlated with Df3, indicating that in smaller pores, the disconnected pore space will increase the degree of heterogeneity of the pore structure (Figure 21D).

The water saturation of permeable irreducible water had a weak positive correlation with Df1 and a weak negative correlation with Df3, indicating that the more bound water there is in the larger pores, the worse the pore structure is and the stronger the heterogeneity is. In smaller pores, the lower the irreducible water saturation is, the stronger the heterogeneity of the pore structure is, which in turn increases the connectivity of the pore space (Figure 21E). In the oil–water relative seepage experiment, the isotonic point means that the relative permeability of the oil phase and the water phase is equal, which also means that the oil phase will lose its dominant seepage ability, and the water phase will begin to dominate. Subsequent development by water injection will greatly increase the water production rate of oil production wells. The water saturation at the isotonic point had a weak negative correlation with Df1, a weak positive correlation with Df2, and a relatively obvious positive correlation with Df3. This finding shows that the higher the water saturation of larger pores at the isotonic point is, the better the pore-throat connectivity is and the lower the heterogeneity is. The medium and small pores need to rely on strong heterogeneity to create better pore-throat connection space, which in turn helps to improve water saturation (Figure 21F). In addition, the water saturation at the residual oil is similar to that at the isotonic point, and the trend is also similar (Figure 21G).

The relative permeability at the isotonic point and residual oil had an obvious negative correlation with Df1, and both had an obvious positive correlation with Df3. This finding shows that the more homogeneous the larger the pore range is, the better the seepage ability of the two phases is. However, in the smaller pore range, due to the small pore throats, a stronger degree of heterogeneity is required to improve the two-phase seepage capacity [71] (Figure 21H,I). The range of the common seepage area had a weak negative correlation with Df1 and a weak positive correlation with Df3, indicating that the more homogeneous the larger the pores are, the better the two-phase common seepage conditions are. In the smaller pore range, the more uniform the extremely small pore space is, the more difficult it is to achieve two-phase seepage. This is because the nonwetting phase needs to overcome larger capillary forces when flowing, so it is extremely difficult to find common-seepage under extremely fine pore conditions (Figure 21J).

The oil displacement efficiency in the anhydrous period was only weakly negatively correlated with Df1, indicating that only larger pores can play a more significant role in oil displacement in the anhydrous period, and the more homogeneous the larger the pores are, the easier the oil displacement is in the anhydrous period (Figure 21K). The oil displacement efficiency in the final stage was negatively correlated with Df1, which still shows that the more homogeneous the larger the pores are, the better the oil displacement effect is. However, the oil displacement efficiency in the final stage had a weak positive correlation with Df3, indicating that the degree of heterogeneity in the smaller pores is beneficial to the oil displacement efficiency (Figure 21L). Notably, the relationship between Df2 and fluid seepage characteristic parameters is not significant because the pore-throat scale represented by Df2 identified by mercury intrusion division varies in different samples. For example, Df2 in sample 6, sample 8, and sample 9 was still in the macropore stage, not in the mesopore or small block range, so the correlation may not be significant. This phenomenon also shows that the influence of the microscopic pore-throat structure on fluid seepage is complex.

4.3. Effect Evaluation of Pore-Throat Structure on Seepage Capacity

4.3.1. Effect of Pore-Throat Structure on Fluid Flowability

This display is the fitting result after removing most of the pore-throat structure parameters with poor correlation (Figure 22). The coefficient of variation reflects the heterogeneity of the pore-throat structure and has a weak positive correlation with the movable fluid saturation. This finding shows that for the low-porosity and ultralow permeability sandstone in the study area, although the coefficient of variation increases the heterogeneity of the pore-throat structure, it also increases the proportion of larger pore-throat development, making the fluid easier to flow (Figure 22A). The median pressure and displacement pressure reflect the size of the pore throat, and both have a good negative correlation with the movable fluid saturation, indicating that the finer the pore throat is, the more difficult it is for the pore medium to flow (Figure 22B,C).

Notably, the correlation between the pore-throat radius at the turning point of the pore-throat structure and the movable fluid saturation was extremely poor, which is presumed to be caused by the influence of the multifractal characteristics of the samples in the study area, resulting in some errors in the determination of the r_apex of different samples. However, Pc_apex was significantly negatively correlated with movable fluid saturation, which still reflects that the pore size has significant control over movable fluid saturation [72] (Figure 22D). The maximum mercury saturation and efficiency of mercury ejection, which reflect the connectivity of the pore-throat structure, did not correlate with the movable fluid saturation. This shows that for the samples in the study area, the occurrence of movable fluid is significantly affected by the heterogeneity of the pore-throat structure and the size of the pore throats (Figure 22E,F).

4.3.2. Effect of Pore-Throat Structure on Two-Phase Seepage

In this paper, only the correlation analysis results of the pore-throat structure on the relative permeability and common seepage areas are shown (Figure 23). Skewness reflects the heterogeneity of the pore-throat structure and has a negative correlation with the relative permeability at the isotonic point and residual oil. Therefore, the stronger the heterogeneity of the pore-throat structure is, the lower the relative permeability is [73] (Figure 23A). Both the median pressure and the displacement pressure are parameters that reflect the size of the pore throat, and both were negatively correlated with the relative permeability. Therefore, the larger the pore size is, the higher the relative permeability and the easier the two-phase seepage (Figure 23B,C). There was a very weak negative correlation between the efficiency of mercury ejection and relative permeability, so the connectivity of the pore-throat structure did not significantly control the relative permeability (Figure 23D). The relative permeability was consistent with the correlation trend of Pc_apex and r_apex; that is, the larger the pores are, the greater the relative permeability is (Figure 23E,F).

The range of the common seepage area was negatively correlated with the skewness, indicating that the more obvious the positive deviation of the sample is, the stronger the heterogeneity is [74], the narrower the common seepage area is, and the more difficult the two-phase seepage is (Figure 23G). However, the coefficient of variation had a weak positive correlation with the range of the co-seepage area. For the samples in the study area, the larger the coefficient of variation is, the larger the pores that will develop, so two-phase seepage will occur more easily [75] (Figure 23H). The median pressure, displacement pressure, and Pc_apex were all significantly negatively correlated with the range of the co-seepage area, indicating that the larger the pore-throat scale is, the easier it is for the two-phase seepage to occur [76] (Figure 23I–K). In addition, r_apex has the same meaning as the first above three parameters (Figure 23L). Notably, the pore-throat size and heterogeneity in the pore-throat structure have a significant control effect on the two-phase seepage [24], while the pore-throat connectivity still has a weak effect on the relationship between the two-phase seepage.

4.3.3. Effect of Pore-Throat Structure on Water Flooding Efficiency

Skewness had a weak negative correlation with the oil displacement efficiency in the anhydrous and final stages, indicating that the more asymmetrical the pore-throat size distribution is, the lower the oil displacement efficiency is [30] (Figure 24A). The coefficient of variation had a positive correlation with oil displacement efficiency, reflecting that the larger the number of pores and the larger the pore scale are, the more favourable it is to improve oil displacement efficiency (Figure 24B). The median pressure, median radius, and displacement pressure all reflect the size of the pore-throat scale, and they have the same meaning as their correlation with oil displacement efficiency; that is, the larger the pore-throat scale is, the higher the oil displacement efficiency is (Figure 24C–E).

The efficiency of mercury ejection and oil displacement efficiency showed a weak negative correlation (Figure 24F), which was consistent with Figure 24D and inconsistent with conventional understanding. It is speculated that the original microscopic pore-throat connectivity of the sample was changed by increasing the injection pressure in the phase permeability experiment and the visual water-flooding experiment, and the test pressure was significantly lower than that in HPMI. In addition, the fact that air-dried samples were used can also complicate the pore-throat structure in the presence of the delicate diagenetic clays illite and I/S, which may be the reason for weak correlations [44,45] (after excluding samples J2/J4 and J11 with relatively high clay contents, the correlation coefficient R² reached 0.33). Therefore, the efficiency of mercury ejection will reflect the false pore-throat connectivity characteristics when compared between different experiments.

5. Conclusions

(1)

The reservoir generally belongs to the range of low porosity and ultralow permeability, the correlation between porosity and permeability is not strong, and the degree of microscopic heterogeneity is high. After full-range pore-throat size characterization, the pore space is dominated by larger pores, and the pore-throat structure has multifractal characteristics.

(2)

Among the pore-throat structure parameters, the pore-throat scale and heterogeneity have a significant impact on porosity, while their impact on permeability is relatively small, but the relationship between pore-throat structure connectivity and physical properties is not significant, which is caused by clay mineral contents, making the porosity and permeability of reservoirs complicated. Quartz and feldspar have obvious controls on porosity, clay minerals have weak controls on permeability, and laumontite cementation is the most important factor in destroying the pore-throat structure. In addition, the correlation of movable fluid with both porosity and permeability is good.

(3)

The better the pore-throat structure is, the more favourable the two-phase seepage is, but the effect of porosity on seepage parameters is significantly greater than that of permeability. In the water-flooding process, the oil displacement efficiency in the anhydrous period has a better correlation with permeability, and the final oil displacement efficiency has a better correlation with porosity.

(4)

Multifractal features have significant control on pore-throat structure and seepage capacity. Df1 generally has a significant correlation with various parameters, followed by Df2. The more developed the larger pores are, the lower the reservoir heterogeneity is and the better the physical properties are. Reservoir quality is mainly determined by the development ratio of macropores and mesopores. For mesopores and micropores, the higher the degree of heterogeneity is, the better the reservoir development is.

(5)

The pore-throat structure has a crucial influence on the occurrence of movable fluid, fluid flowability, and water-flooding effects. The pore-throat scale and pore-throat structure heterogeneity have significant effects on the above aspects, while the correlation between pore-throat connectivity and those parameters is complicated. It is speculated that the pressurization process in the experimental stage changed the pore-throat connectivity characteristics, resulting in the appearance of false pore-throat connectivity characteristics when comparing multiple experimental parameters. Additionally, the fact that air-dried samples were used can also complicate the pore-throat structure in the presence of the delicate diagenetic clays illite and I/S, which may be the reason for weak correlations (after excluding samples J2/J4 and J11 with relatively high clay contents, the correlation coefficient R² can reach 0.33).