The Fractal Characteristics of Pore Networks in Tight Sandstones: A Case Study of Nanpu Sag in Bohai Bay Basin, NE China

Abstract

In the exploration of unconventional petroleum resources in the Nanpu Sag of China, several tight oil sandstone reservoirs have been identified; however, their physical properties display pronounced heterogeneity. Using methods such as scanning electron microscopy (SEM), thin-section petrography, X-ray Diffraction (XRD), and high-pressure mercury intrusion, this study analyzed the mineralogical, petrological, and reservoir characteristics of the tight oil sandstone reservoirs in the second member of the Dongying Formation in the Nanpu Sag. This study also examined the relationship between the heterogeneity of the pore networks in the tight oil sandstone reservoirs and their fractal dimensions. The results indicate that as the fractal dimension (Df) of the tight oil sandstone reservoirs increases, their permeability decreases exponentially. The Df is strongly linked to pore morphology: larger Df values correspond to smaller pore sizes, more complex pore shapes, and greater pore heterogeneity. Additionally, variations in Df are closely linked to mineralogy: lower quartz content and higher clay content, particularly abundant illite–smectite mixed layers and illite along with reduced kaolinite, are associated with higher Df values. These findings highlight the complex, irregular nature of pore structures in tight sandstones and demonstrate that integrating high-pressure mercury intrusion analysis with fractal theory provides an effective approach for quantitatively characterizing their heterogeneity.

1. Introduction

With advances in petroleum exploration technology, tight-oil and tight-gas sandstone reservoirs have emerged as major contributors to unconventional petroleum resources [1,2,3,4]. In China, such reservoirs are widely developed and resource-rich in basins including the Ordos, Tarim, Songliao, and Sichuan basins [1,5]. Tight sandstones are characterized by poor physical properties, fine pore throats, and strongly heterogeneous pore structures, with flow behaviors that differ markedly from those of conventional reservoirs [1,5,6,7,8]. These characteristics exert a strong control on hydrocarbon accumulation patterns, making the study of tight-sandstone reservoir properties critical for unconventional petroleum exploration [1,5,6,8].

In the Bohai Bay Basin (located in northeastern China, spanning Beijing, Tianjin, Hebei, Shandong, Liaoning, and the Bohai Sea), exploration of unconventional petroleum resources has made significant progress, with large tight-oil and tight-gas accumulations discovered in the Zhanhua, Dongying, and Dongpu sags [6,9]. In the adjacent Nanpu Sag, recent discoveries of abundant tight-oil sandstone resources suggest that it will become a key target for future exploration [2,5,9]. However, the reservoir characteristics of these tight sandstones remain poorly understood [5,9]. Here we investigate tight-oil sandstone reservoirs in the second member of the Dongying Formation within the No. 4 structure of the Nanpu Sag. Using thin-section petrography, Scanning Electron Microscopy (SEM), mineral analysis, and high-pressure mercury intrusion, we characterize their pore network fractal properties. Based on high-pressure mercury intrusion data, we perform the first fractal-dimension analysis of Nanpu Sag tight sandstones to quantitatively assess their heterogeneity. The results provide new insights into the microscopic characteristics of these reservoirs and offer a reference for studies of tight sandstones in other regions.

2. Geologic Setting

The Nanpu Sag lies on the northern margin of the Bohai Bay Basin. Its northwestern boundary is defined by the Xinanzhuang Fault, and its northeastern boundary by the Bogezhuang Fault. Together, these faults have strongly influenced the structural evolution of the sag’s northern sector. The southern boundary is marked by the Shabei Fault, which separates the sag from the Shaleitian Uplift. Several secondary faults are also developed within the sag (Figure 1). Structurally, the Nanpu Sag comprises seven main structures—the No. 1 to No. 5 structures, Laoyemiao, and Gaoshangbao—and two sub-sags, Shichang and Linque [5,10]. The present study focuses on Well N4, located in the No. 4 structure on the eastern side of the sag (Figure 1), a key site for understanding the pore-network heterogeneity of tight sandstones in this region.

The Nanpu Sag contains well-developed Paleogene and Neogene strata. From bottom to top, these comprise the Paleogene Shahejie Formation (Es) and Dongying Formation (Ed), the Neogene Guantao Formation (Ng) and Minghuazhen Formation (Nm), and Quaternary deposits (Figure 2). During the Cenozoic, the sag experienced three main stages of structural evolution: a dominant extension phase (Es), a tectonic transtension phase (Ed), and a post-rift depression phase (Ng-Nm). The Ed was marked by high rates of both tectonic and total subsidence (Figure 2) [5,9,10]. Three major sets of lacustrine source rocks occur in the third and first members of the Es and the third member of the Ed. The principal reservoirs are sandstones deposited in Paleogene deltaic and Neogene fluvial settings (Figure 2) [3,5,10]. Recent exploration in the tight sandstone reservoirs of the No. 4 structure has revealed multiple oil accumulations, underscoring the substantial potential of the second member of the Ed for tight oil development [5,9,10].

3. Samples and Methods

3.1. Samples

Nineteen sandstone samples were collected from the second member of the Dongying Formation in the No. 4 structure of the Nanpu Sag. The samples comprise siltstone and fine sandstone deposited in a lacustrine deltaic environment (Figure 1 and Figure 2). All were obtained from depths of 3820 to 3860 meters, and exhibit characteristics typical of oil-bearing tight sandstone reservoirs.

3.2. Methods

Mineralogical analyses of the 19 samples were performed using a D/max-2500 diffractometer (Rigaku, Tokyo, Japan) to determine bulk-rock and clay-mineral compositions, following the treatment process and analytical procedures described by Yang et al. 2018 [11]. X-ray diffraction results provided quantitative mineralogical data for the sandstone samples (

Table 1. X-ray diffraction analysis results of the samples from the tight sandstone reservoir.

Sample	Depth (m)	Quartz (%)	Feldspar (%)	Carbonate (%)	Clay (%)	Illite-Smectite Mixed Layer (%)	Illite (%)	Kaolinite (%)	Chlorite (%)
1	3828.31	64.5	26.1	5	4.4	40.1	7.7	42.9	9.3
2	3830.71	55.5	34.8	3.6	6.1	52	9.2	28	10.8
3	3831.56	59.8	27.8	5.9	6.5	61	8.8	21.4	8.8
4	3832.62	54.9	31	5.5	8.7	66.8	7.9	17.1	8.2
5	3834.25	61.9	31	2.5	4.7	41.2	4.7	40.5	13.6
6	3834.82	59.3	31.9	3.6	5.3	42.2	8.5	37.6	11.7
7	3835.61	64.7	27.5	2	5.7	51.8	10.4	28.3	9.5
8	3837.16	63.4	31.7	0.8	4.1	28.9	4.6	54.2	12.3
9	3838.9	60.1	27.6	9.5	2.8	29	5.2	50.9	14.9
10	3839.8	57.2	34.8	3	5	50	8.1	29.3	12.6
11	3841.18	63.9	28.1	4.2	3.5	38.5	4.3	51.4	5.8
12	3841.65	65.6	27.4	3.1	3.9	42.3	3.7	43.5	10.5
13	3852.68	57.5	21.7	18.4	2.4	79.6	4.3	9.2	6.9
14	3853.68	61	24.6	11	3.4	63	8.3	16.2	12.5
15	3853.99	63.2	24.7	9	3.1	67.7	7.3	13.6	11.4
16	3854.86	63.2	25.4	8.1	3.3	69	8.5	10.1	12.4
17	3855.69	50.2	34.6	9	6.2	73.1	7	10.9	9
18	3855.62	62.9	24.4	9.2	3.5	50.6	5.6	36.4	7.4
19	3858.12	62.4	29.9	3.1	4.2	64.3	5.6	22.3	7.8
Mean value		60.8	28.7	6	4.5	54.2	6.7	28.8	10.4

). Routine core analysis, including grain density, porosity, and air permeability measurements, were carried out using a CMS-300 instrument (Core Lab Instruments, Houston, TX, USA).

Thin-section and scanning electron microscope (SEM) analyses were conducted on all 19 samples. Thin sections were impregnated with blue epoxy resin to enhance the visibility of fractures and micropores. SEM observations were used to characterize pore structures and identify clay-mineral morphologies within the reservoir samples.

High-pressure mercury intrusion testing takes advantage of mercury’s non-wetting behavior on solid surfaces, requiring external pressure to force mercury into a sample’s pores. Smaller pores require higher pressure to be filled. By applying a range of pressures, the corresponding pore sizes can be calculated [6,8,12]. Mercury intrusion measurements were performed using an Autopore IV 9500 mercury intrusion porosimeter (Micromeritics Instrument Corp., Norcross, GA, USA). The volume of mercury intruded at each pressure was recorded to determine pore-size distribution and total pore volume.

3.3. Fractal Theory

In 1975, French mathematician Mandelbrot B.B. introduced fractal theory [13], which has since been widely applied to describe complex and irregular geometries in space. The fractal dimension (Df) derived from high-pressure mercury intrusion data is recognized as an effective parameter for quantifying the complexity and heterogeneity of pore-throat structures in porous media [1,6,8]. Based on sample capillary pressure curves, Df can be calculated using the Brooks-Corey method [12]. Previous studies have proposed optimized models linking Df to rock properties [6,14]. The calculation of Df is given by:

S_Hg = a × P_c^−(2−Df)

Here, S_Hg denotes mercury saturation, P_c is capillary pressure, and a is a constant.

The formula implies that P_c and S_Hg display a linear relationship when plotted on a double logarithmic scale (log(S_Hg) versus log(P_c)). The Df can then be determined from the slope of this linear trend [6,12,14] using: Df = S + 2, where S is the slope of the log(S_Hg) versus log(P_c) plot. This approach provides a quantitative measure of the complexity and heterogeneity of pore structures in porous media.

4. Results

4.1. Mineral Content

The sandstone samples are primarily composed of quartz, feldspar, carbonates, and clay minerals, in decreasing abundance (Table 1). Quartz content ranges from 50.2% to 65.6% (average 60.6%), followed by feldspar at 21.7–34.8% (average 28.7%), carbonates at 0.8–18.4% (average 6.1%), and clay minerals at 2.4–8.7% (average 4.6%). Among the clay minerals, illite-smectite mixed-layer dominate, ranging from 28.9% to 79.6% (average 53.2%), followed by kaolinite at 9.2–54.2% (average 29.7%), chlorite at 5.8–14.9% (average 10.3%), and illite at 3.7–10.4% (average 6.8%).

4.2. Porosity and Permeability

Conventional rock property tests indicate that porosity in the sandstone samples ranges from 5% to 18.9% (average 12.4%), while permeability varies from 0.005 mD to 2.92 mD (average 0.7 mD). Except for five samples (samples 5, 8, 11, 18, 19) with permeabilities exceeding 1 mD, most samples exhibit low permeability (<1 mD), characteristic of tight reservoirs with low porosity and permeability (Figure 2;

Table 2. Microscopic pore structure parameters of the 19 tight oil sandstone samples.

Sam.	Por. (%)	Per. (mD)	r35 (μm)	r50 (μm)	rmax (μm)	Pd (MPa)	Pci (Mpa)	SHgi (%)	Df	Maximum SHg/Pc (%/Mpa)
1	13.2	0.122	0.235	0.100	1.399	0.526	1.50	17.56	2.57	12.3
2	12.9	0.03	0.061	0.027	0.488	1.506	4.96	18.62	2.56	3.81
3	8.1	0.009	0.036	0.024	0.354	2.08	5.04	14.03	2.67	2.8
4	12.9	0.01	0.034	0.025	0.354	2.080	7.93	15.08	2.97	1.92
5	18.9	2.24	0.521	0.105	6.201	0.072	0.30	20.53	2.23	50.2
6	16.2	0.555	0.276	0.101	1.434	0.513	1.01	14.66	2.47	15.75
7	13.6	0.041	0.023	0.011	0.364	2.019	4.95	9.98	2.63	2.21
8	17.3	2.92	0.615	0.287	2.441	0.301	1.01	31.37	2.26	33.06
9	9.8	0.819	0.463	0.253	3.392	0.217	0.51	16.86	2.34	40.99
10	12.4	0.081	0.075	0.039	0.728	1.010	1.50	9.34	2.61	6.97
11	17.5	2.15	0.733	0.377	1.974	0.499	1.00	35.03	2.22	36.86
12	12.4	0.753	0.449	0.243	3.440	0.214	1.02	19.19	2.28	22.91
13	5	0.006	0.045	0.018	0.491	1.099	1.98	9.43	2.59	4.88
14	9.6	0.011	0.050	0.029	0.489	1.505	2.05	11.08	2.45	5.09
15	8.8	0.012	0.105	0.053	1.075	0.499	2.05	18.51	2.49	9.76
16	7	0.005	0.030	0.019	0.370	1.986	6.22	1.72	2.97	1.57
17	10.3	0.01	0.022	0.013	0.062	3.800	8.12	1.73	2.99	0.46
18	13.5	1.17	0.522	0.291	1.472	0.500	1.01	23.93	2.33	26.03
19	16.8	2.21	0.392	0.151	2.453	0.300	1.51	28.87	2.29	22.39

) [1,8]. The permeability-porosity crossplot reveals a weak exponential correlation, with a correlation coefficient (R²) of 0.65 (Figure 3). Microfractures are identified as the primary factor controlling permeability in these tight sandstones. Samples exhibiting well-connected microfractures or enhanced pore connectivity may deviate from the general porosity- permeability trend [1,8,15].

r₃₅, r₅₀ and r_max (pore throat diameter at 35%, 50% and maximum mercury saturation, respectively), P_d (point on the curve where mercury first enters pores of rock), Parameters for the inflection points: P_ci (intrusion pressure) and S_Hgi (mercury saturation).

4.3. Pore Network Characteristics

Figure 4 presents a representative capillary pressure curve obtained from high-pressure mercury intrusion testing (intrusion pressure vs. mercury saturation). The corresponding pore-throat size is shown in Figure 5, illustrating variations in reservoir pore structure. Key parameters derived from the intrusion pressure curves are summarized in Table 2. The displacement pressure (Pd), marking the point at which mercury first enters the rock pores, ranges from 0.072 to 3.8 MPa (averaging 1.1 Mpa). This parameter corresponds to the maximum pore-throat radius (r_max), which varies from 0.062 to 6.201 μm (average 1.5 μm). The pore-throat radii at 35% and 50% mercury saturation (r₃₅ and r₅₀) range from 0.022 to 0.733 μm and from 0.011 to 0.377 μm, with averages of 0.247 μm and 0.114 μm, respectively. Microscopic observations under optical microscopy and SEM (Figure 6) reveal that the pore system is dominated by intergranular pores, intragranular pores, microfractures, and clay aggregate-associated micropores. These pore types exhibit distinct size differences, generally following the order: microfractures > intergranular pores > intragranular pores > clay aggregate-associated micropores (Figure 6). The combination of these pore types, along with the wide variation in measured parameters, reflects the complex and heterogeneous nature of the reservoir’s microscopic pore-throat structure (Table 2, Figure 4, Figure 5 and Figure 6).

Sample No. 1, φ (Porosity) = 13.2%, K (Permeability) = 0.122 mD, P_d (Entry Pressure) = 0.526 MPa, r₅₀ = 0.1 μm, 3828.31 m; Sample No. 4, φ = 12.9%, K = 0.01 mD, P_d = 2.08 MPa, r₅₀ = 0.025 μm, 3832.62 m; Sample No. 9, φ = 9.8%, K = 0.819 mD, P_d = 0.217 MPa, r₅₀ = 0.253 μm, 3838.9 m.

4.4. Fractal Characteristics

Analysis of the log(S_Hg)–log(P_c) plots for the 19 samples revealed strong linear correlations, with R² values consistently exceeding 0.89. All samples exhibited clear fractal characteristics in their microscopic pore structures. As shown in Figure 7a, the log(S_Hg)–log(P_c) curve at P_c = 1.87 MPa (S_Hg = 23.0%) is divided into two distinct segments: the high capillary pressure segment, corresponding to small pores, displays a relatively gentle slope (S = 0.57), while low capillary pressure segment, representing larger pores, exhibits a steeper slope (S = 3.68). Using the relationship Df = S + 2, the corresponding fractal dimensions were calculated as 2.57 for small pores and 5.68 for large pores (Figure 7a). For all samples, the calculated Df values were less than 3, in accordance with the physical constraints of rock microstructures, as fractal dimensions exceeding 3 lack physical meaning [6,12]. The log(S_Hg)–log(P_c) curves consistently exhibited a two-segment pattern across the dataset, allowing individual fractal dimensions to be determined for each segment. Statistical analysis of the Df values less than 3 (Figure 7, Table 2) shows a range from 2.22 to 2.99, with an average of 2.50, reflecting the high degree of complexity and heterogeneity in the microscopic pore structures.

5. Discussion

5.1. Pore Systems Consisting of Pores

Intergranular pores, formed between mineral grains and typically modified by mechanical compaction or cementation, often persists as residual triangular-shaped pores (Figure 6c,d). These pores represent the primary component of the reservoir’s original porosity [1,16]. During diagenesis, dissolution within mineral grains generates intragranular pores, which commonly display irregular morphologies (Figure 6c,e). These secondary pores, primarily resulting from feldspar dissolution, generally exhibit poor connectivity [16,17]. Brittle mineral grains are prone to fragmentation under compaction, producing microfractures (Figure 6g,h) that typically have good connectivity and can markedly enhance reservoir permeability [1,15,16]. In addition, intergranular pores partially filled with authigenic clay minerals contain abundant micropores associated with clay aggregates, whose shapes depend on the mineralogy and morphology of the clays present (Figure 6f–h). Different clay mineral types produce distinct micropore geometries, thereby influencing overall pore connectivity [17,18]. Collectively, these observations demonstrate the highly heterogeneous nature of the reservoir’s pore system, shaped by multiple geological processes during deposition and diagenesis.

5.2. Correlations Between Df and Pore Structure Parameters

The Df exhibits a clear negative correlation with the pore-throat radii r₃₅ and r₅₀, with correlation coefficients of R² = 0.77 and 0.69, respectively (Figure 8). Df also shows a strong negative correlation with the maximum S_Hg/P_c value (R² = 0.87) (Figure 9). This trend indicates that greater pore complexity, as reflected by higher S_Hg/P_c values, is associated with higher Df values. Previous studies have shown that micropores (<10 μm) exert a stronger control on Df than meso- or macropores, making Df a sensitive indicator of micropore development [1,6,14]. Tight oil sandstones, characterized by small pore sizes, narrow pore throat radii, and poor connectivity, display features that are closely linked to Df. Higher Df values correspond to smaller pore sizes, more irregular pore shapes, and greater heterogeneity in the pore system [1,6]. The relationship between Df and permeability is particularly significant, showing an exponential decline in permeability with increasing Df (R² = 0.68) (Figure 10a). By contrast, Df has only a weak negative correlation with porosity (R² = 0.31), indicating that pore shape complexity impacts permeability far more strongly than porosity (Figure 10). This is because Df reflect not only the size of pores and pore throats but also their geometric complexity—both critical factors controlling fluid flow in tight reservoirs [1,6,8]. As pore shapes evolve from regular to highly irregular forms, fluid pathways become more tortuous, reducing permeability and driving Df to higher values [1].

5.3. Correlations Between Df and Mineral Content

The Df shows a weak negative correlation with quartz content (R² = 0.28) and a weak positive correlation with total clay content (R² = 0.24), but no significant correlation with feldspar and carbonate content (Figure 11). Df decreases as quartz content increases (Figure 11a), likely because the relatively smooth surface of quartz grains reduce the abundance of micropores (Figure 6c,d), thereby lowering pore structure irregularity and heterogeneity. This trend is consistent with previous findings [19,20]. Although feldspar and carbonate minerals can increase dissolution porosity and reduce pore structure heterogeneity [14,21], in this study their effect on Df is minimal. This may be because dissolution and intragranular pores within feldspar and carbonate are often isolated or nano-sized, making them difficult to characterize fully via high-pressure mercury intrusion (Figure 11c,d). In contrast, higher clay content tends to increase pore structure complexity and heterogeneity, resulting in higher Df values (Figure 11b) [8,16,18]. Clay minerals typically occur between grains, impeding fluid flow through intergranular pores and microfractures, and thereby enhancing pore-throat tortuosity (Figure 6b,d,f–h). However, the impact varies by clay mineral type (Figure 12): Df shows a weak positive correlation with illite-smectite mixed layer (R² = 0.44) and illite (R² = 0.29), but a weak negative correlation with kaolinite (R² = 0.52) and no significant correlation with chlorite (R² = 0.01). Illite and illite-smectite mixed layer clays, with their fibrous or filamentous morphologies and rough surfaces, tend to occlude pore throats and increase heterogeneity (Figure 12a,c) [8,16,18]. In contrast, kaolinite, often formed from feldspar alteration, has a smoother, platy or accordion-like morphology that reduces pore-throat complexity even when present in pore-filling positions (Figure 12b) [8,17,18,22]. Overall, higher illite-smectite mixed layer and illite contents correspond to higher Df, while higher kaolinite content is associated with lower Df, indicating that clay types exerts distinct and contrasting influence on reservoir quality in tight sandstones.

6. Conclusions

The pore structure of the tight sandstones in the second member of the Ed Formation, Nanpu Sag, is dominated by residual intergranular pores, intragranular pores, microfractures, and micropores within clay aggregates. Pore sizes are mainly in the nano- to micrometer range. High-pressure mercury intrusion data indicate that these reservoirs posses highly complex and heterogeneous pore systems. The Df shows a strong negative correlation with permeability, with permeability decreasing exponentially as Df increases. Higher Df values correspond to smaller pore sizes, more complex pore shapes, and greater heterogeneity. Mineral composition also influences Df: lower quartz content and higher clay content are associated with higher Df values. Among clay minerals, illite-smectite mixed layer and illite contents show a positive relationship with Df, whereas kaolinite content exhibits a negative relationship.