“Tight reservoirs”, with rich oil and gas resource, are generally tight, but strong in heterogeneity still. Tight reservoirs in different areas differ widely in moveable fluid content^[1,2,3]. Pore structure not only determines the storage and flow characteristics of these reservoirs, but also their fracturing effects and ultimate recoverable reserves^[3,4]. Therefore, pore structure and controlling factors of reservoir quality are important for the exploration and development of tight oil.

Pores in tight reservoirs are mostly nano and micron scale, mostly less than 2 μm^[5,6]. For example, the pores in Triassic Yanchang Formation of Ordos Basin are largely 50-900 nm in size^[7]. Since pores of different types vary widely in size, pore size of tight reservoirs may be continuous, unimodal, or bimodal^[4,7-9]. In tight sandstone, large pores often determine the permeability, while small pores contribute the most part of pore volume^{[9,10,11,12,13]}, pore-throats of different orders have different effects on porosity and permeability. But which order of the pore-throat has the major influence on tight sandstone poro-permeability, and how pore size distribution is related to oil occurrence in tight sandstones are rarely discussed.

Usually each testing method characterizes the pore structure based on a single pore model. For example, capillary model is used to represent the pore throat structure during mercury intrusion testing, which is inefficient to reflect the structural diversity of pore throat with different size. Fractal geometries are widely used to describe pore structure in recent years, however different conclusions are exist in recent works. For example, in many works the fractal dimension of small pores show a negative correlation with permeability of sandstone, indicating that small pores controls the complexity of pore systems. The more complicated the small pore structure, the lower the permeability^[14,15]. Some other works had opposite conclusion that macro pores had more important influence on the pore structure as they had larger fractal dimension^[16]. The main cause for these opposite conclusions is that the fractal dimension of pore space is calculated based on a single and simplified pore model which is unable to describe the pore structure variation with pore size.

In this work, the fractal dimension of pore throat of typical tight sandstone samples from Chang 7 member, Yanchang Formation, Ordos Basin, are calculated by mercury intrusion data. The structure of pore throat with different sizes and its differential controls on reservoir quality and oil saturation are further analyzed based on thin sections, porosity, permeability, oil saturation data.

14 core samples of Chang7 tight sandstone from Ordos Basin were selected for thin section petrology, porosity, permeability and mercury intrusion tests (Tables 1 and 2). Fractal dimension of each sample was calculated with the mercury intrusion test data. To find out the effect of pore structure on oil saturation, the sandstone samples with oil and gas shows were taken preferentially.

Plug samples 2.5 cm in diameter were drilled from the core to make cast thin section and to be used in physical property and mercury intrusion tests. Before testing, the core plug was washed to remove crude oil and salt contamination, the sample was washed using a Soxhlet extractor with a solvent mixture of methanol and methylene chloride. Cleaning procedure was finished until the extract remained clear and showed no luminescence under fluorescent light. Then, the sample was dried in microwave at 100 °C for 24 h. Red resin was then injected into the dried sample for pore identification. Thin section 0.03 μm thick was made using finer abrasive grit. Texture, composition, and pores were observed and counted at 300 points per thin section under a polarizing petrographic microscope.

Porosity was measured by core helium porosimeter with air method. Permeability was measured by pressure-falloff gas permeameter with the permeability test range from 0.001× 10^-3 μm² to 30 000×10^-3 μm². Oil saturation data of 11 fresh cores with the same depth was collected in this work. High- pressure mercury intrusion testing was done on AutoPoreIV mercury porosimetry at 22 °C, relative humidity of 46%-68%, and the mercury interfacial tension (σ) of 0.49 N/m.

Mercury is non-wetting phase for most solid interfaces and needs to overcome capillary pressure to get into the capillary. According to the Young-Laplace equation^[17], mercury intrusion pressure p_c is controlled by throat radius r, interfacial tension σ and contact angle θ:

The capillary pressure curve can be obtained based on mercury intrusion volume and the corresponding pressure to work out important parameters such as displacement pressure, and medium pressure (injection pressure when mercury saturation is 50%). Then, by using formula (1), pore structure parameters such as maximum interconnected radius, median radius and pore throat radius distribution curve can be calculated.

Fractal is defined as "a rough or fragmentary geometry that can be divided into several parts, and each part of which has the same statistical character as the whole", namely the self-affinity nature. Fractal dimensions of the 14 samples were calculated with capillary pressure data in this work. According to the fractal theory, the number of the units N(r) has a power-law function with the radius r of the unit chosen to fill the fractal object^[18]:

If reservoir pores have fractal feature, the radius of pore throat (r) is the measured linear scale. N(r) can be calculated with pore throat radius r and injected mercury volume V_Hg according to the capillary tube model:

Arranging Eqs. (1) and (2):

Substituting Young-Laplace Eq. (1) into Eq. (5):

Mercury saturation S_Hg can be expressed as:

Assuming that length l is constant, the relationship between S_Hg and p_c can be obtained by substituting Eq. (6) into Eq. (7):

where α is a constant, mercury saturation S_Hg has a Power-law relationship with capillary pressure P_c. Taking logarithm on both sides of Eq. (8):

lg S_Hg -lg p_c shows a linear relationship with intercept C on a log-log plot. Fractal dimension (D) can be calculated from the slope of linear relationship of lg S_Hg-lg p_c.

Mineralogical data obtained by point-counting shows that the 14 samples include lithic feldspathic sandstone, lithic sandstone and feldspar lithic quartz sandstone. They have a quartz content range from 22.5%-54.0%, 38.6% on average, and feldspar content range from 7.5%-48.0%, 26.0% on average. In the samples, the lithic fragments are mainly metamorphic rock, quartzite, and phyllite, accounting for 9.0% to 25.0%, 14.5% on average; interstitial materials are mainly clay matrix dominated by hydro mica, accounting for 2.0% to 31.8%, 8.3% on average; cement accounts for 5.5% on average, and is mainly composed of ferrocalcite and ankerite (with a mean content of 1.6% and 1.0% respectively), followed by silica, minor clay and albite. The samples are mostly coarse siltstone, fine-grained sandstone and graywacke with grain size ranging from 0.08-0.30 mm, 0.16 mm on average. The clasts are moderately to poorly sorted and mostly subangular.

Observation of thin sections shows the tight sandstone samples have many types of pores. Pores that are large in size and can be clearly identified under polarizing microscope include well-preserved intergranular pores and grain dissolution pores. These large pores were counted mainly in surface porosity statistics. In addition, these samples have some small pores, which are easy to identify because of the adsorbed asphalt, but are difficult to count their surface porosity. These small pores include: small residual pores resulting after intense compaction and cementation, small dissolution pores formed by weak dissolution, intercrystalline pores associated with clay minerals, such as illite, flake-like interlamellar micropores formed as a result of mica alteration and micropores within phyllite and schist metamorphic rock fragments (Fig. 1).

The surface porosity of the 14 samples varies widely from 0.3% to 3.7%, with an average of 1.1%. The porosity of dissolution pores (mainly feldspar dissolution pores) and intergranular pores average at 0.8% and 0.3% respectively (Table 1). Physical property tests show the samples have a porosity range from 5.0% to 13.8%, 9.42% on average, and a permeability range from 0.027 6 to 0.282 0 (×10^-3 μm²). The oil saturation of 11 fresh core samples taken from the same depth ranges from 23.7% to 72.3%, with an average of 42.3% (Table 2). The ratio of the pore volume with oil to the whole rock volume is defined as the oil-bearing porosity. Oil bearing porosity is the product of oil saturation and effective porosity. The calculated results show the oil-bearing porosity of the samples range from 2.3% to 10.0%, with an average of 4.26%.

Capillary pressure curves of the 14 samples are shown in Fig. 2. It can be seen all the curves have small skewness and well sorting. But the samples vary widely in maximum mercury saturation from 48.47% to 84.93%, with an average of 69.6% (Table 2 and Fig. 2). A considerable part of pore throats (30%) are too small to have mercury injected. The samples have displacement pressures from 1.41 to 7.89 MPa, 4.42 MPa on average; medium pressure from 0 to 45.73MPa, 15.43 MPa on average; and maximum interconnected radius from 0.08 to 0.52 μm, 0.19 μm on average (Table 2).

Pore throat radius distribution converted from Pc and V_Hg shows that the 14 samples all have pore throat radius of less than 1 μm (Fig. 3) and single peak in pore throat radius distribution. If peak radius is defined as the apex of radius distribution curve, the samples range from 0.07-0.25 μm in peak radius, with an average of 0.11 μm. Peak radius increases with the increase of porosity, for example, samples No.1-No.5 and No.7-No.9, with small porosity, have peak radius of less than 0.1 μm; while samples No.9-No.14 with porosity of more than 10% have peak radius of more than 0.1 μm.

Fractal dimensions calculated from mercury intrusion data is presented in Table 3 and Fig. 4. Fig. 4 shows that the capillary pressure vs. injection mercury saturation curves of all samples in the log-log diagram have two distinct linear segments with different slopes. The first segment is characterized by low capillary pressure and high slope, representing the fractal characteristics of large pore throat. The second half segment therefore represents the fractal features of small pore throat. The correlation coefficients of both segments are generally greater than 0.90, except for second segment of sample No.5 and No.9 (which are 0.86 and 0.84) (Table 3).

The pore throat radius corresponding to the turn point of the two segments is defined as turning radius. The turning radius is approximately equal to the peak radius, with a correlation coefficient of 0.99 (Table 3 and Fig. 5). Therefore, the turning radius is regarded as the peak radius. According to formula (9), fractal dimension D₁ of large pore throat of the first segment of the samples were calculated, ranging from 4.52-7.52, on average 5.62; and the fractal dimension D₂ of small pore throat of the samples range from 2.14-2.66, with an average of 2.40 (Table 3).

Supposing the pore throat larger than the peak radius is large pore throat with a porosity of ϕ₁; the pore throat smaller than the peak radius allowing mercury injection is small pore throat, with a porosity of ϕ₂, and the pore throat that mercury cannot be injected into under testing condition is micro pore throat, with a porosity of ϕ₃ (Table 3). The 14 samples have an average ϕ₁ of 2.64%, less than ϕ₂ (4.11% on average) and ϕ₃ (2.79% on average). The variation coefficient of ϕ₁ is 0.51, which is larger than that of ϕ₂ (0.37) and ϕ₃ (0.29), indicating that: (1) For the 14 samples, small pore throats make the most contribution to pore volume, followed by micro pore-throats, and large pore throats. (2) The samples vary widely in development degree of large pore throat, but stable and similar small pore throats and micro-pore throats (Fig. 6).

ϕ₁ and ϕ₂ are positively correlated with the porosity ϕ (Fig. 7), with correlation coefficients of 0.68 and 0.57, respectively. ϕ₃ shows no correlation with ϕ. ϕ₁ is positively correlated with permeability, with a correlation coefficient of 0.61, ϕ₂ has poorer correlation with permeability, with a correlation coefficient of (0.31), and ϕ₃ has no correlation with permeability. The correlations of ϕ₁, ϕ₂ and ϕ₃ with porosity and permeability indicate that the large pore throat is the main controlling factor for the variations of porosity and permeability, despite its low contribution rate to pore volume, this is different from the previous understanding that the large pore throat only affects permeability^[13,14,15]. The small pore throat contributes some to porosity variation, but has minor effect on permeability. Whereas the micro pore throat shows no influence on both porosity and permeability change. Therefore, it can be concluded that the large pore throat in tight sandstone is the major factor for the reservoir property heterogeneity.

It is generally believed that oil can be stored in pores with sizes from micron to several nanometers in tight oil reservoirs^[19,20] and is moveable in pores more than 0.02 μm in diameter^[21]. But this study shows oil bearing porosity only has moderate to good correlation with ϕ₁ (R²: 0.76, Fig. 8) and no correlation with ϕ₂ and ϕ₃ (R²: 0.000 4 and 0.050 0 respectively). This indicates: (1) Large pore throat is critical for oil emplacement. During oil accumulation, oil would charge into large pore throats firstly, and then small and micro pore throats. If oil mainly filled in small pore th roats, oil bearing porosity should have been well correlated with ϕ₂. Based on the ϕ₁ of large pore throat and oil-bearing porosity of the samples, if the large pore throats are fully filled with oil, then about 65% of the oil phase on average will be stored in the large pore throats. (2) Pore throat size distribution of tight sandstone during the oil accumulation should be similar to present state. As long as the large pore throats were filled with oil, the oil saturation would probably remain unchanged, because when oil accumulated in Chang7 tight sandstone, the Chang7 sandstone had been deep buried and intensely compacted, and would be fairly stable thereafter; additionally, oil emplacement would prohibit the effects of cementation and compaction from reducing the porosity^[22,23]. Therefore, after large scale oil charge, the pore throat feature of the Chang 7 tight sandstone should be stable. If the porosity changed obviously further after oil emplacement, for instance, many large pore throats reduced to small pore throats, then a large portion of oil should have occurred in small pore throats, and the contribution of small pore throats to oil bearing porosity should have increased, and the correlation of them should have turned better, and the correlation between oil-bearing porosity and large pore throat should have been poor. Therefore, in addition to controlling the porosity and permeability of tight sandstone, the development degree of large pore throat is also critical for oil emplacement, and is a key parameter for evaluating tight oil reservoirs.

The 14 samples have a surface porosity range of 0.3% to 3.7% from thin section observation, which are obviously lower than their porosity range from core test, indicating that there are still many small and micro pores not be counted^[24,25,26]. Thin section observation mainly reflects development situation of large pores, while small and micro pores are difficult to identify by this means^[24]_. Mercury intrusion experiment can only provide information of throat radius and pore volume connected by the throat but can’t reflect pore size distribution^[5]. But thin section surface porosity is in good correlation with core porosity and large pore throat porosity ϕ₁ (with R² of 0.61 and 0.77 respectively)(Fig. 9), indicating that large throats in tight sandstone usually connect with large pores. Therefore, the large pore that can be identified and counted in thin section observation is the major factor controlling porosity, permeability and pore structure, which is consistent with the conclusion from NMR analysis in previous studies ^[16]. In terms of pore type, visible pores in the samples mainly include particle dissolution pores and intergranular pores, with average surface porosity of 0.8% and 0.3%, respectively. Therefore, the development of large pore is an important factor for reservoir quality evaluation and prediction.

According to fractal theory, if an object extends in equal proportion to two directions, its fractal dimension is equal to 2, if it extends in equal proportion to 3 directions, its fractal dimension is 3; and if it extend in 3 directions in unequal proportions, its fractal dimension is more than 3 (Fig. 10). Therefore, the variation in fractal dimension can reflect features and differences in pore structure^[27].

The 14 samples all show the fractal feature of two segments. The pore throats smaller than peak radius have fractal dimensions of 2 to 3, and the pore throats larger than the peak radius have fractal dimensions of over 3. Similar results have been previously reported^[15,17]. It is generally believed that the pore throats with fractal dimension of 2 to 3 have fractal feature, while pore throats with fractal dimension of over 3 have no fractal feature^[28,29,30]. Therefore, according to fractal theory, the pore throats in the tight sandstone samples tested have binary features:

When the pore throat is less than the peak radius (small and micro pore throat), the pore throat structure can be depicted by capillary model (Fig. 11), in which the pore radius approximately equals to throat radius. This is shown as small slope of the fitted straight line of lgp_c and lgS_Hg. In this case, pore throat volume is determined by throat radius and increases slowly with the increase of pore throat radius. The fractal dimension is 2 to 3, suggesting that the pore throats extend between 2 dimensions and 3 dimensions, that is the length l of pore throat increases with the increase of radius r, but with the growth rate smaller than that of r. If the length l increases at the same growth rate with radius r, the fractal dimension would be equal to 3. In this case, the pore structure is self-affinity, or has fractal feature.

When the pore throat radius is larger than the peak radius, the pore structure is similar to the bead-string model (Fig. 11a) and the pore radius is significantly larger than throat radius. As the throat size increases, the mercury volume increases rapidly, and the pores make much more contribution to pore throat volume than throats. In this case, the fractal dimension of large pore throat is over 3 (Fig.11b), indicating that pore structure is not uniformly distribute in three dimensions, and the shaper the slope of the linear relationship of lg S_Hg-lg p_c is, the larger the ratio of pore radius to throat radius is.

Although the 14 samples in this study are different in petrology, porosity, permeability and pore throat size distribution, they all show binary pore structure, suggesting that this pore model is generally applicable.

Pore throats of the studied sandstone samples are less than 1 μm in radius and unimodal in distribution. Pore throats of different size scales have different influence on porosity and permeability. The big difference in large pore throat between the samples is the main factor causing porosity and permeability heterogeneity of tight sandstone. Large pore throats are also the main storage space for oil occurrence. Small and micro pore throats contribute major reservoir space, but are relatively stable, have little effect on the change of physical properties, and low correlation with oil saturation.

The tight sandstone has binary pore structure: when the pore throat radius is larger than the peak radius, the pore structure is similar to the bead-string model with no fractal feature, the pore size is much larger than throat size, and the pore throat volume is determined by the pore volume. When the pore throat radius is smaller than the peak radius, the pore structure is close to the capillary model and shows fractal feature, and the pore throat volume is determined by the throat radius.

The pore throats larger than the peak radius are mainly composed of secondary and intergranular pores. Therefore, even though the tight sandstone contains a large amount of small and micro pores, when evaluating physical properties of tight sandstone, features, origins and main controlling factors of large pores such as intergranular and dissolved pores should be analyzed as focus.

Nomenclature

C—intercept, dimensionless;

D—fractal dimension, dimensionless;

D₁—fractal dimension of large pore throat, dimensionless;

D₂—fractal dimension of small pore throat, dimensionless;

K—permeability, 10^-3 μm²;

V_Hg—mercury injection volume, μm³;

l—capillary length, μm;

L—magnification, dimensionless;

N(r)—the number of the units, piece;

p_c—mercury injection pressure, MPa;

r—capillary radius, μm;

r_p —pore radius, μm;

R, R₁ and R₂—correlation coefficients, dimensionless;

S_Hg—mercury saturation, %;

V₀, V₁, V₂and V₃—pore throat volumes at different magnifications, μm³;

V_p —pore volume, μm³;

α—constant, dimensionless;

θ—contact angle, (°);

σ—interface tension, N/m;

ϕ—total porosity, %;

ϕ₁—porosity of large pore throat, %;

ϕ₂—porosity of small pore throat, %;

ϕ₃—porosity of micro-pore throat, %;

ϕ_o—oil-bearing porosity, %.