Pore-Throat Structure and Fractal Characteristics of Tight Sandstones: A Case Study from the Chang 6 3 Sublayer, Southeast Ordos Basin

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Introduction
Given the increasing demand for fossil energy, the exploration and development of unconventional resources, for instance, tight oil and gas have drawn more attention world-wide [1,2]. Compared to the successful development of tight oil in North America, China just started out and has a promising future in view of the current investigation and reevaluation on its reserves [3]. The tight oil is usually preserved in a tight sandstone reservoir, defined as a reservoir with permeability and porosity of less than 1 mD and 10 percent, respectively [4]. The micropore-throat structure significantly affects the storage capacity and seepage ability of tight sandstone reservoirs. However, it is hard to characterize the micropore-throat structure owing to its poor physical properties and strong heterogeneous [5][6][7][8].
Experimental methods are conducted to evaluate the pore-throat structure, such as image observation methods represented by scanning electron microscopy (SEM) and casting thin sections (CTS), photoelectromagnetic radiation methods by nuclear magnetic resonance (NMR) and CT scanning, and fluid injection method by N 2 gas adsorption measurements and high-pressure mercury injection (HPMI) as well as constant-rate mercury injection (CRMI) [9][10][11][12][13][14][15][16]. Considering the complex pore-throat characteristics and strong heterogeneity caused by complicated deposition and diagenesis processes, it is hard to identify the microporethroat structure of tight sandstone reservoirs by a single method [5,[17][18][19][20][21][22][23][24][25][26]. For instance, although the image observation methods (SEM and CTS) can directly observe the geometry and the size of the pore-throat within sight, its visual field is too narrow to represent the whole sample [27]. CRMI characterizes the pore-throat structure by monitoring changes in pressure and saturation, whereas, it assumed a sphere pore space to calculate its pore radius, which is different from the real pore throat distribution in the reservoirs [28]. N 2 gas adsorption mainly identifies the pore-throat structure at a nanoscale scale with a limited zone of pores radius [29]. In comparison, the acquired HPMI parameters coupled with fractal theory are of great significance in both qualitatively evaluating the pore-throat structure [29,30] and quantitatively describing the complexity of pore-throat structure [31][32][33]. Together with image observation, HPMI, and fractal analysis, this study aims at building a bridge between the micropore-throat structure and macroquality of the reservoir to analyze the characteristics of porethroat structure.
To identify the complexity of pore-throat structure, a variety of experiments, including petro-physical characteristics of reservoir, SEM, CTS, and HPMI were implemented on ten samples gathered in the Chang 6 3 sublayer, Yanchang Formation of southeast of Ordos Basin. The structure of the pore-throat was quantitatively analyzed based on new experimental results. Meanwhile, the fractal dimensions D P-1 , D P-2 , and D P-3 were calculated to discuss the complexity and heterogeneity of the Chang 6 3 sublayer. The conclusion of this study can give some reference for the exploration of tight sandstone reservoirs.

Geological Setting
Located in the west of the North China Craton, the Ordos Basin (Figures 1(a) and 1(b)) is famous for its large reserves of unconventional resources [34,35]. In this basin, the Paleozoic, Mesozoic, and Cenozoic sedimentary rocks were covered on the Archean and Proterozoic metamorphic crystalline basements [36,37]. Multiple sets of oil and gas combinations were well preserved from the Paleozoic to Mesozoic sedimentary strata in the Ordos Basin [38]. In which the Upper Triassic Yanchang Formation is the most vital reservoir for the exploration and development of tight oil and gas. The Yanchang Formation deposited in a lacustrine-delta environment contains ten members (Chang 10 to Chang 1, towards the top) [39]. Generally, in this basin, the tight oil is mainly accumulated in the Chang 6 3 sublayer, Chang 7 layer, and Chang 8 1 sublayer.
Located in the southeast of Yishan slope, Ordos Basin, the tectonic characteristics of the study area (Figure 1(a)) are west-inclined monocline with a dip angle less than 1°. In this area, the Chang 4+5 2 sublayer and Chang 6 layer are the main oil producing layers. According to the characteristics of the standard layer and sedimentary cycle, the Chang 6 layer is divided into four oil sublayers, among which the Chang 6 3 sublayer is a tight sandstone reservoir with a thickness of about 26-40 meters and the lithology is mainly terrigenous clastic rocks, including mudstone and medium-fine sandstone in the study area. The underwater distributary channel sand body would be a favorable oil and gas reservoir. [40]. The porosity of the Chang 6 3 sublayer in the study area ranged from 1.54% to 10.83%, with a mean value of 6.39% while the permeability of most samples is below 0.30 mD, with a mean value of 0.04 mD, which shows a typical feature of a tight sandstone.

Materials and Methods
3.1. Sampling and Processing. Ten samples were collected from the Late Triassic Chang 6 3 sublayer of Yanchang Formation in southeast of the Yishan slope, as shown in Figure 1(c). These samples were firstly drilled into cylinders of about 2.5 cm in diameter and 3.0 cm in length, respectively. Then extraction experiments were carried out in alcohol and benzene after numbering these samples. Then, drying at 50°C for 24 hours, samples were cut into two segments, one part of 2.5 cm in length for helium porosity, nitrogen permeability measurements, and HPMI test while the other part of 0.5 cm in length for CTS and SEM observations.

Experimental Measurements
3.2.1. SEM Observation. The image of SEM can directly reflect characteristics of pore-throat structure, interstitial material, pore types, and cementation types. SEM observation was carried out by MAIA-3 instrument of Tescan field emission electron microscope in the Geological Experiment Test and Analysis Center (GETAC) of Xi'an Shiyou University (XSYU).

CTS Observation.
The pores of the cylindrical samples (0.5 cm in length) were filled with blue casting as well as dye agent and processed into casting thin sections with 0.03 mm in thickness. Based on the CTS analysis, the mineral composition, interstitial material, pore types, and cementation types can be confirmed, and the size of the pores, throats, and grains can be quantitatively characterized [27]. In this study, the CTS of ten typical samples was observed by LEICA 4P research polarizing microscope in the GETAC, XSYU, Xi'an, China.

HPMI Experiment.
The distribution of pore volume fraction of different pore sizes was obtained from HPMI analysis for reservoir evaluation [29,30]. As a nonwetting phase fluid of rocks, mercury was injected into the pores of samples, because the injection pressure overcame the capillary resistance of the pore-throat. When they are equal to each other, the injection pressure and the volume of the injected mercury are measured, which can be used to plot a capillary pressure curve. Therefore, the parameters of pore-throat structure were obtained to analyze petrophysical characteristics, complexity of pore-throat, and fractal features further [31]. The HPMI experiment was performed on five typical samples by using the American MAC AutoPore IV 9505 Automatic Mercury Injection instrument following the GB/T29171-2012 standard. The maximum mercury injection pressure reached up to 200 MPa and the measured maximum pore-throat radius was about 3.6 nm.

Fractal Theory.
In the fractal theory, the most important feature is self-similarity, which is a self-similar object that has similar structural features at different scales. Selfsimilar objects with fractal characteristics are represented by fractal dimension D f or D, which were greatly applied to quantitatively identify the heterogeneity and complexity of the pore-throat structure [19][20][21][22][23][34][35][36][37]. Generally, the value of fractal dimension ranges between 2 to 3, increasing with the heterogeneity and complexity of pore-throat structure [41][42][43][44][45][46]. Accordingly, if the pore-throat structure has fractal characteristics, the amount of pore-throats which radiuses exceeded r can be calculated. Then, the relevant formula can be expressed as follows, and its instructions on parameters are detailed in relevant references [19][20][21][22][23]: where N ð>rÞ is the amount of pore-throats with a radius more than r; r m is the maximum radius of pore (μm); PðrÞ is the distribution function of pore radius; a is scale constant; D is the fractal dimension. Equation (2) is obtained by performing the derivation of r in Equation (1): By transforming Equation (2) into Equation (3), the total volume V ð<rÞ of pores with a radius lower than r can be expressed: where r s is the minimum pore radius (μm). The total pore volume ðVÞ can be listed as follows: By transforming Equations (3) and (4) into Equation (5), the cumulative volume fraction VðcÞ of a pore-throat with  Figure 1: Location of the study area and sampling points in the Ordos Basin (modified from [19]).
3 Geofluids pore radius lower than r is obtained: In the tight sandstone, r s is much smaller than r m , Equation (5) can be simplified as follows [29,30]: Finally, Equation (7) can be obtained after calculating the logarithm of VðcÞ: If the pore size distribution fits the fractal theory, there is a linear dependence between logð1 − S Hg Þ and logr. According to the slope of the line H = 3 − D, D is equal to H − 3.

Petrophysical Characteristics.
The mineral composition and content of ten samples gathered in the study area are shown in Table 1. Combined with the sandstone classification scheme [47] and the analysis results of both SEM and CTS, the Chang 6 3 sublayer is classified as the feldspar sandstone and lithic feldspar sandstone ( Figure 2). The component maturity of tight sandstone is determined by the ratio of stable component (quartz, Q 1 ) to unstable component (feldspar+lithic, F 1 +R 1 ) [48], which is equal to 1.05, indicating that the component maturity of the Chang 6 3 sublayer is low.
The average content of quartz in this area (Table 1) is 44.8%, and the feldspar is 24.3%, of which plagioclase is higher, followed by potassium feldspar. In addition, the average content of lithic fragments is 18.2%, of which metamorphic, sedimentary, volcanic lithic fragments, and mica account for 44.44%, 30.95%, 2.38%, and 22.23%, respectively. Furthermore, the content of phyllite, quartzite, and slate are 1.2%, 1.9%, and 1.14%, respectively.
Clay minerals and carbonate are the main interstitial materials of the Chang 6 3 sublayer. Clay minerals mainly consist of chlorite (2.6%), followed by kaolinite (1.2%) and hydromica (1.1%), and carbonate is dominated by calcite. The characteristics of the Chang 6 3 sublayer in the study area are interpreted as follows: the particle size of debris is fine, ranging from 0.10 mm to 0.20 mm. Their sorting feature is medium, in which mainly are fine sandstone, followed by silty sandstone. And, point-point and point-line contact make up their main contact types. The cementation and support types are mainly pore cementation and particle support, respectively.
The petrophysical property analysis of Chang 6 3 sublayer in southeastern Ordos Basin shows that porosity ranged from 1.54% to 10.83% with a mean value of 6.39% (Figure 3(a)). The permeability of most samples is less than 0.30 mD with a mean value of 0.04 mD (Figure 3(b)), indicating that the Chang 6 3 sublayer is a tight sandstone in this  4 Geofluids study with low porosity and ultralow permeability. Figure 3(c) shows a weak correlation between porosity and permeability with a correlation coefficient 0.6174, hinting at that the porethroat structure was complex and stronger heterogeneous.

Pore Characteristics.
In general, the areal porosity rate is proportional to the number of pores, that is, the lower the areal porosity rate, the fewer number of pores. The CTS results of areal porosity (less than 10%) prove that the Chang 6 3 sublayer is a tight sandstone reservoir. Nevertheless, diverse types of pores were developed in the reservoir due to its strong heterogeneity, which showed irregular shapes, different sizes, and uneven distribution.
The samples in study area are characterized by micron pore-throat, and dissolution pores are more developed than residual pores based on the results of CTS and SEM. The residual pores are mainly composed of intergranular pores which show polygonal, irregular, and clear boundaries (Figure 4(a)) hinting that these pores suffered from compaction, cementation, and hybrid filling. The chlorite films In addition, few lithic dissolution pores as well as carbonate dissolution pores are observed, and no microcracks were found in the samples of Chang 6 3 sublayer, this means that there are strong compaction and weak tectonism.
4.3. The Results of HPMI. The capillary pressure characteristics curves and distribution curves of pore-throat radius of five representative samples were plotted based on the HPMI results ( Figure 5). On the basis of the morphological characteristics of capillary pressure curves and distribution curves of pore-throat radius, the samples can be assigned to three types (Table 2).

Geofluids
Type I, A1 sample shows low displacement pressure with an average of 0.4 MPa in Table 2. The capillary pressure curve of A1 reflects characteristics of the "long-flat section in the middle" (Figure 5(a)). As shown in Figure 5(b), there is a single-peak on the right side with a radius peak ranging between 0.48 μm and 0.63 μm. It shows that the sample has large size pore-throat, which makes mercury easy to be injected into the pore-throat. Type II is composed of A2 and A3 samples with an average displacement pressure of 0.56 MPa, and the relatively-short horizontal mercury injection capillary pressure curves can be observed between 1-8 MPa and 60-80 MPa (Figure 5(c)). In Figure 5(d), a double-peak is presented, in which the distribution of pore-throat radius curves on the left as well as right side are 0.015-0.04 μm and 0.1-0.48 μm, respectively, showing that these samples have pore-throat of middle size, which makes mercury not easy to be injected into the porethroat. A4 and A5 samples are applied to type III, whose patterns (Figures 5(e) and 5(f)) are similar to the curves of type II. However, it is difficult to overcome the capillary pressure owing to the development of thin and microthroats, causing highest displacement pressure and smallest pore-throat size.

Fractal
Feature. Scatter plots of log ð1 − S Hg Þ and log r from each sample were drawn according to the HPMI porethroat structure parameters ( Figure 6). A linear correlation between log ð1 − S Hg Þ and log r with correlation coefficients of more than 0.8 was observed on the basis of fractal curve [19][20][21][22][23]. The result illustrated that the pore-throat structure of each sample was multifractal. Based on the inflection points of the fractal curve, the curve can be split into three sections, thus dividing the pore-throat structure of samples into large,  Geofluids medium, and small pores, respectively. Among the sample of type Ι, medium pores were widely distributed, followed by small and large pores (Figure 6(a)). In terms of type II samples, the number of small pores was increasing (Figures 6(b) and 6(c)), which was approximate with the number of medium pores. Besides, the distribution of small pores accounted for the majority of type III (Figures 6(d) and 6(e)), while large pores were the least. The results above indicate that medium pores were widely developed in the Chang 6 3 sublayer, which was a crucial factor for the reservoir quality.

Geofluids
The fractal dimensions (D P−1 , D P−2 , and D P−3 ), porosity (ϕ 1 , ϕ 2 , and ϕ 3 ), and permeability contributions (K 1 , K 2 , and K 3 ) corresponding to large, medium, and small pores are calculated in Table 3 for further discussion. The D P−1 was the maximum with an average of 2.83, ranging from 2.60 to 2.97. The permeability of large pores is maximum with a mean value of 0.07 mD, showing that the permeability of Chang 6 3 sublayer was mainly contributed by a small number of large pores in study area. Then, the D P−2 ranged from 2.50 to 2.83 with an average of 2.69 while its porosity was the maximum with an average of 2.09%. It can be concluded that the medium pores mainly provided reservoir space. The D P−3 is 2.22 to 2.40, with a mean value of 2.31, and the permeability contribution is 0.0005 mD. Compared with large pores and medium pores, small pores made less contribution to permeability and porosity. The fractal dimensions of large pores were larger than that of the medium pores and small pores, indicating that the former had strong heterogeneity, and relatively discrete distribution. Medium pores and small pores have relatively uniform and regular pore distribution. Therefore, the fractal dimension has a positive correlation with the complexity of porethroat structure, which is close to the previous studies [19][20][21][22][23].

The Pore-Throat Structure Effect on the Petrophysical
Characteristics. Two main inflection points, dividing the curve as large, medium, and small pores, were found according to the correlation between log ð1 − S Hg Þ and log ðrÞ of each sample in Figure 7. In accordance with the coordinates of inflection points and the pore-throat radius of large pores, small pores and medium pores were obtained to be more than 0.3 μm, less than 0.02 μm and between 0.02 μm and 0.3 μm, respectively.
Together with the distribution curves of pore-throat radius, fractal curves, images of CTS (Figure 7), and the parameters of HPMI (Table 4), the pore-throat structures from typical samples were analyzed. The pore-throat structures of sample A1 were mainly large pores and medium pores, the pore types principally consisted of large residual intergranular pores and feldspar dissolved pores, with good connectivity, storage capacity, and seepage ability, but grains are poorly sorted. The pore-throat structures of sample A3 were mainly medium pores and small pores, the pore types consist of residual intergranular pores and throat with good connectivity and seepage ability, but grains are poorly sorted. The pore-throat structures of sample A4 were dominated with more small pores and followed medium pores, pore types were mainly composed of intergranular dissolution pores with small reservoir space, moderate connectivity, and good sorting.
In summary, we consider that the wide distribution of medium pores is of great significance in evaluating reservoir storage capacity and seepage capacity. The distribution of large pores was too limited to improve the quality of the reservoir. Although small pores can be observed, the storage capacity and seepage ability of the small pores are weak in the study area, therefore, the influence on the reservoir is not as strong as that of the medium pores.

The Relationship between the Fractal Dimension and
Petro-Physical Characteristics. A larger fractal dimension can represent a more complex pore-throat structure and lower porosity as well as permeability of the reservoirs. The scatter plot (Figure 8) was obtained based on the fractal dimensions D P−1 , D P−2 , and D P−3 and porosity as well as permeability. As shown in Figure 8, the porosity and permeability were in inverse proportion to fractal dimension. The D P−1 , D P−2 , and D P−3 showed a negative correlation with porosity, in which D P−2 had the strongest correlation. Permeability had a negative correlation with D P−2 and no correlation with D P−1 and D P−3 . Therefore, the storage space and permeability of the reservoir were mainly contributed by medium pores. The distribution of medium pores had a great effect on the storage capacity and seepage capacity of reservoir.
The pore-throat structure was analyzed by plotting a scatter plot between fractal dimension and HPMI parameters ( Figure 9). The fractal dimensions (D P−3 ) of small pores showed a negative relationship with sorting coefficient  Notes: D P-1 , D P-2 , and D P-3 : the fractal dimensions of large pores, medium pores, and small pores. ϕ 1 , ϕ 2 , and ϕ 3 : the porosity of large pores, medium pores, and small pores. K 1 , K 2 , and K 3 : the permeability of large pores, medium pores, and small pores. R 2 : correlation coefficient.  10 Geofluids (Figure 9(b)) and capillary pressure (Figure 9(e)) and a positive relationship with efficiency of mercury withdrawal (Figure 9(d)). The results confirmed that the sorting feature and connectivity of small pores will become better as the fractal dimension increases. Moreover, the correlation between small pores and other parameters was not obvious, and the storage capacity and seepage ability of small pores were weak as discussed in Section 5.1, showing that small pores had weak effect on the pore-throat structure. The D P−2 exhibited a negative correlation with median pore-throat radius (Figure 9(a)) and a positive correlation with sorting coefficient (Figure 9(b)) and variation coefficient (Figure 9(f)). The median pore-throat radius reflected the concentrated distribution of pores. With the decrease of the median pore-throat radius, the distribution of the medium pores became inhomogeneous. Meanwhile, homogeneity of medium pores was influenced by the sorting coefficient and variation coefficient. For instance, homogeneity of medium pores increases while the sorting coefficient and variation coefficient decrease. Thus, medium pores occupy a determining effect in the homogeneity of tight reservoirs.

Geofluids
A negative correlation between D P−2 with the maximum mercury saturation (Figure 9(c)) and the efficiency of mercury withdrawal (Figure 9(d)) can be observed. Under the same pressure, the maximum mercury saturation was positively correlated with reservoir storage capacity. The efficiency of mercury withdrawal and reservoir connectivity also showed a positive correlation. Both maximum mercury saturation and mercury withdrawal efficiency of medium pores will decrease with the increasing fractal dimension, which illustrated that the more complex the pore-throat structure, the weaker the storage capacity and connectivity of the pores.
In a word, the fractal dimensions (D P−2 ) of medium pores showed a negative correlation with median radius of pore-throat, maximum mercury saturation, the mercury withdrawal efficiency, and capillary pressure and a positive correlation with sorting coefficient and variation coefficient, indicating that there is an extremely strong correlation between medium pores and pore-structure parameters. Hence, the size, complexity, and distribution of medium pores determined the reservoir storage space and connectivity of the reservoir.

The Mechanism of Mineral Composition Effect on Fractal
Dimension. The complexity of pore-throat structure was affected by their mineral content and composition in the tight sandstone reservoirs [49][50][51]. It is shown in Figure 10, the relationship between fractal dimension and the content of rock-forming minerals (quartz and feldspar) was analyzed. It is obvious that a negative correlation between quartz and fractal dimensions (D P−2 and D P−3 ) was obtained in Figure 10(a). Quartz, with strong compaction resistance and dissolution resistance, which could preserve the pore space and improve the homogeneity of pore-throat structures. Thereby, following the decrease of quartz content lead to an increase of complexity, heterogeneity, and fractal dimensions of medium and small pores. Moreover, a positive correlation between feldspar content and fractal dimensions D P−2 and D P−3 was revealed in Figure 10(b). If feldspar content increases, fractal dimensions D P−2 and D P−3 do. On account of feldspar widely existed in the study area that various pores with different types, sizes, and complex structures were formed by dissolution of feldspar in the diagenetic process. Although the pore space of the reservoir increased with feldspar content, the complex pore types decreased their fluid seepage capacity.
As discussed above, the content of quartz and feldspar has a certain influence on the complexity of medium pores    and small pores, by which medium pores are strongly influenced with the maximum correlation coefficient. Therefore, reservoir space and seepage capacity are further affected by the complexity and heterogeneity of medium pores.

Conclusions
(1) The pore types of the samples mainly consist of intergranular pores, feldspar dissolved pores, and  intergranular dissolved pores. Quartz and feldspar are the main mineral composition, while clay mineral and carbonate mainly comprise these samples' interstitial materials (2) The D P−1 ranged from 2.60 to 2.97 with a mean value of 2.83, the D P−2 from 2.50 to 2.83 with a mean value of 2.69, and the D P−3 from 2.22 to 2.40 with a mean value of 2.31. Therefore, large pores have the largest fractal dimension due to their complex structure and strong heterogeneity (3) The D P−2 shows a negative correlation with porosity, permeability, maximum mercury saturation, and mercury withdrawal efficiency and a positive correlation with feldspar content, sorting coefficient, and variation coefficient. Thus, reservoir space and seepage capacity of samples are determined by the size, complexity, and distribution of medium pores (4) The storage capacity of the medium pores enhances by increasing of the quartz and feldspar content in the light of both the compaction resistance for quartz and the dissolutive for feldspar. However, the types, sizes, and structures of medium pores also became complex with the increase of feldspar content, resulting in the reduction of fluid seepage capacity

Data Availability
The underlying data is not available.

Additional Points
Highlights. (i) The pore-throat structure for the Chang 6 3 sublayer was analyzed by comprehensive methods. (ii) The fractal characteristics of the pore-throat structure were quantitatively defined into large, medium, and small pores.
(iii) The relationship between fractal dimension and micropore-throat structure was discussed. (iv) The influencing mechanism of mineral composition on fractal dimension was discussed.