Multi-Scale Quantitative Characterization of Pore Distribution Networks in Tight Sandstone by integrating FE-SEM, HPMI, and NMR with the Constrained Least Squares Algorithm

The goal of this study was to investigate the impacts of various sedimentary-diagenetic conditions on the macroscopic petrophysical parameters and microscopic pore structures of tight sandstones from the Lower Jurassic Badaowan Formation in the Southern Junggar Basin, China. Based on the traditional methods for establishing pore size distribution, including integrating the results of high-pressure mercury injection, nuclear magnetic resonance, and scanning electron microscopy, the constrained least squares algorithm was employed to automatically determine the porosity contributions of pore types with different origins. The results show that there are six genetic pore types: residual intergranular pores (RIPs), feldspar dissolution pores (FDPs), rock fragment dissolution pores (RFDPs), clay mineral intergranular pores (CIPs), intercrystalline pores of kaolinite (IPKs), and matrix pores (MPs). Four lithofacies were identified: the quartz cemented-dissolution facies (QCDF), carbonate cemented facies (CCF), authigenic clay mineral facies (ACMF), and matrix-caused tightly compacted facies (MCTF). Modified by limited dissolution, the QCDF with a high proportion of macropores (RIPs, FDPs, and RFDPs) exhibited a slightly higher porosity and considerably higher permeability than those of others. A large number of micropores (MPs, CIPs, and IPKs) in MCTF and ACMF led to slightly lower porosities but considerably lower permeabilities. Due to the tightly cemented carbonates in the CCF, its porosity reduced sharply, but the permeability of the CCF remained much higher those of the MCTF and ACMF. The results highlight that a high proportion of macropores with large radii and regular shapes provide more effective percolation paths than storage spaces. Nevertheless, micropores with small radii and complex pore structures have a limited contribution to flow capability. The fractal dimension analysis shows that a high proportion of MPs is the major reason for the heterogeneity in tight sandstones. The formation of larger macropores with smooth surfaces are more conductive for oil and gas accumulation.


Introduction
Tight sandstone reservoirs are regarded as potential unconventional resources and are widely distributed around the world, especially in Western China. Tight sandstone reservoirs are characterized by low porosity and permeability as well as multi-scale pore networks with strong heterogeneity [1,2]. The relationship between their macroscopic properties (e.g., permeability, porosity, and oil/gas saturation) and microscopic parameters (e.g., pore size distribution (PSD), pore geometry, and pore connectivity) weakens with a large proportion of nanoscale pores [3,4]. Therefore, identifying the factors that control the complexity of the pore networks of tight sandstones and clarifying the relationship between the macroscopic reservoir quality and microscopic pore structure are essential for the evaluation of tight sandstone reservoirs.
Variable depositional environment and various diagenetic processes are the main factors that can cause pore networks in tight sandstones to be more complicated and heterogeneous [4,5]. Although many scholars have studied the impacts of diagenetic processes on reservoir quality, controversies remain: (1) original depositional attributes determine pore network heterogeneities in tight sandstones [3]. In general, tight sandstones with a high content of ductile grains, poor sorting, and fine grains experienced stronger compaction, which causes a sharp reduction in the reservoir quality [6][7][8]. (2) The impact of authigenic clay-related pores (CPs) on reservoir quality remains a controversial issue. Some scholars think that a large amount of CPs could maintain the total storage spaces or slightly increase, while most of these pores are poorly connected, resulting in a severe decrease in seepage capacity [9,10]. However, other scholars suggest that CPs could create seepage paths in sandstone reservoirs [11]. In addition, grain-coating clay minerals can increase the pressure resistance of sandstone and limit the destruction due to compaction [11,12]. (3) Whether dissolution can improve the quality of reservoirs is still unknown. Increasingly more scholars are indicating that the dissolution pores (DPs) rarely provide a large number of pore spaces because of the possibility that the precipitation produced by dissolution occlude the secondary pores [13,14]. Furthermore, the impacts of various sedimentary-diagenetic factors on microscopic pore networks are still poorly studied.
Many scholars have tried to integrate various techniques to describe the multi-scale PSD of tight sandstones [15][16][17]. Nuclear magnetic resonance (NMR) is an effective tool for non-destructively quantifying the multi-range pore structures of tight sandstone reservoirs [18][19][20], but the NMR-derived PSD related to the relaxation time (T 2 ) should be transformed to pore size (µm) through integration with other methods. The NMR-derived PSD has been determined with imaging methods (e.g., casting thin sections and field emission scanning electro microscopy (FE-SEM)) using a large amount of statistical multi-scale pore radii data [21]. The combination of the throat size distribution of rate controlled porosimetry (RCP) and PSD of NMR has been attempted, but the integrated parts of two techniques requires further study [11,[22][23][24]. Besides, the integration of nitrogen adsorption and NMR to recover the total PSD of tight sandstones only effectively investigates the configuration of pores <50 nm. Thus, micron-scale pores remain difficult to describe [25,26]. High-pressure mercury injection (HPMI) is often integrated with NMR to reflect tight sandstone PSD [24,27], due to the resultant relatively full range of PSD characterization, although the relationship between T 2 spectrums and pore radii directly influences the accuracy of the NMR-HPMI-integrated PSD.
The Lower Jurassic strata in the southern Junggar Basin are characterized by multilayer hydrocarbon sources that are connected with shallowly buried reservoirs and many sets of effective caprocks, which is considered a primary focus of current exploration efforts [28]. Developed in coal-bearing and near-source strata, the tight sandstones of the Badaowan Formation (J 1 b), at burial depths of 1600-2000 m, experienced complicated diagenesis but still include several excellent reservoirs with extensive dissolution [29]. Moreover, the tight sandstones are characterized by high gas content, and the gas is mainly derived from the coal seams in the braided delta plain of J 1 b, forming a set of "self-generating and self-accumulating" reservoirs. A series of studies of tight sandstone reservoirs in J 1 b have been conducted that focus on the evolution of the sedimentary environments [30][31][32], petrography [33,34], and diagenetic characteristics. However, the heterogeneous reservoir quality and complex pore networks make further oil exploration more difficult, and the impacts of sedimentary-diagenetic on pore networks in the sandstones of J 1 b have not been thoroughly investigated yet.
In this study, 13 tight sandstone samples from J 1 b in the Southern Junggar Basin (China) were obtained, and the methods of casting thin sections, X-ray diffraction (XRD), FE-SEM, HPMI, and NMR are used to achieve the following goals: (1) characterize the macroscopic heterogeneities (lithofacies, genetic pore types, fluid mobilities, and petrophysical properties) of tight sandstones under different sedimentary-diagenesis conditions; (2) describe the characteristics of microscopic pore networks (pore structures and fractal features) and explore the internal connection between macroscopic reservoir heterogeneities and microscopic pore networks. (3) discuss the impacts of sedimentary and diagenesis settings on the macroscopic reservoir heterogeneities and microscopic pore networks in the tight sandstones of J 1 b.

Geological Setting
The Junggar Basin, which is considered a prolific oil basin in China [35], is located in the northern margin of the Tianshan Mountains and has been a continental basin since the early Paleozoic [36,37]. The Southern Junggar Basin is bounded by Jinghe County to the west and the Dashitou area of Mulei County to the east. It extends to North Tianshan (NTS) to the south and to the Urumqi-Erie Road to the north [30] (Figure 1). sedimentary-diagenetic on pore networks in the sandstones of J1b have not been thoroughly investigated yet. In this study, 13 tight sandstone samples from J1b in the Southern Junggar Basin (China) were obtained, and the methods of casting thin sections, X-ray diffraction (XRD), FE-SEM, HPMI, and NMR are used to achieve the following goals: (1) characterize the macroscopic heterogeneities (lithofacies, genetic pore types, fluid mobilities, and petrophysical properties) of tight sandstones under different sedimentary-diagenesis conditions; (2) describe the characteristics of microscopic pore networks (pore structures and fractal features) and explore the internal connection between macroscopic reservoir heterogeneities and microscopic pore networks. (3) discuss the impacts of sedimentary and diagenesis settings on the macroscopic reservoir heterogeneities and microscopic pore networks in the tight sandstones of J1b.

Geological Setting
The Junggar Basin, which is considered a prolific oil basin in China [35], is located in the northern margin of the Tianshan Mountains and has been a continental basin since the early Paleozoic [36,37]. The Southern Junggar Basin is bounded by Jinghe County to the west and the Dashitou area of Mulei County to the east. It extends to North Tianshan (NTS) to the south and to the Urumqi-Erie Road to the north [30] (Figure 1).   The Jurassic stratum in the Southern Junggar Basin consists of the Badaowan Formation, Sangonghe Formation, Xishanyao Formation, Toutunhe Formation, Qigu Formation, and Kalazha Formation from old to young [39]. The Lower Jurassic Badaowan Formation unconformably overlies the Triassic Haojiagou Formation of the Triassic. During the early period of the Badaowan Formation, a shallow-water braided delta plain with thin coal seams widely developed in the Southern Junggar Basin, and due to the frequent lake level fluctuations and the southward expansion of the Junggar Basin, the delta plain gradually evolved into a delta front but ultimately transitioned back to a delta plain. The environment of the coal-enriched swamp in the proximal shallow braided river delta provides the basis for the high contents of matrix and kaolinite in the tight sandstones, and these factors created favorable conditions for the densification of sandstones with complex pore structures.

Geologic Features of Samples
We collected 49 samples (20 drilling samples in well X1 and 29 field samples) from the J 1 b (Figure 1b, Figure A1), including 12 sandy fine gravel samples, 13 coarse sandstone samples, eight medium sandstone samples, and 16 fine sandstone samples. The locations of the sampled well and the field section are marked in Figure 1, and the location of well X1 is on the high part of containing oil and gas geological structure-a short axis anticline in the central of the southern Junggar Basin. All the samples were obtained from the plain and the front of the braided delta ( Figure 1).

Experimental Methods
To comprehensively investigate the pore structures of the tight sandstone reservoirs in J 1 b, we performed a series of experiments. First, the types of storage spaces and mineral compositions of 49 samples were analyzed by XRD, casting thin sections, and FE-SEM. The clustering analysis of the petrophysical properties and mineral compositions of 49 samples was conducted by heat map ( Figure A1), it is obvious that there are four groups with different mineral compositions and petropysical properties of 49 samples, and the differences of the petrophysical properties and mineral compositions between well samples and field samples are slight. Then, 13 representative samples with constant mineral compositions, the typical diagenetic characteristics, and the high proportion of regularly shaped pores were selected from the 49 samples, and the fresh samples were formed into cylindrical plungers. After drying, the helium porosity and transient pulse decay permeability were measured under a confining pressure of −30 MPa. After fully saturating with 10,000 mg/L under 30 MPa for 48 h, the NMR-derived T 2 spectrums were acquired by using 2 MHz MicroMR20-025V at Peking University (Beijing, China). Then, plungers were centrifuged under an equivalent air-water pressure of 208 psi for 1 h, and the T 2 spectra were measured again. The Carr−Purcell−Meiboom−Gill sequence was applied in NMR tests with an echo spacing of 0.2 ms and a waiting time of 5 s. The number of echoes was 1024, and the scanning number was 128. The NMR-derived PSD, pore structure parameters, and porosity were determined in the samples with saturated water and irreducible water contents. Following the NMR tests, the pore structures of the 13 samples were analyzed using HPMI. The HPMI tests were conducted on an AutoPore-IV9500 mercury porosimeter at Peking University (Beijing, China) according to the Chinese Oil and Gas Industry Standard (SY/T) 5346-2012. The intrusion pressure varied from 0.1 to 414 MPa, which corresponds to pore radii 3.6 nm to 1100 µm. In this paper, the petrographic descriptions, mineral compositions, petrophysical parameters (e.g., porosity, permeability, the contents of immovable fluid (BVI) and movable fluid (FFI)) and fracture evaluations are evaluated by ISRM [40].

Combining NMR and HPMI Methods
Based on the assumption of the ideal pore geometry, the relationship between T 2 and the relaxation effect of the rock grain surface can be expressed as [41]: where r is the pore radius, µm, Fs is the form factor (F s = 3 for spherical pores, and F s = 2 for cylindrical pores), and ρ is the relaxation rate (µm/ms). However, the actual pore structures are more complex than those of the ideal formation. Several scholars have found that an exponential relationship, rather than a linear relationship, exists between the T 2 spectrum (ms) and the pore radius (µm) [23,27,42]: this finding is also supported by Figure 2b,c; the relationship can be expressed as follow: where n is the power exponent and A is a constant equal to 1 ρ×F S . Equation (2) can be reorganized after taking the logarithm of both sides, and r can be expressed as: where C is a constant.
where r is the pore radius, μm, Fs is the form factor (Fs = 3 for spherical pores, and Fs = 2 for cylindrical pores), and ρ is the relaxation rate (μm/ms). However, the actual pore structures are more complex than those of the ideal formation. Several scholars have found that an exponential relationship, rather than a linear relationship, exists between the T2 spectrum (ms) and the pore radius (µ m) [23,27,42]: this finding is also supported by Figure 2b,c; the relationship can be expressed as follow: where n is the power exponent and A is a constant equal to 1 ρ×F S . Equation (2) can be reorganized after taking the logarithm of both sides, and r can be expressed as: where C is a constant. The NMR T2 spectrum (ms) can be converted into the PSD (μm) if the constants C and n are calculated. The key point in matching T2 and r is that the PSD from NMR and HPMI have the same cumulative pore volume fraction. The steps of the converting method modified by Huang and Wang [23,27] are simplified as follows: (1) the cumulative pore volume fraction should be calculated based on the NMR and HPMI data. The cumulative pore volume fraction of NMR, which is greater than the maximum injected mercury saturation (Smax), should be excluded ( Figure 2a). (2) After matching the cumulative pore volume fraction using NMR and HPMI, every cumulative pore volume fraction P(j) has a uniquely corresponding pore radius r(j), and P(j) can correspond to the relaxation time T2 (j) by cubic spline interpolation of the cumulative pore volume fraction of the NMR. Then, the determined C and n can be used to convert the T2 spectrum into the PSD (μm, Figure 2d).  The NMR T 2 spectrum (ms) can be converted into the PSD (µm) if the constants C and n are calculated. The key point in matching T 2 and r is that the PSD from NMR and HPMI have the same cumulative pore volume fraction. The steps of the converting method modified by Huang and Wang [23,27] are simplified as follows: (1) the cumulative pore volume fraction should be calculated based on the NMR and HPMI data. The cumulative pore volume fraction of NMR, which is greater than the maximum injected mercury saturation (S max ), should be excluded (Figure 2a). (2) After matching the cumulative pore volume fraction using NMR and HPMI, every cumulative pore volume fraction P(j) has a uniquely corresponding pore radius r(j), and P(j) can correspond to the relaxation time T 2 (j) by cubic spline interpolation of the cumulative pore volume fraction of the NMR. Then, the determined C and n can be used to convert the T 2 spectrum into the PSD (µm, Figure 2d).

Estimating the Proportion of Different Pores Based on the Least Squares Estimator
Many pore classifications are based on pore sizes without considering the forming mechanism of the pores [43,44]. However, the volume fraction of pores with various geological genesis (e.g., RIPs, DPs, and CPs) would reveal the relationships between the sedimentary-diagenetic conditions and pore structures. In the same study areas, the sizes of pores with the same genesis might be similar, and the pore size ranges of different genetic pore types could overlap. Therefore, it is difficult to obtain accurate pore volume fractions of different genetic pore types from the total PSD by calculating the area ratio. Therefore, the least squares estimator was applied to calculate the pore volume fractions of different genetic pore types for identifying the various characteristics of sedimentary-diagenetic settings.
The total PSD can be expressed as the combination of the PSD of different pore types in a certain proportion [11,45]. This proportion can be approximately considered as the pore volume fraction of different genetic pores.
We assumed that the total PSD derived by NMR-HPMI is a linear combination of the radii probability distributions of different pore types, which is consistent with the assumptions of other studies [43,44]. Thus, the total PSD, y(r), a function of pore radius r, can be expressed as: where x i (r) is the radii probability distribution of the ith pore type and f i is the proportion of the ith pore type. N is the number of pore types. As the total PSD and the PSD of different pore types are determined, the linear combination model can be inverted to estimate the proportion of each pore type. Considering the physical meaning of the proportions of the pore type, an additional unity sum constraint equation can be incorporated to guarantee that the sum of the fractions is 1, and a non-negative constraint is used to avoid negative proportions. Therefore, the constraint condition of Equation (4) is: This overdetermined linear mixing problem, incorporating residual error, can be presented in matrix notation as: where X is the radii probability distribution matrix of pore types and e is the error vector that must be minimized to obtain the fraction vector f that best fits the total PSD Y. This type of problem can be solved in many ways [46][47][48][49]. In this research, we used the least square solution, and the fraction vector f can be computed by: After the successful determination of f, the proportion of each pore type was obtained by decomposing the integrated PSD from NMR-HPMI. Based on Equation (4), the reconstructed PSD can be expressed as the linear combination of the radius probabilities of different pores with the calculated proportions.

Fractal Analysis Based on the HPMI-NMR Integration
The fractal dimensions have been widely employed to quantitatively characterize the complexity and heterogeneity of tight sandstone reservoirs [50]. Based on recent studies [27,44,51], the number of pores with sizes greater than r o (N r ) can be obtained as: where r is the pore radius (µm); r max is the maximum pore radius (µm); B is the fractal factor; f(r) is the density function of the pore radii and D is the fractal dimension of the pore space.
where B is a proportional constant that equals (-DB). The cumulative pore volumes with radii smaller than r can be calculated by substituting Equation (10) into Equation (11): where V r is the cumulative volume of pores with radii smaller than r, B " is a proportional constant that equals B B/(3 − D), and r min is the minimum pore radius. Hence, the total pore volumes of samples (V t ) can be calculated by the following equation: The relationship between the cumulative pore volume fraction (S v ) and the fractal dimension can be expressed as follows: Assuming that r min is considerably smaller than r max , Equation (13) can be simplified as: Taking the logarithm of both sides produces: The pore radii(r) could be transformed from the T 2 using Equation (3), and the fractal dimensions of the pore size distributions could be obtained from the slope of the lgS v -lgr curves.

Mineral Composition and Petrophysical Parameters of Four Lithofacies
Characterized by a high matrix content, the J 1 b sandstones mainly include litharenite with minor feldspathic litharenite and lithic arkose. The main type of quartz is monocrystal, and the feldspars within J 1 b include plagioclase (albite in majority and calcic plagioclase in minority) and K-feldspar. The rock fragments mainly include sedimentary rock fragments, volcanic rock fragments, and small amounts of metamorphic rock fragments. Some authigenic minerals, e.g., calcite, ferrocalcite, kaolinite, illite, illite-smectite mixed layers, and chlorite, prevail in the J 1 b sandstones.
According to the cluster analysis of mineral compositions, sedimentary-diagenetic processes, and reservoir quality, four lithofacies were identified, including the quartz cemented-dissolution facies (QCDF) (Figure 3a (Figure 3i). Within the abundant detrital quartz grains and quartz cements, the QCDF mainly developed medium-to coarse-grained and well-sorted sandstones. The porosity and permeability of the QCDF is the highest among the four lithofacies. The CCF often has high percentage of carbonate minerals (including calcite, ferrocalcite, and siderite), which could exceed 25.14%. The sandstones with extensive carbonate cement are often poorly sorted and fine to medium-grained. The porosity range of CCF is from 4.19% to 5.42%, and the permeability varies from 0.05 to 0.07 mD. In the ACMF, authigenic kaolinite, chlorite, illite, and I/S mixed layers with the form of booklet, fibrous, and bridge significantly block the pores in the tight sandstones. Among these authigenic clay minerals, the content of kaolinite is the highest, which varies from 4.742% to 5.599%. The illite content ranged from 3.35% to 3.96%, and the content of illite/smectite mixed layers is lower than that of illite. The chlorite content in the ACMF ranges from 2.66% to 3.14%. The porosity of the ACMF is widely distributed from 7.78% to 11.20%, whereas the permeability is still poor, ranging from 0.037 to 0.079 mD. The MCTF is usually rich in ductile grains (especially matrix) and is characterized by fine grains and poor-sorting, which results in the MCTF experiencing extensive compaction during the burial. The porosity of the MCTF is stable in the range of 7.02% to 7.75%, and the permeability is concentrated at 0.02 mD. The petrophysical properties and the mineral composition results of 13 samples are presented in Table 1.  Table 1.

Pore Geometry and Size and the Proportion of Six Pore Types
Based on the observations and pore size measurements of 63,137 pores by casting thin section and FE-SEM, six types of pores were identified by genetic characteristics. By decomposing the HPMI-NMR-derived PSD, the proportion of each type was estimated based on the least squares method (Figure 4), as shown in Section 3.4.

Pore Geometry and Size and the Proportion of Six Pore Types
Based on the observations and pore size measurements of 63,137 pores by casting thin section and FE-SEM, six types of pores were identified by genetic characteristics. By decomposing the HPMI-NMR-derived PSD, the proportion of each type was estimated based on the least squares method (Figure 4), as shown in Section 3.4. Modified by extensive compaction and cementation, the shapes of RIPs are commonly triangular or polygonal, with radii ranging from 0.885 to 80.364 μm (Figure 5a) [13]. The proportion of RIPs in the J1b sandstones is relatively low, ranging from 0.39% to 11.30%. The FDPs developed an irregular strip shape and are distributed along the cleavage of feldspar (Figure 5b). FDPs are usually larger than other pores (the pore radii typically range from 0.951 to 10.429 μm) with relatively good connectivity (Figure 5i), and the proportion of FDPs ranged from 4.21% to 19.77%. The RFDPs are smaller than the FDPs, with pore radii ranging from 0.155 to 4.024 μm (Figure 5i). The RFDPs usually exhibit irregular polygonal shapes, with the proportion varying from 0.13% to 14.63% (Figure 5c). The proportions of CIPs and IPKs increase with more authigenic clay mineral precipitation and are especially influenced by kaolinites (Figure 4d,e,g,h). The radii of the CIPs predominantly range from 0.136 to 1.383 μm, and the majority of IPKs are smaller than 0.124 μm (Figure 5i). The shapes of the CPs are mainly influenced by the morphology of the authigenic clay minerals. The proportion of CIPs varies from 4.20% to 33.13%, and that of the IPKs ranges from 0.10% to 35.26%. Generally, the MPs have the smallest radii (mainly from 4 to 118 nm) but a high proportion in tight sandstones (Figure 5i,f).  (Figure 5a) [13]. The proportion of RIPs in the J 1 b sandstones is relatively low, ranging from 0.39% to 11.30%. The FDPs developed an irregular strip shape and are distributed along the cleavage of feldspar (Figure 5b). FDPs are usually larger than other pores (the pore radii typically range from 0.951 to 10.429 µm) with relatively good connectivity (Figure 5i), and the proportion of FDPs ranged from 4.21% to 19.77%. The RFDPs are smaller than the FDPs, with pore radii ranging from 0.155 to 4.024 µm (Figure 5i). The RFDPs usually exhibit irregular polygonal shapes, with the proportion varying from 0.13% to 14.63% (Figure 5c). The proportions of CIPs and IPKs increase with more authigenic clay mineral precipitation and are especially influenced by kaolinites (Figure 4d and that of the IPKs ranges from 0.10% to 35.26%. Generally, the MPs have the smallest radii (mainly from 4 to 118 nm) but a high proportion in tight sandstones (Figure 5i,f). According to the size of pores, the RIFs, FDPs, and RFDPs were identified as macropores, whereas CIPs, IPKs, and MPs were identified as micropores in this study. In addition, micro-fractures caused by compaction and tectonic activities are also important to the seepage capability. These micro-fractures often developed through rigid minerals and surrounding pores (Figure 5b). However, there are few micro-fractures, representing only 1-2% of the pore space. The proportion and porosity of the six pore types are listed in Table 2. CIPs, IPKs, and MPs were identified as micropores in this study. In addition, micro-fractures caused by compaction and tectonic activities are also important to the seepage capability. These microfractures often developed through rigid minerals and surrounding pores (Figure 5b). However, there are few micro-fractures, representing only 1-2% of the pore space. The proportion and porosity of the six pore types are listed in Table 2.   The PSD patterns of the four above-mentioned lithofacies are distinctive. In the ACMF, the PSD from HPMI are continuous without obvious peak values, and the radii are distributed from 0.0025 to 6.3 µm (Figure 6a). The T 2 spectrums have noticeable bimodal characteristics with greater amplitudes of the left peaks, demonstrating that micropores (MPs and CPs) control the PSD of the ACMF (Figure 6e). In the QCDF, the HPMI-derived PSD exhibit unimodal characteristics with radii ranging from 0.1 to 0.63 µm (Figure 6b). The T 2 spectrums display conspicuous bimodal behaviors, with the left peaks ranging from 0.619 to 1.822 ms and the right peaks ranging from 8.829 to 20.256 ms (Figure 6f). The CCF has an obvious bimodal peak pattern in HPMI-derived PSD, which reveals that the samples are dominated by micropores and relatively large pores ranging from 0.04 to 0.0063 µm and 0.25 to 0.4 µm, respectively (Figure 6c). The T 2 spectrums of CCF have noticeable unimodal features, suggesting that the PSD are relatively controlled by micropores (Figure 6g). In the MCTF, the PSD derived from HPMI show single-peak characteristics, with peaks distributed from 0.025 to 0.16 µm, indicating that the MCTF samples have more micropores (Figure 6d). Similarly, the T 2 spectrums of MCTF are also characterized by typical bimodal behaviors and have greater left peaks, with peak values ranging from 0.496 to 1.203 ms (Figure 6h). The PSD patterns of the four above-mentioned lithofacies are distinctive. In the ACMF, the PSD from HPMI are continuous without obvious peak values, and the radii are distributed from 0.0025 to 6.3 μm (Figure 6a). The T2 spectrums have noticeable bimodal characteristics with greater amplitudes of the left peaks, demonstrating that micropores (MPs and CPs) control the PSD of the ACMF ( Figure  6e). In the QCDF, the HPMI-derived PSD exhibit unimodal characteristics with radii ranging from 0.1 to 0.63 μm (Figure 6b). The T2 spectrums display conspicuous bimodal behaviors, with the left peaks ranging from 0.619 to 1.822 ms and the right peaks ranging from 8.829 to 20.256 ms (Figure 6f). The CCF has an obvious bimodal peak pattern in HPMI-derived PSD, which reveals that the samples are dominated by micropores and relatively large pores ranging from 0.04 to 0.0063 μm and 0.25 to 0.4 μm, respectively (Figure 6c). The T2 spectrums of CCF have noticeable unimodal features, suggesting that the PSD are relatively controlled by micropores (Figure 6g). In the MCTF, the PSD derived from HPMI show single-peak characteristics, with peaks distributed from 0.025 to 0.16 μm, indicating that the MCTF samples have more micropores (Figure 6d). Similarly, the T2 spectrums of MCTF are also characterized by typical bimodal behaviors and have greater left peaks, with peak values ranging from 0.496 to 1.203 ms (Figure 6h).

Parameters of Pore Structures Determined by NMR and HPMI
The microscopic parameters of pore networks were evaluated by HPMI and NMR. Quantitative pore structure parameters, such as entry pressure (Pd), maximum pore radius (rmax), medium pore radius (r50), average pore radius (r̅ ), sorting coefficient, skewness and maximum mercury intrusion saturations (Smax), were derived from HPMI measurements. The Pd ranged from 0.1 to 30.625 MPa, corresponding to an rmax in the range of 0.024 to 5.334 μm. The r50 and r̅ of pores were 0.002-0.399 μm and 0.008-0.963 μm, respectively. rapex, which represents the pore radius corresponding to the apex of Pittman's plot, reveals the transition from well-connected pores to poorly connected pores [50], and was 0.027-1.090 μm. The NMR porosities of all samples are consistent with the helium porosities, verifying that the PSD determined using NMR are fully ranged and the diffusion effects can be neglected [27]. The T2cuttoff is defined as the separation between BVI and FFI, and the BVI porosity (ϕBVI) and FFI porosity (ϕFFI) were calculated. The T2cutoff values are not constant, but vary between

Parameters of Pore Structures Determined by NMR and HPMI
The microscopic parameters of pore networks were evaluated by HPMI and NMR. Quantitative pore structure parameters, such as entry pressure (P d ), maximum pore radius (r max ), medium pore radius (r 50 ), average pore radius (r), sorting coefficient, skewness and maximum mercury intrusion saturations (S max ), were derived from HPMI measurements. The P d ranged from 0.1 to 30.625 MPa, corresponding to an r max in the range of 0.024 to 5.334 µm. The r 50 and r of pores were 0.002-0.399 µm and 0.008-0.963 µm, respectively. r apex , which represents the pore radius corresponding to the apex of Pittman's plot, reveals the transition from well-connected pores to poorly connected pores [50], and was 0.027-1.090 µm. The NMR porosities of all samples are consistent with the helium porosities, verifying that the PSD determined using NMR are fully ranged and the diffusion effects can be neglected [27]. The T 2cuttoff is defined as the separation between BVI and FFI, and the BVI porosity (φBVI) and FFI porosity (φFFI) were calculated. The T 2cutoff values are not constant, but vary between 1.25 and 18.64 ms ( Table 2). The T 2peak (the T 2 value corresponding to the highest signal amplitude) and T 2gm (the amplitudes weighted as means on a logarithmic scale) values can be derived from the T 2 spectrum as well. The parameters of the pore structures identified from NMR and HPMI were determined, as shown in Table 3.

Fractal Dimensions from the Combination of HPMI and NMR
The plots of lgS v vs. lgr of samples in accordance with Equations (8)- (14) were used to calculate the fractal dimensions of the pore networks based on the HPMI-NMR-integrated PSD [23,27]. Two distinct linear segments were identified, and the values of radii that correspond to the division points (r d ) were similar to the values of r apex , which is regarded as the boundary dividing poorly-connected pores and well-connected pores [11]. The proportion of pores with radii larger than r d has a positive correlation with the proportion of macropores (Figure 7a). Similarly, a positive linear correlation exists between the proportion of pores whose sizes are smaller than r d and the proportion of micropores (Figure 7a).  Table 2). The T2peak (the T2 value corresponding to the highest signal amplitude) and T2gm (the amplitudes weighted as means on a logarithmic scale) values can be derived from the T2 spectrum as well. The parameters of the pore structures identified from NMR and HPMI were determined, as shown in Table 3.

Fractal Dimensions from the Combination of HPMI and NMR
The plots of lgSv vs. lgr of samples in accordance with Equations (8)- (14) were used to calculate the fractal dimensions of the pore networks based on the HPMI-NMR-integrated PSD [23,27]. Two distinct linear segments were identified, and the values of radii that correspond to the division points (rd) were similar to the values of rapex, which is regarded as the boundary dividing poorly-connected pores and well-connected pores [11]. The proportion of pores with radii larger than rd has a positive correlation with the proportion of macropores (Figure 7a). Similarly, a positive linear correlation exists between the proportion of pores whose sizes are smaller than rd and the proportion of micropores (Figure 7a).   Table 4.

Validation and Limitation of Decomposing the NMR-HPMI Integrated PSD by the Least Squares Estimator
After decomposing the NMR-HPMI-integrated PSD by the least squares estimator mentioned in Section 3.4, the results show the reliability of this method through highly positive correlations between the mineral contents and the porosities of relevant pores: the porosity of MP exhibits a positive correlation with the content of matrix (R 2 = 0.8821, Figure 9a), and a direct correlation was discovered between the content of kaolinite and the porosity of IPK (R 2 = 0.7310, Figure 9b). There is also a significant proportionality relationship between the content of clay minerals and the porosity of CIP (R 2 = 0.8084, Figure 9c).

Validation and Limitation of Decomposing the NMR-HPMI Integrated PSD by the Least Squares Estimator
After decomposing the NMR-HPMI-integrated PSD by the least squares estimator mentioned in Section 3.4, the results show the reliability of this method through highly positive correlations between the mineral contents and the porosities of relevant pores: the porosity of MP exhibits a positive correlation with the content of matrix (R 2 = 0.8821, Figure 9a), and a direct correlation was discovered between the content of kaolinite and the porosity of IPK (R 2 = 0.7310, Figure 9b). There is also a significant proportionality relationship between the content of clay minerals and the porosity of CIP (R 2 = 0.8084, Figure 9c).
The accuracy of the proportion of pores can be indirectly evaluated by calculating the difference between the reconstructed PSD and the HPMI-NMR derived PSD. The root mean square error of reconstruction (X RMS ) can be calculated by, , (15) where y t (r i ) is the pore volume fraction from the HPMI-NMR derived PSD corresponding to the ith pore radius and y c (r i ) is the pore volume fraction from the reconstruction PSD corresponding to the ith pore radius. M is the number of the pore radius. The RMS errors of 13 samples ranged from 0.001 to 0.008 (Table 2), which suggests that the differences between the reconstructed PSD and NMR-HPMI derived PSD are clear, proving that the results could be employed to determine the porosity contributions of pore types from different genetic origins.
However, many flaws in this method cannot be neglected. It is necessary to indicate that self-defects of HPMI would cause the cumulative pore volume fraction of HPMI-derived PSD to be somewhat not consistent with that of NMR-derived PSD. For instance, the pore-blocking effects might mean that the macropores cannot be fully detected [6]. However, compared to the RCP and N 2 adsorption results, the HPMI can characterize a wider ranges of pore sizes (from several nm to hundreds of µm). Hence, the use of HPMI-NMR derived PSD is the best choice for multi-scale pore networks so far.
In addition, the porosity contributions of pores with unfixed sizes (e.g., moldic pores and micro-fractures) cannot be accurately estimated by the least squares estimator. The porosities of these pores could be temporarily ignored because they are rarely observed via thin sections or SEM in the J 1 b sandstones. The above discussion indicates that decomposing the NMR-HPMI-integrated PSD by the least squares estimator is effective for determining the pore volume fractions of different genetic pore types in J 1 b tight sandstones. The accuracy of the proportion of pores can be indirectly evaluated by calculating the difference between the reconstructed PSD and the HPMI-NMR derived PSD. The root mean square error of reconstruction (X RMS ) can be calculated by, where y t (r i ) is the pore volume fraction from the HPMI-NMR derived PSD corresponding to the ith pore radius and y c (r i ) is the pore volume fraction from the reconstruction PSD corresponding to the ith pore radius. M is the number of the pore radius. The RMS errors of 13 samples ranged from 0.001 to 0.008 (Table 2), which suggests that the differences between the reconstructed PSD and NMR-HPMI derived PSD are clear, proving that the results could be employed to determine the porosity contributions of pore types from different genetic origins.
However, many flaws in this method cannot be neglected. It is necessary to indicate that selfdefects of HPMI would cause the cumulative pore volume fraction of HPMI-derived PSD to be somewhat not consistent with that of NMR-derived PSD. For instance, the pore-blocking effects might mean that the macropores cannot be fully detected [6]. However, compared to the RCP and N2 adsorption results, the HPMI can characterize a wider ranges of pore sizes (from several nm to hundreds of μm). Hence, the use of HPMI-NMR derived PSD is the best choice for multi-scale pore networks so far.
In addition, the porosity contributions of pores with unfixed sizes (e.g., moldic pores and microfractures) cannot be accurately estimated by the least squares estimator. The porosities of these pores could be temporarily ignored because they are rarely observed via thin sections or SEM in the J1b sandstones. The above discussion indicates that decomposing the NMR-HPMI-integrated PSD by the least squares estimator is effective for determining the pore volume fractions of different genetic pore types in J1b tight sandstones.

Impact of Diagenesis and Sedimentary Processes on the Macroscopic Reservoir Quality
The sedimentary conditions determine the original reservoir quality by controlling the sediment composition, grain size, and primary porosity. In the sedimentary setting of the proximal-shallow delta plain, sediments accumulated quickly, leading to the poor sorting and small grain size of the sandstones, while generating a large number of matrix at the bottom of the braided channel. Hence, a large number of MPs exist in MCTF, and the highest MP porosity in the MCTF is 6.903%. Most MPs are on the nanometer scale, and their origins are currently being debated. MPs may include the tiny intergranular pores between matrix grains, or the DPs formed by eogenetic dissolution [52,53]. The high MP content resulted in a poor connection between the porosity-permeability and complicated pore network structures. In addition, the high matrix content not only aggravates damage to the reservoirs due to mechanical compaction [52], but also triggers a sharp reduction in the RIP porosity (Figure 9d).
In the burial process, the diagenetic reworking determines the reservoir quality, and the pore types of the four diagenetic facies are different. The CCF is mostly distributed at the interfaces between mudstones and sandstones or the thin sandstone interlayers of massive mudstones (Figure 10a). In the process of pressure solution or under the reworking of acidic fluids, matrix, frame grains, or adjacent mud layers may provide abundant Ca 2+ and Fe 2+ for the cementation of carbonates. In addition, the organic acid dissolved a large number of aluminosilicate minerals, whereas large-scale DPs are rarely discovered in the early calcite cement (Figure 3e-h) because, in a closed diagenesis system, the equilibrium constant of the carbonate leaching reaction is much lower than that of the feldspar (or rock fragments) dissolution reaction. Additionally, more H + is needed by the reaction of carbonate cement dissolution [54]. The cementation of calcite and siderites in the eogenetic period considerably blocked the RIP, and ferrocalcite partially replaced the feldspars or filled some DPs during the mesogenetic period (Figure 9e). In summary, the carbonate cements decreased the proportion of macropores, worsening the petrophysical properties of the reservoirs.
The QCDF mostly developed in the center of the channel sand bodies, which are favorable for the modification and migration of acid [55]. The positive correlation between the quartz overgrowth content and the DP or CP porosity indicates that the Si 4+ in the quartz overgrowth mainly originated from the dissolution of feldspar and rock fragments, especially from the feldspar, due to the higher correlation coefficient between the quartz overgrowth content and the FDP porosity (Figure 9f,g). However, samples with higher matrix contents do not conform to this correlation (Figure 9f), which reveals that the matrix hindered the activity of the diagenetic fluids and even inhibited the cementation of quartz. The mesogenetic quartz overgrowth increased the compression resistance of reservoirs protecting the RIPs from being destroyed by compaction (Figure 9h). In the QCDF, DPs play important roles, constituting 20-40% the macropores. However, the porosity of most of the QCDF is still below 10% (Figure 10a,b), which demonstrated that dissolution products (e.g., authigenic clay minerals and quartz cements) moved slowly in the tortuous aqueous pathways in the closed diagenetic environment by diffusion or deposited in situ and further blocked the pores [14,52]. As a result, the reworking degree of dissolution on the storage spaces in J 1 b sandstones is extremely limited. This finding is proven by the positive correlation between the CP and DP porosities (Figure 9g).
In the ACMF, CPs play dominant roles, with proportions ranging from 4.445% to 5.568%. The continuous reduction in macropores resulted from mat-like, bridge-like, and fibrous illite, and vermicular or booklet kaolinite aggregates filling the pore spaces (Figure 4e,g,h), and a series of nanoscale pores with poor seepage performances were generated by the authigenic clay minerals [11]. The authigenic clay minerals mainly derived from feldspars and rock fragments due to dissolution by the organic acids and meteoric water. However, the positive correlation between the CP and DP porosities is not observed in the ACMF (Figure 9g), which implies that authigenic clay minerals may be generated by dissolution in addition to other reactions. For instance, illite may be converted from kaolinite during the eogenetic period, and chlorite may be converted from berthierine or odinite [56]. converted from kaolinite during the eogenetic period, and chlorite may be converted from berthierine or odinite [56].

Relationship between Petrophysical Properties and Different Genetic Pores
The pore volume fraction of different genetic pores plays the bridge and medium roles in linking the sedimentary-diagenetic factors and microscopic pore structures from the perspective of storage and percolation capacities, the porosity of the QCDF is only slightly higher than that of the other lithofacies, but its permeability is higher than that of the other lithofacies by one order of magnitude (Figure 10b,c), which indicates that the increase in the DP volume is favorable for the increase in percolation pathways, considerably improving the permeability. The porosity of the CCF is the lowest among the four lithofacies, but the permeability is slightly higher than that of the MCTF samples and some of the ACMF samples (Figure 10b,c). The porosities of the MCTF and ACMF are slightly lower than that of the QCDF, although the porosity is higher than 10% in the ACMF, the permeabilities of both the MCTF and ACMF are extremely low, lower than that of the CCF, which has the lowest porosity (Figure 10b,c). MPs and CPs constitute some of the porosity, but these micropores are mostly isolated with poor connectivity at the nanoscale, causing the permeabilities of the reservoirs to be fairly low. The ϕBVI values of the ACMF and MCTF are significantly higher than those of the QCDF and CCF, which also proves that most MPs and CPs are isolated pores ( Figure  10d). The porosity of the ACMF is slightly higher than that of the MCTF, which indicates that porefilling authigenic clay minerals decreased damage due to compaction and thus preserved the reservoir quality to some extent [11] (Figure 10d,e).
From the perspective of porosity, different types of pores provide certain contributions to the volumes of storage spaces in sandstones. Among them, MPs and CPs constitute the majority of the total porosity in J1b tight sandstones (Figure 10a). However, the porosities of samples might increase

Relationship between Petrophysical Properties and Different Genetic Pores
The pore volume fraction of different genetic pores plays the bridge and medium roles in linking the sedimentary-diagenetic factors and microscopic pore structures from the perspective of storage and percolation capacities, the porosity of the QCDF is only slightly higher than that of the other lithofacies, but its permeability is higher than that of the other lithofacies by one order of magnitude (Figure 10b,c), which indicates that the increase in the DP volume is favorable for the increase in percolation pathways, considerably improving the permeability. The porosity of the CCF is the lowest among the four lithofacies, but the permeability is slightly higher than that of the MCTF samples and some of the ACMF samples (Figure 10b,c). The porosities of the MCTF and ACMF are slightly lower than that of the QCDF, although the porosity is higher than 10% in the ACMF, the permeabilities of both the MCTF and ACMF are extremely low, lower than that of the CCF, which has the lowest porosity (Figure 10b,c). MPs and CPs constitute some of the porosity, but these micropores are mostly isolated with poor connectivity at the nanoscale, causing the permeabilities of the reservoirs to be fairly low.
The φBVI values of the ACMF and MCTF are significantly higher than those of the QCDF and CCF, which also proves that most MPs and CPs are isolated pores (Figure 10d). The porosity of the ACMF is slightly higher than that of the MCTF, which indicates that pore-filling authigenic clay minerals decreased damage due to compaction and thus preserved the reservoir quality to some extent [11] (Figure 10d,e).
From the perspective of porosity, different types of pores provide certain contributions to the volumes of storage spaces in sandstones. Among them, MPs and CPs constitute the majority of the  Effective percolation pathways have an important effect on permeability in tight sandstones. From the relationship identified between the permeability and the proportions of different types of pores in tight sandstones indicates that permeability commonly increased as RIP and DP porosities increased (Figure 12g-i). In addition, there is no correlation between permeability and CP porosity, and permeability even presents a decreasing trend with the increase in MP porosity (Figure 11j-l). Effective percolation pathways have an important effect on permeability in tight sandstones. From the relationship identified between the permeability and the proportions of different types of pores in tight sandstones indicates that permeability commonly increased as RIP and DP porosities increased (Figure 12g-i). In addition, there is no correlation between permeability and CP porosity, and permeability even presents a decreasing trend with the increase in MP porosity (Figure 11j-l). The contribution of different pores to the permeability (Ki) can be obtained by considering the bundle of the tube model [57]: where dShgi is the increment of total mercury intrusion corresponding to pores with a radius of ri [18]. The permeability contribution by HPMI is determined on the basis of the Purcell equation. In the QCDF, 31.688% of the pores control 95% to permeability, and the types of the pores that contribute significantly to the permeability are mainly RIPs and DPs (Figure 12a). In the ACMF, 32.256% pores contribute 95% to permeability, and similarly, RIPs and DPs contribute greatly to the permeability (Figure 12b). For the CCF, the pores that contribute considerably to permeability range from 0.177 to 0.63 μm and account for 42.331% of the total pore volume (Figure 12c). We found that the permeability of the CCF is mainly controlled by CIPs, RFDPs, and CIPs. In the MCTF, 54.483% of the pores control 95% of the permeability, of which 92.097% is controlled by the MPs and IPKs with radii of 0.015-0.1 μm, and the rest (2.993%) is controlled by the MPs, which are smaller than 0.015 μm ( Figure 12d). As the proportion of pores that mainly contribute to the permeability increased gradually, the main types of permeability-contributing pores transitioned from macropores to micropores, and the permeability decreased gradually (Figure 12).
To summarize, macropores are better connected and strongly contributed to permeability, possibly due to the formation of effective percolation pathways in the tight sandstones. However, a large amount of immovable fluid exists in the micropores, suggesting that the permeability contributions of micropores are limited, and the higher proportion of micropores, the lower the permeability [44]. Therefore, although micropores could provide considerable storage spaces and slightly increase the total porosity, the percolation capacity of the J1b sandstones is still poor due to the poor connectivity among these pores. The contribution of different pores to the permeability (K i ) can be obtained by considering the bundle of the tube model [57]: where dS hgi is the increment of total mercury intrusion corresponding to pores with a radius of r i [18]. The permeability contribution by HPMI is determined on the basis of the Purcell equation. In the QCDF, 31.688% of the pores control 95% to permeability, and the types of the pores that contribute significantly to the permeability are mainly RIPs and DPs (Figure 12a). In the ACMF, 32.256% pores contribute 95% to permeability, and similarly, RIPs and DPs contribute greatly to the permeability (Figure 12b). For the CCF, the pores that contribute considerably to permeability range from 0.177 to 0.63 µm and account for 42.331% of the total pore volume (Figure 12c). We found that the permeability of the CCF is mainly controlled by CIPs, RFDPs, and CIPs. In the MCTF, 54.483% of the pores control 95% of the permeability, of which 92.097% is controlled by the MPs and IPKs with radii of 0.015-0.1 µm, and the rest (2.993%) is controlled by the MPs, which are smaller than 0.015 µm (Figure 12d). As the proportion of pores that mainly contribute to the permeability increased gradually, the main types of permeability-contributing pores transitioned from macropores to micropores, and the permeability decreased gradually (Figure 12).
To summarize, macropores are better connected and strongly contributed to permeability, possibly due to the formation of effective percolation pathways in the tight sandstones. However, a large amount of immovable fluid exists in the micropores, suggesting that the permeability contributions of micropores are limited, and the higher proportion of micropores, the lower the permeability [44]. Therefore, although micropores could provide considerable storage spaces and slightly increase the total porosity, the percolation capacity of the J 1 b sandstones is still poor due to the poor connectivity among these pores.

Relationships Among the Fractal Dimensions, Petrophysical Properties, and Pore Structures of Four Lithofacies
Previously, many scholars thought that a low fractal dimension represents better seepage and storage capacities, which correspond to a higher proportion of primary pores and weaker diagenetic modification [58]. However, pore networks are often complicated due to multiple fractal characteristics, and tight sandstone is no exception. This study found that the total porosity is negatively correlated with fractal dimensions D 1 and D 2 , whereas the D 2 is generally higher than D 1 because the proportion of micropores is very high (Figures 13 and 14a). As the RIP porosity increases, D 1 and D 2 obviously decrease, as does RFDP porosity (Figure 13a,c). The FDP porosity has an inverse relationship with D 2 , and its relationship with D 1 displayed no obvious trend (Figure 13b). In terms of the correlative degree, the porosities of different macropores have more effects on D 2 than on D 1 , and the CP porosity has more effects on the heterogeneity of micropores than that of macropores (Figure 13d,e). The MP porosity is positively related to D 1 and D 2 (Figure 14f), indicating that the high proportion of MPs is the main reason for the complexity of pore networks in tight sandstones.

Relationships Among the Fractal Dimensions, Petrophysical Properties, and Pore Structures of Four Lithofacies
Previously, many scholars thought that a low fractal dimension represents better seepage and storage capacities, which correspond to a higher proportion of primary pores and weaker diagenetic modification [58]. However, pore networks are often complicated due to multiple fractal characteristics, and tight sandstone is no exception. This study found that the total porosity is negatively correlated with fractal dimensions D1 and D2, whereas the D2 is generally higher than D1 because the proportion of micropores is very high (Figures 13 and 14a). As the RIP porosity increases, D1 and D2 obviously decrease, as does RFDP porosity (Figure 13a,c). The FDP porosity has an inverse relationship with D2, and its relationship with D1 displayed no obvious trend (Figure 13b). In terms of the correlative degree, the porosities of different macropores have more effects on D2 than on D1, and the CP porosity has more effects on the heterogeneity of micropores than that of macropores (Figure 13d,e). The MP porosity is positively related to D1 and D2 (Figure 14f), indicating that the high proportion of MPs is the main reason for the complexity of pore networks in tight sandstones. Permeability is negatively correlated with D2, and the relationship between permeability and D1 is not apparent (Figure 14a). The complexity of macropore networks may dominate reservoir permeability whereas the micropores heterogeneity has less of an effect on permeability (Figure 14b). The pore sizes have a direct effect on the fractal dimension, and the heterogeneity of pore networks determines the percolation capacities of tight sandstones. The maximum and median pore radii can effectively describe the complexity of micropores, whereas the influence of pore sizes on the heterogeneity of macropores is not obvious (Figure 15a,b). In addition, the heterogeneity of  Previously, many scholars thought that a low fractal dimension represents better seepage and storage capacities, which correspond to a higher proportion of primary pores and weaker diagenetic modification [58]. However, pore networks are often complicated due to multiple fractal characteristics, and tight sandstone is no exception. This study found that the total porosity is negatively correlated with fractal dimensions D1 and D2, whereas the D2 is generally higher than D1 because the proportion of micropores is very high (Figures 13 and 14a). As the RIP porosity increases, D1 and D2 obviously decrease, as does RFDP porosity (Figure 13a,c). The FDP porosity has an inverse relationship with D2, and its relationship with D1 displayed no obvious trend (Figure 13b). In terms of the correlative degree, the porosities of different macropores have more effects on D2 than on D1, and the CP porosity has more effects on the heterogeneity of micropores than that of macropores (Figure 13d,e). The MP porosity is positively related to D1 and D2 (Figure 14f), indicating that the high proportion of MPs is the main reason for the complexity of pore networks in tight sandstones. Permeability is negatively correlated with D2, and the relationship between permeability and D1 is not apparent (Figure 14a). The complexity of macropore networks may dominate reservoir permeability whereas the micropores heterogeneity has less of an effect on permeability (Figure 14b). The pore sizes have a direct effect on the fractal dimension, and the heterogeneity of pore networks determines the percolation capacities of tight sandstones. The maximum and median pore radii can effectively describe the complexity of micropores, whereas the influence of pore sizes on the heterogeneity of macropores is not obvious (Figure 15a,b). In addition, the heterogeneity of Permeability is negatively correlated with D 2 , and the relationship between permeability and D 1 is not apparent (Figure 14a). The complexity of macropore networks may dominate reservoir permeability whereas the micropores heterogeneity has less of an effect on permeability (Figure 14b).
The pore sizes have a direct effect on the fractal dimension, and the heterogeneity of pore networks determines the percolation capacities of tight sandstones. The maximum and median pore radii can effectively describe the complexity of micropores, whereas the influence of pore sizes on the heterogeneity of macropores is not obvious (Figure 15a,b). In addition, the heterogeneity of micropores decreases considerably with the increase in φBVI (Figure 15c). Similarly, there is a strongly negative correlation between φFFI and D 2 (Figure 15d). Therefore, in the process of hydrocarbon charging, oil and gas tended to flow into large pores that have regular shapes with smooth surfaces, especially RIPs and DPs. In addition, D 1 and D 2 can be effective parameters for evaluating the percolation characteristics of tight sandstone reservoirs.
Energies 2019, 12, x FOR PEER REVIEW 23 of 27 micropores decreases considerably with the increase in ϕBVI (Figure 15c). Similarly, there is a strongly negative correlation between ϕFFI and D2 ( Figure 15d). Therefore, in the process of hydrocarbon charging, oil and gas tended to flow into large pores that have regular shapes with smooth surfaces, especially RIPs and DPs. In addition, D1 and D2 can be effective parameters for evaluating the percolation characteristics of tight sandstone reservoirs.

Conclusions
The effects of depositional and diagenetic settings on the microscopic pore networks and macroscopic petrophysical properties of tight sandstones from the Lower Jurassic Badaowan Formation (J1b) in the Southern Junggar Basin were investigated in this study. The conclusions are as follows: (1) A high matrix content, strong carbonate cementation, high authigenic clay mineral content, and extensive dissolution are primary reasons for the heterogeneities of the pore networks in the J1b sandstones. Through casting thin sections observation and FE-SEM, six types of pores were identified: residual intergranular pores (RIPs), feldspar dissolution pores (FDPs), rock fragment dissolution pores (RFDPs), clay mineral intergranular pores (CIPs), kaolinite intercrystalline pores (IPKs), and matrix pores (MPs). The pore volume fractions of six genetic pore types were determined according to decomposing the integrated PSD from nuclear magnetic resonance (NMR) and highpressure mercury injection (HPMI). Four lithofacies were determined based on the analysis of the mineral compositions, pore structures, and sedimentary-diagenetic processes: quartz cementeddissolution facies (QCDF), carbonate cemented facies (CCF), authigenic clay minerals facies (ACMF), and matrix caused tightly compacted facies (MCTF).
(2) Due to the limited modification caused by dissolution, the QCDF has a slightly higher porosity but much higher permeability compared to those of the other lithofacies. A slight drop in pore volumes and a considerable reduction in permeability occur as the proportion of MP and CP increases in the MCTF and ACMF. Carbonate cementation decreased the porosity of CCF, although the permeability of CCF is higher than those of the MCTF and ACMF. This difference is because the storage spaces in the J1b sandstones are mainly determined by a large number of CPs and MPs, while the percolation capacity is mainly dominated by RIPs and DPs. However, the contributions of MPs and CPs are limited by their smaller pore sizes and complex pore structures.

Conclusions
The effects of depositional and diagenetic settings on the microscopic pore networks and macroscopic petrophysical properties of tight sandstones from the Lower Jurassic Badaowan Formation (J 1 b) in the Southern Junggar Basin were investigated in this study. The conclusions are as follows: (1) A high matrix content, strong carbonate cementation, high authigenic clay mineral content, and extensive dissolution are primary reasons for the heterogeneities of the pore networks in the J 1 b sandstones. Through casting thin sections observation and FE-SEM, six types of pores were identified: residual intergranular pores (RIPs), feldspar dissolution pores (FDPs), rock fragment dissolution pores (RFDPs), clay mineral intergranular pores (CIPs), kaolinite intercrystalline pores (IPKs), and matrix pores (MPs). The pore volume fractions of six genetic pore types were determined according to decomposing the integrated PSD from nuclear magnetic resonance (NMR) and high-pressure mercury injection (HPMI). Four lithofacies were determined based on the analysis of the mineral compositions, pore structures, and sedimentary-diagenetic processes: quartz cemented-dissolution facies (QCDF), carbonate cemented facies (CCF), authigenic clay minerals facies (ACMF), and matrix caused tightly compacted facies (MCTF).
(2) Due to the limited modification caused by dissolution, the QCDF has a slightly higher porosity but much higher permeability compared to those of the other lithofacies. A slight drop in pore volumes and a considerable reduction in permeability occur as the proportion of MP and CP increases in the MCTF and ACMF. Carbonate cementation decreased the porosity of CCF, although the permeability of CCF is higher than those of the MCTF and ACMF. This difference is because the storage spaces in the J 1 b sandstones are mainly determined by a large number of CPs and MPs, while the percolation