Small-Scale Diagenetic Heterogeneity Effects on Reservoir Quality of Deep Sandstones: A Case Study from the Lower Jurassic Ahe Formation, Eastern Kuqa Depression

Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China University of Chinese Academy of Sciences, Beijing, China Research Institute of Exploration and Development, Tarim Oil Field Company, PetroChina, Korla, China School of Geosciences, China University of Petroleum, Qingdao, China School of Earth Sciences, Northeast Petroleum University, Daqing, China


Introduction
The exploration and development of deep clastic reservoirs have obtained more attention in China. Up to now, there are three most important provinces of deep clastic reservoirs: Kuqa Depression in Tarim Basin, Sichuan Basin, and central Junggar Basin [1]. Most deep sandstones experienced multistage tectonic/burial processes and fluid-rock interactions, and the original pore structure in the sandstones was extensively modified during burial. They have overall ultralow porosity and permeability and small pore throat [2,3].
However, numerous studies indicated that deep reservoirs have strongly heterogeneous porosity and permeability petrophysical properties. Consequently, reservoir rocks with good porosity, permeability, and oil/gas shows are locally common in the heterogeneous reservoirs [4][5][6]. The formation and distribution of the effective reservoir rocks are one of the most important issues for exploration of deep clastic reservoirs and are of great significance for the forecasting of deep petroleum accumulations [7,8].
Heterogeneity in petrophysical properties of deeply buried petroleum reservoirs is the result of original depositional conditions, postdepositional diagenesis, and tectonic activities. Sandstone composition and texture and original porosity and permeability determine the extent and distribution of eodiagenesis (0-2 km depth and >70°C), which in turn exert a substantial control on burial diagenesis (>2 km depth and >70°C) [9][10][11]. Variations in detrital composition and texture can cause strikingly different diagenetic types and contents, contrasting processes within a single intrachannel sand unit [12], and differential porosity reduction rate in different locations.
Thus, a heterogeneous reservoir consists of permeable rocks generally separated by low-permeability/impermeable rocks: e.g., fine-grained, ductile grain-rich sandstones and completely calcite-cemented sandstone zones. These lowpermeability/impermeable rocks are arranged at different scale lengths [7,8]. In such a heterogeneous reservoir, petroleum migration and accumulation are extremely uneven, markedly different from those in a homogenous reservoir [8,13]. Therefore, it is essential to understand the influence of sandstone composition and texture on variations in diagenetic types and processes. This can aid in understanding heterogeneous reservoir evolution and petroleum flow during deep burial, revealing the origin and distribution of effective porosity and permeability in such sandstone reservoirs.
Many wells have been drilled in the Dibei area of the eastern Kuqa Depression since 1998 (Figure 1(a)), and significant  Figure 1: (a) Regional geological map showing structural features of the eastern Kuqa Depression and location of the study area [14]. (b) Typical reservoir profile. 2 Geofluids petroleum discoveries were obtained in the Lower Jurassic Ahe Formation. The natural gas reserves were estimated to be approximately 56. 8 [14,15] (Figure 1(a)). The Dibei area, the focus of this study, lies in the Yiqikelike belt in the eastern Kuqa Depression. The Kuqa Depression is a superimposed basin that was originally a foreland basin from the Late Permian to Triassic, then an extensional depression basin from the Jurassic to Paleogene, and finally a regenerated foreland basin from the Neogene to Quaternary [16]. The foreland basin was initiated by the thrusting of the Southern Tianshan Orogenic Belt since the Late Permian [17] and finished its final evolution until the Early Jurassic. When entering the Early Jurassic, the Tarim   The foreland thrusting activities were dominant, resulting in a large number of thrust nappes and folds in the Kuqa Depression ( Figure 1(b)). The Mesozoic and Cenozoic strata are well preserved in the eastern Kuqa Depression (Figure 2). The Lower Jurassic is dominated by fluvial and deltaic deposits, the Middle Jurassic is dominated by deltaic and lacustrine deposits, and the Upper Jurassic is the combination of alluvial fan, deltaic floodplain, and lacustrine deposits [18][19][20][21][22]. The Lower Jurassic Ahe Formation, the focus of this research, is characterized by the braided deltaic environment [18,23]. The sandstones are mainly deposited in braided channels in the delta plain and in distributary channels in the delta front. These channel sand bodies are generally fining up units ranging mainly from gravel-bearing coarse-grained sandstones to finegrained sandstones with minor siltstone and mudstone laminas. The total thickness is about 240-300 m in the Dibei area with sand fractions of approximately 80-90%.
Source rocks in the eastern Kuqa Depression contain mudstones and coal seams deposited mainly in the Triassic Huangshanjie and Taliqike Formation and the Jurassic Yangxia and Kezilenuer Formation ( Figure 2). The Triassic source rocks have total thickness of less than 582 m; mudstones have total organic carbon (TOC) contents of 0.4%-24.4% [25]. The total thickness of the Jurassic source rocks is 202-1381 m; TOC values of mudstones are 0.3%-16.4% [25]. Organic matter is mainly type III kerogen and minor type II kerogen [24,25]. In the study area, the Jurassic source rocks have Ro values of less than 1.0%, while Ro values of the Triassic source rocks are greater than 1.0% [25]. The burial history of the study area was characterized by the early long-term shallow burial and late rapid deep burial, and this made the source rocks matured rapidly during late burial [26]. The Jurassic mudstones and the Miocene Jidike Formation gypsum deposits serve as good caprocks for petroleum accumulations ( Figure 2).

Samples and Methods
The conventional logging series of 11 wells in the study area ( Figure 1(a)), including natural gamma ray (GR), sonic  Four hundred core porosity and permeability measurements were also made. Detailed core descriptions, including petroleum shows, lithology, grain size, and carbonate cementation, were performed in three wells ( Figure 3). 32 thin sections were made to determine petrology of sandstones. X-ray diffraction clay mineral analysis data were collected from well YN-4 and YN-5. A scanning electron microscope (SEM) with energy dispersive X-ray spectroscopy (EDS) and backscatter electron (BSE) was used to furthermore identify diagenetic minerals, textural relationships between different minerals, and pore structures. Petrography and microthermometry of fluid inclusions were also conducted. Details regarding sampling and experimental procedures for porosity and permeability measurement, thin section petrology, XRD, SEM and BSE, and fluid inclusion analysis are available in Appendix A. 8 Geofluids to subrounded. The sorting is moderate, but the conglomeratic sandstone is poorly sorted. The sandstones are primarily litharenite and minor feldspathic litharenite (Figure 4(a)). They are in a state of low compositional maturity. The following numbers refer to proportions of the detrital fraction of the rock. Quartz gains range from 18% to 72% with an average of 46%. K-feldspar grains are less than 18% with an average of 8%, and plagioclase grains are less than 10% with an average of 1%. Lower-grade metamorphic rock fragments are the most important component of rock fragments (Figure 4(b)) and range between 5% and 65% with an average of 25%. The lower-grade metamorphic rock fragments are schist, phyllite, slate, and metamorphic siltstone fragments. Volcanic rock fragments have contents of 1%-40% with an average of 11%, and sedimentary rock fragments are less than 24% with an average of 8%. In addition,

Intra-GF Inter-GF
Inter-GF  small amounts of muscovite fragments are present in the sandstones with an average of 2% and locally up to 15%.
Detrital matrix in the sandstones is mainly clay matrix and has a content of 2%-25% of the whole rock, with an average of 7%.

Diagenesis
4.2.1. Compaction. The gradual increase in overlying strata loads during burial can cause detrital grains severely deformed, rotated, dislocated, and crushed, resulting in the loss of intergranular porosity. Most ductile grains (obviously deformed lower-grade metamorphic rock fragments, altered volcanic rock fragments, and mudstone fragments) are observed in thin sections to be severely deformed around rigid grains such as quartz and feldspar by mechanical compaction and to be squeezed into intergranular pores ( Figure 5(a)). Because of the variability in sandstone composition and texture, the degree of ductile compaction in the sandstones is differential. The relatively finer-grained, clay 11 Geofluids matrix-rich sandstones have a higher degree of compaction than those coarser-grained sandstones having less matrix ( Figures 5(b) and 5(c)). In addition, in tightly calcitecemented sandstones, framework grains have a floating appearance and show weak compaction ( Figure 5(d)).

Cementation.
Carbonate cement is widely distributed in the Ahe Formation, mainly consisting of Fe-calcite, anker-ite, and siderite. Contents of Fe-calcite are up to 27% of the whole rock. Based on its microtexture and occurrence, two types of Fe-calcite are recognized in the sandstones. The one type represents a poikilotopic texture, almost completely filling intergranular pores and minor replacing grains and clay matrix. Framework grains show a floating appearance indicating precipitation before significant compaction ( Figure 5(d)). The other type displays a rather patchy  13 Geofluids cementation and fills intergranular pores and dissolution pores and replaces framework grains (Figures 5(e) and 6(a)). Based on petrographic evidence, the patchy calcite postdates and/or is synchronous with quartz overgrowths (Figure 5(f)). The content of ankerite is less than 3%. Ankerite cement also has a rather patchy and local cementation, filling pores and replacing detrital grains. The ankerite postdates quartz overgrowths ( Figure 5(g)). Siderite is rare, generally less than 1%, and filling dissolution pores (Figures 6(a) and 6(b)).
Quartz cement is generally less than 5% and mainly occurs as quartz overgrowths (Figures 5(f)-5(h)). Quartz overgrowths predate and/or is synchronous with patchy Fecalcite and ankerite (Figures 5(f) and 5(g)). In places, quartz cement can also be observed to fill pores in the form of stubby bipyramidal crystals (Figure 7(a)).
X-ray diffraction analysis ( Figure 8) indicates that clay minerals in the sandstones are illite (average 69%), chlorite (average 26%), and minor amounts of illite/smectite (average 4%) and kaolinite (average 1%). Mixed-layer illite/smectite is approximately 70% illite. Illite clays have finely hair-like and flake morphology (Figures 7(b) and 7(c)) and occur as grain coats or pore fills (Figures 6(c) and 6(d)). Illite is generally intergrown with quartz crystals (Figure 7(a)) and is engulfed by Fe-calcite (Figures 6(c) and 7(d)). Chlorite typically occurs as finely platelets and is intergrown with illite (Figures 6(d)-7(e)). In finer-grained, clay matrix-rich sandstones, illite is dominated by the flake morphology (Figure 7(c)). Microfractures have radius values usually less than 50 μm, and they have thin porosity generally less than 0.1%, locally up to 0.5%. Propagation paths of microfractures are affected by detrital composition of sandstones and diagenetic types and severity. Petrographic observations indicate the following: those microfractures along grain boundaries accounting for 40%, those cutting through rigid quartz and feldspar grains account for 39.2%, those cutting through ductile rock fragments make up 9.6%, those cutting through clay minerals make up 5.6%, those cutting through other cements make up 0.8%, and those cutting through pores account for 4.8%.  (Figures 7(a)-7(e)). The coarser-grained, matrixpoor sandstones contain primary pores and dissolution pores. They have thin section porosity of 0.9%-2.6% with an average of 1.6%. Primary intergranular porosity is less than 0.5%; dissolution porosity is 0.9-2.1% with an average of 1.5%; microfractures have thin section porosity less than 0.1%. Sporadic dissolution pores are found in the relatively finer-grained, matrix-rich sandstones with thin section porosity less than 1%. Tightly calcite-cemented sandstones contain few pores. Intercrystalline pores within clay minerals can provide storage spaces, but they have small pore radius (mostly micron) and are not well connected with other large primary intergranular pores and dissolved pores.

Reservoir Quality.
The above analyses show that the Ahe Formation sandstones have highly heterogeneous reservoir quality. This is also supported by core-analysis petrophysical properties. The sandstones have porosities in the range from 1.6% to 12.2%, averaging 6.7%, and they have permeabilities ranging between 0.008 and 605 mD, averaging 0.8710 mD (Figure 10(a)). Generally, porosity and permeability properties in gas zones are better for production than those in gas-bearing water zones and dry zones. However, the properties in sandstones vary greatly in gas zones, gas-bearing water zones, and dry zones. It is noted that the porosity and permeability values in this data set have a normal and lognormal distribution, respectively; spatial changes in porosity are invariably associated with changes in the logarithm of permeability ( Figure 10(b)).
Tightly calcite-cemented sandstones are constrained to medium-to coarse-grained sandstones with a median grain size of 0.48-0.72 mm. They have a low degree of ductile compaction with floating framework grains. The cementation is characterized by Fe-calcite cements. The Fe-calcite has a poikilotopic texture filling pores and replacing grains and clay matrix, and it accounts for 22.0-27.0% of the whole rock. In the petrofacies, dissolution of feldspar and rock fragments is very rare, and sporadic dissolution pores are recognized. The petrofacies have porosities ranging from 1.1% to 3.5%, (average 2.9%) and have permeabilities ranging from 0.013 to 1.354 mD (average 0.067 mD) (Figure 10(c)).

Petroleum Charge Dating.
Pore-free oils and adsorbed oils are common in ductile-lean sandstones. They display yellow and blue-white fluorescence (Figures 12(a)-12(d)). In addition, brown solid bitumens are also recognized in pores (Figures 12(e) and 12(f)). Pore-free oils, adsorbed oils, and solid bitumens are rare in ductile-rich sandstones and tightly calcite-cemented sandstones.
Oil inclusions are commonly seen in ductile-poor sandstones. They are elliptical, elongated, and irregular in shape and are often less than 5 μm. Oil inclusions mainly are distributed along healed microfractures cutting through or terminated within quartz grains (Figures 12(a) The homogenization temperature is a minimum trapping temperature of fluid inclusions and represents the minimum precipitation temperature of the host mineral [28]. The measured homogenization temperatures can be related to the burial-thermal history to reveal the timing of petroleum charge. In most geological cases, pressure correction is required to estimate the true trapping temperature. In hydrocarbon-bearing sandstones, the concentration of soluble hydrocarbons approximates or reaches a saturation level in pore waters [29]. Therefore, the measured homogenization temperatures are approximately equivalent to the true trapping temperatures without pressure correction.
Based on the homogenization temperature distribution of aqueous fluid inclusions (converted to age via the thermal history), petroleum charge can be divided into two stages: 25 Ma to 12 Ma and 5 Ma to the present day ( Figure 14). These results are consistent with the results of Li et al. [30,31] and Shi et al. [32]. They indicated that since the deposition of the Miocene Jidike Formation (23 Ma-), the Triassic source rocks began to enter the mature stage; when the Pliocene Kuqa Formation deposited (5 Ma-), the Triassic source rocks reached the peak of gas generation and migration, and the Jurassic source rocks entered the mature stage to generate oil and gas.

Differential Sandstone Diagenetic and Petroleum Charge
History. Combination of thin section, SEM and BSE observations give insights into textural relationships between different diagenetic minerals, which can aid in establishing the diagenetic sequence. The main eodiagenetic alterations includes the following: (1) mechanical compaction of ductile grains, (2) minor early clay coats and pore-filling clays, (3) early Fe-calcite precipitation, and (4) initial dissolution of detrital feldspar and rock fragments ( Figure 14). Mesodiagenetic alterations includes the following: (1) late dissolution of detrital grains, (2) alteration of smectite into illite, precipitation of illite and small amounts of chlorite, (3) authigenic quartz precipitation, (4) late Fe-calcite, ankerite and siderite precipitation, and (5) petroleum charge ( Figure 14). However, diagenetic evolutions of different sandstone petrofacies experienced contrasting pathways due to variabilities in primary texture and compositions of sandstones.

Eodiagenesis.
The Ahe Formation experienced the long-term shallow burial and eodiagenesis since the deposition through the Paleogene (Figure 14). Detrital compositions and texture of sandstones and original porosity and permeability determine the degree and distribution of eodiagenetic alterations [10,33]. The relatively finer-grained, matrix-rich ductile-rich sandstones underwent a higher 18 Geofluids degree of mechanical compaction relative to the coarsergrained ductile-lean sandstones containing less matrix (Figures 14 and 15). Argillaceous ductile grains were easily deformed and became smeared over surfaces of rigid grains and squeezed into pore throats leading to significant loss of intergranular porosity. Unstable detrital feldspar and rock fragments were easily dissolved by meteoric water under near-surface conditions in the early stage of eodiagenesis. Moreover, coals in the Yangxia Formation overlying the Ahe Formation were subject to oxidative degradation or peatification and produced organic acids with much CO 2 [34,35], which also promoted dissolution of detrital feldspar and rock fragments. Grain-coating clays are illite, and they occur tangentially to grain surfaces (Figures 6(c) and 6(d)). The clays are very common in ductile-rich sandstones. These textual characteristics indicate an infiltrated origin, ultimately detrital origin [36,37]. EDS analysis indicates (Figure 6(d)) that the graincoating illite is associated with small amounts of mixedlayer illite/smectite clays and chlorite. In addition, the morphology of the grain-coating illite, in places, is similar to smectite, indicating that the smectite precursors were partially or completely altered into illite. This is supported by the presence of mixed-layer clay minerals as shown X-ray diffraction analysis (Figure 8).
Fe-calcite in tightly calcite-cemented sandstones represents a poikilotopic texture, filling most of intergranular pores; framework grains have a floating appearance with the presence of undeformed ductile grains. These petrographic evidences indicate that the Fe-calcite precipitated before significant compaction ( Figure 5(c)). Rossi et al. [37] reported that the Fe-calcite has δ 13 C values of -5.5-3.6‰, reflecting mixed sources of dissolved carbon from soilderived bicarbonate and the oxidation of C 3 and C 4 plants during early diagenesis [38]. The source of Fe 2+ in Fecalcite is linked to dissolution of Fe-rich, metamorphic, and volcanic rock fragments. EDS analysis indicates that argillaceous rock fragments contain abundant Fe (Figure 6(e)).

Mesodiagenesis.
Since the deposition of the Miocene Jidike Formation, the Ahe Formation underwent rapid subsidence and burial and entered the mesodiagenetic stage ( Figure 14). In the late Oligocene, the Triassic source rocks entered the threshold of hydrocarbon generation [31,32]. The thermal degradation of organic matter released a large amount of organic acids and CO 2 followed or accompanied by oil generation [38][39][40]. Dissolution of feldspar and rock fragments continued in ductile-lean sandstones. Petrographic evidence for the late dissolution is that some dissolved feldspar and rock fragments have delicate and complete structures (Figures 6(f) and 7(f)). In places, dissolved pores are filled with late patchy carbonate minerals and quartz crystals ( Figures 5(e), 6(a)-6(c), and 9(c)). If formed during the early diagenesis, most of the delicate dissolved grains would be destroyed during the subsequent burial.
Authigenic quartz began to precipitate during the mesodiagenetic stage. The dissolution of feldspar and replacement by clays can provide a source of SiO 2 for quartz cement. This possible source is supported by the convincing petrographic evidence that quartz crystals occur in dissolved feldspar pores (Figure 9(c)) and coexist with illite clays (Figure 7(a)). Alteration of smectite into illite in interbedded mudstones can also release silica into pore water [41,42]. Illite and chlorite also 19 Geofluids precipitated in this stage. Illite, formed by the illitization of smectite in the clay matrix, often has the "honeycomb" texture of the smectite precursors and has finely flake morphology (Figures 7(a) and 7(c)). The hair-like illite (Figures 7(a) and 7(b)) was formed by the dissolution of argillaceous rock fragments. EDS analysis of illite indicates small amounts of Fe, indicating the presence of chlorite (Figure 7(b)). In petrographic observations, this mixture of illite and chlorite is in direct contact with Fe-and K-rich clays, and the outer edge of the Fe-and K-rich clays passes into illite and chlorite filling pores (Figures 6(c) and 6(d)). This Fe-and K-rich clay may be recrystallized rock fragments. Fe-calcite, ankerite, and siderite began to precipitate at this stage. Zhang et al. [43] indicated that the late Fe-calcite and ankerite have δ 13 C values of -6.4% to -10.4‰. Ni and Li [44] reported that the Fe-calcite has δ 13 C values of -6.0 to -18.9‰. This indicates a carbon source from the decarboxylation of organic matter [45].
At this stage, early oils and acidic fluids were mainly constrained in ductile-lean sandstones ( Figure 15). On the contrary, ductile-rich sandstones became tight due to strong compaction in the early diagenesis. They were hardly charged by early oils and acidic fluids and were dominated by solidphase alteration of smectite into illite. Tightly calcite cemented sandstones also underwent minimal influx of acid fluids and petroleum.

Geofluids
With further deep burial, pressure dissolution between quartz grains occurred and became extensive ( Figure 5(h)) and could provide a source of SiO 2 for quartz precipitation. Carbonates continued to precipitate. During the deposition of the Kuqa Formation, the late petroleum charge occurred. The fracturing occurred at this period. Late charge mainly occurred in ductile-lean sandstones. Ductile-rich sandstones and tightly calcite-cemented sandstones are poorly charged, although some fractures might help small amounts of hydrocarbons into them ( Figure 15).

Reservoir Quality Forecast for Different
Petrofacies. Due to variations in sandstone texture and grain composition, different sandstone petrofacies experienced contrasting diagenetic evolution pathways resulting in great differences in petrophysical properties. By using the method of Cao et al. [46], the porosity evolution models of the three petrofacies has been established ( Figure 16).
In the eodiagenetic stage, ductile compaction dominated ductile-rich sandstones and caused extensive loss of intergranular porosity. Calcite cements occupied almost all intergranular pores in tightly calcite-cemented sandstones. Ductile-lean sandstones have a relatively lower degree of compaction relative to ductile-rich sandstones, and strong dissolution occurred in them. When early oil arrived, ductile-rich sandstone and tightly calcite cementedsandstone achieved very low porosities, about 10% and 5%, respectively (Figure 16), and they were subsequently not charged by petroleum.
The ductile-lean sandstones remained relatively porous, with a porosity of 18% (Figure 16), and were significantly charged by early oils. With further burial, the porosity of ductile-lean sandstone was further reduced by cementation of quartz, carbonates, and clay minerals. When the late hydrocarbon charge occurred, ductile-lean sandstones still had moderate porosity, about 12%, and were preferentially charged with petroleum. Ductile-lean sandstones constitute effective reservoir rock in deep reservoirs.
In this study, the classification of sandstone petrofacies has been based on texture and compositions of sandstones, diagenesis type and process, and pore types. The classification of petrofacies by this method is consistent with well log responses. Well log responses can be used to identify and forecast petrofacies variations in wells that lack cores. DT value is plotted against GR and RD value ( Figure 17). Ductile-lean sandstones contain less abundant clay-rich lithic fragments and muddy matrix and have relatively lower GR values compared to ductile-rich sandstones. Their DT readings are higher due to abundant pores in them. Ductile-rich sandstones and tightly calcite-cemented sandstones have low DT values, but the GR values of ductilerich sandstones are significantly higher than tightly calcitecemented sandstones. In a typical vertical well profile, the reservoirs are more heterogeneous, and different petrofacies show an alternating spatial distribution ( Figure 18).
The concept of petrofacies can be used to recognize the main controlling factors affecting the petrophysical properties of sandstones [47,48]. The well-log responses of the sandstone petrofacies can be used to calibrate seismic signatures to obtain a consistent understanding of the subsurface reservoirs. This is of great significance to quantitatively evaluate the heterogeneity of deep reservoirs and to forecast reservoir quality of deep reservoirs.

Spatial Correlation of Fluid
Flow. Fluid-rock interactions are spatially correlated at all scale lengths [49,50]. Figure 19 shows well-log property sequence spectra scale SðkÞ as a power law in spatial frequency k, SðkÞ ∝ 1/k β , β ≈ 1. The scaling exponent ranges from 0.96 to 1.36, with mean value β ≈ 1:0 ± 0:15, highly consistent with the study from Leary 21 Geofluids et al. [49]. Gamma logs can track the distribution of radionuclide elements U, Th, and K in soluble minerals and thus indicate where and how fluids flow. The gamma ray activity from solute minerals dispersed through fluid flow displays a pink noise, scale invariant, 1/k power distribution.
As expected from Figures 10(b), 10(d), and 11(a) , the systematical spatial correlations between porosity φ and logarithm of permeability log ðκÞ indicate that the poroperm fluctuations are spatially organized in roughly the same way. This expresses the empirical spatial fluctuation relation δφ ∝ δ log ðκÞ. Furthermore, it is seen that how a normal distribution of porosity results in the lognormal distribution of permeability, shown in Figures 10(a) and 10(c), if it is recognized that permeability requires a connection condition to be met. Well productivity is lognormality distributed due to spatially correlated porosity, κ ∝ exp ðαφÞ. The different sandstone petrofacies have a different range of porosity and permeability (Figure 10(c)), but pores and pore connections in each petrofacies fundamentally control permeability in the form. Additionally, the vertical sequences of the interpreted sandstone petrofacies, ductile-lean sandstone and ductile-rich sandstone, are normally distributed ( Figure 20). The distribution of tightly calcite-cemented sandstones is highly rare and is not calculated. This normal distribution can be well interpreted by the empirics that crustal flow spatial variations are systematically correlated from mm to km. Translating the flow spatial correlation feature into numerical form is helpful for fluid flow simulation [49]. (2) Based on detrital components and texture of sandstones, diagenetic types and degree, and pore types, three petrofacies were defined: ductile-rich sandstone, ductile-lean sandstone, and tightly calcitecemented sandstone. Ductile-lean sandstones are mainly medium-to coarse-grained varieties with less detrital matrix and have relatively low degree of compaction, low total content of cements, and strong dissolution of framework grains. The petrofacies contain primary intergranular pores, intragranular dissolution pores, and microfractures and have good petrophysical properties. On contrary, ductile-rich sandstones are matrix-rich, fineto mediumgrained sandstones, and show strong compaction. They have relatively poorer reservoir quality. Tightly calcite-cemented sandstones are mainly medium-to coarse-grained sandstones with a lower degree of compaction. This petrofacies also has relatively quality (3) In the eodiagenetic stage, intergranular porosity was extensively reduced in ductile-rich sandstones and tightly calcite-cemented sandstones due to strong ductile compaction and complete calcite cementation. Before the early oil charge (25-12 Ma), the two petrofacies had evolved into tight rocks and were hardly charged by early oils. On contrary, the degree of compaction in ductile-lean sandstones in the eodiagenetic stage was relatively low and grain dissolution was extensive. When the early oil arrived, ductile-lean sandstones remained relatively porous and were significantly charged by early oils. With continued burial, the porosity of ductile-lean  Figure 18.