Introduction

With the continuous innovation of natural gas geological theory and a successive improvement of fracturing technology (Feng et al. 2019; Bou-Hamdan and Abbas 2021), tight sandstone gas (TSG) has become an important part of unconventional natural gas resources. The cumulative proven reserves and annual production of TSG in China are 5.2 × 1012 m3 and 410 × 108 m3, respectively (as of 2019), only following that of the USA and Canada (Zou and Qiu 2021). Breakthroughs in the exploration of TSG have been made in the Tarim and Junggar basins in the west, the Ordos and Sichuan basins at the center, as well as the Songliao and Bohai Bay basins in the east of China, forming different levels and scales of TSG fields (Dai et al. 2019; Sun et al. 2019). Specifically, the TSG in the Upper Paleozoic sequences of the Ordos Basin is one of the most representative gas fields in the world (Fu et al. 2008; Yang et al. 2008, 2012; He et al. 2021; Wu et al. 2021b, 2022).

The TSG field group in the central Ordos Basin, comprising the Sulige, Wushenqi, Yulin, Zizhou, and Shenmu gas fields, was formed under favorable conditions described as “gentle tectonic setting, wide overlying hydrocarbon generation, large area sand body distribution, and stable tectonic activity” (Yang et al. 2012; Tang et al. 2012; Huang et al. 2015; Zhao et al. 2017, 2019). However, TSG exploration in the Linxing area along the eastern margin of the Ordos Basin has progressed slowly because of the fact that the coalbed methane is still in its early stages of exploration (Chen et al. 2014; Li et al. 2014, 2016; Xie et al. 2016), and due to the influences of regional fault activity in the Zijinshan Structural Belt (Wang et al. 2007; Chen et al. 2012). With the intensification of TSG exploration and the deepening of gas geological theories, three core ideas have now been elucidated. (1) Coal-measure source rocks distributed from the Carboniferous Benxi Formation to the Permian Shanxi Formation are the main sources for controlling the formation and distribution of TSG (Fu et al. 2016; Xie et al. 2016; Li et al. 2016; Song et al. 2019; Xue et al. 2019; Hu et al. 2020; Zheng et al. 2020; Du et al. 2021; Shen et al. 2021); (2) Sandstone reservoirs mainly have nano-micron pores and are, hence, classified as tight reservoirs (Kong et al. 2020; Yin et al. 2020; Du et al. 2021; Jiu et al. 2021; Mi and Zhu 2021); (3) Activity within the Zijinshan Structural Belt controls hydrocarbon generation by the source rocks and the distribution of shallow gas reservoirs (Zou et al. 2016; Ge et al. 2018; Li et al. 2019a; Shu et al. 2019, 2021). These considerations have accelerated breakthroughs in TSG exploration and led to the discovery of TSG fields in the Linxing area with proven reserves of 1000 × 108 m3 (Du et al. 2021).

The Linxing Gas Field (LGF) contains more than 10 layers of commercial gas flow, including the Carboniferous Benxi Formation, the Lower Permian Taiyuan and Shanxi formations, the Middle Permian Lower Shihezi and Upper Shihezi formations, and the Upper Permian Shiqianfeng Formation (Fu et al. 2016), compared with the TSG field group in the central Ordos Basin that contains concentrated gas-producing layers. The characteristics of multi-layer gas fields in the LGF are rare—not only in China, but also worldwide. According to the theory of gas migration and accumulation, the degree of gas filling in the trap and the yield will decrease with an increase in gas migration distance in the multiple-layer gas reservoirs. However, gas testing results showed that high yields can be obtained in the Upper and Lower Shihezi formations, which are at a greater distance from the source rocks than that of the Shanxi and Taiyuan formations. For example, the absolute open flow (AOF) of the second member (He6 Member) of the Lower Shihezi Formation is 17.7 × 108 m3, whereas that of the fourth member (He4 Member) of the Upper Shihezi Formation can reach 32.6 × 108 m3. Previous studies on LGF have mostly focused on reservoir-forming conditions or the controlling effect of a single formation condition (Chen et al. 2018; Ge et al. 2018; Song et al. 2019). Yet, studies on controlling factors and the enrichment model of multi-layer TSG accumulation have not been published. Therefore, this study delves into the main controlling factors of gas accumulation and establishes an enrichment model using seismic data, drilling, logging, gas testing, laboratory analysis, and other data as an example of multi-layer TSG at the LGF. The aim of this study is to enrich the accumulation theory of TSG and provide theoretical guidance for the discovery of multi-layer gas fields in similar basins.

Geological setting

The Ordos Basin, located in central China (Fig. 1a), is structurally divided into six first-order tectonic units (Fig. 1b), namely, the Yishan Slope, Tianhuan Depression, Western Thrust Belt, Jinxi Flexure Belt, Yimeng Uplift, and Weibei Uplift, with a total area of ~ 25 × 104 km2. The LGF is in the Lin County–Xing County area, in western Shanxi Province. It structurally encompasses the transition between the Yishan Slope and the Jinxi Flexure Belt (Fig. 1b), covering an area of ~ 2000 km2. This rock mass of the Zijinshan Structural Belt is in the southeast of the LGF (Fig. 1c), and it is mainly an alkaline or partially alkaline complex that consists of intrusive and extrusive rocks. Additionally, the rock mass of the Zijinshan Structural Belt has its top exposed at the surface (Huang 1991; Chen et al. 2012).

Fig. 1
figure 1

Map of the Ordos Basin location; (b) map of the Linxing Gas Field (LGF) location; (c) structural map of the top surface of the He8 Member of the Permian Lower Shihezi Formation, which shows a trend of high in the northeast and low in the southwest

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The structure in the middle and eastern part of Ordos Basin is an east dip monocline after the Caledonian uplift, which is a stable sedimentary stage until late Permian. Four uplift and denudation events have occurred since the Indosinian Movement, and the denudation thickness in the eastern part of the basin was the largest since Cretaceous (Chen et al. 2006; Li et al. 2019a), at over 1700 m (Fu et al. 2016), which formed the present west-dipping monocline. A series of intensive fault zones developed around the Zijinshan Structural Belt in the southeast part of the Linxing area owing to the uplift of rock mass in the Cretaceous, and a complex fault system related to regional stress was formed in the east (Ge et al. 2018). The structure of the Upper Paleozoic is characterized by good inheritance: high in the northeast and low in the southwest. For example, the top altitude of the He8 Member of the Lower Shihezi Formation gradually decreases from northeast to southwest, with a distribution range of − 600 to − 850 m (Fig. 1c), while local highs exist near the position of wells G5 and G6 (Fig. 1c). In the southeast, the maximum altitude can exceed − 350 m because of the uplift of the Zijinshan rocks mass. The stratum is composed of Cambrian and Ordovician sequences of the Lower Paleozoic; Carboniferous and Permian sequences of the Upper Paleozoic; Triassic, Jurassic, and Cretaceous sequences of the Mesozoic; and Quaternary sequences of the Cenozoic. A variety of lithologies were developed in the coastal barrier deposits of the Carboniferous Benxi and Permian Taiyuan formations, comprising primarily dark gray mudstone, micritic limestone, light gray medium sandstone, and thin coal seams. The fluvial delta system of regressive deposition is developed in the Shanxi Formation, which is dominated by medium-coarse sandstone, mudstone, and thin coal seam. The fluvial‒deltaic facies occurred in the Permian Upper Shihezi, Lower Shihezi, and Shiqianfeng formations, with medium-coarse sandstone and gray mudstone (Fig. 2).

Fig. 2
figure 2

Comprehensive lithostratigraphic profile of the Upper Paleozoic sequences in the LGF. The red segments represent the gas-producing layers, and the final column shows the source-reservoir accumulation assemblage

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Database and methods

The data for this study comprises the following for Upper Paleozoic sequences of the LGF: gas testing results of 105 layers from 75 wells; reservoir porosity of 5661 samples and permeability of 5659 samples from 92 wells; gas components of 33 wells and gas isotopes of 14 wells; the content of total organic carbon (TOC) of coal seams from 29 samples and that of mudstone from 40 samples; hydrocarbon generating potential (S1 + S2) of coal seams from 25 samples and that of mudstone from 38 samples; vitrinite reflectance (Ro) of coal seams from 70 samples; and the pyrolysis peak temperature (Tmax) from 57 samples. All data were provided by the Unconventional Oil and Gas Branch of China National Offshore Oil Corporation.

Calculation and measurement of reservoir parameters

In total, 30 plain and 30 casting thin sections were used to analyze the lithology and determine the reservoir space. Then, 80 samples were viewed using scanning electron microscopy (SEM) performed with a Quanta FEG 450 system at the Key Laboratory of Hydrocarbon Accumulation Geology of Shaanxi Province in Xi’an Shiyou University. The sand body showed typical well-logging characteristics of “three low and one high,” i.e., low natural gamma (GR), low spontaneous potential (SP), low acoustic time difference (AC), and high resistivity (RT). We used a logging response to analyze and explain the sand body. Then, the average and median values of porosity, permeability, thickness, and argillaceous content corresponding to the depth of the sand body were calculated (Table 1).

Table 1 Statistics of formation condition parameters of TSG reservoirs in the LGF
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Calculation and measurement of source rock parameters

The thickness of the coal seams and dark mudstone were obtained from the cores of wells and their logging response. It was found that the logging features of the coal seam were characterized by high AC, high RT, low GR, high compensated neutrons (CNL), low density (DEN), and a low photoelectric absorption interface index (PE). The dark mudstone was characterized by high SP, high GR, and low AC. These response features were used to determine the thickness of the coal seams and mudstone of 97 wells.

The hydrocarbon generation intensity (HGI) of source rocks is a comprehensive index to evaluate their hydrocarbon generation ability. The HGI was calculated using the following formula:

$${G}_{\mathrm{gas}}=H\times {\rho }_{\mathrm{rock}}\times TOC\times {K}_{\mathrm{g}}\times {10}^{-3}$$
(1)

where, Ggas is the HGI of the source rock, × 108 m3/km2; H is the coal seams and dark mudstone thickness of the source rock, m; ρrock is the density of the source rock, t/km3 (in this study, the coal seam density was 1300 t/km3, and dark mudstone density was 2600 t/km3); TOC is the total content of organic carbon in the source rock, %; and Kgas is the gaseous hydrocarbon rate of the source rock, m3/t·TOC.

Of the variables, ρrock was obtained from the logging curve, while the total content of organic carbon (TOC) was determined via mapping; Kgas was obtained from the thermal compression simulation test of coal seams and dark mudstone (Table 2) (Yang et al. 2016; Gao et al. 2018).

Table 2 Hydrocarbon production rate (Kgas) of coal-measure source rocks with different lithologies in the Ordos Basin
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Results and discussion

Distribution and characteristics of the multi-layer TSG reservoir

Distribution of natural gas

Gas-producing wells were mainly concentrated in the north-central and southwestern parts of the LGF, with fewer wells near the Zijinshan Structural Belt, according to the gas test results (Fig. 3). Moreover, the number of gas-producing wells and AOFs were significantly different across sequences (Fig. 4). A total of 14 gas-producing layers were identified in sequence: the first member (Ben1 Member) of the Carboniferous Benxi Formation; the second (Tai2 Member) and first (Tai1 Member) members of the Lower Permian Taiyuan Formation; the second (Shan2 Member) and first (Shan1 Member) members of the Shanxi Formation; the fourth (He8 Member), third (He7 Member), and second (He6 Member) members of the Lower Shihezi Formation; the fourth (He4 Member), third (He3 Member), second (He2 Member), and first (He1 Member) members of the Upper Shihezi Formation; and the fifth (Qian5 Member) and fourth (Qian4 Member) members of the Shiqianfeng Formation. The number of producing layers and AOFs of the He2, He4, He6, He7, He8, and Tai2 members was greater than those of other layers. Within these members, there were 16 gas-producing layers in the He2 Member, with a maximum AOF of 16.2 × 104 m3/d. The number of gas layers in the He4, He6, He7, He8, and Tai2 members was 8, 11, 11, 19, and 13, respectively, with maximum AOFs of 32.6 × 104, 7.58 × 104, 14.6 × 104, 6.18 × 104, and 13.3 × 104 m3/d, respectively.

Fig. 3
figure 3

Plan view of the fault development and wells in the Upper Paleozoic strata of the LGF. The red well points are gas-producing wells, the hollow points are non-gas-producing wells, and the blue dashed line is the boundary of the Zijinshan Structural Belt. The green-shaded X, Y, and Z areas are typical areas used to explain different gas enrichment model. The black lines with green text indicate the profile line positions, where A‒A′ is shown in Fig. 7, and B‒B′ is shown in Fig. 8

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Fig. 4
figure 4

Histogram of the number of gas-producing layers and maximum AOF in the LGF. The orange columns indicate the number of gas-producing layers according to the left ordinate, and the red line illustrates the maximum AOF values according to the right ordinate

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Reservoir conditions

The lithology of the gas reservoir was mainly lithic arkose, accounting for 55.4% of the total samples (N = 325), followed by arkosic lithic sandstone, while lithic sandstone and arkose was less than 10%. The lithologic grain size was mainly medium-coarse sandstone, followed by medium-fine sandstone, and a small amount of fine sandstone and silty sandstone. The reservoir space mainly consisted of remanent intergranular pores, inter- and intragranular dissolution pores, followed by inter-crystalline and micro-fissure pores.

Based on the analysis of reservoir physical properties, the porosity ranged from 0.3 to 23.5% (N = 5661), with an average of 7.89% and a median of 7.61%, and samples that had less than 10% porosity accounted for 74.9% of the total. The permeability ranged from 0.01 × 10−3 to 549.1 × 10−3 μm2 (N = 5659), with an average of 2.86 × 10−3 μm2 and a median of 0.43 × 10−3 μm2. Furthermore, 77.7% of the samples had permeability less than 1 × 10−3 μm2. Therefore, the reservoir type could be categorized as low porosity and low permeability. In terms of the horizon (Fig. 5), the physical properties of the He4 Member were most favorable, followed by the Qian5, He2, He6, and Tai2 members. Among them, the He4 Member had the highest porosity (11.36%), followed by He2 and He6 members (both over 9.3%), and Shan1 and Shan2 members had the lowest porosity (both less than 6%). The median permeability of He4 Member was the highest, reaching 1.59 × 10−3 μm2, followed by Qian5, He2, and Tai2 members, which were greater than 0.5 × 10−3 μm2, and the permeability of the other layers were all less than 0.1 × 10−3 μm2. The average permeability of the Qian5 Member was the highest, at more than 10 × 10−3 μm2, while that of the He2 and He4 members was higher than 6 × 10−3 μm2, and that of the Qian1, Qian2, Qian3, Shan1, and Tai1 members less than 0.2 × 10−3 μm2.

Fig. 5
figure 5

Line map of reservoir physical properties in the LGF. The green line is the average porosity, the red line is the average permeability, and the purple line is the median permeability. The numbers in brackets at the bottom indicate the number of samples. The left ordinate is porosity, and the right ordinate is permeability

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Overall, the gas reservoir in the Upper Paleozoic strata of the LGF belonged to a TSG reservoir. According to the physical property statistics of the gas-producing sand body (N = 63) (Fig. 6), the porosity ranged from 5.38 to 15.89%, with an average of 10.11%, and the permeability ranged from (0.07 to 32.1) × 10−3 μm2, with an average of 2.61 × 10−3 μm2 and median of 0.81 × 10−3 μm2. For a single horizon, the average porosity and permeability of the Shiqianfeng Formation ranged from 10 to 12% and (1–10) × 10−3 μm2, respectively, while those of the Upper Shihezi and Lower Shihezi formations varied widely, ranging from 4.5 to 16% and (0.1–12) × 10−3 μm2, respectively; and those of the Shanxi and Benxi formations were less than 10% and 1 × 10−3 μm2, respectively. The porosity of gas reservoirs was positively correlated with permeability, i.e., the permeability increased gradually as porosity increased.

Fig. 6
figure 6

Cross-plot of porosity vs. permeability of the gas reservoir in the LGF

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Characteristics of the gas reservoir

Intertidal and distributary channel lenses were the main sandstone types of the gas reservoirs in the LGF developed in the Late Carboniferous–Early Permian barrier coast and tidal flat facies, as well as in the Middle–Late Permian fluvial-delta facies in the eastern margin of the Ordos Basin (Fu et al. 2008; Li et al. 2021). The multi-stage sand bodies were frequently transversely migrated, vertically superimposed, and continuously extended for hundreds of kilometers. Based on 525 logging interpretations of a single gas-bearing sandstone from 52 wells, the thickness ranged from 0.5 to 26.3 m with an average of 4.85 m, and 59.8% of the main body thickness ranged from 2 to 6 m. Among them, the thickness of the Qian5 Member was the largest—up to 10.5 m—followed by the He8 and Tai2 members with thickness 8.4 and 7.5 m, respectively, and the He2 and He4 members with 6.5 and 6.1 m, respectively. The Ben2 and Qian1 members had the smallest thickness—less than 2.5 m.

Fine-grained sedimentary rocks such as mudstone, argillaceous siltstone, and micritic limestone in different sedimentary facies from Benxi to Shiqianfeng formations were characterized by low porosity and permeability, small pore size, and high capillary pressure, with the mudstone dividing the sandstones into multi-layer lenses and sealing the sandstone. Regional geological evolution and seismic profiles show that the displacement of most of the fault developed in the Upper Paleozoic sequences between 5 and 15 m, which was larger than the thickness of the sandstone and played a sealing role. Therefore, lenticular lithologic traps and fault-lithologic traps form the TSG reservoir groups, which were superposed vertically and continuously distributed horizontally (Figs. 7‒8), presenting quasi-continuous distribution (Zhao et al. 2019; Wu et al. 2022). The TSG reservoir had no apparent edge or bottom water, and its formation water was mostly distributed in isolated lenses (Fig. 7). According to the gas testing results of exploration wells (N = 75), 11 water-producing layers were distributed in Ben1, Ben2, Tai1, Tai2, Shan2, Shan1, He8, He4, He2, and Qian5 members, and their water yield was between 0.25 and 32.5 m3, most of which were less than 4 m3. In addition, there is poor connectivity between formation water.

Fig. 7
figure 7

Profile A‒A′ of the gas reservoir distributed from Benxi and Shiqianfeng formations of the LGF. Yellow is sandstone, red is the gas-producing layer, blue is the water-producing layer, and black is the coal seam layer. The dark gray is the source rock location, and light gray is the argillaceous content in the lithologic profiles. The location of the profile is shown in Fig. 3

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Fig. 8
figure 8

Profile B‒B′ of the gas reservoir distributed in the Lower Shihezi and Upper Shihezi formations of the LGF. Yellow is the sandstone layer, red is the gas-producing layer, and blue is the water-producing layer. Gray indicates the argillaceous content in the lithologic profile. The red numbers in the boxes are the porosity (top) and permeability (bottom) of the gas-producing layers, while the purple numbers are the porosity (top) and permeability (bottom) of the sandstone layers. The location of the profile is shown in Fig. 3

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Natural gas properties

The gas reservoir can be described as a dry gas reservoir. Based on the analysis of natural gas components and composition, the methane content ranged from 90.72 to 99.63% (N = 33), with an average of 94.97%, and a methane content between 93 and 97% accounting for 57.5% of total number (Fig. 9a). The dryness coefficient (C1/∑C) ranged from 0.924 to 0.999, with an average of 0.974. The proportion of non-hydrocarbon components varied from 0.17 to 7.51% (N = 33), and the maximum value of N2 was 7.51%, which is related to air mixing in the sampling process. The δ13C1 values ranged from − 41.3 to − 32.8‰ (N = 14), with an average of − 37.8‰, and the δ13C2 values ranged from − 28.9 to − 22.3‰ (N = 11), with an average of − 26.3‰. Based on the gas identification diagram (Dai et al. 2014), the natural gas in the study area was from the coal-measure source rocks of the Benxi and Taiyuan formations, as well as the Shan2 Member of the Shanxi Formation.

Fig. 9
figure 9

Distribution of methane content and carbon isotope of natural gas in the Upper Paleozoic in Linxing gas field, Ordos basin. (a) Histogram of methane content. (b) Cross-plot of δ13C1 vs. δ.13C2

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Main controlling factors of multi-layer TSG accumulation

Controlling effects of the reservoir conditions

Physical properties

The formation and enrichment of the TSG reservoir were notably controlled by the physical properties of the gas-producing sandstone. Based on the relationship of the sandstone physical properties and the AOF values of the gas test (Fig. 10a‒b), the AOF value had a clear positive correlation with the reservoir porosity and permeability, i.e., it increased with increasing gas porosity or permeability. Furthermore, the AOF generally showed an upward trend. Permeability was more controlled than the porosity. Concerning each formation, with an increase in porosity, the AOF of the Upper Shihezi Formation increased notably, and the AOF of the Lower Shihezi Formation also increased to a certain extent, while Taiyuan, Shanxi, and Shiqianfeng formations did not show an increasing trend, and the trend of the Benxi Formation was restricted by the number of data points. With increasing gas permeability, there was an apparent increase in AOF of the Upper Shihezi, Lower Shihezi, Shiqianfeng, and Taiyuan formations, and that of the Shanxi Formation essentially remained unchanged. From the gas reservoir profile of the wells H1–H7 (Fig. 8), the porosity and permeability of the gas-producing layer in each well were better than that of the unaerated sandstone layers. For example, the AOF of the He6 and He7 members in Well H3 was 6.18 × 104 m3/d, the porosity of the reservoirs 12.6 and 12.1%, and the permeability 1.02 × 10−3 and 1.48 × 10−3 μm2, which were significantly higher than the same properties of their adjacent reservoirs. Wells H4 and H6 also had similar characteristics.

Fig. 10
figure 10

Cross-plots of reservoir parameters and absolute open flow (AOF) in gas reservoir of the LGF. (a) Porosity (Φ) vs. AOF. (b) Permeability (K) vs. AOF. (c) Argillaceous content (Vsh) vs. AOF. (d) Sandstone thickness (H) vs. AOF

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Argillaceous content

The AOF was noticeably controlled by the argillaceous content of the gas-producing sandstone. Argillaceous content ranged from 3.2 to 28.6%, and primarily from 6 to 17%. Based on the relationship between the argillaceous content and AOF (Fig. 10c), the AOF presented an apparent downward trend with increasing argillaceous content. The AOF of the Upper Shihezi, Lower Shihezi, and Taiyuan formations decreased markedly with increased argillaceous content, while the AOF of the Shanxi Formation decreased slightly, and the AOF of Shiqianfeng Formation did not show a significant change.

Thickness of gas-producing sandstone

The thickness of the gas-producing sandstone had no clear effect on the AOF. The thicknesses of gas-producing sandstone ranged from 2.8 to 22.3 m, and the major part was 4‒11 m. According to the relationship between the sandstone thickness and the AOF (Fig. 10d), AOF did not show an overall increasing trend as the thickness of the sandstone increased. Only the AOF of the Shiqianfeng Formation increased slightly with increasing sandstone thickness.

Controlling effects of source rock conditions

Overview of source rock conditions

The gas source of the TSG in the LGF was coal-measure source rocks of the Benxi and Taiyuan formations, as well as the Shan2 Member of the Shanxi Formation. The lithology was mainly coal seams and dark mudstone, with some carbonaceous mudstone. Coal seams and dark mudstone were identified based on the core and logging response of different lithologies. The thickness of single-well coal seams ranged from 2.76 to 31.01 m, with an average of 18.8 m (N = 97), and 84.5% coal seam thickness was 10–25 m (Fig. 11a). The w(TOC) value ranged from 27.09 to 78.18%, averaging 53.8% (N = 29), and w(TOC) values of 50–70% accounted for 51.7% of the total (Fig. 11b). The range of S1 + S2 was 2.35–290.8 mg/g, with an average of 87.78 mg/g (N = 25). The thickness of the mudstone was 16.83–119.94 m, with an average of 58.8 m (N = 97), and 70.1% of mudstone was 40–70 m thick (Fig. 11c). The w(TOC) value ranged from 0.086 to 16.91%, with an average of 4.43% (N = 40), and the distribution was relatively balanced (Fig. 11d). The mudstone S1 + S2 ranged from 0.11 to 18.78 mg/g, with an average of 3.42 mg/g (N = 38).

Fig. 11
figure 11

Distribution histogram of different parameters of the coal-measure source rocks in the LGF. (a) Coal seam thickness. (b) Coal seam total organic carbon. (c) Dark mudstone thickness. (d) Dark mudstone total organic carbon

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According to the cross-plot of hydrogen index (HI) and pyrolysis peak temperature (Tmax) (Fig. 12a), the type of organic matter in the source rocks were mainly type III kerogen, followed by type II2 kerogen, type II1; and type I kerogen, which occurred sporadically. According to the statistics of thermal evolution degree, Ro ranged from 0.83 to 4.89%, with an average of 1.26% (N = 70), and values of 1.0–1.3% accounted for 58.8% of the total. This indicates that the source rocks are mature and that some also have abnormally high Ro values (Fig. 12), such as the 3.19 and 4.89% for wells B1 and B2, respectively (Fig. 3). The Tmax of the source rocks ranged from 423.8 to 551 ℃, with an average of 474.6 ℃ (N = 57). It should be noted that the Tmax of some wells exceeded 500 ℃ (Fig. 12b). For example, the Tmax of wells B1, B2, and B3 were 532.8, 540.5, and 538.3 ℃, respectively (Fig. 3). These anomalous high Tmax and Ro values may be related to the tectonic activities of the Zijinshan Structural Belt. In the Late Jurassic–Early Cretaceous (140 ~ 100 Ma), multiple stages of magmatic intrusion occurred in the Zijinshan Structural Belt (Fu et al. 2016; Zou et al. 2016; Ge et al. 2018; Du et al. 2021), with a magma cooling rate as high as 52 ℃/Ma (Ge et al. 2018). This rapid heat dissipation warmed the surrounding rock via heat conduction, resulting in the higher formation temperature adjacent to the Zijinshan rocks and the abnormal thermal evolution of the local source rock.

Fig. 12
figure 12

Cross-plots of HI vs. Tmax and Ro vs. Tmax of Upper Paleozoic source rocks from the Linxing block, Ordos Basin. Note: HI is hydrogen index, Tmax is pyrolysis peak temperature, and Ro is vitrinite reflectance

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Controlling effect of source rock conditions

From the relationship between coal seam thickness and AOF (Fig. 13), with an increase in coal seam thickness, AOF did not show an obvious positive or negative correlation trend. The AOF of the Upper Shihezi, Lower Shihezi, Taiyuan, and Shanxi formations did not change significantly, and only the Shiqianfeng Formation had a slightly decreasing trend. Note that the interpretation of the Benxi Formation data points was limited. Based on Eq. (1), the range of HGI for the coal-measure source rocks was (10.2–44.8) × 108 m3/km2, with an average of 21.4 × 108 m3/km2. In terms of the relationship between HGI and AOF, AOF presented with an insignificant change trend HGI increased. In a single formation, with an increase in HGI, the Taiyuan Formation had a certain downward trend, but the changes were not obvious in the other formations except for Benxi Formation. However, when the thickness of the coal seam was greater than 10 m, or when HGI was greater than 10 × 108 m3/km2, the vast majority of AOF exceeded 0.3 × 104 m3/d, i.e., the condition of commercial gas flow can be met. Moreover, when the thickness of the coal seam was greater than 15 m, or when the HGI was greater than 14 × 108 m3/km2, the AOF could reach 10 × 104 m3/d. These results indicate that neither the thickness of the coal seam nor the HGI had obvious controlling effects on the degree of gas enrichment; however, the conditions of the coal-measure source rocks still provide sufficient natural gas for the formation of a multi-layer TSG reservoir.

Fig. 13
figure 13

Cross-plot of different parameters of coal-measure source rocks and absolute open flow (AOF) in the LGF. (a) Coal seam thickness vs. AOF. (b) Hydrocarbon generation intensity vs. AOF

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Controlling effects of current tectonic and fault distribution

Current tectonic conditions

The current structure does not control AOF; instead, it controls He8 and Tai2 members to a certain extent. As can be seen from the relationship between the current structural height and AOF (Fig. 14), as the structural height decreases, AOF generally first increases, and then decreased. The AOF of the Qian4 and Qian5 members showed a slightly increasing trend, and the AOF of the He4, He6, and He7 members showed a slightly increasing trend, while the AOF of the He2 Member showed no obvious trend. The AOF of the He8 and Tai2 members decreased as the tectonic altitude decreased. These results indicate that the AOF of He8 and Tai2 members may be influenced by local high points of tectonic altitude.

Fig. 14
figure 14

Cross-plot of current tectonic altitude and AOF in the LGF

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Fault conditions

The fault system in the LGF was controlled by regional stress in the eastern area of the Ordos Basin. Moreover, the uplift of the Zijinshan rock mass (Wang et al. 2010; Ge et al. 2018) can be divided into two types. The first type is reverse faults controlled by regional stress, which is mostly present in the NNE‒SSW and N‒S directions, with high angle faults of small vertical distance, extending from the Benxi Formation to the Shiqianfeng Formation, and even into the Mesozoic sequences (Li et al. 2019b). The second type stems from the small-scale radial and arc faults developed around the Zijinshan Structural Belt, which is controlled by the upper arch of the Zijinshan rock mass. The network fault system formed by these two fault types and their associated fractures decreased in density outward from the north and west of the Zijinshan structural belt (Fig. 3), providing vertical migration channels for the formation of multi-layer TSG reservoirs.

The moderately developed fault system is conducive to the formation of an effective transport system for natural gas accumulation, while the over-developed fault system facilitates the formation of natural gas escape channels. The moderate fault system in the LGF was formed by regional stress, which is more conducive to the formation of gas reservoirs. For example, according to the reservoir profile of the Upper Shihezi and Lower Shihezi formations from wells H1–H7 (Fig. 8), the fault system connected multiple layers of tight sandstone with coal-measure source rocks and served as an efficient channel for layers with an AOF higher than 5 × 104 m3/d. These include the He6 and He7 members of Well H3, the He2 and He4 members of Well G3, and the He3 Member of Well H2. In contrast, the over-developed fault system around the Zijinshan Structural Belt cuts sandstone and mudstone, undermining the effectiveness of the sandstone traps, and extending upward to the overlying Mesozoic sequences, or even to the surface (Ge et al. 2018). This type of fault system is not conducive to the formation of TSG reservoirs in the Upper Paleozoic but may form shallow gas reservoirs or dissipate gas to the surface. At present, no gas reservoirs have been discovered near the Zijinshan Structural Belt (Fig. 3). The distance from the fault to the well ranged from 0 to 6 km, with most 0.5 to 3 km away. According to the relationship between the fault–well distance and the AOF (Fig. 15), as the fault–well distance increases, the AOF of the upper and lower Shihezi formations (outside source rocks) showed an obvious decreasing trend, while the AOF of Shiqianfeng Formation had a decreasing trend to a certain extent, and the changing trend of the Taiyuan Formation was not obvious. These results showed that the distribution of faults had a certain control effect on the formation of gas reservoirs outside the source, i.e., the closer the distance between the faults and wells, the more favorable formation of high-yield gas reservoirs.

Fig. 15
figure 15

Cross-plot of the distance from fault to well and AOF in the LGF

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Natural gas enrichment model

The multi-layer tight sandstone produced gas in the LGF with a quasi-continuous distribution, which is characterized by high-quality reservoir enrichment, sufficient gas supply, moderate fault system efficiency, and a favorable local high point. The results show that the yields, from the Taiyuan Formation inside the source to the Shiqianfeng Formation outside the source, are affected by reservoir porosity, permeability, and argillaceous content, with the effect of permeability being the most obvious. In addition, the coal-measure source rocks with high TOC and medium Ro provide sufficient gas source conditions, and their HGI exceeded the formation boundary of the large gas fields (Zhao et al. 2012; Dai et al. 2014). These gas sources can be charged to multiple formations, with AOF reaching commercial gas flows. Considering the two different fault systems, the intermediate fault system provided efficient transport for vertical migration, especially to off-source gas reservoirs. The fault system developed around the Zijinshan Structural Belt was more favorable for gas migration or escape to shallow strata, and not favorable for the formation of the TSG reservoir in the upper Paleozoic. The local structural high point is the favorable position for natural gas accumulation, which is manifested in Tai2 and He8 members. Based on these results, the LGF exhibited three gas enrichment models within three areas of the gas field: X, Y, and Z, respectively (as shown previously in Fig. 3). The enrichment models are described as follows.

  1. (1)

    X area: Excellent reservoir, highly efficient fault system, near-source gas-rich model.

    This model represents the X area (Fig. 3) and virtual well M1 (Fig. 16) with characteristics of sufficient source rock conditions, excellent reservoir physical properties, a moderately developed fault system, and gas-rich accumulation that is near the source (He7 Member and above). The gas-producing layers are mainly concentrated in the He2, He3, He4, He6, and He7 members, with an average AOF of over 6 × 104 m3/d. The model has the following favorable reservoir forming conditions: (i) The source rock conditions are sufficient. The w(TOC) of the coal seam ranges from 44.5 to 71.35%, with an average of 59.52%, and Ro ranges from 1.05 to 1.26%, with an average of 1.13%. The HGI is (13.6–24) × 108 m3/km2, with an average of 16.9 × 108 m3/km2. (ii) The reservoir conditions are excellent. The porosity ranges from 2.1 to 19.2% (N = 538), with an average of 9.34%. The permeability ranges from (0.01 to 50.2) × 10−3μm2, with an average of 1.88 × 10−3 μm2 and a median of 0.52 × 10−3 μm2. The argillaceous content is low, around 15.3% (N = 46). (iii) The density of faults developed under regional stress is moderate, connecting the coal-measure source rocks to tight sandstone traps and migrating the gas to the trap (outside source rocks, but only by a small distance), forming several TSG reservoirs along the fault system.

  2. (2)

    Y area: Excellent reservoir, favorable high point, in- and adjacent-source gas-rich model.

    This model represents the Y area (Fig. 3) and virtual well M2 (Fig. 16) with characteristics of sufficient source rock conditions, excellent reservoir physical properties, a favorable local high point, gas-rich accumulation of in-source (Tai2 Member), and adjacent-source (He 8 Member) formations. The main gas reservoirs are concentrated in the Tai2 and He8 members, and the maximum AOF can reach 13.3 × 104 m3/d. The favorable conditions are as follows: (i) The source rock conditions are sufficient. The w(TOC) of the coal seams ranges from 44.5 to 71.35%, with an average of 59.52%, and Ro between 0.94 and 1.38%, with an average of 1.18%. The HGI ranges from (15.6 to 33.9) × 108 m3/km2, with an average of 20.2 × 108 m3/km2. (ii) The reservoir conditions are extremely good. The porosity is between 0.6 and 14.1% (N = 429), with an average of 9.03%. The permeability ranges from (0.011 to 12.66) × 10−3 μm2, with an average of 1.06 × 10−3 μm2 and a median of 0.62 × 10−3 μm2. The argillaceous content of sandstone is ~ 19% (N = 32). (iii) The tectonic high point of the thick sand body is the favorable position for gas migration, and the gas enrichment degree is relatively high.

  3. (3)

    Z area: Middle reservoir, over-developed fault system, in- and out-source gas-poor model.

    This model has the characteristics of excellent source rock conditions, moderately good reservoir physical properties, an over-developed fault system, gas-poor distribution of in- and out-source in the Upper Paleozoic sequences, is represented by the Z area (Fig. 3) along the Zijinshan Structural Belt and marked by the virtual well M3 (Fig. 16). To date, no natural gas reservoirs have been identified in the Upper Paleozoic sequence of this area. The model has the following conditions: (i) The source rock conditions are sufficient. The Ro of the source rock is 1.32%, which is better than in some other areas. (ii) The reservoir conditions are moderately good. The porosity ranges from 1.4 to 16.1% (N = 245), with an average of 6.71%, and the permeability is between (0.14 and 8.41) × 10−3 μm2, with an average of 0.42 × 10−3 μm2 and a median of 0.22 × 10−3 μm2. (iii) Because of the uplift of the Zijinshan rock mass, the overlapping and interlacing fault system with high angle and excessive development cut through the sandstone reservoir and mudstone cap, leading to the upward migration of natural gas to the shallow layer and ultimately surface leakage.

Fig. 16
figure 16

Enrichment models of multi-layer tight sandstone gas in the LGF, eastern Ordos Basin, Northern China

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Conclusion

Although the main controlling factors and enrichment model of TSG have long been a focus of research, limited attention has been paid to the multi-layer TSG reservoirs, which comprise a considerable component of unconventional natural gas exploration targets. In this study, the distribution and characteristics of the multi-layer TSG reservoirs in the LGF of the Ordos Basin in China were defined. In addition, the main controlling factors of natural gas accumulation in the reservoir were discussed, and the natural gas enrichment modes of different areas of the gas field were established. To achieve this, seismic, drilling, logging, gas testing, laboratory, and other accumulated data were comprehensively analyzed using interpretive geo-analytical techniques. Three main findings can be summarized as follows:

  1. (1)

    There are 14 sets of gas-producing layers in the Upper Paleozoic strata of the LGF, of which, the Tai2, He8, He7, He6, He4, and He2 members are the chief layers. The porosity of the gas reservoir ranged from 7 to 13%, with an average of 10.11%, and the permeability ranged from (0.5 to 7) × 10−3 μm2, with a median of 0.81 × 10−3 μm2. The tight sandstone gas reservoir comprises two sub-types: a lenticular lithological reservoir and a lithological-fault reservoir, showing quasi-continuous distribution with characteristics of being vertically superimposed and laterally continuous.

  2. (2)

    The accumulation of multi-layer TSG is controlled by reservoir properties, gas source, fault system, and structural high points, and has the laws of “high-quality reservoir enrichment, sufficient gas source supply, moderate fault efficiency, and a favorable local high point.”

  3. (3)

    Gas enrichment models were categorized into three types and corresponding areas: (i) An X-area: Excellent reservoir, highly efficient fault system, near-source gas-rich model; (ii) Y area: Excellent reservoir, favorable high point, in- and adjacent-source gas-rich model; and (iii) the Z area: Moderately good reservoir, over-developed fault system, in- and out-source gas-poor model, distributed around the Zijinshan Structural Belt.

The findings of this study provide novel insight into the accumulation theory of TSG, as well as provide theoretical guidance for the discovery of multi-layer gas fields in the LGF and similar basins worldwide.