Lacustrine nearshore sand bars are formed by sand bodies that have converged into lakes (such as rivers, deltas and fan deltas) after being stirred up, transported, and deposited again by waves, lake currents, and other hydrodynamic forces^[1,2,3]. Their sedimentary characteristics, scale, and spatial distribution mainly depend on geomorphological conditions, wave energy, sedimentary source recharge, and other factors^[4,5,6,7,8]. Traditionally, it has been assumed that lacustrine sand bar deposits form high-quality reservoirs with high sand content and good physical properties in the beach bar depositional system. This was assumed to be largely due to sand purity, good separation behaviors of sand bodies, and undeveloped internal interlayers^[9]. However, with the in-depth development of oilfields, complicated injection-production relationships showed that the connectivity between sand bodies in sand bars is not as simple as that of homogeneous reservoirs. Moreover, mud components that influence fluid percolation also develop in them^[10,11]. In fact, during the depositional process, lacustrine sand bars frequently migrate and oscillate under the influence of lake level fluctuations, and a complicated superposition relationship exists between sand bodies^[12,13]. However, existing studies on nearshore sand bars still lack adequate understanding of their spatial distribution. To clarify the internal structure of sand bar reservoirs, studies on reservoir configuration play an increasingly important role for the refined description of nearshore sand bar reservoirs.

Due to changes in water body energy, lake level fluctuations, wave action, and other factors, nearshore sand bar deposits are ordered, and different orders of sand bodies obey some constraint relationships in sedimentary distribution. For sand bar reservoirs, configurational units that require special attention are sand bodies in compound sand bars, individual sand bars, and accretionary bodies in bars (corresponding to grade 5-3 configurational elements in Miall’s configurational system)^[14]. Sand bodies in compound sand bars are configurational elements limited by medium-term base-level cycles, that consist of one or several individual bars. Controlled by ultra-short-term cycles, sand bodies in individual bars can be further divided into one or more accretionary bodies (rhythmic layerings). Between configurational elements, there are three orders of configurational interfaces (interlayers between sand bodies), and different orders of interlayers differ from each other in genesis, distribution, and sedimentary characteristics^[10].

Currently, despite the basic clarification of the overall distribution of sand bodies in compound sand bars, a clear understanding of the internal structure of sand bar reservoirs still has not been achieved. This results in ambiguity about the distribution of cross-well sand bodies and interlayers, reduces the characterization precision of the influence of sand bodies in compound sand bars on individual sand bars and their accretionary bodies, and affects the development effect of oilfields.

Analysis of reservoir configuration focuses on two aspects: the spatial superposition of configurational units and the distribution characteristics of configurational interfaces (interlayers). For lacustrine nearshore sand bar reservoirs, the former aspect corresponds to the combinatorial patterns and space-matching relationship between sand and mud in sand bars, while the latter aspect corresponds to the genesis and distribution rules of argillaceous sediments in sand bars. A commonality between the two aspects is that studies in both fields depend on guidance by geological models. In this study, two lacustrine basins with similar tectonic and sedimentary characteristics were taken as study objects. Based on new understandings of the depositional matching relationship between sand and mud in modern sand bars of the Xiashan Lake, the internal structure of the sand bar reservoir in the Banqiao Sag is performed. The obtained results enrich theories about the deposition of lacustrine nearshore sand bar reservoirs and guide the efficient development and remaining oil recovery of similar reservoirs.

The ancient lacustrine sand bar reservoir investigated in this work is located in the Banqiao Sag in the Bohai Bay Basin, China. The Banqiao Sag is a secondary sag of the Huanghua Depression, with the characteristics of faulted lacustrine basin^[15]. It is steep in the north wing and gentle in the south wing (Fig. 1a). The depositional stage of the Member 2 of the Paleogene Shahejie Formation is a faulting intermission of several sags in the Bohai Bay Basin with stabilizing tectonic activities and wide, shallow lake water distribution^[16,17]. According to coring, logging, seismic data, as well as existing research findings, the braided river delta in the Beidagang buried hill belt supplied abundant sedimentary-source sand bodies for the lacustrine basin. After transported by wave action, the sand redeposited, forming large-area nearshore sand bars and sheet-like flat beach sediments on the gentle slope belt side south of the Banqiao sag^[18,19]. They constitute a depositional system with the widest distribution in the depositional stage of the Member 2 of the Paleogene Shahejie Formation.

The observation of cores collected from 38 wells in the Banqiao Sag shows that the sediments of the Member 2 of the Paleogene Shahejie Formation have no obvious scouring-filling sedimentary structures, and feature interbedding of dark grey mudstone and grey sandstone with different thicknesses. Depending on lithology distribution, and other characteristics, the sand bodies in beach bars can be divided into two subfacies, i.e., beach sand and bar sand (Fig. 2a). To be specific, the subfacies of beach sand mainly consist of thin sand layers, which are further divided into nearshore beach, offshore beach, and inter-bar microfacies based on their locations relative to the bar sand^[9]. The subfacies of bar sand (i.e., lacustrine nearshore sand bar) is the most important component unit in the beach bar depositional system, with many internal interlayers and high sand content of single-stage sand bar deposit. Based on sedimentary locations, they can be further subdivided into bar center and bar wing microfacies^[9,11]. The lacustrine sand bar reservoir is mainly composed of siltstone, fine sandstone, medium sandstone, and pebbly sandstone, with a quartz content of about 60% in sandstone and high component maturity in general^[9]. In terms of grain size distribution, the sand bodies are dominated by saltation component, and have a suspension component content below 1%, which reflects the characteristics of bar sand depositions far from the estuary without effect of source sand bodies^[9]. In addition, the Member 2 of the Paleogene Shahejie Formation in the Banqiao Sag developed with multiple wave-induced sedimentary structures. Swash cross bedding, low-angle cross bedding, and wave ripple cross bedding all testify to the presence of polymodal currents. Bedded plant charcoal debris, wave ripples, and other bedding-plane structures indicate that this region was subject to wave erosion and alteration in a shallow-water environment^[9].

At present, the lacustrine nearshore sand bar reservoirs of this oilfield have proved reserves of tens of millions of tons. In the past decade, more than 150 wells have been drilled in the reservoirs of the Member 2 of the Paleogene Shahejie Formation in this oilfield, and achieved good development effect. Larger in thickness and good in reservoir quality, and distributed in parallel to lacustrine basin edge in bands, the sandbody in sand bar constitute the main part in the analysis of the beach bar reservoir configuration and the description of interlayers. From developed wells, oil layers perforated in high production wells are largely bar sand sediments. Therefore, the correct understanding of the spatial distribution of sand bodies and interlayers in sand bars is an important task for the further exploration and development of sand bar reservoirs in this oilfield.

The lacustrine sand bar investigated in this study, Holocene recent sediments of the Quaternary period, is located in the Xiashan Lake in Weifang, Shandong Province, China (Fig. 1b). The trumpet-shaped lake has an area of about 140 km², and is surrounded by the Weihe River, the Honggou River, and other sedimentary source recharge systems. The Xiashan Lake also manifests the characteristics of faulted lacustrine basins in terrain (steep in the west and gentle in the east), and has multiple types of lacustrine depositional systems and related sedimentary structures^[20]. Affected by the north wind and the southwest monsoon, the lake surface is frequently subject to actions of waves and alongshore currents. A large-scale aggregated sand bar zone has also emerged on the gentle slope belt side of the lake^[10]. Due to the arid climate and sharp drop of the lake level in recent years, several nearshore sand bars have been exposed above the lake surface. In the vicinity of Houdian Village and Zhenggong Village on the southeast-shore gentle slope belt with sand bars developed, away from the disturbance of steep slope belt and estuarine deposits, the sand bar deposition is completely controlled by wave action (Fig. 1b). Moreover, the alternate sand and mud layers are clear and distinct, which offers ideal materials to mark the internal structures of sand bars.

The nearshore sand bars of the Xiashan Lake are mostly arranged in rows along both shores. The sand bar closest to the shore is roughly 4 m above lake level and 22-45 m wide. On the transverse profile, it is lentoid (flat at the bottom and elevated at the top), and gentle on the back slope and steep on the front slope (Fig. 2b). On the plane, the sand bar is elliptic or crescent-shaped (i.e., sharp on both ends), and its long axis approximately points to NNE (Fig. 3a). The main sediments of the modern sand bar of the Xiashan Lake are yellow medium sand and fine sand, which are locally mixed with coarse sand and gravel sediments (average gravel diameter 0.3 m). The modern sand bar is mainly composed of quartz and feldspar, and has tabular cross bedding, wave ripple cross bedding, wavy bedding, and other multiple sedimentary structures (Fig. 3b). Its front-end sediments are moist, and have accumulated shells; the main part of the sand bar is dominated by pure yellow sandy sediments, with good sorting and worm burrows (Fig. 3c). The sand bar surface has undulating bedding-plane structure formed by sand wave migration, and ripples are especially obvious on the back side of the sand bar (Fig. 3d). Beach sand sediments developed between sand bars and at the peripheries, lower than the sand bars in terrain. Beach sand is dominated by fine sand and silt, and did not develop tabular cross bedding or other sedimentary structure with strong hydrodynamic forces. Multiple unidirectional ripples with small areas but large depths exist. Due to the reduced wave flow rate, suspended clay substances deposit easily, form mud, and engage in alternate deposition with the sand bodies in beach.

Affected by the lake area, sedimentary source recharge, climate, and deposition time, and other factors, the scale of sand bar reservoirs far exceeds that of recent sand bar deposits. According to statistics, the average scale of the individual sand bars in the Member 2 of the Paleogene Shahejie Formation of Banqiao Sag (2200 m in length, 553 m in width, and 20 m in maximum thickness) is about 13-14 times of that of the modern sand bar deposits in the Xiashan Lake. However, with regard to sand bar morphology (i.e., the length-width ratio (about 4.2) and width-thickness ratio (about 26)), modern sand bar and ancient sand bar reservoirs are highly consistent. Given that the deposition of sand bars is uniformly dominated by wave action and that their depositional processes are similar, sand bars are comparable with each other in terms of filling characteristics, sand-mud spatial distribution, and other internal structures^[10]. To make clear the sedimentary characteristics of sand bodies and fine-grained mud in these sand bars, a total of 45 shallow boreholes were drilled in the southeast-shore modern sand bars of the Xiashan Lake, with an average borehole depth of 1.3 m and a total sampling depth of about 60 m. The deepest borehole has a drilling depth of about 2.8 m, and can be used to directly observe lithologic changes of sand bar deposits, phase sequence characteristics, and vertical accumulation relationships in configurational units (Fig. 4). The shallow boreholes are combined with two trial pits (at inner and outer edges of a sand bar, respectively) and one trial trench to allow better observation of the filling changes and sedimentary structures of sediments and the lateral distribution of sand and mud sediments, and define the sediment boundaries.

Argillaceous sediments are closely related to sand bars over the course of their development, and individual sand bars can directly cover original sand bar, beach, or lacustrine argillaceous sediments^[21]. The emergence of sand bars in rows on the plane reflects the migration and superposition of individual sand bars. In the vertical direction, the alternate deposition of different configurational orders of sand bodies and mud also happens.

This paper uses the following general idea: By analyzing the combinatorial patterns of sand and mud and their compositional sequences in the longitudinal direction at different sites of modern lacustrine sand bars, the spatial distribution laws of sand and mud in sand bars and their influencing factors can be summarized. The aim is to establish a geological model that can uncover the inner structures of sand bars and provide a reliable basis for the guidance of a refined analysis on similar sand bar reservoirs.

In the depositional process of a sand bar, mud layers and sand layers frequently alternate. During the deposition of an individual sand bar, filling of sand and mud may happen due to lake level fluctuations. During the transition from one sand bar to another sedimentary unit (e.g., another stage of individual sand bar, beach sand, or lacustrine mud), sand layers and mud layers may also stack over each other. Since sand bodies and mudstone thickness vary in different facies, a refined comparison of each sand layer or mud layer could lead to large errors. In contrast, finding out the combination characteristics of sand layers and mud layers in the longitudinal direction can make the spatial comparison easier. Based on the sand bar depositional sequences on cores taken from the nearshore shallow boreholes of the Xiashan Lake and the actual drilling data of the sand bar reservoir in the Banqiao Sag, according to buildup conditions of different sedimentary facies and the thickness of sand and mud layers in the longitudinal direction (Fig. 4), three combination patterns of sand and mud layers (i.e., thin sand and thin mud interbed pattern, thick-mud thick-sand pattern, and thin-mud thick-sand pattern) were identified (Table 1).

The thin sand and thin mud interbed pattern appears as the alternate deposition of thin sand and thin mud layers which are similar in thickness (about 1-5 cm each) in the longitudinal direction. According to the observation of multiple shallow boreholes drilled in the modern sand bar of the Xiashan Lake, the number of interbeds varies at different sand bar locations: Between two individual sand bars, more sand and mud interbeds can be found (about 3-6). This is mainly due to frequent changes in hydrodynamic forces in the sand bar superposition zone during sand bar migration^[7,10]. At the top of a recently deposited sand bar, the number of interbeds is much less (about 1-3), as shown in Table 1. The sand here is dominated by fine sand and medium-fine sand, which are intermingled with silty mud. Such thin sand and thin mud interbed pattern often occurs at the top of an individual sand bar, reflecting short-term fluctuations in lake levels.

For the lacustrine sand bar reservoir in the Member 2 of the Paleogene Shahejie Formation in the Banqiao Oilfield, drilling data shows that this combination pattern is frequently seen at the top of a set of thick sand body. The sandstone layer is dominated by fine sandstone of beach sand subfacies. The sandstone layers are basically equal in thickness with the mudstone layers (about 1-2 m). There are about three interbeds, the overall thickness of which (about 5-8 m) changes greatly due to the influence of sediments. They take on finger shape on logging curve.

The thick-mud thick-sand pattern is also characterized by clear alternate deposition of mud and sand, except that both mud and sand layers are thick and less in number (1-2) in this case, and usually the mud is at the bottom and sand at the top. The argillaceous sediments in this pattern are noticeably darker than those in thin sand and thin mud interbed pattern, and have a thickness of about 10-20 cm; whereas the sandy sediments in this pattern range from 5 cm to dozens of centimeters in thickness (Tab 1). Comparison of multiple shallow boreholes shows single-layer mud or sand sediments at the same longitudinal level (supposedly formed in the same period) have a stable thickness in the direction parallel to the shoreline; however, in the direction perpendicular to the shoreline, they vary widely in thickness and gradually thin and pinch out toward the shore. The sand layers consist of silt and fine sand sediments, the mud layers are pure in component, and dominated by silty mud and clay sediments, with shells.

In the sand bar reservoir of the Paleogene Shahejie Formation in the Banqiao Sag, this pattern of sediments is about 4.2-15.0 m thick, and usually occurs at the top or bottom of individual sand bars. Sometimes, thin beach sand sediments can also be observed. The sandstone layers are dominated by fine sandstone and medium sandstone, with visible cross bedding and other sedimentary structures that can reflect sand bars. Oilfield drilling data shows that the sandstone segments appear as either toothed box or funnel shapes on log curves, suggesting that the initial water body energy of new-stage sand bar deposits fluctuates to some extent.

The thin-mud thick-sand pattern is characterized by alternate thick sand layer and thin mud layer, and has 1-4 interbeds. The number of interbeds and the total thickness vary at different positions on the plane. The mud layers are stable in thickness (0.5-5.0 cm) and dominated by brownish grey argillaceous silt and silty mud. The sand layers are 10-25 cm thick and dominated by fine sand and medium sand, and have swash cross bedding and wave ripple cross bedding with obvious opposite tendencies, which suggest strong hydrodynamic force environment during the sedimentary period of the sand bar. In sediments of the same stage, the sand layers show a thickening and coarsening trend upward, and certain reverse graded bedding characteristic (Fig. 4). This pattern often turns up at the top of thick-sand thick-mud pattern sediments, and transits to thin sand and thin mud interbed pattern. Sometimes, it has no clear boundary with the above two filling patterns, and together they form compound combination.

In the sand bar reservoirs of the Banqiao Oilfield, this combination pattern occurs within individual sand bars, and its sand lithology is dominated by medium-coarse sandstone, with clear wave-induced sedimentary structures. It has more interbeds in the bar center (about 3-5); the sand layers are about 4-8 m thick each and the mud layers are about 1-2 m thick each. In bar wings, this combination pattern decreases in scale and the sand thickness decreases (about 2-4 m). This pattern of sediment takes on thick box shape, and has the characteristic of return in the thin mudstone layer on log curves.

Argillaceous sediments in nearshore sand bars are mostly caused by differences of sediment lithology due to changing hydrodynamic forces during the deposition of sand bars, which appear as deposits of multiple fine-grained lithofacies^[10,22]. These fine-grained sedimentary components form interlayers in sand bar reservoirs, which severely influence the heterogeneity of reservoirs and the percolation of underground fluids (Table 2). Taking modern sand bar deposits of the Xiashan Lake as example, this study examined the types, sedimentary characteristics, spatial distribution, and scale of argillaceous sediments, sorted out the combination patterns of sand and mud layers, to find out the spatial configuration of mud and sand in sand bars. These results can be consulted in configurational analysis of the sand bar reservoirs in the Banqiao Oilfield (or similar sand bar reservoirs) to get a better understanding on the genesis and distribution of argillaceous interlayers in sand bar reservoirs, and provide a reliable basis for tapping the remaining oil in the middle-late stage of reservoir development.

4.1.1. Argillaceous sediments caused by lake level fluctuations

(1) Semi-deep to deep lacustrine mud sediments: a series of lacustrine nearshore sand bars formed during a relatively stable period, at the bottom of which, a set of stable argillaceous fine- grained sediments can be found. These fine-grained sediments are typically below lake level in modern deposits (site A shown in Fig. 2b), where the sediments are soft mud with water, so it is difficult to collect samples from shallow boreholes. But (semi-)deep lacustrine argillaceous sediments can be clearly observed in the coring data of ancient sand bar reservoirs and other data. The sediment lithology is dominated by black and dark grey mudstone as well as black brown shale, and contains grey argillaceous limestone. In summary, it is characterized by dark color, small grain size, and high organic content. Semi-deep to deep lacustrine mudstone has simple sedimentary structures, and massive bedding or horizontal bedding. Seasonal cyclic bedding and algae fossils can also be observed.

(2) Sand and mud interbedded beach sediments: thick sand layers in sand bodies in compound sand bars are composed of many individual sand bars stacking over each other. The development termination of one stage of individual sand bars is in most cases caused by changes in the hydrodynamic force environment as a result of changing lake level^[10]. In comparison, the hydrodynamic force conditions between two stages of individual sand bars frequently change, often leading to the development of sand and mud interbedded beach sediments. These fine-grained lithofacies mostly turn up in the sedimentary sequence of thin sand and thin mud interbed pattern, and can be identified in the cores of both modern sand bar deposits and ancient sand bar reservoirs. The thickness of these fine-grained lithofacies varies in different individual sand bar deposits. In modern sand bar deposits, the overlying beach sand comes in multiple sand and mud interbeds, with a total thickness of about 0.2-0.4 m. On the plane, it is distributed about 10-20 m perpendicular to the shoreline. Toward the shore, the number of interbeds decreases and scattered shells can be seen (Fig. 5a).

4.1.2. Argillaceous sediments formed by lake water retention

The deposition of a sand bar blocks waves to some extent. As a sand bar reaches or is above the lake level, a still water area would come up shielded by the sand bar, where the suspended matters in the water would gradually settle down, forming fine-grained sediments with a high mud content^[23]. The mud behind the bar is thicker in the vicinity of the sand bar (about 10-20 cm), and thins or even wedges out with the increase of distance from the sand bar, with an extension width of a dozen or dozens of meters. Different from (semi-) deep lacustrine mud, the mud behind the bar deposits in a sedimentary environment characterized by still water and poor circulation, so the mud behind bar has typically large amounts of shells, small amounts of terrigenous debris and Chara, and laminations and horizontal beddings. Furthermore, during dry seasons, the mud sediments behind the bar are exposed on the surface on a long-term basis, resulting in visible mud cracks (Fig. 5b).

4.1.3. Fall-silt seams from flood discharge

In modern sand bars of the Xiashan Lake, thin fall-silt seams dominated by argillaceous and silty fine-grained sediments occur frequently (Fig. 6a). Argillaceous fall-silt seams are usually developed in sand bodies. In the longitudinal direction, they combine with sand and form a thin-mud thick-sand pattern, with thicknesses from 0.5 cm to a dozen of centimeters under normal circumstances (Fig. 6b). The development of individual sand bars is a process of vertical or lateral aggradation of multiple accretionary bodies, and argillaceous sediments often deposit between accretionary bodies^[7,10]. In the bar center, sand bodies are thicker, and accretionary bodies are the most in number^[24], so more fall-silt seams also come up between accretionary bodies, with a density of 2-4 layers/m. In the bar wings, accretionary bodies are less in number, so are fall-silt seams, with a density of about 1-2 layers/m. On the side of the sand bar facing waves, intense wave erosion results in small thickness and poor continuity of fall-silt seams. From the top of the sand bar to the other back from the waves, argillaceous suspended matters blocked by sand bodies during wave backflow are likely to deposit, so fall-silt seams are most developed^[10], and about 3-4 cm thick and stable in plane distribution (with traceable distance reaching up to 15 m). In brief, from the outer edge of the sand bar to its inner edge, argillaceous fall-silt seams increase in number and thickness as a result of better preservation.

In the lacustrine nearshore depositional system, (semi-) deep lacustrine mud is located in the vast expanses of water far away from the sand bar. This mud extends toward the lake, and is often distributed below the lake surface under normal circumstances. In high water season, due to rapid rise of lake level, the original nearshore sand bar group would be quickly submerged under water. With the deepening of lake water, the water body energy gradually declines, and is less influenced by waves. Floating and suspended fine-grained substances in the lake gradually accumulate, and form argillaceous sediments that are characterized by stable distribution and a specific thickness. Semi-deep to deep lacustrine mud typically fully covers the top of sand bodies in compound sand bars, and serves as the lakebed for the next stage of sand bar deposition. When the lake level drops and the area turns into wave action zone, a new stage of nearshore sand bar would deposit at the top of this (semi-) deep lacustrine mud. Thus, semi-deep to deep lacustrine mudstone can be seen as an interface between two adjacent stages of compound sand bar deposits (grade 7 configurational interface, also a stable interlayer), and also represents a large-scale advance and retreat of one stage of lake water.

Lake level fluctuations induce frequent changes in wave energy belts at the same location, and cause most individual sand bar deposits to manifest the spatial distribution of mutual superposition^[9,25]. The sand and mud interbedded beach is most commonly occur at the top of individual sand bars, and alternately deposit with individual sand bars in the longitudinal direction. On the plane, they are often seen in the superposition zone between two stages of individual sand bar sand bodies (grade 8 configurational interface, typically forming physical interlayers). Therefore, identifying and dividing individual sand bars is the key to predicting the distribution of these fine-grained lithofacies. Argillaceous sediments formed by lake water retention occur in areas of flat terrain behind sand bars. In the case the water level quickly increases and spills over the existing sand bar and the mud behind the bar, a new stage of sand bar would deposit on it. Thus, the argillaceous sediments behind the bar also represent the interface between two adjacent stages of individual sand bars (grade 8 configurational interface, a stable lithology interlayer)^[26]. On the plane, the mud layers behind bar typically alternate with sand bars (Fig. 7).

The material base of fall-silt seam is the lake water carries some mud, silty mud, and other fine-grained suspended matters^[26,27]. During the formation of individual sand bars, when a flood season comes, terrigenous debris with large amounts of mud and sand would be fed into the lacustrine basin. Under specific hydrodynamic force conditions, lighter fine-grained suspended matters would be stirred up by the waves, and deposit on the surface of accretionary bodies in the sand bar developed during the same stage, thus forming fall-silt seams. Consequently, fall-silt seams represent the interface between accretionary bodies in an individual sand bar (grade 9 configurational interface, typically an instable argillaceous interlayer), their distribution characteristics are closely related to the accumulation patterns of accretionary bodies in the individual sand bar^[10]. Both the steepness of the surface micro-morphology of accretionary bodies and the degree of erosion by wave action influence the width and continuity of the fall-silt seams.

Due to changing hydrodynamic force conditions in various sedimentary facies belts of the sand bar, fall-silt seams vary in thickness and continuity in different areas. This in turn influences the connectivity between sand bodies in individual sand bars. For instance, in areas where fall-silt seams don’t develop, two adjacent stages of sedimentary accretionary bodies (sand) are typically in large-area contact, and have good connectivity between sand bodies. In areas where continuous fall-silt seams occur, two adjacent stages (upper/lower) of accretionary bodies (sand) are separated by fall-silt seams over a large area, resulting in poor connectivity between sand bodies. Fall-silt seams are characterized by fine lithology and lower porosity and permeability, and have some percolation blocking ability. They are the primary interlayer type within sand bars, and are an important factor leading to heterogeneity of sand bar deposits.

According to the analysis on shallow boreholes in modern lacustrine sand bar deposits, in the same individual sand bar deposit, the scale and morphology of the sand bar control both the thickness and distribution of the combination pattern of sand and mud. For instance, in the center of the bar, a thin- mud thick-sand pattern is well developed and has a large total thickness, while the thick-mud thick-sand pattern is rarely seen. In the area behind the bar, the opposite is the case.

Based on the different combination patterns of sand and mud layers at different sites of one individual sand bar, the genesis and distribution rules of argillaceous sediments in the sedimentary environment of the lacustrine nearshore sand bar were analyzed. On this basis, the combination and distribution model of argillaceous sediments (interlayers) in the sand bar reservoir was established (Fig. 8) to find out the spatial combination relationships of different types of argillaceous sediments (interlayers) of grade 7-9 configurational orders and provide a conceptual geological model to understand the geometric morphology of sand bars, the distribution rules of argillaceous sediments, and the space-matching relationship between sand and mud.

An ideal sand bar can be described as the combination of fine-grained argillaceous sediments and sandy debris of multiple genetic types^[26]. During the deposition of individual sand bars, argillaceous sediments (interlayers) of different genesis have specific developmental locations. In the longitudinal direction, they form specific sedimentary combination patterns with the sand layers. Fall-silt seams appear as fine-grained argillaceous sediments that are either inclined or approximately parallel to the lacustrine basin direction along the interface of accretionary bodies^[10]. They often combine with accretionary bodies into thin-mud thick-sand pattern, and are inside individual sand bars. The mudstone behind the bar is equivalent to a change of sedimentary facies, formed after the deposition of an individual sand bar, and is distributed on the shore side of the sand bar^[10,26]. It typically combines with upper sand into thick-mud thick-sand pattern. The beach of thin sand and thin mud interbed pattern often develops during the end stage of an individual sand bar deposition, and is mainly distributed in the longitudinal superposition zone between two adjacent stages of individual sand bars.

In this model, it is not necessary to conduct a statistical assessment of related parameters of individual sand bars (such as length-width ratio or width-thickness ratio). Instead, the thickness, extension scope, and connectivity of sand bodies in the sand bar reservoir can be inferred from the quantitative information of argillaceous sediments (interlayers) and the spatial comparison of both sand and mud. Notably, this argillaceous sediments combination model for sand bar is an ideal geological model established by analyzing the modern sand bar of the Xiashan Lake. It does not fully correspond to all lacustrine sand bar reservoirs, and to fit with the internal structure of a reservoir, it needs to be revised according to the deposition mechanism of the sand bar, the sedimentary source, hydrodynamic forces, base-level changes, and other main controlling factors.

Lacustrine sand bars are more likely to form lithologic or stratigraphic reservoirs^[28,29,30]; therefore, previous studies mostly focused on the identification of related sand bodies, and analysis of their distribution rules. In this work, by analyzing the modern lacustrine sand bar in detail, it is found that the development and distribution of argillaceous sediments are not random but obey specific regularities, and that such regularities recur with the deposition of multiple sand bars on a large time scale. Therefore, exploring the accumulation patterns and preservation of the argillaceous sediments in sand bars under geological historical conditions helps us to better understand the space configuration of sand and mud layers in sand bar reservoirs.

In the geological historical period when lacustrine nearshore sand bar reservoirs were formed (tens of thousands or even millions of years ago), multiple individual bars mutually superposed and combined on the spatial scale in response to fluctuations of lake level and wave energy belts. In a compound sand bar, each time an individual sand bar migrated, fine-grained mud components previously deposited were preserved at various degrees. Furthermore, the argillaceous sediments between sand bodies in sand bars also present related spatial accumulation rules. Consequently, various combination patterns of sand and mud vary in different sand bar sites in developmental frequency, vertical locations, and combination sequence. Based on the principle of high-resolution sequence stratigraphy and the relationship between the volumetric subdivision and accumulation patterns of sediments, the spatial configuration of mud sediments and sand bars were analyzed from three aspects, accommodation space change, frequency of base-level cycles (lake level fluctuations), and exposure-erosion time, and two typical stratigraphic structures were sorted out.

In sand bar reservoirs, the development and preservation of argillaceous sediments are typically related to large accommodation space, low lake level fluctuations, and short exposure-erosion time. For instance, in the case that the accommodation space is small, the deposition range of the sand bar would be narrow in the transverse direction, meanwhile, the distribution of argillaceous sediments is also confined by the scale of individual sand bars. Under a stable sand bar deposition rate, if there are slight but frequent changes of base-level in short-term (reflecting the lake level), lateral migration of the individual sand bars would be confined to a narrow scope^[4], or even be dominated by vertical aggradation (Fig. 9a). After the formation of each stage of individual sand bar, its top is still subject to wave rework, and fine-grained mud components are typically eroded and destroyed prior to full preservation. As a result, argillaceous sediments are thin and poor in continuity, and argillaceous sediments combination is incomplete. In contrast, in the case with large accommodation space and slow lake level change, the individual sand bar would be large in scale and extension width of lateral migration, fine-grained mud components would have sufficient deposition time and therefore be large in thickness, and argillaceous sediment combination would be well preserved (Fig. 9b). In addition, in the case of an excessively long exposure time, the argillaceous sediments would dry and shrink, forming mud cracks prone to erosion by waves during the late stage.

To some extent, in sand bar reservoirs, the distribution characteristics and preservation degree of fine-grained argillaceous sediments affect the connectivity between sand bodies. For instance, (semi-)deep lacustrine mudstone can have large-scale continuous distribution on the plane, forming impermeable interlayers, and blocking the longitudinal flow of reservoir fluids. The sand and mud interbedded beach has some sand components, and thus weaker blocking ability vertically. But as these two types argillaceous sediments cover the top of sand bars, when lake level changes frequently, or they were exposed long, they are prone to wave erosion, consequently, the reservoir may have “mud in sand” in some places, resulting in good continuity of sand bodies (Fig. 9a). On the contrary, the better and well preserved the argillaceous sediments, the “sand-in-mud” configuration would come up, in which sand layers (despite their wide transverse distribution) are vertically separated by mudstone layers on a large scale,resulting in poor connectivity (Fig. 9b). Therefore, to develop lacustrine nearshore sand bar reservoirs, it is necessary to consider the spatial configurations of sand and mud reflected in different layers and different compound sand bars.

The spatial configuration of sand and mud will be very important information that can be used to provide a reliable prototype geological model for more detailed anatomy of sand bar reservoir in the process of fine characterization and establishment of geological model in Banqiao sag. In addition, in geostatistical analysis and flow unit simulation and other aspects, it will provide constraints for spatial distribution and quantitative relationship of sandstone and mudstone^[31,32]. Within a compound sand bar in the BinⅣ-2 layer in the Member 2 of Shahejie Formation in Banqiao sag (Fig. 10a), for example, the sand and mud interbedded beach at the top of the sand bar is very common (that is, it is well preserved), indicating that there was sufficient accommodate space and the lake level was relatively stable in this sedimentary period. According to the sand and mud combination patterns in wells drilled there and the identification marks of individual bars^[9], four individual sand bars were identified. For example, Well bG5 has two sets of thin-mud thick-sand combination pattern sediments in this layer, and a set of thin sand and thin mud interbed pattern sediment between them. It is believed that they are two individual sand bars and beach sediment between them. In another well bn5-4, thin-mud thick-sand pattern was also found, and above this set of sediment is relatively thick mudstone containing thin beach sand. It is considered that this well encountered an individual sand bar, and the argillaceous sediments behind the bar deposit. Ultimately, the spatial distribution and configuration of sandstone and mudstone in this compound sand bar was reconstructed from the information of argillaceous sediments combination model and the superposition pattern of the individual sand bar (Fig. 10b).

According to analysis, the compound sand bar is divided into three stages of deposits (bar 1 and 2 deposited first, while bar 3 and 4 deposited in stages 2 and 3). The individual bars migrated to the center of the lacustrine basin (Fig. 10c). In this compound sand bar, the mudstone behind the bar is distributed on the shore side, the (semi-) deep lacustrine mudstone is mostly on the lake-facing side, the sand and mud interbedded beach is in the individual bar superposition area, and the fall-silt seams are scattered in each individual bar and generally consistent in distribution with the compound sand bar. The results were applied to guide 3D geological modeling, to make the model able to reflect the internal structure of sand bar reservoir, especially the spatial configuration of sand and mud, and different property parameters can be given in simulation according to the fine-grained lithofacies of different genesis. For example, (semi-) deep lacustrine mud should be given low or even zero permeability^[33], while the sand and mud interbedded beach a permeability range, so as to be closer to the inner structure and permeability law of the real sand bar reservoir.

Sand bars developed under different environmental conditions have different deposition and preservation degrees of argillaceous components^[9]. As a result, the sand and mudstone content and proportion of argillaceous components of different genetic types are also reflected in the reservoir of sand bars. Therefore, in a particular reservoir of sand bar, a more reliable understanding of the distribution of sedimentary strata of sand bar and the spatial combination of sand and mudstone can be obtained by sorting out the accommodate space, the frequency of lake level oscillation (or the speed of base-level cycles change) and the length of exposure-erosion time. On the other hand, in the later stage of oilfield development, due to the influence of deposition, structure, water injection property, pressure and other factors, the distribution of remaining oil is complex. The lack understanding of remaining oil distribution restricts the efficient development of oilfield, and the existence of muddy interlayers is the main geological factor controlling the complex water-flooding form of oil and gas layers^[34]. Therefore, in the process of development of sand bar reservoir, it is necessary to make clear the origin and distribution of fine-grained muddy deposits, and adopt corresponding development strategies or optimize development plans according to the sand and mud configurations in different parts of the reservoir, so as to avoid the blocking effect of interlayers to fluids.

Typical modern nearshore sand bar deposits developed on the east and south bank of Xiashan Lake. During the deposition of sand bars, mud and sand layers alternate frequently. According to the analysis of borehole samples from the modern deposits, sand bars show three patterns of sand and mud combinations: thin sand and thin mud interbed pattern, thick- mud thick-sand pattern, and thin-mud thick-sand pattern.

The mud components in sand bars are fine-grained sedimentary facies of three genetic types caused by changes in lake level, namely (semi-) deep lacustrine mud and sand and mud interbedded beach, argillaceous sediments formed by water retention area behind the bar and fall-silt seams caused by flood discharge. The distribution characteristics of mud deposits of different origins are different. Semi-deep to deep lacustrine mud is located in the vast water area extending to the lake far from the bar; the sand and mud interbedded beach is mostly on the top of an individual bar; the argillaceous sediments behind the bar is in the quiet water environment on the shore side; and the fall-silt seams are scattered in the interior of an individual bar.

The internal structure of a sand bar can be described as a combination of different orders of sand bodies and mud deposits. The spatial distribution and preservation of muddy layers in sand bars are related to the scale, migration and superposition degree of the individual sand bars. The spatial configuration of sand and mud is affected by three factors: the accommodate space, the frequency of base-level cycles and the exposure-erosion time.

Mud deposits of different genetic types would form different orders of interlayers and influence the heterogeneity and fluid flow in sand bar reservoir. The distribution and preservation degree of muddy layers affect the spatial configuration of sand and mud and the proportion of mud content in the reservoir of sand bar, which could control the distribution of remaining oil in sand bar reservoir to some extent.

Thanks to the No.4 Oil Production Plant and Exploration and Development Institute of Dagang Oilfield for the actual oilfield data, they provide sufficient data basis for the research and discussion of the related results in this study.