During the sedimentation of the muddy carbonate rocks, the sedimentary environments, including deep-water environment and restricted water environment, are low in energy. The rock types include generally mudstone, grainstone, wackestone and packstone, and the interstitial materials are lime mud or micrite. In the Middle East, oil and gas are produced mainly from the Cretaceous reef-shoal facies with high energy. Muddy carbonate reservoirs have received less attention, and they are usually regarded as interlayers or poor reservoirs in oilfield development^[1,2,3,4]. However, in the thick muddy carbonate rocks, there are considerable reserves, which are important resources for oilfield development. Muddy carbonate reservoirs have been developed in existing oilfields in southeastern Iraq. The Middle East was in a warm and humid tropical climate during the Cretaceous period, with various biological communities and widespread bioturbation in sedimentary strata. Bioturbation refers to the sedimentary structures formed by agitation, mixing and destruction of surrounding sedimentary particles by organisms, including identifiable and unidentifiable burrows, boreholes, footprints and relics, etc.^[5] Great breakthrough has been made in the early researches on bioturbation. Bioturbation is found in a broad array of environments, even in storm deposits^[6,7,8,9], but most developed in a low-energy environment. Biological burrows have dual physical properties, and their permeability contrast is the largest, exceeding two orders of magnitude^[10]. Generally, bioturbation is positively correlated with reservoir physical properties. The stronger the bioturbation is, the better the reservoir physical properties are^[11,12]. The influence on reservoir physical properties depends on the way of biological movement and burrow infillings^[13,14]. In addition, the permeability contrast between the matrix and the burrows, the connectivity and abundance of the burrows also affect the reservoir physical properties^[15]. Dissolution can significantly improve the burrow permeability^[14], and a large number of intercrystalline pores can be formed due to dolomitization. Therefore, the permeability may be increased by 2-4 orders of magnitude^[16]. High permeability bands can be developed due to connected burrows, resulting in ineffective water circulation during water drive development^[15]. However, the following problems are still unclear about the bioturbation: (1) the transformation method of muddy carbonate rocks by organisms; (2) the coupling mechanism of bioturbation and penecontemporaneous dissolution; (3) the mode and evolution of dolomitization in burrows; (4) the controlling factors of bioturbation on physical properties of muddy carbonate rocks. With the Cretaceous strata in A, H, M, W and R oilfields in southeastern Iraq as examples, the transformation mechanisms of the coupling of bioturbation and diagenesis on muddy carbonate rocks are made clear through this study.

The study area is located in the structural front of the Mesopotamia Basin, and is an important oil and gas producing area in the Middle East (Fig. 1). Bioturbation is widely developed on Cretaceous cores in the study area, especially in the Middle Cretaceous Mishrif Formation and the Upper Cretaceous Khasib Formation. The Mishrif Formation was deposited in a shallow-water carbonate platform environment^[17], mainly in the open shallow sea during the early stage. With the decline of the global sea level, it gradually evolved into a platform margin, and the deposited thick rudistid reef-beach hindered the normal circulation of water. During the late sedimentation stage of the Mishrif Formation, southeastern Iraq was dominated by a restricted marine environment^[18]. During the sedimentation stage of the Khasib Formation, it was generally in the period of the global sea level rise, the shale content was higher.

This study is based on the data from 15 typical coring wells in five oilfields. The total length of cores is 2403.39 m, and the sampling density is 1-8 samples/m, including 1085 cast thin sections and 4848 samples for analyzing physical properties. Based on the geological theories of ichnology, petrology, sedimentology and sequence stratigraphy, through the combined analysis of core, thin section andbioturbation structure, by comparing the petrophysical characteristics of bioturbated areas with unbioturbated areas, the diagenetic evolution in the burrows is restored and the transforming mechanism of bioturbation on rock physical properties is explored.

Cretaceous bioturbation in the Middle East is mainly developed in lagoons, inter-shoals, medium ramp, outer ramp and deep-water basins etc. Organisms usually build regular branched or cylindrical burrows, which are vertically connected with the sedimentary interface, and can be densely discrete, widely spaced discrete and strongly disturbed thick layers^[19,20]. The strata that are not disturbed by organisms and retain the original sedimentary structure are called matrix. The characteristics of Cretaceous burrows in the Middle East are diverse. On cores, the matrix is grayish or yellowish white and dense, while burrows are usually dark brown, brown or dark gray (Fig. 2). According to the characteristics of burrows, they are mottled, patched, thick-branched, vein-like, mazy, and thick-layered. Mottled and patched burrows are isolated, with clear boundaries. Thick branched and vein-like burrows are connected by points and have certain connectivity. Mazy burrows have a higher connectivity, and the boundary with the matrix is not obvious. The contours of the thick-layered burrows are fuzzy, and the matrix characteristics are overlaid. The thick-layered bioturbation is mainly caused by the strong dissolution of the burrows. The characteristics of mottled burrows and patched burrows indicate that the water depth is deep, the biological density is small or the biological activity is low, which are most developed in the upper part of the transgressive system tract and the lower part of the highstand system tract. The characteristics of thick-branched burrows, vein burrows and mazy burrows indicate a shallower water body, larger biological density, and higher biological activity, which are usually developed during the period of sea level decline. The characteristics of thick-layered burrows usually reflect the exposure and dissolution of the strata, which is mainly distributed in the lowstand system tract.

The burrow infillings include four categories: (1) Granular composition formed at the same time as the matrix. The matrix is mud supported, while the psammitic infillings are particle supported (Fig. 3a). (2) Contemporaneous clasts, namely the sediments refilling the burrows during the formation or after abandonment of the burrows, including the following types: (A) bioclastic mudstone which is similar to the matrix, with fuzzy burrow boundary (Fig. 3b); (B) wackestone which is obviously different from the matrix; their burrow boundaries are clear, and the bioclasts are mainly spheroids and benthic foraminifera (Fig. 3c); (C) Packstone: the bioclasts in burrows are dissolved and form secondary solution pores (Fig. 3d); the pores may be filled again, and the bioclasts include benthic foraminifera, spheroids, bivalves and a small amount of echinoderms (Fig. 3e); (D) granular limestone: the burrows are calcsparite-supporting structures, and the bioclasts are tightly filled with calcite (Fig. 3f). (3) Calcite, the product of diagenesis, can tightly fill the entire burrow or leave pores in the middle of the burrow (Fig. 3g). (4) Dolomite, the product of diagenesis, can be divided into three types according to the grain size and crystal shape of dolomite: (A) Dolomicrite, usually distributed in burrows in a discrete form (Fig. 3h); (B) Fine-medium crystal dolomite with a higher degree of crystal automorphism and metasomatic residual bioclasts or mudstone (Fig. 3i), and the composition of mudstone or bioclasts can be dissolved, forming an obvious contrast with the non-dissolution zone (Fig. 3j); (C) Hypautomorphic mosaic dolomites with linear contact to each other, which decrease the intercrystal pores (3k) or completely occupy the intercrystal pores (Fig. 3l). In general, only when a burrow is filled with granular composition, coarse-grained syngenetic debris and fine-medium crystal automorphic dolomite etc., can the bioturbation play a constructive role in rock physical properties.

Organisms changed the composition and structure of original sediments through inversion, compression, mixing, excavation, backfilling of sediments, remineralization, chemical alteration and other manners. Generally, burrow infillings are looser than surrounding rocks, and it is more convenient for the migration of diagenetic fluids^[21,22]. There are discrete, tubular and coarse-grained burrows in muddy carbonate rocks, which can form macropores through dissolution in shallow water and seepage zones, significantly improving the effective permeability of rocks^[21]. For example, in the lagoon facies of M oilfield, the average porosity of the undisturbed strata is 6.0% and the average permeability is 0.3×10^-3 μm²; the average porosity of the disturbed strata is 12.8%, and the average permeability is 3.1×10^-3 μm². The oil-bearing level of biological burrows on the core is higher. In general, there are three ways to improve rock physical properties by bioturbation: (1) Biomechanical modification can loosen rock structure and improve the seepage performance of the rock. (2) Biological burrows are backfilled with coarse-grained debris and dissolution occurs. (3) Biological burrows undergo chemical alteration and dolomitization to form intercrystalline pores.

Organisms can transform rock debris, mineral particles and organic matter to change the original physical structure of sediments^[23]. After low degree of compaction, muddy sediments are dense, pore-throats are small and fluid infiltration is difficult. Biological activities destroy the dense structure of the matrix, the burrow sediments become loose, the permeability is improved, and the intergranular interstitial materials will be scoured by water and gradually form intergranular pores. The infillings in the burrows and the matrix are deposited at the same time, and later water scouring makes them have different structures from the matrix. In the Khasib Formation of A oilfield, the matrix is muddy bioclastic and psammitic limestone which is brightly white and dense, and whose pores are rarely found by naked eyes (Fig. 4a-4c). The permeability of the matrix is less than 1×10^-3 μm². The structures of the burrows are different from that of the matrix, and the interface between them is obvious (Fig. 4d). The burrow structure is loose, the grains are relatively clean, and intergranular pores are well developed. The permeability is (10-100) ×10^-3 μm² (Fig. 4e).

If a burrow is filled with coarse-grained debris, it has different permeability from the matrix. The permeability contrast between the two can reach eight orders of magnitude, so the burrow can become an important pathway for fluids to penetrate into the sediment^{[12,14-15,24]}. Within a few centimeters below the interface between carbonate sediments and water, dissolution, precipitation and changes in the chemical properties of pore water can occur in the burrow^[24]. The physical properties of the infillings are greatly improved after dissolution, which increases the permeability contrast with the matrix. However, the pores in the burrow may be cemented and filled in an atmospheric fresh water subsurface flow zone or a buried diagenetic environment. For example, in the Mishrif Formation of M oilfield, the matrix is bioclastic mudstone (Fig. 5a-5c), and the infilling is calcsparite bioclastic limestone. Bioclasts include benthic foraminifera, bivalves, rudistids fragments, echinoderms and algae, as well as a small amount of spheroids (Fig. 5d). After bioclastic corrosion, strong cementation occurs, the pores are densely filled again (Fig. 5e) and become difficult to be observed by naked eyes.

Chemical alteration in burrows is usually dolomitization, which can be promoted by fine-grained infillings and organic matter produced by biological metabolism. Fine-grained materials increase the surface area in contact with dolomitized fluids and provide more crystal nuclei in a given volume^[26]. As the dolomite molar volume is smaller than calcite molar volume, after the calcite metasomatosis by the dolomite with the same mass, a large number of intercrystalline pores will be generated^[26]. Mudstone is often impermeable, and organisms dig holes in muddy carbonate rocks to connect seawater and matrix. Diagenesis will first transform the burrow and affect the matrix near the burrow^[25,27]. Dolomitization occurs from the burrow to the matrix, and the dolomite in the matrix is similar to the crystal in the burrow^[25]. In the Cretaceous Mishrif Formation of M oilfield, the burrows are mainly euhedral fine-crystal dolomite; the residual bioclasts after metasomatism can be seen; the crystals are relatively dirty; the particle size is 10-50 μm; and the intercrystalline pore connectivity is appreciable (Fig. 6a-6c). The burrow halo is the transition zone between the burrow and the matrix, with a width of 1500 μm. The dolomite within burrow halo has small grains and matrix micropores. The micropores in the burrow halo are the result of the loose structure and the dissolution of fluid in the burrow. With the distance away from the burrow, the development of micropores and dolomite gradually decreases to disappearance (Fig. 6d). The matrix is mudstone, where it is difficult to observe pores with naked eyes, and occasionally contains bioclasts such as ostracods and benthic foraminifera (Fig. 6e).

In general, except biomechanical modification, backfilling and chemical alteration are closely related to diagenesis. Dissolution occurred after the backfilling of the burrows, and the chemical alteration is mainly dolomitization. In the formation where bioturbation is widely developed, there are mold pores formed by selective dissolution (Fig. 7a), dissolution pores and vugs formed by non-selective dissolution (Fig. 7b) and geopetal crystal siltstone (Fig. 7c), which all indicate the diagenetic environment of exposed leaching and seepage^[28]. During the Cretaceous period, the structures in southern Iraq were stable, there were fewer faults, and it was difficult for large-scale dissolution to occur in the burial environment. Strong dissolution mainly occurred during the early diagenetic stage. Dolomitization occurred from the penecontemporaneous stage to the burial stage. There are indicators of a buried diagenetic environment such as suture and coarse-crystal ferric calcite in thin sections, and fine-crystal dolomite is developed in sutures (Fig. 7d). The coarse-crystal ferric calcite compactly fills the burrows (Fig. 7e) and coexists with dolomite in the burrows (Fig. 7f), which indicates that it is buried dolomitization which mainly occurred in the burrows.

Rich organic matters in the burrows are oxidized and produce CO₂. It then reacts with water to form a slightly acidic environment which promotes the dissolution of the infillings in the early diagenetic environment. After the dissolution of the burrows, the pores in burrows can be further widened to produce a higher permeability than the matrix^[25]. Meter-scale cycles have an important influence on sedimentation and early diagenetic environment. In order to study the coupling relationship between bioturbation and dissolution in the early diagenetic environment, the MB1 Member of the Mishrif Formation in H oilfield is taken as an example. The MB1 Member is dominated by lagoon environment. According to the lithologic change and combination, 50 meter-scale cycles have been identified, with thickness of 0.35-4.10 m and an average thickness of 2.00 m for each cycle (Fig. 8). The coupling relationship between bioturbation and dissolution is divided into seven types according to the factors such as dissolution intensity, bioturbation degree, distribution and characteristics of burrows.

Type I: the whole cycle went through intense dissolution, dominated by bioclastic micrite limestone, 0.6-2.2 m in single layer thickness (averaging 1.34 m), and 8.05 m in total cycle thickness. Bioclastic micrite is occasionally developed at the bottom of the cycle. The cores are dark brown, and the burrow boundaries are fuzzy (Fig. 9a). Type I coupling relationship is mainly affected by the change of sea level. The low depositional rate in the lagoon provided a long disturbance time for organisms. The burrow density was high and burrows are interconnected. After filled with coarse-grained debris, the burrow permeability increased significantly. As the sea level declined significantly, the strata were in an atmospheric fresh water environment, intense dissolution occurred in the burrows, and the dissolution scale of burrows were expanded.

Type II: the whole cycle went throughslight dissolution, dominated by bioclastic micrite and clastizoic micrite, 1.12-2.00 m in single layer thickness (averaging 1.58 m), and 4.75 m in total cycle thickness. The burrows were dissolved and enlarged, the scales were expanded, and the burrow boundaries can still be identified (Fig. 9b). Type II coupling relationship is mainly affected by the decline of sea level. The bioturbation was relatively sufficient, the burrow density was higher, and the sea level decline is small. The formations were still in a seawater diagenetic environment, and the dissolution was slight.

Type III: in the upper part of the meter-scale cycle, dissolution was intense. In the lower part, dissolution was slight. The upper part of the cycle is dominated by micritic bioclastic limestone and bioclastic micrite, 0.25-1.15 m in single layer thickness (averaging 0.73 m), and 2.20 m in total thickness. It is not easy to identify the burrow boundaries. The lower part is dominated by bioclastic micrite, 0.18-1.00 m in single layer thickness (averaging 0.56 m), and 1.68 m in total thickness. The burrow boundaries are clear (Fig. 9c). Type III coupling relationship is controlled by the decline of sea level and formation thickness. The burrow connectivity of the whole cycle is appreciable, and the decline of sea level is little. Only the top of the formation was leached by atmospheric fresh water, while the bottom of the cycle was still in the seawater diagenetic environment and the dissolution was slight. The greater the formation thickness, the greater the range of the slight dissolution zone.

Type IV: the upper part of the meter-scale cycle went through slight dissolution, and no dissolution in the lower part. The slight dissolution part is dominated by bioclastic micrite, 0.2-2.3 m in single layer thickness (averaging 1.1 m), and 3.32 m in total thickness. The burrow boundaries are fuzzy, but they can still be identified. The non-dissolution part is mainly micrite, 0.35-1.00 m in single layer thickness (averaging 0.62 m), and 1.85 m in total thickness. The burrows are well preserved and isolated (Fig. 9d). Type Ⅳ coupling relationship is controlled by the decline of sea level, bioturbation intensity and rock type. The burrows in the upper part are well connected, and the content of grains is higher than that in the lower part, the decline of sea level was little, and the dissolution was slight in the seawater diagenetic environment. The burrows at the bottom of the formation were not connected, and it is difficult for dissolution to occur.

Type V: the upper part of the meter-scale cycle went thtough intense dissolution, and no dissolution in the lower part. Type V is the most developed in the MB1 Member. The thickness of the dissolution section is 0.25-3.60 m (averaging 1.19 m), and the cumulative thickness is 32.10 m. It is mainly bioclastic micrite and micritic bioclastic limestone, and locally clastizoic micrite, so the biological burrows are not easy to identify. The thickness of the non-dissolution section is 0.10-2.30 m (averaging 0.56 m) and the cumulative thickness is 15.16 m. It is mainly micrite, locally clastizoic micrite, and most of the burrows are spotted or patchy shape. There is a sudden change from the dissolution section to the non-dissolution section, and the boundary between the two is obvious (Fig. 9e). This type is mainly controlled by the amplitude of sea level decline, rock type and bioturbation intensity. The grain content in the upper part of the cycle is high. Therefore, intense dissolution occurred in the atmospheric fresh water environment. The connectivity of burrows at the bottom of the cycle is low, the muddy content is high, and diagenetic fluid cannot penetrate, so no dissolution occurred.

Type VI: the upper part of the meter-scale cycle suffered from strong dissolution, totally 1.4 m in thickness. The lower part was undisturbed, totally 0.4 m in thickness. The dissolution intensity of the upper meter-scale cycle in the core decreases downward. The undisturbed zone is dominated by micrite, and the core is white and dense (Fig. 9f). Type VI coupling relationship is mainly affected by water depth. In the lower part of the cycle, the water depth was deep, which was not favorable for the survival of benthos. The formations were not reconstructed. The water depth in the upper part of the cycle became shallow, the grain content increased, burrows were developed, and the sea level declined, resulting in dissolution.

Type VII: The upper part of the meter-scale cycle went through intense dissolution, with a transition zone in the middle, while the lower part has no dissolution. The thickness of a intense dissolution section is 0.30-2.00 m (averaging 0.88 m) per layer. The cumulative thickness is 6.13 m. It is mainly bioclastic micrite, and locally clastizoic micrite. It is difficult to identify biological burrows. The thickness of the transition zone is 0.35-0.95 m (averaging 0.54 m) per layer, and the cumulative thickness is 3.78 m. It is mainly bioclastic micrite. The burrow boundary at bottom is easy to identify, with the increase of dissolution intensity, the burrow boundary near top is gradually blurred. The thickness of a non-dissolution section is 0.45-0.90 m (averaging 0.64 m) per layer, and the cumulative thickness is 4.50 m. It is mainly micrite, and the burrows are in the shape of spots or patches (Fig. 9g). Type VII coupling relationship is controlled by the degree of sea level decline, burrow connectivity and rock type. The intense dissolution zone has a high content of grains, good burrow connectivity and intense dissolution in an atmospheric fresh water environment. The transition zone is in a seawater diagenetic environment with better burrow connectivity, but the dissolution is weaker. The burrows in the lower part of the cycle are not connected, and the content of muddy composition is higher, so they are difficult to be dissolved.

Based on the above research, we have established the coupling sequence of bioturbation and dissolution (Fig. 10). In the meter-scale cycles, dissolution zones, slight dissolution zones, transition zones, non-dissolution zones and undisturbed zones are developed in descending order from top to bottom, and one or more zones have been developed in each single cycle. The thickness of a dissolution zone is 0.25-3.60 m, averaging 1.17 m. It is usually located at the top of the meter-scale cycle, with a higher grain content and better seepage performance. The decline of sea level determined whether it was in an atmospheric fresh water environment. The connected burrows were backfilled with coarse-grained debris to promote dissolution. The thickness of a slight dissolution zone is 0.18-2.30 m, with an average of 0.97 m. The rock types are similar to the dissolution zone, with higher burrow connectivity and weaker fluid dissolution, forming a slight dissolution zone. The decline of sea level is the controlling factor, and the formation is usually in a seawater diagenetic environment. The thickness of the transition zone is 0.35-0.95 m, averaging 0.54 m. It is mainly bioclastic micrite, located in the middle of a meter-scale cycle. In the upper part, a dissolution zone was usually developed. The development of the transition zone is controlled by the decline of sea level and the connectivity of burrows. The transition zone was usually in a seawater diagenetic environment. The upper dissolution zone was rich in Ca²⁺ fluid, which migrated downward, and the dissolution capacity of fluid was weaker. Although the connectivity of burrows is appreciable, the dissolution influence is not obvious. The thickness of a non-dissolution zone is 0.10-2.30 m, averaging 0.54 m. It is mainly developed at the bottom of a meter- scale cycle, controlled by rock type and burrow connectivity. The non-dissolution zone is mainly micrite with lower permeability. The burrows are usually isolated spots or patches, and it is difficult for diagenetic fluid to penetrate. The undisturbed zone is controlled by rock type and water environment. Where water is deep, the rock is mainly micrite, and the environment is not favorable for the survival of benthos. Not modified by biological burrows, the rocks retain their original dense structures.

To sum up, the coupling relationship between bioturbation and dissolution is mainly controlled by rock type, the degree of sea level decline, burrow density, infilling and water environment. The higher the content of grains in rock, the lower the dependence of dissolution on bioturbation. The burrows only promoted the dissolution of rocks. At the top of a meter-scale cycle, the depositional rate was high, and the bioturbation was insufficient. While at the bottom of the cycle, the shale content was higher, and the burrow density and connectivity were higher. Only when the formation was in an atmospheric fresh water environment, the dissolution was intense. The density and infillings of burrows determined the effectiveness of bioturbation. Only when burrows were connected and filled with coarse-grained debris, burrows can act as channels for diagenetic fluid to flow, and the water environment controls the population density and activity range of organisms.

Burrows can provide migrating channels for dolomitizing fluids, and dolomitization usually occurred along the burrow trajectories^[29]. The burrows have material basis, redox conditions and an acid-base environment favorable for dolomitization.

(1) Material basis: the demand on Mg²⁺ ions by dolomitization in the burrows is huge, and the only source which can provide a large amount of magnesium ions is seawater^[30,31]. Magnesium in seawater and metals in organic matter lead to a cation enrichment in burrows, which is favorable for dolomitization^[32]. Fractures or sutures connect the burrows with other diagenetic systems, and provide foreign Mg²⁺ ions. In addition, sulfate reducing bacteria in the burrows release Mg²⁺ ions from MgSO₄, increasing the content of free Mg²⁺ ions^[33,34]. When the burrows are in a surface oxidation zone, a large amount of CO₂ will be produced by organic matter oxidation. Hydrated CO₂ becomes H₂CO₃. Deprotonation reaction releases CO₃^2- ions. The mineralization of organic carbon by bacteria and the increase of pH value also contribute to the formation of CO₃^2- ions^[34].

(2) Redox conditions: in the oxidizing environment, SO₄^2- ions bind Mg²⁺ ions, reducing the content of Mg²⁺ ions and inhibiting the precipitation of dolomite^[25]. Dolomitization tends to develop in a reducing environment which may be made by burrows^[25]. In the modern environment, sulfate reducing bacteria play an indispensable role in early dolomite precipitation at near-surface temperature^[34], and the presence of organic matter will produce sulfate reducing bacteria. The sulfide concentration in burrows increases^[35], and sulfate reduction occurred in or around burrows^[34].

(3) Acid-base environment: the necessary geochemical conditions for dolomitization include the removal of SO₄^2- ions, the increase of pH value, the increase of CO₃^2- ions, the enrichment of divalent cations and the chemical diffusion gradient, and the microenvironment of burrows just fitted perfectly^[36]. In the early diagenetic environment, the increase of pH value and the decrease of SO₄^2- ions were the main reasons for dolomite precipitation^[32]. Abundant NH₃ in burrows reacted with water, forming an alkaline environment. High pH value can improve the activity of HCO₃^- ions and promote the precipitation of dolomite^[25]. It is worth noting that the oxidation (or mineralization) of organic carbon can lead to the increase of burrow alkalinity, and the pH value can be increased by 2-5^[34].

The dolomite crystals in burrows has various forms, and the dolomitization is continuous and multi-staged^[37]. Considering the sedimentary process, redox conditions and diagenetic environment, we have established a burrow dolomitization model. Appropriate temperature and pressure, sufficient time, appropriate fluid supply for dolomitization and dissolution are favorable for the development of intercrystalline pores in burrows^[38].

Organisms usually live in an aerobic to slightly anoxic environment. In deeper anoxic seawater, they will also grow with appropriate seawater energy, food supply, hydrology and matrix conditions^[39]. The oxidation of organic matter at the opening of a burrow is not favorable for dolomitization. The organic matters in deep burrows are small grains with worse permeability, thus they can be preserved due to weak fluid modification (Fig. 11a).

The organic matters in the upper part of burrows can backfill with syngenetic coarse-grained debris after decomposition to improve permeability. Seawater provides a large amount of Mg²⁺ ions to the burrows. In the reduction environment, the reducing bacteria produced by microbial fermentation promote dolomitization, and biological sediments can act as crystal cores^{[25, 36]} for the formation of dolomicrite (Fig. 11b). Due to relatively short reaction time of dolomitization, the grain size of dolomite is small, the crystal automorphic degree is lower, and it is dispersed in the micrite in burrows.

With the continuation of sedimentation, the burrows are gradually separated from the sedimentary interface and placed in a closed shallow burial environment. The burrows transit to a reduction environment. A large amount of Mg²⁺ ions left in seawater are used for dolomitization, and the content of micritic dolomite increases continuously (Fig. 11c).

With the increase of burial depth, the burrows will be in a reduction environment. Compaction reduced the burrow volume, increased formation temperature and pressure were favorable for dolomitization. Due to the more sufficient reaction time, the crystal automorphic degree was higher, mainly fine-crystal dolomite, and the crystal grain size is 100-200 μm. A small amount of dolomite also precipitated in the matrix adjacent to the burrows, forming the burrow halo. The particle size and content of dolomite in the burrow halo are lower than those in the burrows. At this stage, the burrows were in a closed diagenetic system, and the Mg²⁺ required for dolomitization was still from the residual of previous seawater. Dolomite replaced micritic calcite, and the residual unsaturated fluid dissolved the micritic matrix. Intercrystalline dissolution pores appeared. New burrows formed at the sedimentary interface, and then undergo a similar evolution process (Fig. 11d).

In the burial environment, fractures may be created, which can connect external fluids, and the burrows were placed in an open diagenetic system. The unsaturated fluid dissolved the residual muddy composition^[26] (Fig. 11e). If the dissolution was strong enough, the burrow boundaries, surrounding rocks and fractures might be enlarged^[26].

If the materials needed for dolomitization are continuously supplied, hyperdolomitization will occur after the limy composition is completely replaced. As long as it is permeable between the dolomites and Mg²⁺ supply, new dolomitization will occur^[26], and Mg²⁺ ions come from mixed groundwater and early dolomite^[25]. Dolomite fills the intercrystalline pores and intercrystalline dissolved pores formed during the early stage. Due to the continuous reduction of growth space, the crystal gradually changed from automorphic-hypautomorphic and point-line contact to heteromorphic and concave-convex contact^[27], and the crystal particle size is 120-250 μm (Fig. 11f).

The higher the granular content of muddy carbonate rocks, the better the original physical properties, the easier the diagenetic modification^[40,41], and the lower the dependence on bioturbation. The rock type is mainly controlled by the sedimentary environment. During the process of sea-level decline, the sedimentary water dynamic increased continuously, resulting in a higher granular content at the top of a meter-scale cycle, and easy to be exposed to atmospheric fresh water. With the increase of the depositional rate at the top of the cycle, the degree of biological disturbance decreased too.

Biological modification to muddy carbonate rock is controlled by factors such as burrow density, burrow connectivity, infilling, burrow structure and so on^[12,16]. The depositional rate controlled the disturbance intensity of organisms. A slow depositional rate is the necessary condition for the formation of connected burrows. The bioturbation depth of a single organism to the sediments during the same period was limited. The number of trace fossils contained in thicker and rapid deposits is generally less than that in slow deposits. The biological disturbance in thin sediments is relatively stronger than that in thick sediments. A few centimeters at the top of the thick layer are widely modified, but only slightly modified at the bottom of the layer^[5]. According to the statistical analysis of biologically disturbed samples in M oilfield, it is found that Type I patched disturbance has almost no influence on rock physical properties. With the increase of bioturbation degree, micro pore-throats, physical properties and oil content of the reservoir are better. Type IV thick-bedded bioturbation has the most significant modification influence on rock physical properties. In addition, with the increase of bioturbation degree, the development of fine-crystal dolomite increased, and dissolution was easy to occur (Table 1). The burrow density has an important influence on the vertical permeability. When the burrow density reaches 50%, the vertical permeability will increase significantly^[15]. The greater the burrow density, the more media available for fluid flowing, and the easier it is to form a continuous flowing path. This is more favorable for diagenetic modification.

When a burrow is filled with coarse-grained debris and fine-crystal dolomite, the physical properties of the burrow will be better than the matrix. Adding dissolution effect into account, the physical properties of muddy carbonate rock will be greatly improved. After the abandoned burrows were filled, the physical properties may be similar to or even worse than the matrix. For example, mudstone can block the burrow and deteriorate the overall physical properties of the rock^[13-14,27]. Mosaic calcite occupies pores and limits fluid migration, resulting in a negative correlation between bioturbation intensity and rock physical properties^[14,42]. In addition, dolomicrite has little influence on the physical properties of the burrow. Hyperdolomitization and recrystallization cause dolomite to block pores and throats, and reduce the permeability of the burrow^[26].

Biological burrows and surrounding rocks have different tortuosity and fractal characteristics. Tortuosity is one of the important parameters affecting the effective flow and transmission of porous media^[43]. Although bioturbation is relatively homogeneous at a meter level, heterogeneity at a decimeter level has an important influence on fluid properties and recovery factor^[44]. The distribution of burrows or boreholes and other relics is irregular, and their spatial geometrical changes are frequent. For example, in a sunny environment, the organisms are diverse in species and mainly feeding, the layered structure is developed obviously and widely distributed. There are few biological relics in the coastal zone and mainly residential organisms, and the storm will limit the diversity of biological species^[34]. The same organism species have different active trails, different organisms have different burrow patterns and habits, and burrows of different organisms overlap each other. All these factors cause the burrows to have complex tortuosity and seepage characteristics. Generally, the more organism species, the greater the tortuosity of a burrow, the greater the fluid seepage resistance and the worse the seepage performance of the burrow.

Biological modification on muddy carbonate rocks transforms muddy carbonate rocks in three ways, namely mechanical modification, burrow backfilling with coarse- grained debris, and chemical alteration. The modification intensity is controlled by rock type, burrow density and connectivity, infilling and burrow structure etc. The lower the depositional rate, the more sufficient the bioturbation, and the higher the burrow density and connectivity. If a burrow is filled by grains and has a small tortuosity, the fluid seepage resistance through it will be small, more favorable for improving the physical properties of muddy carbonate rocks.

During the penecontemporaneous period, bioturbation and dissolution were coupled to modify the physical properties of rocks, and the intensity of modification was controlled by rock type, sea level decline, burrow density, infilling and water environment. With the increase of granular components, the dependence of dissolution on bioturbation decreased. In the formation with meter-scale cycles, different zones are developed alternately from top to bottom. Although the dissolution zone and the slight dissolution zone have the best physical properties and their hydrocarbon bearing and cumulative thickness is higher, their single-layer thickness is small and the heterogeneity is stronger. Therefore, the dissolution zone and the weakly dissolution zone are difficult for oilfield development.

During the burial period, bioturbation was mainly coupled with dolomitization to modify the rock physical properties. Intercrystalline pores can be developed in the burrows only when sufficient equimolar metasomatism occurred in the closed environment. However, the capability to modify rock physical properties by dolomitization was limited, and no large-scale dissolution occurred in the closed burial environment. While in the opened burial environment, dolomitization usually occurred, destroying the pores formed during the early stage. The influence of dolomitization on muddy carbonate rocks is limited and it is difficult to form large-scale reservoirs.