Acoustic travel time is subject to the effects of many factors (e.g., the borehole diameter, fractures, gas-bearing potential, and tight-zone characteristics); thus, it does not typically have a linear relationship with porosity. By comparing the acoustic qualities, as well as the resistivity, density, compensated neutrons, and other logging data from the same lithology, it can be generally confirmed to what extent the acoustic travel time reflects the corresponding change in porosity. This method is known as the comprehensive compaction curve comparison method (Wang et al., 2003). In this study, from a pure mudstone interval, we acquired the acoustic and resistivity logging data, which reflect the rock conduction effect, as well as the density and neutron logging data, which reflect the rock volume property. These four conventional logging sequences were combined for compaction analysis.

The comprehensive compaction curve (Figure 3) plotted for all 10 members in the study area (Chang 1–10), shows a trend that, from Chang 1 to Chang 4 + 5, the acoustic travel time decreases, while the deep lateral resistivity increases, the formation density increases, and the neutron porosity decreases; below Chang 4 + 5, from Chang 6 to Chang 8, the acoustic travel time, resistivity, density, and neutron porosity show reverse behavior and are synchronized. Only when this synchronization occurs can the segmented compaction of mudstone be confirmed (Fertl and Timko, 1972; Hermanrud et al., 1998). Thus, it can be confirmed that Chang 1 to Chang 4 + 5 is a normal compaction segment, and Chang 6 to Chang 8 is an under-compaction segment. The normal compaction segment is usually characterized by the following equation (Eq. 1): Δ t = Δ t 0 e − c z (1) where z is the buried depth, Δt is the acoustic travel time at the buried depth z, Δt ₀ is the surface acoustic travel time, and c is the compaction slope.

The compaction process of mudstone is predominantly affected by the formation deposition rate. Generally, if the deposition rate is low, the mudstone particles experience a sufficient time for achieving better (horizontal) arrangement, such that the porosity may decrease rapidly with the buried depth, resulting in a larger compaction slope. In contrast, if the deposition rate is high, the mudstone particles do not have enough time to arrange horizontally, resulting in a higher porosity at the given depth, and thereby a smaller compaction slope. As shown in Figure 4; Table 1, the deposition rate in the study area is apparently negatively correlated with the compaction slope for the normal compaction segment, that is, the higher the deposition rate, the smaller the compaction slope. In other words, for the study area, a higher deposition rate has caused unfavorable conditions for mudstone compaction. In addition, the lithologic combination, argillaceous content, and sediment source can also affect the slope of mudstone compaction.

Microscopic diagenetic fluid information (e.g., authigenic illite dating, carbon/oxygen isotope analysis of authigenic calcite, and fluid inclusion temperature measurement) show that the oil of Chang 8 in the Longdong area extensively accumulated mainly at the end of the Early Cretaceous, when the buried depth reached its maximum (Fan et al., 2013). The high-quality Chang 7 source rocks are considered the main source rocks of the Mesozoic in the Ordos Basin, and the study area is located within those high-quality source rocks (Zhang et al., 2009). Under the action of source–reservoir pressure differences and capillary pressure, oil first migrated from Chang 7 source rocks to the Chang 8 member. After entering the Chang 8 tight reservoir, the oil experienced a secondary migration under the overpressure caused by under-compaction in Chang 8, in addition to the residual pressure carried from the source rock.

The equivalent depth method (Magara, 1968) is widely used in the calculation of overpressure caused by under-compaction. For this method, essentially, an equation is established assuming that the effective stress at a point in the under-compacted interval is equal to the effective stress in the normal compaction segment with the same porosity. Then, Terzaghi’s equation (Terzaghi, 1943) is used to calculate the fluid pressure and overpressure in the under-compacted interval. At the same time, based on the assumption of compaction as an irreversible process, it is considered that the current compaction curve can reflect the compaction in the period with the maximum buried depth, and thus the equivalent depth method can be used to calculate the overpressure in such a period. In fact, however, the current compaction curve can reflect the compaction pattern, but its application for abnormal pressure restoration in the period with the maximum buried depth may involve significant uncertainties. Accordingly, the occurrences of demonstrated formation resilience after intense uplifting, denudation, and unloading in the later stage need to be better determined by experiments. Many studies have reported the formation resilience after structural uplifting (Ren and Sun, 2005; Li D. et al., 2020).

Rock mechanics experiments with surface mudstone cores are difficult to implement due to the strong elasticity of such cores. We measured the porosity of seven shale samples taken at different buried depths of Chang 7 in the study area. The results show that the pore volume of shale increases with the decline of effective stress, indicating that the mudstone of the study area exhibited resilience to a certain extent during the process of structural uplifting. Also, according to the correlation between pore volume and effective stress (Figure 5A), the resilience of shale pores conformed to a good logarithmic relationship, with a correlation coefficient of more than 0.9. The curve was morphologically consistent with the Bowers unloading curve (Bowers, 1995). Using the slope (Eq. 2) obtained by fitting these data according to the linear relationship (Figure 5B), the pore resilience coefficient during structural uplifting could be determined as follows: C r = Δ ϕ Δ σ (2) where C _r is the pore resilience coefficient, ΔΦ is the change in pore volume, and Δσ is the change in effective stress. It was indicated in the experiment that the faster the pressure dropped, the more the shale pores swelled, owing to the speed of structural uplifting, which has a significant impact on shale resilience. Through the statistical analysis, the denudation rate was found to have a certain positive correlation with the resilience coefficient (Figure 6), with the square of correlation coefficient reaching up to 0.84. Accordingly, the resilience coefficient of Chang 8 mudstone in the untested portions of the study area could be calculated.

By using the resilience coefficient and the present-day shale porosity, the shale porosity in the period with the maximum buried depth could be restored. According to the exponential relationship between effective stress and porosity (the loading curve) of the Bowles method (Bowers, 1995), the loading curve (Eq. 3; Han, 2020) was plotted using the restored mudstone porosity and effective stress for the normal compaction segment in the period with the maximum buried depth. Moreover, the unloading curve (Eq. 4; Han, 2020) could be plotted using the resilience coefficient and the measured present-day pressure (Figures 7A,B):

Loading curve: ϕ b = a e b σ b (3)

Unloading curve: C r = ϕ p − ϕ b σ b − σ p (4)

It should be noted that the porosity at the intersection of the loading curve and the unloading curve is equal (Han, 2020). a e b σ b = ϕ p − C r ( σ b − σ p ) (5)

Next, the effective paleo-stress could be obtained by using the iterative method, and then, the overpressure caused by under-compaction in the period with the maximum buried depth could be calculated (Eq. 6; Han, 2020): Δ P d c = S b − σ b − P w b (6) where Φ _P and Φ _b are the porosity in the present day and the porosity in the period with the maximum buried depth, respectively; σ _P is the present-day effective stress; a and b are fitting constants of loading curves; C _r is the pore resilience coefficient; ΔΦ is the resilience of porosity; Δσ is the effective stress reduction during porosity resilience; and ΔP _dc is the overpressure caused by under-compaction in the period with the maximum buried depth (see Figure 6A for relevant parameters).

The overpressure of the Chang 8 member in the study area at the end of the Early Cretaceous, when the buried depth reached its maximum, was restored using the method described above, and the overpressure gradient was plotted (Figure 8). It was found that the overpressure gradient ranged from <0.5 MPa/m (in the southwest part of the study area) to ˃7.5 MPa/m (in the northeast part of the study area). Specifically, the overpressure gradient was higher in the Baibao Oil Field as well as areas further south (3.0–4.5 MPa/m), and smaller in the area surrounded by the Huachi, Yuele, Qingcheng, and Gucheng oil fields, which is conducive to the stagnation and accumulation of oil. Southward, in the Qingyang, Heshui, and Gucheng oil fields, the overpressure gradient increases and peaks, which is conducive to oil migration and accumulation in ideal traps.

Research spanning 20 years confirms that tight oil flow in a reservoir typically follows the low-velocity non-Darcy flow pattern, that is, oil starts to flow at a certain start-up pressure gradient (Zeng et al., 2014). In addition, multiple core flow experiments for tight reservoirs in the Ordos Basin have also suggested that oil could migrate only when the start-up pressure gradient reaches a certain level (Zeng et al., 2014). Based on this, the start-up pressure gradient shows obvious characteristics as the dynamic driver for oil migration in tight reservoirs.

The start-up pressure gradient at which oil enters the transport layer and corresponding permeability data obtained from flow experiments for the Mesozoic tight oil reservoirs in the Ordos Basin were fitted (Figure 9) (Wu et al., 2013; Xue and Tian, 2014), and it was found that the start-up pressure has a good correlation with the permeability of samples. The two parameters conform to the power function, with the correlation coefficient of 0.99, expressed as Eq. 7: Gp = 0.071 K 1.341 (7) where Gp is the start-up pressure gradient, MPa/m; and K is the permeability, mD. Using this correlation, the start-up pressure gradient for the formation with permeability data but without flow experiment data could be obtained.

As described above, the start-up pressure gradient was obtained using permeability data and Eq. 7. Accordingly, the paleo start-up pressure during tight oil accumulation could also be calculated using the paleo-permeability in the reservoir-forming period. Some scholars have performed diagenesis analyses and determined diagenetic sequence divisions on the basis of sedimentary setting, core observation, and logging data interpretation. They indicated that after the hydrocarbon expulsion peak at the end of the Early Cretaceous, three types of diagenesis occurred: 1) the replacement of intergranular materials and grain margins by crystalline-connected calcite, 2) the dissolution of matrix and grain margin by highly acidic fluid, and 3) also that by feldspar dissolution. Then, through physical property inversion, they restored the paleo-porosity and paleo-permeability at the maximum buried depth at the end of the Early Cretaceous (Bowers, 1995). From the restored paleo-permeability recovery (Bowers, 1995) and Eq. 7, the paleo start-up pressure in this study was determined to be 0.01–0.31 MPa/m. The low start-up pressure gradient (<0.06 MPa/m) was distributed mainly in N-S orientated segments, located in the central part of the area surrounded by the Zhenyuan, Heshui, and Qingcheng oil fields, as well as in the southern part (especially the center of the distributary channel sand body). Finally, the start-up pressure gradient was high in the eastern part and lowest in the western part (Figure 10).

Fluid potential is an important parameter to determine the potential migration and accumulation direction of oil and gas. Using the restored paleo-structure during the main reservoir-forming period from previous studies (Fan et al., 2013) and the restored paleo-fluid pressure determined in this study, the paleo-fluid potential in the main reservoir-forming period could be calculated from Eq. 8, followed by outlining the stream lines with PetroMod software: h o = z + P ρ o g (8) where h _o is the oil potential; ρ _o is the oil density; z is the height; P is the fluid pressure; and g is the gravitational acceleration.

According to the distribution of oil potential stream lines at the end of the Early Cretaceous (Figure 11), it can be concluded that the oil potential is generally higher in the northeast and lower in the southwest. The highest oil potential is located in the northeast of the study area, while the lowest oil potential is located in the Heshui Oil Field in the south and the Zhenyuan Oil Field in the southwest, reflecting a trend of oil migration from northeast to southwest and an accumulation in the southwest and south. The stream lines (Figure 9) show that oil has migrated from the northeast to the southwest along dominant pathways in the Baibao, Huachi, and Yuele oil fields before accumulating within favorable traps of the Qingcheng, Qingyang, and Heshui oil fields.

Comparison (Figure 8 and Figure 10) indicates that the overpressure gradient in the study area is basically higher than the start-up pressure gradient during the main reservoir-forming period, and the large difference between the overpressure gradient and start-up pressure gradient falls basically on the dominant migration pathways indicated by the oil potential stream lines (Figure 10). Additionally, the reservoir became weakly lipophilic at the end of Early Cretaceous^[14], allowing oil to more easily migrate laterally along these areas. The coupling of migration dynamics and pathway height suggests that oil in the study area mainly migrated from the northeast to the southwest along these areas at the end of the Early Cretaceous and finally accumulated in the large nose-like uplift structure highlighted by the paleo-structure in the southwest (Fan et al., 2013), forming the present Qingcheng, Heshui, and other large oilfields.

After the end of the Early Cretaceous, the Chang 8 member in the north of the Longdong area saw a depleting oil migration for five reasons. First, the subsequent Late Yanshanian structure began to weaken the oil generation capacity of Chang 7 source rocks, which is now very low. Second, the structure rotated counterclockwise and gradually changed from a north-dipping monocline with higher south end and lower north end to a west-dipping monocline with higher east end and lower west end (Fan et al., 2013). Third, the distribution direction of the sand bodies is inconsistent with the trend of monocline. In some areas, sand bodies are distributed almost along the monoclinic trend, with minor structural fluctuation (Fan et al., 2013). Fourth, the physical properties of the reservoir are far inferior to those in the hydrocarbon charging period at the end of the Early Cretaceous (Chen et al., 2006). Fifth, as the abnormal overpressures basically disappeared, the reservoir tended to normal or negative pressure. Therefore, the Huachi Oil Field and other lower abundance reservoirs developed in the oil migration areas in the northeast. In these two stages, the change in intensity of migration dynamics dominated the accumulation and enrichment of tight oil.