Introduction

Overpressure commonly develops in sedimentary basins (Osborne and Swarbrick 1997), where many oil and gas fields have been found. There are more than 180 known overpressure basins in the world, of which about 160 are rich in oil and gas (Du et al. 1995). Overpressure can affect the maturity of organic matter (Hao et al. 2006; Shi et al. 2015a), oil and gas migration (Zheng et al. 2000), and hydrocarbon accumulation (Xu et al. 2011). It also has an important impact on drilling safety (Osborne and Swarbrick 1997; Radwan et al. 2020; Radwan 2021). Consequently, it is significant for deep-seated oil and gas exploration that the identification of the overpressure causes and the estimation of its formation time.

There are many mechanisms that can cause overpressure, including (1) an increase in fluid pressure caused by under-compaction or unbalanced compaction of mudstone (Rubey and King Hubbert 1959; Du et al. 1995; Tingay et al. 2009; Li and Zhao 2012; Ma et al. 2020; Radwan 2022) or tectonic compression (Berry 1973; Zhang et al. 2020); (2) an increase in fluid volume resulting from kerogen hydrocarbon generation (Broichhausen et al. 2005; Huo et al. 2020), gas from hydrocarbon cracking (He and Middleton 2002; Su et al. 2017), or clay mineral dehydration (Liu et al. 2006; Li and Zhao 2012); (3) the pressurization mechanism for overpressure transfer due to difference of fluid potential energy (Zhang et al. 2012); and (4) the multi-factor control mechanism of gypsum-salt rock that causes overpressure in the inter-salt and sub-salt layers, controlled by depositional dehydration, compactness, plasticity, fluidity, and other properties (Zhang et al. 2016). Early researchers used well-logging responses to analyze the causes of overpressure, interpreting the deviation of sonic logging from the normal compaction trend as under-compaction (Magara 1978). Alternatively, purely theoretical approaches with numerical simulations were used. These methods are either too simplistic or too indirect, resulting in uncertain conclusions (Zhao et al. 2017). More recently, both direct empirical methods and indirect analytical methods have been used to identify the causes of overpressure (Zhang et al. 2012, 2013), but these methods can only provide qualitative guidance and cannot be used for quantitative identification.

Although overpressure is a major concern in oil and gas exploration, but it has been difficult to identify its main causes from many mechanisms and to determine the formation time. In this paper, a new method is proposed to quantitatively determine the cause of overpressure by disequilibrium-compaction and to estimate its formation time, which is demonstrated by being applied to the northwestern Bozhong subbasin in the Bohai Bay Basin, China.

Theoretical basis

Effective stress law

The effective stress law, which is the basic theory describing hydrostatic pressure, states that strata pressure is composed of two parts: the hydrostatic pressure of the water filling the pores and the effective stress (or average stress) in the skeleton (Biot 1941; Terzaghi et al. 1996). The effective stress affects the compaction, while the hydrostatic pressure does not (Terzaghi et al. 1996).

Although compaction is the result of the combined action of skeleton pressure and lateral stress, skeleton pressure is the dominant factor, and the effect of lateral stress is ignored in practice (Drews et al. 2018). The skeleton pressure and lateral stress are quite different in direction, magnitude, action time, influence range, and compaction effect (see Table 1). Lateral stress can only be transmitted a small distance from an area of strong tectonic activity, where lateral compaction develops. The skeleton pressure only needs a solid skeleton, and it is transmitted sequentially with burial. For example, the plastic mica deforms or fractures in only one direction (see Fig. 1), indicating that the particles are compacted by pressure acting in a constant direction (similar to an indoor uniaxial pressure experiment), which must be the skeleton pressure.

Table 1 Characteristics of skeleton and lateral pressure
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Fig. 1
figure 1

Compressed mica characteristics in the study area A W1, 3343.9 m, E3d2L, Plane polarized light; B W2, 3453 m, E3d2L, Perpendicular polarized light; C W3, 2801.7 m, E3d2L, Plane polarized light; D W3, 3384.6 m. E3d2L, Plane polarized light. E3d3 represents the Dongsan Member in the Paleogene, E3d2L represents the Lower Dong’er Member, E3d2U + d1 represent the Upper Dong’er Member and the Dongyi Member, N1g represents the Guantao Group in the Neogene, N1mL represents the Lower Minghuazhen Member, and N1mU + Qp represent the Upper Minghuazhen Member in the Neogene and the Pingyuan Group in the Quaternary

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If diagenesis is ignored, the porosity of mudstone should be the result of the maximum effective stress during the burial process because mechanical compaction is irreversible. The maximum effective stress is approximately the maximum skeleton pressure corresponding to the maximum burial depth. Issler (1992) concluded that the effect of the maximum burial depth on the reduction of mudstone porosity is much greater than that of the maximum paleo-geotemperature, so the reduction of mudstone porosity is primarily dependent on the maximum burial depth.

Disequilibrium compaction and the equilibrium depth method

In sedimentary basins, the current burial depth in most areas is the maximum burial depth, and the current skeleton pressure is the maximum skeleton stress. The skeleton pressure is approximately equal to the effective stress, thus the current porosity of the mudstone is the effect of the current skeleton pressure. If the porosity of two different points is the same, their effective stress is equal according to the effective stress law (Liu and Wang 2001), and their skeleton pressure is also equal.

The equilibrium depth method can be used to calculate the effective stress based on the normal compaction curve of mudstone. In this study, we use the equilibrium depth method to calculate the present pressure of mudstone. The hydrostatic pressure of mudstone in the overpressure area in the sedimentary basin is approximately equal to the hydrostatic pressure of the adjacent sandstone (Magara 1978; Chen and Luo 1988; Osborne and Swarbrick 1997; Liu and Wang 2001).

Normal compaction curve of mudstone

Because the equilibrium depth method is based on the compaction curve of mudstone, the accuracy of the normal compaction curve directly determines the accuracy of the method. Before applying the equilibrium depth method, the normal compaction curve of mudstone in the study area should be established. The compaction curve of mudstone has been characterized as two types of relationship: (1) an exponential relationship, proposed by Athy (1930) based on the experimental data of indoor compaction and improved by Rubey and King Hubbert (1959); and (2) a power law relationship, proposed by Baldwin and Butler (1985). The former is widely used (Hansen 1996; Vejbæk 2008; Tingay et al. 2009; Zhang 2011).

Mudstone porosity is obtained indirectly by means of well-logging and seismic surveys, since it is difficult to measure burial mudstone porosity directly in sedimentary basins. The acoustic transit time is the best method to measure mudstone porosity, so mudstone compaction curves are often expressed as the relationship between logging acoustic transit time and depth (Chen and Luo 1987). As depositional conditions are similar, the normal compaction curve of the mudstone can approximately represent the compaction history of other mudstone in the study area (Magara 1978).

In sedimentary basins, the sedimentary environment can be relatively stable. For example, the Bozhong subbasin is made up of lake-fluvial sediment from the Paleogene to the Neogene. The normal compaction curve for the study area is obtained by measuring the variation of the acoustic transit time with depth, then by using the formula proposed by Martin et al. (1988) or the time-average equation proposed by Wyllie et al. (1956) to transform the acoustic transit time to mudstone porosity.

The porosity of mudstone, calculated using the Wyllie equation (Wyllie et al. 1956), can be substituted into the equilibrium depth equation (Chen and Luo 1988; Liu and Wang 2001), yielding the mudstone compaction curve

$$D = - b^{ - 1} \ln \left( {\Delta t - \Delta t_{ma} } \right) + b^{ - 1} \left[ {\ln \left( {\Delta f - \Delta t_{ma} } \right) + \ln P_{0} } \right]$$
(1)

If the relationship between porosity and burial depth in mudstone is taken to be a power law (Baldwin and Butler 1985), the mudstone porosity, calculated using the equation of Martin et al. (1988), is substituted into the power law, yielding

$$D = A\left( {\frac{\Delta t}{{\Delta t_{ma} }}} \right)^{{ - \frac{B}{X}}}$$
(2)

When the mudstone porosity, calculated by the time-average equation (Wyllie et al. 1956), is substituted into the power function, the result is

$$D =A\left(\Delta t_{f} - \Delta t_{ma}\right)^{ - B} \left(\Delta t_{f} - \Delta t \right)^{B}$$
(3)

The accuracy of Eqs. (1), (2), and (3) can be compared by taking well W1 in the study area as an example, for which the appropriate parameters are X = 2.19,\(\Delta t_{ma}\) = 220 μs/m (Wyllie et al. 1956), and \(\Delta t_{f}\) = 660 μs/m (Deming 1994). The results show that there are significant differences between the actual sonic transit time and that predicted by Eq. (1) in the ranges < 1200 m and 1700 m–2800 m (see Fig. 2A), and similarly the predictions of Eq. (2) are inaccurate in the ranges < 1000 m, 1600 m–2300 m, and > 2900 m (see Fig. 2B), while Eq. (3) is close to the real value across all ranges, with the highest correlation coefficient among the three equations (see Fig. 2C). Therefore, Eq. (3) is selected to calculate the normal compaction curve in the study area.

Fig. 2
figure 2

Normal compaction curves of mudstone in well W3 in the study area A, B, and C are obtained using Eqs. (1), (2), and (3), respectively

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Calculation of mudstone overpressure

Now that the normal compaction curve of mudstone in the study area has been obtained, the acoustic transit time at the depth can be substituted into Eq. (3), and then the equilibrium depth corresponding to the abnormal acoustic transit time of mudstone at the depth can be obtained as

$$Ze = A\left(\Delta t_{f} - \Delta t_{ma}\right)^{ - B} \left(\Delta t_{f} - \Delta t \right)^{B}$$
(4)

The overpressure value caused by mudstone disequilibrium compaction at a given depth Z can be found by substituting Eq. (4) into the equilibrium depth equation (Chen and Luo 1988; Liu and Wang 2001),

$$P_{z} = \rho_{r} gZ - \left( {\rho_{{r^{\prime}}} - \rho_{w} } \right)g\left\lfloor {A\left(\Delta t_{f} - \Delta t_{ma}\right)^{ - B} \left(\Delta t_{f} - \Delta t \right)^{B} + M} \right\rfloor$$
(5)

Equation (5) is the main equation used to calculate the overpressure value of disequilibrium mudstone in this study. Two details must be accounted for before applying it. First, to obtain the average density of the strata (ρr and ρr′), the density logging curve should be corrected by the core, and then the equivalent density of every depth should be calculated iteratively yielding the average density for the strata. Second, for the sandstone fluid density, we use the tested result of fluid water for the first choice, and then the result suggested by Baldwin et al. (1985) for the second, which is 1040 kg/m.

Analysis of the causes of overpressure

Mudstone overpressure can be approximately equal to sandstone pressure resulting from disequilibrium compaction (Drews et al. 2018). Thus, the ratio of mudstone overpressure to sandstone pressure determines the contribution percentage of disequilibrium compaction, allowing for quantitative analysis of the overpressure's origins.

In this study, the recommended judgment criteria are as follows. If the percentage falls between 80 and 100%, it indicates that mudstone overpressure primarily results from disequilibrium compaction. If the percentage falls between 50 and 80%, it suggests that disequilibrium compaction is the main cause of overpressure, but other factors may contribute. If the percentage is below 50%, it implies that the primary cause is other factors such as kerogen hydrocarbon generation, with disequilibrium compaction playing a secondary role in overpressure.

The start time of overpressure

If overpressure in a certain area is caused by disequilibrium compaction, it can be inferred by the formation process of overpressure that the start time of disequilibrium compaction during the burial is at the depth Zmax (m) with maximum overpressure, and the equilibrium depth Zemax (m) corresponding to depth Zmax (m) is the origin depth of disequilibrium compaction, and then the start time of overpressure can be calculated quantitatively using the burial history of the strata obtained by the back-stripping algorithm.

Is the start time of disequilibrium compaction mudstone the same as the start time of overpressure in adjacent sandstone? In fact, it is not. The former should be earlier than the latter because disequilibrium compaction in the mudstone should occur first, and then the overpressure should be transmitted from the mudstone to the adjacent sandstone. What is more, as the mudstone is under-compacted, the fluid can still seep from the area with high potential energy (the center of the disequilibrium compaction) to the adjacent area with low potential energy because the mudstone with disequilibrium compaction is not absolutely closed, but is relatively closed (Osborne and Swarbrick 1997), and the seepage velocity is relatively slow. However, it can also be considered that the two are approximately equal due to the long geological history.

Results and discussion

This method is now applied to evaluate the causes and start time of overpressure at the northwestern Bozhong subbasin. We then discuss the feasibility and practicability of the approach.

Geological overview

The Bohai Bay Basin can be sub-divided into two tectono-stratigraphic units (see Fig. 3): a synrift stage during the Paleogene and a postrift stage during the Neogene and Quaternary (Huang and Pearson 1999; Hao et al. 2009; Huang et al. 2012; Xu et al. 2018). During the synrift stage, a series of grabens and half grabens developed (Huang and Pearson 1999). These grabens and half grabens progressively became one large basin during the late Oligocene, and the Bohai Bay Basin entered the postrift stage (see Fig. 4).

Fig. 3
figure 3

A Location map showing the Bohai Bay basin. B Location of the Bozhong subbasin, Bohai Bay Basin, after Xu et al. (2018)

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Fig. 4
figure 4

Generalized stratigraphy of the Bohai Bay basin after Hao et al. (2009). The target stratum is showing in the black dashed box. Form = Formation; PY = Pingyuan

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The Bozhong subbasin, belonging to the secondary structural unit of the Bohai Bay Basin, is the center of sedimentation and oil and gas generation in the basin, and is also the largest subbasins with a total area of about 8660 km2 (see Fig. 3B). In ascending order, the syn-rift sediments in the Bozhong subbasin are composed of the Kongdian (E1k), Shahejie (E2s4, E2s3, E2s2 and E2s1), and Dongying (E3d3, E3d2 and E3d1) Formations (see Fig. 4). The postrift sediments consist of the Guantao (N1g), Minghuazhen (N1mL and N2mU), and Pingyuan (Qp) formations (see Fig. 4). These formations mainly contain fluival-lacustrine sediments (Gong 1997).

The main source rocks are found in the E2s3, E2s1 and E3d3 (Hao et al. 2009; Fu et al. 2010; Xu et al. 2018), which have significant potential for petroleum exploration (see Fig. 4). The thickness of the Paleogene sediment in the Bozhong subbasin is 2000–5000 m. It is composed of gray sandstone, siltstone, and dark gray mudstone, and is characterized by rapid subsidence. The study area is the northwestern of the Bozhong subbasin, whose overpressure formations are the E3d2L and the E3d3 (see Fig. 3A). The faults in the study area are not well-developed, and the main sedimentary facies are braided river delta, fan delta, and shallow lake–semi-deep lake sediments (Zhu et al. 2011; Bo et al. 2012; Pang et al. 2017).

Overpressure generation mechanism

The causes of overpressure in the Ed in the study area are a subject of differing opinions among different scholars. For instance, scholars like Hao et al. (2004) argue that the primary causes of overpressure in the Bohai Bay Basin are the combined results of rapid sedimentation leading to disequilibrium compaction and the effects of hydrocarbon generation. On the other hand, others believe that the reservoir overpressure in the Bohai Bay Basin results from a combination of disequilibrium compaction, overpressure transfer, and the generation of fracture gas (Liu et al. 2008). These previous studies were speculative and did not provide a rigorous theoretical derivation or calculation process.

Based on the computational method proposed in this study, our calculations indicate that the overpressure in the Ed is primarily caused by under-compacted mudstone, accounting for over 90% of the overpressure in the current sandstone layers (see Table 2). Therefore, it can be concluded that the overpressure in the study area is not a complex combination of factors but rather a single factor—disequilibrium compaction.

Table 2 Measured and calculated pressure in the E3d in the study area
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Developmental conditions with disequilibrium compaction

The study area is a large lake with long-term inheritance, where a large set of dark mudstones were deposited during the depositional period of the E3d3 and the E3d2. The cumulative thickness of the mudstones is greater than 750 m, and the ratio of sandstone to mudstone is low: the sandstone-to-mudstone ratio in the E3d2L is 0.26–0.47, while the ratio in the E3d3 is 0.21–0.26. There are 38 single-layer mudstones with thicknesses greater than 15 m in well W3, the largest being 168 m. Full details are shown in Table 3. The deposition rate in the study area has remained high from the Paleogene to the present (Hao et al. 2004). Based on regression analysis in the Bozhong subbasin, the deposition rate of the E3d is about 300 m/Ma, the N1g is about 120 m/Ma, the Minghuazhen Formation is higher than 180 m/Ma, and the Quaternary is about 400 m/Ma. Therefore, the study area has the key prerequisites for the development of disequilibrium compaction (Du et al. 1995; Jin et al. 2011): (1) high deposition rate and (2) low sandstone-to-mudstone ratio and thick layers of mudstone.

Table 3 Statistical parameters of sandstone and mudstone in the E3d in the study area
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Based on the results of measurements of recent sediments at the bottom of the Bohai Sea and Weishan Lake in Shandong, the initial porosity of the mudstone in these regions is about 55% (He 1979), which can also be used as the initial porosity of the mudstone in the study area because it is adjacent to the Bohai Sea. When the mudstone is compacted to a burial depth of 1900 m in the study area, the porosity is reduced to about 16.3% according to the equation for porosity in terms of equilibrium depth, and then the permeability of mudstone at this depth is about 10−6 mD by use of the relationship between mudstone porosity and permeability proposed by Bryant et al. (1975) (see Fig. 5). The fluid can be blocked for more than 1 Ma as the permeability of the mudstone is between 10–6 and 10−8 mD (Deming 1994). Therefore, the thick mudstone buried at a depth of 1900 m in the study area has moderate sealing ability.

Fig. 5
figure 5

Plot of permeability versus porosity sediments consisting of more than 80% clay (after Tingay et al. 2009)

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Table 4 Water analysis parameters of well W1 in the E3d in the study area
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Evidence of disequilibrium compaction

Pressure analysis

According to the test fluid density results in well W3, the average density of the fluid (water) is 1010 kg/m3; this is the equivalent density value obtained by iterative calculation using the density logging correction value; other parameters in Eq. (5) are obtained with reference to the compaction curve above.

The mudstone pressure in the study area can be calculated using Eq. (5) based on the variation of the mudstone acoustic wave time difference with depth and the normal mudstone compaction curve. The starting depth of disequilibrium compaction can then be determined using the relationship between mudstone pore pressure and hydrostatic pressure. For example, the initial depth of disequilibrium compaction in well W1 is about 2000 m (Fig. 6A), and the initial depth in wells W2 and W3 is 1900m (see Fig. 6B and C). The difference in the starting depth between the three wells may be related to the distance between the wells and the basin edge. W1 is closer to the basin edge than W2 and W3 (see Fig. 6B), the mudstone there is thinner, and the permeable sandstone is more developed, thus W1 is less conducive to disequilibrium compaction.

Fig. 6
figure 6

Plots of pressure versus vertical depth in the study area. A, B and C are pressure versus vertical depth from well W1, W2 and W3. P sandstone is the initial overpressure reservoir in well W1, and its cap rock is ① mudstone with 57 m thick. Q sandstone is the lower overpressure layer in well W1, and ② mudstone with 77 m thick is its cap rock

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Combined with the measured pore pressure data, the onset depth of overpressure in the northwest Bozhong subbasin is 3230 m in the well W1 (see Fig. 6A), and about 3200 m in wells W2 and W3 (see Fig. 6B and Fig. 6C). The calculated percentage of overpressure formed by disequilibrium compaction accounts for 90.4–97.6% of the measured overpressure (see Table 2), indicating that the main reason for overpressure in the E3d is the disequilibrium compaction of mudstone.

Formation water analysis

In the overpressure area formed by disequilibrium compaction, the fluid cannot be discharged quickly, but it does seep out over time to some extent. As shown in Fig. 6, both the measured pressure value and the calculated value increase with burial depth, indicating that the formation fluid has a potential energy difference in the vertical direction. The fluid seeps continuously from the overpressure center with high potential energy to the low, which is called centrifugal flow of mudstone (Lou et al. 2003) or compacted water flow (Zeng 2000), and the seepage velocity is relatively low. The fluids in the overpressure area and the nearby normal pressure area (pressure relief area) should belong to the same fluid system, and the fluid types should be the same.

The fluid source is the center of overpressure. During the fluid migration from the fluid source to the low-potential or pressure relief area, water–rock reactions will occur continuously. For example, carbonate cementation requires continuous absorption of CO32− and HCO3− ions from the fluid, and the dissolution of feldspars releases Na+ and K+ ions into the fluid (Shi et al. 2015b). As a result, the total salinity and the concentrations of K+ and Na+ gradually increase during fluid migration, and the concentrations of CO32− + HCO3− decrease—this was confirmed by routine analysis of fluid in well W1 in the study area (see Table 4). The type of fluid is the same from bottom to top in the E3d: a solution rich in sodium bicarbonate. The total salinity and concentrations of Cl−, K+, and Na+ gradually increase, and the concentrations of CO32− and HCO3− decrease, from bottom to top, which is direct evidence of overpressure being caused by mudstone disequilibrium compaction in the study area.

Formation process of overpressure

There are high deposition rates and large mudstone thicknesses (both cumulative and single-layer) in the Neogene stratum in the study area. With increasing burial depth, the porosity and permeability of the overlying mudstone decrease rapidly, and the sealing performance greatly increases. This sealing performance prevents large amounts of fluid seeping from the mudstone, thus the fluid should bear part of the rock skeleton pressure, and the porosity of the thick mudstone remains high in the sealed compartment (Hunt 1990), which is called the first sealed compartment, containing the first overpressure-fluid system. During the process of overpressure, fluid seepage between the sandstone and mudstone layers balances their hydrostatic pressure within the sealed compartment. As the strata continue to descend, the hydrostatic pressure in the first sealed compartment increases accordingly. If there is another regional sealed layer outside the first compartment, the second sealed compartment is nested outside the first, and the fluid between the two compartments comprises the second overpressure-fluid system. The hydrostatic pressure in the first compartment is higher than the pressure in the second, and they form an overpressure system. As this cycle repeats with the burial process, the current abnormal overpressure system forms, with several overpressure-fluid systems (see Fig. 7). This is the formation process of the overpressure caused by the under-compacted mudstone, and the center of the abnormal overpressure is located inside the first sealed compartment.

Fig. 7
figure 7

Sketch map of overpressure system. The number represents pressure coefficient; ① and ② represent the outer sealing layer and the inner in well W1

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If the sandstone layer adjacent to the under-compacted mudstone is thick and has good connectivity with the upper and lower strata, then the fluid discharged from the under-compacted mudstone will be quickly exhausted, and thus the hydrostatic pressure of the sandstone will remain normal. For example, as shown in Fig. 6, in the 2000–3200 m section, although the mudstone is under-compacted, the hydrostatic pressure of the sandstone is normal. Therefore, the development of abnormal overpressure by disequilibrium compaction of mudstone depends critically on the existence of regional seals.

The regional seal and the sealed compartment play a relative isolation role. In other words, the fluid inside and outside the sealed compartment is not completely closed, and there is still pressure transmission between sealed compartments, at a relatively low rate. In addition, there is a pressure gradient in the formation hydrostatic pressure between each sealed compartment. As shown in Fig. 6A, the measured (sandstone layer) pressure coefficient in the overpressure area increases in a gradient.

Based on the relative positions, the seal is divided into the outer and the inner. The outer seal refers to the regional thick mudstone or gypsum layer that is adjacent to the overpressure system, has a relatively fluid sealing effect and constitutes the outermost sealed compartment. The inner seal refers to the regional thick mudstone or gypsum layer with a relatively high sealing effect in the overpressure system, which forms one or more sealed compartments.

The regional sealing layer in the study area is a thick mudstone layer with disequilibrium compaction. As shown in Fig. 6, the outer seal of the overpressure is the single layer of mudstone with a thickness of 57 m which overlaps the P sandstone layer in well W1. The reasons are as follows: (1) the thick mudstone layer in the W2 and W3 well blocks is 111–123 m, which is the deposition of the high-stand system tract of the E3d3 and covers the entire basin; and (2) the thick mudstone layer with disequilibrium compaction can effectively prevent the fluid of the underlying P sandstone from communicating with that of the overlying sandstone layer, since the fluid of the mudstone is only released from the under-compacted center to the upper or lower (see Fig. 6).

The calculated pressure of the 3650–3800 m section of the E3d3 in well W1 using mudstone acoustic waves is lower than the measured value and is in a “ < ” shape (see Fig. 6A) because the section belongs to the sandstone–mudstone interbed, and the thickness of the mudstone single layer is thin (3–14 m). In the period of thick mudstone with disequilibrium compaction, the fluid of the thin mudstone layer drains normally at first, and then the interbedded sandstone layer is blocked due to the overlying seal, leading to poor drainage. The overpressure fluid from the under-compacted mudstone is continuously discharged, and finally the section forms a unified abnormal system with the upper and lower thick mudstones, so that the mudstone in this section presents the weakest under-compaction in the middle, and gradually strengthens up and down until it matches the single-layer thick mudstone. Therefore, the disequilibrium compaction is preferentially developed in mudstone with a thick single layer.

Estimation of overpressure start time

To determine the formation time of overpressure, some scholars have proposed to estimate the occurrence time of high pressure qualitatively by assuming that the initial depth of overpressure generation in the basin remains unchanged during the geological period (Liu et al. 2006), but no theoretical basis has been found for this assumption. The principle of equilibrium depth can be used to estimate the start time of the overpressure because overpressure in the study area is mainly caused by disequilibrium compaction.

The sealing layer is the key to the formation of abnormally high pressure in under-compacted mudstone, so the time for the sealing layer to have relative fluid storage performance is approximately equal to the start time of overpressure. Therefore, it is thought that the time when the sealing layer (mudstone) is under-compacted is close to the time when overpressure is formed.

It is estimated that the start time of the under-compacted sealing layer is later than that in the geological history because the process of slowly releasing pressure from high-pressure mudstone to the surrounding low-pressure mudstone or sandstone has always taken place as disequilibrium compaction in the sealing layer progressed. In other words, the real time when the under-compacted mudstone acts as a sealing layer should be slightly earlier than the time inferred by the porosity of the present mudstone, and there is a time difference between the two. As the sealing layer with thick mudstone has the ability to store the fluid, it will take a period of time for the hydrostatic pressure of the isolated formation (sandstone) to accumulate and form an abnormally high pressure, which means there is also a time difference between the formation time of the sealing layer and the overpressure. We suggest that the two time differences can be offset, so that the estimated formation time of the sealing layer and the overpressure formation time are roughly consistent.

Above all, it is a significant feature of the gradual stages in the formation process of overpressure that the formation time of the overpressure center is the earliest, and the outermost overpressure is the latest.

If we select a representative constant point of acoustic wave time difference in the sealing layer (inner or outer), and determine the equivalent depth of this point, then the equivalent depth is the initial burial depth of the under-compaction of mudstone in the sealing layer. Then, based on the normal compaction trend curve of sandstone and mudstone, the burial history of the stratum in the study area is calculated using the “peeling method” (Luo et al. 1989), and the stratum age corresponding to the equivalent depth at this point can be obtained. The stratum age is the start time of the overpressure. The following will take well W1 as an example to estimate the formation time of overpressure in the study area.

The start time of overpressure was estimated by drilling the innermost Q sandstone layer and the outermost P sandstone layer in well W1 (see Fig. 6). The ② mudstone in the range 3802–3879 m is the inner sealing layer of the Q layer (see Fig. 6). The representative overpressure point below the sealing layer is at a depth of 3878 m, whose equivalent depth is about 1899 m. It is possible that mudstone under-compaction occurred in the ancient burial to 1899 m because the initial depth of mudstone under-compaction in well W2 is about 2000 m, the initial depth of well W2 is about 1900 m, and the thickness of the sealing layer is nearly 80 m. According to the burial history of the formation from well W1 in the study area or the burial history curve drawn based on the data, it can be concluded that the formation time of mudstone under-compaction in the inner sealing layer is about 15.7 Ma (see Fig. 8). According to the burial history curve of well W1, it can be concluded that the start time of mudstone under-compaction in the inner sealing layer is about 15.7 Ma (see Fig. 8), which is the middle and late N1g. In the same way, the ① mudstone with 57m is the outer sealing layer of the P sandstone layer(see Fig. 6), which represents an overpressure point with 3217 m whose equivalent depth is about 2355 m, and the start time of under-compaction is about 5.7 Ma, which is the end of the N2mU (see Fig. 8).

Fig. 8
figure 8

The buried line of formation from well W1 in study area. Q’ and P’ represent location of the Q and P sandstone (see Fig. 6) as the overpressure started

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Well W1 has been drilled to a depth of 3910 m, which is the deepest well in the study area. It is not known whether the bottom of the E3d3 is the center of overpressure. However, according to the measured data and the mudstone pressure data, the overpressure coefficient at the bottom is higher than that in the upper part. It can be inferred that well W1 has not been drilled to the overpressure center, and the starting time of the overpressure center of the E3d3 was earlier than 15.7 Ma in the study area. The results about starting time of overpressure can serve as a reference for oil and gas exploration in the study area.

Above all, we introduce a pioneering method for estimating the initiation time of overpressure conditions. However, the credibility of its results remains challenging to verify due to the absence of prior assessments regarding the timing of overpressure formation in the study area, which hinders comparative analysis and in-depth discussion. The study area is still in the early stages of oil and gas exploration, and we anticipate that as exploration efforts in the region continue to advance, future findings regarding the period of overpressure formation will emerge, thereby allowing for the validation of the reliability of this method.

Discussion

The above results demonstrate that the application of the method described in this paper can effectively determine the causes of overpressure in the study area and estimate their formation time. However, this method has certain limitations and is primarily suitable for regions with relatively weak tectonic activity. One critical prerequisite for applying this method is the assumption that sandstone and mudstone layers in the geological formation exist within the same pressure system. In cases of intense tectonic movement where fractures disrupt the original pressure system of the sandstone-mudstone combination, causing pressure unloading in sandstone while mudstone unloads very slowly due to its ultra-low permeability, there can be a discrepancy in pressure systems between sandstone and mudstone. This can lead to a calculation of the mudstone-to-sandstone pressure ratio exceeding 100%, rendering this method inapplicable. Therefore, the method is primarily suitable for regions with relatively stable tectonics and not suitable for regions with intense tectonic activity. Additionally, in areas where carbonate rock layers are interbedded with mudstone in a structurally stable environment, further research and validation by subsequent investigators are required to determine the applicability of this method.

In summary, the method proposed in this paper offers the following advantages: it allows for the quantitative determination of the contribution of under-compacted mudstone to adjacent sandstone high-pressure levels, enabling the identification of the causes of overpressure. The calculation process is relatively straightforward, with a minimal computational burden, leading to straightforward and accurate results. However, this method has certain limitations: its accuracy depends on the availability of regional data, such as trends in mudstone compaction and formation water parameters. Moreover, its applicability is limited and is not suitable for regions with active tectonic movements.

Conclusions

  1. 1.

    A new method of determining the cause of overpressure in the formation is proposed. Especially, a pioneering method for estimating the initiation time of overpressure conditions is introduced. The feasibility and practicability of both methods are demonstrated for the case of the northwestern Bozhong subbasin. The calculation process for methods is relatively straightforward, with a minimal computational burden, leading to straight-forward and accurate results.

  2. 2.

    The overpressure of the E3d in the northwestern Bozhong subbasin is not a complex combination of factors, but rather a single factor—disequilibrium compaction accounting for 90.4 to 97.6%.

  3. 3.

    The paper proposes firstly the concept of the multiple relative fluid containment boxes, sealed sealed compartment characterized by stages and the coexistence of multiple relative fluid storages. The overpressure, formed by the under-compaction mudstone, is the result of the nesting of multiple relative fluid containment boxes and the gradual sequestration of pore fluids.