*4.1. In-Situ Stress and Mechanical Properties of the Cap Rock* 4.1.1. Pore Fluid Pressure

Drill pipe or wireline test data obtained from DST and MDT show that most of the wells in the Yinggehai Basin have encountered abnormal high fluid pressure formations in the middle and deep layers. In the study area, gas reservoirs are distributed in both overpressure and normal pressure layers, and the Huangliu Formation contains the main regional cap rocks for overpressure gas reservoirs in the deep layer. The maximum fluid pressure can be reached 96 MPa and the fluid pressure coefficient is close to 2.3. The fluid pressure increases with the burial depth longitudinally, and the magnitude of overpressure in the diapir zone is stronger than the slope zone at the same depth. This overpressure distribution may be due to the fact that overpressure can be transferred from deep to shallow layers in diapir zone.

#### 4.1.2. Vertical Principal Stress

In this study, the density–depth relationship of five Wells in the three blocks of the study area (Figure 6a, Equation (2)) was used to integrate to obtain the magnitude of vertical principal stress in the study area (Figure 6b, Equation (3)). The vertical stress gradient increases with depth and is close to 22.8 MPa/km in Huangliu Formation.

$$
\rho = 1158 \times h^{0.0949},
\tag{3}
$$

$$Sv = 0.010576h^{1.0949} - 0.607\tag{4}$$

**Figure 6.** (**a**) The density measurements of 5 Wells in the three blocks of the study area. The relationship between density and depth follows a power function. (**b**) Vertical principal stress obtained by the density log from the 5 wells. The vertical stress gradient is shown to increase with depth and close to 22.8 MPa/km in Huangliu Formation.

4.1.3. Horizontal Principal Stress Minimum Horizontal Principal Stress

According to the statistics of the LOTs and XLOTs data from the study area, they can be divided into three types. The first type is the XLOTs, although only one pressure cycle was performed, we can observe the FBP, FPP, and ISIP clearly (Figure 5b). In the second category, the well was shut in immediately after LOP was observed, with no significant pressure drop and no formation fracture (Figure 5c). The third category of data is that the formation did not fracture, and no significant losses were observed (Figure 5d). We cannot determine whether the shut-in was performed before or after the LOP was reached, but it can be inferred from the data of the offset wells.

For the first category of date, ISIP can better reflect *Shmin* than LOP, so ISIP is chosen to represent *Shmin*. For the second category, *Shmin* was represented by LOP. As for the third category of data, it is not possible to determine whether the maximum pressure is between FIT and LOP or between LOP and FBP, since no LOP formation was observed and no fracture occurred. However, compared to the offset well, the later well date can be used as the upper limit of *Shmin*. Synthesizing three categories of data analysis in the study area, the *Shmin* can be described by ISIP and LOP data in depths (Figure 7).

**Figure 7.** Horizontal principal stress in study area. *SHmax* is calculated by the Hubbert–Willis equation [50] under the assumption of zero tensile strength. *SHmax* is interpreted from LOTs and XLOTs. The data show the characteristics of stress pressure coupling, that is, the horizontal principal stress increases with the pore fluid pressure increasing [51–53].

Maximum Horizontal Principal Stress

According to the XLOT curve of the study area, Equation (2) is used to calculate the maximum horizontal principal stress. The tensile strength is approximated by the difference between the fracture pressure and the loss pressure. The results show that the in-situ stress state is *Sv* > *SHmax* > *Shmin* when the depth is above 2700 m and corresponds to the normal faulting stress regime. The in-situ stress state is *SHmax* > *Sv* > *Shmin* when the depth is below 2700 m and corresponds to the strike-slip faulting stress regime (Figure 7). The horizontal principal stress is obviously affected by the pressure-stress coupling, that is, the horizontal principal stress shows a trend of significant increase with the increase of fluid pressure.

#### 4.1.4. Geomechanical Properties of the Cap Rock

The Huangliu Formation cap rock in the Yinggehai Basin is a shallow-marine-facies deposit composed of mudstone which is a regional cap layer widely developed in the study area with a maximum thickness of up to 400 m. The mechanical properties of the cap rock directly control the fracture conditions and the required fracture pressure. As mentioned above, we used the GCTS Rapid Triaxial Rock Test System to test the mechanical parameters of cap rocks. The laboratory temperature was 25 ◦C, the humidity was 50%, the strain rate was 0.03 mm/min, and the sample was a cylinder with a diameter of 25 mm and a height of 50 mm taken from cap rock in the Huangliu Formation's well cores. According to the real geological background, the pore fluid pressure was set to 55 MPa. Through data processing and calculation, the friction coefficient (μ) and cohesion (C) were 0.426 and 17 MPa. The tensile strength of rock is 8.5 MPa (Figure 8). Furthermore, the well logging data can be used to calculate the tensile strength of the strata by Equation (5) [54]. The prediction of tensile strength is shown in Figure 9.

$$\rm{T} = \left[ 0.0045 \rm{E\_d} \left( 1 - \rm{V\_{sh}} \right) + 0.008 \rm{E\_d} \rm{V\_{sh}} \right] / \rm{K} \tag{5}$$

where T is tensile strength (MPa), Ed is dynamic modulus of elasticity (MPa), Vsh is mudstone content (%), and K is the correction coefficient obtained by fitting the experimental test data and logging calculation data, which is approximately 16 (dimensionless).

**Figure 8.** Mohr diagram plotting shear stress against effective normal stress.

#### *4.2. Risk of Hydraulic Rupture of Mudstone Cap Rock*

Hydraulic fracture is characterized by episodic opening, which not only provides channels for fluid migration, but also damages the integrity of cap rock, leading to the loss of oil and gas. It is, therefore, of great significance for evaluating the effectiveness of oil and gas traps and finding favorable exploration targets to determine whether hydraulic fracturing is occurring or about to occur in the cap rock.

**Figure 9.** Prediction of tensile strength from the well XD-A1. The one quarter of the differential stress is always less than the tensile strength in the whole depth, it means that extensional fracture always occurs for the intact cap rock.

#### 4.2.1. Risk of Hydraulic Fracture of Cap Rock in Present Conditions

The development of hydraulic fractures depends on the pore fluid pressure, the characteristics of in-situ stress field, and the mechanical properties of the cap rock. As mentioned above, when the differential stress of the cap rock is less than four times the tensile strength, the cap rock will suffer extensional fracture; when the difference stress is more than six times the tensile strength, the cap rock will suffer shear fracture; and when the difference stress is between the two conditions, the cap rock will suffer tensile shear mixed fracture (Table 1). The comparison of tensile strength and differential stress shows that the differential stress of strata at different depths in the study area is generally less than four times the tensile strength, and the difference between differential stress and four times the tensile strength gradually increases with the increase of depth, which means that extensional fracture is always developed in the strata. Due to the different fracture conditions of the cap rocks with early fracture development and those without fracture development, the existence of fractures increases the risk of hydraulic fracture of the cap rocks to a large extent and makes the cap rocks more prone to hydraulic fracture. Considering the geological background of early strike-slip fault activity and diapir

structure, subsequent hydraulic fracturing will occur along the pre-existing fracture weak surface. In this paper, the minimum horizontal principal stress is used to represent the minimum fracture pressure required for hydraulic fracturing of cap rock, and the ratio of fluid pressure to the minimum fracture pressure is defined as the hydraulic fracture risk factor of cap rock (*Rf*) (Equation (6)). When its value is greater than 1, it indicates that hydraulic fracture has occurred in fractured cap rock.

$$R\_f = P\_{\rm HF} / P\_{\rm p\ \ \prime} \tag{6}$$

where *Rf* is the hydraulic fracture risk factor of cap rock, *PHF* is the minimum hydraulic fracture pressure (MPa), equal to the minimum horizontal principal stress (MPa), *Pp* is the pore fluid pressure (MPa).

Five blocks with relatively complete data in the diapir zone and the slope zone in Ledong area were selected for analysis and evaluation. We interpolated the *Rf* values from the 19 wells to generate a contour map of *Rf* (Figure 10). The results show that at the top of XD-A and XD-B reservoirs have developed strong overpressure so that the *Rf* ratio is greater than 1, means that it is still in the period of hydraulic leakage. Blocks XD-C, XD-D, and XD-E maintain hydraulic seal in Huangliu Formation. It can be concluded from the plane variation of the risk coefficient that the closer to the center of the diapir, the higher the fracture risk, which reflects the control effect of the burial depth of the cap rock and the degree of overpressure development on the gas reservoir distribution.

**Figure 10.** Hydraulic fracture risk of Huangliu Formation in the present stress and pressure condition.

## 4.2.2. The Evolution Process of Hydraulic Fracture in Cap Rock

At present, the natural gas in the Yinggehai Basin is enriched in multiple reservoirs, and the enrichment of shallow oil and gas reflects the fracture of cap rock during the historical period, which leads to the migration of natural gas from deep to shallow layers. The risk of cap rock hydraulic fracture in geological history mainly depends on the paleofluid pressure, paleo-in-situ stress, and the strength of cap rock (cap rock fracture pressure) in geological history. Compared with the in-situ stress in present conditions, it is very difficult to recover the palaeo-stress which is controlled by many factors (e.g., depth, tectonic activity, and palaeo-pressure) [55]. Due to the limitation of the original data, the subsequent research of this paper assumes that the tectonic environment is stable after the middle Miocene, and the burial history is combined with the current stress data to analyze the magnitude of the palaeo-stress. Based on that assumption, the vertical principal stress at the same depth varies little in geological history, but the magnitude of horizontal principal stress is mainly composed of tectonic stress and the Poisson effect of overburden, so the strength of tectonic activity has a great influence on it. As stated earlier, the Yinggehai Basin experienced multiphase tectonic evolution, in middle-late Miocene into a period of rapid subsidence and basin tectonic activity is weak overall. The strata of Meishan Formation and above formations generally not develop large faults, and the faults in deep layers mostly have stop activities. The Ledong area is in a relatively stable tectonic environment. The key horizon of this study is the cap layer of the Huangliu Formation and Meishan, which are overpressured strata developed during the period of structural stability. Therefore, the present in-situ stress (Figure 7) combined with burial history can be roughly used in this paper to predict the magnitude of paleo-stress under a stable tectonic setting (Figure 11). Although there are some uncertainties in the prediction of paleo-stress, it can still provide some reference for the evaluation of whether hydraulic fracture occurs in the cap rock. In addition, compaction is the main factor to control the variation of rock tensile-strength with similar mineral content, and compaction is closely related to the stress on the stratum. Therefore, this paper also assumes that the tensile strength of mudstone cap rocks in different geological periods has little difference under the same burial depth. The relationship between differential stress and tensile strength in the study area should also be referred to when studying whether hydraulic fracture occurs in the cap rock in historical periods. As shown in Figure 9, the differential stress from shallow to deep layers is always less than four times tensile strength, which indicates that even in geological historical periods, the hydraulic fracture of intact rock is dominated by tensile fracture. Therefore, approximate vertical fractures developed in the diapir structural zone confirm the conclusion of extensional fracture in the rock [41]. We calculated hydraulic fracture risk factor (*Rf*), the ratio of paleo-fluid pressure, and rock fracture minimum pressure in different periods in cap rock to evaluate whether hydraulic fracturing occurred in the historical period.

**Figure 11.** Burial history of the five blocks in study area and the hydraulic risk analysis of Huangliu and Meishan Formation in geological time. (**a**–**c**) is the XD-A, the palaeopressure was larger than the hydraulic, indicating continuous leakage in whole geological time in both Huangliu and Meishan Formation. The Xd-B show in (**d**–**f**) is similar to the XD-A, the leakage time was later than XD-A, and still leaking today. (**g**–**i**) and (**j**–**l**) is present XD-C and XD-D block, hydraulic fracture occurred about 2 Ma. (**m**–**o**) is the XD-E which is farthest from the diapir, has not reached the hydraulic fracture pressure in the historical period until now.

The paleo-pressure data of hydraulic fracture evaluation are mainly from CNOOC. We evaluated gas reservoirs in the diapir zone and slope zone. Taking XD-A area as an example in the diapir zone, it can be seen that the paleo-fluid pressure is consistently higher than the hydraulic fracturing pressure of rock strata, indicating that with the passage of geological time, the hydraulic fracturing of cap rock continues to occur in Huangliu and Meishan Formation, providing an effective channel for oil and gas migration, enabling natural gas to enter the shallow Ledong Formation and Yinggehai Formation from the deep source rock and finally to form reservoirs (Figure 11b,c). The evolution process of hydraulic fracture of XD-B block is similar to that of the XD-A block. Although the hydraulic fracture started later than XD-A block, both the cap rocks of Huangliu and Meishan Formations were in the stage of hydraulic fracturing after 2 Ma (Figure 11e,f) and finally formed shallow gas reservoirs or showing gas-bearing properties (Figure 11e,f). In relatively distant slope zones, the XD-C and XD-D blocks, in the historical period, hydraulic fracture occurred about 2 Ma in Huangliu and Meishan Formation, but later, as the pressure was released, hydraulic fractures began closing again; only a small amount of oil and gas shows but failed to form oil and gas accumulation (Figure 11h,i,k,l). The XD-E block, which is farthest from the diapir, has not reached the hydraulic fracture pressure in the historical period until now, although the pressure has accumulated to a certain extent (Figure 11n,o). The cap rocks have always been sealed, and the oil and gas have not migrated or diffused through the layers, and finally accumulated in the sandstone of the Meishan Formation (Figure 3). From the whole evaluation results, the evolution of hydraulic fracture of cap rock has obvious characteristics. It can be divided into three categories, "continuous fracturing" in diapir zones, "continuous sealing" in slope zones, and "sealed-fractured-sealed" in between.

#### **5. Discussion**

#### *5.1. The Uncertainty of Calculation in Hydraulic Fracture Risk Factor*

The evaluation method of this study is the FAST method which can be used to evaluate both tensile and shear hydraulic fracture. We first determined the hydraulic fracture mode of cap rock, and then selected the appropriate evaluation method for evaluation. In the evaluation process, we fully applied the formation test data of the oil field to analyze the hydraulic fracture risk of the cap rock under real geological conditions as far as possible. In the measurement of rock mechanics parameters, we also restored the real geological conditions to the greatest extent within the scope of instrument testing.

In spite of our efforts, there is still some uncertainty in the determination of *Rf*, mainly because it is controlled by many factors, including the state of paleo-stress, mechanical properties of rock in historical period, and paleo-fluid pressure. The stress field can be divided into three scales [56]: the first-order stress field mainly comes from the plate driving force; the second-order stress field is derived from major intraplate stress, such as isostatic compensation, glaciation retreat, and lithospheric bend; and the third-order stress field is determined by stress and strain such as faults activity, local intrusion, horizontal detachment, and density inversion. The influences of the various factors described above bring great difficulties to the evaluation of the current stress field, especially the determination of the maximum horizontal principal stress. In our study, the in-situ stress is determined based on two assumptions. Firstly, it is assumed that the in-situ stress in the study area is homogeneous as is the magnitude of the in-situ stress in different locations. Secondly, it is assumed that the influence intensity of various factors on the in-situ stress in the geological history period is the same as that of today, so that the magnitude of the ancient in-situ stress can be obtained from the burial-depth. In addition, the study in this paper ignored the heterogeneity of stratigraphic sedimentation in the same geological history period and assumed a consistent tensile strength of rocks, which was obviously inconsistent with reality. However, due to the limited core samples, we cannot test drill cores at different locations, so more tensile strength data could not be obtained. In theory, at some locations in the cap rock, due to the influence of the rock's mineral composition, it is possible to have lower tensile strength, leading to other fracture modes and lower

hydraulic fracture pressure. Fortunately, the data show that the differential stress is always less than the four times the tensile strength (Figure 9) and the fracture mode of cap rock is mainly extensional fracture.

#### *5.2. Control Effect of Hydraulic Fracturing on Gas Accumulation*

The preservation condition of the cap rock is very important to the hydrocarbon accumulation in the trap, which is mainly reflected in the microscopic sealing ability of the cap rock itself and whether the cap rock is damaged. Scholars have conducted a lot of studies on the cap rocks in Yinggehai Basin [33–38]. The mathematical model and the test method show that the cap rock of Yinggehai Basin has strong displacement pressure, which is enough to seal up the hydrocarbon column of a certain height. However, there are still some traps that fail to be explored due to inadequate preservation conditions. The primary reason of this phenomenon is that the cap rocks have been damaged. In accordance with the process of the hydraulic fracture of mudstone, it is not hard to see that hydrocarbons leak episodically at the geological timescale. In particular, some scholars have found evidence of the existence of hydraulic fractures in the three-dimensional seismic reflection and cores of Yinggehai Basin [36], and the cemented fractures also show multiphase characteristics, which all indicate that fractures are an important channel for fluid migration. In addition, other geochemical parameters in the study area, such as fluid inclusion homogenization temperature, natural gas isotope difference, and quantitative reservoir fluorescence analysis, can also reflect the multi-stage fluid charging caused by the fracturing of mudstone cap rocks in the past.

These phenomena mean that gas accumulation in the study area is actually a process of dynamic equilibrium of accumulation and dispersion. Although oil and gas will be leaked at a certain stage in geological history, as long as the rate of oil and gas charging is greater than the rate of loss, oil and gas can accumulate in traps and even form large and medium-sized oil and gas fields. In the future, if accurate in-situ stress and mechanical properties of cap rock can be obtained based on the analysis of gas generation capacity and dominant migration path, the hydraulic fracture pressure of cap rock can be effectively predicted, which will be an important method to reduce the risk of gas exploration in deep overpressured reservoirs.

In our present study, the hydraulic fracture status of cap rock in different periods is given, but the current data do not completely cover the entire historical period, it is difficult to construct a complete and accurate hydraulic fracture process of mudstone with existing data and means. Further and comprehensive work may be carried out in the future.

It is clear to see from the above formula for calculating hydraulic fracture pressure that the effectiveness of overpressure cap rock is controlled by three types of factors: (1) the in-situ stress factor, (2) the fluid in the formation, and (3) the mechanical properties of the cap rocks. In this paper, we only discuss the effect of overpressure in lithologic traps on the preservation conditions of traps and its effect on gas accumulation in Yinggehai Basin. As we all know, there are many diapir structures developed in Yinggehai Basin [57]. Diapirism formed a series of associated high-angle faults; these faults and diapirs can conduct deep pressure to shallow layers. Under the action of strong overpressure, the periodic rupture and healing of the cap rocks at the top of trap can regulate the fluid pressure in the formation and control the accumulation and loss of natural gas. Moreover, the faults in conjunction with hydraulic fracturin allow fluid to migrate more easily. The seismic reflection fuzzy zone above the Meishan Formation is the evidence of a large amount of hydraulic fracturing. By compacting the hydraulic fracture processes of gas reservoirs or gas-bearing structures in the different structural zones, it can be seen that the diapir zone has a more obvious hydraulic fracture response and higher risk than the slope zone. On the plane, the closer to the diapir structure, the greater the risk of hydraulic fracture. For example, XD-C and XD-D are more affected by diapir activities and more likely to fracture than XD-E. Under the background of the overall lack of large faults in the study area, the tectonic activities of the diapir promote the occurrence of hydraulic

fracture, which is mainly reflected in two aspects: (1) diapir structure has conduction effect on deep overpressure; (2) the diapir structure activity will deform the overburden strata, accompanied by a many structural fractures (small faults and fractures), making mudstones more prone to hydraulic fracture. This is the main reason why hydraulic fracturing is more likely to occur in the diapir zone, and it also explains why only in the diapir zone oil and gas can accumulate in shallow layers, while the natural gas in the slope zone cannot break through to the shallow layers.

#### **6. Conclusions**

In this paper, the hydraulic fracture of the main cap rock in the study area is analyzed based on the in-situ stress, pore fluid pressure, and rock mechanical parameter in the geological historical period and present time. The difference in the evolution process and risk of hydraulic fracture is the fundamental reason for the obvious difference in gas distribution between diapir zone and slope zone.

The research of hydraulic fracturing shows that gas leakage has occurred in cap rocks in the diapir zone throughout geological time and remains in the leakage period like XD-A and XD-B; as a result, the natural gas accumulated in both deep and shallow reservoirs at this locations. However, in the slope zone, except XD-E block, gas leakage has occurred in the Huangliu cap rock and Meishan cap rock at a certain geological time in XD-C and XD-D block. Therefore, gas accumulated only in the Meishan Formation in XD-E, but both in the Huangliu and Meishan reservoirs in XD-C and XD-D.

The tectonic activity of the diapirs weakened the strength of the strata and made them more prone to hydraulic fracturing, thus providing the vertical channel for fluid migration, resulting in differential distribution of natural gas in diapir zone and slope zone. This general phenomenon has two main causes: a. diapirism transfers deep overpressure to shallow layers; b. the activity of diapir cause strata to deform and form structural fractures (small faults and fractures), reduce critical stress condition, and make the cap rock more susceptible to hydraulic fracturing. The slope zones may have better preservation conditions than the diapir zones.

**Author Contributions:** Conceptualization, R.J.; methodology, C.F.; software, Y.J.; investigation, R.J. and C.F.; data curation, Y.J.; writing—original draft preparation, R.J. and B.L.; writing—review and editing, B.L. and X.F.; supervision, X.F.; funding acquisition, R.J. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, grant number 42002152; Science and Technology Project of Heilongjiang Province, grant number 2020ZX05A01.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Nomenclature**


#### **References**

