Introduction

Ultra-deep carbonate formations are increasingly recognized as critical zones for future oil and gas exploration1. Ultra-deep carbonate reservoirs exhibit a complex reservoir space characterized by intricate pore and fracture configurations2,3that has significant implications for exploration and production4. The distribution of reservoir spaces in ultra-deep formations is governed by multiple factors resulting in distinct anisotropic properties, and their formation and preservation mechanisms diverge considerably from those observed in conventional carbonate reservoirs5,6,7. One of the crucial factors that lead to the unpredictable petroleum development pattern of ultra-deep carbonate rocks is the insufficient comprehension of connected pore space8,9. It’s also important for understanding large variation of production capacity between wells10,11,12.

Carbonate hydrocarbon reservoirs exploration has gone through a process from shallow to deep13. Scholle (1983)concluded that there are no hydrocarbon reservoirs in carbonates formations deeper than 3000 m, but with the exploration of deeper carbonates formations, the lower depth limit of hydrocarbon reservoirs has been increasing2,7. In recent years, Chinese companies have made significant discoveries, exploring and developing a series of hydrocarbon reservoirs at depths greater than 7000 m14. In the Qixia formation of the Shuangyushi Tectonic Zone, northwestern Sichuan Basin, gas reservoirs have been discovered at depths exceeding 7800 m15. It is a commonly accepted view that the dolomites in the Qixia formation in the Shuangyishi area are generally modified by hydrothermal fluids2,16. Despite the various studies conducted, there is still no comprehensively unified understanding of the mechanism of pore preservation in the reservoirs. The question of which spaces connect the pores and how to recognize these spaces is an ongoing concern. Zhao suggest that fractures formed by tectonic action can not only directly form fractures that connect pore spaces, but also connect deep and shallow fluids so that reservoirs could be modified11.

Interconnected pores is defined as the portion of a pore network that allows fluids flow easily, which is a critical factor controlling reservoir rock petrophysical properties and heterogeneity17,18. The research methods of connected pores include direct observation and indirect measurement, but some methods are not suitable for ultra-deep carbonate reservoirs19,20. Computed tomography (CT) can reconstruct pores at all scales by combining the results of multiple scans at different scales21,22,23. Through the use of thin section and scanning electron microscope (SEM) pore structure scan be qualitatively described, especially FIB-SEM can be used to characterize pore structures in three dimensional spaces24,25. Parameters obtained from high pressure mercury injection (HPMI) can be used to quantify the pore struc/ture of rock18,26. The rmax (maximum pore throat radius), r35 (the throat radius corresponding to the mercury saturation of 35%, which is considered to be the basis for the division of reservoir seepage units), rapex, etc., but most of them are proposed for clasolite25,27. Which of these parameters is threshold radius that represents the transition from poorly-connected small pores to well-connected large pores in ultra-deep carbonate reservoirs. Nuclear magnetic resonance test (NMR) is usually used to evaluate the pore structure of rock through the T2spectrum, and obtain the movable fluid saturation28,29,30. The testing medium of NMR is water, and the water in the macropores is easy to flow out, so there may be some errors in the NMR characterization of macropores in ultra-deep carbonate reservoirs31.

For the world’s petroleum industry, ultra-deep carbonate reservoirs are crucial exploration areas in the future7,32. The ultra-deep carbonate reservoir in Qixia formation, Shuangyushi area is regarded as one of China’s most significant accomplishments in recent years, with multiple wells in the area yielding gas production rates surpassing 10 × 105m3/d. In this paper, we take the Qixia formation gas reservoirs in Shuangyushi area as an example. Firstly, we analyzes the basic geological characteristics of ultra-deep carbonate reservoir in the Qixia Formation, including rock composition, pore type, etc., basing on core, SEM and thin section. Subsequently, employing high pressure mercury intrusion (HPMI) methods, we investigate key factors influencing pore connectivity, including multi-type specific pore-throat radii, and propose new connectivity evaluation parameters. Combined with fractal dimension and RQI, the effects of pore structure complexity and reservoir quality on pore connectivity of ultra-deep carbonate reservoir are analyzed. Based on the proposed connectivity evaluation parameters, the non-wetting phase seepage behavior of different reservoir types is analyzed, and the permeability contribution patterns and connectivity characteristics of different reservoir types is demonstrated. The characteristics of carbonate reservoirs at different depths are compared, and the changes of carbonate reservoirs with increasing depth are defined. Finally, the comprehensive characteristic maps of different types of ultra-deep carbonate reservoirs are formed. This research well help to predict the gas production pattern and productivity differences between wells.

Geological setting

The Shuangyushi structure area is a part of the Longmenshan pre-folded tectonic zone located on the northern edge of the Yangzi Craton33, with a large number of faults (Fig. 1). The region underwent persistent tension from the Sinian to the Late Triassic periods, and subsequently, multiple phases of extrusion led to the formation of numerous faults distribute in a northeast-southwest direction2. The Qixia formation in the Shuangyushi area is conformable contact with both the Liangshan Formation and the overlying Maokou Formation16. In the middle Permian, the Shuangyushi area was at the edge of a shallow marine carbonate platform, and a large amount of bioclastic and granular were deposited7. After a series of diagenetic evolution, a coexisting stratum of limestone, dolomitic limestone and dolomites was formed, and the original pore almost disappear with a large number of secondary pores appear33.

Fig. 1
figure 1

Geological information map and stratigraphic column map of the study area. (a). Location diagram of Sichuan Basin; (b). Distribution diagram of the tectonic division and basement faults in Sichuan Basin; (c). Distribution diagram of the sedimentary facies in the middle Permian Qixia Formation of northwest Sichuan; (d). Comprehensive histogram of the sedimentation in the middle Permian Qixia Formation of northwest Sichuan.

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Samples and methods

Sample

We viewed the cores of wells ST3, ST8, and ST12 and obtained 80 rock samples from the reservoir sections using wire cutting to minimize the creation of new cracks in the rock (Fig. 1d). Then we tested gas porosity, permeability and captured SEM on each sample, make rock casting thin sections and stain it by alizarin red. Additionally, according to the 4 reservoir types, micropore type, fracture-micropore type, fracture-vug (disolution) pore type, and vug (disolution pore) type occupied in the Qixia Formation, 9 samples were selected and HPMI was tested.

Methods

(1) HPMI.

HPMI testing uses a Quanta Chrome Poremers-60 high pressure mercury intrusion apparatus. The pore throat radius distribution and related parameters were obtained from the HPMI tests, including rmax, r35, average pore-throat radius (ra), drainage pressure, sorting coefficient, and rapex. The pore-throat radius can be obtained using the Washburn Eq. (1):

$$\:r=\frac{2{\upsigma\:cos}\theta\:}{{P}_{c}}$$
(1)

where r is the radius of the pore throat, µm, σ is the interfacial tension; θ is the contact angle, Pc is the capillary pressure, MPa.

The ratio of permeability of pore throat with different radius to total permeability was defined as the permeability contribution rate of the pore throat (LKr, %).

Using the following Eqs. (2, 3), the permeability contribution for different pore-throat radii can be obtained from the HPMI data:

$$\:{L}_{Kr}=\frac{\varDelta\:{K}_{\left(r\right)}}{{\int\:}_{0}^{{r}_{max}}{K}_{\left(r\right)}dr}$$
(2)

where \(\:\varDelta\:{K}_{\left(r\right)}\) is the permeability contributed by the pore throat with radius r in the entire pore network, mD; rmax is the max radius, µm.

Based on the relationship between radius and permeability and Eq. (1), \(\:{L}_{Kr}\), %, can be calculated by Eq. (3):

$$\:{L}_{Kr}=\frac{{\int\:}_{Sj}^{{S}_{j+1}}{r}_{\left(S\right)}^{2}dS}{{\int\:}_{0}^{{S}_{max}}{r}_{\left(S\right)}^{2}dS}$$
(3)

where j is the interval number of the pore throat radii, Sj is the saturation of mercury that intruded in the sample, %.

The\(\:{L}_{Kr}\) can also be calculated by Eq. (5) for mercury injection data.

$$\:{L}_{Kr}=\frac{{{r}_{S}}^{2}S}{{\sum\:}_{0}^{Smax}{{r}_{S}}^{2}S}$$
(4)

Where \(\:{r}_{Sj}\) is the radius corresponding to the Sj, µm.

Figure 2 shows the conversion of the capillary curve into the permeability contribution curve for sample No. 2 based on Eq. (3). Define the SHg with the highest value of permeability contribution in the curve as SHgf.

Fig. 2
figure 2

The mercury injection curve is transformed into the permeability contribution rate curve for sample 2. (a) mercury injection curve. (b) permeability contribution and cumulative permeability contribution curve.

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(2) RQI.

Amaefule introduced the concept of the Reservoir Quality Index (RQI)34. The concept is based on pore throat, pore size and grain size distributions, among other macroscopic parameters. If permeability is expressed in milli-darcies and porosity is expressed as a fraction, the RQI can then be written as:

$$\:RQI=\sqrt{K/{\varphi\:}_{e}}$$
(5)

where RQI are in µm; K is permeability, md; e is effective porosity, %.

(3) Fractal dimension.

Numerous studies have shown that fractal dimension (D) is able to characterize the complexity and self-similarity of pore structure in reservoirs. Therefore fractal dimensions were used to verify the effectiveness and anaylzing the phycial property of the key paramaters in this research. There are many models to calculate fractal dimension, such as the Hausdorff dimension, box dimension, and multifractal spectrum, can be used to characterize fractal geometries. Multifractal characteristics are represented in the form of singularity spectra and generalized dimension spectra, which describe the heterogeneity and connectivity of pore size distributions in porous media. The Hausdorff dimension and Hurst index is mathematically rigorous but hard to calculate35,36,37, whereas the calculation of the box dimension is simple and common38,39,40. The mathematic model of Dbased on MIP as follow41:

$$lg\left( {1 - {S_{Hg}}} \right) = \left( {D - 3} \right)lg{P_c} - \left( {D - 3} \right)lg{P_{min}}$$
(6)

Where, SHg is the mercury saturation corresponding to Pc, %; Pc is the pressure of mercury injection, MPa; Pmin is the minimum pressure of mercury injection, MPa.

Since the fractal dimensions obtained by the HPMI method have segmental characteristics, according to the average porosity of the pores with different fractal property, the corresponding fractal dimension is weighted average, and comprehensive fractal dimension is obtained42. The calculation methods for the total fractal dimension (D) of MIP is shown in Eq. (6).

$$\:D={D}_{1}\frac{{\phi\:}_{1}}{\phi\:}+{D}_{2}\frac{{\phi\:}_{2}}{\phi\:}+\dots\:{+D}_{n}\frac{{\phi\:}_{n}}{\phi\:}$$
(7)

Where, \(\:{D}_{n}\) is the fractal dimension with different fractal characteristic;\(\:\:\phi\:\) is tatol porosity, %; \(\:{\phi\:}_{n}\) is segmental porosity of the pore with \(\:{D}_{n}\) fractal characteristic, %; n is usually less than 3.

Results

Rock types

The previous research results have shown that the ultra-deep reservoir of Qixia Formation in Shuangyushi area is basically composed of Marine carbonate rocks2,16. This time, the reservoir minerals are identified by thin section staining method to determine whether calcite or dolomite (Fig. 3). Based on the mineral composition of the rocks, the rocks in Qixia formation in the Shuangyushi area can be classified into three types of, limestone, dolomitic limestone and dolomite. The dolomite is further divided into 2 subtypes: fine-medium crystalline dolomites (FMD), medium- coarse crystalline dolomites (MCD) (Fig. 3(a)-(g), Table 1). According to the statistics of thin sections, the rocks in reservoir sections is mainly composed of dolomite, accounting for about 90%, while fine-medium crystal dolomite accounts for about 30% and medium-coarse crystal dolomite accounts for about 60%. Dolomitic limestone accounts for about 7%, and Grainstone accounts for about 3% in the reservoir sections. MCD has the highest porosity, 1.40–7.54% with an average value of 3.58%. The permeability of MCD is range between 0.22 and 50.45 mD with an average value of 2.14 mD. FMD’s porosity range from 0.85 to 4.76%, with average value 3.58%. The permeability of FMD is range between 0.74 and 74.13 mD with an average value of 2.34 mD. The porosity of two types of dolomite are different, but the permeability is similar. Through thin section observation, it is found that fractures are common in all dolomites. Therefore, fractures increase the permeability of all types of dolomite, and it is important connecting channels for pore network in ultra-deep carbonate reservoirs.

Fig. 3
figure 3

Rock Types and Reservoir Spaces in the Qixia Formation. (Thin sections: (a)-(g); blue areas represent resin-filled pores; SEM images: (h)-(i); core images: (h)-(k)). (a) Granular micritic limestone with no visible pores, 7312.17 m, ST8 well. (b) Micritic granular limestone with no visible pores, 7313.30 m, ST8 well. (c) Dolomitic limestone showing no visible pores, 7437.47 m, ST3 well (the red area indicates alizarin red stained calcite, while the white area represents dolomite). (d) Fine-medium dolomites with intercrystalline pores (IP), 7462.44 m, ST3 well. (e) Medium-coarse dolomites featuring IP and intercrystalline dissolution pores (DP), 7448.69 m, ST3 well. (f) Medium-coarse dolomites with DP and fractures (F), 7457.51 m, ST3 well. (g) Medium-coarse dolomites with fractures enlarged by dissolution and further dissolution pores (DP), 7457.51 m, ST3 well. (h) Medium-coarse dolomites showing IP and intercrystalline dissolution pores (IDP), 7327.69 m, ST8 well. (i) Medium-coarse dolomites featuring micropores (MP), 7324.23 m, ST8 well. (j) Macroscale fractures observed between 7323.70 m and 7323.76 m, ST8 well. (k) Vugs located between 7076.32 m and 7076.45 m, S12 well.

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Table 1 Rock types of Qixia formation.
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Reservoir space

The reservoir space include micropores, vug and fractures. Based on the genesis and morphological characteristics, micropores are further divided into two subtypes of intercrystal pores and dissolution pores. The edges of solution pores are usually irregular with dissolution remnants of dolomite around. The intercrystal pores typically have regular edges. The rock thin section shows that few micropores are visible in limestone and dolomitic limestone, and micropores with radius less than 3 μm can be observed in SEM. Intercrystal pores are mainly distribute in FMD with pore size concentrated between 20 and 100 μm (Fig. 3). Intercrystal pores and dissolution pores are common in MCD with pore size concentrated between 200 μm and 2 mm. Part of pores and fractures in the FMD and MCD are filled with organic matter, indicating that these pores were used as spaces for oil and gas transport and storage. Vugs are mainly present in MCD, with pore sizes ranging from a few millimeters to tens of millimeters with irregular shape usually. SEM shows that micropores are commonly developed in dolomite, with pore diameters in the range of 20 μm-2 mm. Additionally, dolomite exhibits visible macroscale and microscale fractures formed through multiple phases of intersection, including horizontal, vertical, and oblique fractures.

The reservoir contains four distinct types: micropore type (MPT, sample No. 1, 7), fracture-micropore type (FMPT, sample No. 2, 3, 9), fracture-vug (disolution) pore type (FVT, sample No. 4, 5), and vug (disolution pore) type (VT, sample No. 8, 6) (Fig. 4).

Fig. 4
figure 4

Core photo of the sampling location.

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Micropore type (MPT)

MPT are distributed across all rock types. The reservoir space of MPT is primarily composed of intercrystalline pores, followed by dissolution pores, with few fractures present. The characteristics of micropores have been described in the previous section. The porosity of MPT reservoirs is generally less than 4%, with permeability also below 0.1 mD, resulting in poor pore connectivity.

Fracture-Micropore type (FMPT)

The storage and seepage spaces of FMPT predominantly consist of micropores and numerous fractures. This pore type is mainly found in fine to medium dolomites (FMD), exhibiting porosity less than 4% and permeability greater than 0.1 mD. The presence of fractures enhances both pore connectivity and permeability.

Fracture-Vug type (FVT)

In FVT reservoirs, which are primarily found in medium to coarse dolomites (MCD), vugs and fractures serve as the main storage and seepage spaces. These reservoirs typically have porosity greater than 4% and permeability above 0.1 mD.

Vug type (VT)

Vugs are the primary storage and seepage spaces in VT reservoirs, which are predominantly located in MCD, exhibiting porosity greater than 4% and permeability less than 0.1 mD.

Notably, reservoirs of higher quality are primarily located in MCD, which formed due to hydrothermal activity. This observation suggests that the reservoir formation within the Qixia Formation may be significantly influenced by deep hydrothermal processes2.

Figure 5 illustrates that there is no distinct linear correlation between pore structure and permeability. This observation suggests that the architecture of interconnected pores is complex, and its influence on permeability is more significant than that of porosity alone.

Fig. 5
figure 5

Pore and permeability of Qixia formation.

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HPMI

The HPMI result of samples show the great heterogeneity of the reservoir. Displacement pressure (Pcd) of all samples is range between 0.01 and 0.12 MPa, with average 0.11 MPa. Median pressure (Pc50) is range between 0.15 and 7.39 MPa, with average 3.22 MPa. Maximum mercury saturation (Smax) is range between 25.70 and 96.78%, with average 66.48%. Mercury exit efficiency (We) is range between 6.98 and 67.61%, with average 22.43% (Table 2).

Table 2 MICP characteristic parameter data table.
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The HPMI data indicate significant differences among the samples, suggesting that the pore-throat radius of Qixia reservoirs varies considerably, highlighting substantial heterogeneity. Figures 6 and 7 illustrate the distribution curves of pore-throat radii for all samples, exhibiting a multi-peak pattern. The discontinuity between peaks indicates extreme heterogeneity in the pore network of ultra-deep reservoirs. This heterogeneity is related to the diverse pore types found within the Qixia Formation. The reservoirs have undergone multiple stages of diagenetic and tectonic transformations, such as dolomitization and dissolution, resulting in the formation of various scales of reservoir spaces. As a consequence, the distribution of pore-throat radii becomes heterogeneous.

Fig. 6
figure 6

Capillary pressure curves of various samples. (a) sample with fracture. (b) sample without fracture.

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Fig. 7
figure 7

Pore-throat radius distribution curve for samples. (a), (b) corresponding to Fig. 4 (a), (b).

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RQI and D

The carbonate rocks of the Qixia Formation feature multi-scale pore spaces, including vugs (macropores), pores (mesopores and micropores), and fractures. Each type of pore space exhibits distinct fractal characteristics, contributing to complex fractal nature of the overall sample. We define the fractal dimension of macropores (vugs and fractures) as D1, while the fractal dimension corresponding to mesopores is designated as D2, and the dimension for micropores is denoted as D3 (Fig. 8). The parameter D represents the comprehensive fractal characteristics of the multiscale pore structure within the samples, calculated using Eq. (6). It is important to note that, due to the limited connectivity of micropores, mercury injection is impractical, which may prevent the acquisition of D3 data in some cases. In general, the D1 of the 9 samples in the Qixia formation ranged from 2.62 to 2.99, with an average of 2.83, and the D2 ranged from 2.77 to 2.99, with an average of 2.89. D3 exists in only part of the samples, and almost all D3 are close to 3. This can be attributed to the intricate micropores structure, characterized by significant tortuosity, poor connectivity, and a highly uneven distribution of pore sizes. Consequently, it becomes notably challenging to inject mercury into these micropores, and resulting in the absence of D3 data in certain samples. Based on Eqs. (5) and (6), D of all samples was calculated, ranging from 2.77 to 2.99, with an average of 2.90 (Table 3). RQI can characterize the seepage capacity per unit pore. The RQI of 9 samples is calculated based on Eq. (5). The RQI of the samples ranged from 0.01 to 1.28 μm, with an average of 0.46 μm. The Reservoir Quality Index (RQI) is relatively higher in fracture-pore type reservoirs, range from 0.52 to 1.28, due to their higher permeability and lower porosity. The RQI values do not exhibit significant differences among the other three reservoir types. This is primarily attributed to the overall weak flow capacity of ultra-deep reservoirs, and increased complexity of pore structures caused by the presence of fractures and dissolution vugs. Unlike the reservoirs with relatively homogeneous property19, the RQI alone is insufficient to fully distinguish different reservoir types in ultra-deep carbonate reserviors.

Fig. 8
figure 8

Multi fractal characteristic of sample 2.

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Table 3 Data of D, RQI and FZI of all sample.
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Discussion

The threshold radius of well-connected pore

Pore-throat radius is a crucial factor in determining reservoir petrophysical properties, and many previous studies have identified specific radiu as important parameters for characterizing pore size and petrophysical properties of reservoir17(Table 2). Numerous studies have examined the linear relationship between the square of various special pore-throat radius parameters and permeability, establishing threshold radii based on the degree of correlation between the squares of these radius parameters and permeability26,27. Table 4 shows all the special radius used in this study. Figure 9 shows the relationship between different special radius and permeability. The correlation coefficient between r15 and permeability is the highest, which is 0.84, and that between r25and permeability is 0.83, which indicate that only 15–25% of the large pores have a controlling effect on permeability26,27. For clastic and shallow carbonate reservoirs, rapex and r35typically considered threshold radii indicative of well-connected large pores and poorly connected small pores, with correlation coefficients to permeability generally exceeding 0.926,43. However, statistical analysis of nine samples reveals that the correlation coefficient between rapex and permeability is only 0.67, indicating that rapex cannot serve as the threshold radius in ultra-deep reservoirs.

Table 4 Pore throat radius parameters and corresponding meaning.
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Fig. 9
figure 9

Square of pore-throat radius vs. K.

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CPC15 is the cumulative permeability contribution corresponding to r15, and similarly, CPC25 and CPC35 is the cumulative permeability contribution corresponding to r25 and r35. The square of r15 exhibits the highest correlation coefficient at 0.915. Nonetheless, cumulative permeability contribution analysis suggests that r15 is not the threshold radius (Fig. 9). Figure 10 shows the distribution of various CPC parameters and their relationship with permeability. The average value of CPC15 for the nine samples is 67.24%, with the lowest being 50.07%. This suggests that there are connected pores unfilled at 15% saturation of the mercury, which means that the percentage of connected pores should be greater than 15%, and r15 is greater than the threshold radius. CPC25 are basically close to 100%, with an average 92.73% and the distribution pattern is similar to CPC35, independent of the corresponding permeability. This indicates that the mercury has completely fille the connected pores. The correlation coefficient between square of r25 and permeability is the 0.91 which is close to correlation coefficient between square of r15 and permeability. Thus, r25 may be utilized as the threshold radius for distinguishing well-connected pores from unconnected pores.

Fig. 10
figure 10

CPC radius vs. K.

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The key parameter of pore connectivity

Figure 6 presents the capillary pressure curves of samples from the Qixia Formation. The majority of these curves exhibit pronounced hysteresis, indicative of poor pore connectivity. This contrasts sharply with the smooth profiles typically observed in conventional sandstone or carbonate reservoirs, highlighting the unique characteristics of the Qixia Formation. The lack of a distinct plateau in the curves further underscores the heterogeneity in pore-throat radii within the samples. Ultra-deep carbonate rocks frequently contain numerous poorly connected pores, such as isolated pores within the matrix, making it challenging for the fluid contained within them to escape. However, when fractures intersect these closed pores, they can establish connections with other pores, facilitating fluid flow. Samples containing fractures exhibit lower displacement pressures, often by an order of magnitude, compared to those without fractures. For instance, sample No. 2, which is identified as a fracture-micropore type (FMPT), has a displacement pressure of 0.08 MPa, while sample No. 1, classified as a micropore type (MPT), displays a displacement pressure of 0.14 MPa (Table 2). Thus, fractures are a critical factor in determining pore connectivity within ultra-deep carbonate reservoirs. Quantitative identification of fractures through parameter establishment can aid in evaluating pore connectivity and assessing the productivity of the reservoir.

In this study, we employed the permeability contribution model (as described in Eq. (3)) to calculate the permeability contribution of pores with varying radii based on mercury intrusion capillary pressure (MICP) data. Subsequently, we plotted the distribution spectrum of the permeability contribution.

The permeability contribution curves for all samples exhibit a single-peak shape (Fig. 2). These peaks are typically narrow and correspond to mercury saturation levels between 0% and 35%, indicating that permeability is primarily influenced by larger pores, with only a limited number of smaller pores facilitating fluid flow. The samples No. 1, 6, 7, and 8 have SHgf values of less than 7%, and their mercury saturation levels remain below 70%, suggesting poor inter-pore connectivity. In contrast, the permeability contribution curves for samples No. 2, 3, 4, 5, and 9, which contain fractures, demonstrate broader ranges, typically encompassing mercury saturation levels from 0 to 35%, with SHgf values exceeding 7%. The presence of fractures in these samples enhances overall pore connectivity by allowing mercury to access a greater number of pores.

By comparing samples with and without fractures, we observed that the morphology of the permeability contribution curve effectively indicates whether a sample contains fractures. Additionally, SHgf can be employed to quantitatively assess the presence of fractures in the samples. Figure 11 illustrates a linear correlation between SHgf and permeability, with a correlation coefficient of 0.7295. This finding further confirms that SHgf can be used as a parameter for evaluating pore connectivity within ultra-deep carbonate reservoirs.

Fig. 11
figure 11

SHgf vs. K, red point is semple with fractures, blue point is semple without fractures.

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Relationship between parameters

The objective of conducting a comprehensive interpretation of HPMI tests was to enable the determination of one set of parameters based on another, by establishing correlations between parameters and factors identified through laboratory investigations43.

The fractal dimension is utilized to characterize the complexity of the pore network and describe pore size etc17. By conducting a correlation analysis between the parameters proposed in this study and the fractal dimension, the physical significance of these parameters in characterizing pore size heterogeneity and the complexity of pore networks can be elucidated. Figure 12 illustrates the correlation between the fractal dimension and SHgf. A negative correlation is observed between D1 and SHgf, indicating that since the seepage capacity in rocks is primarily governed by macropores, an increase in D1 directly affects the seepage capacity of the rocks. This negative correlation further suggests that SHgf can effectively describe the seepage capacity of the pore network in the samples.

Fig. 12
figure 12

Relationship between fractal dimension and SHgf.

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Elevated values of D2 and D3 indicate the complex networks of mesopores and micropores present within the samples. This complexity is primarily attributed to increased tortuosity and a more intricate distribution of pore radii in the mesopores and micropores. Additionally, a clear negative correlation exists between D and SHgf, with a correlation coefficient of 0.77. The strong correlation between D and SHgf implies that SHgf is capable of effectively characterizing the seepage characteristics of the full-scale pore network within the samples.

Figure 13 illustrates the correlation analysis between RQI and SHgf, showing a lack of significant correlation between the two parameters. RQI is a metric for assessing the seepage capacity of individual pores within the samples. Previous analyses have confirmed that only a small proportion (< 20%) of the macropores and fractures function as conduits for fluid flow. These macropores and fractures contribute to the formation of high-permeability channels, which complicates fluid flow through the smaller mesopores and micropores20. However, RQI is calculated for the entire pore network, encompassing macropores, fractures, mesopores, and micropores26. Consequently, its value does not accurately reflect the flow capacity of macropores and fractures alone. Therefore, RQI is not suitable for characterizing the multiscale pore network within the Qixia Formation, which contains a diverse range of pore sizes from micro to millimeters.

Fig. 13
figure 13

Relationship between fractal dimension and SHgf.

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Mechanism analysis of differences in permeability contribution distribution

This analysis of mercury seepage behavior during the mercury injection process elucidates the formation mechanisms responsible for variations in permeability contribution distributions and SHgf across different reservoirs (Fig. 14; Table 5).

Fig. 14
figure 14

Fluids seepage pattern and corresponding permeability contribution pattern of four reservoir types.

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Table 5 Comprehensive characteristics of reservoir connectivity.
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MPT.

Figure 14 illustrates the fluid flow process and the corresponding permeability contribution pattern in the MPT. Due to poor connectivity within the pore network, fluids are only able to invade a limited number of well-connected large pores during the AB stage. In contrast, poorly connected small pores remain inaccessible to the fluids, leading to low incoming mercury saturation. Consequently, the well-connected large pores account for nearly all the permeability. The permeability contribution distribution exhibits a narrow single peak, with SHgf values remaining below 7%.

FMPT.

In the FMPT reservoir, fluids first invades easily into the relatively large pores and fractures during the AB stage, that is correspond to the peak of permeability contribution curve with high permeability contribution, and the SHgf is greater than 7%. Due to the communication effect of fractures, the fluids can continue to invade the small pores near the fractures through the fractures after filling the relatively large pores during the BC stage, and the corresponding permeability contribution is much smaller than that of the large pore. However, the small pores far from the fractures cannot be filled by the fluids due to poor connectivity, resulting in the saturation of the fluids less than 100%.

VT.

Despite the absence of fractures in the VT reservoir, the pore connectivity including large pore part small pores and is still good due to the good connectivity of dissolution pores and large porosity. After the fluids invades the large pores (AB stage), it can continue to fill part of the small pores with better connectivity, and this part of the small pore volume accounts for less (BC stage). The contribution curve formed in the AB section is a narrower peak, the SHgf is less than 7%, and the distribution range of the BC section is narrower.

FVT.

The FVT reservoir is the type with best pore connectivity among all reservoir types due to the well-connected dissolved pores which is predominant pore type, and numerous fractures in the reservoirs. Actually, most pores in this reservoir type have good connectivity, regardless of their size, because of numerous fractures. After filling the large pores and fractures (AB stage), the fluids will fill the small pores continually (BC stage). The permeability contribution curve has a widest range among all type and the maximum fluids saturation can approach 100%. The AB stage is a narrower peak with SHgf greater than 7%. Since the permeability is mainly contributed by large pores, the permeability contribution in BC stage is with low value. The point of C can be very close to 100%.

Comparison with shallow and other deep carbonate rocks

Carbonate rocks exhibit significant differences in pore types across varying depths and regions. These differences are primarily influenced by the sedimentary environment of the rock, as well as subsequent diagenesis and tectonic activities. By summarizing the characteristics of carbonate reservoirs at different depths and in various regions, we compare the properties of ultra-deep carbonate reservoirs with those of medium-depth carbonate reservoirs.

Table 6shows that as depth increases, the characteristics of the carbonate reservoir transition from limestone to dolomite. Concurrently, porosity decreases, and pore types evolve towards intercrystalline pores, accompanied by an abundance of solution pores, cavities, and fractures. The formation of ultra-deep carbonate reservoirs in the Qixia Formation is closely linked to the dissolution of freshwater, dolomitization, and the influence of deep hydrothermal fluids, as well as tectonic activity2,12. Significant dissolution pores and vugs were created through freshwater dissolution. During the Indochinese and Himalayan tectonic movements, the reservoirs in the Qixia Formation experienced stress, resulting in the formation of faults and microfractures that enhanced pore connectivity. Additionally, hydrothermal fluids have further transformed the reservoirs, leading to the development of numerous intercrystalline pores, intraparticle pores, and intercrystalline dissolution pores, ultimately resulting in the predominant rock type within these reservoirs being dolomite.

Table 6 Comparison of physical properties of carbonate reservoirs at different depths.
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The reservoir depth of the Dengying Formation is approximately 5000 m, primarily consisting of dolomite, while also containing a significant amount of limestone. Notably, this formation features a large number of algal moldic pores, which are largely absent in the ultra-deep reservoirs of the Qixia Formation. In contrast, the Khasib Formation, with a reservoir depth ranging from 2500 to 2800 m, is classified as a middle-depth reservoir. Its characteristics differ significantly from those of the ultra-deep reservoirs in the Qixia Formation. The Khasib Formation is predominantly composed of limestone, exhibiting a substantial presence of primary intergranular and moldic pores, resulting in porosity levels that are considerably greater than those found in the reservoirs of the Qixia Formation. The reservoir characteristics of the Yingshan Formation in the Tarim Basin are largely similar to those of the Qixia Formation, with both being significantly influenced by tectonic modification. Fractures play a crucial role in the formation of these reservoirs. In the Yingshan Formation, reservoirs are predominantly characterized by dissolution vugs developed along faults, further underscoring the critical importance of fractures in ultra-deep carbonate reservoirs.

Conclusion

This study takes the Qixia Formation in the Shuangyushi Tectonic Belt of the Sichuan Basin as a case example. The characteristics of four reservoir types, the parameters of connected pore throat radii, and the connectivity evaluating method for different reservoir types were studied. The specific conclusions are as follows:

  • Ultra-deep carbonate reservoirs have multiple scale pore and seepage channel including intercrystal pore, dissolution pore, vug and fracture, etc., forming four reservoirs type, MPT, FMPT, VT, and FVT, which is characterize with significant non-homogeneous.

  • The connectivity between pores in ultra-deep carbonate reservoirs is poor, the permeability of these reservoirs is predominantly controlled by large pores with excellent connectivity and fractures. r25 represents the threshold radius between the well-connected large pores and the small pores with poor connectivity.

  • The proposed parameter, SHgf, can comprehensively characterize the seeape capacity and complexity of pore networks, and is suitable for the connectivity analysis of pore networks that coexist with factures and pores at multiple scales.

  • SHgf can be used to quantitatively distinguish whether the fractures are abundant in the reservoirs by determining whether the value is greater than 7%.

  • By analyzing the seepage pattern of fluids, the permeability contribution distribution model of four reservoir types and comprehensive characteristics of reservoir connectivity (Table 5) is analyzed, which can be use as a criterion to evaluate the pore connectivity in reservoirs.