Introduction

The wide distribution and substantial exploration potential of carbonate reservoirs have attracted the research interest of many geological scientists (Li et al., 2020a, 2020b; Chen et al., 2022). Carbonate rocks are characterized by wide distribution, multiple rock types, rapid phase transformation, and general dolomitization (Wei et al., 2022). For carbonate rocks, researchers have conducted numerous studies from various aspects including sedimentary rhythm, lithofacies combination, hydrocarbon source rock evaluation, reservoir space, and seepage characteristics. These studies indicate that carbonate rocks are both source rocks and reservoirs as well as important areas of tight oil and shale oil exploration (Hamd et al., 2022; Rashid et al., 2022). However, as carbonate reservoirs are mainly affected by sedimentation and diagenesis, their heterogeneity is very strong, generating a very complex pore structure (Jarvie et al., 2007; Wang et al., 2020a, 2020b; Tan et al., 2021). The complexity of pore structure determines the fluidity of oil and gas. Hence, determining the complexity of pore structure is crucial for reservoir evaluation (Liu et al., 2020; Zhang et al., 2020a, 2020b, 2020c; Hu et al., 2022a, 2022b; Pan et al., 2022; Shi et al., 2022). Moreover, since 2013, after occupying the Marsel exploration area in the Chu-Sarysu Basin, Geo-Jade Petroleum Corporation partnered with the China University of Petroleum (Beijing) to conduct numerous exploratory well deployments and experimental studies to obtain a deeper understanding of the carbonate reservoirs in this area. However, the related results were rarely reported. Therefore, summarizing and evaluating the pore structure characteristics quantitatively in this area is necessary.

Currently, several methods are available for studying the pore structure characteristics of carbonate rocks. For example, x-ray diffraction (XRD) is used to analyze mineral composition (Li et al., 2020a, 2020b; Yang et al., 2020). Casting thin section analysis and SEM can be used to identify lithology, pore throat type, and connectivity (Dou et al., 2018; Wang et al., 2019). High-pressure mercury injection (HPMI) can be used to quantitatively determine nitrogen adsorption, carbon dioxide adsorption, pore volume, and pore throat characteristics as well as to obtain fractal dimension (Mastalerz et al., 2017; Chang et al., 2021; Zhou et al., 2021). Fractal dimension theory can then be used to determine the complexity of pore network and the contribution of various pore parameters to pore heterogeneity (Sahouli et al., 1996; Fu et al., 2017; Hassan et al., 2020). Computed tomography (CT) scanning can distinguish pore types, simulate fluid flow in pore spaces, and demonstrate the spatial characteristics of pore spaces and fractures using a three-dimensional perspective (Sok et al., 2010; Zhang et al., 2022). Imaging logging can characterize natural fractures and identify their characteristics and occurrence (Aghli et al., 2018; Xu et al., 2020). The aforementioned methods adopt different principles; hence their applications differ. Considerable errors will be encountered if only a single method is used to analyze pore structure characteristics (Hu et al., 2020). Therefore, various methods are used in this study to characterize pore structures comprehensively.

Mandelbrot (1975) proposed the fractal theory (Degiorgio et al., 1984; Brandano and Civitelli, 2007). Several theoretical and experimental studies have shown that the pore structures of a reservoir posses fractal properties. Fractal theory can thus be used to describe pore structures quantitatively, and it is an important parameter in describing rock pore evolution and studying pore properties and throat characteristics (Lai and Wang, 2015; Sakhaee-pour and Li, 2016; Li et al., 2017). Currently, the fractal dimension obtained through HPMI is 2–3. The closer it is to 3, the stronger the heterogeneity is. The closer it is to 2, the weaker the heterogeneity is (Pan et al., 2021). The carbonate rocks in the Marsel exploration area are tight reservoirs; hence, HPMI has been used to analyze the fractal characteristics of the tight rocks. HPMI allows good characterization of the fractal properties of pore throats and connected pores; it has thus become the preferred method for calculating the fractal dimension of pore structures (Li et al., 2010, 2020a, 2020b; He et al., 2016; Zambrano et al., 2017). In addition, as high-resolution pore image data acquisition is more intuitive, convenient and statistically more representative, it is widely used to characterize pore fractal dimension quantitatively (Peng et al., 2011; Xu et al., 2014a, 2014b). Xie et al. (2010) used SEM images to systematically describe the micropore structure of a carbonate reservoir through fractal and multifractal methods. Qin et al. (2021) used fractal and multifractal methods to characterize quantitatively different structures of vesicular andesite reservoir samples, providing a basis for predicting high-quality reservoirs. Xin et al. (2022) used fractal dimension to characterize the pore structure characteristics of ultradeep and dense reservoirs quantitatively based on nuclear magnetic resonance T2 spectrum data. Recently, it has gradually developed from a typical two-dimensional pore quantitative characterization to the application of multifractal parameters to a three-dimensional micropore description (Xie et al., 2010; Zhang et al., 2020a, 2020b, 2020c; Qin et al., 2021; Xin et al., 2022). Therefore, HPMI data and SEM images were used in this study to analyze the fractal dimension of regional reservoir pore structure.

The foregoing discussion shows that research on pore structure characteristics of carbonate reservoirs in the Marsel exploration area is lacking. Herein, the mineral composition and pore throat characteristics were first analyzed via conventional core photos, XRD, SEM, and HPMI. Moreover, the pore structure characteristics were characterized qualitatively, semiquantitatively, and quantitatively. Imaging logging and casting thin section analysis were used innovatively to analyze the shape and characteristics of fractures; the fractal dimensions obtained through SEM and HPMI were used to study the heterogeneity of pore structure. The influence of fractal dimension on pore structure parameters is then discussed. Finally, the formation mechanism of the high-porosity and high-permeability zone in the study area is discussed. Therefore, a new understanding of the pore structures of carbonate reservoirs in this area and in other areas is presented in this study, facilitating the hydrocarbon development of carbonate reservoirs.

Geological Setting

The Chu-Sarysu Basin, which is a typical inland basin, is located in the south-central part of Kazakhstan. There are several structural units in the basin, and the basin area reaches 16 × 104 km2 (Brunet et al., 1999; Jaireth and Hustone, 2010; Pang et al., 2016; Fig. 1b). The basin is a long strip that is roughly distributed in the NW–SE direction, wide in the west and narrow in the east.

Figure 1
figure 1

Geographical location maps of the (a) Marsel exploration area and (b) Chu-Sarysu Basin, Kazakhstan. (c) Top structure of the Carboniferous system in the Marsel exploration area. (d) Comprehensive stratigraphic histogram of the Chu-Sarysu Basin, Kazakhstan (modified from Zhao et al., 2017a, 2017b; Li et al., 2018; Zhang et al., 2018)

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The Marsel exploration area, measuring 1.85 × 104 km2, has a square distribution in the southwestern region of the Chu-Sarysu Basin, spanning the Kokpansor Depression and the Suzak Baykadam Depression (Bykadorov et al., 2003; Zhao et al., 2017a, 2017b; Zhang et al., 2020a, 2020b, 2020c; Fig. 1a). Based on its structural style and characteristics, the interior of the Marsel exploration area can be divided into three small areas (Fig. 1a), namely, the squeeze uplift zone in the east, which is characterized via deep and large faults close to the basement; the stratum, which is strongly uplifted and denuded; and a series of developed NW-trending reverse faults. Presently, the Marsel exploration area is the key natural gas exploration field in the Chu-Sarysu Basin. Its west and northwest host slope depression zones with gentle strata that exhibit weak uplift and denudation. A small number of NE-trending reverse faults are developed, and strong dolomitization and dissolution are developed in some areas, which are potential carbonate gas reservoir exploration targets. To the south is the uplift slope zone, in which the stratum has been uplifted and denuded. Moreover, a series of NW-trending reverse faults and normal faults have been developed, resulting in the formation of fault-nose and fault-anticline structures. The overall exploration degree of the area is low (Zhang et al., 2018).

The basement of the Chu-Sarysu Basin comprises lower Paleozoic metamorphic crystalline rock, and the sedimentary caprock includes the upper Paleozoic, Mesozoic, and Cenozoic (Bykadorov et al., 2003). Of these, the upper Paleozoic is the main caprock system of the basin and the main oil-bearing reservoir system. Therefore, the main target layer of this study is the Lower Carboniferous (Fig. 1d), which contains the Tournasian (C1t), Visean (C1v), and Serpukhovian (C1sr) stages from bottom to top. The Visean stage is the Mississippi stage, with a time limit of 346.7–330.9 Ma. This set of strata can be divided into three sets of stratigraphic units, C1v1, C1v2, and C1v3, from bottom to top. The C1v1 stratum is approximately 55–125 m and contains primarily limestone. The C1v2 stratum is approximately 50–190 m, with limestone developed at the top and bottom, marl with high argillaceous content, and argillaceous crystal limestone developed at the bottom. The C1v3 stratum is approximately 45–140 m, comprising mainly argillaceous limestone and dark-gray micritic limestone. The Serpukhovian stage is the Late Mississippian deposit with an age range of 330.9–323.2 Ma. The overall thickness of the stratum is approximately 100–200 m (Cook et al., 2007; Pang et al., 2014). Based on the differences in its main lithofacies characteristics, it can be divided into four sections from bottom to top: the lowermost reef section, which is mainly marl; reef limestone, which is the main lithofacies of the reef limestone section; granular limestone, which is developed in the lower segment of gypsum salt rock; and the evaporite section, which comprises mainly gypsum, anhydrite, salt rock, and other lithofacies. The main source rocks are distributed mainly in C1v and C1sr, with a wide distribution area and large thickness. The lithology contains limestone that is approximately 160–405 m thick (Xu et al., 2014a, 2014b; Li et al., 2018).

Samples and Methods

Samples

From six wells (A2, K5, K6, P18, T6, and T1) in the study area, 226 core samples were collected, and plunger samples were made. All samples were collected from carbonate rocks in the C1sr and C1v horizons. Figure 1c shows the location of each well. Of the collected samples, 226, 10, 13, and 18 samples were tested via conventional petrophysical measurements and cast thin section analysis, XRD, SEM, and HPMI, respectively. All tests were conducted at the Central Asia Institute of China Exploration and Development Research Institute. In addition, imaging logging of well A2 was performed by the Schlumberger Company to study its fracture characteristics.

Experimental Methods

A D8 ADVANCE X-ray diffractometer was used to identify the whole-rock minerals of 10 samples, and the contents of various mineral components and clay minerals in sedimentary rocks were obtained. Samples were crushed to 200 mesh before the experiment. The scanning speed of the instrument, the step size, and angle range were 2°/min, 0.02°, and 2°–60°, respectively (Zhou et al., 2021). The porosity and permeability of 226 samples were measured using an ES-V gas permeability meter. Porosity was determined via the helium expansion method, and the permeability was determined by measuring the air flowing through the sample. An Axioskop 40 POL polarizing microscope was used to determine the cast thin section analysis of 12 samples. Prior to the experiment, the sample was dyed with blue epoxy resin and quantitatively analyzed using a CIAS-2007 image analyzer (Chang et al., 2021). A Zeiss EVO MA15 scanning electron microscope was used to analyze and test the 14 samples. Before the experiment, the samples were cut into dimensions of 1 × 1 × 0.5 cm and polished with an argon ion beam for observation (Qiao et al., 2022). A 9505 mercury porosimeter was used to test the 18 samples. Prior to the test, the samples were cleaned with ethanol, dried, and placed into the head of the measuring instrument, before applying different pressures to force mercury to enter the pores. Mercury inlet saturation was recorded under different pressures to obtain a series of parameters, including mercury inlet saturation, sorting coefficient, and pore volume. The imaging logging data were normalized statically and dynamically to generate high-resolution color images. Different image colors can reflect fluid complexity (Lai et al., 2018a, 2018b; Wang et al., 2020a, 2020b). Subsequently, the Techlog software was used to fit the sinusoidal curve and manually characterize the cracks (Lai et al., 2018a, 2018b).

Theory of Calculating Fractal Dimension by HPMI

Currently, several experimental models and methods, including the thermodynamic, Frenkel–Halesy–Hill, and Brunauer–Emmett–Teller models, are used to calculate fractal dimension (Pfeifer, 1990; Yang et al., 2014; Jiang et al., 2016; Zhao et al., 2017a, 2017b; Wang et al., 2018). Of these, the gas adsorption method of the Frenkel–Halesy–Hill model has proven to be the most effective method (Pfeifer, 1990; Sun et al., 2016).

During the experiments, interfacial tension is generated when immiscible liquids come in contact, and the pressures on both sides are not equal. The liquid with a concave liquid surface bears greater pressure than the contact liquid. This pressure difference is called capillary pressure (Pc), which is expressed as:

$$\begin{array}{*{20}c} {P_{{\text{c}}} = P_{{{\text{nw}}}} - P_{{\text{w}}} } \\ \end{array}$$
(1)

where Pnw represents the pressure borne by the nonwetting-phase fluid, and Pc and Pw represent the internal pressure of the wetting-phase fluid, MPa. Pc can be calculated according to Laplace’s equation as:

$$\begin{array}{*{20}c} {P_{{\text{c}}} = \sigma_{L} \left( {\frac{1}{{R_{1} }} + \frac{1}{{R_{2} }}} \right)} \\ \end{array}$$
(2)

where σL represents the interfacial tension (N/m), and R1 and R2 represent the principal radii (m) of curvatures of a point on the curved surface. For an equal-diameter capillary with R1 + R2 = R and r = Rcosθ, Eq. 2 can be expressed as:

$$\begin{array}{*{20}c} {P_{{\text{c}}} = \frac{{2\sigma_{L} \cos \theta }}{r}} \\ \end{array}$$
(3)

where θ is the wetting contact angle (°), and r is the capillary radius (m). Equation 3 gives the main formula for analyzing a mercury injection curve. The formula used to calculate the fractal dimension using mercury injection data is derived as:

$$\begin{array}{*{20}c} {S_{{\text{w}}} = \left( {\frac{{P_{{\text{c}}} }}{{P_{{{\text{min}}}} }}} \right)^{{D_{1} - 3}} } \\ \end{array}$$
(4)

where Pmin is the capillary pressure (MPa) that corresponds to the maximum pore throat radius of the reservoir rock, and Sw is the saturation (%) of the reservoir rock. This formula is converted to logarithmic form to obtain:

$$\begin{array}{*{20}c} {{\text{lg}}S_{{\text{w}}} = \left( {D_{1} - 3} \right){\text{lg}}P_{{\text{c}}} - \left( {D_{1} - 3} \right){\text{lg}}P_{{{\text{min}}}} } \\ \end{array}$$
(5)

As shown in Eq. 5, lgSw and lgPc exhibit good correlation when the pore structure of a reservoir rock has fractal characteristics. Moreover, if the two are linearly correlated, the pore fractal dimension D1 can be obtained using the slope of the line.

First, HPMI experiments were performed on the core to obtain mercury injection data. The obtained data were then processed according to Eq. 5. Finally, the data points in the scatter diagram were linearly fitted. For fractal cores, D1 was calculated using the slope K = D1 − 3. The closer the fractal dimension is to 3, the lower is the fractal fitting degree (Jiang et al., 2016).

According to Eq. 5, D1 can be obtained, which is calculated using the slope of a straight line fitted using all logarithmic scatter points. According to the curve shape of the scatter diagram, the fractal dimension D of the piecewise linear regression is piecewise fitted, and D2 and D3 are calculated. D is calculated as:

$$\begin{array}{*{20}c} {D = D_{2} \cdot S_{{\text{w}}}^{\prime } + D_{3} \cdot \left( {S - S_{{\text{w}}}^{\prime } } \right)} \\ \end{array}$$
(6)

where Sw′ is the saturation (%) of wet facies in the coarse pore throat of a reservoir rock D is the fractal dimension of the piecewise linear regression, D1 is the overall linear regression fractal dimension of the core pore structure, D2 is the fractal dimension of the coarse pore throat, D3 is the fractal dimension of the fine pore throat, and S is the maximum mercury saturation (%) of the core.

Theory of Calculating Fractal Dimension by SEM

From the perspective of image analysis, high-resolution pore images are obtained via SEM, and pore structure parameters are counted quantitatively to evaluate the characteristics of pore heterogeneity (Xie et al., 2010; Peng et al., 2011; Xu et al., 2014a, 2014b; Qin et al., 2021). In this study, a professional image processing software, JMicroVision, was used to obtain pore structure parameters quantitatively from SEM images. It is a powerful image acquisition, processing, and analysis software that can extract the perimeter, area, number of pores, and other parameters of different regions and types of pores, making it very convenient and effective.

The high-resolution image obtained via SEM is a grayscale image, which can identify different types of pores. Distinguishing pores from the skeleton is necessary to obtain the pore structure parameters quantitatively. Threshold segmentation is the most commonly used pore segmentation method, which is performed mainly in two steps. First, a reasonable threshold is determined. Pixels with a gray value less than the threshold in the image are then divided into pores, and those with a gray value greater than the threshold are divided into backgrounds (Xu et al., 2014a, 2014b). Based on the above steps and fractal theory, the pore fractal dimension can be calculated.

Previous research results indicate that if the pore morphology in a sample image has fractal characteristics, the pore area and its equivalent perimeter have the following relationship (Voss et al., 1991):

$$\begin{array}{*{20}c} {{\text{Lg}}P = \frac{{D_{0} }}{2}{\text{Lg}}S + C} \\ \end{array}$$
(7)

where P and S are the equivalent perimeter and area of any polygon in the image, C is a constant, and D0 is the fractal dimension of pore morphology that correspond to the image.

Results

Mineral Composition

Based on the XRD analysis results obtained for the samples, it was concluded that the content of different minerals in the target reservoir considerably changes. Calcite was the main mineral type, constituting 38.0% of all minerals (Fig. 2a), with dolomite, quartz, and feldspar contents of 22.7%, 21.6%, and 12.1%, respectively. The content of pyrite and clay minerals was less in a single rock sample. The content of clay minerals ranged from 0.84 to 7%, among which the content of illite/smectite mixed layers (I/S) was the highest (41.2%), followed by illite (35.5%), and chlorite (23.3%). Kaolinite or montmorillonite was not detected in the sample (Fig. 2b).

Figure 2
figure 2

(a) Mineral and (b) clay composition of the 10 samples (some data from Zhang et al., 2018)

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Conventional Petrophysical Measurements

A very poor correlation was observed between the porosity and permeability of carbonate samples in the study area, which were both generally low (Fig. 3a). This indicates that the entire pore network controls permeability. Owing to the development of microfractures, the permeabilities of some samples were abnormally high, and those of samples without microfractures were mostly < 0.1 mD.Footnote 1 Generally, this is because different sedimentary environments determine the difficulty of carbonate reservoir reconstruction in the process of later diagenesis and tectonic movement. Moreover, it controls the formation and spatial combination of pores, fractures, and karst caves, which result in a complex pore permeability relationship of the carbonate reservoir (Westphal et al., 2004; Haines et al., 2016).

Figure 3
figure 3

(a) Intersection diagram of porosity and permeability. (b) Porosity distribution histogram. (c) Permeability distribution histogram

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The porosity of the samples ranged from 0.1 to 20.8%, of which 61.5% samples had a porosity of < 1% (Fig. 3b). The average permeability was 14.10 mD (Fig. 3c). Most samples were very dense; however, the maximum porosity and permeability reached 20.8% and 18.8 mD, respectively, in well K6 with a depth of 1522.85–1525.05 m. Overall, carbonate rocks can be classified as tight reservoirs; however, they have some high-porosity and high-permeability zones (their genesis is described in detail below in Section “Causes of High-Porosity and High-Permeability Zones”). Overall, according to the oil and gas industry standard of the People’s Republic of China: Oil and gas reservoir evaluation method (SY/T 6285-2011) drafted by Ren et al. (2011), the reservoir in this area is an ultralow-porosity and ultralow-permeability carbonate reservoir.

Pore Characteristics

Pore Characteristics by Core Observation

The core observations showed that most cores were dense and of a cryptocrystalline structure (Fig. 4) with highly developed fractures (Fig. 4a and h). Calcite (Fig. 4c) and anhydrite (Fig. 4e and h) commonly filled the fractures. The specific characteristics of each core photo are as follows: from Figure 4a, a sawtooth suture structure can be seen, and two discontinuous straight split fractures can be seen in the middle with maximum fracture width of 2 mm and maximum length of 10 cm, which were fully filled with white gypsum. The crystal cave filled with other crystal gypsum can be seen sporadically, the maximum crystal cave being 2 × 50 mm, and a small amount of bioclastic fossils is irregularly distributed in the whole section (Fig. 4b). As shown in Figure 4c, a large karst cave can be seen in the middle with dimensions of 80 × 100 mm, which is fully filled with white euhedral crystal calcite. Figure 4d shows a wavy suture structure. As shown in Figure 4e, there is a middle hole at 0.35 m from the top with size of 4 × 10 cm, which is fully filled with gypsum. As shown in Figure 4f, 1.01 m away from the top, there is a middle hole with size of 4 × 6 cm, which is fully filled with mud. As shown in Figure 4g, the argillaceous limestone exhibits horizontal bedding. As shown in Figure 4h, there are two distinct oblique fractures and one fracture that is fully filled with gypsum.

Figure 4
figure 4

Observations of carbonate surfaces: (a) 2340.23–2343.85 m, limestone, cryptocrystalline structure, fracture, suture. (b) 2340.23–2343.85 m, limestone, cryptocrystalline structure, paleontological fossils. (c) 2497.30–2498.16 m, dolomitic limestone, cryptocrystalline structure, karst cave fully filled with calcite. (d) 2499.56–2501.00 m, siliceous limestone, silty structure, suture. (e) 2600.42–2603.60 m, limestone, argillaceous structure, middle hole fully filled with gypsum. (f) 2600.42–2603.60 m, limestone, argillaceous structure, middle hole fully filled with argillaceous. (g) 2604.55–2605.08 m, argillaceous limestone, argillaceous crystal structure, horizontal bedding. (h) 2607.63–2608.50 m, bioclastic limestone, bioclastic structure, oblique fracture, gypsum full filling

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Pore Characteristics Derived from Cast Thin Sections

After analyzing the cast thin section information for the 226 rock samples, it was concluded that the lithology in this area comprises mainly fine-grained limestone, bioclastic limestone and silty limestone. Moreover, the lithology contains a small amount of micritic limestone, sandy limestone, dolomitic limestone and calcareous dolomite (Fig. 5).

Figure 5
figure 5

Cast thin section images: (a) K5, 2015-00,214, 1681.2 m, gray fine-grained limestone, microcracks. (b) K6, 2015-03,352, 1522.85 m, gray fine-grained limestone, solution pore. (c) K5, 2015-00,230, 1687.5 m, gray bioclastic limestone, semifilled joints. (d) K6, 2015–03,402, 1720.61 m, dark-gray bioclastic limestone, structural fracture. (e) K5, 2015-00,255, 1733.7 m, gray dolomitic silty limestone, microcracks. cavity holes. (f) P18, 2015-00,189, 1574.8 m, dark-gray silty limestone, semifilled joints. (g) A2, 2015–00,271, 2326.55 m, dark-gray silty limestone, body cavity hole. (h) K6, 2015–03,350, 1522.2 m, gray silty limestone, solution pore. (i) K5, 2015–00,204, 1678.7 m, dark-gray micrite limestone, microcracks. (j) K6, 2015–03,362, 1524.25 m, gray sandy limestone, solution pore, body cavity pore. (k) K5, 2015-00,248, 1730.15 m, gray dolomitic limestone, cavity hole. (l) K5, 2015–00,259, 1734.8 m, dark-gray calcareous dolomite, microcracks

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The reservoir space types of the Carboniferous carbonate reservoir in this area are complex and diverse. The primary pores were mainly biological cavities (Fig. 5e, g, j and k). The pore size was approximately 10–60 μm, with different sizes and irregular shapes. The primary pore diameter was small, containing mostly isolated individuals, with poor connectivity and weak seepage capacity. The secondary pore spaces, such as solution pores and fractures, are the main reservoir spaces in this area. The secondary solution pores in this area were mainly intergranular solution pores, intragranular solution pores (Fig. 5b, h and j), and microfractures (Fig. 5a, e, i and l), with pore diameter of approximately 30–80 μm. Structural fractures are relatively developed in this area (Fig. 5d), which can increase its permeability. However, some structural fractures are filled with calcite (Fig. 5c and f), destroying the effectiveness of fractures and reducing permeability.

For gray fine-grained limestone, the bioclastic in the rock was mainly echinoderms and brachiopods. The matrix was mainly argillaceous calcite, partially cemented by bright calcite. Terrigenous clasts comprised silty quartz and feldspar, which mainly developed microcracks and intergranular dissolved pores (Fig. 5a and b). For gray bioclastic limestone, the organic argillaceous matter in the rock was distributed in a laminar form, and the terrigenous debris comprised rock debris and silty quartz and feldspar. The bioclastic was dominated by echinoderms, which mainly developed semifilled fractures and structural fractures (Fig. 5c and d). The calcite in the silty limestone was in the shape of euhedral grains, and the gypsum was distributed in a porphyritic and uneven manner, which mainly developed solution pores, microcracks, body cavity pores, and semifilled joints (Fig. 5e, f, g and h). In the sandy limestone, the sandy debris in the rock was nearly round or short strips and the composition was argillaceous calcite. The particle size was mostly 0.125–0.25 mm. The sand debris was composed of powdery calcite and a small amount of gypsum, which mainly developed intergranular dissolved pores and body cavity pores (Fig. 5j). The average homogenization coefficient for the 12 samples was 0.64, the average pore diameter was 42.06 μm, and the average sorting coefficient was 20.49.

Pore Characteristics Derived from SEM Images

SEM images of varying magnification showed that the rock structure was generally dense and the connectivity was poor (Fig. 6). There were mainly euhedral calcite grains in the rock, with developed pores, intergranular pores, and intergranular dissolved pores with good connectivity (Fig. 6). As shown in Figure 6b, c, and f, the pores were not developed, dissolved pores and intergranular dissolved pores in the matrix were found, and the connectivity was poor. As shown in Figure 6d, the intergranular dissolved pores and micron matrix dissolved pores were in the matrix, and the size of the dissolved pores was approximately 1.1 μm with poor connectivity. As shown in Figure 6e, the pores were not developed. Dissolved pores and nanodissolved pores were found in the matrix, the size of the pores was approximately 305.8 nm, and the connectivity was poor.

Figure 6
figure 6

SEM images: (a) K6, 2015–03,362, 1524.25, gray arenaceous limestone, intergranular solution pores in the matrix. (b) K6, 2015-03,366, 1526.9, gray silty limestone, dissolved pores in the matrix. (c) K6, 2015-03,379, 1530.95, gray silty limestone, intergranular solution pore. (d) K6, 2015-03,393, 1535.95, dark gray marl, micron matrix solution pore. (e) K6, 2015-03,420, 1727.05, gray silty limestone, nanocrystalline intracrystalline solution pore. (f) T6, 2015-03,234, 2608.1, dark gray fine-grained limestone, intercrystalline pore

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The specific morphology of various minerals in the rock samples can be observed in the SEM images under different magnifications. Rock sample particles mainly comprised calcite grains (Fig. 7). Euhedral calcite grains were mainly seen in the rock, and irregular illite/smectite mixed-layer minerals (Fig. 7b) and irregular flake chlorite (Fig. 7e) were distributed in the rock matrix. Moreover, gypsum aggregates (Fig. 7c), zeolite minerals (Fig. 7d), and quartz aggregates (Fig. 7f) were distributed in the matrix. Figure 7g shows how pyrite particles were distributed in the matrix. Figure 7h shows feldspar fragments in the matrix.

Figure 7
figure 7

SEM images: (a) K6, 2015-03,362, 1524.25, gray arenaceous limestone, fine calcite grains between calcite crystals. (b) K6, 2015-03,366, 1526.9, gray silty limestone, irregular illite/smectite mixed-layer minerals. (c) K6, 2015-03,366, 1526.9, gypsum aggregate in the matrix. (d) K6, 2015-03,379, 1530.95, gray silty limestone, zeolite minerals in the matrix. (e) K6, 2015-03,420, 1727.05, gray silty limestone, irregular flake chlorite in the matrix. (f) T1, 2015-03,258, 3167.9, black gray micrite limestone, quartz aggregate in the matrix. (g) T1, 2015-03,255, 3166.5, gray micrite limestone, pyrite particles. (h) T6, 2015–03,234, 2608.1, dark-gray fine crystalline limestone, feldspar clasts in the matrix

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Pore Throat Characteristics Obtained by HPMI

Many parameters that reflect pore structure were obtained through the analysis of capillary pressure curves of 18 samples (Table 1). These 18 samples were divided into three types according to different curve shapes (Fig. 8a, c and e). The coexistence of three types of curves indicates very strong reservoir heterogeneity. The middle gentle section of the type I curve was very long, indicating a very concentrated distribution of rock pore channels, and a good sorting. The displacement pressure was less than 0.1 MPa, indicating that the rock had good permeability, large pore radius, and good physical properties (Fig. 8a). Moreover, the pore throat radius corresponding to the type I curve was distributed mainly within 0.1–10 μm. Based on the Xoaoth classification criteria (Xoaoth, 1966), it was a mesopore, which is larger than the pore throat radius corresponding to type II and type III curves (Fig. 8b, d and f). The shape of the type II curve was similar to that of the type III curves. However, the saturation median pressure of the former was greater than 100 MPa (Fig. 8b), whereas that of the latter was less than 20 MPa (Fig. 8c). This indicates that the porosity and permeability characteristics of the type III curve were better than those of the type II curve. The displacement pressure of type II and type III curves was approximately 1 MPa, which was greater than that of the type I curve. This indicates that the physical properties of type II and type III curves were worse than those of the type I curve. This is consistent with the porosity and permeability results measured via conventional physics shown in Figure 3.

Table 1 Pore structure parameters obtained from capillary pressure curves of 18 samples
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Figure 8
figure 8

HPMI curves (a, c and e) and corresponding pore throat radius distributions (b, d, and f) of the three types of samples

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The greater the throat uniformity coefficient of a reservoir rock, the greater the throat radius of its constituent rock. Therefore, the closer it is to the maximum radius of reservoir throat, the more uniform is the reservoir throat. The average uniformity coefficient of the type I curve was 0.19, which was greater than that of types II and III curves, indicating that its throat radius was the largest. A sorting coefficient close to 1.0 indicates that the pore network is well sorted. The higher the sorting coefficient, the worse is the uniformity of the pore network (Li et al., 2017). As presented in Table 1, the sorting coefficient of the type II curve was the largest, with average of 2.745, indicating that the sorting of the reservoir pore network was the worst. Table 1 presents that the skewness of the type I curve was 0.56–0.72 (average 0.64), which was greater than that of types II and III curves. This indicates that the reservoir corresponding to the type I curve was mainly of macroporous throat. Therefore, based on the shape of capillary pressure curve and relevant parameters, it can be concluded that the types I, II, and III curves represent the best, worst, and intermediate rock physical properties, respectively.

Fractal Dimension Obtained from HPMI

Using the mercury injection data presented in Table 1, a scatter diagram was created on the double logarithm coordinate system of lgPc–lgSw to obtain the piecewise linear fitting trend line and the overall linear fitting trend line. Equations 5 and 6 were used to calculate fractal dimension (Table 2). The slope of a straight line fitted by all logarithmic scatter points was used to calculate the overall linear regression fractal dimension D1. Piecewise linear regression fractal dimension D was fitted piecewise according to the shape of scatter plot curve. Two samples (2015-03,353 and 2015-03,362) located in a high-porosity and high-permeability zone showed piecewise linear fitting trend lines and that D2 was larger than D3 of the fine pore throat (Fig. 9), indicating a complex pore structure of the coarse pore throat. As presented in Table 2, little difference was found between a fractal dimension obtained by fitting an overall linear regression and by piecewise fitting a linear regression; however, the curve fitted by the latter is more realistic, and the calculated fractal dimension were more accurate. Therefore, the piecewise linear regression fractal dimensions were used for subsequent experiments. The fractal dimensions of all samples ranged from 2.5028 to 2.8866. The fractal dimensions of samples 2015-03,353, 2015-03,362, and 2015-03,364 that correspond to a type I curve were 2.5028–2.6833, with average of 2.5864, which was the lowest among the samples. This indicates that the pore network is not complex, consistent with the results obtained using the mercury injection curves.

Table 2 Evaluation parameters of fractal dimension of the core pore structure
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Figure 9
figure 9

Fractal dimension obtained by piecewise linear fitting trend line for (a) sample 2015-03,353, and (b) sample 2015-03,362. (blue plots represent coarse pore throat, green plots represent transition pore throat, and red plots represent fine pore throat)

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Fractal Dimension Obtained from SEM

Some SEM images in Figures 6 and 7 are used to extract the identified pore equivalent perimeter and area (Fig. 10) in the JMicroVision image analysis software. The pore structure parameters were plotted in double logarithmic coordinates (Fig. 11). Straight lines were obtained through least square fitting. Fractal dimensions of different pore types were calculated using the slope of the straight lines. The closer D0 is to 1, the smaller is the heterogeneity. The calculation results show (Fig. 11) that the fractal dimensions D0 varied between 1.0970 and 1.4520, with average of 1.3186, and the correlation coefficient varied between 0.9192 and 0.9623, indicating strong porosity heterogeneity of carbonate rocks in this area, with significant fractal characteristics.

Figure 10
figure 10

Pore distribution extracted by JMicroVision software. (a) K6, 2015-03,362. (b) K6, 2015-03,366. (c) K6, 2015–03,379. (d) K6, 2015-03,393. (e) K6, 2015-03,420. (f) T6, 2015-03,234. (g) K6, 2015-03,362. (h) K6, 2015-03,366. (i) K6, 2015-03,420

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Figure 11
figure 11

Fractal relationships between pore perimeter and area calculated based on high-resolution scanning electron microscope photos. (a) K6, 2015-03,362. (b) K6, 2015-03,366. (c) K6, 2015-03,379. (d) K6, 2015-03,393. (e) K6, 2015-03,420. (f) T6, 2015-03,234. (g) K6, 2015-03,362. (h) K6, 2015-03,366. (i) K6, 2015-03,420

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Fracture Characteristics and Occurrence Statistics

After observing the imaging logging image, it was determined that the fractures in well A2 included conductivity fractures, fissures, and resistive fractures (Fig. 12). Conductivity fractures are natural fractures that are crucial in determining reservoir characteristics and oil and gas migration. The FMI image showed a dark sinusoidal curve (Fig. 13) caused by drilling mud invasion or argillaceous and conductive mineral filling. Few conductivity fractures were found in the carbonate section of the well, which were mainly developed in gypsum limestone and argillaceous limestone. The conductivity fractures trend mainly NW–SE and near E–W, with inclinations of 16°–76° (Fig. 12). The effectiveness of some conductivity fractures was poor because they were partially filled with calcite or gypsum.

Figure 12
figure 12

Occurrence characteristics of fractures in the whole section of well A2

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Figure 13
figure 13

FMI image characteristics of fractures in well A2. High-conductivity fracture, red; Micro-fissure, purple; High-resistance fracture, yellow

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Fissures are also a type of conductivity fracture, including condensation shrinkage fractures, joint fractures, and intergravel fractures, which can effectively improve the porosity and permeability of a reservoir. Fissures refer to conductivity fractures that are difficult to fit theoretically on a FMI image. They are characterized by a dark color in FMI images. Some fissures were very short, some had a high angle or large length, and some were characterized by partial sinusoidal curves (Fig. 13). In this study, partial sinusoidal curves were used to obtain the occurrence characteristics of fissures. Fissures were mainly developed in gypsum, gypsum limestone, and argillaceous limestone, striking nearly N–S and NW–SE with medium–low angles of 9°–60° (Fig. 12).

Resistive fractures are formed by filling with high-resistivity materials or fracture closure and do not contribute to a reservoir. In the FMI image (Fig. 13), resistive fractures exhibit a relatively high-resistance (light color to white) sinusoidal curve, which is formed by the filling of high-resistance material or the closure of the fracture. Resistive fractures of the well mainly strike nearly N–S and NE–SW, with angles of 40°–80°. They are mainly developed in C1v2 limestone and C1v3 argillaceous limestone (Fig. 12).

Discussion

Influence Factors of Fractal Dimension

Porosity and Permeability

The correlations among porosity, permeability, and fractal dimension were drawn to study the relationships among them (Fig. 14). The fractal dimension gradually approached 3 with decrease in porosity and permeability; that is, the complexity of pore network became increasingly high. A strong negative correlation was observed between pore throat fractal dimension and porosity (Fig. 14), and the correlation coefficient was − 0.7999. Porosity reflects the proportion of pore space volume in a rock. Generally, the complexity of pore distribution does not affect the porosity of conventional reservoirs (Shao et al., 2017). However, a previous study found that the irregular distribution of fine pore throats in tight reservoirs may inhibit large pores (Chalmers and Bustin, 2008). A negative but weak correlation was observed between permeability and fractal dimension (Fig. 14b). A large fractal dimension indicates change in pore shape from regular to complex, which will hinder fluid flow and reduce permeability accordingly. However, the correlation may not be particularly obvious as there are several fractures in carbonate reservoirs in this area (Wei et al., 2019).

Figure 14
figure 14

(a) Correlation of fractal dimension with porosity. (b) Correlation of fractal dimension with permeability

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In conclusion, a good correlation exists between fractal dimension and the physical properties of the reservoir. Therefore, in the study area, the pore throat fractal dimension can be used to characterize the complexity of reservoir micropore structures. The larger the pore throat fractal dimension, the more complex the reservoir micropore structure.

Pore Structure Parameters

The effect of pore structure parameters on fractal dimension was studied in this work (Fig. 15). The fractal dimension was correlated positively with displacement pressure and saturation median pressure, with correlation coefficients of 0.5936 and 0.3622, respectively (Fig. 15). The pore structure becomes complex with increasing fractal dimension, and it is relatively more difficult for mercury to enter the pore throat network system. Consequently, displacement pressure and saturation median pressure also increase. It was observed that fractal dimension had strong negative correlations with pore volume and average pore throat radius, with correlation coefficients of − 0.8246 and − 0.4034, respectively. These parameters decrease gradually with increasing fractal dimension. The correlation of fractal dimension with sorting coefficient and skewness was poor, with correlation coefficients of 0.0877 and 0.0048, respectively. This indicates that fractal dimension has a little effect on reservoir pore throat sorting. The foregoing results show that fractal dimension can well characterize the heterogeneity of pores.

Figure 15
figure 15

Correlation between fractal dimension and pore structure parameters. (a) Displacement pressure. (b) Saturation median pressure. (c) Pore volume. (d) Average pore throat radius. (e) Sorting coefficient. (f) Skewness

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Causes of High-Porosity and High-Permeability Zones

As discussed in Section “Conventional Petrophysical Measurements”, although most samples were very dense, the maximum porosity and permeability reached 20.8% and 18.8 mD, respectively, in well K6 with depth of 1522.85–1525.05 m (Fig. 3a). Moreover, the pore types in this interval were mainly intergranular dissolved pores, intragranular dissolved pores, and microfractures, which were well developed (Fig. 5b and j). There were mainly euhedral calcite grains in the rock, with developed pores, intergranular pores, and intergranular dissolved pores. Good connectivity was also noted (Fig. 6a). The distribution of rock pores and channels in this depth section was very concentrated and had good sorting (Fig. 8a and b). This is closely associated with the sedimentary environment and diagenesis.

In the process of reservoir deposition in this section, the sedimentary environment changed from an open platform to an evaporation platform (Fig. 1c), and dolomite was associated with high micritic dolomite and gypsum content, characterized by an evaporation environment. This was conducive to quasi-syngenetic dolomitization (Fig. 16a). In addition, the maximum content of iron dolomite in the reservoir of this section can reach 98.17% (Fig. 2a). The dolomite crystal was very small, resulting from the rapid crystallization of dolomitization in the quasi-syngenetic stage. It can thus be inferred that the pore network was transformed by dolomitization (Sun et al., 2005; Li and Li, 2019; Pei et al., 2021). Under an overall arid climate background, when there is atmospheric fresh water supply, aragonitic particles or cements dissolve to produce holes and release a large amount of Mg2+, providing a source of Mg2+ for quasi-syngenetic dolomitization. In an arid and hot climate, the surface seawater or pore water is concentrated and salted continuously due to strong evaporation, forming brine with high Mg2+/Ca2+ values, leading to dolomitization of the surrounding sediments. When excess brine permeates downward, dolomitization of sediments passing by with high-porosity and high-permeability occurs (Zhou et al., 2015). Usually, after dolomitization, the crystal volume of calcite decreases, which will produce secondary pores and increase porosity. Microscopically, biological cavity pores, intergranular dissolution pores, intragranular dissolution pores, and microfractures were developed in this interval (Fig. 5); however, most of the pores formed by dissolution in this period were filled by later cementation filling, indicating that they were formed early. Therefore, it is speculated that dissolution in this period occurred in a syngenetic–quasi-syngenetic period (Fig. 16b) (Meng et al., 2015). In this sedimentary stage, the decline of sea level caused the shallowing of water bodies. The beach facies, such as the granular beach and Tainei beach developed in this section, were exposed to the sea. In an atmospheric fresh water environment, unstable minerals, such as aragonite and high-magnesium calcite, are dissolved to form selective pores and fractures. Quasi-syngenetic dissolution and quasi-syngenetic dolomitization complement each other. During long geological evolution, and owing to periodic changes in climate and sea level rise and fall, dissolution and dolomitization occur alternately or dissolution occurs mainly in one period and dolomitization in another, resulting in holes and sediments being transformed into dolomite. After diagenetic evolution of this stage, the pore type changed from original intergranular pores to solution pores and karst caves, supplemented by intergranular pores. Therefore, quasi-syngenetic dolomitization and syngenetic–quasi-syngenetic dissolution had greatly improved the physical properties of the reservoir and promoted the formation of high-porosity and high-permeability zones.

Figure 16
figure 16

Evolution model of the Lower Carboniferous granular beach dolomite vuggy reservoir (modified from Zhou et al., 2015)

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Conclusions

In this study, various experimental means and related theories were used to evaluate comprehensively the pore structure of the Lower Carboniferous carbonate reservoirs in the Marsel exploration area of the Chu-Sarysu Basin and the following conclusions were drawn.

  1. (1)

    Based on cast thin section and SEM, it is concluded that the lithology in this area comprises mainly fine-grained limestone, bioclastic limestone, and silty limestone. The rock structure was generally dense, but it had some high-porosity and high-permeability zones. This was due mainly to the considerable improvement in the physical properties of the reservoir caused by quasi-syngenetic dolomitization and syngenetic–quasi-syngenetic dissolution. The primary pores were mainly biological cavities. The secondary dissolution pores were mainly dissolution pores and microfractures. Through observation of FMI images, the fractures of well A2 were identified, including conductivity fractures, fissures and resistive fractures. Structural fractures were relatively developed in this area, which can increase the percolation capacity of the reservoir. However, some structural fractures were filled with calcite, reducing the percolation capacity of the reservoir.

  2. (2)

    By analyzing the capillary pressure curve of the samples, they were divided into three types according to different curve forms. The rocks corresponding to type I curves in high-porosity and permeability zone had good sorting, good permeability, large pore radius, and good physical properties. The physical properties of the rock represented by type II curves were the worst, and those of type III curves were intermediate.

  3. (3)

    According to the mercury injection data, the average fractal dimension of the sample corresponding to type I curves was 2.5864, which was the lowest, indicating that the pore network was not complex. Two samples (2015-03,353 and 2015-03,362) located in the high-porosity and high-permeability zones showed piecewise linear fitting trend lines, indicating that the fractal dimension of coarse pore throats was larger than that of fine pore throats, and that the pore structure of coarse pore throats was more complex. Overall, a good correlation exists between fractal dimension and physical properties of the reservoir. The larger the fractal dimension of the pore throats, the more complex the micropore structure of the reservoir.