In recent years, the focus has shifted towards unconventional natural gas reservoirs such as shale gas and coalbed methane due to the diminishing conventional oil and gas reserves and production. Shale gas, in particular, has garnered significant global attention in the realm of oil and gas exploration and development due to its abundant reserves, widespread distribution, and extended extraction lifespan (Jia, 2020; Zhang et al., 2020; Zhao et al., 2025). Shale formations typically exhibit extremely low porosity and permeability. Enhancing individual well productivity and extending stable production periods necessitate fracturing operations, with the assessment of rock brittleness playing a crucial role in the design of fracturing processes for shale oil and gas reservoirs (Lei et al., 2022; Zhu et al., 2022; Wang et al., 2021).

Brittle rocks are susceptible to inelastic deformation, such as cracking, when subjected to external forces (Wang and Wang, 2021; Hucka and Das, 1974; Hajiabdolmajid et al., 2003; Hajiabdolmajid and Kaiser, 2003; Jarvie et al., 2007; Tarasov and Potvin, 2013). Various methods exist for assessing rock brittleness, with no standardized approach. Researchers have proposed diverse methods for calculating the brittleness index (BI), including the mineral composition method (Jin et al., 2015; Jin et al., 2014; Zhang et al., 2016), elastic parameter method (Rickman et al., 2008; Sun et al., 2013; Luan et al., 2014), rock strength method (Hucka and Das, 1974; Altindag, 2003; Meng et al., 2016; Zhang et al., 2016), and stress-strain curve method (Hajiabdolmajid et al., 2003; Hajiabdolmajid and Kaiser, 2003; Mandal et al., 2022). Among these, the mineral composition and elastic parameter methods are commonly utilized in wellbore logging data due to their theoretical clarity, operational convenience, and high-resolution longitudinal profiles derived from the integration of logging and core experiments. Furthermore, some scholars aim to develop a comprehensive brittleness evaluation model by incorporating multiple factors such as mineral composition, mechanical properties, strength parameters, porosity, and energy evolution. A brittleness assessment model was developed utilizing multiple regression analysis, incorporating factors such as friction coefficient, bulk modulus, and shear modulus (Chen et al., 2016). Another study introduced a novel approach for calculating brittleness index, taking into account elastic parameters, mineral composition, and in situ stress conditions (Luo et al., 2024). Nonetheless, the applicability of such a comprehensive evaluation method across different geological layers and regions requires further validation. The key to assessing shale reservoir brittleness using elastic parameters hinges on accurately determining parameters like Young’s modulus and Poisson’s ratio, leveraging triaxial compression test data and array acoustic logging data. It is widely accepted that rocks characterized by higher Young’s modulus and lower Poisson’s ratio exhibit greater brittleness (Makowitz and Milliken, 2003; Jahandideh and Jafarpour, 2014).

Young’s modulus and Poisson’s ratio are key indicators of rock brittleness, reflecting factors such as mineral composition, cementation degree, and pore structure. However, the current elastic parameter method has limitations. Firstly, it assumes equal contributions of Young’s modulus and Poisson’s ratio to rock brittleness without a theoretical basis (Zhang et al., 2017). Secondly, studies have shown its ineffectiveness in distinguishing between brittle rocks rich in quartz and limestone. Thirdly, parameters like bulk modulus and pore pressure also influence brittleness. Given the high cost of acquiring shear wave time difference logging data, the mineral composition method becomes a valuable and often necessary complement. To assess shale reservoir brittleness using this method, identifying mineral compositions and their proportions through ECS (Element Capture Logging), Litho Scanner (Lithology Scanning), or XRD (Whole Rock Mineral Diffraction) experiments is crucial. Currently, this method faces several key challenges. Firstly, varying identification standards for brittle minerals result in significant discrepancies in calculation outcomes. Secondly, distinct minerals exert varying influences on the overall rock brittleness due to their unique physical properties and fracture mechanisms. Existing calculation models typically assign equal importance to all minerals, disregarding variations in their brittleness contributions (Hu et al., 2015; Huo et al., 2018). Lastly, limited research has investigated the nonlinear correlation between minerals and brittleness. Effectively enhancing the accuracy of brittleness assessment depends on scientifically determining the quantitative impact of different minerals on the overall brittleness characteristics of rocks.

To address challenges in shale brittleness assessment, such as ambiguous definitions of brittle minerals and complexities in quantifying individual mineral contributions to overall brittleness, this study introduces a novel approach. Initially, the brittleness index of each mineral constituent is computed based on variations in Young’s modulus and Poisson’s ratio. Subsequently, the contribution coefficient of each mineral to shale brittleness is determined using the analytic hierarchy process. A new brittleness evaluation model, the mineral component method, is then formulated, accounting for the nonlinear relationship between minerals and brittleness. The model’s efficacy is validated through its application to evaluating shale gas reservoirs in the Qiongzhusi formation in the southwest of the Sichuan Basin, China. The study investigates the effects of factors such as confining pressure and temperature on shale brittleness. This research offers a precise methodology for assessing shale reservoir brittleness, furnishing theoretical underpinning and technical guidance for the refined evaluation of unconventional reservoirs and the optimization of favorable zones.

The study area is located within the Cambrian Qiongzhusi Formation in the southwestern Sichuan Basin, encompassing parts of Leshan and Zigong cities in Sichuan Province. Structurally, it is situated in the northwestern portion of the southwestern Sichuan depression and forms the southwestern segment of the Weiyuan structure. Influenced by the third phase of the Tongwan movement and the Xingkai movement, the region evolved into the Mianyang–Changning extensional trough, where high-quality hydrocarbon source rocks from the Maidiping and Qiongzhusi formations were deposited. The study area lies on the gentle western slope of this extensional trough (Li, 1998; Li et al., 2020; Liu et al., 2013). The Qiongzhusi Formation is primarily composed of silty shale and black mudstone, with burial depths ranging between 3,400 and 4,000 m. The successful extraction of industrial gas flows from multiple exploratory wells demonstrates the promising potential for shale gas development in this region.

Helium porosity measurements from 281 shale samples in the study area indicate porosity values ranging from 0.4% to 9.2%, with an average of 2.3%. Helium-based permeability ranges from 0.02 to 0.98 millidarcies (mD), averaging 0.20 mD. These results suggest that the reservoir is characterized by ultra-low porosity and ultra-low permeability.

The mineralogical composition of shale directly influences the development of fracturable space within the reservoir. X-ray diffraction (XRD) analysis of whole-rock minerals from Qiongzhusi Formation shale samples in the study area reveals that the shale is primarily composed of seven minerals: quartz, plagioclase, clay minerals, calcite, k-feldspar, dolomite, and pyrite. Quartz content ranges from 13.1% to 51.5%, with an average of 35.38%; plagioclase content ranges from 5.1% to 35.5%, averaging 21.83%; clay mineral content varies between 6.4% and 44.7%, with an average of 20.4%; and calcite content ranges from 0% to 64.2%, with an average of 10.8%. Overall, the shale reservoir in the study area is characterized by high quartz and feldspar contents and moderate clay mineral content. Notably, core brittleness does not vary with the content of any single mineral (Figure 1). Correlation analysis indicates that there is no significant relationship between mineral composition and the brittleness index (Figure 2). Furthermore, the wide range and significant fluctuations in mineral content (Figure 3) reflect a high degree of heterogeneity in the shale.

The mechanical properties of shale have a direct impact on its brittleness. Considering the in situ effective confining pressure and formation temperature, triaxial compression tests were conducted on shale samples under a confining pressure of 50 MPa and a temperature of 100 °C. The Young’s modulus of the Qiongzhusi Formation shale ranges from 9,375 MPa to 53,585 MPa, with an average of 24,383 MPa. The Poisson’s ratio varies from 0.09 to 0.26, with an average of 0.14. As previously discussed, brittle rocks typically exhibit high Young’s modulus and low Poisson’s ratio. However, in the study area, no typical negative correlation is observed between these two parameters (Figure 4), indicating a more complex brittleness behavior, which poses challenges for accurate brittleness evaluation.

According to the characteristics and distribution of shale rocks and minerals in the study area, the shale is simplified as an aggregate of seven minerals (pyrite, dolomite, quartz, k-feldspar, plagioclase, calcite, and clay), whose composition jointly determines the shale’s overall brittleness, as shown in Figure 5. The physical model of rock volume, which simplifies real rock into sections of uniform properties and treats its macroscopic physical quantities as the sum of their contributions, aligns with the construction philosophy of our brittleness model. This approach is fundamentally different from conventional metrics that define brittleness merely by the proportion of brittle minerals.

According to The Rock Physics Handbook by Mavko (2008) and other related literature, significant differences exist in Young’s modulus and Poisson’s ratio among different mineral components. Further analysis indicates that the brittleness index also varies considerably between minerals. Therefore, based on the elastic parameter method, the brittleness indices of seven typical minerals—such as quartz and clay—can be calculated using their respective Young’s modulus and Poisson’s ratio values. Considering the variations in mineral composition across different regions and to enhance the general applicability of the model, the brittleness index of mineral components is calculated using the method proposed by Luan et al. (2014), as shown in Equation 1.

Although the brittleness formula proposed by Rickman et al. (2008)—as shown in Equation 10—is more widely recognized, it may not be well-suited for determining the brittleness weights of different minerals. However, Equation 10 requires the determination of maximum and minimum values of elastic parameters, and variations in mineral composition can lead to significant fluctuations in the calculated weights. Furthermore, there is no consensus in the field of brittleness evaluation regarding which formula is the most accurate. Formula 1 can maximize the preservation of the differential characteristics of different minerals in terms of Young’s modulus and Poisson’s ratio, which not only enhances the generalization ability of the model, but also facilitates practical operation. B I = E v (1) where B I is the brittleness index; E is Young’s modulus; and v is Poisson’s ratio. The calculated brittleness indices of the minerals are presented in Table 1.

In this study, organic matter was grouped with clay minerals during the brittleness modeling process. This treatment is justified for two primary reasons. First, the mechanical properties of organic matter (Young’s modulus of 6.26 GPa, Poisson’s ratio of 0.14) and clay (Young’s modulus of 14.2 GPa, Poisson’s ratio of 0.30) are comparable, resulting in similar calculated brittleness indices via Formula 1. Second, given that the reservoir is characterized by low organic carbon content (average TOC of 0.27%), the volume and consequent impact of organic matter on the overall rock brittleness are negligible. It is important to note that this simplification is specific to low-organic reservoirs; for formations with high organic content, explicit inclusion of organic matter as a separate component is necessary for accurate modeling.

In order to more accurately and reasonably determine the contribution of each mineral to shale brittleness, the Analytic Hierarchy Process (AHP) is used to determine the weight coefficients of the mineral components in the brittleness evaluation. Differences in the brittleness index calculated by the elastic parameters method for each mineral are used as the basis for constructing the judgment matrix, thereby avoiding the subjectivity and uncontrollability of relying on expert scoring to determine the weights. The elements in the judgment matrix are determined by the ratio of two minerals (Equation 2): a i j = B I i B I j (2) where a i j is the element of the judgment matrix, and B I i and B I j are the brittleness indices of minerals i and j, respectively. The constructed judgment matrix is shown in Table 2.

After the judgment matrix is constructed, the weight (brittleness contribution coefficient) of each mineral can be determined. Comparing the weights determined by three methods, such as feature vector method, geometric average method and arithmetic average method, it is found that the weights solved by the three methods are only different in five decimal places, so the arithmetic average method with the simplest operation is selected to determine the weight results. The idea is to normalize each column first (Equation 3), and then average each row of the normalized matrix to determine the weight (Equation 4). The formula is as follows: a i j ′ = a i j ∑ i = 1 n   a i j (3) w i = 1 n ∑ j = 1 n   a i j ′ (4)

Where, a i j is the element of the judgment matrix, i.e., the brittleness contribution of mineral i relative to mineral j; a i j ′ denotes the sum of the elements in the j-th column; and w i is the brittleness contribution coefficient (weight) of mineral i.

After determining the weights (Table 3), a consistency check of the judgment matrix is required to verify the rationality of its construction. The consistency ratio (CR) of the constructed matrix was calculated to be approximately 0.0087, which is much lower than the threshold value of 0.1. Therefore, the consistency check is satisfied, confirming the validity of the judgment matrix.

After the brittleness contribution coefficient of minerals is determined, the brittleness contribution value of minerals at a single depth point can be determined by combining the volume fraction of mineral components. B I v = ∑ j = 1 n   w i * V i (5) where B I v is the mineral brittleness contribution value; w i and V i are the brittleness contribution coefficient and volume fraction of mineral i, respectively.

In Equation 5, the overall brittleness of rock has a linear relationship with the volumes of rocks and minerals, but in reality, the functional relationship between rock brittleness and mineral volume is complex, and has a large relationship with the microstructure of rock and mineral (Zhang et al., 2016; Liu et al., 2018). Most of the minerals listed above are brittle minerals (Table 1), while clay is a recognized plastic mineral. Ignoring the mineral structure, it is assumed that the rock consists solely of clay and quartz, an increase in clay content leads to a reduction in rock brittleness. However, the relationship between rock brittleness and clay mineral content is not directly linear. When the clay content is low, the rock brittleness is primarily governed by quartz, resulting in a dominantly brittle response where brittleness decreases gradually. In contrast, at higher clay contents, clay minerals become the controlling factor, and the mechanical behavior shifts toward plasticity, causing brittleness to decrease rapidly and eventually plateau. This transition in the controlling mechanism results in a nonlinear relationship between rock brittleness and clay mineral content.

To further account for the nonlinear relationship between rock brittleness and clay content, the nonlinear response function from the rock volume model is adopted (Xiao et al., 2016), and the above equation is rewritten as: B I n e w = W c l * V c l + 1 − V c l * ∑ j = 1 6   w i * V i (6)

In the equation, B I n e w is the brittleness index based on the new evaluation method; w c l and V c l denote the brittleness contribution coefficient and volume fraction of clay minerals, respectively. The calculated brittleness values are finally normalized to facilitate comparison with other methods. When V c l = 1 , the lithology corresponds to pure mudstone, and the brittleness index is controlled solely by clay minerals; when V c l = 0, the brittleness is determined entirely by other minerals; when V c l lies between 0 and 1, clay minerals contribute plastically to the overall brittleness, a consensus widely accepted in current research.

When the clay mineral content significantly decreases, the value of ( 1 − V c l ) increases, leading to a greater contribution of brittle minerals to the overall brittleness and a relatively smaller contribution from clay minerals. Conversely, when the clay mineral content significantly increases, the value of ( 1 − V c l ) decreases, resulting in a reduced contribution of brittle minerals and a relatively larger contribution from clay minerals. This effectively characterizes the nonlinear relationship between brittleness and variations in mineral composition.

Based on the brittleness evaluation method developed in this study, Equation 6 is applied to the Qiongzhusi Formation shale interval from Well J1 in the southwestern Sichuan Basin. A continuous vertical brittleness index profile is obtained through the following steps: First, the mineral composition is derived from elemental data acquired by lithology scanning logging and is then calibrated against XRD analysis results. Then, the brittleness index is calculated, and the final interpretation result is presented as a logging interpretation diagram (Figure 6). In Figure 6, Track 9 compares the continuous brittleness index curve (curve) calculated by the new method with core-based experimental brittleness index data (bar line). As shown, the two exhibit consistent vertical variation trends.

To validate the new method, a scatter correlation plot between the calculated brittleness index and the experimental brittleness index was drawn (Figure 7). Statistical analysis shows a significant positive correlation between the two, with a coefficient of determination R ² of 0.64, an average relative error of 9.45%, and a maximum absolute error of 0.1108. These results confirm the effectiveness of the nonlinear mineral-weighted brittleness evaluation method proposed in this study.

In the vertical direction, the shale brittleness of the Qiongzhusi Formation varies significantly, with the 4th and 8th layers having higher brittleness, with an average of 0.70, while the 10th layer with higher clay content has lower brittleness, with an average of 0.24.

In Figure 6, the tracks from left to right are arranged as follows: Track 1: depth (DEPTH: m); Track 2: stratigraphic subzone; Track 3: uranium-depleted gamma (KTH: gAPI), natural gamma logging (GR: gAPI) and caliper (CAL: in); Track 4: apparent resistivity logging curve (RD/RS: ohm. m); Track 5: acoustic-wave slowness logs (AC: us/ft), bulk density (DEN: g/cm3), and neutron porosity (CNL:m3/m3); Track 6: Weight percentage of minerals obtained by lithology scanning logging inversion (kg/kg); Track 7 to 9: core experimental brittleness index (CORE-BI), original mineral composition method brittleness index (BI₁), elastic parameter method brittleness index (BI₂) and new method brittleness index (BI_new); Tracks 10 to 13 provide enlarged views of Tracks 6 to 9.

In Table 4, MAE refers to Mean Absolute Error; RMSE refers to Root Mean Square Error; MAPE refers to Mean Absolute Percentage Error; and R refers to the Pearson Correlation Coefficient.

The shale of the Qiongzhusi Formation in the southwestern Sichuan Basin is mainly composed of seven minerals, including quartz, plagioclase, clay, dolomite, calcite, K-feldspar, and pyrite. The mineral composition varies widely, and there is no typical correlation between the single mineral content and brittleness index, so it is a highly heterogeneous and ultra-low porosity and permeability reservoir.