Integrated image analysis and statistical modeling for the morphological characterization of porous microstructures

REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 1 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. Integrated image analysis and statistical modeling for the morphological characterization of porous microstructures Análise de imagens e modelagem estatística integradas para a caracterização morfológica de microestruturas porosas Análisis de imágenes y modelado estadístico integrado para la caracterización morfológica de microestructuras porosas DOI: 10.54033/cadpedv22n9-169 Originals received: 6/9/2025 Acceptance for publication: 7/2/2025 Jean Firmino Cardoso Bachelor in Civil Engineering Institution: Universidade Federal de Pernambuco (UFPE) Address: Recife, Pernambuco, Brazil E-mail: [email protected] Pedro Pereira de Amorim Neto Bachelor in Civil Engineering Institution: Universidade de Pernambuco (UPE) Address: Recife, Pernambuco, Brazil E-mail: [email protected] Samuel do Nascimento Pereira Junior Bachelor in Civil Engineering Institution: Centro Universitário Maurício de Nassau (UNINASSAU) Address: Recife, Pernambuco, Brazil E-mail: [email protected] Daiane Francisca do Nascimento Silva Master in Energy and Nuclear Technologies Institution: Universidade Federal de Pernambuco (UFPE) Address: Recife, Pernambuco, Brazil E-mail: [email protected] Abel Gámez Rodríguez Doctor in Energy and Nuclear Technologies Institution: Universidade Federal de Pernambuco (UFPE) Address: Recife, Pernambuco, Brazil E-mail: [email protected] REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 2 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. Yaicel Ge Proenza Doctor in Chemistry Institution: Universidade Federal de Pernambuco (UFPE) Address: Recife, Pernambuco, Brazil E-mail: [email protected] Daniel Milian Pérez Doctor in Energy and Nuclear Technologies Institution: Universidade Federal de Pernambuco (UFPE) Address: Recife, Pernambuco, Brazil E-mail: [email protected] ABSTRACT This study presents a methodology for the quantitative and spatial characterization of porous materials, grounded in digital image-processing techniques (DIP) and statistical modelling. The proposal stems from the need for methods that are more accessible, scalable, and reproducible than traditional porosimetry and micro-CT approaches. To this end, three-dimensional image sets obtained via X-ray micro-computed tomography are employed. The primary objective is to accurately quantify total porosity, map its spatial distribution, and analyze microstructural descriptors such as connectivity, anisotropy, tortuosity, and pore-size distribution. The workflow integrates pre-processing, binarization with multiple techniques (Otsu, Sauvola, and K-means), morphological operations, and statistical evaluation of the porosity models. Additionally, polynomial regressions and normality tests are applied to assess porosity profiles along the Z-axis. Results reveal significant heterogeneity in porosity and connectivity among the samples, underscoring the importance of a multiscale approach. Evaluated in light of the literature, the methodology shows that outcomes are strongly influenced by the chosen segmentation method and the number of morphological operations applied, yet it provides a faithful representation of porous structures for flow, filtration, and energy-related modelling applications. Keywords: Porosity. Image Processing. Microstructure. Statistical Modeling. Morphological Analysis. RESUMO Este estudo apresenta uma metodologia para a caracterização quantitativa e espacial de materiais porosos, baseada em técnicas de processamento digital de imagens (PDI) e em modelagem estatística. A proposta surge da necessidade de métodos mais acessíveis, escaláveis e reprodutíveis em comparação às abordagens tradicionais de porosimetria e microtomografia. Para tanto, utilizamse conjuntos de imagens tridimensionais obtidas por microtomografia de raios X. O objetivo central é quantificar com precisão a porosidade total, mapear sua distribuição espacial e analisar descritores microestruturais, tais como conectividade, anisotropia, tortuosidade e distribuição dos tamanhos de poro. O fluxo de trabalho combina etapas de pré-processamento, binarização por REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 3 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. múltiplas técnicas (Otsu, Sauvola e K-means), operações morfológicas e avaliação estatística dos modelos de porosidade. Adicionalmente, aplicam-se regressões polinomiais e testes de normalidade para avaliar os perfis de porosidade ao longo do eixo Z. Os resultados revelam heterogeneidade significativa na porosidade e na conectividade das amostras, ressaltando a importância da abordagem multiescalar. A metodologia, avaliada à luz da literatura, evidencia que os resultados dependem fortemente do método de segmentação escolhido e do número de operações morfológicas empregadas, proporcionando, contudo, uma representação fiel das estruturas porosas para modelagens de escoamento, filtração e aplicações energéticas. Palavras-chave: Porosidade. Processamento de Imagens. Microestrutura. Modelagem Estatística. Análise Morfológica. RESUMEN Este estudio presenta una metodología para la caracterización cuantitativa y espacial de materiales porosos, basada en técnicas de procesamiento digital de imágenes (PDI) y en modelado estadístico. La propuesta surge de la necesidad de métodos más accesibles, escalables y reproducibles en comparación con los enfoques tradicionales de porosimetría y microtomografía. Para ello, se utilizan conjuntos de imágenes tridimensionales obtenidas mediante microtomografía de rayos X. El objetivo central es cuantificar con precisión la porosidad total, cartografiar su distribución espacial y analizar descriptores microestructurales tales como conectividad, anisotropía, tortuosidad y distribución de tamaños de poro. El flujo de trabajo combina fases de preprocesamiento, binarización mediante múltiples técnicas (Otsu, Sauvola y K-means), operaciones morfológicas y evaluación estadística de los modelos de porosidad. Además, se aplican regresiones polinómicas y pruebas de normalidad para evaluar los perfiles de porosidad a lo largo del eje Z. Los resultados revelan una heterogeneidad significativa en la porosidad y la conectividad de las muestras, resaltando la importancia del enfoque multiescalar. La metodología, evaluada a la luz de la literatura, muestra que los resultados dependen en gran medida del método de segmentación elegido y del número de operaciones morfológicas empleadas; no obstante, proporciona una representación fiel de las estructuras porosas para modelos de flujo, filtración y aplicaciones energéticas. Palabras clave: Porosidad. Procesamiento de Imágenes. Microestructura. Modelado Estadístico. Análisis Morfológico. 1 INTRODUCTION Granular porous materials, such as sedimentary rocks and artificial media modeled by sphere packings, play fundamental roles in diverse applications, particularly in filtration processes, enhanced oil recovery (EOR), percolation REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 4 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. studies, and understanding transport phenomena in geological media (Lao et al., 2024). Their intrinsic structural properties including porosity, connectivity, tortuosity, and pore size distribution directly influence critical macroscopic properties such as permeability, effective diffusion, and mechanical strength (Xiao et al., 2023). Consequently, the precise characterization of the porous microstructure is essential for predicting functional performance and optimizing practical applications. Traditionally, structural analysis of these materials has employed techniques like mercury intrusion porosimetry (MIP), gas adsorption by Brunauer–Emmett–Teller method (BET method), and X-ray computed microtomography (μCT-RX). While providing valuable data, these approaches exhibit significant limitations, including high dependency on theoretical models (especially MIP and BET), high cost (high-resolution μCT-RX), and constraints regarding spatial resolution or volumetric representativeness (Yang et al., 2024; Yu, B. et al., 2022). In this context, digital image processing (DIP)-based techniques emerge as promising alternatives for the direct and quantitative extraction of morphological parameters from two-dimensional images (Scanning Electron Microscope (SEM)) or three-dimensional images (μCT-RX data) of rock samples and granular assemblies. The use of DIP, combined with robust statistical methods, enables detailed quantification of internal morphology, emphasizing parameters such as pore/grain size and shape distribution, connectivity, structural anisotropy and number of connected components (Sarkar et al., 2025). These methods allow for the analysis of large data volumes in an automated, objective, and highly reproducible manner, while also generating intuitive visual representations that facilitate qualitative and quantitative interpretation of results. Despite these advances, studies that systematically integrate advanced digital segmentation techniques, mathematical morphology analysis, and spatial statistical modelling to characterize complex porous materials, such as heterogeneous rocks and sphere columns with different packing arrangements, remain scarce (Cao et al., 2024). A gap exists in the literature regarding the combined application of these tools to quantitatively and explicitly investigate the REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 5 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. topological and geometric aspects of porosity in systems with heterogeneous feature distributions, as is common in geological samples and granular media (Cao et al., 2024). Given this context, and utilizing three-dimensional image datasets acquired via μCT-RX, this work aims to perform a quantitative and spatially resolved characterization of porous microstructures, employing these representative images of rocks and percolation columns composed of spheres. The proposed approach is based on DIP techniques applied to the μCT-RX data and statistical modelling, aiming to: (i) quantify the global average porosity; (ii) evaluate the spatial distribution of porosity along specific axes; (iii) determine metrics of connectivity, anisotropy, and tortuosity; and (iv) statistically analyze the morphology and size distribution of pores or interstitial voids. The obtained results contribute to a deeper understanding of the internal structure of the investigated materials and provide essential insights for future applications in computational flow and transport modelling, as well as in the optimization of functional properties. 2 THEORETICAL FRAMEWORK Porous materials are ubiquitous across a wide range of natural and engineered systems, playing a crucial role in key processes such as fluid transport, energy storage, thermal exchange, and heterogeneous chemical reactions. Sedimentary rocks, in particular, are composed of intricate networks of interconnected pores whose geometric and topological characteristics, including porosity, connectivity, tortuosity, and pore size distribution, directly influence macroscopic properties such as permeability, effective diffusivity, and mechanical strength (Xiao et al., 2023). Over recent decades, the quantitative characterization of porous microstructures has relied primarily on conventional laboratory techniques such as MIP, gas adsorption using the BET method, and μCT-RX. While these techniques have provided valuable data, they are not without significant limitations. MIP and BET, for instance, are heavily dependent on simplifying REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 6 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. theoretical models and offer no spatially resolved insights. μCT-RX, although capable of providing three-dimensional structural detail, is constrained by high equipment costs and limitations in volumetric representativeness due to resolution–scale trade-offs (Yang et al., 2024; Yu, B. et al., 2022). In this context, DIP techniques have emerged as promising alternatives for the direct and quantitative morphological characterization of porous media. DIP allows for the automated and reproducible extraction of structural parameters from 2D or 3D image datasets, including petrographic thin sections, SEM images, or volumetric data from μCT-RX scans (Liu et al., 2024; Qin et al., 2021). Among the structural parameters accessible via DIP, key metrics include global porosity, pore size and shape distribution, structural anisotropy indices, the number of connected components and tortuosity (Sarkar et al., 2025). These descriptors not only enable geometrical and topological descriptions of the pore space, but also serve as essential inputs for computational models of flow and mass transport in porous media. Such applications span multiple disciplines from geosciences and petroleum engineering to biomedical domains, including studies of trabecular bone and bioinspired porous scaffolds (Wenran et al., 2025). Furthermore, the integration of open-source computational libraries such as PoreSpy, scikit-image, and OpenCV into Python-based programming environments has facilitated the development of robust analytical workflow for segmentation, morphological analysis, and statistical modeling of porous microstructures. Binarization methods such as Otsu’s thresholding, Sauvola’s adaptive method, and k-means clustering are employed to accurately segment the solid and void phases of the material (Chengzhen et al., 2025). Threedimensional morphological operations including dilation, erosion, opening, and closing, provide insights into structural robustness and connectivity, while statistical tools such as the two-point correlation function and anisotropy index allow for the quantitative assessment of spatial organization (Chirol et al., 2021; Rueden et al., 2022). Despite recent advances, current literature rarely integrates advanced segmentation algorithms, mathematical morphology, and spatial statistical modeling to systematically characterize complex heterogeneous porous REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 7 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. structures, like carbonate rocks or granular columns with variable packing (Cao et al., 2024; Ziganshin et al., 2023). Specifically, there's a significant gap in using these combined tools to resolve both the geometric and topological aspects of porosity in systems with strong local heterogeneity, a common feature in both geological formations and artificial granular media. 3 METHODOLOGY 3.1 SAMPLES AND ENVIRONMENT PREPARATION AND PREPROCESSING Four porous media Samples—A), B), C), and D) (Figure 1)—were analyzed. Samples A) and D) were columns packed with glass beads (4mm for A), and a 3mm/4mm mix for D), sourced from Silva's 2024 porous media study. Meanwhile, Samples B) and C) were rock samples from the X-ray Computed Tomography Laboratory at the Federal University of Pernambuco's Department of Nuclear Energy. Figure 1. Samples A) 4mm pebble Glass, B) rock type X, C) rock type Y, D) mixed pebble glass (3mm and 4mm). Source: Prepared by the authors. The methodology was implemented in a Python environment, leveraging specialized libraries for image analysis, numerical processing, and graphical visualization. Key libraries included PoreSpy for characterizing porous microstructures, scikit-image for filtering, segmentation, and morphological operations, and OpenCV (Li; Asbjörnsson; Lindqvist, 2021) for adaptive contrast equalization. Additionally, NumPy was used for 3D array manipulation, SciPy for spatial filtering and transform operations, matplotlib, seaborn, and Plotly handled A ) B ) C) D ) REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 8 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. the graphical visualization. To ensure visual reproducibility and quality in the presentation of results, graphical parameters were configured to standardize styles, color palettes, fonts, and resolutions. A perceptually uniform color palette was implemented using the seaborn library (Kochukrishnan et al., 2024), and plots were optimized for publications through predefined DPI settings, figure dimensions, refined gridlines, and typographic styles compatible with PDF outputs. The process commenced with the loading of 2D image datasets acquired in .tiff format, representing sequential slices of a three-dimensional porous material sample. The images were systematically organized in dedicated directories and loaded using a custom-adapted implementation of the scikitimage library's “imread_collection” function. To ensure computational efficiency and complexity management, a maximum limit of 300 images per dataset was imposed. During loading, fundamental metadata were extracted, including total image count, slice dimensions (height and width), data type (dtype), and minimum/maximum grayscale intensity values. Preprocessing of the three-dimensional image volumes involved an advanced operational sequence focused on standardization and enhancement of relevant morphological features. Initially, 3D median filtering (Zou; Yao; Wang, 2021) was applied for noise reduction, effectively smoothing abrupt variations while preserving structural boundaries. Subsequently, illumination correction was performed using a large-scale Gaussian filter (σ = 50) (Lei et al., 2022), enabling background variation compensation and intensity normalization across all planes. The following stage employed CLAHE (Contrast Limited Adaptive Histogram Equalization) (Chen; Liang, 2024) via the OpenCV library to implement adaptive histogram equalization for each 2D slice. This approach enhances local contrast, particularly in regions exhibiting low intensity variation. This step plays a critical role in differentiating between solid and void regions, thereby facilitating subsequent segmentation and quantitative analysis stages. REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 9 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. 3.2 BINARIZATION OF IMAGES After preprocessing, the three-dimensional image volumes underwent binarization, a crucial step for distinguishing between the solid and porous phases of the sample. To ensure accurate segmentation of regions of interest, three distinct approaches were employed, each offering varying levels of complexity and spatial sensitivity. The first method applied was Otsu's technique, a global thresholding approach effective for images with well-defined contrast, though limited in cases with local intensity variations (Yu et al., 2025). To overcome these limitations, an adaptive thresholding strategy based on Sauvola's method was adopted, which calculates thresholds locally and proved robust in segmenting regions with subtle illumination gradients (Bipin Nair; Anusha; Anusha, 2022). Additionally, a clustering-based method using K-means was implemented. As an unsupervised segmentation technique, K-means classifies image pixels into porous and solid phases based on statistical similarity, offering greater flexibility in identifying poorly defined phase boundaries and contributing to a more accurate representation of the microstructure (Tabianan; Velu; Ravi, 2022). Each method was independently applied to the 3D volume, generating three distinct binarized representations of the sample, as exemplified in Figure 2 for Sample A. The original slices exhibit visible noise, a common artifact in μCT images. Figure 2. Comparison between binarization methods for Sample A. Source: Prepared by the authors. To determine the most suitable binarization for quantitative characterization, an objective metric based on edge contrast was implemented. REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 16 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. Figure 3. 3D porosity maps of Sample A, bright tones correspond to regions with higher solid content. Source: Prepared by the authors. Figure 4. 3D porosity maps of Sample B, bright tones correspond to regions with higher solid content. Source: Prepared by the authors. Figure 5. 3D porosity maps of Sample C, bright tones correspond to regions with higher solid content. Source: Prepared by the authors. REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 17 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. Figure 6. 3D porosity maps of Sample D, bright tones correspond to regions with higher solid content. Source: Prepared by the authors. Analysis of porous structure connectivity, crucial for fluid transport, revealed considerable variation among the four samples: Sample C exhibited 242,014 connected components, Sample A had 3,708, Sample D displayed 49,084, and Sample B contained 36,396. Tortuosity along the Z-axis was 1.012 for Sample C, 1.047 for Sample A, 1.098 for Sample D, and 1.029 for Sample B, reflecting slight variations in flow pathway complexity in accordance with each sample’s microstructure. Structural anisotropy varied from 1.081 in Sample A, 3.486 in Sample B, and 5.344 in Sample D up to 9.131 in Sample C, confirming directional architectures that favor transport along specific orientations (Xiao et al., 2023). Mean sphericity, 0.932 in Sample B, 0.860 in Sample C, 0.861 in Sample D, and 0.860 in Sample A, further underscores differences in pore shape uniformity across the samples. Even with high connectivity, irregular pore distribution and pronounced anisotropy can complicate accurate transport behavior predictions in computational simulations like CFD. Advanced statistical tools provided in-depth analysis of porosity distribution. Normality tests (Shapiro-Wilk and D'Agostino-Pearson) rejected the null hypothesis of normal distribution for all samples (p-values < 0.05), a finding that contrasts with Yang's observations (Yang et al., 2024) regarding the stochastic nature of geological samples. Further, skewness coefficients (ranging from -1.535 to -0.419) indicated a predominance of smaller pores, resulting in a left-tailed distribution, while kurtosis values (-0.742 to 3.457) showed varying pore concentration around the mean, reflecting the diverse pore shapes and sizes within the samples (Figure 7). The Quantile-Quantile (Q-Q) plots (Figure 8) REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 18 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. visually supported these findings, highlighting significant deviations from the expected normality, especially evident at distribution tails. Figure 7. Analyses of skewness and kurtosis to Samples A), B), C) and D). Source: Prepared by the authors. Figure 8. Evaluation of the normality of porosity distributions using Quantile-Quantile (Q-Q) plots. Source: Prepared by the authors. Statistical modeling of porosity along the Z-axis, using a third-degree polynomial, yielded low coefficients of determination (R² = 0.092 and 0.481). This suggests the model inadequately explains porosity's spatial variability, indicating a dominance of random factors or complex geometric influences, consistent with A ) B ) C ) D ) A ) C ) B ) D ) REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 19 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. Yu et al. (2022) who advocate for spatial statistics and machine learning for nonlinear patterns in porous structures. A morphological evaluation using dilation, erosion, opening, and closing operations revealed porosity changes consistent with literature: dilation increased porosity, while erosion significantly reduced it, highlighting structural fragility (Figure 9). Connectivity was also affected, particularly by opening operations, which fragmented continuous porous structures. These observations reinforce morphological analysis as a valuable tool for simulating physical processes like sintering, dissolution, and pore blockage, as noted by Sarkar et al. (2025). The results obtained were compared with analogous studies that employed X-ray microtomography and digital image processing techniques. In particular, the works of Lao (Lao et al., 2024) and Cao (Cao, Danping; Hou; Hou, 2024) reported similar values of anisotropy and tortuosity in packed sphere columns, as well as asymmetric porosity distributions. The strong agreement between the results presented here and the literature reinforces the validity of the methodology employed, both in the processing stage and in the morphostatistical quantification. REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 20 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. Figure 9. Porosity changes in Samples A), B), C), and D) due to morphological operations. Source: Prepared by the authors. 5 CONCLUSION This work proposed a methodology for the quantitative and spatial analysis of porous materials using digital image processing and statistical modeling. The workflow allowed extraction of key descriptors, such as porosity, connectivity, tortuosity, anisotropy, and pore size distribution, from μCT-RX datasets in an automated and reproducible way. The preprocessing steps and segmentation methods, especially adaptive enhancement and thresholding, were effective in A) B) C) D ) REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 21 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. highlighting porous structures. Among the binarization techniques, Otsu’s method provided the best results based on the contrast evaluation. Morphological operations revealed how structural features change under topological transformations, while connectivity analyses showed the complex nature of the pore networks. Tortuosity and anisotropy metrics provided insights into directional flow and structure orientation. Statistical analysis of porosity profiles showed spatial heterogeneity and limited model fit, indicating complex internal variation rather than smooth gradients. Overall, the proposed framework offers a detailed and spatially resolved approach to porous structure characterization, particularly useful for flow modeling and material optimization. Future work may extend the method to more heterogeneous samples and integrate machine learning to enhance segmentation and predictive modeling. ACKNOWLEDGEMENTS This research was partially supported by the National Council for Scientific and Technological Development (CNPq), project number: 465764/2014-2 - Observatório Nacional da Dinâmica da Água e de Carbono no Bioma Caatinga (ONDACBC) and 403842/2022-0 - PhD scholarship for the author Daiane Francisca do Nascimento Silva. Additionally, the authors acknowledge funding from the Human Resources Training Program of the Brazilian National Agency for Petroleum, Natural Gas, and Biofuels (PRH-ANP) via PRH 48.1/UFPE (ANP/FINEP Grants No. 48610.201019/2019-38 and FAPESP Grants No. 2024/10544-2 and 2024/12259-3), supported by resources from oil companies qualified under Clause P (Research, Development, and Innovation) of ANP Resolution No. 50/2015. REVISTA CADERNO PEDAGÓGICO – Studies Publicações Ltda. ISSN: 1983-0882 Page 22 REVISTA CADERNO PEDAGÓGICO – Studies Publicações e Editora Ltda., Curitiba, v.22, n.9, p. 01-25. 2025. REFERENCES BEN-NOAH, I.; HIDALGO, J. J.; DENTZ, M. 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