This study focuses on a hydrocarbon reservoir located in southeastern Mexico. The analysis uses well log data derived from petrophysical evaluations of storage capacity. The structural complexity of the reservoir and observed heterogeneity in Cretaceous units motivate a fractal-based characterization of spatial fluctuations. The objective is to assess the fractal scaling of storage capacity fluctuations using the Family–Vicsek dynamic framework. Critical exponents α (roughness), β (growth), and z (dynamic) are obtained through structure function metrics. Data collapse techniques and local Hurst exponent distributions are used to explore long-range memory and spatial heterogeneity across wells. This study aims to classify storage capacity fluctuation records based on Euclidean or fractal geometries. This analysis allows a novel characterization of storage trends in the reservoir. The analysis reveals persistent scaling behavior, indicating long-range correlations in the storage capacity fluctuations. Multiscale patterns and variations in local Hurst exponents highlight the presence of multifractality and regional heterogeneity. Specifically, the spatial distribution of local Hurst exponents obtained in this study enables the inference of statistical properties in synthetic wells, providing key input for the structural and functional characterization of the reservoir’s geological model. This approach aims to identify preferential subsurface flow pathways for hydrocarbons, gas.

This study focuses on a hydrocarbon reservoir located in southeastern Mexico. The analysis uses well log data derived from petrophysical evaluations of storage capacity. The structural complexity of the reservoir and observed heterogeneity in Cretaceous units motivate a fractal-based characterization of spatial fluctuations. The objective is to assess the fractal scaling of storage capacity fluctuations using the dynamic Family–Vicsek framework. Critical exponents $\alpha$ (roughness), $\beta$ (growth), and z (dynamic) are obtained through structure function metrics. Data collapse techniques and local Hurst exponent distributions are used to explore long-range memory and spatial heterogeneity across wells. This study aims to classify storage capacity fluctuation records based on Euclidean or fractal geometries. This analysis allows a novel characterization of storage trends in the reservoir. The analysis reveals persistent scaling behavior, indicating long-range correlations in the storage capacity fluctuations. Multiscale patterns and variations in local Hurst exponents highlight the presence of multifractality and regional heterogeneity. Specifically, the spatial distribution of local Hurst exponents obtained in this study enables the inference of statistical properties in synthetic wells, providing key input for the structural and functional characterization of the reservoir’s geological model. This approach aims to identify preferential subsurface flow pathways for hydrocarbons and gas.

Reservoir evaluation and interpretation are fundamental for production and reserve management, and they require, as a key input, an information matrix describing petrophysical properties within the static model. This study provides the scalar distribution of the petrophysical property associated with flow capacity, $kh$ (where k is permeability and h is sample thickness). This distribution is generated in a three-dimensional space from six locally distributed well-log series. These well logs were derived from measurement, evaluation, calibration, and interpretation processes and correspond to producing reservoirs in southeastern Mexico. To characterize the heterogeneity of the well-log data through the Hurst exponent, the structure-function metric was employed. Subsequently, these exponents were distributed throughout the three-dimensional domain of interest by linear interpolation. Finally, pseudo-well logs for the studied reservoir were generated using the random midpoint displacement algorithm. A local petrophysical information matrix for the $kh$ property containing 52,800 pseudo-records was obtained. The resulting information matrix is suitable for capturing both fine- and coarse-scale heterogeneity. The methodology applied here suggests a substantial saving in reservoir analysis as a first approximation to the evaluation model.