Three-Dimensional Fractal Modeling and Construction of Flow Capacity (kh) from Well Logs: A Case Study in Southeastern Mexico

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.