Integrated geostatistical-fractal modeling of multivariate reservoir properties for enhanced characterization: Insights from Kirkuk oilfield

Characterizing complex carbonate reservoirs in tectonically active regions like the Kirkuk oilfield, Iraq, is challenging due to pronounced heterogeneity driven by both depositional facies and structural deformation. This study develops an integrated geostatistical-fractal workflow to enhance reservoir characterization, leveraging data from 76 wells. To overcome the smoothing effect of Ordinary Kriging and inadequate fracture modeling in conventional approaches, Sequential Gaussian Simulation (SGS) was implemented with anisotropic variograms. These anisotropic variograms yielded principal spatial correlation ranges: 1,280 m for porosity (NW-SE), 2774 m for thickness (NW-SE), and 1,097 m for water saturation (NW-SE), with shorter perpendicular ranges reflecting structural control, and anisotropy ratios of 1.2:1, 1.8:1, and 1.2:1 respectively. Fractal number-size analysis identified power-law scaling behavior and established critical reservoir quality thresholds at 20% porosity and 37% water saturation. Results quantify the northern sector's superior quality, with porosity reaching 18.2% and thickness peaking at 12 m, contrasting with elevated water saturation (47%) in the south. A lithology-informed multiplicative index delineated the pay-zone with 80% confidence, reducing reservoir volume by 12% while increasing average hydrocarbon saturation to 65%. Volumetric calculations confirmed 50.4 million m³ of reservoir rock and 24.3 million barrels of in-place oil. SGS demonstrated superior performance, reducing porosity RMSE from 1.9% to 1.5% and better preserving thickness extremes. The framework provides a replicable approach for optimizing development in complex carbonate reservoirs.