Investigation of Anomalous Diffusion and Fractional Dynamics in Nigerian Geophysical Media

Anomalous diffusion, characterised by mean-squared displacement scaling non-linearly with time, arises in heterogeneous and disordered media such as fractured rock aquifers, oil-saturated sediments, and laterite soils. Understanding anomalous transport in these geophysically relevant Nigerian materials is important for contaminant transport modelling, hydrocarbon reservoir simulation, and geothermal energy resource assessment. This study investigates anomalous diffusion and fractional dynamics in Nigerian geophysical media through a combination of laboratory experiment, stochastic theoretical modelling, and numerical simulation. Pulsed field gradient NMR diffusometry is applied to characterise water diffusion in laterite cores from Ogun State and sandstone cores from Niger Delta analogue outcrops in Anambra State. The time-dependent self-diffusion coefficient and diffusion propagator are measured over time scales from 10 milliseconds to 10 seconds. A fractional Fokker-Planck equation with space-time fractional derivatives is derived and solved analytically using Mittag-Leffler function representations. The anomalous diffusion exponent and generalised diffusivity are extracted from NMR data by fitting fractional model predictions. Results indicate sub-diffusive behaviour with exponents of 0.61 to 0.82 in laterite samples and 0.74 to 0.91 in sandstone samples, reflecting different degrees of pore space connectivity and tortuosity. Keywords: anomalous diffusion, fractional dynamics, NMR diffusometry, Nigerian geophysical media, Fokker-Planck