Theoretical Framework for Non-Linear Seismic Wave Interaction with Oil and Gas Reservoir Fluids in the Niger Delta Basin

Non-linear seismic wave interactions in fluid-saturated porous reservoirs produce second and third harmonic generation, wave mixing, and amplitude-dependent attenuation effects that carry diagnostic information about reservoir fluid properties and saturation state. Existing seismic wave theories largely rely on linear acoustic approximations that lose information encoded in these non-linear signatures. This research develops an original theoretical framework for non-linear seismic wave propagation and fluid interaction in Niger Delta reservoir formations. The theoretical development begins with the Biot theory of poroelastic wave propagation, extends it to include geometrical non-linearities through the Murnaghan third-order elastic constant formulation, and introduces fluid flow non-linearity through a modified Darcy flow equation incorporating inertial and turbulent regime corrections appropriate for high-permeability Niger Delta sands. Original derivations of analytical expressions for the non-linear frequency mixing coefficient and second-harmonic generation efficiency as functions of reservoir fluid bulk modulus, porosity, and permeability are presented. The theoretical framework is validated against controlled laboratory experiments using saturated sandstone core samples from a Niger Delta formation in collaboration with a major operator's core repository, using an ultrasonic non-linear measurement system designed and built at the University of Port Harcourt, Rivers State. Measured non-linear coefficients show strong sensitivity to gas saturation changes below 20 percent, offering a theoretical basis for a new seismic attribute for gas saturation mapping below conventional impedance inversion detection thresholds. The framework provides a physics foundation for a new class of non-linear seismic reservoir characterization methods. Keywords: nonlinear seismic, wave propagation, Niger Delta, reservoir fluid, porous media