A Robust Numerical Framework for Ultrasonic Wave Characterization in Complex Petrophysical Environments

Characterizing internal rock heterogeneities, such as pores, vugs, and micro-fractures, represents a fundamental challenge in petrophysics and reservoir engineering. This study presents a robust numerical framework based on the k-space pseudospectral method (k-Wave) to model 1 MHz ultrasonic wave propagation within complex petrophysical environments. A heterogeneous rock model was developed, consisting of a fluid-saturated host matrix with a longitudinal velocity of 2500 m/s, embedded with five discrete circular inclusions assigned a lower velocity of 350 m/s to simulate high-contrast impedance mismatches typical of vuggy porous media. The wave propagation was excited using a 51-element linear source array, and the resulting steady-state acoustic field was analyzed using a 16384-point Fast Fourier Transform (FFT). The simulation results revealed significant scattering effects, wavefront distortions, and the formation of pronounced acoustic shadow zones behind inclusion clusters. Quantitative evaluation was performed using several key metrics, including a Contrast Ratio (CR) of 3.51 dB and an effective attenuation coefficient of 421.95 dB/m, which reflect the combined influence of intrinsic absorption and extrinsic scattering. The stability of the framework was further enhanced by integrating the Convergent Born Series (CBS) protocol and fractional viscoacoustic modeling to account for frequency-dependent power-law absorption. Crucially, a comparative validation between the k-Wave results and the Modified Born Approach (MBA) showed a numerical discrepancy of less than $1\%$, confirming the high precision of the proposed model. This framework provides an accurate and computationally efficient tool for interpreting ultrasonic testing data, facilitating the non-destructive estimation of porosity and inclusion density in heterogeneous porous media.