The heterogeneous spatial distribution of fluids induced by capillarity leads to the difficulty to accurate describe seismic wave dispersion and attenuation in partially saturated rocks, affecting the precision of hydrocarbon reservoir exploration. In this work, based on the Santos framework, a modified Santos-Rayleigh model was developed for partially saturated double-porosity medium by reformulating the Biot-Rayleigh equations to incorporate capillarity and kinetic energy effects within fluid inclusions. Numerical analysis reveals that the presence of capillarity induces an additional enhancement of P-wave velocity within low-frequency. Furthermore, under varying configurations of water, oil and gas, the P-wave velocities in the low-frequency band fall below the Gassmann-Wood limit due to coupled capillarity and mesoscopic flow. Significant dispersion and attenuation occur when gas serves as the inclusion, and a smaller modulus contrast between the host and inclusions leads to weaker low-frequency dispersion. The internal kinetic energy of inclusion gives rise to a shift of both dispersion and attenuation toward lower frequencies. Comparison with the experimental data confirms that the modified model exhibits a good low-frequency agreement, providing reliable velocity predictions under varying water saturation levels.