Under the excitation of elastic waves,local fluid flow in a complex porous medium is a major cause for wave dispersion and attenuation.When the local fluid flow process is simulated with wave propagation equations in the double-porosity medium,two porous skeletons are usually assumed,namely,host and inclusions.Of them,the volume ratio of inclusion skeletons is low.All previous studies have ignored the consideration of local fluid flow velocity field in inclusions,and therefore they can not completely describe the physical process of local flow oscillation and should not be applied to the situation where the fluid kinetic energy in inclusions cannot be neglected.In this paper,we analyze the local fluid flow velocity fields inside and outside the inclusion,rewrite the kinetic energy function and dissipation function based on the double-porosity medium model containing spherical inclusions,and derive the reformulated Biot-Rayleigh(BR)equations of elastic wave propagation based on Hamilton’s principle.We present simulation examples with different rock and fluid types.Comparisons between BR equations and reformulated BR equations show that there are significant differences in wave response characteristics.Finally,we compare the reformulated BR equations with the previous theories and experimental data,and the results show that the theoretical results of this paper are correct and effective.
Tight gas sandstone reservoirs in Guang＇an are characterized by wide distribution and low abundance. Sandstone samples from this area usually have low porosity and poor connectivity. We analyze the observed velocity data of tight sandstone samples with the Mori- Tanaka model, and give the sandstone framework physical model in this area based on theory and experiment analysis. The matrix modulus was obtained by an empirical relationship and then the experiment data were compared with the values predicted by the Mori-Tanaka model with different pore shapes. The results revealed that the experiment data were close to the model with low pore aspect ratio. Considering the matrix modulus and pore shape variation, we find that, under the condition of small mineral composition change, the effective pore aspect ratio of these samples increased with porosity evidently.
Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based on the optimal steep descent methods, we present an algorithm which combines the preconditioned bi-conjugated gradient stable method and the multi-grid method to compute the wave propagation and the gradient space. The multiple scale prosperity of the waveform inversion and the multi-grid method can overcome the inverse problems local minima defect and accelerate convergence. The local inhomogeneous three-hole model simulated results and the Marmousi model certify the algorithm effectiveness.
In heterogeneous natural gas reservoirs, gas is generally present as small patchlike pockets embedded in the water-saturated host matrix. This type of heterogeneity, also called "patchy saturation", causes significant seismic velocity dispersion and attenuation. To establish the relation between seismic response and type of fluids, we designed a rock physics model for carbonates. First, we performed CT scanning and analysis of the fluid distribution in the partially saturated rocks. Then, we predicted the quantitative relation between the wave response at different frequency ranges and the basic lithological properties and pore fluids. A rock physics template was constructed based on thin section analysis of pore structures and seismic inversion. This approach was applied to the limestone gas reservoirs of the right bank block of the Amu Darya River. Based on poststack wave impedance and prestack elastic parameter inversions, the seismic data were used to estimate rock porosity and gas saturation. The model results were in good agreement with the production regime of the wells.
