Fractional-order Wave Propagation Models In Fluid-saturated Porous Media And Their Applications

The dynamic modeling in complicated reservoirs has been a hotspot in petroleum exploration for a long time.In view of the multi-scale heterogeneity of the reservoir media and multiple mechanisms coupling inside it,it is difficult for traditional poroelastic models to describe the wave propagation pattern precisely.To solve this problem,this thesis applies the fractional derivative to modify physical mechanisms in fluid-filled porous media,and develop new wave propagation models in reservoir media based on these modified mechanisms.Firstly,considering the effects of the fractal structure of pores on the fluid flow in porous media,this thesis introduces the fractional derivative into the traditional dynamic permeability theory and make some revisions.Then,under the Biot framework,a new fractional-order poroelastic model based on the revised dynamic permeability theory(simply called the FRDP model)is suggested.Based on the plane-wave analysis,the numerical results show that the fractal dimension of the pore structure has critical effects on the mechanical response of fast P-and S-waves.Specifically,as the fractal dimension increases,dispersion transitions of phase velocities become wider,attenuation peak values decrease,and high-frequency asymptotic behaviors of inverse quality factors become more moderate.Secondly,this thesis applies a new proposed fractional viscoelastic constitutive relationship to describe the intrinsic dissipation of the solid frame.Then by combining this new intrinsic dissipation mechanism with the Biot theory,a new fractional-order porovicoelastic model(simply called the FRVE model)is developed.Several viscoelastic parameters are introduced in the FRVE model,and they have distinct effects on the mechanical response of fast P-and S-waves.Using two groups of experimental data from rock cores of different types,the validity of the FRVE model is verified.Moreover,the results show that the FRVE model can make accurate predictions of the wave dispersion and attenuation in both conventional and unconventional reservoirs at seismic band.Considering complicated conditions existing in practical reservoirs,this thesis generalizes the FRVE model to satisfy different cases,such as the heavy oil case,the multi-phase flow case,the anisotropic case,and so on.After that,this thesis studies the dispersion and attenuation mechanism of waves predicted by these generalized models,broadening the application of the FRVE model.Thirdly,to investigate wavefield characteristics of the FRVE model,this thesis uses a SSM method to do forward modeling based on the FRVE model.This numerical method utilizes the idea of symplectic schemes and NAD operators,which can effectively suppress the numerical dispersion.The wavefield results show that the introduction of the viscoelastic mechanism will indeed enhance the energy loss of waves propagating in the fluid-filled porous media,which are consistent with theoretical results of the plane-wave analysis.Finally,to determine the viscoelastic parameters in the FRVE model,this thesis applies a robust hybrid genetic algorithm to invert for their values by using seismic data.Using synthetic data,this thesis shows that the robust hybrid genetic algorithm is superior to the traditional genetic algorithm in terms of the convergence rate,computational efficiency,and stability.Furthermore,using experimental data,the inversion results based on the robust hybrid genetic algorithm again verify the effectiveness of the FRVE model on characterizing the wave dissipation mechanism in low frequency band.