| Fractures,as an important oil and gas storage space,have been paid attention by exploration and development personnel.When wave propagates in medium,fluid flow will occur between apertures of different scales,which is an important factor causing wave attenuation.Obtaining the law between wave attenuation,velocity dispersion and fracture parameters is of great significance for exploration and development.In order to accurately predict fracture parameters,it is necessary to study the influence of different fracture parameters on wave propagation characteristics from theoretical and numerical simulation.For plane fracture,periodic layered White model is used to conduct numerical simulation.Biot equation is transformed into frequency domain,and the propagation of wave in cracks is simulated by finite difference method in frequency domain.By solving the linear matrix equations composed of displacement,stress and boundary conditions,the rock strain at each frequency can be obtained,and then the corresponding velocity and attenuation can be obtained.This method can be applied not only to single periodic fracture element,but also to multi-periodic fracture model.Compared with the conventional analytical method,it is faster and more stable.Usually there are a lot of cracks in fractured reservoirs.In order to study the attenuation caused by wave-induced fluid flow in a cracked fractural medium,fractures can be modeled as highly thin and porous layers in a porous background,and the fractured medium can be equivalent to a periodically layered White model.Considering the influence of squirt-fluid between different types of cracks and pores,the relation between stiffness and frequency in the periodically layered medium is obtained by a modified version of Biot equation.Then the attenuation and dispersion characteristics of the wave can be simulated and analyzed.For penny shaped fracture,a method directed by Galvin is used to carry out numerical simulation.However,the conventional integral method has the singularity problem in solving the frequency dependent elastic modulus,and the method can only obtain a single normal frequency dependent modulus.In order to quickly and accurately perform numerical simulation of the penny shaped fracture,based on the Gauss-Lobatto discrete integral,the second Fredholm integral equation is transformed into a discrete integral in a finite interval.And then,through the high-order approximation method,the problem of solving the zero-limit of far field multiple scatter equation is unified with that of the discrete integral procedure.Further,in order to obtain the frequency-dependent elastic tensor,using anisotropic Gassmann equation,combined with the linear slip theory and the Hudson crack model,the analytic elastic moduli equation at the high and low frequency limits are given respectively.Analysis of phase velocity and viscoelastic reflection coefficient shows the wave response.Conventional pre-stack multi-parameter inversion method has poor speed and stability in fracture parameters inversion.Utilizing azimuthal Fourier coefficients expansion,the inversion method in orthogonal media is improved.If there are orthogonal fractures in purely isotropic layer,the fractured medium can be described as orthorhombic model.Based on the Schoenberg's linear slip theory,dimensionless quantities normal and tangential weaknesses are introduced,and by ignoring the high order terms,The Fourier series of P-wave azimuthal reflection coefficient formula for the orthorhombic model was derived from general reflection coefficients for weakly anisotropic elastic media;Furthermore,combining with Hudson's fracture model,The relationship between the Fourier coefficients and fracture density is presented,therefore,the fracture densities in different directions can be calculated. |
PDF Full Text Request