Equivalent Medium Modeling And Seismic Inversion Based On Frequency-dependent Anisotropy For Fractured Reservoirs

The key of exploration and development for fractured reservoirs is the prediction of fracture spreading range and development intensity.With the deepening of exploration and development,the demanding of prediction accuracy for fractured reservoirs is gradually increasing.The relationship between the parameters of fractured reservoir and seismic data can be established by the equivalent medium theory.The static equivalent medium model ignores the geometric characteristics of fractures and does not consider the fluid exchange between cracks and pores.Therefore,the dispersion and attenuation of actual seismic data can not be explained.Dynamic equivalent medium model describes the interaction between cracks,porosity and fluid.Therefore,the seismic response with frequency dependence based on dynamic equivalent medium theory is closely related to fracture parameters,fluid properties and rock matrix properties.The dynamic equivalent medium model constructs the mapping function of seismic data to fracture parameters,which can be adopted for the quantitative prediction of the fracture reservoirs.At present,the common dynamic equivalent fracture models mainly consider only contains a set of aligned fractures whereas there are often contains more than one set of fracturesdeveloping in the reservoirs and the fluid saturated in pores and fractures are usually not the same type.In order to adapt to the complex geological conditions,based on the Chapman mesoscale fracture model,we rederive the parametric process of the model.By introducing two new parameters(fluid density ratio and viscosity ratio),the new model can handle the case of different kinds of fluid in fractures and the background medium.The new model is used to study the seismic wave propagation characteristics of seismic waves in a mixed saturated fluid medium.The results show that the characteristic frequency of attenuation and dispersion is mainly determined by the fluid type in the fracture,while the dispersion and attenuation magnitude is determined by the fluid both in the fractures and the background medium.Comparing the velocity and attenuation of the new model with the patch saturation model and the double porous medium model,the rationality of the new model is verified.According to the good correspondence between Chapman model and standard linear solid(SLS)model,we take Chapman double fracture model as an example,and discuss the problem of simulating the complex anisotropic fractured reservoir with generalized standard linear solid(GSLS)model.The results show that the frequency denpendent moduli,velocity and attenuation of the complex anisotropic models can be simulated by using the high frequency limit modulus,the low frequency limit modulus and the corresponding characteristic frequency for each set of fractures.The modulus defect of each set of fractures is used to characterize the contribution of each fracture set to the equivalent model.The low frequency modulus of the equivalent model is calculated by the Chapman model of the low frequency limit and the Gassmann equation.The high frequency modulus of the equivalent model is calculated from the Chapman model at the high frequency limit.The practicability of the method is verified by numerical simulation of three sets of orthogonal fracture models.The frequency dependent dispersion and attenuation related with fluid flow will have a greater impact on the frequency dependent AVO and AVAZ and cause the variation of the reflection coefficient.Furthermore,the frequency dependence of anisotropy is very sensitive to the fluid.Through numerical experiments based on the Chapman model,the P wave velocity,P wave dispersion,dispersion of gradient P anisotropy are analyzed,and finally the P wave anisotropy parameter dispersion gradient(PADG)are selected as the fluid identification factor for fractured reservoir with meter-scale fractures.By rewriting the Ruger equation,we get the objective function of retrieving the PADG attribute.We use the orthogonal matching pursuit method to decompose the prestack azimuth gather and get the frequency divided seismic data.Finally,we get the PADG attribute body through the frequency dependent AVAZ least-square inversion.The theoretical model test shows that the method adapts to the high signal to noise ratio.Finally,the practicability of the method is verified by the actual seismic data.The inversion of the fracture parameters is the most important problem in the prediction of fractured reservoirs.The mapping between seismic data and fracture parameters can be established by the reflection coefficient formula.Due to the complexity of the model,the deterministic inversion method has strong multiple solvability and large amounts of computation.Therefore,the inversion method based on stochastic theory is applied.The inversion method based on Bayesian theory uses the prior information and likelihood function of the model to solve the posterior distribution,which not only can get the maximum probability solution of the inversion target,but also can evaluate the uncertainty of the solution.The MCMC method is used to solve the inverse problem of the fracture parameters.Through the test of numerical model and the actual seismic data,we can see that when priori information is uninformative,the uncertainty of the solution is strong.When the effective prior information is available,the inversion result is reliable.This provides a new way for the parameter inversion and quantitative prediction of fractured reservoirs.