Simulation Of Elastic Parameters Based On Finite Difference Method And Application In Digital Rock Physics

Digital core is a new field of petrophysics experiments,which simulates response of multi physics fields and calculates equivalently elastic parameters of rocks through three-dimensional imaging techniques and mathematical methods under the condition of geological information.We can study the relationship between microstructures,components and equivalent parameters in macro-scale.Compared with the traditional rock physics experiments and technology,digital core model can depict the microstructure of rocks more accurately.In this paper,a new approach is proposed to acquire modulus of rocks based on high-order finite difference method,which is easy to understand and implement,taking up less memory compared with the finite element modelling and making up the weakness of the conventional rock physics experiment with long period,high costs and big errors.For the purpose of estimating availably elastic moduli,the digital rock sample is embedded in a homogeneous elastic region assigned elastic properties of the grain material.With receivers at the bottom of the model,it is possible to measure the time-delay of the peak amplitude of the plane P-or Swaves caused by the inhomogeneous structure of the digital rock sample.With the time-delay(compared to the reference model)we estimate the effective velocity of both the compressional and the shear waves.The study of random models、theoretical model and digital rock samples indicates that simulation results agree well with the experimental solution,which verifies the validity of the method.The method is further improved based on the three-dimensional qP wave equation.The study of the three-layer model and five-layer model indicates that simulation results agree well with the theoretical values based on Backus theory,which is a new approach for anisotropic theory.Petrophysical parameters can be computed directly by numerical simulation based on Finite Difference Method in digital rock physics.Focusing on the boundary theory(H-S,VR,Hill),effective medium theory(K-T,SCA,DEM),dry-rock frame model(Krief、Nur、Pride),we analysis the equivalence and the conditions which must be satisfied.The digital rock physics can depict the actual structure of underground medium more precisely.The prior information at the point of constraint can be computed reasonably by digital rock physics.We can correct constraint parameters through the comparison between numerical simulation results and Pride model to provide theoretical support for the model of P-wave or Swave velocity estimation.Finally,the results of shear wave are applied to discriminate fluid of reservoir in the pre-stack elastic impedance inversion.