The Calculation Models Of Permeability And Saturation And The Study Of Constraint Inversion Method For Fracture-Vug Reservoir

Permeability is one essential parameter in reservoir evaluation of quality and productivity and difficult to be acquired by geophysical exploration methods even by now.Instead,people still count on experimentally empirical relations or ideal microscopical models for approximated solutions.Yet,such approaches obviously meet obstacles in case of unavoidable differences of micro-structures caused by differences among rock types and reservoir properties.Considerable improvements were made with the development of digital core technique and high-speed computer technology.Former allows permeability to be calculated by renormalization method with isotropic gird blocks.Assumed the pore structure can be accurately described by discrete grid blocks,then the fore-mentioned renormalization method can give the effective permeability results.However,such method is no longer applicable when the permeability of the grid blocks varies severely.This paper offers a renormalization method in anisotropic conditions,which we assume that the permeabilities of each block differ in three orthogonal directions.We test its validity on calculation of permeabilities of idealized porous media and digital rocks.We also offer another way of calculating the effective permeability of digital cores by using Finite Difference Method(FDM).This method partitions the irregular pores into connected elliptic sections.A general laplace equation can be derived by mass conservation equation,and then the fluid pressure distribution can be obtained.Finally,the effective permeability of the model can be calculated by Darcy's law.Firstly,we apply the FDM on four idealized porous media and make comparative analysis with the analytical or empirical solutions.Secondly,we apply the FDM to calculate the permeabilities of digital rocks in three orthogonal directions and make comparative analysis with the results calculated by Lattice Boltzmann Method(LBM),which indicates that the predicted permeabilities calculated by FDM usually agree with permeabilities calculated by LBM within an order of magnitude.In this paper,we offer two kinds of models to calculate the saturations of fractured-vuggy reservoirs while one is improved Archie equation,the other is effective media model with non-conductive phase,secondary pores and matrix pores.In this case,we partition the sediment into two parts,one with parallel circuit of pores and fractures,and the other with series circuit of pores and vugs.The series of these two parts renders the final resistivity of the sediment.Other related parameters in this model can be provided through core analysis and then a constraint inversion with resistivity logging data is proceeded for the final result of saturation.However,limitation of this modified Archie equation exists which refers to the difficulty of acquiring of cores for fractured-vuggy reservoir.Thus,we present another calculation method of saturation by effective medium model.This model includes matrix porosity,secondary porosity,percolation rate and percolation exponent.Percolation rate and percolation exponent are commonly used to characterized the pore structures.During practical data processing,these parameters can be calculated by formation micro-scanner image(FMI)data.Same constraint inversion process is necessary for this method.The final saturation results can be obtained when the model gives the minimium difference between effective resistivity and resistivity logging data.