The Multiphase Conductivity Model And Its Application To The Study Of Crustal Fluids In The Tibetan Plateau

Saturated porous media,such as loam,rock,and fracture networks,generally consist of a solid phase with low electrical conductivity and a salt solution that conducts electricity in the pores.To calculate the conductivity of mixed multiphase media,a series of multiphase conductivity models have been developed,which are mainly divided into empirical formulas based on experimental data,boundary and mixing models,pore network models and theoretical models.The multiphase conductivity model is a bridge between resistivity logging response and reservoir parameters,so it is widely used in the petroleum industry.In recent years,the application of magnetotelluric sounding to deep fluid detection has become a hot topic in geoscience research,and the multi-phase conductivity model is the key to calculate deep fluid content.Archie formula based on sandstone resistivity experiment is the most widely used conductivity model in reservoir description.However,Archie’s formula is based on the assumption that the solid phase medium is not conductive.With the increase of muddy content in sandstone,or with the increase of temperature deep in the earth,the conductivity of rock skeleton cannot be ignored,thus Archie’s formula becomes inaccurate.The Hashin-Shtrikman Upper Bound(HS+)and Hashin-Shtrikman Lower Bound(HS-)conductivity models apply only to two-phase media.The Parallel model and Perpendicular model constrain the upper and lower boundaries of effective conductivity of the medium,but the model is too simple.Although these models play an important role in certain situations,they are not sufficient to simulate complex multiphase media systems in the real world.In this paper,a global conductivity model of mixtures doped with several conductor components is studied.It is not only possible to calculate the effective conductivity of the multiphase medium in the whole product space,but also its model parameters are related to the shape and connectivity of each phase particle in the medium and represent structural variables.According to the fitting results of conductivity data of the Parallel model,Hashin-Shtrikman Upper Bound(HS+),Random model,and the Perpendicular model,we found that the structural variable of the four conductivity models is fixed,indicating that these four conductivity models only represent a special case of the model in this paper.However,with the change of structure variable,the model in this paper can calculate the effective conductivity of any mixed medium.By fitting the experimental data of rock conductivity,we summarize the numerical range of common rock structural variables,which is of great significance to the understanding of the connectivity of rock microstructure.Current models and theories for calculating the conductivity of rock in partial melting have little or no consideration for the connectivity of the melt or solid phases.In practice,connectivity is complex.Therefore,it is necessary to find more practical models and formulas to describe the conductivity of partially molten rock.Based on magnetotelluric data,three conductivity models are used to calculate the melt fraction in the Kunlun fault,Songpan-Ganzi fault,Qiangtang fault,Southern Tibet,and the Northwestern Himalaya.The range of melt fractions calculated by the model in this paper is between the results of the HS+and the Parallel model.By comparison,it is found that the results of this model are consistent with the melt fractions obtained by previous models based on seismology,electromagnetism,and geochemistry.