The generalized mixture rule （GMR） is usually applied in determining mechanical properties such as the rheological property and Young’s modulus of multi-phase rocks. However, it is rarely used to determine electric...The generalized mixture rule （GMR） is usually applied in determining mechanical properties such as the rheological property and Young’s modulus of multi-phase rocks. However, it is rarely used to determine electrical conductivity of multi-phase rocks presently. In this paper, we calculate the effective conductivity using the 3D finite element method for a large number of two-phase medium stochastic models. The GMR is then employed as an effective conductivity model to fit the data. It shows a very close relationship between the parameter J of GMR and the ratio of conductivities of the two phases. We obtain the equations of the parameter J with the ratio of conductivity of two phases for the first time. On this basis, we can quickly predict （or calculate） the effective conductivity of any twophase medium stochastic model. The result is much more accurate than two other available effective conductivity models for the stochastic medium, which are the random model and effective medium theory model, laying a solid base for detailed evaluation of oil reservoirs.展开更多
A perturbation method is used to study effective response of nonlinear Kerr composites, which are subject to the constitutive relation of electric displacement and electric field, Dα=εαE＋xα｜E｜^2E. Under the ext...A perturbation method is used to study effective response of nonlinear Kerr composites, which are subject to the constitutive relation of electric displacement and electric field, Dα=εαE＋xα｜E｜^2E. Under the external AG and DC electric field Eapp = Eα（1 ＋ sinωt）, the effective nonlinear responses and local potentials are induced by the cubic nonlinearity of Kerr materials at all harmonics. As an example in three dimensions, we have investigated this kind of nonlinear composites with spherical inclusions embedded in a host. At all harmonic frequencies, the potentials in inclusion and host regions are derived. Furthermore, the formulae of the effective linear and nonlinear responses are given in the dilute Iimit.展开更多
基金sponsored by National Natural Science Foundation of China (Grant No. 40874034)the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KZCX2-YW-QN508)
文摘The generalized mixture rule （GMR） is usually applied in determining mechanical properties such as the rheological property and Young’s modulus of multi-phase rocks. However, it is rarely used to determine electrical conductivity of multi-phase rocks presently. In this paper, we calculate the effective conductivity using the 3D finite element method for a large number of two-phase medium stochastic models. The GMR is then employed as an effective conductivity model to fit the data. It shows a very close relationship between the parameter J of GMR and the ratio of conductivities of the two phases. We obtain the equations of the parameter J with the ratio of conductivity of two phases for the first time. On this basis, we can quickly predict （or calculate） the effective conductivity of any twophase medium stochastic model. The result is much more accurate than two other available effective conductivity models for the stochastic medium, which are the random model and effective medium theory model, laying a solid base for detailed evaluation of oil reservoirs.
文摘A perturbation method is used to study effective response of nonlinear Kerr composites, which are subject to the constitutive relation of electric displacement and electric field, Dα=εαE＋xα｜E｜^2E. Under the external AG and DC electric field Eapp = Eα（1 ＋ sinωt）, the effective nonlinear responses and local potentials are induced by the cubic nonlinearity of Kerr materials at all harmonics. As an example in three dimensions, we have investigated this kind of nonlinear composites with spherical inclusions embedded in a host. At all harmonic frequencies, the potentials in inclusion and host regions are derived. Furthermore, the formulae of the effective linear and nonlinear responses are given in the dilute Iimit.
