A New Calculation Method of Rock Elastic Modulus Based on Kuster-Toksöz Model

In the process of combining the Kuster-Toksöz (KT) model with the differential effective medium theory (DEM), the rock elastic modulus of the porous medium is finally obtained by continuously replacing the matrix with the pore inclusions. The pore volume that is replaced each time is constant in the existing method. While the matrix volume is decreasing, the calculated rock elastic modulus is greatly deviated from the Xu-White model. In this paper, it is by improving the pore volume calculation formula for each replacement so that the replacement volume is gradually decreased with the increase of the number of iterations. And it keeps the ratio of the replacement volume to the matrix volume constant. When the number of iterations is large enough, The ratio is sufficiently small. The requirements of the KT calculation formula are satisfied and the calculation result is closer to the theoretical value. The test results show that with the increase of porosity, the equivalent elastic modulus of rock gradually converges to the elastic modulus of the pore inclusions, indicating that the method accords with the physical understanding; compared with the existing KT iterative model, the calculation results using this method are closer to the Xu-White model. The new method proposed that the calculation formulas of the actual volume and the calculated volume of pore inclusions are more in line with the pore segmentation process of KT model.