摘要
在Kuster-Toks?z(KT)模型与差分等效介质理论(DEM)结合过程中,通过用孔隙包含物逐渐替换基质的方法获得孔隙介质的岩石弹性模量。现有方法每次替换的孔隙体积是常量,而基质体积不断减小,实际参与替换的包含物体积与孔隙包含物计算体积是不同的。本文通过改进每次替换的孔隙体积计算公式,使得替换体积随迭代次数的增加而逐渐减小,保持替换体积相对基质体积的比率不变,在迭代次数足够大的条件下使得该比率足够小,满足了K-T计算公式的要求,计算结果更接近理论值。测试结果显示:随着孔隙度的增大,岩石等效弹性模量逐渐收敛于孔隙包含物的弹性模量,说明本方法与物理规律一致;与现有的KT迭代方法相比,采用本方法的计算结果与Xu-White模型更接近,本方法提出孔隙包含物的实际体积与计算体积的计算式更符合KT模型孔隙切分过程。
In the process of combining the Kuster-Toks?z(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.
引文
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