数字岩石物理中弹性参数的有限差分计算方法

Simulation of elastic parameters based on the finite difference method in digital rock physics

数字岩石物理利用三维成像技术和数学方法,建立数字岩心,开展多场物理响应模拟,计算岩石的等效弹性参数,为岩石物理学研究开拓了新的领域.本文发展了一种基于高阶有限差分的岩石模量数值计算的新方法,该方法便于理解,容易实现,占用内存相对较少,计算效率高,结果合理,弥补了常规岩石物理实验周期长,成本高,误差大等不足.该方法将三维数字岩心样本嵌入一个具有与岩心样本骨架颗粒相同弹性性质的区域中扩充成一个新模型,测量由数字岩石样本非均匀结构带来的纵波或横波峰值振幅的时间差,利用该时间差(相对参考模型)估算纵横波的等效速度,进而求取等效弹性模量.理论模型和实际岩心的计算结果表明,数值模拟结果与实验结果有较高的吻合度,验证了该方法的合理性.

Digital core is a new field of petrophysics experiments,which simulates responses of multiple physics fields and calculates equivalently elastic parameters of rocks through threedimensional imaging techniques and mathematical methods.In this paper,a new approach is proposed to acquire modulus of rocks based on the high-order finite difference method,which is easy to understand and implement,taking up less memory and making up the weakness of the conventional rock physics experiment with long periods,high costs and big errors.For the purpose of estimating elastic moduli available,the digital rock sample is embedded in a homogeneous elastic region assigned elastic properties of the grain material.With receivers at the bottom of the model,it is possible to measure the time-delay of the peak amplitude of the plane Por S-waves caused by the inhomogeneous structure of the digital rock sample.With the time-delay（compared to the reference model）we estimate the effective velocity of both the compressional and the shear waves.The study on a theoretical model and digital rock samples indicates that simulationresults agree well with the experimental solution,which verifies the validity of the method.