求取岩石基质体积模量的线形拟合方法(英文)

Calculations of rock matrix modulus based on a linear regression relation

岩石基质的体积模量或其倒数--压缩系数,在进行油气预测的流体替换和孔隙度反演时,是重要的输入参数,但是利用现有方法很难准确求得。文中提出了一种求取该参数的线形拟合方法,该方法通过对Gassmann方程的合理简化并引入Eshelby-Walsh干燥岩石椭球包体近似公式,获得了计算岩石基质压缩系数的拟合公式,可方便地利用公式计算该参数。实际碳酸盐岩岩样的岩石物理测试分析显示:利用饱和岩样和干燥岩样测得的基质压缩系数的差异小于1%,说明所求参数是正确的,可靠的。

The rock matrix bulk modulus or its inverse, the compressive coefficient, is an important input parameter for fluid substitution by the Biot-Gassmann equation in reservoir prediction. However, it is not easy to accurately estimate the bulk modulus by using conventional methods. In this paper, we present a new linear regression equation for calculating the parameter. In order to get this equation, we first derive a simplified Gassmann equation by using a reasonable assumption in which the compressive coefficient of the saturated pore fluid is much greater than the rock matrix, and, second, we use the Eshelby- Walsh relation to replace the equivalent modulus of a dry rock in the Gassmann equation. Results from the rock physics analysis of rock sample from a carbonate area show that rock matrix compressive coefficients calculated with water-saturated and dry rock samples using the linear regression method are very close （their error is less than 1%）. This means the new method is accurate and reliable.