连续胶结声速理论胶结半径表达式的一般性推广及应用

Generalization of the expression of cementation radius in Contact Cement Theory and its application

针对Dvorkin和Nur(1996)提出的连续胶结声速理论(CCT)中的胶结半径表达式仅适用于孔隙式胶结疏松砂岩的局限性,通过胶结物与颗粒之间的空间几何关系,在胶结物中心厚度不为零的前提下,推导了胶结物胶结半径的一般表达式,并考察了胶结物中心厚度对疏松砂岩声波速度的影响,探讨了该表达式在基底式胶结疏松砂岩纵横波速度预测中的应用.结果表明:随胶结物中心厚度变大,纵、横波速度均减小,且孔隙度越大,胶结物含量越少,速度下降越快;孔隙度或胶结物含量不变时,纵横波速比随胶结物中心厚度的增大而增大;纵横波速比随孔隙度的变化规律与胶结物中心厚度有关,当胶结物中心厚度较小时,孔隙度增大,纵横波速比略微减小,而当胶结物中心厚度较大时,孔隙度的增大会引起纵横波速比略微增大;对于基底式胶结疏松砂岩,使用推广后表达式修正的CCT模型相对原CCT模型能够更好地预测其声波速度,同时发现,利用其纵横波速比无法预测由孔隙度或胶结物含量变化引起的疏松砂岩软硬的变化,但是在胶结物含量或孔隙度不变的情况下,纵横波速比可指示由胶结物中心厚度变化引起的疏松砂岩软硬的变化.

The general expressions of cementation radius in the loose sandstone are proposed on the basis of the geometry relationship between the grain and cement with the assumption that the contact thickness is not zero. The expressions of cementation radius of Contact Cement Theory （CCT） proposed by Dvorkin et al. （1996） dontt consider the effect of contact thickness, which makes it only applicable for the pore cemented loose sandstone. To solve this problem, the general expressions of cementation radius are proposed. With the general expressions, the effect of contact thickness on the velocity of loose sandstone is analyzed and its application in the prediction of the compressional and shear wave velocity of basally cemented loose sandstone is discussed. The results show that when the contact thickness increases, the compressional and shear wave velocity decreases, the trend is more obvious when the porosity increases or the content o{ cement decreases. The ratio o{ compressional wave velocity to the velocity of shear wave （Vp/Vs） increases with the contact thickness i{ the porosity or cement content stays stable. Vp/Vs changes with porosity in different way for different contact thickness. When the thickness is small, the ratio decreases a little with the increase of porosity, but when the thickness becomes large, it goes in the other way. For the basally cemented loose sandstone, the modified model using the general expression of cementation radius predicts both the compressional and the shear wave velocity better than the original CCT, the study also shows that the change of the rigidity of the basally cemented loose sandstone caused by porosity or cement content change can＇t be predicted by Vp/Vs, but it can predict that caused by the change of contact thickness.