岩石的等效孔隙纵横比反演及其应用

摘要

通过融合Gassmann方程和由微分等效介质理论建立的干岩石骨架模型——DEM解析模型,本文提出根据纵波(和横波)速度反演岩石等效孔隙纵横比进行储层孔隙结构评价和横波速度预测的方法.首先,利用Gassmann方程和DEM解析模型建立岩石的纵、横波速度与密度、孔隙度、饱和度和矿物组分等各参数之间的关系；其次,将岩石孔隙等效为具有单一纵横比的理想椭球孔,应用非线性全局寻优算法来寻找最佳的等效孔隙纵横比使得理论预测与实际测量的弹性模量之间的误差最小；最后,将反演得到的等效孔隙纵横比代入到Gassmann方程和DEM解析模型中构建横波速度.实验室和井孔测量数据应用表明,反演得到的等效孔隙纵横比可准确反映储层的孔隙结构,对于裂缝型储层如花岗岩,其孔隙纵横比通常小于0.025,而对于孔隙型储层如砂岩,其孔隙纵横比通常大于0.08.只利用纵波与同时利用纵、横波反演得到的孔隙纵横比结果几乎完全一致,而且由纵波构建的横波与实测横波吻合良好,说明本文提出的等效孔隙纵横比反演及其横波速度预测方法是有效的.%By integrating Gassmann equations with the dry rock frame model, which is called as DEM analytical model, derived from the differential effective medium theory, this paper presents a method for pore structure evaluation and shear wave velocity prediction from the effective pore aspect ratios inverted from the P-wave (and S-wave) velocity. First, we build a relationship among P-wave and S-wave velocity, density, porosity, saturation and mineral compositions through Gassmann equations and the DEM analytical model. Then, by assuming that the porous rock contains spheroidal pores with a single aspect ratio, we apply a nonlinear global optimization algorithm to find the best estimate for the effective pore aspect ratio in terms of minimizing the error between theoretical predictions and experimental measurements. Finally, we estimate the S-wave velocity from the inverted effective pore aspect ratios. The experimental and well logging examples show that the inverted aspect ratio can be used to accurately indicate the pore structure of the reservoir. For fracture reservoirs, such as granite, its pore aspect ratio is typically less than 0.025, and for pore reservoirs such as sandstone, the pore aspect ratio is usually greater than 0. 08. Comparison of the inversion of pore aspect ratio between only from P-wave and from both P-wave and S-wave demonstrates that the pore aspect ratios from these two methods are almost the same. And, the predicted shear-velocity only from P-wave is in good agreement with the measured one. These results show that our method of shear-velocity prediction by using pore aspect ratios inverted from P-wave is effective.