多重孔岩石微分等效介质模型及其干燥情形下的解析近似式

经典的微分等效介质(DEM)理论可用于确定多孔介质的弹性性质,但由于缺乏多重孔DEM方程,其估计的多重孔岩石的等效弹性模量依赖于包裹体(即不同孔隙纵横比的孔或缝)的添加顺序.本文首先从Kuster-Toksöz理论出发建立了Zimmermann和Norris两种形式的多重孔DEM方程.Norris形式的多重孔DEM方程预测的等效弹性模量总是位于Hashin-Shtrikman上下限内,而Zimmermann形式的多重孔DEM方程有时会越界.然后,通过使用干燥岩石模量比的解析近似式,对两个相互耦合的Norris形式DEM方程进行解耦得到干燥多重孔岩石的体积和剪切模量解析式.用全DEM方程的数值解对解析近似式的有效性进行了测试,解析公式的计算结果在整个孔隙度分布区间与数值解吻合良好.对实验室测量数据在假设岩石含有双重孔隙的情形下用双重孔DEM解析公式对岩石的弹性模量进行了预测,结果表明,解析式准确地预测了弹性模量随孔隙度的变化.双重孔(即软、硬孔)DEM解析模型可用来反演各孔隙类型的孔隙体积比,它可以通过实验室测量与理论预测之间的平方误差最小反演得到.砂岩样品的反演结果揭示,软孔的孔隙体积百分比与粘土含量没有明显的相关性.     

多孔可变临界孔隙度模型及储层孔隙结构表征

碳酸盐岩、致密砂岩和页岩等储层具有孔隙类型多样、孔隙结构复杂和非均质性强等特征,属于典型的多重孔隙储层,孔隙结构表征是多重孔隙储层预测和流体识别的关键.现有的孔隙结构表征方法大多利用孔隙纵横比或者构建一种新参数来描述孔隙结构.岩石临界孔隙度模型是一种常用的岩石物理模型,具有一定的物理意义和地质含义.本文推导了岩石临界孔隙度与岩石孔隙结构(孔隙纵横比)之间的关系,进而利用极化(形状)因子建立临界孔隙度与弹性参数之间的关系,构建了能够包含多种孔隙类型的多孔可变临界孔隙度模型.利用多孔可变临界孔隙度模型由储层的弹性参数反演不同孔隙类型的体积含量.实验室测量数据和实际测井数据表明,多孔可变临界孔隙度模型能够适用于多重孔隙储层岩石物理建模和孔隙结构表征.     

Rock physics modelling of porous rocks with multiple pore types: a multiple-porosity variable critical porosity model

A critical porosity model establishes the empirical relationship between a grain matrix and a dry rock by the concept of critical porosity. The model is simple and practical and widely used. But the critical porosity in the model is a fixed value that cannot relate to pore structure. The aim of this paper is to establish the theoretical relationship between critical porosity and pore structure by combining Kuster–Toksöz theory with the critical porosity model. Different from the traditional critical porosity model, critical porosity is not an empirical value but varied with pore shape and the ratio of bulk modulus versus shear modulus of the grain matrix. The substitution of the theoretical relationship into Kuster–Toksöz theory will generate the formulae for the bulk and shear moduli of multiple-porosity dry rocks, which is named the multiple-porosity variable critical porosity model. The new model has been used to predict elastic moduli for sandstone and carbonate rock. We compare the modelling results for P- and S-wave velocities and elastic moduli with the experimental data. The comparison shows that the new model can be used to describe the elastic properties for the rocks with multiple pore types.