一种简化的二维规则多边形孔隙岩石物理模型

A simplified 2D petrophysical model for regular polygon pores

将岩石中的孔隙等效为二维(2D)椭圆形或三维(3D)椭球体是目前岩石物理建模的主流做法,鲜见其他孔隙类型模型研究。针对Kachanove 2D规则多边形孔隙岩石物理模型存在孔隙形状因子参数多、仅能表征几种孔隙形态,且难以与自适应等数学算法相结合等问题,引入单一等效孔隙形状因子g替代上述模型中多个形状因子参数,得到一种简化的2D规则多边形孔隙岩石物理模型,并给出g的理论取值范围。数值正演结果显示:随着g增大,弹性模量降低;g越接近于1,弹性模量越大;弹性模量降低速率随g增大而降低;弹性模量的变化率随孔隙度变小而降低;实际应用中g的取值上限不是正无穷,而是一个有限的数。将所提简化2D规则多边形孔隙岩石物理模型应用于实验室砂泥岩测试及实际测井资料,结果表明该岩石物理模型在横波速度预测中具有良好应用效果。

It is common for petrophysical modeling to make pores in rock equivalent to two-dimensional(2 D)ellipses or three-dimensional(3 D)ellipsoids,while the modeling of other pore types is rarely studied.The Kachanove 2 D model is a classical petrophysical model for regular polygon pores,which involves multiple pore shape factors and can only characterize a few pore shapes.It can hardly be combined with mathematical algorithms such as adaptive algorithms.Considering this,we introduce a single pore shape factor gto act as the equivalent of multiple shape factors in the above model.In this way,a simplified 2 Dpetrophysical model for regular polygon pores is obtained,and the theoretical value range of gis given.The numerical forward modeling of sandy mudstone illustrates several conclusions:When gis greater,the elastic modulus is smaller,and thus when gis closer to 1,the elastic modulus is greater.Moreover,the decline rate of the elastic modulus decreases with the growth of g,and the change rate of the elastic modulus becomes smaller as the porosity declines.In practical applications,the range of gdoes not reach infinity.The proposed model is applied in laboratory tests on sandy mudstone and actual logging data,and the results show that the proposed model in this paper can achieve good performance in applications.