一种适用于孔隙体积应变的有效应力方程

An effective stress equation for pore volume strain

土力学奠基石Terzaghi有效应力原理被广泛应用于油藏孔隙和渗透率应力敏感研究中,然而其对于岩石孔隙体积应变的适用性存在争议。对颗粒不可压缩和颗粒可压缩的多孔介质分别进行了受力分析,推导了总体积、颗粒骨架、孔隙体积的有效应力表达式,与Biot、Skepmton有效应力方程对比,建立了适用于孔隙体积应变的新型有效应力方程,并进行了试验论证和应用举例。研究表明:在颗粒不可压缩多孔介质中,有效应力为超出平衡孔隙流压之外的颗粒间宏观等效应力;在颗粒可压缩变形多孔介质中,有效应力为其相同应变下的等效应力,有3种有效应力分别适用于总体积应变、颗粒体积应变、孔隙体积应变;新提出的孔隙体积有效应力方程与孔隙度、岩石总体积压缩系数、颗粒压缩系数、总应力和流压相关,4个理论计算式计算结果在3种多孔介质试验测试结果中的偏差均在5%以内;孔隙体积有效应力系数解决了如何定量增总应力来等效模拟储层降流压生产过程这一关键问题,3个压缩系数关系式理论计算准确方便。

The effective stress principle of Terzaghi,the foundation of soil mechanics,is widely used in reservoir stress-sensitive research for pore volume and permeability.However,its applicability to the pore volume strain of rock is controversial.Force analysis on porous media with incompressible grains and compressible grains are conducted,and expressions of effective stress for total volume,grain skeleton and pore volume are deduced,which are further compared with effective stress equations proposed by Biot and Skepmton.Then,a new effective stress equation for pore volume strain is established.Finally,the experimental demonstration and application are conducted.The results show that the effective stress is the macroscopic equivalent stress of intergranular beyond the pore pressure in the porous media with incompressible grains.While the effective stress is equivalent stress for the same strain in the porous media with compressible particles.There are three kinds of effective stress equations for total volume strain,particle volume strain and pore volume.The new effective stress for pore volume is related to porosity,compression coefficient of total volume and particles,total stress and pore fluid pressure.The deviations between four theoretical calculations and experimental tests on three kinds of pore media are within 5%.With increasing the total stress quantitatively,the coefficients of pore volume effective stress can be used for equivalently simulating reservoir production with pore pressure dropping.The calculation of the three compressibility equations is convenient and accurate.