非牛顿流体孔隙介质弹性波动方程  

Elastic wave equation for porous media saturated with non-Newtonian fluid

作　　者：孙卫涛 熊繁升 曹宏[3] 杨志芳[3] 卢明辉[3] SUN Weitao;XIONG Fansheng;CAO Hong;YANG Zhifang;LU Minghui(School of Aerospace Engineering,Tsinghua University,Beijing 100084,China;Zhou Pei-Yuan Center for Applied Mathema-tics,Tsinghua University,Beijing 100084,China;Research Institute of Petroleum Exploration and Development,PetroChina,Beijing 100083,China)

机构地区：[1]清华大学航天航空学院,北京100084 [2]清华大学周培源应用数学研究中心,北京100084 [3]中国石油勘探开发研究院,北京100083

出　　处：《石油地球物理勘探》2021年第3期519-527,I0010,共10页Oil Geophysical Prospecting

基　　金：国家自然科学基金项目“部分饱和孔隙介质地震波频散和衰减机理研究”(41874137)、“脉冲压力提高复杂储层孔隙—裂缝网络渗透率机理研究”(42074144);国家重点研发计划项目“高分辨率地震实时成像理论与技术”(2018YFA0702501)和“盐下超深储层地球物理表征与油气预测技术”(2019YFC0605504)联合资助。

摘　　要：重油、聚合物和压裂液等非牛顿流体普遍存在于油气勘探和开发过程中,研究孔隙尺度非牛顿流体流动及其对地震波场的影响具有重要意义。Biot理论忽略了流体黏性系数及剪切应力的非线性变化,虽然可用于描述完全饱和固体与经典牛顿流体在波场作用下的相互作用,但是对于非牛顿流体孔隙填充物来说不准确,因此需要研究含非牛顿流体效应的孔隙介质波动方程。通过建立非牛顿流体的分数阶导数麦克斯韦(fdMaxwell)模型,发现非牛顿流体孔隙介质波场传播特征与常规波动方程明显不同,波场频散和衰减存在共振现象,而牛顿流体饱和的孔隙介质波场频散和衰减未表现出这种特殊效应。同时,非牛顿流体本构关系的流变参数和分数阶导数对流—固耦合作用有明显影响。计算结果表明,含非牛顿流体效应的波动方程对重油砂岩纵波速度预测结果更准确。非牛顿流体本构关系对流—固耦合带来新的变化,对孔隙介质波场频散和衰减的影响不可忽视。文中研究是对真实地震岩石物理模型非牛顿流体效应的探索,对致密油储层地震勘探、含压裂液的裂缝储层微地震模拟等领域可产生积极的推动作用。Non-Newtonian fluids like heavy oil,polymer and fracturing fluid are common in oil and gas exploration and development.The Biot theory ignores the nonlinear changes in the fluid viscosity coefficient and shear stress.Although it can be used to describe the interaction between fully saturated solids and classical Newtonian fluids under the action of wave field,it is not correct for the pore filling of non-Newtonian fluids.After establishing a fractional order derivative Maxwell model of non-Newtonian fluid,we found that there was a significant difference in the features of wave field propagation between regular wave equation and elastic wave equations in porous media saturated with non-Newtonian fluid.Resonance phenomenon exists in wave dispersion and attenuation.Such special effects have not been found in wave field dispersion and attenuation in porous media saturated with Newtonian fluid.At the same time,the rheological parameters and fractional derivatives of the constitutive relations of non-Newtonian fluids have obvious effects on the fluid-solid coupling.Numerical results show that the wave equation with non-Newtonian fluid effect is more accurate to predict the P wave velocity of heavy oil sandstone.Non-Newtonian constitutive relation brings new changes to fluid-solid coupling mechanism,which cannot be ignored for the influence on wave field dispersion and attenuation.This study explored the petrophysical model for field seismic survey.The results are useful to other related fields,such as seismic exploration of dense oil reservoir,and micro seismic simulation in cracked reservoirs filled with fracturing fluid.

关 键 词：非牛顿流体 孔隙介质 弹性波动方程 

分 类 号：P631[天文地球—地质矿产勘探]