考虑固液界面作用的表观渗透率分形模型  

Apparent permeability model for fractal porous media considering the effect of solid-liquid interface

作　　者：娄钰[1] 朱维耀[1] 宋洪庆[1] 黄小荷[1] 王小锋[1] 张雪龄[1] 

机构地区：[1]北京科技大学土木与环境工程学院,北京100083

出　　处：《东北石油大学学报》2014年第2期69-73,9,共5页Journal of Northeast Petroleum University

基　　金：国家重点基金项目(50934003)

摘　　要：考虑微流动中固液界面作用,基于Navier-Stokes理论,推导牛顿流体在圆管中的流速分布及流量表达式,引入界面因子以表征固液界面作用的影响;利用分形渗流理论及界面因子,得到表观渗透率表达式,建立综合考虑微流动固液界面作用和复杂孔隙结构特征的渗流数学模型.结果表明:考虑固液界面作用时,微流动流速下降;其影响程度与管径有密切关系,微管直径越小,界面因子越大,表明固液界面作用的影响越大.存在着临界直径,当小于临界直径时,固液界面作用的影响随微管直径减小呈非线性迅速增加;大于临界直径时,流速趋于泊肃叶定律的预测.在分形多孔介质中,随着固液界面作用增大,表观渗透率首先呈非线性迅速下降,随后趋于稳定,说明固液界面作用对渗流影响不可忽略.该数学模型能清晰表征固液界面作用对渗流的影响,为低渗透和致密油藏开发提供依据.Considering effect of solid-liquid inter-molecule force,the paper modelled fluid flow at pore scale and derived a relation for flow velocity depending on solid-liquid interface parameters.Interface coefficient is subsequently defined to account for influence of solid-liquid interface on flow rate.Based on fractal characteristics of porous media and the above flow rate formula,a motion equation is presented considering effect of solid-liquid interface.According to Darcy's law,apparent permeability model is obtained,which could account for the comprehensive effect of porous media characteristics and solid-liquid interface.Numerical analysis presents relationship among flow rate,apparent permeability and influential factors.It is shown that the smaller the pore radius,the larger the effect of solid-liquid interface.There exists critical pore radius,smaller than which the effect increases nonlinearly with decrease of pore radius.Given fractal characteristics of porous media,the apparent permeability model could clearly simulate the effect of solid-liquid interface on fluid dynamics in porous media.Apparent permeability first decreases nonlinearly with solid-liquid interface effect increasing and then tends towards stability.The models presented here provide additional theoretical perspective of liquid flow in low permeability reservoirs and tight oil reservoirs.

关 键 词：固液界面作用 多孔介质 分形 表观渗透率 流量 

分 类 号：TE312[石油与天然气工程—油气田开发工程]