纳米孔隙储集层动态渗吸数学模型

Mathematical model of dynamic imbibition in nanoporous reservoirs

在考虑动态接触角效应、纳米限域效应、惯性效应和入口端效应的基础上,建立了纳米尺度孔隙中油-水渗吸方程,推导出固-油-水三相接触线摩擦系数与界面区流体黏度的关系式,结合毛细管束模型和对数正态分布理论,得到了致密岩心渗吸模型,并对影响渗吸动态的关键参数进行了分析。研究表明,纳米孔隙渗吸过程中,动态接触角效应对渗吸的影响最为显著,纳米限域效应(多层黏附效应和滑脱效应)次之,惯性效应和入口端效应影响最小;渗吸初期,惯性力的作用减小,接触线摩擦力的作用增加,动态接触角从初始的平衡接触角逐渐增大至最大并基本保持稳定;渗吸后期,接触线摩擦力的作用减小,接触角则从最大动态接触角逐渐降低并趋于初始的平衡接触角;孔隙半径减小,渗吸初期动态接触角效应增强,渗吸中后期动态接触角效应减弱;油水界面张力增加,渗吸动力增大,动态接触角效应增强;界面张力对渗吸动态的影响存在临界值,致密储集层渗吸提高采收率,过低的界面张力并不能获得更好的渗吸效果,最佳的界面张力需通过优化获得。

The oil-water imbibition equation in the nano-scale pores considering the dynamic contact angle effect,nanoconfinement effect,inertia effect,and inlet end effect was established,and the relation between the friction coefficient of solid-oil-water three-phase contact line and the fluid viscosity in the interface zone was derived.In combination with the capillary bundle model and the lognormal distribution theory,the imbibition model of tight core was obtained and key parameters affecting imbibition dynamics were analyzed.The study shows that in the process of nanopore imbibition,the dynamic contact angle effect has the most significant impact on the imbibition,followed by nanoconfinement effect(multilayer sticking effect and slippage effect),and the inertia effect and inlet end effect have the least impact;in the initial stage of imbibition,the effect of inertial force decreases,and the effect of contact line friction increases,so the dynamic contact angle gradually increases from the initial equilibrium contact angle to the maximum and then remains basically stable;in the later stage of imbibition,the effect of contact line friction decreases,and the contact angle gradually decreases from the maximum dynamic contact angle and approaches the initial equilibrium contact angle;as the pore radius decreases,the dynamic contact angle effect increases in the initial stage of imbibition and decreases in the later stage of imbibition;as the oil-water interfacial tension increases,the imbibition power increases,and the dynamic contact angle effect increases;there is a critical value for the influence of interfacial tension on the imbibition dynamics.In improving oil recovery by imbibition in tight oil reservoir,interfacial tension too low cannot achieve good imbibition effect,and the best interfacial tension needs to be obtained through optimization.