Mathematical Model Of Tight Oil Imbibition Based On Fractal Theory

Due to the small pore throat and the high heterogeneity,the spontaneous imbibition based on capillary can effectively exploit crude oil in small pores,so it is of great importance to study the spontaneous imbibition of tight reservoirs.Based on the previous research,this paper takes a tight sandstone reservoir in Xinjiang Oilfield as the research object.Combined with porosity and permeability experiments,high pressure mercury intrusion and electron microscope scanning,the pore-throat structural characteristics of the tight sandstone reservoir in this study area are studied.Based on the above analysis and fractal theory,the fractal characteristics of pore-throat structure in tight sandstone reservoir are analyzed,The pore throat fractal dimension D_f in this block is 1.4192¹.6920,and the tortuocity fractal dimension D_T is 1.1885¹.4056.The spontaneous imbibition experiments were conducted on tight sandstone cores using mass method.Spontaneous imbibition phenomenon was observed under the action of capillary force and the change of core expulsion over time was recorded.Through influencing factor analysis experiments,the influencing factors of tight sandstone imbibition are determined,and methods for improving the infiltration and recovery of tight sandstone are proposed.The effects of non-wetting phase viscosity,contact angle,interfacial tension,water saturation,and pressure on spontaneous imbibition were experimentally studied.The experimental results showed that the imbibition recovery decreased with the oil-water viscosity ratio,contact angle,and original water saturation,and increased with pressure and interfacial tension,but the pressure has little effect on the imbibition recovery.The irreducible water saturation has the greatest influence on the imbibition recovery,and imbibition recovery of tight sandstone in the high water cut period is less than 5%,and the potential for imbibition recovery is small.Based on the fractal theory,this paper considers the interface microstructure effect and the original water saturation,and combines the Poiseuille equation to derive the mathematical model of imbibition.The capillary imbibition mathematical model are deduced,this model is a function of the core's maximum pore throat radius(r_max),pore throat radius fractal dimension?D_f?,tortuocity fractal dimension?D_T?,contact angle???,water saturation?S_w?,wettability??_w?and non-wetting phase viscosity(?_nw),porosity???,interfacial tension???,and time?t?.Comparing the results of the model calculations with the experimental results under different conditions,it can be seen that both the imbibition recovery curves of the two processes are relatively close to each other from the curve trend to the final imbibition recovery,and the maximum relative error is8.11%.The derived model can accurately predict the imbibition recovery of tight sandstone and provide a reliable theoretical basis for the development of tight oil.