裂缝性页岩油藏多孔介质渗吸数学模型及应用

Mathematical model of imbibition in porous media of fractured shale reservoir and its application

提出考虑重力作用的圆形毛细管和板状管自发渗吸的隐式解析解。首先,对毛细管和板状管中的渗吸动力学进行分析,建立圆形毛细管和板状管中的渗吸模型,得到单管中自发渗吸的隐式解析解。其次,基于分形理论和毛管束模型进行模型的尺度升级,建立岩心尺度不同截面形状毛管自发渗吸的数学模型,提出考虑孔隙和微裂缝自发渗吸的最终半解析解模型。同时,开展不同因素对渗吸驱油速度和采出程度的影响研究,定量评价水湿裂缝性页岩储层中自发渗吸的产油量,分析孔隙分布、微裂缝分布、流体黏度和界面张力等因素对渗吸规律的影响。研究结果表明:渗吸速度主要受较小尺寸的孔隙和微裂缝控制,其随油水界面张力的增大而增大,原油黏度的增大而减小。利用室内自发渗吸实验和核磁共振技术对上述数学模型进行拟合和验证,确保数学模型的准确性和有效性。

An implicit analytical solution of SI of circular capillary and plate tube considering gravity was presented.Firstly,the imbibition dynamics in capillary and plate tubes were analyzed,the imbibition models in circular capillary and plate tubes were established,and the implicit analytical solution of spontaneous imbibition in a single tube was obtained.Secondly,the scale of the model was upgraded based on fractal theory and capillary bundle model,a mathematical model of SI of capillaries with different cross-sectional shapes at core-scale was established,and the semi-analytical solution model considering the SI of pores and micro-fractures was presented.At the same time,the influence of different factors on oil displacement rate and oil recovery was studied.The oil production of SI in shale flow spaces was quantitatively evaluated,and the influence of pore distribution,fracture distribution,fluid viscosity and interfacial tension was analyzed.The results show that imbibition rate is mainly controlled by smaller pores and fractures,which increases with the increase of oil-water interfacial tension and decreases with the increase of crude oil viscosity.The mathematical model is fitted and verified by laboratory experiment and NMR of imbibition,which ensures the accuracy and effectiveness of the mathematical model.