一维两相同向渗吸模型的求解方法

Solution to co-current imbibition of immiscible two-phase flow

李帅 2 丁云宏² 吕焕军³ 张彬⁴ 余芳⁵ 石善志⁶

中国石油勘探开发研究院，北京 100083 中国石油勘探开发研究院廊坊分院，河北 廊坊 065007 新疆油田宇澄热力有限公司，
新疆 克拉玛依 834000 中国石油华北油田分公司采油工程研究院，河北 任丘 062552 中国石油渤海钻探井下作业公司，河北 任丘 062550 中国石油新疆油田分公司工程技术研究院，新疆 克拉玛依 834000

渗吸作用是裂缝性储层提高原油采收率的重要机理，润湿相在毛细管力、重力的作用下进入储层基质，通过同向或逆向渗吸作用置换基质内的非润湿相。基于渗吸模型的局限性，文中推导了一维两相同向渗吸模型的通式，在相对渗透率曲线和毛细管压力曲线简化的基础上进行无因次化处理，并采用差分法进行了求解，获得了饱和度前缘移动曲线。采用COMSOL软件，对上述模型进行结果验证，并与逆向渗吸模型进行了对比。结果表明：COMSOL求解结果与文中求解结果近似，同向渗吸模型饱和度前缘推进速度比逆向渗吸更快，同向渗吸效率更高，采出原油更多。在裂缝性储层、常规甚至致密储层中，如果采用体积改造，密集切割储层基质，形成裂缝网络，则可发挥同向渗吸作用，提高原油采出程度。

Imbibition is an important mechanism to enhance oil recovery for fractured reservoir. Wetting phase enters the porous media with the force of capillary pressure and gravity and displaces non-wetting phase out from matrix in terms of co-current imbibition or counter-current imbibitions. Considering the limitation of imbibition model, this paper derived a one dimension, two-phase co-current imbibition mathematic model, and on the basis of simplified and dimensionless relative permeability curves and capillary pressure curves, numerical solution to saturation front profile was obtained using difference method. This model was verified via COMSOL and compared with counter current imbibition. The results indicate that values obtained in our model are approximate to the results using COMSOL. In co-current imbibition, saturation profile moves faster, and the imbibition efficiency is higher and oil output is much larger. In the development of fractured, traditional or even tight reservoirs, if complex fracture network is formed via volume fracturing, co-current imbibition can be used to enhance oil recovery.

10.6056/dkyqt201701013