In this paper, an approximate integral equation solution for a horizontal, unsteady flow of two viscous incompressible fluids is derived. Wettability variation of the porous medium is also considered in the present study. The non-wetting phase recovery fraction is obtained in terms of dimensionless time for 1D model from the derived solution. The derived approximate recovery fraction has been compared with the existing experimental data and empirical correlations for spontaneous imbibition from water-wet medium. It is observed that the normalized water saturation profiles show sharp gradients indicating some instability of the water front. Hence, a linear stability analysis is developed to study viscous instability of the co-current spontaneous imbibition. Viscous instability phenomenon for a two-phase oil–water system is also discussed. The corresponding instability number related to co-current imbibition recovery is estimated. The present study clearly spells out the effect of the instability number on the recovery process and estimates a critical instability number for co-current spontaneous imbibition.

中文翻译：

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部分覆盖均质烃油藏并流自吸采油模拟

在本文中，导出了两种粘性不可压缩流体的水平非定常流动的近似积分方程解。本研究还考虑了多孔介质的润湿性变化。非润湿相恢复分数是根据一维模型的无量纲时间从导出的解决方案中获得的。已将导出的近似回收率与现有的实验数据和水湿介质自吸的经验相关性进行了比较。据观察，归一化的水饱和度剖面显示出陡峭的梯度，表明水前沿的一些不稳定性。因此，开发了线性稳定性分析来研究并流自吸的粘性不稳定性。还讨论了油水两相系统的粘性不稳定现象。估计与并流渗吸恢复相关的相应不稳定性数。本研究清楚地阐明了不稳定数对恢复过程的影响，并估计了并流自吸的临界不稳定数。