Tufan Ghosh

Abstract

This work deals with finding exact solution of the Stokes' problem analogue to a composite free flow and porous matrix layers. The upper free flow region is bounded above by a plate moving with a time dependent velocity and the bottom porous layer is of unbounded depth. The velocity field corresponding to this Stokes' problem is obtained by means of Laplace transform, Mellin-Fourier transform and Faltung theorem on convolution. This study investigates the effect of the transition zone (mushy layer) length on the interfacial velocity profile. We have compared these results with the classical Stokes' problem. We realize that the findings of this work are useful in understanding flow mechanics in solidification process of multi-component melts, the impact of viscous shearing inside the lumen region of an endothelial glycocalyx layer of human arteries.

Abstract

Fractured carbonate reservoirs are principal crude oil and natural gas resources. These reservoirs are composed of matrix block with interconnected network of fractures. Oil or gas recovery from such low porous and low permeable reservoirs is important because a large amount of such hydrocarbon fluids are trapped inside those reservoir formulations. Water-flooding or more specifically spontaneous imbibition is one of the most effective recovery mechanisms to increase the production from fractured reservoirs. However, the performance of water-flooding mainly depends on the wettability of the reservoirs. In co-current imbibition, wetting phase displaces the non-wetting phase in such a way that the non-wetting phase moves in the same direction of the wetting phase. Hence the corresponding mathematical model requires a total flux condition. This study deals with the mathematical modeling of co-current spontaneous imbibition from heterogeneous porous reservoirs. The resulting governing equations are highly non-linear in nature. We solve these equations numerically and show that the co-current imbibition recovery is very much sensitive to the viscosity ratio, porosity variation models and the wettability of the reservoir. The impact of the viscosity ratio on the water saturation gradient and the end point mobility ratio is also analyzed. In addition, the variations in the heterogeneity and wettability of the medium and the corresponding influence on the sweeping efficiency of the co-current imbibition is investigated.

Abstract

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.