Tufan Ghosh

Zusammenfassung

We develop a phase-field model for evaporation from a porous medium by explicitly considering a vapor component together with the liquid and gas phases in the system. The phase-field model consists of the conservation of mass (for phases and vapor component), momentum, and energy. In addition, the evolution of the phase field is described by the Allen–Cahn equation. In the limit of vanishing interface width, matched asymptotic expansions reveal that the phase-field model reduces to the sharp-interface model with all the relevant transmission conditions on the moving interface. An energy estimate is derived, which suggests that for the diffusion-dominated regime, energy always decreases with time. However, this is not trivial in the case of other regimes. Through numerical examples, we analyze the efficiency of the developed phase-field formulation in modeling the evaporation process. We observe that our formulation is able to capture shrinking liquid droplet, in other words evaporation. Further, the phase-field model is upscaled to the Darcy scale using periodic homogenization for the diffusion-dominated regime. The effective parameters at the Darcy scale are connected to the pore scale through corresponding cell problems.

Zusammenfassung

In this study, co-current spontaneous imbibition in two-dimensional reservoir formations saturated with two immiscible and incompressible fluids is investigated. A computational workbench is proposed assuming that the porosity of the medium is constant however permeability is anisotropic i.e., direction-dependent. Numerical experiments are performed for two geometrically distinct reservoir domains, namely, narrow channel and square duct. The numerical experiments reveal that the dynamics of the recovery significantly depend on the ratio of the vertical to the horizontal intrinsic permeability i.e., anisotropic ratio. Specifically, the front propagation shows a striking dependency on the anisotropy of the medium. This analysis indicates that the cross-flow behavior triggers early water breakthrough and consequently substantial amount of oil/non-wetting phase bypassing. In addition, it is noted that the onset of forced imbibition is regulated by the mean pressure distribution of the underground formation. This article develops a correlation between the oil recovery percentage (\%) and the reservoir quality index (RQI). This can predict the oil recovery trend at a particular instance for a given reservoir configuration depending on the corresponding RQI values.

Zusammenfassung

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.

Zusammenfassung

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.

Zusammenfassung

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.