Viscous fingering is important in the oil industry. Viscous fingering can be a serious problem when one is displaces viscous oil by water in the form of waterflooding. Very few studies have been done to tnathematic8ally model the onset and propagation of viscous fingering. In this paper, twodimensional viscous Jngering in porous media is considering, both numerically and experimentally. The Barakat and Clark ]J Heat Transfer ASME, Nov., 19661 scheme is used to solve the governing equation. This is the first study reported in solving viscous lingering using this method. In addition, the momentum balance, the continuity equation, the energy balance and the mass balance equation were solved numerically. In the experiment, the fresh water was injected at a constant injection pressure into a consolidated porous medium saturated with glycerin. This consolidation produced a very unfavorable mobility ratio, leading to profuse viscous fingering that were captured with a digital camera. Limestone rock was used as the porous medium. The experimental results were compared with the numerical results and the comparison wigs favorable.
Viscous fingering generally refers to the onset and evolution of viscous instability that occurs in the displacement of fluids in porous materials. In most but not all cases, the mechanism of the instability is intimately linked to viscosity variations between phases. A fingering pattern that occurs when a more viscous material is displaced by a less viscous one fully miscible with it. In the oil industry, this viscous fingering can be a serious problem when one is trying to displace viscous oil to enhance oil recovery.
Viscous fingering in miscible fluids was first studied by Hill (1952). He conducted experiments on the displacement of sugar solution by water. In his results, he explained the instability by the difference of the driving pressure of small perturbations on the interface.
Lenormand and Zarcone (1985) studied numerically and experimentally the displacement of immiscible fluid in porous media. The purpose of their study was to show the experimental result for crossover between capillary and viscous fingering. Results show that when the injected fluid was the more viscous one, the increase of the flow rate decreases the fingering, thus this mechanism was described as a crossover between invasion percolation and a flat interface. Also Paterson et at (1984) examined the water fmgering into an oil-wet porous medium. Results showed that fmgering was wider in water-wet media than in oil-wet media. In addition, fingers were several times wider when the displacing fluid was wetting, rather than non-wetting.
Tan and Homsy (1986) studied the stability of miscible displacement processes in porous media. In their study, they used the quasi-steady-state approximation (QSSA) to deal with time dependence of the base states. They found that dispersion is the main mechanism to damp small fingers and to allow the preferred wavelength to grow. Also they conducted some initial value calculations and showed that there is a good agreement between the QSSA and the initial value calculation. In addition, they described the phenomenon of the onset of viscous fingering in the miscible displacements.