Experimental Study of Cocurrent and Countercurrent Flows in Natural Porous Media

Abstract

Summary Flow experiments involving cocurrent and countercurrent spontaneous water/oil imbibition were performed on the same laterally coated sample of a natural porous medium with local saturation measurements and various boundary conditions. The experiments with countercurrent imbibition showed slower oil recovery, a smoother water/oil front, and slightly lower ultimate oil recovery than those with predominantly cocurrent imbibition. Numerical simulations revealed that the relative permeabilities that enabled good prediction of countercurrent oil recovery rate are about 30% less than the conventional cocurrent relative permeabilities at a given water saturation. Viscous coupling is assumed to permeabilities at a given water saturation. Viscous coupling is assumed to be the origin of this difference. A new formulation of Darcy equations that uses a matrix of mobilities was found to be in qualitative agreement with experimental results. Introduction Fractured reservoirs contain a substantial share of the world's oil reserves. Forecasts of the efficiency of a water-injection process for such reservoirs remain difficult because of poor knowledge of the different fracture networks and the individual production behavior of the matrix blocks in contact with water; i.e., each block produces its oil more or less independently from its neighbors produces its oil more or less independently from its neighbors under the combined effects of gravity and capillarity. Two-phase displacement of this kind is called spontaneous or free imbibition, and the mechanisms controlling such flow are analyzed in this study. Spontaneous imbibition involves both cocurrent and countercurrent flows in proportions that depend on the ratio of gravity to capillary forces and on the conditions applied at the boundaries of the block. The main concern has been finding a reliable procedure for scaling up laboratory imbibition tests performed on small cores. Experimental and numerical approaches have been considered. In the experimental approach, the scaling laws that apply to waterflooding were extended to spontaneous imbibition. Kyte proposed a centrifuging method for scaling up the effect of both gravity and capillary forces. Lefebvre du Prey, however, found that, when this centrifuging method was used to keep the ratio of gravity to capillary forces constant, a large discrepancy existed between the scaled-up recovery curves corresponding to different-sized blocks. The validity of standard macroscopic equations of two-phase displacements then became questionable because relative permeabilities are defined for fluids moving in the same direction and not permeabilities are defined for fluids moving in the same direction and not for countercurrent flows. Other possible origins of this discrepancy were suggested, such as imperfect knowledge of the boundary conditions and local heterogeneities of the porous medium that cannot be scaled up. Jacquin et al. therefore undertook a careful study of the mechanisms of spontaneous imbibition. Spontaneous imbibition tests (ID) on laterally coated sandstone samples 9.8 to 39 in. [25 to 100 cm] in length gave results in good agreement with conventional scaling laws. Therefore, the experimental scaling-up procedure requires numerous rules to be respected. The selection of the rock sample and the applied boundary conditions used for performing the imbibition test can strongly influence the results and prevent scaling up to reservoirblock sizes. The numerical method may be an alternative for solving this problem because the heterogeneities of the reservoir and various boundary conditions can easily be considered. It is necessary, however, to introduce the exact capillary pressure and relative permeability curves. Blair and Torsaeter and Silseth showed that these curves have an important impact on the oil recovery rate, with capillary pressures probably having a stronger effect than relative permeabilities. Some questions arise about using water/oil relative permeabilities, always determined from a cocurrent waterflood, to predict permeabilities, always determined from a cocurrent waterflood, to predict countercurrent imbibition flows. Unfortunately, there are very few experimental determinations of countercurrent relative permeabilities.

Chemical Flooding in Naturally Fractured Reservoirs: Fundamental Aspects and Field-Scale Practices

“…Although some experiments have shown that the waterflood performance in the water-wet and intermediate-wet fractured chalks may be nearly independent of wettability state (Tang and Firoozabadi, 2000), the general perception is that under favorable water-wet condition, capillary imbibition significantly improves the oil recovery (Babadagli, 2001a). An important type of capillary imbibition is the spontaneous imbibition, which involves both cocurrent and countercurrent flows in proportions depending on the ratio of gravity-to-capillary forces and on the existing conditions at the matrix boundaries (Bourbiaux and Kalaydjian, 1990). Rock properties such as matrix permeability, size and shape, wettability, heterogeneity, and boundary conditions control the capillary imbibition.…”

Simulation of Naturally Fractured Reservoirs. State of the Art

“…Indeed, due to capillary forces, water spontaneously invades the matrix blocks thus producing oil by countercurrent and cocurrent flows (Bourbiaux et al, 1990). However, intermediate to oil-wet field situations are often encountered in practice.…”

A Rapid and Efficient Methodology to Convert Fractured Reservoir Images Into a Dual-Porosity Model

“…The matrix medium is assumed to have constant petrophysical properties throughout the bedding plane. Capillary imbibition of a matrix block involves countercurrent flows of water and oil [8] with a gradual advance of a smoothly-tilted front from the boundaries to the center of the block. The geometrical method is a simplified representation of this flow mechanism, based on the two following assumptions: -piston-type invasion of the matrix medium by displacing fluid; -a distance X of the front from block boundaries changing with time t according to a function which is independent of block shape for a given rock-fluid system.…”

“…A(X) is computed using a rapid, patented procedure for image processing. A eq (X) is a second-order polynomial: (8) Normalized area versus distance curves are discretized with a constant normalized area step to give the same weight to any volume of oil recovered independently of the time at which it is produced. The geometrical method can be applied to a stack of layers with similar petrophysical properties of the matrix medium.…”