Modeling of radial water/oil displacement in water-wet porous media.

Abstract

The effects of five operating variables and four dimensionless groups on oil recovery and finger formation during the immiscible radial displacement of oil by water in a consolidated water-wet porous medium were investigated using statistical model building techniques. Two different approaches were used. In the first approach, experiments were carried out according to a central composite design with partial replication over the following operating region: (UNFORMATTED TABLE OR EQUATION FOLLOWS)$$\vbox{\halign{#\hfil&&\quad#\hfil\cr &Flow rate of injection fluid&0.65 $\le$ Q $\le$ 510.00 (mL/h)\cr &Radius of breakthrough&2.5 $\le$ R $\le$ 7.0 (cm)\cr &Viscosity difference&15 $\le\mu\sb{\rm o}$-$\mu\sb{\rm w} \le 152$ (mPa.s)\cr &Permeability&13.33 $\le$ K $\le$ 77.41 ($\mu$m$\sp2$)\cr&Interfacial tension (IFT)&0.3 $\le \gamma \le$ 30.0 (mN/m)\cr}}$$(TABLE/EQUATION ENDS) A second-order polynomial of the general form $$\rm Y = \beta\sb{o} + \sum\sbsp{i=1}{5} \beta\sb{i}X\sb{i} + \sum\sbsp{i=1}{5} \sum\sbsp{j=1}{5} \beta\sb{ij}X\sb{i}X\sb{j}$$was fitted to the data. It was found that for water-wet systems, the recovery decreased as the viscosity difference increased and this effect became more significant as the flow rate increased. Conversely, as the breakthrough radius or permeability of the cell increased, the recovery increased. The effect of IFT was negative and depended on the level of viscosity difference and permeability. In addition, an increase in flow rate, breakthrough radius or the viscosity difference resulted in an increase in the number of fingers, while high permeability reduced the number of fingers. The operating variables were grouped together in dimensionless terms such as the capillary number and the viscosity ratio, and the parameters ($\beta\sbsp{\rm i}{\prime}$s) were estimated for these terms. The recovery was found to be enhanced with an increase in the ratio of breakthrough radius to the cell thickness (R/h). It was reduced as the viscosity ratio increased and this attenuating effect became more significant as the flow rate increased. The effect of ratio of the cell thickness to the square root of the permeability (h/$\sqrt{K})$ and capillary number depended on the value of other variables. The number of fingers increased as any of the above ratios was increased with the exception of (h/$\sqrt{K})$ where the effect was more complex. (Abstract shortened by UMI.)