Modelling of Radial Water/Oil Displacement Processes In Water-wet Porous Media: Part II. The Capillary Regime
Authors: Agharazi-Dormani N. , Hornof V. , Neale G.H. 
Published: March 2010

Abstract
The effects of five important 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 model porous medium were investigated using statistical model building techniques. Two different approaches were used. In the first approach the operating variables studied included:the flow rate of the injected fluid,the radial distance from the injection point,the viscosity difference between the displaced and displacing phases,the permeability of the porous medium, andthe oil/water interfacial tension.
The measured responses were the fractional oil recovery and the number of fingers estimated at breakthrough. The present investigation was confined to the low flow rate (i.e., capillary flow) regime, and it produced results that are potentially useful in practical enhanced oil recovery schemes.
It was found that the recovery decreased as the oil/water viscosity ratio 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 interfacial tension on oil recovery was negative and it also 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 effect of interfacial tension on the number of fingers was more complex and depended on the value of other operating variables.
In the second approach, the operating variables were grouped together in dimensionless terms such as the capillary number and the viscosity ratio among others. The recovery was found to be enhanced with an increase in the ratio of breakthrough radius to the cell thickness. It was, however, reduced as the viscosity ratio increased and this attenuating effect became more significant as the flow rate increased. The effects of the ratio of the cell thickness to the square root of the permeability and of the capillary number depended on the values of the other variables. The number of fingers increased as the values of the above ratios increased, although the actual effects were not always straightforward. The results obtained are in good agreement with previous work and theory. By considering all five variables and their interactions simultaneously, a better understanding of the oil recovery process has been achieved.

Introduction
Previous analysis of Enhanced Oil Recovery (EOR) processes(1,2) has identified the flow rate of the injection fluid, the viscosity difference between the displaced and displacing fluids (or their ratio), the permeability of the porous medium, the oil/water interfacial tension (IFT), and the breakthrough radius, as the primary operating variables affecting finger formation and oil recovery. However, the underlying mechanisms are not well understood. Investigations to date have been limited to individually examining the influence of only one or two of these variables(3–14). As a result, little information exists as to the joint or interactive effects of all of these important factors.