Modelling Of Radial Water/Oil Displacement Processes In Water-Wet Porous Media
Authors: Agharazi-Dormani Nader , McLean David D. , Hornof Vladimir , Neale Graham H. 
Published: March 2010

Abstract
Response surface methodologies were used to study the effects of five important variables on oil recovery and finger formation during immiscible radial displacement of oil by water ma consolidated water-wet porous medium. Using a modifiedcentral composite experimental design, the following operating variables were investigated: flow rate of injection fluid, radial distance from injection point, viscosity difference between displaced and displacing phases permeability of porous medium and oil/water interfacial tension. Empirical models based directly on the operating variables and indirectly on pertinent dimensionless terms were developed to describe fractional recovery and number of fingers at breakthrough. The resulting models provide valuable new information about the individual and the joinl effects of the operating variables. Many previously reported ffects were confirmed and quantified under the more rigorous and extensive experimental conditions employed in this paper. Moreover, identification of interactions among operatingariables allowed some discrepancies in previously reported effects to be reconciled.

Introduction
Of the many enhanced oil recovery schemes, immiscible flooding, including water flooding, is the most widely used. Unfortunately, whenever the mobility ratio, M = (Kw/ μw)/(Ko/ μo), is greater than one, interfacial instabilities can lead to viscous fingering, whereby the displacing aqueous phase tends to flow preferentially through paths of lesser hydrodynamic resistance, leaving large regions of unrecovered oil. Despite its importance to the success of commercial oil recovery operations, fingering remains a relatively poorly understood phenomenon.
Most previous displacement studies concerning viscous fingering have used unconsolidated porous media in spite of erious problems with respect to reproducibility of critical factors such as porosity, permeability, wettability and structural heterogeneity. Investigators who have used consolidated porous edia((1, 2)) employed linear flow setups in which it is very difficult to establish an initial planar displacement front. Furthermore, enhanced oil recovery in the field typically employs injection of the displacing fluid a(a point creating an initial radial displacement pattern. To overcome these limitations, adial displacement in a consolidated porous medium consisting of sintered glass beads sandwiched between two parallel glass plates was investigated in the present work(3).
Previous analysis of enhanced oil recovery processes(4, 5) has identified the primary factors affecting finger formation and recovery as; flow rate of injection fluid, viscosity difference (or ratio) between the displacing and displaced fluids, permeability of the porous medium, oil/water interfacial tension and breakthrough radius. Typically such studies have been limited to an examination of the individual effects of these variables(1–32). As a result, little information as to the joint or interaction effects exists. Indeed, the physico-chemical processes involved suggest that the effect of anyone of these factors on finger formation and recovery may well depend upon the levels of the other factors. Such information is essential for an improved understanding of enhanced oil recovery.
Experimental design and model building techniques for the empirical evaluation of the individual and joint effects of operating variables on a given response have been well described in the literature (Box et al. (33)) and they fall within the domain of response surface methodology.