A New Stability Theory For Designing Graded Viscosity Banks
Authors: Coskuner G. , Bentsen G.G. 
Published: March 2010

Abstract
Immiscible secondary recovery operations, even when successful, may leave behind significant amounts of oil. A possible candidate for recovering more of the oil is a process which uses an injection fluid which is miscible with the oil ill the reservoir. However, if such a process is to be viable, it is important to amid the continuous injection of an expensive solvent. This may be accomplished by injecting a small slug of solvent and then chasing it with a less expensive fluid which is miscible with the solvent. The success of such a scheme depends, to a large extent, upon whether the displacement process is stable or unstable. That is, if the displacement is unstable, viscous fingering greatly increases the amount of solvent required. Thus, when designing a miscible slug process, it is important to know whether the displacement is stable or unstable. Moreover, if the process is unstable, it is important to take into account the effect of viscous fingering.
This paper presents a newly-developed theory which is based on the small perturbations method. In particular, a dimensionless number, which is a function of the dimensions of the porous medium as well as the properties of the fluids and the porous medium and its critical value for the onset of viscous fingering, is derived. With the help of this dimensionless number, it is possible to design a graded viscosity solvent bank which is able to resist the adverse effects of viscous fingering. That is, the theory enables the prediction of the minimum size and configuration of a graded viscosity bank so as to maximize recovery by avoiding bank breakdown due to viscous fingering.

Introduction
Miscible flooding has received widespread attention as an enhanced oil recovery method because of its potential for recovering all of the oil contacted by the solvent. However, it is not usually economically feasible to displace the oil and entirely replace it with a solvent. Therefore, a process, in which only a small slug of solvent chased by a cheaper fluid which is miscible with the solvent, has been devised for use in field operations(1,2). Nevertheless, experiments carried out in areal models supported by field data have revealed that channeling and fingering of both the solvent into the oil and the chase-fluid into the solvent, because of the adverse mobility ratios encountered, reduced the areal sweep efficiency drastically. Thus, lower recoveries than expected were attained(3,4).
In an oil reservoir two factors significantly affect the sweep efficiency: in-homogeneity of the reservoir rock and frontal instability. Only the latter will be considered in this paper, Frontal instability can be reduced by controlling the mobility of the displacing fluid. It has been shown experimentally that one way to achieve this goal is to gradually change the viscosity of the injected fluid from that of the displaced fluid to that of the displacing fluid(5,6). Because the viscosity of a mixture depends upon composition, the desired change in viscosity can be achieved by gradually changing the composition of the fluids in the system from that of high viscosity to that of low viscosity.