A Scaling Criterion For Miscible Displacements
Authors: Coskuner Gokhan , Bentsen Ramon G. 
Published: March 2010

Abstract
The use of scaled laboratory models to simulate reservoir conditions is one of the more effective methods for evaluating the merit of a miscible oil recovery process. When using this approach it is important to keep in mind that, because of the adverse solvent to oil viscosity ratio, most miscible displacements are dominated by viscous fingering. Because viscous fingering plays a critical role in the recovery process, it is important that its impact be handled correctly. However, conventional scaling methods cannot account properly for the viscous instabilities usually associated with miscible displacement.
In this paper a recently developed scaling group, which can be used for scaling instability in the laboratory, is presented. The new scaling group includes explicitly, for the first time, the effect that the length of a porous medium has on the instability of a miscible displacement. Moreover, it is shown that, while the individual effects oftransver.se and longitudinal dispersion cannot be scaled, their combined effect on the controlling mechanism/or most miscible displacements (viscous fingering) can be scaled using the new scaling criterion.

Introduction
One of the more effective methods for evaluating a miscible oil recovery process is that of displacements in laboratory models scaled to simulate reservoir conditions. In scaling of miscible displacement, an inspectional analysis, complemented by a dimensional analysis, is used usually to obtain a set of scaling criteria(1–3). Moreover, it has been shown that, in order to represent correctly the behaviour of the prototype in the laboratory, the model must be geometrically similar, and the ratios of all the forces present in the model must be equal to those in the prototype. However, it is sometimes impossible to construct a model so that every one of the forces that exist in the reservoir is scaled simultaneously in the model(3–7). In particular, when microscopic dispersion in the transverse and longitudinal directions is scaled simultaneously with the macroscopic parameters, impractically large models are required for most laboratory investigations, Therefore, relation of some of the scaling requirements s undertaken, and models which represent the prototype for a restricted number of conditions are devised. However, if some other parameter which has not been scaled exercises significant control over the displacement, then the significance of the laboratory results for prediction of field operations becomes questionable.
It has long been recognized that miscible displacement with a low viscosity solvent driving a more viscous oil will be an unstable process leading to the formation of viscous fingers. Therefore, although the effects of mixing should be considered in any attempt to predict miscible flood performance, it is viscous fingering that is likely to dominate the behaviour of a miscible flood(9). It has been shown that, when viscous fingering is the dominant phenomenon, the breakthrough recovery is a function only of the viscosity ratio for both miscible and immiscible displacements(10). As a consequence, it seems that the most important controlling factor in a miscible displacement is the viscous fingering.