An Experimental Verification Of A Modified Instability Theory For Immiscible Displacements In Porous Media
Authors: Sarma H.K. , Bentsen R.G. 
Published: March 2010

Abstract
Most enhanced recovery schemes involve the displacement of one fluid by another. In the design of such schemes, it is important to know whether the displacement is stable or unstable. Thus, it is of interest to be able to predict the boundary which separates stable displacements from those which are unstable.
Recently, a new theory was developed to predict the onset of unstable behavior. However, when this theory was compared with Hele-Shaw experiments, it was found that the non-linear time function used in the development of the theory was inappropriate. It is the purpose of this paper to show how the earlier theory can be modified so as to include a linear time function. Moreover, the modified theory is validated by comparing theoretical results with those obtained experimentally. In particular, the results obtained from carrying out a series of runs using rectangular shaped core holders packed with unconsolidated sand demonstrate that the modified theory correctly predicts the stability boundary. In addition, it is possible to use the theory to predict not only the breakthrough recovery for stable displacements, but also that for pseudostable displacements.

Introduction
Two of the more important factors determining the efficiency of any immiscible displacement process are the heterogeneity of the reservoir and the stability of the displacement process. While nature dictates the scale of the heterogeneities and the manner in which they are distributed throughout the reservoir, man has some control over the parameters which dictate whether a displacement is stable or unstable. Thus, it is of interest to study the conditions under which a displacement becomes unstable.
Early stability studies of immiscible displacement demonstrated that mobility ratio, displacement velocity, system geometry and dimensions, capillary and gravitational forces system permeability and wettability were all parameters pertinent to the stability problem(1–9). However, none of these studies sought to combine these variables into one dimensionless group which could be used to quantify the stability classification. The first authors to derive such a dimensionless group, together with its critical value, were Peters and Flock(10). These authors also demonstrated that the system dimensions were the most critical parameters, because they appeared in the dimensionless group raised to the second power, whereas all the other parameters were raised to the first power.
Because the analysis of Peters and Flock was based on the concept of a velocity potential, they were unable to determine completely how variations in rock and fluid properties might affect the stability boundary. By basing his analysis on the concept of a force potential rather than that of a velocity potential, Bentsen(11) was able to take proper account of the effect of rock and fluid properties on the stability problem, As a consequence, his instability number was proportional to that derived by Peters and Flock. However, a recent experimental study has demonstrated that the non-linear time function used by Bentsen in his analysis was inappropriate(12). That is, the experiments described in Reference 12 demonstrated that the distance travelled by the tip of a finger, with respect to the moving boundary, was a linear rather than a non-linear function of time.