A Study of Immiscible Fingering in Linear Models
Authors: Perkins T.K. , Johnston O.C. 
Published: December 2007

Abstract
Recent improvements in processes for recovering viscous reserves has renewed interest in the phenomenon of immiscible fingering. This paper phenomenon of immiscible fingering. This paper describes studies of immiscible fingering in linear Hele-Shaw and bead-packed models. immiscible fingers were readily initiated in all models. The fingers, however, were damped out before traveling very far in the uniform bead packs that contained connate water. The damping mechanism is believed due to the movement of the two phases in a direction transverse to the direction of gross flow.
To study the transverse flow phenomenon under controlled conditions, oil and water were injected simultaneously and side by side in linear models. Transition zones were formed that grew broader as the distance from the inlet increased. The saturation distribution in the transition zones could be described mathematically by an "immiscible dispersion coefficient" and the well known error function solution of the dispersion equation. The immiscible dispersion coefficients were found to be proportional to the interstitial velocity and proportional to the product of the bead diameter proportional to the product of the bead diameter and packing inhomogeneity factor.

Introduction
In the literature of the petroleum industry, there is an obvious inconsistency in the descriptions of immiscible displacements occurring with unfavorable viscosity ratios. There is a vast literature that treats such displacements as being stable and capable of being described by relative permeability concepts such as those incorporated in the Buckley-Leverett approach. Furthermore, several experiments have been described that apparently confirm the validity of such an approach. On the other hand, there is also a considerable wealth of literature that argues that such displacements are unstable and will be characterized by immiscible fingers. Several mathematical studies have shown the inherently unstable nature of such displacements, and the appearance of fingers is confirmed by numerous experimental studies.
In recent years, improvements in processes for recovering viscous reserves has renewed interest in the phenomenon of immiscible fingering. Consequently, we have recently pursued the question of immiscible fingering along the same conceptual lines used successfully in a study of miscible fingering. This has led to concepts about the mechanics of immiscible finger growth that have not previously been reported in the literature. This paper, which describes these studies, is divided into two main sections. The first section covers conceptual studies of immiscible displacements in linear, transparent models. It was found that immiscible fingers were readily initiated in the models, but the fingers were damped out before traveling very far in uniform bead packs containing connate water. The damping mechanism is believed due to movement of the two phases in a direction transverse to the direction of gross flow.
Further studies of the transverse flow phenomenon are reported in the second section of the paper. Oil and water were injected simultaneously and side by side in linear models. Transition zones were formed that grew broader as the distance from the inlet increased. The saturation distribution in the transition zones could be described mathematically with an "immiscible dispersion coefficient" and the well known error function solution of the dispersion equation. This relationship is very similar to descriptions of transverse adding in miscible systems, and there is hope that a mathematical theory describing immiscible finger growth can ultimately be developed along the lines previously developed for miscible fingers.

CONCEPTUAL EXPERIMENTS
Exploratory or conceptual experiments of several types have been devised.
SPEJ
P. 39