A Model Study of Viscous Fingering
Authors: Benham A.L. , Olson R.W. 
Published: December 2007

Abstract
Viscous fingering was studied as it occurred in an open Hele-Shaw model (1 ft × 4 ft × 1/16 in.); it was also studied in the same model packed with 80-mesh glass beads during miscible displacements under unfavorable viscosity ratio conditions. It was determined that the lengths of 20 elements of the front were distributed normally around the average position of the combined elements under all conditions. Represented by the normal distribution, the length of the viscous fingers grew linearly with the distance traveled from the point of finger formation, increased with displacement velocity, and increased with increasing mobility ratio. Results obtained during the first few inches of displacement were of little or no use in predicting finger growth and/or finger length throughout the 4-ft model since the point of finger initiation cannot be predicted and would often occur several inches from the point-of injection with either positive or apparent negative coordinates. The fingering occurring during a miscible slug displacement was much greater than would be predicted based upon the actual mobility ratios between in-place fluid and slug and between slug and following fluid, using the results described above for miscible displacement in the absence of a slug. Many of the experiments in the packed model showed that the rate of growth of the viscous fingers was diminishing toward the end of the displacement in the 4-ft long model, indicating that microscopic mixing, such as diffusion or dispersion, was decreasing the viscous fingering effect.

Introduction
Viscous fingering is a manifestation of a finger-shaped interface between displaced and displacing fluids occurring during typical miscible displacement projects for oil recovery. Its cause may be traced to the instability of a viscous fluid being displaced by a more mobile fluid. Viscous fingering takes on important significance in the miscible slug process where it may be a dominant factor in determining minimum slug size.Experimental and theoretical studies of viscous fingering have been made by other investigators. However, an exhaustive study of the variables affecting viscous fingering had not been made. The present study was undertaken in an effort to determine the effects of some of the more obvious variables-such as mobility ratio, displacement velocity, distance displaced, and packing-upon viscous finger length and growth in a small laboratory model. It does not necessarily follow that conclusions reached by studying the results of this model study may be applied to the field. Future studies would have to evaluate the effect of model size on extension of these results.

EQUIPMENT AND EXPERIMENTAL PROCEDURES
A flow diagram for the equipment used in this study is shown in Fig. 1. Basically, it consisted ofa constant-rate pump for the injection of displacing fluid intoa model made up of two flat transparent plates spaced a small distance apart andprovisions for the production of fluid into a calibrated graduate.
The displacing fluid contained a dye which allowed visual observation of finger spacing and length. The pump performed at rates from 2.5 cc/hr to 480 cc/hr, while pumping a light mineral oil into a bladder in a closed glass container holding the displacing fluid.The model was made up of two plates of 1-in. Plexiglass with dimensions 1-ft wide by 4-ft long.
SPEJ
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