Effect of Lateral Diffusivity on Miscible Displacement In Horizontal Reservoirs
Authors: Van Der Poel C. 
Published: December 2007

Abstract
When oil is displaced from a horizontal formation by another fluid of lower density, the latter tends to override the former in the shape of a tongue owing to gravity segregation. This gravity tongue has an adverse influence on the oil recovery. If the fluids are miscible, diffusion (mixing) takes place at the interfacial boundary of the gravity tongue. This mixing should have a favorable effect on oil recovery. The report describes a laboratory study of the magnitude of the mixing zone under various conditions, so as to assess the effect of diffusion on oil recovery both in laboratory experiments and under actual field conditions. The technique used enables visual observation and measurement of the size of the mixing zone in transparent glass-powder packs. The results show that in experiments in small models and cores the width of the mixing zone may well be of the same order of magnitude as the height of the model. In such cases oil recovery is favorably affected by mixing. It can further be concluded that, under conditions prevailing in the field, mixing of the injected fluid with reservoir oil is equal to that caused by molecular diffusion alone, eddy-mixing not taking place to any appreciable extent. A simple calculation, then, shows that molecular diffusion is too small for a beneficial effect to be expected from the injection of miscible fluids in horizontal or nearly horizontal reservoirs unless pay zones are thin.

Introduction
This paper gives results of experiments made on the mixing which occurs when a miscible displacement is carried out in a horizontal reservoir. This mixing takes place at the interfacial boundary of the gravity tongue formed when the lighter injected fluid overrides the oil present in the reservoir. The object of the experiments was to simulate the field case where, for example, propane with a viscosity of 0.075 cp under reservoir conditions displaces an oil of viscosity 0.6 cp. In the experiments the lighter fluid had a viscosity of about 1 cp and the heavier one a viscosity of about 8 cp, so as to obtain the same viscosity ratio. In order to enable the results to be compared with those published in the literature, a set of experiments with viscosity ratio equal to one was also performed.

EXPERIMENTAL TECHNIQUE
The technique developed for the purpose enables the width of the mixing zone to be studied as a function of time and place. A glass-powder pack is saturated with a water-glycerine mixture of suitable viscosity, which represents the reservoir fluid. The pack is then rendered transparent by dissolving sufficient ammonium thiocyanate in the mixture to obtain a solution with a refractive index matching that of the glass powder. Alkaline water to which phenolphthalein has been added is used as the lighter and less-viscous displacing fluid. In those places where mixing or diffusion of the two liquids occurs, the slightly acidic ammonium-thiocyanate solution neutralizes the alkali in the water, and the glass pack shows up white against the red-colored invading water. If a black cloth is hung over the back of the apparatus, the transparent part of the glass pack appears black. In this way the position of the two phases and the transition zone between them is clearly visible, as shown in Fig. 1 (where the red-colored invading water is the grey-shaded zone lying uppermost).In all experiments the amount of alkali in the water was chosen such that the upper contour corresponded to a concentration of 5 per cent of the dense liquid. The lower contour is determined by the size of the glass grains and the thickness of the pack and, consequently, varies from experiment to experiment.
SPEJ
P. 317^