Sweep Efficiency by Miscible Displacement in a Five-Spot
Authors: Mahaffey J.L. , Rutherford W.M. , Matthews C.S. 
Published: December 2007

Abstract
This paper gives results of an experimental study of the sweep efficiency of a miscible displacement in a five-spot. The study was carried out in a parallel-plate glass model in which effects of diffusion were scaled at or near the molecular diffusion level.
The experiments show that very early breakthrough (25 to 35 per cent of pore volume (PV) injected) may be expected in miscible floods because of the unfavorable viscosity ratio. However after 1 PV of displacing fluid is injected, the sweep rises to a reasonable value (50 to 60 per cent). Photographs show that small slugs of less than 10 per cent of PV tend to dissipate before breakthrough. A minimum slug size of 15 per cent of PV would appear to be necessary even in a relatively homogeneous formation.
Presence of a slug whose viscosity is intermediate between that of oil and gas increases the sweep efficiency of the oil-gas system. In a typical system the sweep at breakthrough rose from 26 to 37 per cent of PV for a 25 per cent slug. The increase in sweep brought about by use of a large slug could well pay for the extra deferment cost of the additional slug material.

Introduction
Most miscible displacement processes involve the displacement of oil with fluids of much lower viscosity and density. The displacement process at these adverse viscosity and density ratios is dominated by instability phenomena, i.e., viscous fingers and gravity tongues. These phenomena have highly adverse effects on oil recovery. Although a number of laboratory studies have been made to determine the effect of adverse viscosity ratios on five-spot sweep patters,1,2 the scaling of diffusion effects is uncertain. In the series of scaled model studies reported herein, an attempt was made to scale diffusion.
Model studies of miscible displacements in which molecular diffusion predominates are permitted by controlling the parallel plate spacing which reduces convective mixing to arbitrarily small levels. To decide how this scaling relates to any particular field displacement necessitates an estimation of diffusion effects for the natural rock being considered and conditions under which displacement will be conducted. The approach normally taken is to extrapolate data obtained from stable miscible displacements performed in the laboratory, such as those presented by Brigham et al.3 The validity with which such an extrapolation can be applied to an unstable flow system has yet to be established. If this approach is accepted, a family of oil recovery curves can be generated for a single viscosity ratio based on Brigham's observation that the magnitude of the dispersion coefficient is dependent, among other things, upon specific rock properties. Objective of our test was to define the lower limit of this range by presenting the case where dispersion effects were reduced to the molecular diffusion level in both the transverse and longitudinal directions.
The scaling of diffusion effects can be handled in two-dimensional systems by the usse of narrow-gap, parallel-plate models. In parallel-plate models the Taylor diffusion coefficient for convective mixing in the direction of flow at low flow rates is given by (following Taylor4):Equation 1
where h is the plate spacing and D is the molecular diffusion coefficient. Clearly, convective mixing can be reduced to arbitrarily small levels by manipulating the gap spacing h. This was the method used in these studies.