This paper investigates the impact of aspect ratio on the growth rate of viscous fingers using high resolution numerical simulation in reservoirs with aspect ratios of up to 30:1. The behaviour of fingers in porous media with such high aspect ratios has been overlooked previously in many previous simulation studies due to limited computational power. Viscous fingering is likely to adversely affect the sweep obtained from any miscible gas injection project. It can also occur during polymer flooding when using chase water following the injection of a polymer slug. It depends upon the viscosity ratio, physical diffusion and dispersion, the geometry of the system and the permeability heterogeneity. It occurs because the interface between a lower viscosity displacing fluid and a higher viscosity displaced fluid is intrinsically unstable. This means that any small perturbation to the interface will cause fingers to grow. It is therefore almost impossible to predict the exact fingering pattern in any given displacement although many previous researchers have shown that it is possible predict average behaviour (such as gas breakthrough time and oil recovery) provided a very refined grid is used such that physical diffusion dominates over numerical diffusion. It is impossible to use such fine grids in field scale simulations. Instead engineers will tend to use standard empirical models such as the Todd and Longstaff or Koval models, calibrated to detailed simulations, to estimate field scale performance. At late times in high aspect ratio systems, we find that one finger dominates the displacement and that this finger grows with the square root of time, rather than linearly. We also observe that this single finger tends to split, during which time the solvent oil interface length grows linearly with time before one finger again dominates and grows with the square root of time. This cycle can repeat several times. We also find that industry standard empirical models cannot properly capture the average behavior of the fingering in these cases because they assume linear growth as a function of time. We show that a modified Peclet number can be used to estimate when these empirical models are no longer valid.
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