Rate Dependence of Unstable Waterfloods

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Abstract
Summary: Viscous fingering is part of the flow mechanisms that are operative in waterflooding and in a wide range of EOR methods. This work presents a laboratory and computer model analysis of the viscous-fingering dynamics that develop when a less mobile fluid is immiscibly displaced by a more mobile fluid in a permeable medium. Physical experiments of horizontal fluid displacements conducted in a rectangular bead pack show that the amplitude/frequency character of the wave-like fingers that form depends on flow rate and mobility ratio. The nature of these wave-like features is shown for two viscosity ratios and several displacement rates. Spatial frequency domain analyses of finger shapes at fixed time intervals were conducted on digitized records of the laboratory experiments. The results of these analyses indicate that fluctuations comprising the fingered zone have a wave number corresponding to a maximum growth rate. The analyses suggest that the amplitude of flow fluctuations can be characterized by a root mean square (RMS) growth rate that is linear in time. Finite-difference solutions of a set of two-dimensional (2D) flow-in-porous-media equations were made to exhibit similar frontal instability. The linear growth rate of the mixing zone suggests that fractional flow relationships can provide an adequate and practical method of representing space-averaged two-phase flow variations for many reservoir engineering applications.