Unit Mobility Ratio Displacement Front Passing a Circular Permeability Discontinuity

Abstract

Abstract When a displacement front encounters an isolated permeability heterogeneity, it will be perturbed permeability heterogeneity, it will be perturbed The details of this perturbation will depend on the heterogeneity size and shape, the permeability contrast, and the mobility ratio. This paper deals with the displacement front behavior for one, simple, mathematically tractable model: a circular permeability discontinuity and unit mobility ratio. The progress of an initially planar front is shown or four permeability planar front is shown or four permeability contrasts: k2/k1 = 0, 1, 2,... The front distortion is more pronounced than streamline and isopotential distortion and it approaches a constant shape downstream from the discontinuity. Introduction The impact of reservoir heterogeneities on oil displacing processes depends upon the variation of the heterogeneous property (frequency distribution), its disposition (spatial distribution), and the inherent stability of the displacement mechanism. The interplay of these factors plus the impracticability, if not impossibility, of describing a natural rock system in any detail makes exact displacement front movements difficult to determine. It is useful, however, to be able to qualitatively visualize what heterogeneities will do to a displacement front. In this respect certain simple models that can be treated analytically are of value. The following analysis will show the displacement front behavior for one such model. MODEL DESCRIPTION The flow field two-dimensional and infinite in extent. The fluid flow is single phase, steady state and unidirectional at x, y - +/- 00, or before insertion of the discontinuity. A circular permeability discontinuity is placed at the origin. permeability discontinuity is placed at the origin. Porosity and thickness are the same within and exterior to the Porosity and thickness are the same within and exterior to the heterogeneity. This is exactly the same model that was used by Greenkorn et al. to check analytically streamlines as determined by Hele-Shaw flow models and finite difference computer techniques. FRONT POSITION CALCULATIONS The results of displacement front calculations are presented in Figs. 1 through 4 for four different permeability contrasts: k2/ki = 0, 1/2, 2. m. The permeability contrasts: k2/ki = 0, 1/2, 2. m. The times corresponding to the front locations are the same for the 0 and oo cases, and for the 1/2 and 2 cases. The determination of front positions at various times is based on known analytical expressions for velocity potentials (phi) and stream functions (psi). SPEJ P. 347