This paper introduces a novel approach to quantify the dependence of injectivity on the heterogeneity and auto correlation of the reservoir permeability distribution. The mathematical formulation of the problem was derived for two geometries representing a vertical cross section and a five-spot pattern. The heterogeneity is modeled by stochastically generated permeability distributions. The scaling of the governing equations, by inspectional analysis, generates a minimal set of dimensionless groups that is able to describe fracture-free injectivity in heterogeneous permeable media. The scaling procedure was validated against available analytical solutions and the importance of each dimensionless group on the dimensionless injectivity evaluated with an extensive set of numerical experiments. The results obtained provide a better understanding of how vertical well injectivity depends on heterogeneity and gives insight into why injectivity calculated from a core permeability average is frequently different from the injectivity manifested by the well in question.

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