The effect of strong heterogeneity on the onset of convection induced by a vertical density gradient in a saturated heterogeneous porous medium governed by Darcy's law is investigated. A computer package has been developed to study the applicability of an average Rayleigh number as a criterion for the onset of convection in strongly heterogeneous geologic media. The heterogeneous geologic media have been described using random spatial functions for the permeability field which are lognormally distributed and spatially correlated. Both isotropic and anisotropic correlation lengths within the geologic structure are considered. This paper presents the first 3D theoretical treatment of the conditions for the onset of convection (Rayleigh stability criteria) in strongly heterogeneous porous media. We elucidate the critical role that spatial dimensionality (2D versus 3D flow) plays in controlling convection processes and stability criteria. Our results quantitatively demonstrate for the first time that spatial dimensionality is a dominant control on the onset of convection in a strongly heterogeneous geologic medium. Unbounded Rayleigh number behavior is observed in 3D. This leads to the important new conclusion that a Rayleigh number (based on mean quantities) is unlikely to be a valid predictor for the onset of convection in 3D strongly heterogeneous porous media. Furthermore, we systematically and quantitatively demonstrate that the onset of convection in a heterogeneous geologic medium is highly sensitive to changes in the standard deviation of the lognormal permeability field, moderately sensitive to changes in the level of correlation length, and relatively insensitive to the anisotropy of correlation length.