The motivation for this work is a dramatically improved understanding of the fluid mechanics of drainage processes with applications such as CO_{2} storage in saline aquifers and water-alternating-gas injection as an enhanced oil recovery method. In this paper we present in situ distributions of wetting and nonwetting fluids obtained during core-scale two-phase immiscible drainage experiments. The ratio of the viscosity of the resident fluid to that of the invading fluid varies across a range of 0.43 to 150. Saturation distributions observed during dynamic displacement experiments are surprisingly smooth and do not display only one or a few dominant fingers, contrary to the indications of the current literature. The analysis of the saturation distribution using the fractal dimensions of the dynamic three-dimensional saturation distributions suggests that the constitutive relationships for porous media, namely, the relative permeability functions, are history dependent. Accordingly, it is suggested that the nonlinear, unstable flow regime is the regime where efforts to improve physical understanding must be focused.