AbstractThe imbibition of water in oil in Hele‐Shaw cells is described as an asymmetric random walk of water in a globally disordered medium. The disorder is modeled by an external, nonwhite, dichotomic noise, and the resulting random walk is described in terms of an effective Markovian master equation. The solution to this equation is given, and the mean‐squared‐displacement (MSD) of fluid particles in an effective ordered medium is calculated. This same quantity was also measured in squared cells with a fixed separation, where Soltrol 170 was displaced by twice‐distilled water. The flow generated by spontaneous displacement of oil presented three sequential stages, each with a characteristic speed and advancing front structure. In the first and third stages viscous fingering was not detected, but in the intermediate development stage it was observed. From the recorded time evolution of the front, its average displacement speed and the MSD of water in oil as a function of time were determined. Imbibition of water shows an enhanced diffusion regime in the first stage where MSD varies with t2, without any external noise effect. This is followed by a simple diffusion behavior in an effective medium in the second stage, where the external noise effect is large. In the third stage Gaussian diffusion prevails again. Numerical regression techniques were used to determine the best values of model parameters that fit experimental values for different stages, so that the sum of squared errors between theoretical predictions and experimental measurements is minimized. Good agreement was found with average errors of 14.3%, 5.9% and 0.6%, respectively.