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Context.In high mass X-ray binaries, an accreting compact object orbits a high mass star, which loses mass through a dense and inhomogeneous wind.Aims.Using the compact object as an X-ray backlight, the time variability of the absorbing column density in the wind can be exploited in order to shed light on the micro-structure of the wind and obtain unbiased stellar mass-loss rates for high mass stars.Methods.We developed a simplified representation of the stellar wind where all the matter is gathered in spherical “clumps” that are radially advected away from the star. This model enables us to explore the connections between the stochastic properties of the wind and the variability of the column density for a comprehensive set of parameters related to the orbit and to the wind micro-structure, such as the size of the clumps and their individual mass. In particular, we focus on the evolution with the orbital phase of the standard deviation of the column density and of the characteristic duration of enhanced absorption episodes. Using the porosity length, we derive analytical predictions and compare them to the standard deviations and coherence time scales that were obtained.Results.We identified the favorable systems and orbital phases to determine the wind micro-structure. The coherence time scale of the column density is shown to be the self-crossing time of a single clump in front of the compact object. We thus provide a procedure to get accurate measurements of the size and of the mass of the clumps, purely based on the observable time variability of the column density.Conclusions.The coherence time scale grants direct access to the size of the clumps, while their mass can be deduced separately from the amplitude of the variability. We further show how monitoring the variability at superior conjunctions can probe the onset of the clump-forming region above the stellar photosphere. If the high column density variations in some high mass X-ray binaries are due to unaccreted clumps which are passing by the line-of-sight, this would require high mass clumps to reproduce the observed peak-to-peak amplitude and coherence time scales. These clump properties are marginally compatible with the ones derived from radiative-hydrodynamics simulations. Alternatively, the following components could contribute to the variability of the column density: larger orbital scale structures produced by a mechanism that has yet to be identified or a dense environment in the immediate vicinity of the accretor, such as an accretion disk, an outflow, or a spherical shell surrounding the magnetosphere of the accreting neutron star.