Applying the Nernst-Planck formalism of 1D diffusive flux equations for ionic species of salts dissolved in water, Pitzer formalism for activity coefficients and PHREEQC software for species diffusion coefficients, with ionic strength-dependence coefficients optimized, we obtained expressions for apparent diffusion coefficients of sodium chloride, calcium chloride, and sodium sulphate, prevalent in deep aquifers. PHREEQC 1D transport simulations of free-diffusion experiments yielded temporal evolution of the concentration and gradient vertical profiles. The dynamics of concentrations non-equilibrium fluctuations during the free-diffusion experiments have been recorded by shadowgraphy. Thanks to the calculated gradient profiles the thickness of the sample has been integrated in the analysis equations of the structure functions. From the earliest stages of the diffusion process we measured the diffusion coefficients for the three salts, in very good agreement with reference measurements, validating the technique and method of analysis for studying free-diffusion in reservoirs targeted for CO2 and energy vectors storage.