Matrix diffusion in northern Negev fractured chalk and its correlation to porosity

In this paper we report on vertical variations in the values of the effective diffusion coefficient determined on 19 chalk samples collected throughout most of the Eocene section (285 m) in the northern Negev desert, Israel. The dependence of the measured values on sample depth, porosity, permeability and mineralogy was also evaluated. Finally, a correlation between the measured effective diffusion coefficient and porosity is suggested for these samples. The calculated values of the diffusion coefficient ranged from 1.22 to 2.55 × 10^-6 cm²/s. These values are significantly higher than those measured on consolidated rock samples, and similar to values reported for British Cretaceous chalk. Our results demonstrate that the effective diffusion coefficient values for the Eocene chalk in the northern Negev desert, Israel are exclusively dependent on the porosity of the chalk matrix by D_c = D₀ε² (m = 2 in Archie's law) and not on its mineralogy or permeability. The fitted exponent, m, falls between the two extreme values of 1.5 and 2.5 that were mentioned by [Diffusion in Natural Porous Media (1998)] for porous media. However, a linear relationship between the effective diffusion coefficient and porosity fits better the data within the range of the measured of porosities. These correlations provide an easier and less costly method of estimating the diffusion coefficient in chalk samples from the Eocene Group in the northern Negev desert, Israel.