Due to their crystallochemical properties, clay minerals feature different types of structural surfaces which have their own adsorption energy distribution. To study that type of surface heterogeneity, the DIS (derivative isotherm summation) method has been developed by us. Now, a modified version of the DIS method is derived by using the Jagiello-Rudziliski approach and assuming that the local energy distributions are represented by the Dubinin-Asthakov distributions. Two different types of isotherms equations are used, one to describe adsorption in micropores and another one for describing adsorption on external surfaces. The derivatives of experimental adsorption isotherms with regard to In(p/p(s)) are simulated by combinations of the derivatives of corresponding local adsorption isotherms. This best fit provides information on adsorption capacity of the local existing domains, on the symmetry of their energy distribution function, and on the parameters characterizing the lateral interactions in each adsorption domain. Using the new equations for the local isotherm derivatives allows now to simulate very accurately derivatives of experimental adsorption isotherms, obtained by using our high-resolution quasi-equilibrium volumetric technique. This was proven in the case for three different well characterized clay minerals : a structural microporous one (palygorskite) and two nonporous lamellar ones (kaolinites). The obtained parameters allow a description of the adsorption energy distribution of their different surfaces, their textural parameters, as well as the energy distribution in micropores for the microporous samples. In addition to the experimental adsorption isotherms, the related experimental heats of adsorption were employed as a second independent source of information about the energetic heterogeneity of the studied clay minerals. Using the parameters determined from adsorption isotherms, the corresponding isosteric heats of adsorption were calculated and compared with experimental values. The simultaneous good fit of the experimental isotherm derivatives and of the experimental heats of adsorption was a solid check for the correctness of the determined parameters characterizing the adsorption energy distributions and the lateral interactions between the adsorbed molecules.