The interstitial water contained in the microporosity of highly compact clay-rich media does not obey the classical condition usually used to derive the ionic composition of a solution. This is because the requirement for global electroneutrality of a charged microporous body (one having a significant fraction of pores with dimensions of the same order of size as the diffuse double layer) implies that the net charge density of the pore water must balance the deficiency (or the excess) of electrical charge carried by the solid matrix. In order to determine the solution composition in the micropores of a clay-rock, we first generalize the Donnan equilibrium conditions for the case of a multi-ionic electrolyte, with partitioning of the charge compensating counterions between the Stern and the diffuse layers A material-specific geochemical equilibrium model, incorporating an electrical triple layer model for adsorption reactions, is used to calculate the partition coefficient for the compensating ion charge (i.e., the fraction of charge in the Stern layer). This is then used to calculate the osmotic pressure and ionic composition of the pore water in the micropores. The material considered in this study is the argillite clay-rock sampled from the Callovo-Oxfordian geological formation under consideration in France for a deep geological disposal facility for radioactive waste.