In this paper and its sequel we report the results of Molecular Dynamics simulation of single component and binary gas mixtures in a porous medium with interconnected pores. The porous medium used in the study is a model pillared clay. In the present paper we study adsorption of binary gas mixtures, and investigate in detail the effect of various factors, such as the morphology of the pore space and the adsorbent-adsorbate interactions. A new mean-field statistical mechanical theory of adsorption is developed, and shown to provide very accurate predictions for the simulation results over wide ranges of the pressure, temperature and porosity of the system.