We present a kinetic approach to the Monte Carlo-molecular dynamics (MC-MD) method for simulating reactive liquids using non-reactive forcefields. A graphical reaction representation allows definition of reactions of arbitrary complexity, including their local solvation environment. Reaction probabilities and molecular dynamics (MD) simulation times are derived from ab initio calculations. Detailed validation is followed by studying the development of the solid electrolyte interphase (SEI) in lithium-ion batteries. We reproduce the experimentally observed two-layered structure on graphite, with an inorganic layer close to the anode and an outer organic layer. This structure develops via a near-shore aggregation mechanism.