In computer simulations of reactions in a disordered no homogeneous medium consisting of a solvent containing randomly located stationary spherical obstacles, reagent first encounter rate ν depended on the volume fraction of reagents ϕ in accordance with the law ν = KϕRβ, where the prefactor K and the scaling factor β both depend on both the volume fraction of obstacles, ϕ, and the size of the obstacles relative to the reagents. Below a critical obstacle concentration ϕc, both K and β increase with ϕ; above ϕc, both fall with increasing ϕ. The value of ϕc is roughly the value at which there is a 99% probability that clusters of closely spaced obstacles stretch from side to side of the simulation cell. The increase in K at lower obstacle concentrations, which is largely attributable to increasing effective reagent concentration, results in enhancement of the reagent first encounter rate at moderate to high bulk reagent concentrations (whereas at low reagent concentrations this effect is outweighed by the simultaneous increase in β). Enhancement is most marked for larger obstacles, which cause less compartmentalization of the medium for a given increase in effective reagent concentration. © 2002 American Institute of Physics.