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 nu depended on the volume fraction of reagents phi in accordance with the law nu=Kphi(R)(beta), where the prefactor K and the scaling factor beta both depend on both the volume fraction of obstacles, phi, and the size of the obstacles relative to the reagents. Below a critical obstacle concentration phi(c), both K and beta increase with phi; above phi(c), both fall with increasing phi. The value of phi(c) 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 beta). Enhancement is most marked for larger obstacles, which cause less compartmentalization of the medium for a given increase in effective reagent concentration.