Brownian dynamics simulations were performed to determine the first collision and recollision rates of spherical reagent particles in a reaction medium made heterogeneous by the presence of randomly located inert spherical obstacles in a continuum solvent. The recollision rate v(p) (and hence the overall reactive collision rate when activation energy is high) was always enhanced by the presence of obstacles, the degree of enhancement increasing with the volume fraction occupied by obstacles (phi) and with decreasing reagent concentration phi(R). Enhancement increased with obstacle size at high phi(R), and fell with increasing obstacle size at low phi(R). The v(p)-phi(R) data follow a power law, where the scaling factor beta(p) decreased with decreasing obstacle size and increasing phi, and the prefactor k(p) initially increased with phi and then fell (except for large obstacles). The behavior of beta(p) appears to be largely due to the obstacles reducing the probability that reagent particles escape from each other after collision, while the dominant factors responsible for the behavior of k(p) appear to be initially the effect of obstacles in enhancing effective local reagent concentration, and then (for small obstacles), their reduction of the reagent-particle coordination number. As the energy of activation falls, the reactive collision rate becomes less influenced by the reagent recollision rate and more influenced by the rate of first collision. For low-activation-energy reactions, the presence of obstacles depresses the reactive collision rate if reagent concentration is low or if the obstacles are small and their concentration high. The fall in the reactive collision rate with decreasing activation energy is steeper, the lower the reagent concentration and the smaller the obstacles. (C) 2004 American Institute of Physics.