We report a computer simulation study of diffusion influenced reactions in a disorder medium constituting by immobile spherical obstacles when the concentration of reagents is smaller than the concentration of obstacles. We found that the compartmentalization of the embedding medium leads to a strong decrease of the rate of the first collision between reagents and a strong increase of the rate of recollision after a no-reactive encounter. The behavior of the full rate of reaction depends on the probability that a collision leads to reaction (value of the activation energy) and on the relationship between the decrease of the rate of collision and the increase of the rate of recollision. Thus, totally diffusion controlled reactions are always unfavored in these mediums, while partially diffusion controlled reactions with very high activation energy are more favored in mediums with a bigger degree of compartmentalization.