Reactive oxygen species (ROS) have important functions in cell signaling and, when present at overly high levels, may cause oxidation of important biological molecules. Kinetic models to study diffusion of ROS inside of mitochondria often assume dynamics similar to that in solution. However, it is well-known that separation of proteins in the cytosol or inside of mitochondria, where ROS are most predominant, can be smaller than 1 nm. Diffusion of small molecules can be better regarded as a percolation process. In this article, we report results of diffusivity and residence of water and hydrogen peroxide in the proximity of proteins. In carrying out this study, we found some issues with the conventional way of computing residence times by means of survival time correlation functions. The main problem is that particles remaining on the surface of a protein for long times and for which one has very poor statistics contribute significantly to the short time behavior of the survival time correlation function. We mathematically describe this problem and propose methodology to overcome it.