  Rate-equation models are a widely-used and inexpensive tool for the
simulation of interstellar chemistry under a range of physical conditions.
However, their application to grain-surface chemical systems necessitates a
number of simplifying assumptions, due to the requirement to treat only the
total population of each species, using averaged rates, rather than treating
each surface particle as an independent entity. While the outputs from
rate-equation models are strictly limited to such population information, the
inputs -- in the form of the averaged rates that control the time-evolution of
chemical populations -- can be guided by the results from more exact simulation
methods. Here, we examine the effects of back-diffusion, wherein particles
diffusing on a surface revisit binding sites on the lattice, slowing the total
reaction rate. While this effect has been studied for two-particle systems, its
influence at greater surface coverage of reactants has not been explored.
Results from two Monte Carlo kinetics models (one a 2-D periodic lattice, the
other the surface of a three dimensionally-realized grain) were used to develop
a means to incorporate the grain-surface back-diffusion effect into
rate-equation methods. The effects of grain size, grain morphology, and surface
coverage on the magnitude of the back-diffusion effect were studied for the
simple H+H reaction system. The results were fit with expressions that can be
easily incorporated into astrochemical rate-equation models to reproduce
accurately the effects of back-diffusion on grain-surface reaction rates.
Back-diffusion reduces reaction rates by a maximum factor of around 5 for the
canonical grain of $\sim$10$^6$ surface sites, but this falls to unity at close
to full surface coverage.
