  By performing Monte Carlo simulations of the evolution of binary primordial
black hole (PBH) systems, we estimate the effect of distant encounters with
single PBHs upon the coalescence time and merger rate of binary PBHs. We find
that, for models where PBHs compose a large fraction of dark matter,
$f_\mathrm{PBH}\sim 1$, the expected fractional change in coalescence time is
negligible, of order $10^{-6}$ for most binaries. For models with significantly
lower PBH abundances, $f_\mathrm{PBH}\ll 1$, we find that the average change in
binary lifetime due to encounters can be as large as $\mathcal{O}(10^{-2})$,
with a small number of binaries experiencing an order unity change in lifetime.
In the absence of encounters, we also compare the use of an analytic
approximation for the coalescence time to numerically evolving the binary
system, finding that the analytic approximation results in an order $10\%$
error in the coalescence time. However, when these effects are taken into
consideration, there is a negligible change to the calculated merger rate,
placing previous constraints on the PBH abundance arising from observed
gravitational wave signals from merging binary black holes on a more secure
footing.
