  Active regions (ARs) play an important role in the magnetic dynamics of the
Sun. Solar surface flux transport models (SFTMs) are used to describe the
evolution of the radial magnetic field at the solar surface. There is however
uncertainty about using these models in the early stage of AR evolution. We aim
to test the applicability of SFTMs in the first days after the emergence of ARs
by comparing them with observations. The models we employ range from passive
evolution to models where the inflows around ARs are included. We simulate the
evolution of the surface magnetic field of 17 emerging active regions using a
local surface flux transport simulation. We selected regions that do not form
fully-fledged sunspots that exhibit moat flows. The simulation includes
diffusion and advection. We use observed flows from local correlation tracking
of solar granulation, as well as parametrizations of the inflows around ARs. To
evaluate our simulations, we measure the cross correlation between the observed
and the simulated magnetic field, as well as the total unsigned flux of the
ARs, over time. We also test the validity of our simulations by varying the
starting time relative to the emergence of flux. We find that the simulations
using observed surface flows can reproduce the evolution of the observed
magnetic flux. The effect of buffeting of the field by supergranulation can be
described as a diffusion process. The SFTM is applicable after 90% of the peak
total unsigned flux of the AR has emerged. Diffusivities in the range between
$D=250$ to $720$ km$^2$/s are consistent with the evolution of the AR flux in
the first five days after this time. We find that the converging flows around
emerging ARs are not important for the evolution of the total flux of the AR in
these first five days; their effect of increasing flux cancellation is balanced
by the decrease of flux transport away from the AR.
