  The binary neutron star merger gravitational-wave signal GW170817 was
followed by three electromagnetic counter-parts, of which a kilonova arising
from the radioactivity of freshly synthesized r-process elements in ejecta from
the merger. Finding kilonovae after gravitational-wave triggers is crucial (i)
to the search for further counterparts such as the afterglow, (ii) to probe the
diversity of kilonovae and their dependence on the system's inclination angle
(iii) to build a sample for multimessenger cosmology. During the third
observing run of the gravitational-wave interferometer network, no kilonova
counterpart was found. We aim to predict the expected population of detectable
kilonova signals for the upcoming O4 and O5 observing runs of the
LIGO-Virgo-Kagra instruments. Using a a simplified criterion for
gravitational-wave detection and a simple GW170817-calibrated model for the
kilonova peak magnitude, we determine the rate of kilonovae in reach of
follow-up campaigns and their distributions in magnitude for various bands. We
briefly consider the case of GW190425, the only confirmed binary neutron star
merger since GW170817, and obtain constraints on its inclination angle from the
non-detection of its kilonova, assuming the source was below the follow-up
thresholds. We also show that non gravitational-wave-triggered kilonovae can be
a numerous class of sources in the future surveys and briefly discuss
associations with short bright gamma-ray bursts. We finally discuss the
detection of the jetted outflow afterglow in addition to the kilonova, and
confirm former conclusions on the rareness of such counterparts in future
observations.
