  The European Spallation Source (ESS) is intended to become the most powerful
spallation neutron source in the world and the flagship of neutron science in
the upcoming decades. The exceptionally high neutron flux will provide unique
opportunities for scientific experiments, but also set high requirements for
the detectors. One of the most challenging aspects is the rate capability and
in particular the peak instantaneous rate capability, i.e. the number of
neutrons hitting the detector per channel or cm$^2$ at the peak of the neutron
pulse. The primary purpose of this paper is to estimate the incident rates that
are anticipated for the BIFROST instrument planned for ESS, and also to
demonstrate the use of powerful simulation tools for the correct interpretation
of neutron transport in crystalline materials. A full simulation model of the
instrument from source to detector position, implemented with the use of
multiple simulation software packages is presented. For a single detector tube
instantaneous incident rates with a maximum of 1.7 GHz for a Bragg peak from a
single crystal, and 0.3 MHz for a vanadium sample are found. This paper also
includes the first application of a new pyrolytic graphite model, and a
comparison of different simulation tools to highlight their strengths and
weaknesses.
