We discuss an experiment to investigate neutrino physics at the LHC, with emphasis on tau flavour. As described in our previous paper Beni et al (2019 J. Phys. G: Nucl. Part. Phys. 46 115008), the detector can be installed in the decommissioned TI18 tunnel, ≈ 480 m downstream the ATLAS cavern, after the first bending dipoles of the LHC arc. The detector intercepts the intense neutrino flux, generated by the LHC beams colliding in IP1, at large pseudorapidity η, where neutrino energies can exceed a TeV. This paper focuses on exploring the neutrino pseudorapity versus energy phase space available in TI18 in order to optimize the detector location and acceptance for neutrinos originating at the pp interaction point, in contrast to neutrinos from pion and kaon decays. The studies are based on the comparison of simulated pp collisions at √s = 13 TeV: PYTHIA events of heavy quark (c and b) production, compared to DPMJET minimum bias events (including charm) with produced particles traced through realistic LHC optics with FLUKA. Our studies favour a configuration where the detector is positioned off the beam axis, slightly above the ideal prolongation of the LHC beam from the straight section, covering 7.4 < η < 9.2. In this configuration, the flux at high energies (0.5-1.5 TeV and beyond) is found to be dominated by neutrinos originating directly from IP1, mostly from charm decays, of which ∼50% are electron neutrinos and ∼5% are tau neutrinos. The contribution of pion and kaon decays to the muon neutrino flux is found small at those high energies. With 150 f b-1 of delivered LHC luminosity in Run 3 the experiment can record a few thousand very high energy neutrino charged current (CC) interactions and over 50 tau neutrino CC events. These events provide useful information in view of a high statistics experiment at HL-LHC. The electron and muon neutrino samples can extend the knowledge of the charm PDF to a new region of x, which is dominated by theory uncertainties. The tau neutrino sample can provide first experience on reconstruction of tau neutrino events in a very boosted regime