Inelastic nucleon-nucleon cross section at LHC energies

Atlas has published a measurement at 7TeV

Measurement of the inelastic proton–proton cross-section at √s=7 TeV with the ATLAS detector

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An inelastic cross-section of 60.3±2.1 mb is measured for ξ>5×10−6, where ξ is calculated from the invariant mass, MX, of hadrons selected using the largest rapidity gap in the event.

A figure is given outside a pay wall:

The ATLAS measurement for ξ>5×10−6 is shown as the red-filled circle and compared with the predictions of Schuler and Sjöstrand and Phojet for the same phase space. Data (filled circles for pp data and unfilled circles for pp macron data) from sever…

Will be lower for what you are looking at.

The "fit" to models might help you to decide which to use to get what you need for your phase space.