Insoluble trace gases are trapped in polar ice at the firn-ice transition, at approximately 50 to 100 m below the surface, depending primarily on the site temperature and snow accumulation. Models of trace gas transport in polar firn are used to relate firn air and ice core records of trace gases to their atmospheric history. We propose a new model based on the following contributions. First, the firn air transport model is revised in a poromechanics framework with emphasis on the non-homogeneous properties and the treatment of gravitational settling. We then derive a nonlinear least square multi-gas optimisation scheme to calculate the effective firn diffusivity (automatic diffusivity tuning). The improvements gained by the multi-gas approach are investigated (up to ten gases for a single site are included in the optimisation process). We apply the model to four Arctic (Devon Island, NEEM, North GRIP, Summit) and seven Antarctic (DE08, Berkner Island, Siple Dome, Dronning Maud Land, South Pole, Dome C, Vostok) sites and calculate their respective depth-dependent diffusivity profiles. Among these different sites, a relationship is inferred between the snow accumulation rate and an increasing thickness of the lock-in zone defined from the isotopic composition of molecular nitrogen in firn air (denoted d15N). It is associated with a reduced diffusivity value and an increased ratio of advective to diffusive flux in deep firn, which is particularly important at high accumulation rate sites. This has implications for the understanding of d15N of N2 records in ice cores, in relation with past variations of the snow accumulation rate. As the snow accumulation rate is clearly a primary control on the thickness of the lock-in zone, our new approach that allows for the estimation of the lock-in zone width as a function of accumulation may lead to a better constraint on the age difference between the ice and entrapped gases.