Dense gas dispersion for risk assessment is usually modelled by simple box models or shallow-water type models in which vertical distributions are parameterized by similarity profiles. The dilution by ambient air will depend on cloud density and the available turbulent kinetic energy generated by shear production and convective heatflux driven by the temperature differences between the ground and a cloud released with negative enthalpy. The vertical integral of excess buoyancy is gradually moderated, as the cloud accumulates heat from the ground and spreads in the crosswind direction. Eventually the mixing will approach passive dispersion. A simple entrainment function is presented, compared to existing models, and calibrated by empirical knowledge from a range of relevant mixing conditions including the case of passive dispersion.