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Ammonia is expected to play an important role in the green transition, both as a hydrogen carrier and a zero-emission fuel. The use of refrigerated ammonia is attractive due to its relatively high volumetric energy density and increased safety compared to pressurized solutions. Ammonia is highly toxic, and with new applications and increased global demand come stricter requirements for safe handling. Cold gaseous ammonia following a spill of refrigerated ammonia will in contact with humid air cause fog formation. In an environment rich in ammonia, these droplets will due to ammonia's strong hygroscopicity consist of considerable amounts of liquid ammonia as well as water. Fog formation affects the ammonia-air density and thus influences the dispersion dynamics, with a potentially significant impact on hazardous zones. In this work, we present a CFD model including an ammonia-water fog formation model based on accurate thermodynamics. This includes modeling the vapor-liquid equilibrium and accounting for the exothermic mixing of ammonia and water. We apply this CFD model to relevant cases and demonstrate the significant impact of the fog. We analyze the effect of varying relative humidity, fog visibility, influence of wind, and pool evaporation rate. Finally, we model the experimental Red Squirrel test 1F.