Methods for simulating hydrocarbon (HC) migration and accumulation in a subsurface formation are provided. The methods include determining a plurality of HC mass associated with a plurality of grid cells representing the subsurface formation. The methods also include determining a plurality of HC mass outflow magnitudes for one or more grid cells in the plurality of grid cells, the HC mass outflow magnitude for each of the one or more grid cells having an upper bound value based on the HC mass in that grid cell. The methods update the HC mass of the plurality of grid cells based on the plurality of HC mass outflow magnitudes. The methods also determine that a set of grid cells in the plurality of grid cells contain an excess mass of HC, and perform an accumulation process to model filling of a trap associated with the set of grid cells.
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