The Groningen gas field in the Netherlands has been a major source of natural gas in Europe for the past few decades. There are approximately 350 wells drilled in the field that either already are or will be plugged and abandoned in the near future. In this work, we developed a two-phase, two-component numerical model based on the stratigraphy and the petrophysical data from a well in the Groningen field. The focus was to estimate the magnitude of methane leakage from the abandoned reservoir and the shallow gas-bearing formations. Methane is a potent greenhouse gas and fugitive methane emission from abandoned wells is of concern. The results indicate that highly depleted reservoirs are not a likely source of leakage, as long as they are not re-pressurized. However, shallow gas-bearing formations capable of bulk gas flow can pose a significant leakage risk. Permeable intermediate formations between the gas source and freshwater aquifers can act as a buffer zone, reducing the maximum rate of leakage into the atmosphere/aquifer system. For a mildly damaged cement sheath (1 mD) with a viable gas source, the leakage rate is relatively small (less than 30 kg/year of methane). The high leakage rate scenario results in a leakage rate as high as 4500 kg/year, with a methane plume in the freshwater aquifer that extends up to 450 m away from the well after 100 years. The results of this study can be used to identify wells that are at a higher risk of gas leakage, and the relative consequence of such phenomena on greenhouse gas emissions and local freshwater quality.