How does the lifetime of methane vary in the atmosphere?
This wikipedia article, says that the hydroxical radical is the most important sink of atmospheric methane:

In addition to being the largest known sink for atmospheric methane, this reaction is one of the most important sources of water vapor in the upper atmosphere.
$$\ce{CH4 + ·OH -&gt; ·CH3 + H2O}$$
This reaction in the troposphere gives a methane lifetime of 9.6 years. Two more minor sinks are soil sinks (160 year lifetime) and stratospheric loss by reaction with ·OH, ·Cl and ·O1D in the stratosphere (120 year lifetime), giving a net lifetime of 8.4 years.

However, it goes on to say:

increasing emissions of methane over time reduce the concentration of the hydroxyl radical in the atmosphere. With less OH˚ to react with, the lifespan of methane could also increase, resulting in greater concentrations of atmospheric methane.