When gas influx is dissolved in SOBM it will after some time diffuse to the wellhead and riser. In a similar but different way free gas will migrate in WBM. In the wellhead and riser area the mud is colder and temperature will also rapidly decrease after circulation stops, see figure B. The hydrate formation temperature is depending on salt content and on pressure (water depth and mud weight). In deep water it will only be matter of time to reach conditions when gas hydrates may form. When gas hydrates is formed, gas is "consumed" and the fluid volume is reduced even more.
In a static riser, dissolved gas that is not trapped as hydrates will typically diffuse higher up in the riser and "boil out" of the SOBM when pressure is sufficiently low. Free gas may "boil" out in an open riser or collect in top of the booster line, without any flow in the flow line.