A vessel is adapted to perform subsea wellbore related operations, involving a riser string that extends between a subsea wellbore and a vessel and that is assembled from releasably interconnected riser sections that each comprise a main riser pipe and at least one auxiliary pipe. The vessel includes an auxiliary pipe filling device adapted to fill the at least one auxiliary pipe of a riser section during a lowering step of said riser running operation, the auxiliary pipe filling device including a liquid source, e.g. for water, at least one nozzle adapted to dispense water into said auxiliary pipe, a liquid flow line, connecting the liquid source with the nozzle, and a nozzle mount that is adapted to mount the nozzle in a filling position in which the nozzle is positioned to dispense liquid into the at least one auxiliary pipe of the riser section during said lowering step.