In a method for sealing and controlling fluid pressure in an annular fluid passageway in a wellbore related process, use is made of an annular fluid passageway sealing device, which includes a chamber delimited by chamber end members each provided with an opening therein so that the drilling tubulars string passes through said chamber and said chamber end members. The lower chamber end member is exposed, at least partially, to wellbore related fluid pressure in the annular fluid passageway. The housing is provided with an inlet and an outlet in communication with said chamber. Use is made of a pump that circulates a high viscosity liquid. The inlet and the outlet are vertically offset from each other and the chamber is provided with one or more narrow annular gap defining members that are arranged between vertically spaced apart feed and discharge zones. The circulation of liquid and the narrow annular gap are such that shear of the high viscosity liquid is induced resulting in a pressure drop between the discharge zones such that high viscosity liquid pressure in the feed zone assists the lower chamber end member in absorbing the wellbore related fluid pressure.