A system for drilling a wellbore into an earth formation comprises an expandable tubular element extending into the wellbore, wherein a lower end portion of the wall of the tubular element extends radially outward and in an axially reverse direction so as to define an expanded tubular section extending around a remaining tubular section of the tubular element. The expanded tubular section is extendable by downward movement of the remaining tubular section relative to the expanded tubular section whereby said lower end portion of the wall bends radially outward and in an axially reverse direction. A drill string extends through the remaining tubular section into the wellbore, such that a space is formed between the drill string and the remaining tubular section, and the system further comprises sealing means arranged to seal said space from an open-hole lower section of the wellbore.