In the Beowulf story, where does Grendel go to die?

In the epic adventure of Beowulf, the
monster attacks the mead hall for twelve winters. Eventually, Beowulf, a hero in his own
right, who has heard of the problems of the Danes, travels across the seas to see if he
can help.

On the night that Beowulf and Grendel finally
face each other, the creature enters expecting to go unchallenged and have his way in
the hall, unthwarted. Beowulf is something of a surprise not only because he resists,
but because he is so strong. The monster manages to take the life of one unsuspecting
warrior, but when he grabs Beowulf, the battle ensues. As the creature realizes he faces
no ordinary man, he tries to flee, but Beowulf will not release him, and rips off
Grendel's arm.

Bleeding "nigh unto death," the creature
returns to his lair in the fens (swamps) to die.