There are only two methods of disposal I find nearly all scholars to be in agreement over.
1) Wrapping it in a pure piece of cloth and burying it respectfully in a place where people (normally) do not walk about. In cold climate countries (such as the UK), one may dig a Shiq grave, but a slab should be placed first and over it the soil.
2) Fastening the Qur’an with a heavy object like a stone and then placing it respectfully in flowing water.
Method one seems to be the most practical and respectable.