An oilfield apparatus includes an oilfield element made of a composite that includes a matrix material; and a plurality of functionalized graphene sheets dispersed in the matrix material. A method of oilfield operation includes selecting an oilfield apparatus having an oilfield element, wherein at least a portion of the oilfield element is made of a composite comprising a plurality of functionalized graphene sheets dispersed in a matrix material; and using the oilfield apparatus in an oilfield operation, thereby exposing the oilfield element to an oilfield environment. A method for modifying a functionalized graphene sheet includes obtaining the functionalized graphene sheet; and subjecting the functionalized graphene sheet to atom transfer radical polymerization to attach polymers on surfaces of the functionalized graphene sheet. The polymers attached to the surfaces of the functional graphene sheet may comprise co-polymers or magnetic particles.