A wellbore fluid and method of use including grafted block copolymer, wherein the grafted block copolymer comprises at least one poly(vinylaromatic) segment and at least one elastomeric segment. The elastomeric segment can be a polymer from conjugated diene monomers having 4-6 carbons atoms per molecule. The poly(vinylaromatic) segment can be a monovinyl aromatic polysegment. The block copolymers can be a hydrogenated poly(styrene-b-isoprene) (SEP), a hydrogenated poly(styrene-b-butadiene) (SEB), a hydrogenated poly(styrene-b-isoprene/butadiene) (SEEP), a hydrogenated poly(styrene-b-isoprene-b-styrene) (SEPS), a hydrogenated poly(styrene-b-butadiene-b-styrene) (SEBS), or a hydrogenated poly(styrene-b-isoprene/butadiene-b-styrene) (SEEPS).