Methods for acid diversion in a hydrocarbon-containing subterranean formation are disclosed. The methods include injecting an acid diversion agent comprising a water-soluble or dispersible branched polyhydroxyetheramine and injecting an acidic solution into a well which is in contact with the hydrocarbon-containing subterranean formation. Preferably, the acid solution is diverted toward a zone of the formation that has a lower permeability to fluid than an adjacent zone. This process improves the permeability of the hydrocarbon-containing subterranean formation to hydrocarbons, while decreasing the permeability of the formation to water or brine.