Compositions based on hydrochloric acid and clay acid (a mixture of hydrochloric and hydrofluoric (hydrofluoric) acids) are more effective, which is explained by the mechanism of action in which they do not destroy the structure of clay particles, but dissolve clay and silicate formations, creating channels. The processing time in this case is limited to 4 hours due to the gelation of the reaction products. Such compositions are good for treating the near-wellbore area of the formation, for increasing its permeability, followed by deeply penetrating treatment with organic acids.