The treatment of a reservoir formation with a stimulation fluid containing a reactive acid. In sandstone formations, the acid reacts with the soluble substances in the formation matrix to enlarge the pore spaces. In carbonate formations, the acid dissolves the entire formation matrix. In each case, the matrix acidizing treatment improves the formation permeability to enable enhanced production of reservoir fluids. Matrix acidizing operations are ideally performed at high rate, but at treatment pressures below the fracture pressure of the formation. This enables the acid to penetrate the formation and extend the depth of treatment while avoiding damage to the reservoir formation.