Production capability of cased hole perforations in a cased completed well lined with a casing in an under-pressured gas producing reservoir is tested. A sonde of a dipole shear or array sonic (full waveform) acoustic well logging tool is moved in a well bore of the cased completed well in the reservoir across a depth interval of interest, which covers cased hole perforations zones in the reservoir. The well logging sonde has in it an acoustic energy source and acoustic energy receivers. Responses are logged at depth intervals of interest to the transit of Stoneley waves along the casing walls from the acoustic energy source to the acoustic energy receivers. Measures of characteristics (e.g., travel time and attenuation) of the Stoneley wave are obtained. The responses are then processed to indicate production capability of the cased hole perforations.