Method for evaluating cement integrity in a cased well environment using a logging tool that has a neutron source and one or more neutron or gamma ray detectors. Neutron porosity logs are obtained from the well before (42) and after (41) casing. This log data along with well dimensions and material composition parameters are the input quantities to a multi-parameter database (43) that is constructed by computer modeling or laboratory experiments to relate volume fraction for fluid filled channels in the cement sheath to the input quantities. The channel volume fraction (45) corresponding to the input quantities is identified or interpolated (44) from the multi-parameter database.