Moment-based analysis was applied to determine successfully inter- and intrapellet diffusion coefficients from experimental TAP outlet pulse responses over a one-zone bed with porous particles. Different temperatures, gas molar masses, and pellet sieve fractions were used to validate the Knudsen diffusion relation for inert gases inside porous catalyst pellets. The zeroth to third moments of the outlet pulse response were analytically derived for rectangular, cylindrical and spherical pellets. The third moment provides a significantly more accurate access to the intrapellet diversivity than the second moment does. The experimental window of the TAP reactor is explored for porous silica as catalyst support bed filling. The relevance of concentration gradients inside the pellet is illustrated with model simulations.