Carr-Purcell-Meiboom-Gill (CPMG) experiments were made upon sedimentary rock samples at different RF pulsation rates. A dispersion of the transversal relaxation rate was observed. The experiments revealed that due to the diffusional processes there is a diminution of the second moment of the absorption line with the delay time between the RF pulses and the echo time, with a complex evolution characterized either as a stretched exponential or a power-law behavior as a function of the echo time, with parameters dependent on the characteristic time of the experiment, i.e., the delay between RF pulses. Results show that the observed behavior is dependent on permeability and geometrical properties of the sedimentary rock.