A recent clinical pilot study demonstrated the feasibility of offline PET/CT range verification for proton therapy treatments. In vivo PET measurements are challenged by blood perfusion, variations of tissue compositions, patient motion and image co-registration uncertainties. Besides these biological and treatment specific factors, the accuracy of the method is constrained by the underlying physical processes. This phantom study distinguishes physical factors from other factors, assessing the reproducibility, consistency and sensitivity of the PET/CT range verification method. A spread-out Bragg-peak (SOBP) proton field was delivered to a phantom consisting of poly-methyl methacrylate (PMMA), lung and bone equivalent material slabs. PET data were acquired in listmode at a commercial PET/CT scanner available within 10 min walking distance from the proton therapy unit. The measured PET activity distributions were compared to simulations of the PET signal based on Geant4 and FLUKA Monte Carlo (MC) codes. To test the reproducibility of the measured PET signal, data from two independent measurements at the same geometrical position in the phantom were compared. Furthermore, activation depth profiles within identical material arrangements but at different positions within the irradiation field were compared to test the consistency of the measured PET signal. Finally, activation depth profiles through air/lung, air/bone and lung/bone interfaces parallel as well as at 6 degrees to the beam direction were studied to investigate the sensitivity of the PET/CT range verification method. The reproducibility and the consistency of the measured PET signal were found to be of the same order of magnitude. They determine the physical accuracy of the PET measurement to be about 1 mm. However, range discrepancies up to 2.6 mm between two measurements and range variations up to 2.6 mm within one measurement were found at the beam edge and at the edge of the field of view (FOV) of the PET scanner. PET/CT range verification was found to be able to detect small range modifications in the presence of complex tissue inhomogeneities. This study indicates the physical potential of the PET/CT verification method to detect the full-range characteristic of the delivered dose in the patient.