Simulations of deuterium (D) atom exposure in self-damaged polycrystalline tungsten at 500 K and 600 K are performed using an evolution of the MHIMS (migration of hydrogen isotopes in materials) code in which a model to describe the interaction of D with the surface is implemented. The surface-energy barriers for both temperatures are determined analytically with a steady-state analysis. The desorption energy per D atom from the surface is 0.69  ±  0.02 eV at 500 K and 0.87  ±  0.03 eV at 600 K. These values are in good agreement with ab initio calculations as well as experimental determination of desorption energies. The absorption energy (from the surface to the bulk) is 1.33  ±  0.04 eV at 500 K, 1.55  ±  0.02 eV at 600 K when assuming that the resurfacing energy (from the bulk to the surface) is 0.2 eV. Thermal-desorption spectrometry data after D atom exposure at 500 K and isothermal desorption at 600 K after D atom exposure at 600 K can be reproduced quantitatively with three bulk-detrapping energies, namely 1.65  ±  0.01 eV, 1.85  ±  0.03 eV and 2.06  ±  0.04 eV, in addition to the intrinsic detrapping energies known for undamaged tungsten (0.85 eV and 1.00 eV). Thanks to analyses of the amount of traps during annealing at different temperatures and ab initio calculations, the 1.65 eV detrapping energy is attributed to jogged dislocations and the 1.85 eV detrapping energy is attributed to dislocation loops. Finally, the 2.06 eV detrapping energy is attributed to D trapping in cavities based on literature reporting observations on the growth of cavities, even though this could also be understood as D desorbing from the C-D bond in the case of hydrocarbon contamination in the experimental sample.