The ionization region model (IRM) is applied to model high power impulse magnetron sputtering (HiPIMS) discharges with a Cu target. We apply the model to three discharges that were experimentally explored in the past, or applied to deposit thin copper films, with the aim to quantify internal plasma process parameters and thereby understand how these discharges differ from each other. The temporal variation of the various neutral and ionic species, the electron density and temperature, as well as internal discharge parameters, such as the ionization probability, back attraction probability, and ionized flux fraction of the sputtered species, are determined. We demonstrate that the Cu+ ions dominate the total ion current to the target surface and that all the discharges are dominated by self-sputter recycling to reach high discharge currents. Furthermore, the ion flux into the diffusion region is dominated by Cu+ ions, which represents roughly 80% of the total ion flux onto the substrate, in agreement with experimental findings. For the discharges operated with peak discharge current densities in the range 0.9 - 1.3 A cm-2, the ion back-attraction probability of the Cu+ ion (beta t) is low compared to previously investigated HiPIMS discharges, or in the range 44 - 50%, while the ionization probability (alpha t) is in the range 61 - 69%, and the ionized flux fraction is in the range 32 - 40%. It is, furthermore, found that operating these Cu HiPIMS discharges at lower working gas pressures (in the present case around 0.5 Pa) is beneficial in terms of optimizing ionization of the sputtered species.