We have developed a modular semi-numerical code that computes the time and spatially dependent ionization of neutral hydrogen (HI), neutral (HeI) and singly ionized helium (HeII) in the intergalactic medium (IGM). The model accounts for recombinations and provides different descriptions for the photoionization rate that are used to calculate the residual HI fraction in ionized regions. We compare different semi-numerical reionization schemes to a radiative transfer (RT) simulation. We use the RT simulation as a benchmark, and find that the semi-numerical approaches produce similar HII and HeII morphologies and power spectra of the HI 21cm signal throughout reionization. As we do not track partial ionization of HeII, the extent of the double ionized helium (HeIII) regions is consistently smaller. In contrast to previous comparison projects, the ionizing emissivity in our semi-numerical scheme is not adjusted to reproduce the redshift evolution of the RT simulation, but directly derived from the RT simulation spectra. Among schemes that identify the ionized regions by the ratio of the number of ionization and absorption events on different spatial smoothing scales, we find those that mark the entire sphere as ionized when the ionization criterion is fulfilled to result in significantly accelerated reionization compared to the RT simulation. Conversely, those that flag only the central cell as ionized yield very similar but slightly delayed redshift evolution of reionization, with up to 20% ionizing photons lost. Despite the overall agreement with the RT simulation, our results suggests that constraining ionizing emissivity sensitive parameters from semi-numerical galaxy formation-reionization models are subject to photon nonconservation.
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