The Arthrospira-B experiment is the first experiment in space ever allowing the online measurements of both oxygen production rate and growth rate of Arthrospira sp. in batch photobioreactors running in ISS. A 4 bioreactors system was integrated in the ISS Biolab incubator. Each reactor is composed of two chambers (gas/liquid) separated by a PTFE membrane and have been running in batch conditions. Oxygen production is measured by online measurement of the pressure increase in the gas chamber. The experiments are composed of several successive batch cultures for each reactor, performed in parallel on ISS and on ground. In this work, a model for the growth of Arthrospira sp in these membrane photobioreactors is proposed and the simulations results obtained are compared to the experimental results gathered in microgravity and on ground. The photobioreactor model is based on a light transfer limitation model, already used to describe and predict the growth and oxygen production in small to large scale ground photobioreactors. This approach is completed by a model for pH in the liquid phase. This permits to consider the pH increase associated to the bicarbonate consumption for the biomass growth. A membrane gas-liquid transfer model is used to predict the gas pressure increase in the gas chamber. Substrate limitation, pH inhibition, as well as oxygen inhibition must be considered in the biological model. A good fitting is achieved between experimental and simulation results when a good mixing of the liquid phase is maintained. These data show that microgravity has no first order effect on Arthrospira growth rate in a photobioreactor operating in space in ISS.