The Arthrospira-B experiment is the first experiment in space ever allowing the online measurements of both oxygen production rate and growth rate of Limnospira indica PCC8005 in batch photobioreactors running on-board ISS. Four bioreactors were integrated in the ISS Biolab facility. Each reactor was composed of two chambers (gas and liquid) separated by a PTFE membrane and was run in batch conditions. Oxygen production was monitored by online measurement of the total 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 the cyanobacterium Limnospira indica PCC8005 (also known as Arthrospira or spirulina) in these space membrane photobioreactors was proposed and the simulation results obtained are compared to the experimental results gathered in space and on ground. The photobioreactor model was 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. It was completed by a model for pH prediction in the liquid phase allowing assessment of 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 is considered in the biological model. A quite satisfactory fit was achieved between experimental and simulation results when a suitable mixing of the liquid phase was maintained. The data showed that microgravity has no first order effect on the oxygen production rate of Limnospira indica PCC8005 in a photobioreactor operating in space in zero gravity conditions.