The formation of oxygen bubbles in the anodic circuit of a polymer electrolyte membrane (PEM) electrolyser is a major technological problem as it greatly affects heat transfer, process performance and safety. Overall, bubbles evolve in the pipe flow upstream of the gas separator due to oxygen super-saturation created by the chemical reaction at the anode. The accurate prediction of bubble formation in the pipes is important for the correct positioning and design of the gas separator. This paper therefore presents a cell-based one-dimensional numerical model that estimates bubble evolution in a horizontal pipe-flow. For this purpose, the model considers bubble growth at nucleation sites and in the flow, enabling the prediction of the corresponding gas fraction at different locations within the cooling circuit. Furthermore, a sensitivity analysis was conducted based on the derived model to evaluate the impact of various parameters on the degassing rate. It was found that the smaller the pipe diameter, the greater the initial gas content and the greater the number of nucleation sites, the shorter the pipe length required to achieve solubility.