Microbubbles have attracted much attention due to their high mass-transfer efficiency. Computational fluid dynamics (CFD) simulations are performed for the flows in a membrane distributor and a bubble column. Gas permeation in the membranes is simulated using Darcy's law, while the two-fluid model is employed for studying gas-liquid flow in the membrane channel and bubble column. It is revealed that Darcy's law can describe the gas flow in dry ceramic membranes. For the membrane coated with a skin layer of smaller pore size, more gas permeates into the inner membrane channels. The relative permeability model is capable of predicting the gas permeation flow in the membrane partially saturated with water. The water saturation makes membrane pores unavailable, and a large pressure drop is caused. Gas holdup is well predicted using the Schiller-Naumann drag coefficient for the spherical microbubbles. In future work, scaling-up of the membrane distributor will be guided by CFD simulations.