An apparatus for removing gas bubbles from a fluid includes a fluid inlet and a separation chamber that is in fluid communication with the fluid inlet. The separation chamber has first and second end portions, with the first end portion being operably oriented gravitationally above the second end portion. The apparatus further includes a first gas-permeable, liquid-impermeable membrane disposed in the separation chamber and extending substantially along a first axis defined as extending between the first and second end portions. A permeate side of the membrane is exposed to an environment having a second partial pressure of a target gas, which second partial pressure is lower than a first partial pressure of the gas in the fluid.