A gas extraction device for a fluid delivery apparatus includes a first layer and a vent membrane coupled to the first layer. The vent membrane enables a gas to pass through the vent membrane and prevents a fluid from passing through the vent membrane. The gas extraction device also includes a second layer coupled to the vent membrane opposite the first layer. The second layer has a first channel formed therethrough. In addition, the gas extraction device includes an impermeable membrane coupled to the second layer opposite the vent membrane. The first channel is configured to receive a fluid having a gas dispersed therein. The fluid is pressurized to move the fluid through the first channel against the vent membrane and to move the gas through the vent membrane.