Gas separation modules and methods for use including an integrated adsorbent and membrane. In certain refining applications, it is paramount to obtain high purity product gases. Adsorbent beds are effective at removing certain contaminants, such as CO2, from gas streams containing product and contaminant constituents to form a product-rich stream. The integrated membrane permits a further separation of products from any unadsorbed contaminant to produce a high purity product, such as hydrogen, stream. The gas separation modules described herein include stacked, radial, and spiral arrangements. Each modules includes a configuration of feed and cross-flow channels for the collection of contaminant gases and/or high purity product gases.