A membrane supported bioreactor arrangement and method for anaerobic conversion of gas into liquid products including membrane modules having hollow fibers packed across a cross sectional area of the membrane module, each of the hollow fibers formed from an asymmetric membrane wall having a porous outer layer defining biopores for retaining a porous biolayer about the outer surface of the membrane wall and a less permeable hydration layer around the hollow fiber lumen; a membrane vessel for surrounding the outside of the hollow fibers with a process gas from a gas supply conduit; and a liquid supply conduit operably connected to the hollow fibers for supplying a process liquid to the hollow fiber lumens. The gas supply conduit enables the formation of a biolayer on the outer surface of the hollow fiber wall by interaction of microorganisms with the process gas and the production of a liquid product.