In this paper, we report on the characterisation of transport in membrane modules for blood oxygenation where blood is circulated outside hollow fibre membranes arranged in double layer cross-laid mats at an angle with respect to the main direction of blood flow. The effect of design and operating variables on module performance was investigated with respect to oxygen transfer into water, as gaseous oxygen and water are circulated counter-currently, respectively inside the membrane lumen and through the membrane assembly. Increasing water flow rates and membrane angles enhanced oxygen transfer across the membrane and resulted in robust operation but also in high pressure drops. Module pressure drop and oxygen transfer rate were correlated to module geometry, fibre packing density, water how rate and membrane angle with respect to the main direction of the liquid Row in non-dimensional equations that can be used by membrane module manufacturers for the design of optimal ELF blood oxygenators. The results suggest that an optimum membrane angle exists, beyond which module operation is not convenient in terms of energy.