This paper numerically investigates non-Newtonian blood flow with oxygen and carbon dioxide transport across and along an array of uniformly square and staggered arranged fibers at various porosity (ε) levels, focussing on a low Reynolds number regime (Re < 10). The objective is to establish suitable mass transfer correlations, expressed in the form of Sherwood number (Sh = f(ε, Re, Sc)), that identifies the link from local mass transfer investigations to full-device analyses. The development of a concentration field is initially investigated and expressions are established covering the range from a typical deoxygenated condition up to a full oxygenated condition. An important step is identified where a cut-off point in those expressions is required to avoid any under- or over-estimation on the Sherwood number. Geometrical features of a typical commercial blood oxygenator is adopted and results in general show that a balance in pressure drop, shear stress, and mass transfer is required to avoid potential blood trauma or clotting formation. Different definitions of mass transfer correlations are found for oxygen/carbon dioxide, parallel/transverse flow, and square/staggered configurations, respectively. From this set of correlations, it is found that transverse flow has better gas transfer than parallel flow which is consistent with reported literature. The mass transfer dependency on fiber configuration is observed to be pronounced at low porosity. This approach provides an initial platform when one is looking to improve the mass transfer performance in a blood oxygenator without the need to conduct any numerical simulations or experiments.