Hepatic cell cultures are exploited for different applications in liver disease studies, drug toxicity testing and bioartificial liver (BAL) devices. Despite the development of various 3D cell culture systems, mass transfer properties and limitations, especially oxygen supply, still remain a controversial topic. In this paper, oxygen transport in a convection-enhanced, crossed-configuration hollow fibre membrane bioreactor hosting hepatocyte spheroids has been investigated through coupled free/porous media flow hydrodynamics and mass transfer modelling using finite-element simulations. Starting from experimental measurements of the oxygen concentration in the bioreactor, a systematic parametric study was performed to evaluate the effect of different parameters - oxygen partial pressure, perfusion rate, hollow fibre spacing, spheroid size, Michaelis-Menten kinetics for oxygen uptake and porosities of the spheroid and the membrane - on dissolved oxygen concentration profile. These parameters were studied in relation to dimensionless groups and variables. Among the operational conditions, oxygen concentration was much more influential than perfusion rate. As for the Michaelis-Menten parameters, oxygen concentration profile inside the spheroids was strongly affected by the maximum consumption rate (V-max) and weakly dependent on the constant K-M. Culturing smaller spheroids minimized the exposure of cells to hypoxic conditions, owing to the short diffusive penetration depth of oxygen especially at low porosities (0.2). An in vivo-like microenvironment in terms of physiological oxygen concentration range was achieved in large spheroids (400 mu m diameter) at spheroid porosity of 0.47. Membrane porosity also affected the intra-spheroid oxygen concentration and an improvement in oxygen supply to the spheroids could be achieved by reducing the corresponding transfer resistances. The mechanical stress on the spheroid surfaces was found to be within the tolerated ranges. Overall, the most important parameters for optimization of the bioreactor were identified.