The main focus of this investigation is to design a scaffold that will accommodate a growing Bio-Artificial Liver (BAL) with oxygen. The two design objectives are to find the maximum length and the distance between the artificial capillaries of the scaffold to provide adequate oxygen supply above 1.98 x 10-19 g/um3 to prevent hypoxia to the growing liver tissues. By utilizing industrial modeling software, FIDAP and GAMBIT, a model of a single capillary with liver tissue attached directly was constructed to simulate the oxygen delivery by means of diffusion and convection from the capillary wall to the tissue and the uptake by metabolism. From the results obtained, it was concluded that diffusion, not convection of the oxygen flow within the capillary was the dominant process of oxygen transport throughout the tissue. The maximum distance traveled into the tissue with capillary length of 60 ?m was 147 ?m from the capillary at the inlet side of the tissue while diffusion at the outlet tissue was at a modest 108 ?m. These values are unacceptable for the feasible construction of oxygen transport system solely based on diffusion. Thus, this investigation concludes that novel methods of greater complexity are needed to construct a more efficient and economically applicable oxygen delivery system for the mass production of bio-organs.