The human placenta is a fetal life-support system, where the primary exchange units, terminal villi, contain disordered networks of fetal capillaries and are interfaced with maternal blood percolating a complex porous medium. While placental transport at the micro-scale can be described by established models, systematically upscaling the transport and quantifying the associated uncertainty at the organ-scale remain open challenges. On the porous side, we consider flow past a one-dimensional random array to understand the interplay between the physics of transport and microscopic disorder. Our analysis reveals surprising long-range correlations in the upscaled approximation that strongly depend on the statistics of the microstructure. On the network side, we integrate three-dimensional image-based geometric and transport features into new non-dimensional parameters to show how the irregular internal structure of a terminal villus determines its exchange capacity for a wide range of solutes. The developed theory provides a robust and efficient tool for quantifying solute exchange in complex microvascular systems.
