“…Lubricated pipe flow has been applied in a specific industrial context for transporting viscous oils like heavy oil and bitumen with limited success in many cases [1,3,9,18,20,21]. A challenge to the broader application of LPF technology is the lack of a reliable model to predict frictional pressure losses, even though numerous empirical (e.g., [12,13]), semi-mechanistic or phenomenological (e.g., [10,11,15]) and idealized models (e.g., [14,32,33,[35][36][37]) have been proposed to date. The existing models were developed based on either single-fluid or two-fluid approach.…”