Flow development and interface sculpting in stable lubricated pipeline transport

In Sarmadi et al. (2017) [1] we introduced a novel methodology for efficient transport of heavy oil via a triple-layer core-annular flow. Pumping pressures are significantly reduced by concentrating high shear rates to a lubricating layer, while ideas from Visco-plastic lubrication are used to eliminate the possibility of interfacial instabilities. Specifically, we purposefully position a shaped unyielded skin of a visco-plastic fluid between the transported oil and the lubricating fluid layer. The shaping of the skin layer allows for lubrication forces to develop as the core settles under the action of transverse buoyancy forces: adopting an eccentric position where buoyancy and lubrication forces balance. In Sarmadi et al. (2017) [1] we focused on a steady periodic length of established flow, to establish feasibility for the pipelining application. Here we address the equally important issue of how in practice to develop a triple layer flow with a sculpted/shaped viscoplastic skin, all within a concentric inflow manifold. First, we use a simple 1D model to control layer thickness via flow rates of the individual fluids. This is used to give the input flow rates for an axisymmetric triple-layer computation using a finite element discretization with the augmented Lagrangian method to represent the yield surface behavior accurately and a Piecewise Linear Interface Calculation (PLIC) method to track the interface motion. This establishes that these flows may be stably established in a controlled way with a desired interface shape. The shaped interface induces extensional stresses in the skin layer. We study this directly by developing a long-wavelength/quasi-steady analysis of the extensional flow. This allows us to predict the minimal yield stress required to maintain the skin rigid, for a given shape, all while maintaining a constant flow rate of the transported oil.