A Maxwell-Stefan Approach for Predicting Mixing Effects in Contiguous Batches of Multi-Product Pipelines

Transient phenomena in the liquid batch interfacial zone are addressed based on: (i) a reliable compositional description; and (ii) mass transfer modeling. In phase (i), compositional models are proposed for transported fluids, with parameters estimated by maximum likelihood procedures to match known characterizing data, like distillation curve, density, viscosity and heteroatom weight fractions. In phase (ii), the transient mixing problem is posed on the continua of axial position in the duct, and described by Maxwell-Stefan formalism for multicomponent mass transfer between two contiguous semi-infinite fluids. Turbulent effects are considered on calculation of mass transfer coefficients, and rigorous thermodynamic driving forces are accounted for through component fugacities predicted by equations of state. The model was solved by the finite element method and the resulting set of ordinary differential equations in time was numerically integrated enabling determination of the mixing zone, calculation of property profiles and monitoring loss of product specifications.