On the computation of compressible multiphase flows with heat and mass transfer in elastic pipelines.

The present work is motivated by the engineering need to simulate the multiphase flows in the course of the start-up of a long-distance crude oil pipeline. We propose a model for compressible multiphase flows with heat and mass transfer and diffusion processes in elastic pipelines. The model is derived with two approaches, i.e., (a) the spatial averaging procedure of a single phase model and (b) the Arbitrary Lagrangian Eulerian (ALE) formulation of the Baer-Nunziato model with quasi-1D approximation. The diffusion processes include the viscous dissipation, wall friction, heat conduction, and heat exchange with external environment. In particular, the wall friction consists of steady friction term calculated by Darcy-Weisbach formula, and the unsteady friction determined by the instantaneous-acceleration-based (IAB) model. The unsteady friction modifies the characteristic structure of the hyperbolic part of the model. For the solution of the hyperbolic part, we propose a three-wave approximate Riemann solver incorporating the unsteady friction term. Mass and heat transfer are realized via instantaneous relaxations of the chemical potential and temperature, respectively. Efficient iterative relaxation procedures for N -phase flows have been proposed. We have validated the proposed model and numerical methods against some benchmark multiphase problems and applied the model to calculate the start-up of a realistic liquid pipeline with intermediate pump station boundary condition. • The derivation of the quasi-1D BN-type model with diffusion physics and its reduction. • The development of a HLLC Riemann solver taking into consideration the unsteady wall friction term. • Efficient pressure and temperature relaxation methods for N-phases. • The application in simulating realistic pipe-startup problem.