Numerical simulation of weakly compressible Bingham flows: The restart of pipeline flows of waxy crude oils

In this paper we examine the numerical simulation of isothermal transient flows for a weakly compressible viscoplastic fluid in an axisymmetric pipe geometry. We use the Bingham model to describe the viscoplastic feature of the fluid and the compressibility is introduced in the continuity equation using the isothermal compressibility coefficient. Particular attention is devoted to the velocity–pressure problem in which the “true” (without regularization procedure) viscoplastic model is accounted for by using Lagrange multipliers techniques and augmented Lagrangian/Uzawa methods. The mass, momentum and constitutive equations are discretized using a finite volume method on a staggered grid with a TVD (Total Variation Diminishing) scheme for the convective terms. The resulting numerical method highlights strong and robust convergence properties. Obtained results regarding the transient solution underline the influence of compressibility on the flow pattern, especially in terms of yielded/unyielded regions, pressure and time to restart the flow.