A 1.5D Numerical Model for Weakly Compressible Viscoplastic and Thixotropic Flows: Application to the Start-up of Waxy Crude Oils in Pipeline

Abstract

In this paper, we examine the numerical simulation of a weakly compressible viscoplastic and thixotropic fluid in an axisymmetric pipe geometry using a new 1.5D lubrication‐like numerical model which is a compromise between a fully 1D and a fully 2D scheme. Indeed, pressure is assumed to be constant in a section and only the axial velocity component is non‐zero and can vary both in axial and radial directions. The industrial situation refers to the start‐up of gelled waxy crude oil flows in pipeline, modelled by a thixotropic and viscoplasctic Houska model. Actually, the main difficulty concerning the restart of waxy crude oils relies on the estimation of the minimum pressure required at the pipe inlet. In a previous paper [1], we have pointed out that compressibility leads to strong pressure drop at the upstream part of the pipe and provides high strain rates at the first stages of the restart. So since the breakdown gel mechanism of the Houska model is governed by shear rate, we believe that a thixotropic and viscoplastic fluid, which usually can not restart in incompressible situations, should restart thanks to the combined effects of compressibility and gel breakdown mechanism. We show that this intermediate model yields accurate results which are consistent with the predictions of the fully 2D model. At the practical level, we evidence that the flow is able to restart for a pressure drop Δp below the value predicted by the conservative relation Δp = 4τyLD where τy is the yield stress, L the pipe length and D the pipe diameter