Numerical simulation of temperature-dependent flow dynamics in drilling operations

Abstract

This thesis is a description of the research and improvements on solving hyperbolic conservation laws by defining a hybrid explicit/implicit numerical scheme. Former researches have been done by (Evje and Flåtten 2005) on the weakly implicit mixture flux method (WIMF) for the isothermal two-phase flow model. The research consists of proposing a semi-implicit numerical scheme for a two-phase flow system by defining a hybrid model incorporating the advection upstream splitting method (AUSMD) to develop an implicit scheme conjugated with an upwind explicit flux. While the WIMF scheme can demonstrate precise resolution of the moving discontinuity, it is bounded by a CFL condition restricting the timestep and grid sizes for numerical simulation (Evje and Flåtten 2005). The aim of the current research is to formulate and systematically code a numerical scheme named X-Force predictor-corrector, as a contribution to previous works of (Evje and Flåtten 2005) and (Evje, Flåtten et al. 2008). The new research has been done on a hybrid scheme consisting of pressure-based and density-based steps to traverse from Isothermal Euler model in the previous works to full Euler model by associating energy equations. The material stated in the thesis is based on unpublished work by Tore Flåtten and Trygve Wangensteen in a collaboration for TechnipFMC with respect to their FlowManager process surveillance software.