Flux corrected transport solver for solving 1D multiphase equations for drilling applications

摘要

A numerical solver is designed and implemented to solve a simplified set of equations modeling 1D multi-phase flow for the oil and gas drilling industry. The main motivation of this work is to capture the key features of kicks taken while drilling vertically using an oil based mud. The physical setup of a two fluid two phase (liquid and vapour phase) flow with solubility of one component is considered. A numerical method is devised to solve the system using the finite volume strategy. The difficulty in obtaining the analytical Jacobian of the fluxes leads to the decreased accuracy in capturing the contact wavefront. To address this issue a fully explicit second order numerical solver based on Flux corrected transport (FCT) is implemented. The code is validated and the physical test cases of gas injection inside the well annulus and shut-in of the well are presented. The results conclude that the FCT solver is a better and efficient method for multiphase models involving slip velocities given by algebraic relations.