Numerical Simulation of Non-Isothermal Two-Phase Flows in Vertical Pipelines with the Two-Fluid Five-Equations Model Using a 2nd Order MUSCL-Type Scheme

Resumo

In the oil industry, problems frequently arise that depend on the understanding of multiphase flow in pipelines, such as in flow assurance management. To determine flow parameters such as velocities, pressures, and temperatures, numerical simulations of multiphase flow within wells and oil risers can be employed. Due to the great length of these pipes, 2D or 3D models are often prohibitive, and one-dimensional models are preferred, such as the drift-flux model and the two-fluid model. The latter has the advantage of solving a momentum equation for each phase. The non-isothermal two-fluid five-equation model is a version of these models that includes a global energy equation, allowing the prediction of a shared temperature. However, this model is typically solved using low-order numerical schemes, as commonly reported in the literature and in commercial code technical manuals. Therefore, the objective of this work is to numerically model and solve the two-fluid five-equation model, which also includes heat transfer effects, using high-order numerical schemes, such as the second-order MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws) method for spatial discretization and the third-order Total Variation Diminishing Runge-Kutta (TVD-RK3) method for time integration. For the pressure-velocity coupling, a SIMPLE-like algorithm (Semi-Implicit Method for Pressure Linked Equations) is used, and the implementation is done using the Julia programming language. A vertical pipe is considered with core-annular flow, formed by either a liquid and a gas or two immiscible liquids. The models include heat transfer through the pipe wall and account for frictional effects. The results are compared with those from a commercial 1D simulator (ALFAsim) and have proven to be promising.