Analysis of time integration methods for the compressible two-fluid model for pipe flow simulations

Abstract

In this thesis, a 7-field Lagrangian slug capturing and slug tracking model with higher order methods and an adaptive grid is investigated for predicting the behaviour of two-phase gasliquid flow in multiphase flow pipelines. The model is capable of simulating both compressible and incompressible slugs, and pigs. The model has the possibility to simulate gas-liquid flow, including a liquid droplet field in the gas and entrained gas in the liquid.Walls consisting of multiple layers of different materials can be added to the pipes, and the energy equations for both the pipe walls and the fluids are solved. The mass, momentum and energy equations are solved in an iterative manner. Several additional tools and features have also been developed, like a steady state solver for the velocity, holdup, pressure and temperature, a unit-cell model which can be used as a standalone tool or as a sub-grid model in the dynamic model, fully period boundary conditions, curved pipe geometry, usage of tabulated PVT-files, and modelling of interfacial mass transfer. Higher order schemes are available for both spatial and temporal discretization. Different details in the two-fluid model have also been investigated, amongst other how to handle changes in the pipe cross-sectional area correctly for the border movement and level gradient. It is also shown how the upwind velocity must be modified by scaling factors to obtain the correct Bernoulli effect in the case of incompressible flow.The work resulted in four papers. In Paper 1 the model was tested against large scale experimental data, and was shown to give good predictions of the slugging periods after including a liquid droplet field and including the separator in the simulations. In Paper 3 the slug capturing capabilities of the model are tested against experimental data from a medium Furthermore I want to thank Jon Harald Kaspersen, my superior at SINTEF Petroleum, who allowed me to take a partial absence of leave in order to do this work. ..................................................................................................................... 92 2.9.7 Generic equation class ................................................................................................................ IntroductionIn the petroleum industry, multiphase flow occurs when transporting oil and gas (and possibly water) in the same pipe through long multiphase pipeline systems. The behaviour of the flow can take many forms (flow patterns), depending on several parameters like fluid velocities, pipe diameter, pipe inclination, and the fluid properties. The fluid properties are again dependent on the pressure and temperature in the system, especially the gas density and the fluid viscosity. Certain flow patterns can cause significantly reduced production, or even such operational challenges that the pipeline must be abandoned. It is therefore of crucial importance to be able to predict the behaviour of the flow when investigating how to design the pipeline. The simplest of the...

Constraint-consistent Runge–Kutta methods for one-dimensional incompressible multiphase flow

“…The wetted and interfacial perimeters P g , P l and P gl can be expressed in terms of the hold-ups A g or A l via a non-linear algebraic expression, see Appendix A.1. The same is true for the interface height h (measured from the bottom of the pipe), which appears in the expression for the level gradient terms E [45]:…”

“…[12] (note that the treatment of the constraint via the pressure equation is fully implicit and does not affect the stability). For convection-dominated problems (for example in case of the inviscid model), we have shown in previous work that the eigenvalues of the semi-discrete equations lie on the imaginary axis [45]. From a stability point of view, RK3 and RK4 are therefore to be preferred, because the stability domain of these methods contains a part of the imaginary axis.…”

Machine Learning for Closure Models in Multiphase Flow Applications

“…In this research the 'Rosa' code developed by Sanderse et al [35,36,37] is employed for solving the incompressible form of (8).…”

Development of temporal and spatial high‐order schemes for two‐fluid seven‐equation two‐pressure model and its applications in two‐phase flow benchmark problems

“…Then, the TOU scheme, which fulfills TVD and Courant limit, is developed and implemented for convective terms in the semi‐implicit algorithm to achieve third‐order accuracy without compromising its high‐order accuracy whenever possible. Considering that BDF1 for temporal discretization is low‐order accuracy, the second‐order Euler method (BDF2) is highly recommended for accurate transient calculations and it has been adopted in RELAP‐7 and used in the work of Zou et al, Zhang Xiao‐ying et al, and Sanderse et al In this paper, the second‐order Euler scheme for varying time‐step sizes will be derived by the Taylor series expansion method and then will be implemented for transient terms in the conservation equations of the two‐pressure model.…”