Aline Barbosa Figueiredo

Numerical Simulation of Non-Isothermal Two-Phase Flow in a Pipeline Using the Flux-Corrected Transport Method

Two phase flows occur in many engineering problems, especially in the nuclear, gas and petroleum industries. In oil and gas applications, specifically, a mixture of oil and natural gas is transported in pipelines from offshore platforms to the continent. The prediction of how the flow behaves in time as it moves along the pipe is extremely important, mainly during the pipeline design stage or regular operation. This paper presents simulations for stratified gas-liquid two-phase flow in a horizontal pipeline that is subject to the temperature gradients that exist in the bottom of the ocean, and the resulting heat transfer process that may lead to wax formation and deposition. A one-dimensional two-fluid mathematical model was employed that includes conservation equations of mass and momentum for each fluid and one energy equation for the mixture of liquid and gas. The problem was formulated as an initial-boundary value problem of the hyperbolic type and it was solved using the Flux Corrected Transport (FCT) numerical method, which is second-order accurate in space, coupled with an explicit discretization in time that is first-order accurate. The FCT method is appropriate to solve problems characterized by hyperbolic equations that may contain discontinuities and shock waves, and it presents small dispersive effects. The results showed excellent accuracy results when compared to commercial software widely used in the oil and gas industry.Copyright

Hyperbolicity Analysis of a One-Dimensional Two-Fluid Two-Phase Flow Model for Stratified-Flow Pattern

Two-phase flows in pipelines occur in a variety of processes in the nuclear, petroleum and gas industries. Because of the practical importance of accurately predicting steady and unsteady flows along the line, one-dimensional two-fluid flow models have been extensively employed in numerical simulations. These models are usually written as a system of non-linear hyperbolic partial-differential equations, but some of the available formulations are physically inconsistent due to a loss of the hyperbolicity property. In these cases, the associated eigenvalues become complex numbers and the model loses physical meaning locally. This paper presents a numerical study of a one-dimensional single-pressure four-equation two-fluid model for an isothermal stratified flow that occurs in a horizontal pipeline. The diameter, pressure and volume fraction are kept constant, whereas the liquid and gas velocities are varied to cover the entire range of superficial velocities in the stratified region. For each point, the eigenvalues are numerically computed to verify whether they are real numbers and to assess their signs. The results show that hyperbolicity is lost near the boundaries of the stratified pattern and in a vast area of the region itself. Moreover, the eigenvalue signs alternate, which has implications on the prescription of numerical boundary conditions.Copyright

Numerical Simulation of Stratified Two-Phase Flow in a Nearly Horizontal Gas-Liquid Pipeline With a Leak

The capability of producing accurate numerical simulations of transient gas-liquid flows in gas pipelines has long been a serious concern in the oil industry. In this paper we are particularly interested in simulating this type of flow during the occurrence of a leak in the pipe. We use the flux-corrected transport (FCT) finite-difference method, which is second-order in space, to solve a one-dimensional single-pressure four-equation two-fluid model. We consider this two-phase flow to occur in a nearly horizontal pipeline characterized by the stratified-flow pattern, and we assume that the flow is isothermal with a compressible gas phase and an incompressible liquid phase. We model the leak as a source term in the mass conservation equations. The results of the numerical simulations allow the model sensitivity to be studied by changing the leak diameter and the leak location. From this analysis, we may observe how these parameters affect the pressure gradients along the pipeline that develop upstream and downstream of the leak.© 2014 ASME

Featuring Pig Movement in Two-Phase Gas Pipelines

This paper presents a mechanical model, along with a numerical scheme for obtaining approximating solutions for the resulting initial-boundary-value problem, for describing the pig movement in transient two-phase gas pipelines. By taking advantage of the best features of the existing models presented in the literature so far, an idealized general purpose pig model is proposed, contemplating the possibility of representing, within a same context, different types of pigs or pig functions. Both mechanical and hydrodynamic friction forces at the interface of the pig and the pipe wall, as well as by-pass flow rates for the liquid and gaseous phases, are naturally incorporated in the modeling in a coherent mechanical context. The governing equations of the two-phase flow model are intentionally written in a general form, so that different existing models can be used within the framework presented herein. Following this same strategy, a detailed numerical scheme is presented in which the discretization of the flux terms are left open, so that different numerical strategies of first or higher orders can be accommodated without any additional difficulties.Copyright

Accuracy Study of the Flux-Corrected Transport Numerical Method Applied to Transient Two-Phase Flow Simulations in Gas Pipelines

The ability to produce accurate numerical simulations of transient two-phase flows in gas pipelines has long been an important issue in the oil industry. A reliable prediction of such flows is a difficult task to accomplish due to the numerous sources of uncertainties, such as the basic two-phase flow model, the flow-pattern models, the initial condition and the numerical method used to solve the system of partial differential equations. Several numerical methods, conservative or not, of first- and second-order accuracies may be used to discretize the problem. In this paper we use the flux-corrected transport (FCT) finite-difference method to solve a one-dimensional single-pressure four-equation two-fluid model for the two-phase flow that occurs in a nearly horizontal pipeline characterized by the stratified-flow pattern. Because the FCT algorithm is of indeterminate order, we use a test case to assess the spatial and time accuracies for the specific class of hyperbolic problem that we obtain with the modeling employed here. The results show that the method is first order in time and second order in space, which have important consequences on the choice of mesh spacing and time step for a desired accuracy.Copyright

On the Comparison of Different Multiphase Flow Kernels for Gas Pipeline Real Time Advanced Functions

The nature of real time advanced functions or systems for gas pipelines carrying two phase mixtures is complex, especially when the dominant phase is gaseous. In this case, the flow quite often requires periodic pig runs, among several other specific operational procedures. Thus, a robust, accurate, reliable and fast kernel is mandatory for good performance on leak detection, location and quantification, as well as any other real time function such as virtual instrumentation or inventory management and reconciliation. This work aims at comparing different transient two-phase one-dimensional kernels under the perspective highlighted above. Specifically, one may cite: (i) a two-fluid model, implemented in 20 years consolidated commercial flow simulator, bringing a kernel of first order in time and second-order in space, three continuity equations, and three momentum equations, where 2 different pressures are possible to be calculated; (ii) a simple two-fluid model to serve as the basis of a different way to approach the same problem. The main focus of this paper is on real time applications, then its main goal is to provide considerations and comparisons on accuracy, reliability and processing speed (CPU performance) coming from six different numerical methods and schemes. The commercial flow simulator is then being used as the basis of comparison, as it is considered highly reliable and robust by the market.© 2010 ASME