Felipe Bastos de Freitas Rachid

Modelling of hydraulic transient in damageable elasto-viscoplastic piping systems

Abstract This paper is concerned with the modelling of the damage induced by pressure transients in liquid-filled pipes at high temperatures. The fluid dynamics and pipewall deformation are modelled by the classical water hammer theory, whereas pipewall mechanical behavior is described by an internal variable constitute theory. The resulting nonlinear system of hyperbolic equations is solved by means of a numerical technique based on Glimms method. Numerical examples concerning the damage evolution induced by pressure transients are presented and analyzed to demonstrate the applicability of the theory.

A thermodynamically consistent model for cavitating flows of compressible fluids

Abstract This work presents a logically consistent thermodynamic model to describe the isothermal cavitation phenomenon in compressible fluid flows. The fluid is regarded as a continuum mixture of liquid and vapor phases (both having the same velocity and temperature), which can or cannot coexist at a same material point and time. The volume fraction is considered as an internal variable and its constraint is treated as a material property, being part of the constitutive relations. Dissipative effects associated with the liquid–vapor phase change transformation and with the vapor volume fraction evolution are taken into account in such a way the Second Law of Thermodynamics is always satisfied. It is shown that the dissipative mechanisms are responsible for a cavitation threshold rule that leads to cavity formation under completely different situations from that characterized by the traditional (reversible) theory. The potentiality of the model as well as its basic features are illustrated and highlighted through a simple numerical example. It is demonstrated that the irreversibility associated with the phase change transformation may be seen as an intermediate case between two physically different non-dissipative situations. One in which the phase change takes place at a constant pressure (the saturated vapor pressure) and the other in which the vapor expands and contracts in the mixture without transforming into liquid.

Modelling the Damage Induced by Pressure Transients in Elasto-Plastic Pipes

This paper is concerned with the analysis of pressure transients in damageable elasto-plastic piping systems. The fluid dynamics and pipewall deformation are modelled by the classical water hammer theory, whereas pipewall mechanical behavior is described by an internal variable constitutive theory. The constitutive model coupling plasticity and damage used herein gives rise to a nonlinear hyperbolic problem in which the wavespeeds are altered by damage evolution. The problem is numerically approximated by means of a technique based on an additive decomposition together with the Glimms method and a special Euler-type time integration scheme. Examples concerning the structural integrity analysis of a reservoir-pipe-valve installation, where hydraulic transients are generated by valve slam, are presented to illustrate the applicability of both theory and numerical method.

On the Suitability of the Low Mach Number Assumption in the Modeling of the Damage Induced by Pressure Transients in Piping Systems

One-dimensional models for predicting the damage induced by pressure transients in piping systems conveying liquids have been proposed and analysed recently. However, such works have been concerned mainly with the adequacy of the constitutive equations adopted for different pipe materials and with the numerical techniques used for approximating the solution of the resulting mathematical problems. In the present paper the suitability of the simplifying low Mach number assumption adopted in the modeling is investigated. The analysis is carried out based on the eigenvalue problem associated to the governing equations, without appealing to any specific mechanical behavior of the pipe material. Numerical results obtained for the most used pipe materials show that this simplifying assumption is adequate for metallic tubes, but may fail when plastic tubes are considered.

Estimating Mixing Volumes Between Batches in Multiproduct Pipelines

It is presented in this paper a new model for estimating mixing volumes which arises in batching transfers in multiproduct pipelines. The novel features of the model are the incorporation of the flow rate variation with time and the use of a more precise effective dispersion coefficient, which is considered to depend on the concentration. The governing equation of the model forms a non-linear initial-value problem that is solved by using a predictor-corrector finite difference method. A comparison among the theoretical predictions of the proposed model, a field test and other classical procedures show that it exhibits the best estimate over the whole range of admissible concentrations investigated.Copyright

The Influence of Pipe Motion on the Integrity of Liquid-Filled Pipes Subjected to Pressure Transients

This work presents a structural itegrity model for piping systems conveying liquids which takes the axial fluid-structure interaction into account. The model is used to numerically investigate the influence of pipe motion on the degradation of the piping when fast transients are generated by valve slam. The resulting mathematical problem is formed by a system of non-linear partial differential equations which is solved by means of an operator splitting technique, combined with a Glimm’s method. Numerical results obtained indicate that high piping flexibility may introduce a substantial increase in damage growth along the pipes.Copyright

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