University of Wollongong University of Wollongong

Research Online Research Online

Faculty of Engineering and Information Sciences - Papers: Part A

Faculty of Engineering and Information Sciences

1-1-2013

Two-dimensional CFD modelling of gas-decompression behaviour Two-dimensional CFD modelling of gas-decompression behaviour

Alhoush Elshahomi University of Wollongong, aes738@uowmail.edu.au

Cheng Lu University of Wollongong, chenglu@uow.edu.au

Guillaume Michal University of Wollongong, gmichal@uow.edu.au

Xiong Liu University of Wollongong, xiong@uow.edu.au

Ajit R. Godbole University of Wollongong, agodbole@uow.edu.au

See next page for additional authors

Follow this and additional works at: https://ro.uow.edu.au/eispapers

Part of the Engineering Commons, and the Science and Technology Studies Commons

Recommended Citation Recommended Citation Elshahomi, Alhoush; Lu, Cheng; Michal, Guillaume; Liu, Xiong; Godbole, Ajit R.; Botros, K K.; Venton, Phillip; and Colvin, Philip, "Two-dimensional CFD modelling of gas-decompression behaviour" (2013). Faculty of Engineering and Information Sciences - Papers: Part A. 3342. https://ro.uow.edu.au/eispapers/3342

Research Online is the open access institutional repository for the University of Wollongong. For further information contact the UOW Library: research-pubs@uow.edu.au

Two-dimensional CFD modelling of gas-decompression behaviour Two-dimensional CFD modelling of gas-decompression behaviour

Abstract Abstract ONE OF THE key issues in the design and construction of any gas pipeline is the prevention of material fracture. Since the gas is generally transported under high operating pressures, it must be ensured that the gas pipeline is sufficiently tough to arrest the propagation of any potential fracture. For several decades, control of gas pipeline fracture propagation has been under scrutiny due to economic considerations and ecological and safety hazards related to pressurised pipe failure. The Battelle Two Curve approach has been widely used to determine the minimum material arrest toughness by comparing the gas decompression wave velocity with the fracture velocity, both as functions of the local gas pressure. Sufficient knowledge of the gas decompression behavior following the rupture is therefore crucial in determining running fracture arrest toughness levels. The decompression behaviour is influenced by the operating conditions, fluid composition and the material properties of the pipeline itself. This paper describes a two-dimensional decompression model developed using the commercial Computational Fluid Dynamics (CFD) software ANSYS Fluent. The GERG-2008 Equation of State has been implemented into this model to simulate the rapid decompression of common natural gas mixtures. The evolution of the decompression wave speed and phase changes under arbitrary initial conditions is reported. Comparison with experimental results obtained from shock tube tests showed good agreement between simulation and experiment.

Disciplines Disciplines Engineering | Science and Technology Studies

Publication Details Publication Details Elshahomi, A., Lu, C., Michal, G., Liu, X., Godbole, A., Botros, K. K., Venton, P. & Colvin, P. (2013). Two-dimensional CFD modelling of gas-decompression behaviour. The 6th International Pipeline Technology Conference (pp. S18-02-1 - S18-02-23). United States: Clarion Technical Conferences.

Authors Authors Alhoush Elshahomi, Cheng Lu, Guillaume Michal, Xiong Liu, Ajit R. Godbole, K K. Botros, Phillip Venton, and Philip Colvin

This conference paper is available at Research Online: https://ro.uow.edu.au/eispapers/3342

Two-dimensional CFD Modelling of Gas Decompression Behaviour

A. Elshahomi1, C. Lu1, G. Michal1, X. Liu1, A. Godbole1, K.K. Botros2, P. Venton3, P. Colvin4

1 University of Wollongong, Wollongong, NSW, Australia 2 Nova Research and Technology Centre, Calgary, AB, Canada 3 Venton and Associates Pty Ltd, Bundanoon, NSW, Australia 4 Jemena Ltd, Sydney NSW, Australia

ABSTRACT

One of the key issues in the design and construction of any gas pipeline is the prevention

of material fracture. Since the gas is generally transported under high operating pressures, it

must be ensured that the gas pipeline is sufficiently tough to arrest the propagation of any

potential fracture. For several decades, control of gas pipeline fracture propagation has been

under scrutiny due to economic considerations and ecological and safety hazards related to

pressurised pipe failure. The Battelle Two Curve approach has been widely used to determine

the minimum material arrest toughness by comparing the gas decompression wave velocity

with the fracture velocity, both as functions of the local gas pressure. Sufficient knowledge

of the gas decompression behavior following the rupture is therefore crucial in determining

running fracture arrest toughness levels. The decompression behaviour is influenced by the

operating conditions, fluid composition and the material properties of the pipeline itself. This

paper describes a two-dimensional decompression model developed using the commercial

Computational Fluid Dynamics (CFD) software ANSYS Fluent. The GERG-2008 Equation

of State has been implemented into this model to simulate the rapid decompression of

common natural gas mixtures. The evolution of the decompression wave speed and phase

changes under arbitrary initial conditions is reported. Comparison with experimental results

obtained from shock tube tests showed good agreement between simulation and experiment.

INTRODUCTION

A running ductile facture is a particularly disastrous kind of pipeline failure. Such a

failure includes the rapid axial cracking or tearing of the pipeline, sometimes running for long

distances. This may result in considerable damage to the environment, loss of tens of millions

of dollars and sometimes loss of life [1-2]. The Battelle Two Curve Method (BTCM) has

been widely used to determine the minimum toughness required for ductile fracture

propagation arrest [3-4]. This method involves the superposition of two curves: the gas

decompression wave speed characteristic and the ductile fracture propagation speed

characteristic, each as a function of the local gas pressure [4-5]. According to this approach,

the gas decompression wave velocity needs to be faster than the fracture propagation velocity

of the pipe wall at any pressure above the arrest pressure to prevent long running fractures of

gas pipelines [6].

Since the 1970s a number of full-scale burst tests for gas and liquid pipelines were

conducted to investigate gas decompression behaviour [7-15] . However, full-scale burst tests

are expensive and are economically feasible only for major projects. Phillips and Robinson

reported measurements of decompression wave speed using an NPS 6 ‘shock tube’ [16-17].

In recent years, Botros et al. [4, 18-22] have experimentally investigated the decompression

wave speed using a small diameter NPS 2 shock tube. In both the ‘shock tube’ test and full-

scale burst test, the decompression wave speed can be determined from pressure-time traces

measured by transducers mounted at different locations along the pipe length [18, 21].

MODELLING

A number of models have been developed for predicting the gas decompression wave

speed [16]. Many of the models assume a one-dimensional (along the pipe axis) and

isentropic flow[23]. They also rely on the fundamental thermodynamic expansion of the gas

at the crack point independent of the pipe diameter [4]. The Finite Difference Method (FDM)

[24] and the Method of Characteristics (MOC) [25-26] are used in many models. One of the

most widely used decompression model, implemented in GASDECOM [27], was developed

at the Battelle Memorial Institute in the 1970s [16, 18, 22, 28]. GASDECOM uses the

analytical solution of the propagation of an infinitesimal decompression front to determine

the decompression wave speed without solving the fluid transport equations explicitly. One-

dimensional, frictionless, isentropic and homogeneous fluid flow are assumed in the model.

GASDECOM uses the Benedict-Webb-Rubin-Starling (BWRS) Equation of State (EOS)

with modified constants to estimate the thermodynamic parameters during the isentropic

decompression. GASDECOM has been validated against measured results of full-scale

fracture propagation tests and shock tube tests [4]. It has been largely accepted as a

benchmark model to predict the decompression curve of lean natural gas mixtures.

GASDECOM calculates the gas decompression wave speed (W) as:

(1)

where C is the speed of sound behind the decompression wave, and u is the outflow velocity

behind the decompression wave. Pressure or density drops are used to calculate C and u

iteratively. The outflow velocity u at any given pressure is the sum of the incremental

velocities Δu determined from:

∑ ∆ (2)

where

∆ ∆ (3)

and is the density, and the subscript s indicates a value on the isentrope.

Several models have followed the assumptions of GASDECOM for predicting the gas

decompression wave speed [16]. The differences between these models are mostly the use of

different EOS. Groves et al. [12] formulated a computer program to calculate the gas

decompression velocity using an approach similar to shock tube theory. This model uses the

Soave-Redlich-Kwong (SRK) EOS to determine the required thermodynamic properties.

This model assumes that the pipe is of a large diameter and that the heat transfer within the

boundary layer has a negligible effect on the gas decompression behaviour [12]. The DECAY

model was established by Jones and Gough [29] to model single-phase decompression in a

pipe undergoing fracture propagation. This model uses assumptions similar to GASDECOM,

and the Peng-Robinson (PR) EOS [16]. The Advantica model developed in the late 1990s by

Cleaver and Cumber [30] is also based on the theory of one-dimensional shock tube test.

This model uses the cubic London Research Station (LRS) EOS, which is similar to the

Redlich-Kwong-Soave (RKS) EOS. The results in the Advantica model are adjusted by a

scaling factor applied to the speed of sound to match the initial conditions of sound speed

predicted using the PR EOS [16]. Makino et al. [31] proposed a one dimensional

decompression model at the University of Tokyo to simulate the decompression accompanied

by phase change in natural gas pipelines. This model uses the theoretical approach of British

Gas that has been implemented in the DECAY model along with the BWRS EOS. Qiu et al.

[32] developed a one-dimensional decompression model called DECOMWAVE using four

EOS(s): PR, SRK, BWRS-PR, and BWRS-SRK. For calculating the speed of sound in the

two phase region, the united equation developed by [33] was adopted. Cosham et al. [28]

established a one-dimensional, isentropic and homogeneous-equilibrium model named

DECOM to model the decompression behaviour of CO2 pipelines. This model has

assumptions identical to that used in GASDECOM but replaced the BWRS EOS by two

EOS(s) Span and Wanger [34]and GERG-2004[35], which are built in the NIST Standard

Reference Database 23 (REFPROP version 9.0)[36]. Simulation results generated by

DECOM were validated against measurements on shock tube tests commissioned by National

Grid [28].

More complex models for simulating transient flow in pipelines use the

Computational Fluid Dynamics (CFD) approach. The non-isentropic flow condition can be

assumed in those models to examine the effects of friction, heat transfer and pipe diameter on

the decompression behaviour. Picard and Bishnoi [37-38] introduced a one-dimensional, non-

isentropic model to investigate the decompression characteristics in ductile fracture

propagation. The thermodynamic properties were determined using the PR EOS. The result

shows that the non-isentropic assumption could be relaxed for pipe diameters larger than 508

mm [37-38]. The commercially available OLGA software [39] is a two-phase, transient

computational pipeline simulators. The basic model of OLGA contains separate one-

dimensional mass conservation equations for the gas and continuous liquid phases. It can

account for the presence of liquid droplets coupled with inter-phase mass transfer terms [19].

OLGA uses an implicit finite-difference discretisation method with a staggered mesh to

numerically solve the conservation equations. This approach is suitable for both rapid and

slow transient flows. OLGA often under-predicts the fast decompression wave speed of

common hydrocarbon gas mixtures. This issue was linked to the assumption made to

calculate the speed of sound [21]. While OLGA was validated for slow transient flows, rapid

transients associated with full pipe rupture have not been tested [19]. PipeTech is another

transient multi-phase, non-isentropic simulator based on the model of Mahgerefteh et al. [40-

41]. PipeTech uses the MOC to solve the conservation equations by following the Mach-line

characteristics inside the pipe. Numerical diffusion related to the finite difference

approximation of partial derivatives is avoided by this method [25, 42]. PipeTech uses the

cubic PR EOS [43] to calculate the thermo-physical properties of multi-component gas

mixtures [25, 40-42, 44]. This model has been validated against a number of full bore rupture

tests performed by Shell and BP on the Isle of Grain for hydrocarbon pipelines. Simulations

using both the Finite Volume Method (FVM) and MOC have been found to produce results

that agree remarkably well with some of the measured data [1].

In contrast to the FVM, the MOC needs significantly longer computation runtime and

cannot predict non-equilibrium or heterogeneous flows [1, 44]. Jie et al. [44] developed a

one-dimensional decompression model named CFDDECOM using the FVM technique based

on the Arbitrary Lagrangian Eulerian (ALE) approach and the Homogeneous Equilibrium

Method (HEM) [45-46] for simulating multi-phase transient flow following the rupture of

pipelines conveying rich gas or pure carbon dioxide (CO2). The Peng-Robinson-Stryjek-Vera

EOS, in addition to the Peng-Robinson and Span and Wanger EOS[34], are implemented into

this model [44]. CFDDECOM results were compared to the recently published shock tube

tests for pure and multi-component CO2 mixtures commissioned by National Grid [44].

Most of the existing decompression models are one- dimensional flow models. Their

accuracy varies greatly with the EOS employed. The use of an EOS depends on the fluid

region where the calculation of the thermodynamic properties is required. It also depends on

the uncertainty ranges of the EOS in representing the experimental data [35, 47]. Botros et al.

[13, 17] compared the predicted densities in the dense phase region by five different

equations of State (GERG, AGA-8, BWRS, PR and RKS), with measured values for different

hydrocarbon mixtures. They concluded that the GERG EOS outperforms all other equations

in the region up to P = 30 MPa and T > -8 0C. However, the GERG-2008 EOS has not been

implemented in the CFD decompression models to date.

The GERG-2008 EOS [35, 48] covers the gas phase, the liquid phase, the supercritical

region, and vapour-liquid equilibrium states for natural gases and other mixtures consisting of

up to 21 components: methane, nitrogen, carbon dioxide, ethane, propane, n-butane,

isobutane, n-pentane, isopentane, n-hexane, n-heptane, n-octane, hydrogen, oxygen, carbon

monoxide, water, helium, argon, n-nonane, n-decane, and hydrogen sulphide. The normal

range of validity of GERG-2008 covers temperatures from 90 K to 450 K and pressures up to

35 MPa. The uncertainty in estimating the gas phase density and speed of sound is less than

0.1% for temperatures ranging from 270 K to 450 K at pressures below 35 MPa. In the liquid

phase, the uncertainty in the density amounts for less than 0.1 to 0.5% for many binary and

multi-component mixtures. The estimated uncertainty in liquid phase (isobaric) enthalpy

differences is less than 1%, and can be as low as 0.5% for some mixtures. The vapour-liquid

equilibrium is described with reasonable accuracy. Accurate vapour pressure data for binary

and ternary mixtures consisting of the natural gas main components are reproduced by

GERG-2008 to within their experimental uncertainty, which is approximately 1 to 3%.

As reported in our previous study [5], the GERG-2008 EOS was implemented in a one-

dimensional decompression model named EPDECOM developed at the University of

Wollongong. The current study aims at developing a two-dimensional decompression model

using the commercial CFD package ANSYS Fluent. The built-in EOS(s) in ANSYS-Fluent

are not capable of predicting the fluid properties of natural gas mixtures accurately. GERG-

2008 EOS was successfully implemented in ANSYS-Fluent to calculate the thermo-physical

behaviour of most common gas mixtures. This imparts flexibility to this model which can

simulate the phase change of gas mixtures over a wide range of initial conditions. Since the

model is two-dimensional, it is possible to examine effects of parameters such as friction,

heat transfer and pipe diameter. 

CFD DECOMPRESSION MODEL

The modelling of gas decompression behaviour requires solving the transient form of

the flow governing equations using an accurate model of the fluid properties. The CFD

package ANSYS-Fluent can simulate a wide range of compressible, laminar and turbulent,

steady-state or transient flows of ideal or real fluids, in multi-dimensional geometries [49].

The decompression of rich and lean natural gas mixtures is not modelled accurately using an

ideal gas model. Real gas models are better suited to the application.

GERG 2008 is not available in Fluent by default. The equation of state must be

implemented by using the “User Defined Functions” (UDF) available through the “User-

Defined-Real-Gas Model” (UDRGM). The UDRGM implements a library of functions

written by the end user in the C programming language. These functions are compiled and

grouped in a shared library, which is later linked by ANSYS Fluent at runtime. The

calculated fluid properties are passed to Fluent through the UDF as a single and

homogeneous fluid. More details on using UDFs can be found in [50]. The procedure of how

ANSYS Fluent solver works with the new UDF are illustrated in Figure 1.

NUMERICAL SOLUTION

In ANSYS-Fluent, the Finite-Volume technique is employed to discretise the

governing equations of fluid flow [51]. The basic methodology involves dividing the

computational domain into a number of sub-regions called ‘control volumes’ or ‘cells’. The

governing equations are integrated over all the control volumes of the computational domain

[51-52]. The resulting integral equations are discretised into a system of algebraic equations

that is solved numerically [51].

In this model the ‘coupled-implicit density-based’ solver was chosen [52]. This solver

is designed for high-speed compressible flows and allows the implementation of user-defined

real gas models. The governing flow equations of mass, momentum and energy conservation,

supplemented by the auxiliary equations (e.g. EOS) are solved simultaneously while the

turbulence equations are sequentially treated. The advective terms are treated using the

‘second-order upwind’ scheme [53]. In the density-based solver, the momentum equations

are used to obtain the velocity field, and the continuity equation is used to find the density

field while the pressure field is determined from the EOS.

The physical flow domain consists of the initially highly pressurised gas in a straight

pipeline, which undergoes a full-bore opening. It is beneficial to take advantage of the axial

symmetry to construct a two-dimensional computational domain, thereby reducing the

computational runtime. The forms of the unsteady, two-dimensional governing differential

equations of conservation of mass, momentum and energy required to be solved in this model

are:

Continuity: (4)

where, x is the axial coordinate, r is the radial coordinate, is the axial velocity, is the

radial velocity, and is the source term [52].

x-momentum:

2 . (5)

r-momentum:

2 . 2 . (6)

where F is the external body force, is the swirl velocity and

. (7)

ANSYS Fluent solves the general energy equation in the following form:

. . ∑ ̿ . (8)

where E is the fluid energy, keff is the effective conductivity (= k + kt), where is the

turbulent thermal conductivity, hj is the enthalpy per unit mass of species j, and is the

diffusion flux of species j.

The first three terms on the right-hand side of Equation 8 represent the energy flow due to

conduction, species diffusion, and viscous dissipation, respectively. In the present study there

are no multiple species. Thus, the term may be considered similar to axial dispersion the

effect which wanes as the flow velocity increases. includes enthalpy sources where heat

transfer can be quantified [52]. The above four equations (4, 5, 6 and 8) involve five

unknowns: velocity components vx, vr, pressure p, temperature T and density . For closure,

the fifth equation is the GERG-2008 EOS (invoked using UDF).

BOUNDARY CONDITIONS AND ASSUMPTIONS

Based on the physical dimensions of the shock tube test facility described in [21], a

horizontal pipe with 30 m length and 49.3 mm internal diameter is employed as the flow

domain for the simulation. The length of the pipe was reduced from the original 172 m to 30

m to limit the computational runtime. The 30 m length was sufficient to ensure that the

decompression wave would not be reflected off the closed far end in the simulated time of the

decompression. The scored rupture disc in the shock tube test is modelled using “pressure-

outlet” boundary condition at atmospheric pressure. A boundary condition of axial symmetry

was imposed. The no-slip condition was specified at the wall boundaries. The physical flow

domain and the computational domain are shown in Figure 2.

The fluid, considered at rest, filled the pipe at the initial pressure and temperature

conditions before a full bore opening was instantaneously created (time t = 0). Driven by the

large pressure drop at the opening, the gas escapes from inside the pipe to the low pressure

region. The decompression wave front immediately progresses away from the opening.

Ahead of the decompression front, the fluid remains at rest and at the initial conditions. The

local Mach number ranges from 0 at the decompression front to 1, corresponding to the

choked condition, at the full bore opening end.

Because the flow generated after rupture is considered compressible, viscous and

turbulent, the turbulence models available in ANSYS-Fluent need to be applied. The mesh

grid was refined in regions of large flow gradients, i.e. near the outlet and along the boundary

layer in the vicinity of the wall. The “two layer modelling approach” offered in ANSYS-

Fluent was used in the latter region. This approach divides the flow domain into a viscosity-

affected region (near the wall) and a fully-turbulent region (away from the wall). The

Realizable k-ε turbulence model was adopted to model the fully-turbulent region while the

near wall region was treated using the ‘enhanced wall treatment’ function. More details about

the formulations can be found in [52]. In ANSYS-Fluent, these two regions are defined using

the turbulence Reynolds number Re:

√ (9)

where, , y, , and k are fluid density, the distance from the wall, dynamic viscosity and

turbulent kinetic energy respectively. The flow is considered fully turbulent when Re > 200.

The dimensionless wall distance y+ for a wall tube-bounded flow is defined as:

(10)

where, is the distance to wall, and is the friction velocity. The dimensionless distance

(theoretical) was used to find out the proper location and the size of the cell nearest to the

wall.

Since axial symmetry was assumed, the computational grid was generated over the 30

m length of the pipe and 0.025 m pipe diameter. At both wall boundaries 10 cells were

generated to cover the boundary layer. The cell adjacent to the wall was set at 0.05 mm from

the wall with a mesh-growth factor (from the wall) of 1.2. Following the 10th cell in both

radial and axial directions, the cells dimensions were kept constant at 1 mm up to the pipe

axis and the outlet boundary respectively. Overall, 1,020,306 rectangular cells of quadratic

mesh distribution were generated for the entire 2-dimensional axi-symmetric pipe. A detail of

the mesh distribution of flow domain near wall boundaries is shown in Figure 3.

SOLUTION STRATEGY

The implicit density-based solver was used. The default convergence criteria were

assumed (limits on the residual values of continuity, x-, r-velocities, turbulent kinetic energy,

turbulent dissipation energy and energy equation). A constant time step of 10-5 s was used to

capture the transient flow features at the monitor point nearest to the full bore opening.

Properties such as pressure, temperature, outflow velocity and speed of sound were

monitored as a function of time traces to calculate the decompression wave speed. These

were recorded at four different locations from the opening at the identical locations of the

pressure transducers P3, P4, P6 and P7 in the shock tube tests [19]. The pipe wall was smooth

and adiabatic.

CALCULATION OF DECOMPRESSION WAVE SPEED

Two different methods can be used to determine the decompression wave speed. The

first method involves calculating the local decompression wave speed using equation (1).

This can be done by monitoring the change in both the speed of sound and the outflow

velocity against time. Afterwards, the outflow velocity is subtracted from the speed of sound

for several pressures below the initial pressure. However, experimental tests such as shock

tube test and/or full-scale burst test do not provide the local gas decompression wave speed.

In these tests, the gas decompression wave speed w is calculated by determining the times at

which a certain pressure level reaches several given locations (pressure transducer locations)

on the pipe. By plotting these locations against time, the decompression wave speed is

obtained by performing a linear regression of each isobar curves. The slope of each

regression represents the average decompression wave speed for each isobar. Both methods

are used in this model to calculate the gas decompression wave speed.

CFD RESULTS AND VALIDATION

The following paragraphs present the results of the two-dimensional CFD

decompression model using the GERG-2008 EOS. Validation of this model was performed

through comparison with the measured results of shock tube tests [19, 21]. The shock tube

test was conducted at the TransCanada Pipeline Gas Dynamics Test Facility in Didsbury,

Alberta Canada [21-22]. In this facility, the main test section of the shock tube had a total

length of 172 meters. All spools were made from NPS2 x5.5 mm WT, seamless tube with an

internal diameter of approximately 49.3mm. These spools were designed for a maximum of

22 MPa pressure, with a design factor of 0.8 and location factor of 0.625. The internal

surface of the first spool near to the rupture disc was honed to a roughness better than 1.0 µm.

Eight pressure transducers and three temperature probes were mounted along the length of

the shock tube. The locations of the pressure transducers and temperature probes are shown

in Table 1. The test program consisted of a total of 10 tests performed with various gas

mixtures at different initial conditions.

In this work, three different gas mixtures undergoing decompression were simulated using the

CFD model: pure nitrogen, conventional natural gas and rich natural gas. The objective is to

examine whether the current CFD model can predict the decompression behaviour of gas

mixtures. Firstly, the decompression process of pure nitrogen was simulated to examine the

decompression behaviour of single-phase flow. The second set of simulations was performed

for conventional gas mixture (case 2) with ~95% Methane where the flow is expected to

cross the two-phase region. The rich natural gas mixture contained ~80% of Methane for the

third case. The distinctive feature of this mixture is that the two-phase region appears at high

pressure (~7.5 MPa). Table 2 lists the initial conditions and the gas compositions of these

cases. The predicted results of gas decompression velocity were compared with the measured

data of shock tube test, and also against results from OLGA and GASDECOM.

CASE 1: DECOMPRESSION OF PURE NITROGEN

Figure 4 shows the predicted pressure-time traces of pure nitrogen at four locations:

P3, P4, P6 & P7 along the pipeline. It can be seen that the pressure at these monitored points

starts to drop rapidly once the decompression wave front reaches each location in turn. The

pressure becomes gradually steady at pressures below 4 MPa. The rate of change in both

speed of sound and outflow velocity as functions of time is presented in Figures (5 & 6)

respectively. The results of outlet velocity indicates that the flow was at rest (v = 0 m/s)

inside the pipe until the outlet boundary was removed.

Comparison of the predicted average and local decompression wave speed with the

measured data is shown in Figure 7. The results of both GASDECOM and OLGA are also

presented. The comparison shows that the current 2D CFD decompression model predicts the

decompression wave speed well. A good agreement can be observed between the measured

data and the average decompression wave speed calculated using the pressure-time traces

(similar way of measured calculation). Note that the measured data of decompression wave

speed deviates further to the left forming a plateau approximately at pressure ratio of 0.4. The

local decompression wave speed predicted at the four locations is identical to that predicted

by GASDECOM yet a constant local decompression wave speed was observed at the latter

stages of the decompression. This shows that using the same definition of W, GASDECOM

and the CFD model obtained the same results, indicating that GASDECOM performs as good

as CFD (at a fraction of the computation time) despite using a different principle and different

equation of state. The only difference that GASDECOM calculates the decompression speed

independently of time or location while the CFD results were predicted at several locations

away from the outlet boundary and inherently functions of the time.

CASE 2: DECOMPRESSION OF LEAN NATURAL GAS

Figure 8 shows the CFD prediction and the measured pressure-time traces of the lean

gas mixture. The predicted pressure starts to decompress at nearly the same time as the

measured data at every locations. This indicates that the decompression wave speed was at

the correct operating pressure and temperature. The predicted rate of change in pressure was

consistent with the experimental results until the appearance of a kink in the P-t curves at

pressures slightly below 5 MPa. This kink is due to the change in fluid properties which

results from the phase change. After this stage the measured pressure time traces become

almost steady while the predicted P-t traces drops further. At the same time, a sharp drop in

the speed of sound was noticed as shown in Figure 9. The observed kink also appeared in the

curves of outflow velocity and temperature results, as shown respectively in Figures 10 & 11.

By referring to the results of pressure and temperature, the kink was observed to occur at

P=4.6 MPa and, T=200.24 K. This point was found to be exactly at the phase boundary of the

mixture as expected.

Comparison of the predicted decompression speed and the measured data is shown in

Figure 12. The predicted results of the current CFD model are more consistent with the

measured data than that predicted by GASDECOM and OLGA although there is still

discrepancy at the end of the decompression. Referring to Figure 12, a significant decrease in

the decompression wave speed is observed, forming a pressure plateau at a pressure ratio of

~0.43 when crossing the dew curve. Figure 13 shows the phase envelope of case 2 and the

point at which the decompression enters the two-phase region. A significant drop in the speed

of sound at a constant pressure occurs during this process.

The current CFD decompression model successfully predicted the plateau found in

the measured data. The decompression speed calculated using the pressure time traces best

compared with the measured results. The appearance of such plateau for gas mixtures is

significant in terms of fracture propagation arrest requirements as it can lead to high

minimum arrest toughness. GASDECOM was not able to predict the plateau for this mixture

although its results show good agreement at high pressure ratio while OLGA predictions were

inaccurate. The issue in OLGA was linked to the definition used to calculate speed of sound

[19, 21].

CASE 3: DECOMPRESSION OF RICH NATURAL GAS

Figure 14 shows a comparison between the predicted and experimental results of

pressure-time traces of case 5 recorded at locations 4, 6 & 7. The predicted pressure-time

traces were in good agreement with the measured data. The two-phase flow region was

predicted and clearly observed on the P-t curves for this mixture. The discrepancy between

the predicted and the measured data occurred at pressure ratios lower than 0.5. The rate of

change for speed of sound, outflow velocity and temperature are shown in Figures 15, 16 &

17 respectively.

In Figure 15, a sharp drop in the speed of sound occurred once the decompression

crossed the two-phase boundary. The sharp decrease in speed of sound was reflected on the

result of decompression wave speed where a long plateau was formed as shown in Figure 18.

From this figure, it should be seen that the predicted average and local decompression speed

is in good agreement with the measured results except at low pressure ratios where the

predicted results deviate further to the right. The major observation for this mixture is that the

speed of sound increases towards the end of the decompression until it finally levels off at

around 250 m/s. To emphasis that this model predicted the decompression behaviour of gas

mixtures with taking account for phase change, the decompression process of pressure

against temperature was plotted on the phase envelope of the mixture. The procedure was

also performed as in lean gas mixture to find out at which point the flow entrance the two-

phase region. Figure 19 highlights the point where the flow crosses the two-phase boundary.

DISCUSSION

It is been found that if the shape and temporal location of the predicted pressure

matches the experimental results, the predicted value of W, should be in close agreement with

the measured data. As seen from plots in Figures 12 &18, there is a slight difference at the

plateau between the measured and the predicted results, however this difference is small as it

is ranging between 2.9-4.8% for case 2 and 1.5-1.8% for case 3. While the reason behind this

difference might be due to the uncertainties inherent in the numerical method that could

possibly be improved. Other factors such as delayed nucleation and/or the rapid dynamics of

the phase change (whereas the EOS uses equilibrium conditions at all time), roughness,

thermal exchange all can influence the results to various degrees.

The predicted results of decompression wave speed based on the local formulation

deviate at the latest stage of the decompression process in all cases. W becomes constant with

a continuing drop in pressure. This phenomenon begins at different values of pressure ratio

and depends on the location. At the location nearest to the full bore opening, W became

constant at lower pressure ratio than that further away from the outlet. This indicates that the

difference between the speed of sound and the outflow velocity became constant. This trend

is likely to be related to the increase of entropy due to the turbulences at the vicinity of the

wall. The increase of entropy limits the decrease of the local speed of sound and limits the

rate of increase of the flow velocity. The combined effects on the speed of sound and flow

velocity indirectly limit the local decompression wave speed. Further work is under way to

study the phenomenon.

The most notable difference between the numerical and measured data is that the

measured data shows a pressure drop downstream of the decompression wave levelling off at

the latter stages of the decompression. Experimental measurements show that this levelling

off occurs more rapidly at a higher pressure than that predicted by the model. For locations

P3 and P4, where results are available for the longest duration of time after the initial arrival

of the decompression wave, the difference between the low pressure values is on the order of

0.4 to 0.8 MPa. This is also reflected on the decompression wave speed curves where, in all

cases, the measured data deviates further to the left creating an apparent second plateau. This

is attributed to the piezoelectric pressure transducers (PCB) used in these particular

experiments. The apparent increase in the measured pressure-time traces (Figs. 8 and 14)

should be taken with caution at these low pressure parts of the traces. Later tests using

Endevco pressure transducers did not exhibit this increase in the pressure time traces [18, 20].

CONCLUSION

The following remarks can be inferred from this study.

(a) A two-dimensional CFD model based on the finite volume technique was

developed using ANSYS-Fluent to simulate the decompression behaviour of

gas pipelines.

(b) The GERG-2008 EOS was successfully implemented into this model to

provide an accurate calculation of the thermodynamic properties for gas

mixtures containing 21 different components.

(c) The results predicted by the current CFD model are in good agreement with

the experimental results obtained from shock tube tests.

The current work demonstrates that the CFD technique can be used to predict rapid

and severe gas decompression by solving the governing flow equations, in conjunction with

the wide-range GERG-2008 EOS. This is an effective tool for determining the decompression

wave speeds for different gas mixtures. This tool is valuable to develop fracture-

decompression coupled models and deliver a better understanding of the interaction between

the decompressing fluid and the fracturing pipeline. It is applicable in two or three

dimensional problems and for large pipe sizes where experimental tests are impractical.

Future work is also needed to examine the capability of this model in simulating the

decompression behaviour of other fluids such as CO2 mixtures.

ACKNOWLEDGMENTS

This work was funded by the Energy Pipelines CRC, supported through the Australian

Government’s Cooperative Research Centres Program. The funding and in-kind support from

the APIA RSC is gratefully acknowledged.

REFRENCES

[1] S. F. Brown, "CFD Modelling of Outflow and Ductile Fracture Propagation in Pressurised Pipelines," Doctor of Philosophy, Department of Chemical Engineering, University College London, London, 2011.

[2] H. Mahgerefteh, G. Denton, and Y. Rykov, "A hybrid multiphase flow model," AIChE Journal, vol. 54, pp. 2261-2268, 2008.

[3] W. A. Maxey, J. F. Kiefner, and R. J. Eiber, Ductile fracture arrest in gas pipelines, 1976. [4] K. K. Botros, J. Geerligs, L. Fletcher, B. Rothwell, P. Venton, and L. Carlson, "Effects of

Pipe Internal Surface Roughness on Decompression Wave Speed in Natural Gas Mixtures," ASME Conference Proceedings, vol. 2010, pp. 907-922, 2010d.

[5] C. Lu, G. Michal, A. Elshahomi, A. Godbole, P. Venton, K. K. Botros, L. Fletcher, and B. Rothwell, "INVESTIGATION OF THE EFFECTS OF PIPE WALL ROUGHNESS AND PIPE DIAMETER ON THE DECOMPRESSION WAVE SPEED IN NATURAL GAS PIPELINES," presented at the 9th International Pipeline Conference 2012, Calgary, Alberta, Canada, 2012.

[6] A. B. Rothwell, "Fracture propagation control for gas pipelines––past, present and future," In: Denys R, editor. Proceedings of the 3rd International Pipeline Technology Conference, vol. 1, pp. 387–405, 2000.

[7] "Final Report on the Test Program at the Northern Alberta Burst Test Facility," Foothills Pipe Lines (Yukon) Ltd. , Calgary, Alberta, Canada1981.

[8] R. M. Andrews, N. A. Millwood, A. D. Batte, and B. J. Lowesmith, "The fracture arrest behaviour of 914 mm diameter X100 grade steel pipelines," in IPC 2004, 2004.

[9] B. Eiber, L. Carlson, B. Leis, and A. Gilroy-Scott. (1999) Full-scale tests confirm pipe toughness for North American pipeline. Oil & Gas Journal. 48-54.

[10] R. Eiber and L. Carlson, "Fracture control for the alliance pipeline," in ASME International pipeline conference IPC-2000, Calgary, Alberta, Canada 2000.

[11] R. J. Eiber and W. A. Maxey, "Full-scale experimental investigation of ductile fracture behavior in simulated arctic pipeline," Materials Engineering in the Arctic , Proceedings of Int. Conf., St. Jovite, Quebec, Canada, Sept 27-Oct 1, 1976, also Canadian Arctic Gas Study Limited (CAGSL), Engineering in the Arctic/ASM, St. Jovite, Quebec,, 1977.

[12] T. K. Groves, P. R. Bishnoi, and J. M. E. W. allbridge, "Decompression Wave Velocities In Natural Gases In Pipe Lines," Canadian Journal of Chemical Engineering, vol. 56, pp. 664-668, 1978.

[13] S. Igi, S. Kawaguchi, and N. Suzuki, "Running ductile fracture analysis for X80 pipeline in JGA burst tests," presented at the Pipeline Technology Conference, Oct 12-14, Ostend, Belgium, 2009.

[14] S. Kawaguchi, N. Hagiwara, T. Masuda, C. Christensen, H. Nielsen, P. Ludwigsen, D. Rudland, and G. Wilkowski, "Application of X80 in Japan: fracture control," in 4th International Conference On Pipeline Technology, Ostend. Belgium, 2004.

[15] D. Rudland, D. J. Shim, H. Xu, D. Rider, P. Mincer, D. Shoemaker, and G. Wilkowski, "FIRST MAJOR IMPROVEMENTS TO THE TWO CURVE DUCTILE FRACTURE MODEL PART I MAIN BODY," U.S. Department of Transportation Research and Special Programs Administration Washington DC 20590 and Pipeline Research Council International, Inc. Arlington, VA 222092007.

[16] A. G. Phillips and C. G. Robinson, "Gas decompression behavior following the rupture of high pressure pipelines - Phase 1, PRCI Contract PR-273-0135," Pipeline Research Council International, Inc.2002.

[17] A. G. Phillips and C. G. Robinson, "Gas Decompression Behavior following the Rupture of High Pressure Pipelines – Phase 2: Modeling Report, PRCI Contract PR-273-0135," 2005.

[18] K. K. Botros, J. Geerligs, and R. J. Eiber, "Measurement of Decompression Wave Speed in Rich Gas Mixtures at High Pressures (370 bars) Using a Specialized Rupture Tube," Journal of Pressure Vessel Technology, vol. vol. 132, pp. 051303-15, 2010a.

[19] K. K. Botros, J. Geerligs, and R. Given, "Decompression Response of High-Pressure Natural Gas Pipelines Under Rupture or Blowdown Conditions," Pipeline Research Council International, Inc.August 26 2004.

[20] K. K. Botros, J. Geerligs, B. Rothwell, L. Carlson, L. Fletcher, and P. Venton, "Transferability of decompression wave speed measured by a small-diameter shock tube to full size pipelines and implications for determining required fracture propagation resistance," International Journal of Pressure Vessels and Piping, vol. 87, pp. 681-695, 2010b.

[21] K. K. Botros, J. Geerligs, J. Zhou, and A. Glover, "Measurements of flow parameters and decompression wave speed following rupture of rich gas pipelines, and comparison with GASDECOM," International Journal of Pressure Vessels and Piping, vol. 84, pp. 358-367, 2007.

[22] K. K. Botros, W. Studzinski, J. Geerligs, and A. Glover, "Determination of Decompression Wave Speed in Rich Gas Mixtures," The Canadian Journal of Chemical Engineering, vol. 82, pp. 880-891, 2004.

[23] A. Oke, H. Mahgerefteh, I. Economou, and Y. Rykov, "A transient outflow model for pipeline puncture," Chemical Engineering Science, vol. 58, pp. 4591-4604, 2003.

[24] R. W. Lewis, P. Nithiarasu, and K. Seetharamu, Fundamentals of the Finite Element Method for Heat and Fluid Flow: John Wiley and Sons, Ltd, 2004.

[25] H. Mahgerefteh, Saha, Pratik, Economou, and I. G., "Fast numerical simulation for bore rupture of pressurized pipelines," American Institute of Chemical Engineers. AIChE Journal, vol. 45, pp. 1191-1191, 1999.

[26] H. Mahgerefteh, P. Saha, and I. G. Economou, "A Study of the Dynamic Response of Emergency Shutdown Valves Following Full Bore Rupture of Gas Pipelines," Process Safety and Environmental Protection, vol. 75, pp. 201-209, 1997.

[27] R. Eiber, T. Bubenik, and W. Maxey, "GASDECOM, computer code for the calculation of gas decompression speed that is included in fracture control technology for natural gas pipelines. NG-18 Report 208," American Gas Association Catalog1993.

[28] A. Cosham, D. G. Jones, K. Armstrong, D. Allason, and J. Barnett, "THE DECOMPRESSION BEHAVIOUR OF CARBON DIOXIDE IN THE DENSEPHASE," in Proceedings of the 2012 9th International Pipeline Conference, Calgary, Alberta, Canada, 2012a, p. 18.

[29] D. G. Jones and D. W. Gough, "Rich Gas Decompression Behaviour in Pipelines," AGA-EPRG Linepipe Research Seminar IV, Duisburg, 1981.

[30] R. Cleaver and P. Cumber, "Modelling pipeline decompression during the propagation of a ductile fracture," in INSTITUTION OF CHEMICAL ENGINEERS SYMPOSIUM SERIES, 2000, pp. 201-212.

[31] H. Makino, T. SUGIE, T. KUBO, T. SHIWAKU, S. ENDO, T. INOUE, Y. KAWAGUCHI, Y. MATSUMOTO, and S. MACHIDA, "Natural Gas Decompression Behavior in High Pressure Pipelines.," ISIJ Int (Iron Steel Inst Jpn), vol. 41, pp. 389-395, 2001.

[32] W. Qiu, J. Gong, and J. Zhao, "A Study on Natural Gas Decompression Behavior," Petroleum Science and Technology, vol. vol. 29, pp. pp29 - 38, 2011.

[33] X.-X. Xu and J. Gong, "A united model for predicting pressure wave speeds in oil and gas two-phase pipeflows," Journal of Petroleum Science and Engineering, vol. 60, pp. 150-160, 2008.

[34] R. Span and W. Wagner, "A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa," ISSN, vol. 25, pp. 1509-1596, 1996.

[35] O. Kunz, R. Klimeek, W. Wagner, and M. Jaeschke, "The GERG-2004 Wide-Range Equation of State for Natural Gases and Other Mixtures-GERG TECHNICAL MONOGRAPH 15," Groupe Européen de Recherches Gazières2007.

[36] E. W. Lemmon, M. L. Huber, and M. O. McLinden, "NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP," Version 9.0 ed. Gaithersburg: National Institute of Standards and Technology, 2010.

[37] D. J. Picard and P. R. Bishnoi, "The Importance of Real-Fluid Behavior and Nonisentropic Effects in Modeling Decompression Characteristics of Pipeline Fluids for Application in Ductile Fracture Propagation Analysis," THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, vol. 66, pp. 3-12, 1988.

[38] D. J. Picard and P. R. Bishnoi, "The Importance of Real-Fluid Behavior in Predicting Release Rates Resulting From High-Pressure Sour-Gas Pipeline Ruptures," THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, vol. 67, pp. 3-9, 1989.

[39] K. H. Bendiksen, D. Maines, R. Moe, and S. Nuland, "The Dynamic Two-Fluid Model OLGA: Theory and Application," SPE Production Engineering, vol. 6, pp. 171-180, 1991.

[40] H. Mahgerefteh, S. Brown, and G. Denton, "Modelling the impact of stream impurities on ductile fractures in CO2 pipelines," Chemical Engineering Science, vol. 74, pp. 200-210, 2012.

[41] H. Mahgerefteh, S. Brown, and S. Martynov, "A study of the effects of friction, heat transfer, and stream impurities on the decompression behavior in CO2 pipelines," in Greenhouse Gases: Science and Technology vol. 2, ed: John Wiley & Sons, Ltd., 2012, pp. 369-379.

[42] H. Mahgerefteh, A. Oke, and O. Atti, "Modelling outflow following rupture in pipeline networks," Chemical Engineering Science, vol. 61, pp. 1811-1818, 2006.

[43] D.-Y. Peng and D. B. Robinson, "A New Two-Constant Equation of State," Industrial & Engineering Chemistry Fundamentals, vol. 15, pp. 59-64, 1976/02/01 1976.

[44] H. E. Jie, B. P. Xu, J. X. Wen, R. Cooper, and J. Barnett, "PREDICTING THE DECOMPRESSION CHARACTERISTICS OF CARBON DIOXIDE USING COMPUTATIONAL FLUID DYNAMICS," in Proceedings of the 2012 9th International Pipeline Conference, Calgary, Alberta, Canada 2012, p. 11.

[45] C. W. Hirt, A. A. Amsden, and J. L. Cook, "An arbitrary Lagrangian-Eulerian computing method for all flow speeds," Journal of Computational Physics, vol. 14, pp. 227-253, 1974.

[46] L. G. Margolin, "Introduction to “An Arbitrary Lagrangian–Eulerian Computing Method for All Flow Speeds”," Journal of Computational Physics, vol. 135, pp. 198-202, 1997.

[47] B. E. Poling, J. M. Prausnitz, J. P. O'Connell, and Ebrary, The properties of gases and liquids, 5th ed. ed. New York: McGraw Hill Companies 5th ed., 2001.

[48] W. Wagner, "Description of the Software Package for the Calculation of Thermodynamic Properties from the GERG-2004 XT08 Wide-Range Equation of State for Natural Gases and Other Mixtures," RUHR-UNIVERSITÄT BOCHUM2009.

[49] ANSYS, "ANSYS Fluent 13.0 Getting Started Guide," pp. viii, 18, 2010. [50] ANSYS/Fluent, "ANSYS Fluent UDF Manual," p. 522, 2010. [51] H. K. Versteeg and W. Malalasekera, An introduction to computational fluid dynamics : the

finite volume method 2nd ed. New York: Pearson Education Ltd, 2007. [52] ANSYS, "ANSYS Fluent 13.0 Theory Guide ", ed, 2010, pp. xxviii, 720. [53] T. BARTH and D. JESPERSEN, "The design and application of upwind schemes on

unstructured meshes," in AIAA, Aerospace Sciences Meeting, 27 th, Reno, NV, 1989, p. 1989.  

 

 

 

 

 

Table 1: The location of monitoring points

Node P2 P3 P4 P6 P7

Location from Rupture (mm) 59 240 440 840 1240

Table 2: Shock tube test conditions and gas compositions

Case 1 Case 2 Case 3

Pi (MPa) 10.059 10.58 9.94

Ti (K) 260.44 247.65 273.21

C1 (mole %) 0 95.4741 79.3089

C2 (mole %) 0 2.9363 14.1967

C3 (mole %) 0 0.1902 5.2556

iC4 (mole %) 0 0.0156 0.0114

nC4 (mole %) 0 0.0253 0.0164

iC5 (mole %) 0 0.0041 0.0029

nC5 (mole %) 0 0.003 0.002

C6+ (mole %) 0 0.0013 0.0009

N2 (mole %) 100 0.5689 0.5513

CO2 (mole %) 0 0.7812 0.6539

 

Figure 1: ANSYS Fluent density based solver integrated with GERG-08 EOS

 

 

Figure 2: Flow domain and computational domain – schematic -

Figure 3: Two-dimensional computational grid 

Figure 4: Pressure-time traces at four locations (case 1)

Figure 5: Speed of sound-time traces at four locations (case 1)

Figure 6: Outflow velocity-time traces at four locations (case 1)

Figure 7: Comparison of the predicted decompression wave speed with the measured, GASDECOM and OLGA results (case 1)

Figure 8: Comparison of predicted and the measured pressure-time (case 2)

Figure 9: Speed of sound-time traces at four locations (case 2)

Figure 10: Outflow velocity-time traces at four locations (case 2)

Figure 11: Temperature-time traces at four locations (case 2)

Figure 12: Comparison of the predicted decompression wave speed with the measured, GASDECOM and OLGA results (case 2)

Figure 13: The interaction between the decompression behaviour of Pressure and Temperature with the Phase Envelope (case 2)

Figure 14: Comparison of the predicted and the measured pressure-time (case 3) 

Figure 15: Speed of Sound-time traces at four locations (case 3)

Figure 16: Outflow velocity-time traces at four locations (case 3)

Figure 17: Temperature-time traces at locations P3, P6 & P7 (case 3)

Figure 18: Comparison of the predicted decompression wave speed with the measured, GASDECOM and OLGA results (case 3)

Figure 19: The interaction between the decompression behaviour of Pressure and Temperature with the Phase Envelope (case 3)