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VALIDATION OF DISPERSION MODELS FOR HIGH PRESSURE CARBONDIOXIDE RELEASES†

C.M. Dixon1, S.E. Gant2, C. Obiorah3, and M. Bilio4

1 Shell Global Solutions (UK), Shell Technology Centre Thornton, PO Box 1, Chester, CH1 3SH2 Health & Safety Laboratory, Harpur Hill, Buxton, SK17 9JN3 Shell Global Solutions International, Kessler Park 1, 2288GS Rijswijk, Netherlands4 Health & Safety Executive, Redgrave Court, Merton Road, Bootle, L20 7HS

Predictions from an integral model and two Computational Fluid Dynamics (CFD) models are com-

pared to experimental data for confined and unconfined jet releases of dense phase carbon dioxide

(CO2). The releases studied are relevant in scale to leaks from above-ground pipes or vessels. For

the unconfined cases, the jets consist of a horizontal discharge through either a 12′ ′ or 1′ ′ orifice, with

the dense-phase CO2 reservoir maintained at approximately 150 bar and close to ambient tempera-

ture. The confined release involves a 12′ ′ diameter jet discharging into a largely-enclosed steel con-

tainer of dimensions 6 × 2 × 2 metres. Measurements of temperature and concentration in the

dispersing CO2 plumes were obtained for these tests from experiments commissioned by Shell at

the GL Spadeadam facility.

The integral model used is Shell FRED, which adopts a semi-empirical jet model for the momen-

tum-dominated part of the release and a similarity model for the subsequent dense gas dispersion, if

required. FRED assumes Homogeneous Equilibrium (HE) between the CO2 particles and the

vapour phase, i.e. the particles and surrounding vapour share the same temperature and velocity.

Since FRED was primarily designed for hydrocarbon hazards it does not actually consider solid

particles but, rather, the liquid-vapour line is extrapolated down to atmospheric pressure and the

particles are treated as liquid; the effect of this approximation is discussed.

Two different CFD dispersion models are tested: the first has been developed in the OpenFOAM

CFD software and assumes HE, whilst the second has been developed in Ansys-CFX and uses a

particle-tracking approach to simulate the sublimating solid CO2 particles. Both FRED and the

two CFD models account for the latent heat effects associated with humidity and the condensation

of water vapour in the cold CO2 cloud.

The results from the model comparisons are used to assess the suitability of fast consequence

models like FRED to simulate unconfined jet releases of dense phase CO2. The findings provide

useful information for the assessment of potential hazards presented by Carbon Capture and

Storage (CCS) infrastructure.

1. INTRODUCTIONA number of industrial-scale Carbon Capture and Storage(CCS) projects are currently being planned in the UK1

including the Don Valley Power Project2 in Yorkshire,and the Peterhead power station3 in Aberdeenshire. Intotal, there are nine UK CCS projects that have appliedfor EU funding from the New Entrant Reserve (NER)scheme4. In many of these projects, carbon dioxide (CO2)will be transported or stored in its liquid state, i.e. at apressure above 74 bar and temperature below 31ºC.As part of the design and risk assessment process for the

CCS infrastructure, an understanding is required of theconsequences of an intentional or accidental release ofliquid CO2. The relevant CCS infrastructure will includecompressor stations, pipelines transporting the CO2 fromthe power station to the reservoir injection site and, insome cases, equipment on offshore platforms.

The focus of the present work is on the validation ofCO2 release models against experimental data. For the pur-poses of model validation, predictions are compared tomeasurements from a programme of CO2 release exper-iments commissioned by Shell at the GL Spadeadam testsite in Cumbria in late 2010. These experiments consistedof steady-state horizontal discharges onto an open test padwith a well-defined mass flow rate of liquid CO2. The padwas well instrumented to provide measurements of tempera-ture and gaseous CO2 concentration at numerous locations,for distances up to around 80 m from the release orifice. Inaddition, a more limited set of tests was conducted in whichliquid CO2 was discharged into a largely-enclosed steel con-tainer of dimensions 6 × 2 × 2 metres.

†# Crown Copyright 2012. This article is published with the permission of the Controller of HMSO and the Queen’s Printer for Scotland.

1http://www.ccsassociation.org/why-ccs/ccs-projects/current-projects

(accessed May 2012)2http://www.2coenergy.com/don_valley_power_project.html (accessed

May 2012)3http://www.sse.com/EnergyPolicy/FutureEnergyNeeds/Generation/

CCS/ (accessed May 2012)4http://www.decc.gov.uk/en/content/cms/news/pn11_013/

pn11_013.aspx (accessed May 2012)

SYMPOSIUM SERIES NO. 158 Hazards XXIII # 2012 Crown Copyright

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The results from various models are compared to themeasured concentrations and temperatures to assess thestrengths and weakness of different underlying modelassumptions, and the degree of error in model predictions.The findings will prove to be useful for the assessment ofpotential hazards presented by CCS infrastructure.

2. REVIEW OF PREVIOUS STUDIESThere have been a number of recent publications examiningthe release and dispersion of CO2. In the earlier of thetwo papers published by MMI Engineering (Dixon andHasson, 2007), dispersion simulations were performedusing the ANSYS-CFX Computational Fluid Dynamics(CFD) code. Solid CO2 particles were not included expli-citly in the model but were instead simulated using ascalar representing the particle concentration. This approachwas taken to avoid the additional computing time associatedwith Lagrangian particle tracking. However, one of its limit-ations was that in calculating the heat and mass exchangebetween the particles and the gas phase, it was necessaryto assume a constant particle diameter. The distribution ofthe source of CO2 gas resulting from particle sublimationmay have therefore been poorly predicted, since the rateof sublimation increases as the particle size decreases inthe jet. In addition, the particle temperature was assumedto remain constant at the sublimation temperature of278ºC i.e. a “boiling” assumption was made.

In the second MMI paper (Dixon et al., 2009), theparticles were modelled using a Lagrangian particle trackingapproach. However, particles were still assumed to remainat a constant temperature of 278ºC. It is discussed later, inSection 4, that in reality the particle temperature is expectedto fall in the jet, to perhaps as low as 2100ºC. In both of theMMI studies, the release rate was calculated using a Hom-ogenous Equilibrium Model (HEM) rather than the Ber-noulli equation which has been used in the present paper.The method used to model the expansion of CO2 from theorifice to the atmospheric pressure was, however, essentiallythe same as that described later in this paper.

The UK Health and Safety Executive (HSE) havepublished a number of papers on CO2 release and dispersionmodelling. In the first of these, Shuter et al. (2010) provideda review of CCS safety issues from the perspective of theUK HSE. Modelling was not considered in detail, butsource term modelling was included under the heading of“knowledge gaps” where it was stated that hazard rangesare sensitive to the source term model assumptions. McGil-livray et al. (2009) compared the risks from CO2 pipelinesand natural gas pipelines. PHAST was used to calculatethe CO2 gas dispersion and HSE in-house tools were usedto compare the risks. Only gaseous inventories were con-sidered and two hole sizes were modelled in addition tofull-bore ruptures. Interestingly, some analysis was includedof the deflection of the jet angle due to its impact on thecrater walls. Overall, the hazard due to a CO2 pipeline inthe pressure range considered was found to be similar to acorresponding natural gas pipeline. Harper (2010) carried

out a number of modelling exercises for CO2 dispersionusing the DRIFT model and two versions of PHAST.The paper was mostly concerned with releases due tocatastrophic vessel failures that lead to large instantaneousreleases, rather than the jet releases that are considered inthe present paper.

Webber (2011) presented a methodology for extend-ing existing two-phase homogeneous equilibrium integralmodels for flashing jets to the three-phase case for CO2.As the flow expands from the reservoir conditions to atmos-pheric pressure, it was assumed that the pressure, tempera-ture, density and the jet cross-sectional area would varycontinuously through the triple point, whilst the mass andmomentum would be conserved. This led to the conclusionthat there must be a discontinuity in the enthalpy and CO2

liquid fraction, in a similar manner to the energy loss associ-ated with flow passing through a hydraulic jump. The paperonly considered theoretical model development and did notshow any comparisons to data.

Gant and Kelsey (2012) examined the effect of concen-tration fluctuations in gaseous releases of CO2. The ToxicLoad (TL)5 is proportional to concentration to the powereight for CO2 and therefore it increases rapidly if there areany concentration fluctuations in the plume. To examinethe significance of this effect, the TL in jets of gaseous CO2

was examined using three different models: a quasi-empiricalProbability Density Function (PDF) model that accountedfor concentration fluctuations, a model based solely on themean concentration with no fluctuations, and a third modelwhich assumed that the concentration fluctuated with anassumed square wave variation over time. The SpecifiedLevel of Toxicity (SLOT) and Significant Likelihood ofDeath (SLOD) hazard distances were shown to be under-pre-dicted if the effects of concentration fluctuations wereignored. It was also demonstrated that the assumed square-wave fluctuation model provided conservative predictionsof the distances from the CO2 source to the SLOT and SLOD.

DNV Software has produced two key papers on CO2

release and dispersion modelling. In the first, Witlox et al.(2009) described an extension to the existing model inPHAST version 6.53.1 to account for the effects of solidCO2. The modifications consisted principally of changingthe way in which equilibrium conditions were calculatedin the expansion of CO2 to atmospheric pressure, toensure that below the triple point, conditions followed thesublimation curve in the phase diagram, rather than extrapo-lating the evaporation curve. Although the revised modelwas validated against experimental data, the measurementswere confidential and could not be reported. In the second ofthe papers (Witlox et al., 2011), the results of sensitivitytests were reported for both liquid and supercritical CO2

releases from vessels and pipes with the revised PHASTversion 6.6 model. Again, no experimental validation waspresented due to data confidentiality.

E.ON have published a number of studies in supportof their proposed CCS programme (Mazzoldi et al.,

5http://www.hse.gov.uk/chemicals/haztox.htm (accessed August 2012)


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2008a, 2008b, 2011; Hill et al., 2011). The most relevantpublications to the present work are by Mazzoldi et al.(2011) and Hill et al. (2011), which considered atmosphericdispersion from pipeline and vessel releases. The formerpaper compared simulations from the heavy gas modelALOHA to the CFD model Fluidyn-Panache. Althoughthe work focused on discharges of dense-phase CO2 froma 100 bar release, only the gaseous stage of the dischargeswere modelled. The bulk of the analysis consisted of com-parisons between the two models, rather than experimentaldata. Some sample data from an earlier study of the Kit Foxtrials (Mazzoldi et al., 2008a) was included in the paper,where the same models were compared to experimentaldata at one measurement location, which showed thatALOHA over-predicted the gas concentration. It was con-cluded from this that “Gaussian/dense-gas simulationscan over-estimate the risk in a way that would prejudicethe widespread introduction of the technology”. However,a more complete analysis of the ALOHA and Panachemodel predictions against multiple Kit Fox trial measure-ments in their previous work showed that both modelsunder-predicted concentrations on average.

Hill et al. (2011) presented CFD and PHAST simu-lations of dense-phase CO2 releases from a 0.5 m diameterhole in a pipeline, located at an elevation of 5 m above flatground. Rather than model the time-varying depressuriza-tion of the pipeline, steady-state flow rates were calculatedat the orifice assuming saturated conditions. The methoddescribed by Fauske and Epstein (1988) was used to calcu-late the source conditions once the two-phase jet hadexpanded to atmospheric pressure. CFD simulations wereperformed using the ANSYS-CFX code with a Lagrangianparticle-tracking model for the solid CO2 particles. Toexamine the effect of the particle size, three size distri-butions were tested: from 10 to 50 mm, from 50 to 100 mmand from 50 to 150 mm. Simulations were also performedwith no solid CO2 particles. The results showed that subli-mation of the particles led to cooling of the CO2 plume,which affected its dispersion behaviour, although theresults were relatively insensitive to the particle size. Pre-dicted gas concentrations downwind from the release weresomewhat lower using PHAST version 6.6 as compared tothe CFD results but there was no comparison of model pre-dictions to experiments.

One of the differences between the CFX model usedby Hill et al. (2011) and that used in the present study isthat it appears that their Lagrangian model did not accountfor the effects of turbulence on the dispersion of the solidCO2 particles. The particle tracks were not spread through-out the plume but instead followed closely the plume centre-line. Ignoring turbulent dispersion effects can have asignificant influence on the model predictions, particularlythe temperature. Turbulence has the effect of bringing par-ticles into contact with parts of the jet at a higher tempera-ture and lower CO2 concentration. This tends to increase therate of sublimation and increase the radius of the regioncooled by the sublimating particles. In the present work,turbulent dispersion effects have been included in the

CFX model, although this has required a greater numberof particles to be simulated, with consequently longer com-puting times.

A second difference between the model used in thepresent work and that presented by Hill et al. (2011) isthat it is assumed here that the solid CO2 particles aremuch smaller (i.e. an initial particle diameter of 5 mm).This choice has been made based on analysis of CO2 exper-iments, which showed that gas temperatures in the plumefell well below 278ºC. In addition, the particle size distri-bution model recently developed by Hulsbosch-Dam et al.(2012) suggested that the particle diameter would bearound 5 mm for CO2 releases at a pressure of 100 bar,when the difference between the CO2 and ambient tempera-tures was around 80ºC. The effect of having smaller par-ticles in the present model is likely to cause more rapidsublimation, which should produce a more significantreduction in gas temperature in the jet.

3. EXPERIMENTAL ARRANGEMENTIn the experiments conducted at GL Spadeadam, the CO2

inventory was contained within a 24′′ diameter vessel witha volume of 6.3 m3. Two pipes were connected at oppositeends of this vessel. From one end, a length of pipework con-nected the vessel to an orifice which was located at a heightof 1 m above the surface of the concrete test pad. The pipe-work connected to the orifice included a Coriolis flow meterwhich was used to measure directly the CO2 mass flow rate.Orifice sizes up to 1′′ were used in the tests, with releasesdirected horizontally.

At the opposite end of the vessel, a connection led to apad gas line which was filled with liquid CO2 at the sameconditions as within the vessel. The inlet to the pad gas linewas connected to a nitrogen reservoir at a constant supplypressure, which enabled steady-state CO2 releases to be pro-duced. The pad gas line was inclined from the horizontal tominimise the surface area between the nitrogen and liquidCO2, and releases were stopped prior to nitrogen enteringthe test vessel, to prevent it from contaminating the CO2.The temperature and pressure were measured at a numberof locations within the vessel and the pipework, includingone location immediately upstream of the orifice.

In addition to the instrumentation of the vessel andpipework, there was significant field instrumentation onthe test pad. Temperature and oxygen depletion measure-ments were taken on arcs at 20, 40, 60 and 80 m from therelease, together with centreline locations at 5, 10 and 15 m.The oxygen depletion measurements were used to infer CO2

concentration. All of the measurement stands were fittedwith temperature and concentration instruments at 1 mabove pad level (i.e. at the same height as the orifice) andsome stands featured additional instruments at heights of0.3 m and 3 m above the pad. On the jet centreline therewere additional temperature measurements at 1, 2, 3 and 4m from the release and at other locations there were concen-tration measurements from sampling devices and commer-cial point CO2 detectors in some of the tests.


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Two anemometer masts were used to measure theatmospheric conditions. Both masts used sonic anem-ometers to record both wind speed and direction. Measure-ments from the mast positioned upwind from the releasepoint were used to define the wind speeds in the dispersionsimulations.

4. CALCULATION METHODSThe simulations were split into three consecutive stages: forthe outflow, expansion and dispersion. In the first, outflowstage, the mass flow rate was calculated together withvarious properties at the release plane (i.e. the orifice). Inthe second, expansion stage, the process by which theliquid or liquid/vapour mixture at the orifice was trans-formed into a gas/solid mixture at atmospheric pressurewas modelled. Finally, in the third stage, the dispersion ofCO2 downstream from the expansion zone was modelled,which required the physical processes associated with sub-limation of solid CO2 particles and condensation of watervapour in the jet to be taken into account. It should benoted that FRED does not consider solid particles but,rather, the liquid-vapour line is extrapolated down to atmos-pheric pressure and the particles are treated as evaporatingliquid droplets.

Calculations were performed using three differentmodels: FRED Pressurised Release (PR), OpenFOAM andANSYS-CFX. The first of these, PR, is an integral modelthat forms part of the Shell FRED software package (Better-idge and Roy, 2010). It has been used to calculate all stagesof the release, including the outflow, expansion and dis-persion. The second and third models, OpenFOAM andANSYS-CFX, are both CFD models that were used to cal-culate only the final stage dispersion process. Both PR andOpenFOAM assumed thermodynamic equilibrium whereasANSYS-CFX used a Lagrangian particle-tracking approach.

4.1 THERMODYNAMIC EQUILIBRIUMA brief discussion of the thermodynamic equilibriumconcept is provided here since it forms a key part of thePR and OpenFOAM models. The starting point for the dis-cussion corresponds to a position at the end of the expan-sion zone in a jet of pure CO2, which contains bothvapour and solid CO2 particles at the sublimation tempera-ture of 278ºC. As air is added into such a mixture, the CO2

gas concentration starts to decrease so that the vapour pres-sure exerted by the solid CO2 particles exceeds the CO2

partial pressure in the surrounding gas mixture. The solidtherefore starts to sublime and its temperature falls in orderto supply the heat of sublimation. There is an exchange ofheat from the warmer gas mixture to the cold particlesso that the temperature of both the gas and solid phasesdecreases. If the particles are sufficiently small, this transferof heat occurs rapidly, i.e. the solid and gas phases shareessentially the same temperature. The solid CO2 continuesto sublime and the temperature of the solid-gas mixture fallsto a point where eventually the saturation vapour pressure at

the particle surface matches the partial pressure of CO2 inthe gas mixture. At this point, no further sublimation takesplace and equilibrium conditions are established. Movingfurther downstream in the jet, this process occurs con-tinuously, with further air entrainment producing lowertemperatures. The resulting behaviour is such that the temp-erature follows the saturation curve for solid-vapour equili-brium in the pressure-temperature phase diagram as thedistance from the orifice increases (where the pressure inthe phase diagram refers to the partial pressure of CO2

rather than the atmospheric pressure). This process con-tinues up to the point where all of the solid CO2 has subli-mated. Further entrainment into the jet beyond this pointcauses the temperature to increase, as the cold CO2-airmixture mixes with warmer ambient air.

A second application of the thermodynamic equili-brium analysis relates to interpretation of the experiments.Analysis of the measurement data from the experimentsshowed that the oxygen depletion sensors (which reliedupon a chemical reaction to measure the oxygen concen-tration) were adversely affected by the very low tempera-tures in the jet and produced unreliable measurements atlater times in a release. Since the solid CO2 particles wereexpected to be very small (Hulsbosch-Dam et al., 2012), itwas considered reasonable to assume thermodynamic equi-librium in the jet. By making this assumption, the total CO2

concentration and the gas temperature could be directlyrelated. This approach is explained by Witlox et al. (2009)and it will not be repeated here, but in this way CO2 concen-trations have been inferred from temperature measurements,which are presented in later sections. It should be noted thatthe results of this analysis are sensitive to the initial solidfraction of CO2, which was not measured directly in theexperiments, and this introduces a degree of uncertaintyinto the inferred concentration data.

4.2 OUTFLOW MODELThe mass flow rate of CO2 from the orifice was calculatedusing the Bernoulli equation. Use of the Bernoulli equationis based on the assumption of a meta-stable liquid at theorifice due to the residence time of the fluid through theorifice being too short for nucleation of vapour bubbles.The Bernoulli equation results in the well-known formulafor the mass flux, G:

G = CdA��2r(P0 − Patm)

√(1)

where Cd is the discharge coefficient, A the orifice area, r thefluid density, P0 the stagnation pressure and Patm the atmos-pheric pressure. A value of 0.6 was assumed for Cd in thepresent work, which accounts for the narrowing of the jet(i.e. the vena contracta) at the location where the pressurereaches atmospheric.

Comparison of the predicted mass flow rate to the mea-surements showed that Equation (1) slightly over-estimatedthe mass flow rate, giving a value up to around 10% greaterthan the measured values.


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4.3 EXPANSION TO ATMOSPHERIC PRESSUREThe flashing process that takes place as the jet expands fromthe orifice to the atmospheric pressure was calculated usingglobal conservation laws for mass, momentum and energy(Post, 1994; Harper, 2005). The inlet to the CFD calcu-lations was taken to be at the end of the flashing depressur-isation zone.

To calculate the post-flash conditions, it was assumedthat there is a distinct depressurisation zone in which thefluid rapidly expands to atmospheric pressure and that atwo-phase jet exists beyond this point. In the depressurisa-tion zone it is assumed that there is no entrainment, and fric-tion is neglected. A control volume is then constructedaround the expansion zone, and equations are derived forthe mass, energy and momentum conservation betweenthe inlet and outlet of this volume. Assuming thermodyn-amic equilibrium then allows the source radius, velocityand solid fraction to be obtained. The orifice pressure isabove atmospheric pressure so that the gas is acceleratedin the expansion zone.

4.4 FRED DISPERSION MODELThe Shell FRED (Fire Release Explosion Dispersion) soft-ware is composed of a suite of hazard modelling codeswith a common interface. For the calculations presentedhere the Pressurised Release (PR) model is employed,which makes calls to a number of underlying codes. Follow-ing the flashing calculation, described in Section 4.3, thedispersion of CO2 is calculated using a jet dispersionmodel, AEROPLUME, the results of which may then bepassed on to the dense gas dispersion model HEGADAS.These models have been described in detail elsewhere(Post, 1994). An important aspect of the code to note inthe present context is that it is assumed that a homogenousequilibrium exists between the particles and the air, i.e. thevelocity, temperature and pressure of the two phases areassumed to be equal.

In the present work, the thermodynamics libraryemployed by FRED did not account for solid CO2, butinstead the liquid-vapour saturation line was extrapolatedto atmospheric pressure. Hence, following the flashprocess, FRED gave a gas/liquid mixture with liquiddrops rather than solid particles. The subsequent gasplume consisted of a mixture of vapour and liquid CO2,together with liquid and vapour water, and air.

4.5 OPENFOAM DISPERSION MODELIn addition to the standard transport equations for mass,momentum, turbulence and energy, the OpenFOAM CFDmodel solved transport equations for two scalars, one toaccount for the mass fraction of pollutant (in this caseCO2) in the gas phase and another to track the mass concen-tration of solid (or liquid) pollutant. The gas-phase thermo-dynamic and transport properties were pre-calculatedassuming thermodynamic equilibrium using a real gasequation-of-state and were presented to the solver as a setof lookup tables over temperature, pressure and pollutant

mass fraction. Water vapour and liquid water were includedin the gas phase using a homogenous equilibrium assump-tion so that the effects of condensation and evaporationwere automatically captured. Only one set of momentumequations was solved since it was assumed that the solidCO2, air and condensed water droplets shared the samevelocity.

The density used by the solver was the gas densityrather than the mixture density, and it did not include thecontribution from the solid particles. The conservationequation for the transport of solid CO2 was thereforeexpressed in terms of concentration (in kg/m3), ratherthan a mass fraction, as follows:

∇ · uc − ∇mt

Stc

( )= Sc (2)

where c is the mass concentration of solid CO2 in kg/m3, uis the velocity vector, mt the turbulent viscosity, St theSchmidt number and Sc a source term due to particle subli-mation. A source term of equal magnitude and opposite signto Sc was included in the mass fraction equation. Anadditional term was also included in the enthalpy equationto account for the latent heat effects associated with subli-mation, which was given by Sh ¼ 2SY hsg, where hsg isthe latent heat of sublimation and SY the sublimation rate.

To determine the source terms Sc, SY and Sh it wasassumed that thermodynamic equilibrium holds, i.e. thatthe solid particles and surrounding gas shared the sametemperature. The equilibrium vapour pressure (which is afunction of temperature) divided by the fluid pressure isthen equal to the mole fraction of CO2 in the vapour phase:

Peq(T)

Patm

= mCO2 (3)

To enforce this condition, the following source termswere used, which reduced the solid concentration if theequilibrium vapour pressure exceeded the CO2 mole frac-tion, until equilibrium was established:

SC = −SY = −b(Peq − mCO2 Patm)Y (4)

In the above equation, b is a constant that was chosento be sufficiently large that the condition in Equation (3) wasmet, yet sufficiently small to retain numerical stability. Themass fraction, Y, was included in Equation (4) to ensurethat the source term was zero if there was no solid CO2

present. The equilibrium pressure, Peq, was calculated fromAntoine’s equation.

Due to the presence of solid particles in the flow,small modifications were also necessary in the momentumequation. Turbulence was modelled using the standardk–1 model.

The meshes employed in the OpenFOAM calcu-lations were primarily hexahedral and were refined ongeometrical surfaces and in specified regions, such asaround the jet. In the present work, the source geometry


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comprised a hemisphere representing the expanding “tulip”,characteristic of the flashing zone, with a circular face forthe jet inlet.

Sample results from the OpenFOAM model in thevicinity of the jet source are shown in Figure 1 for Test 3.Gas temperatures were predicted to fall from an initialvalue of 278ºC to reach a minimum of around 290ºC at adistance of around 2.5 m downstream from the source.Many of the solid CO2 particles had sublimated completelyby this distance. The maximum distance travelled by the par-ticles was predicted to be around 3 m.

4.6 CFX DISPERSION MODELThe CFX dispersion model was developed using a Lagran-gian particle-tracking model in ANSYS-CFX version 13(Ansys Inc, 2010). The process of sublimation was simulatedusing the standard droplet evaporation model as follows:

dm

dt= min pdrgDgSh

Wc

Wg

ln1 − Xg

max [1 − Xc, 10]

( ), 0

[ ](5)

where dm/dt is the rate of mass loss from a particle, subscriptc refers to the gas-phase CO2 properties and g to the proper-ties of the air-CO2 gas mixture, W is the relative molecularmass, d the particle diameter, D the diffusivity, Sh the Sher-wood number and 10 is a small number used here to avoidnumerical difficulties when Xg becomes close to unity. Themolar fractions, Xc and Xg, were calculated from:

Xc =gcrg

WcCg

Xg = Psatc

P(6)

where g is the mass fraction, r the density, C the molar con-centration (C = P/RuT), P sat

c the vapour pressure for thecomponent evaporating, found from Antoine’s equation,and P is the total pressure in the gas mixture.

At the CO2 jet source in the CFX model, the solid par-ticles were assigned an initial diameter of 5 mm, the samevelocity as the surrounding CO2 gas and a temperatureequal to 278ºC. Unlike the approach taken in OpenFOAM,the CFX model allowed for slip between the gas and solid

phases. The particle velocities were determined using thestandard drag model of Schiller and Naumann (1933) com-bined with the stochastic dispersion model of Gosman andIoannides (1981) to account for turbulence effects. Themass transfer from sublimation of the particles (Equation 5)produced a drop in the particle temperatures due to latentheat effects. The resulting temperature gradient betweenthe gas and solid particles produced a transfer of heat,which was modelled using the Ranz-Marshall correlation(Ranz and Marshall, 1952).

In Lagrangian particle-tracking CFD simulations, thenumber of computational particles injected at the source iscontrolled independently of the mass flow rate or particlesize. In the present simulations, 10,000 particles werereleased and tests were performed to ensure that increasingthe number of particles had no effect on the results.

The way in which solid CO2 particles interact withsolid walls is subject to significant uncertainty and in thepresent simulations any particles impinging onto wallswere assumed to rebound elastically and remain in theflow rather than to be deposited.

The modelled gas-phase consisted of a mixture ofthree components: dry air, CO2 gas and water vapour. Aseparate additional Eulerian phase was used to model con-densed water droplets, which were assumed to have thesame velocity as the surrounding gas phase. To model theprocess of condensation, as the temperature fell belowthe dew point, a source term in the continuity equation forthe gas mixture was used to remove the mass of watervapour in excess of the saturation concentration. The samemass, but of liquid water, was added into the dispersedEulerian water droplet phase via another source term. Athird source term in the energy equation was used toaccount for the release of latent heat. The reverse processof water droplet evaporation was modelled similarly. Inde-pendent verification tests were undertaken to ensure that themodel was coded correctly. A similar approach to modellingcondensation and evaporation was previously tested in thestudy by Brown and Fletcher (2003).

Sample results from the CFX model in the vicinity ofthe jet source are shown in Figure 2 for Test Case 3. Gastemperatures were predicted to fall from an initial value of278ºC to reach a minima of nearly 2100ºC at a distanceof around 2.5 m downstream from the source. Many ofthe solid CO2 particles had sublimated completely by thisdistance. The maximum distance travelled by the particleswas predicted to be around 3.5 m.

4.7 CFD BOUNDARY CONDITIONSFor both OpenFOAM and CFX dispersion models, sourceconditions for the CO2 jet were prescribed using values cal-culated at the position where the jet had expanded to atmos-pheric pressure, as described in Section 4.3. Theseconditions included the velocity, the solid CO2 fractionand the diameter of the source (which was considerablylarger than the orifice).

A logarithmic velocity profile was used to model theatmospheric boundary layer in the CFD simulations, using

Figure 1. Gas temperature predicted by the OpenFOAM

model for Test Case 3. Cross symbols are spaced at 1 m

intervals along the jet axis


158

the approach described by Richards and Hoxey (1993). Toaccount for the obstructions upstream of the test pad, aground surface roughness of 0.1 m was used in the logarith-mic profile. For the thermal boundary conditions, it wasassumed that the boundary layer was neutral. Sensitivitytests showed that the CFD results were unaffected by pre-scribing either adiabatic or fixed ambient temperature con-ditions for the ground. Results were also insensitive to thedetails of the prescribed atmospheric velocity profile. Essen-tially, in the region of interest for model validation, the flowbehaviour was found to be dominated by the jet momentumrather than the atmospheric boundary layer conditions.

The size of the CFD flow domain was set on a case-by-case basis and sensitivity tests were undertaken toensure that results were unaffected by the location of thedomain boundaries. Typically, it extended 100 × 50 × 30metres in the streamwise × spanwise × vertical directions.Sensitivity tests were also undertaken to ensure that the

results were reasonably grid-independent. For the CFXresults shown here, simulations were performed usingapproximately 1 million nodes using an unstructured grid,with cells clustered in the jet. Typically there were 600nodes across the face of the circular source area.

5. RESULTSIn the results shown here, the distance from the jet orifice tothe end of the expansion zone has been assumed to be neg-ligible in comparison to the dispersion distances, i.e. theCO2 source in the dispersion models is located at an axialposition of zero.

5.1 DISPERSION FOR UNOBSTRUCTED RELEASESThree unobstructed steady-state tests at ambient tempera-ture are available from the GL Spadeadam experimentsfor model validation. The conditions for each of thesetests are shown in Table 1. In Test 3 the wind was verywell aligned with the jet direction whilst in Tests 5 and 11the wind direction was slightly less well aligned, with thedownstream plume shifting slightly to one side of theinitial jet axis. The conditions during the tests were gener-ally either overcast or with a relatively high wind speed.Under such conditions it was considered reasonable toassume neutral stability.

The field temperature measurements on the test padwere found to be relatively steady over the period duringwhich the CO2 release rate was constant. However, analysisof the CO2 concentrations measured by the oxygendepletion cells suggested that the devices were adverselyaffected by the low temperatures in the jet. Rather thanaverage the CO2 concentrations over the duration of therelease, the peak concentration was found to be a better esti-mate of the true concentration, particularly for thosemeasurements located close to the orifice. Peak valueswere similar to both the concentrations measured by alterna-tive instruments that did not rely on chemical reactions andto concentrations inferred from the temperature measure-ments. In the results presented below, two types of exper-imental concentration results are given – the peak valuesfrom the oxygen depletion cells and values inferred fromthe temperatures.

For the purposes of model validation, the dispersionpredictions from the three models can be compared to the

Table 1. Test conditions

Process Conditions Ambient Atmospheric Conditions

Test

Pressure

[bara]

Temperature

[C]

Hole Size

[mm]

Temperature

[C]

Relative

Humidity

[%]

Wind speed

[m/s]

3 150 9 12.7 11.2 66 3.9

5 149 17 25.4 9 91 1.3

11 82 21.5 12.7 3.6 78 2.7

Figure 2. Gas temperature (top) and solid particle

temperatures (bottom) predicted by the CFX model for Test

Case 3. Cross symbols are spaced at 1 m intervals along the

jet axis


159

experimental data in several ways, such as comparing cen-treline profiles of concentration or temperature, plumewidths at various downstream locations or statistical per-formance measures (e.g. mean geometric bias). In thepresent work, centreline values and plume widths are exam-ined. Due to the nature of the experiments, statistical per-formance measures were found to generally fall wellwithin accepted bounds.

Centreline predictions of the CO2 concentration andtemperature are compared to the measured values at aheight of 1 m above grade (i.e. at the release height) forTest 11 in Figure 3. There is a degree of scatter in the exper-imental concentration values, which were derived from themeasured peak concentrations and temperature, as discussedabove. However, there is generally good agreement betweenthe experiments and the model predictions for both thetemperatures and concentrations. Since FRED treated thesolid CO2 as a liquid, it underpredicted the initial post-flash vapour fraction and underpredicted the temperaturein the near-field. The OpenFOAM and CFX results are prac-tically identical to one another, demonstrating that for smallparticle sizes the flow is close to homogeneous equilibrium.

The CO2 concentrations on two arcs at 40 m and 60 mat 1 m above ground level are shown in Figure 4 for Test 3.The measured concentrations shown were derived from the

temperature measurements and there is therefore a degree ofuncertainty in their absolute values. However, the profilesshould provide an accurate indication of the plume width.Concentrations inferred from temperature are shown heresince the time constant associated with the thermocouplesmeant that they produced a smoother spanwise plumeprofile than the raw data from the oxygen depletion cells.The OpenFOAM and CFX results are again similar to oneanother and show a slightly narrower plume than wasmeasured in the experiments. The FRED model producedslightly better agreement with the data.

Overall, the degree of agreement between the threecalculation methods was found to vary from test to test,but in general the predicted plume width at a height of 1 mabove the ground was in reasonable agreement in all threeexperiments with all three codes.

In addition to the concentration and temperaturemeasurements, a large amount of video footage was col-lected during the experiments. Footage taken from theside of the jet and perpendicular to the jet was found to beuseful in order to estimate the initial jet diameter close tothe release, where the jet edge was reasonably sharp.

Figure 5 compares the recorded visible jet shape forTest 3 to the OpenFOAM predictions. The edge of thevisible jet was digitized at several instants in time from

Figure 3. Measured and predicted centreline mole fraction (left) and temperatures (right) for Test 11

Figure 4. Measured and predicted plume widths at 40 m (left) and 60 m (right) for Test 3


160

video footage of a side-on view of the jet, with the resultsshown as black crosses in Figure 5. Superimposed ontothis is the predicted plume width from OpenFOAM. Theconcentration which best corresponded to the visible jet isnot known, but contours have been plotted at a concen-tration of 1% CO2 by volume. A contour at a value of0.1% is only slightly wider, so it is expected that this willgive a reasonable indication of the jet edge. The agreementbetween the model predictions and the measurements isreasonable. The FRED and CFX codes gave comparableresults.

5.2 DISPERSION FOR ENCLOSED RELEASESSome progress has been made in modelling the releases intoan enclosure using CFD. It is not possible to simulate thistype of release with integral codes such FRED except in avery approximate way. Figure 6 shows the real geometryused in the experiments (shown here by the computer-aided design drawings for the steel fabrication) and the sim-plified CFD geometry.

The enclosed tests were carried out primarily to studyeffects such as solid CO2 deposition within the enclosure,rather than to examine the far-field dispersion. Unfortu-nately, there were therefore no measurements of tempera-ture or concentration outside of the enclosure. Themeasurements within the enclosure are also of limited usefrom a validation perspective – there were several tempera-ture measurement locations but only a single concentrationmeasurement. The temperature measurements were madefar inside the enclosure and they all recorded similar temp-eratures of around 2848C. The OpenFOAM and CFXresults agreed well with these measurements. The resultsfrom CFX are shown in Figure 7.

The single concentration measurement was located inthe lower corner of the enclosure at the enclosed end, andrecorded a concentration of around 60% CO2 by volume.Since the temperature was below 278ºC this implies thatthere were solids present. The OpenFOAM model predicteda concentration of around 52% at this location while theCFX model gave a value of around 57%. Both of these

values are considered to be in reasonable agreement withexperiment.

Although it is not possible to compare the CFD resultsto measurements outside of the enclosure it is possible to

Figure 5. Measured (crosses) and OpenFOAM predictions

(line) of plume size in the near field

Figure 6. Real enclosure geometry and CFD geometry for the

enclosure

Figure 7. CFD predictions of temperatures on a horizontal

plane through the jet in the enclosure


161

compare the models to each other. Figure 8 shows the con-centrations plotted on arcs at 20 m and 40 m from the releaselocation, at the release height for the enclosure experiment.The agreement between the two models is reasonable, con-sidering that they were constructed completely indepen-dently and they employed different sub-models for thesolid CO2 particles.

6. CONCLUSIONSThree different models have been used to simulate releasesof liquid CO2: FRED, OpenFOAM and CFX. All threemodels used mass release rates that were calculated usingthe Bernoulli equation, which was found to provide reason-able predictions of the flow rate for the sub-cooled liquidCO2 releases considered here.

For the free releases studied, all three models pro-vided generally good predictions of the concentrationsalong the centreline of the plume. Plume widths wereslightly better predicted by FRED than the two CFDmodels. This may be due to the turbulence models employedin the CFD codes. At a distance of a few metres downstreamfrom the nozzle, the jet became attached to the ground andthe flow exhibited behaviour similar to a wall jet. The stan-dard k21 turbulence model used by CFX and OpenFOAMis known to have weaknesses in predicting the spreadingrate in this type of flow (Craft and Launder, 2001). Amore appropriate model could potentially be applied toimprove upon this, but it is questionable whether theeffort is justified in the context of hazard analysis.

The thermodynamics model employed by FRED didnot simulate solid CO2 particles, but instead extrapolatedthe liquid-vapour saturation line down to atmosphericpressure. This led to the post-flash vapour fraction beingtoo low and the temperatures being underpredicted in thenear-field of the jet. However, this appeared to have alimited effect on the concentration profiles, and even thetemperature profiles a few metres downstream were inreasonable agreement with the measurements. Hence it is

concluded, for the scale of releases considered here, thatFRED performs adequately for the purpose for which it isintended, which is providing hazard distances from freereleases.

The CFX model used a particle-tracking approach forthe solid CO2 particles with an initial diameter of 5 mm,whilst the OpenFOAM model assumed homogeneous equi-librium between the particles and the surrounding vapour.The results from the two models were found to be remark-ably similar, especially considering that CFD models areknown to be sensitive to user inputs and the two modelsin this case were set up independently by different authorsin different organisations. The good agreement betweenthe model predictions and the experiments suggest that itis reasonable to assume a small initial CO2 particle size,for the scale of releases considered here. Furthermore, thehomogenous equilibrium assumption appears to providean adequate description of the solid CO2 transport in thesecases. For larger-scale releases, such as pipeline full-boreruptures or catastrophic vessel failures, the size of theCO2 particles remains uncertain. The effect of larger par-ticles could potentially be examined in the future usingthe CFX model tested here.

7. DISCLAIMERThe contribution made to this paper by Simon Gant (HSL)and Mike Bilio (HSE) was funded by the Health andSafety Executive (HSE). The contents, including anyopinions and/or conclusions expressed, are those of theauthors alone and do not necessarily reflect HSE policy.

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