Study on two-phase cloud dispersion from liquefied CO2 release

Chaojie Li,Xianxin Fang,Meiling Sun,Jihai Duan,Weiwen Wang,

1 College of Environment and Safety Engineering,Qingdao University of Science and Technology,Qingdao 266042,China

2 College of Chemical Engineering,Qingdao University of Science and Technology,Qingdao 266042,China

3 Himile Chemical Technology (ShanDong) Co.Ltd,Qingdao 266000,China

Keywords:Two-phase cloud Carbon dioxide CFD Dispersion Phase change

ABSTRACT The knowledge of two-phase cloud dispersion mechanism from HLG (hazardous liquefied gas) release is the prerequisite for accurate assessment and precise rescue of such accidents.In this paper,an experiment of two-phase cloud dispersion from liquefied CO2 hole release is performed.The source terms,such as vapour mass fraction,release velocity and mean droplet diameter,are calculated based on thermodynamic theory.Taking phase transition of CO2 droplets to gas into account,CFD (computational fluid dynamics) model for two-phase cloud dispersion is established.The predicted cloud temperatures at the downstream agree well with the experimental data,with the maximum relative error of 5.8% and average relative error of 2.3%.The consequence distances in the downstream direction and in the crosswise direction calculated through two-phase model are larger than those through single-phase model,with the relative differences of 57.8% and 53.6% respectively.CO2 concentration calculated by twophase model is smaller in the vicinity of release hole,and larger beyond 0.135 m downstream.A smaller leakage rate results in a lower CO2 concentration and a higher cloud temperature.

1.Introduction

There are increased concerns related to accidents involving HLG(hazardous liquefied gas)release[1-5],such as Festus railcar accident [6] and Viareggio LPG (liquefied petroleum gas) accident [7-10].Developing a method to accurately predict hazard area plays a critical role in risk assessment and quantification of accident consequences.

The process of HLG release can be divided into three stages,namely discharge,jet,and dispersion [11-14].Due to the wide variation of cloud physical properties in the vicinity of the release hole,the simulation of jet process needs a dense mesh and is computationally expensive[15-17].Thus,a vast majority of researches calculate the equivalent release conditions at the ‘‘pseudo-source”located at the point where the jet pressure returns to ambient.Venetsanos and Giannissi [18] studied release and dispersion of hydrogen stored at cryogenic temperature and high pressure by 3d CFD (computational fluid dynamics) methodology combined with a notional nozzle approach to bridge the expansion to atmospheric pressure region that existed near the nozzle.The true nozzle was replaced with a notional nozzle of higher diameter further downstream,where dispersion simulation started from.Witloxetal.[19] used the consequence modelling package,which imposed the ATEX (ATmospheric EXpansion) model for modelling the expansion from orifice conditions to the final conditions at atmospheric pressure,and the latter post-expansion conditions were used as the source terms for the PHAST (process hazard analysis software tool) UDM (unified dispersion model),for vessel orifice release.

The application of equivalent ‘‘pseudo source” can typically be beneficial for practical dispersion simulation.However,the flows resulting from HLG release are likely to be multi-phase,consisting of liquid droplets and corresponding vapour mixed with air.In this situation,phase transition occurs between liquid droplets and corresponding vapour.Meanwhile,phase transition involves both heat transfer between droplets and vapour as well as mass dispersion of the chemical species in the gas phase,which can significantly affect the consequence distance and hazard area [20,21].Woolleyetal.[22] illustrated the integration of different models for the pipeline outflow,near-field and far-field dispersion,and demonstrated that it would be useful to further develop and validate models that were able to predict the extent of the visible CO2plume,as well as its extent in terms of its instantaneous hazardous CO2concentration.Woolleyetal.[23]demonstrated that it was possible for three phases to be present due to the expansion and subsequent Joule-Thomson cooling in CO2accidental release,and described the importance of a CFD model capable of accurately representing the complex physics observed in the release for prediction accuracy.Furthermore,the rapid development of computing resources in recent years makes it possible to apply multiphase model to risk analysis from HLG release.

The main focus of this study is on two-phase cloud dispersion mechanism from liquefied CO2hole release.A CFD model capable of accurately predicting two-phase cloud dispersion is developed.And an experiment of liquefied CO2release and dispersion is performed to make available data for model validation.Consequence distance,CO2concentration,dispersion velocity and cloud temperature are calculated by two-phase model and compared with those by single-phase model,to describe the effects of movement and phase transition of droplets on cloud dispersion.In addition,the influence of leakage rate is analyzed in detail.

2.Description of Liquefied CO2 Release and Dispersion

This research divides the whole process into two stages,namely release and dispersion,as shown in Fig.1.The release stage accounts for the decompression from storage conditions and source conditions,and determines the leakage rate,cloud temperature and pressure at the release hole.These parameters are then used as the inlet boundary conditions for the CFD simulation of two-phase cloud dispersion,which is the coupling of phase transition and turbulent dispersion.Note that the dry ice formation is not taken into account in the simulation due to that the Joule-Thomson effect is not likely to freeze CO2much below its freezing point[24,25].Also,humidity condensation is not considered as the region where water vapour will make a difference is limited [26].Therefore,the main physical phenomena are flash evaporation of liquefied CO2at the release hole due to pressure reduction [27]and full vaporization of CO2droplets at the downstream.

Fig.1.Schematic of liquefied CO2 release and dispersion.

3.Experimental

In the past,only few experiments involving HLG release were conducted for the integrated study of two-phase cloud formation and dispersion [28-30].Therefore,an experiment is performed to obtain source terms and cloud temperatures at the downstream for liquefied CO2hole release.

3.1.Experimental setup

Schematic of the release device and sensor arrays is shown in Fig.2.Liquefied CO2is stored in a steel cylinder under its saturating vapour pressure and off through a siphon of 0.004 m inner diameter.The siphon is plunged to the liquid phase,and is equipped with a manual valve.The cylinder is placed on a load cell(Loadcell Central GCB3-100 KG,with a range of 0-100 kg,an accuracy of 0.001 kg and a response time of 0.58 s) for an independent check of the released mass.By means of an infrared thermal imager(Testo 875-2,with a range of 223.15-1173.15 K and an accuracy of 0.5 K+0.3%),the cylinder outer wall temperature(storage temperature is not controlled and therefore is close to cylinder outer wall temperature) and temperature immediately upstream of the source (regarded as the source temperature) are measured.

Fig.2.Schematic diagram of experimental setup.

Cloud temperature in the downstream is selected as the parameter for model validation in this work,as it is affected by depressurization,phase transition,turbulent entrainment.Six infrared temperature sensors (Soway T116,with measurement range of 233-358 K and accuracy of ±0.5%,are characterized by small size design,strong anti-interference ability and response time of less than 1 s) are used for temperature measuring.The temperature sensors are located along the centre-line axis of release at the distances of 0.47,0.62,0.77,0.92,1.07 and 1.22 m downstream from the source.This is in the area where significant evaporation is taking place.The output signals of temperature sensors are collected at 1 Hz(that is to say a measure every 1 s)through data acquisition system,and recorded by the labview program.The hygrothermograph is used to measure ambient temperature and humidity.Hot-wire anemometer and wind direction indicator are deployed at the experimental site,in order to measure wind velocity and direction.The experiments are conducted at the wind velocity of about 0.62 m,which is far less than the release velocity to avoid wind significantly affecting CO2cloud dispersion.

3.2.Experimental conditions

Liquefied CO2is released horizontally at 1.47 m height.In order to specify the ambient conditions and source terms for the steadystate simulation presented later,the average storage temperature,average source temperature,average leakage rate,average ambient temperature and humidity during steady period (Case 1 for 61-140 s and Case 2 for 76-125 s) are summarized in Table 1.

Table 1 Summary of experimental conditions

Due to the absence of additional pressurizing equipment,the storage pressure of pure liquefied CO2is equal to the saturation pressure at the storage temperature.The flow at the release hole can be regarded as thermal equilibrium flow as the pipe length(including the pipe length both inside and outside the cylinder)is larger than 0.1 m [31-33],so the source pressure can also be obtained from the liquid-vapour saturation curve based on the source temperature.Thus,the storage pressures in Case 1 and Case 2 are 6.49×106Pa and 6.15×106Pa respectively,and the source pressures are 11.47 × 106Pa and 1.54 × 106Pa.

3.3.Source terms

In the experiment,only the storage temperature of liquefied CO2,cloud temperature at the source and leakage rate are measured.The other source terms required by the simulation of twophase cloud dispersion,such as vapour mass fraction,release velocity and mean droplet diameter,are calculated as follow.

3.3.1.Vapourmassfraction

In the present study,the flow is homogeneous two-phase(thermal equilibrium) at the source.Isenthalpic process is assumed between storage conditions and source conditions to estimate the vapour mass fraction [34].Then it is calculated by Eq.(1):

where α is the vapour mass fraction at the source,Hrefers enthalpy,the subscripts 1 and 2 respectively denote storage and source conditions,VandLrespectively refer to the saturated vapour and liquid phases.

3.3.2.Releasevelocity

During a prolonged release,a fully expanded dispersion cloud will be connected to the release hole by a underexpanded jet.However,the homogeneous equilibrium model,assuming equal velocities between liquid and vapor phases (mechanical equilibrium)[35-37],is utilized to calculate the release velocity of two-phase cloud at the source in this work.The mixture density ρ at the source is given by Eq.(2):

And then the mixture velocity v at the source can be derived by Eq.(3):

wheremdenotes the leakage rate andSis the release hole area.

3.3.3.Dropletdiameter

Initial droplet size is required as input in the CFD model for predicting droplets movement and evaporation.During the release,CO2droplets form due to mechanical and flashing break up [38-42].Following empirical relationship,SMD (Sauter Mean Diameter),expressed asd32,is calculated as a function of release velocity and fluid properties [43] by Eq.(4):

where σ is the liquid surface tension.

Table 2 shows the source terms,which will be used as the inlet boundary conditions for the CFD simulation of two-phase cloud dispersion.

Table 2 Summary of source terms

3.4.Cloud temperatures

The measured cloud temperatures at the sensor positions in the experiment are plotted in Fig.3.As shown,cloud temperatures decline notably after release,due to the Joule-Thompson effect[44,45] and flash evaporation,and then tend to be steady.During the ‘‘steady” periods of the release (over a 80 s period in Case 1 and a 50 s period in Case 2),the pressure and temperature changes are less significant as the release duration is short and the released mass of CO2is very small relative to the total mass in the cylinder.Yet,There are still minor fluctuations at this stable stage because of the turbulent dispersion of two-phase cloud.

Fig.3.Curves of cloud temperatures with time.

The average cloud temperatures at the measuring points at the steady state are calculated for model evaluation,as shown in Table 3.

Table 3 The average cloud temperatures at the measuring points/K

4.Numerical Simulations

4.1.Modeling approach

The continuous gas-phase is solved in the Eulerian reference frame,with SSTk-ω turbulence model and DPM (Discrete Particle Model)for CO2droplets.The simulation is performed in two steps.The flow field is computed before the release of two-phase cloud by a steady simulation,and then used as the initial and inflow boundary conditions to study the transient dispersion of twophase cloud.

4.2.Mathematical equations

CO2droplets are modeled by DPM.The droplets trajectories are computed by integrating the force balance equation,which defined by Eq.(5):

where,uandudrespectively denote fluid phase velocity and droplet velocity,ρ and ρdrefer to fluid density and droplet density,F refers to thermophoretic force,saffman lift force,virtual mass force and pressure gradient force here.FD(u-ud) is the drag force per unit droplet mass andFDis defined as Eq.(6):

where,ddis droplet diameter,CDis drag coefficient,Reis the relative Reynolds number and defined as Eq.(7):

where μ is the molecular viscosity of fluid.

Modelling of the phase-transition of CO2droplets to gas is included in the simulation,and solidification is neglected.In this study,vaporization (Law 2) to boiling (Law 3) laws are employed to account for phase transition.By default ANSYS Fluent will switch from the vaporization to the boiling law when the droplet temperature has reached the boiling point defined for the droplet material.When the droplet temperature is higher than its boiling point,the rate of vaporization is calculated by the boiling rate equation,defined as Eqs.(8):

where,k∞is thermal conductivity of the fluid,cp,∞is heat capacity of the fluid,T∞andTdrespectively refer to fluid temperature and droplet temperature,andhfgis the latent heat.

Once the droplet temperature falls below the boiling point,the evaporation rate is calculated by Eq.(9):

whereNiis molar flux of vapor,kCis mass transfer coefficient,Ci,sis vapor concentration at the droplet surface,andCi,∞is vapor concentration in the fluid.

4.3.Domain and mesh

The CFD simulation is implemented in a 2 m-wide,10 m-long and 2 m-high computational domain,as shown in Fig.4.The computational domain is large enough to capture the features of the dispersion flow.When considering CO2source as the origin withymeasured as positive in the downstream direction andzpositive upwards,the computational domain’ coordinates are(-1,1) × (0,10) × (-1,1) in thex,yandzdirection respectively.Structural grid is adopted to discrete the computational domain.The grid consisting of approximately 8.9 million of hexahedral volume elements is selected by performing a grid dependency study.Grids close to CO2source are refined to capture the wide variation of physical properties.The grid is expanding away from the source.

Fig.4.Grid of the computational domain.

4.4.Boundary conditions

The detailed settings of the boundary conditions are shown in Table 4.The CO2source is set as mass-flow-inlet.The velocityinlet is employed to the air inlet and the pressure-outlet with ambient pressure and temperature to the outlet.The left,right,top and bottom surfaces,which presumably are far enough from the cloud,are specified as symmetry conditions.

Table 4 Summary of boundary conditions

4.5.Model evaluation

The simulated cloud temperatures at the downstream for Case 1 and Case 2 are compared with experimental data,as shown in Fig.5.There is a very good agreement between them in terms of numeric value,with the maximum relative error of 5.8% and average relative error of 2.3%.However,the simulation results show an increasing trend with respect to the distance from the source while the experiment data from different positions are almost identical.The reason may be that the condensation of ambient humidity near the source is neglected in the simulation,and the liberated heat capable of influencing the cloud temperature is not taken into account.On the whole,the temperature variances of the simulation basically have the similar trends with the experimental data and the model can accurately describe the two-phase cloud dispersion from liquefied CO2hole release.

Fig.5.Comparison of calculated cloud temperatures with experimental data.

5.Results and Discussion

5.1.Phase transition effect

To justify the effects of droplets movement and phase transition on cloud dispersion,the simulation of CO2dispersion for Case 1 is also performed by single-phase model assuming all droplets evaporate and specify the source term of the gas dispersion.That is,CO2is released at the gas phase.

5.1.1.Consequencedistance

CO2is a colourless and odourless gas under ambient conditions,and is toxic if inhaled in air concentration around 0.05[22].Calculation results are evaluated using the vertical plane atx=0 m and CO2concentration iso-surfaces representing zones with concentration calculated by two-phase model higher than 0.05,as shown in Fig.6.The results show that the effect of gravity on cloud dispersion is limited because of the great release velocity.In the initial stage,CO2cloud has a high velocity due to that the storage pressure is much higher than the ambient pressure.The consequence distance in theydirection is up to 0.23 m att=0.01 s and 0.66 m att=0.05 s.As dispersion progresses,CO2cloud interacts with ambient air,leading to the decrease of momentum.CO2cloud forms a stable consequence distance of 2.23 m in theydirection and 0.175 m in thezdirection.

Fig.6.Contours of CO2 concentration calculated by two-phase model.

Fig.7 shows CO2dispersion scenario calculated by single-phase model.The consequence distances in theydirection and in thezdirection are 1.23 m and 0.101 m respectively,both smaller than those obtained by two-phase model.

Fig.7.Contour of CO2 concentration calculated by single-phase model.

In the research,relative difference,defined as Eq.(10),is adopted for the comparison of the results calculated by the two models.

whereX1is the value calculated by two-phase model,X2is the value calculated by single-phase model.

The relative difference of the consequence distances in theydirection and in thezdirection are 57.8% and 53.6%.

5.1.2.CO2concentration

Comparison of CO2concentrations at the central line calculated by the single-phase and the two-phase model is shown in Fig.8.From the source to 0.135 m downstream,CO2concentrations in the gas phase obtained by two-phase model are lower,as a amount of constituent is still in the form of droplet.Relative difference firstly increases and then decreases with distance.The phase transition of droplets make them the ‘‘moving source”.Thus,CO2concentrations calculated by two-phase model are larger further downstream.Meanwhile,the relative difference increases with distance,reaching a stable value of 56.0%.

Fig.8.Comparison of CO2 concentrations calculated by the two models.

5.1.3.Dispersionvelocity

Comparison of cloud velocities along the centre-line axis of the release hole calculated by the two models is depicted in Fig.9.From the release point to 0.03 downstream,the amount of gas for single-phase model is larger and the density of cloud is smaller,thus a more obvious expansion and a higher velocity are displayed.The maximum gas velocity reaches 294 m.s-1with expansion wave,reflecting the characteristic features of high-velocity compressible flow.From 0.03 m to 1.0 m in theydirection,decreasing trend of velocity for two-phase cloud is more gentle due to its larger density.Beyond 1.0 m downstream,the cloud velocity calculated by single-phase model is still larger than that calculated by two-phase model.

Fig.9.Comparison of cloud velocities calculated by the two models.

5.1.4.Cloudtemperature

Fig.10 shows a comparison of cloud temperatures at the central line calculated by the two models.It can be seen that the results obtained from two-phase model show a better agreement with the measured temperatures in experiment.In the vicinity of the release hole,the amount of gas is larger and expansion effect is stronger,thus cloud temperatures calculated by single-phase model are lower due to Joule-Thomson effect.Further downstream,the single-phase model predicts higher temperature for being inconsiderate to phase transition of droplets.

Fig.10.Comparison of cloud temperatures calculated by the two models.

From 0.06 to 0.35 m downstream,the evaporation heat quantity is equal to that of heat-exchange between cloud and static air,so cloud temperature obtained from two-phase model has a stable value of 251 K.Further downstream,from 0.35 to 0.75 m,heat transfer comes to play the dominant role,leading to an increase of temperature.

5.2.Leakage rate effect

The characteristic behaviour of two-phase cloud dispersion and the hazard area strictly depend on HLG leakage rate.To investigate the effect of leakage rate,the simulation of CO2dispersion for Case 2 is performed by two-phase model in this part,and the results are compared with those for Case 1.Note that the change of leakage rate will induce the change of source terms,as shown in Table 2.

5.2.1.Consequencedistance

Fig.11 shows CO2concentration iso-surface with concentration higher than 0.05 in the vertical plane atx=0 m for Case 2.The consequence distances in theydirection and in thezdirection are 0.98 m and 0.05 m respectively,far smaller than those for Case 1.

Fig.11.Contour of CO2 concentration for Case 2.

5.2.2.CO2concentration

Fig.12 compares CO2concentrations on the central line for two cases.And Fig.13 shows CO2droplet diameter distribution in the vertical plane atx=0 m att=3 s.

Fig.12.Comparison of CO2 concentrations for two cases.

Fig.13.CO2 droplet diameter distribution for two cases.

Due to the small droplet size,CO2droplets evaporate within 0.5 m downstream from the source in Case 1.The relative difference of CO2concentrations for the two cases is larger than 90%from 0.33 to 0.52 m downstream.CO2droplet size in Case 2 is large,and evaporation of droplets still takes place from 0.5 m to 1 m downstream.The relative difference at the distance of 0.84 m from the source reaches the minimum value of 68.3%.

5.3.Cloud temperature

Comparison of cloud temperatures for Case 1 and Case 2 is depicted in Fig.14.It is clear that the temperatures in the vicinity of the release hole for Case 2 are higher,due the small amount of gas and weak expansion.The temperatures at the downstream are also higher because of weak evaporation.The relative difference is large from the source to the distance of around 0.5 m,and diminishes with distance from 0.5 to 1.0 m downstream,which is also caused by the evaporation which still exists in Case 2.

Fig.14.Comparison of cloud temperatures for two cases.

6.Conclusions

Experiment of two-phase cloud dispersion from liquefied CO2hole release is performed.The storage temperature of liquefied CO2,the cloud temperatures at the release hole and at the downstream are measured.The other source terms,such as vapour mass fraction,release velocity and mean droplet diameter,are calculated based on thermodynamic theory.The cloud temperature declines notably after release,due to Joule-Thompson effect and flashing evaporation.

The ANSYS Fluent are applied to simulate cloud dispersion.Two different models are applied: single-phase model specifying the source term of gas dispersion and regardless of modeling droplets phase transition,and two-phase model comprising droplets phase transition.The predictions are compared with the experimental temperatures.It is found that the results calculated by the twophase model show a better agreement with the experimental temperatures,with the maximum relative error of 5.8% and average relative error of 2.3%.Thus,the droplets phase transition should not be ignored in the modeling of HLG release and dispersion.

The movement and phase transition of droplets can promote the dispersion of cloud.The consequence distances in the downstream direction and in the crosswise direction obtained by twophase model are larger than those by single-phase model,with the relative differences of 57.8% and 53.6% respectively.CO2concentrations calculated by two-phase model are smaller than those by single-phase model within 0.135 m downstream,and larger further downstream.The decrease of leakage rate can lead to the decrease of CO2concentration and the increase of cloud temperature.

Clearly,two-phase cloud dispersion from HLG in realistic terrains,such as urban environment or industrial environment,is needed to provide meaningful reference for emergency responders.

Data Availability

No data was used for the research described in the article.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work is supported by the Natural Science Foundation of Shandong Province (ZR2021QB144).