A simple model for CALCULATING CHLORINE concentrations behind a water spray in case of SMALL releases
DANDRIEUX-BONY*A.; DIMBOUR J-P., DUSSERRE G.
Risk Department Laboratoire Génie de l’Environnement Industriel Ecole des Mines d’Alès, 6 Avenue de Clavières, Alès Cedex 30319, France
*Corresponding author. Tel.: 33-(0)4-66-78-27-13; fax: 33-(0)4-66-78-27-01.
E-mail address: aurelia.dandrieux@ema.fr
Abstract
Accidental dangerous releases either toxic or flammable can occur during process, storage or transportation.
Though the dispersion and modelling of large releases of dangerous products have already been studied, small releases (small plumes dispersion) are seldom concerned even if they are more likely to occur.
The effectiveness and particularly the modelling of cloud dispersion downwind a water spray for small releases are even less studied, even if water sprays are proved to be good protection devices against toxic or flammable clouds.
Therefore, this paper focuses on dispersion of small plumes of chlorine both in open field dispersion and dispersion in presence of a water spray and on its modelling.
The description of the dispersion model called RED elaborated during this study is followed by the comparison between the predicted concentrations and the observed concentrations collected during field experiments. Conclusions are presented.
Keywords: Water sprays, modelling; chlorine; dense gases, atmospheric dispersion
1. Introduction
Process, storage and transportation of dangerous goods have considerably increased these last ten years. Due to several accidents (Bhopal, 1984; Mexico, 2004; and Toulouse, 2001) people become aware of the industrial risks and competent authorities take dispositions (by means of regulations) to decrease risks inherent to industrial activities (Grasa, Navarro, Rubio, Pena & Santamaria, 2002).
Accidental dangerous releases either toxic or flammable can occur during process, storage or transportation, as mentionned by Dicken (1974), Harris (1978) and Marco, Pena & Santamaria (1998) for chlorine.
Most of accidents are toxic releases (Khan & Abasi, 1999) and particularly heavy gaseous releases (Vilchez, Sevilla, Montiel & Casal, 1995). In unfavourable atmospheric conditions, these dense clouds consist in a dense layer at ground level which spreads over large distances before becoming passive clouds (Koopman, Ermak & Chan, 1989). Such a dense cloud may stay and persist at ground level, which corresponds to human breath level and thus magnifies its harmful potential to people.
The dispersion of these clouds can be controlled by using more or less expensive technics as thermal inactivation, fans, specific foams, water or air sprays (Ftenakhis; 1989).
Fixed or portable water sprays appear to be a good technic to mitigate heavy gas clouds (toxic or flammable) in so far as they require few energy and also for protection of small storages (as chlorine storage in public swimming pools) where other mitigation means are economically or technically unachievable.
A water curtain is composed of several sprays, generally with a vertical and downward orientation.
The actions of water sprays are threefold, and consist mainly in reducing the density difference between the ambiant air and the dense gas (McQuaid &Fitzpatrick, 1981).
First, the mechanical dilution of the cloud by entrainement of the pollutant and 'clean' air in the spray consists in momentum exchange between the droplets and the gas phase. It induces air entrainment inside the spray and affords mechanical dispersion of the noxious cloud (Prétrel & Buchlin, 1997).
Secondly, the forced dispersion of the toxic cloud is enhanced by physico-chemical absorption of the pollutant by the water droplets and finally by cloud heating (due essentially to entrainment of warm 'clean' air in the cold cloud).
The two phases interaction, the gaseous phase and the polydisperse liquid phase, makes the water spray be a very sophisticated reactor. Its modelling is consequently very complex but fundamental to assess its real effectiveness in mitigating dangerous clouds and to deduce concentrations and safety distances downstream of the water spray.
The water spray effectiveness depends on its own characteristics (droplets distribution, types of nozzles, width and height, water pressure …) or extrinsic parameters, such as cloud features, gas nature, wind speed, atmospheric stability....
Nevertheless, despite the complexity, several models exist to assess the efficiency of water sprays, with different approaches either macroscopic (box models) or microscopic.
Then, some of them are based on semi-empirical formulations (Moore & Rees, 1981; Buchlin, 1994) which is a macroscopic modelling of the interaction between the two phases, whereas others are based on fluid dynamics and reproduce the movement and the transfers between the liquid phase and the gaseous phase (Uznanski & Buchlin, 1998; Buchlin & Alessandri, 1997; Fthenakis, 1993; Fthenakis & Blewitt, 1993, 1995).
These last models are more complete and deal with all the implied phenomena (air entrainment, heating, mass transfer ...) but they require acute information on the hydrodynamics of the spray.
These models generally just specifiy the mitigation ability of the water curtain without assessing the subsequent dispersion of the cloud (concentrations downwind of the water spray), which is the essential parameter to assess the consequences of an accident and in particular, safety distances.
2. Problematic
This study is a part of a research program which problematic was the security of small storage sheds of chlorine and their protection with water sprays. It aims at controlling the consequences of chlorine dispersion in public swimming pools where bottles of liquefied chorine are stored in these small storage sheds.
Although the involved quantities are small, an accidental loss of containment of chlorine presents a seriouschemical hazard. It may kill or injure a large number of people because of its high toxicity, as highlighted by its very low IDLH, Immediatly Dangerous to Life or Health, value of 10 ppm (Tissot & Pichard, 2000; Sexton & Pronchik, 1998; SHD, 2002; Lauwerys, 2003; The Chlorine Institute, 1999).
Furthermore, few studies relate on atmospheric dispersion of small releases at small distances form the source, so that models are not often validated for such accidents scenarii.
In this goal, experiments of chlorine dispersion, in open field and in presence of water sprays have been carried out, in order to, first identify the associated risks (safety distances) and in a second time, to propose a dispersion model for both open field dispersion and dispersion in presence of a water spray.
The study was led as follows. In a first time, chlorine dispersion experiments have been carried out, both in open field conditions (without water curtain) and with specific configurations of water sprays to study mitigation of toxic clouds by forced dispersion. The experiments aimed at reproducing an accident on small chlorine storage shed (figure 1).
Open field dispersion concentrations have been compared to the simulations on several models (two heavy gas dispersion models and a Gaussian model). These results (Dimbour, 2003) enhanced that models are not always efficient to predict concentrations in particular conditions such as small releases of product (chlorine in that case) and short distances to the source (dozens of meters – near field of the release). Indeed, dispersion models are mostly validated on the basis of past dispersion experiments which implied large quantities of hazardous products and great distances from the source.
Now, a dispersion model for 'open field dispersion' has been developed.
Furthermore, as previously mentioned, it is necessary to have models that predict the dilution factor of the water curtain but above all, concentrations downstream the water spray. Thus, a model has been proposed for the specific conditions of a chlorine storage shed.
First, the dispersion model RED (Rideaux d’Eau Descendants) is presented: the open field dispersion and the dispersion in presence of the water sprays are described. Statistical tools allowing assessment of the performances of dispersion models are then presented. Finally, the database of the dispersion experiments is detailed and the differences between the predictions and the observed concentrations are calculated and discussed both for open field dispersion and dispersion downwind of the water spray.
3. Model and results for open and forced dispersion
3.2. The RED (Rideaux d’Eau Descendants) model
3.2.1. General features
The RED model is built on Bosanquet equation of air entrainment, as developed by Moore & Rees (1981). Several modifications have been integrated in the model to take into account the phenomena that seem important and the specificities of the problem under study (in particular the storage shed).
The model is based on the hydrodynamics of the sprays, especially on air entrainment in the spray which can be either measured or calculated (Briffa & Dombrowski, 1966; Benatt & Eisenklam, 1969; Heskestad, Kung & Todtenkopf, 1976; McQuaid, 1975). The model does not take into account physico-chemical absorption or cloud heating.
Nevertheless, chlorine (gas of interest) is a heavy gas (vapour density of 2.48) with low solubility in water (7.3 g/L). Thus, the water curtain mainly acts by mechanical dispersion or forced dispersion, and the other mechanisms can be neglected. For example, absorption effectiveness was found to be less than 3 % responsible of the concentrations reduction when the water curtain was operating (Dimbour, 2003).
Forced dispersion is mainly characterized by air entrainment, parameter included in the model of Moore and Rees. Specifically, the model relies on the increase of cloud dimensions (of circular section) which is submitted to atmospheric turbulences and to air entrainment due to the water spray. Three zones are defined (see figure 2), the first one before the water spray (open field dispersion), the second one where the cloud interacts with the water curtain and the third zone, where the dispersion of the plume is again due to atmospheric turbulences (open field dispersion).
Moore and Rees defined several equations to determine the cloud radius in the three zones, in order to finally deduce the dilution factor for the forced dispersion due to the water spray. The forced dispersion coefficient FD is defined as the ratio of the open field dispersion concentration (Copendispersion) to the concentration in presence of the water curtain (Cwatercurtain). Several assumptions are proposed owing to the different approaches developed by Moore and Rees, but for downward water sprays and assuming that vertical speed given to the gas by the spray is neglected, FD becomes:
where:
cs: entrainment coefficient in the spray (dimensionless),
D: thickness of the spray (m),
u: wind speed (m/s),
r0: initial radius of the plume (m),
c: entrainment parameter (dimensionless),
x: distance downstream from the source (m).
One can notice that the dilution factor FD increases for weak winds (when u is close to 0, the expression of FD diverges), short distances to the source and indirectly for small releases of gas (short r0).
The dilution factor deduced from Moore and Rees' formulas or from Curtain predictions, model more complete but based on the same general equations as Moore and Rees formulas (Buchlin, 1994) have been compared to laboratory experiments. But, these models have never been validated for concentrations assessment neither for open field dispersion nor for dispersion with water spray, which is in fact the most important result in order to define safety distances.
It was therefore of prime interest to modify Moore and Rees’ model in order to consider important parameters neglected in the early model and to identify its performances in simulating these two kinds of dispersion, on basis of field experiments results.
Therefore, the following model RED (Rideaux d’Eau Descendants) was deduced from Moore and Rees approach but includes three major modifications.
First, the initial radius was modified to better take in account the initial jet process, actually represented with c (air entrainment parameter).
Then, the atmospheric stability which is not included in Moore and Rees’ model is included in RED, as it is a very important parameter in atmospheric dispersion, particularly in the passive phase of dispersion (where atmospheric turbulences are predominant).
Furthermore, the storage shed leads, among others, to modifications in turbulence conditions and wind pattern in the wake of this obstacle (Fackrell, 1984), which disrupt the cloud dispersion as wind controls transport of the cloud and the turbulence its diffusion (Kitabayashi, 1991). This induced turbulence leads to an increase of the heavy gas dispersion dilution, so making its transition to the passive dispersion easier (Brighton, 1986; Nielsen & Jensen, 1991). This phenomenon is enhanced by the presence of the water spray (Buchlin, 1994). Therefore finally, a specific wind pattern in the wake of the storage shed is included in this model.
From Moore and Rees model and from the above considerations, concentrations in the three zones (figure 2) are deduced from the following formula:
where :C(x) : concentration at x (m) downstream of the source (m3/m3),
Q: gaseous release rate (m3/s),
u(x): wind speed at the distance x from the source (m/s),
r (x): plume radius at x (m),
x: distance downstream to the source (m).
r is given by :
in Z1
in Z2
in Z3
where:cs : entrainment coefficient in the spray (dimensionless),
catm: entrainment coefficient in the spray (dimensionless),
va: air entrainment in the spray (m/s),
X2: distance between the water curtain and the source of gas (m),
D: thickness of the spray (m),
r0: initial radius of the plume (m).
The dilution factor FD is deduced from these formula.
3.2.2. Assessment of the initial radius of the cloud
The entrainment coefficient, c which is a longitudinal dispersion parameter of the gaseous jet defined by Bosanquet (1957) contributes to the increase in the plume dimensions and to the heating of the cloud. The pollutant concentration is inversely proportional to the radius (thus to the air/gas volume of the section defined in figure 2). In RED model, the coefficient c is thus replaced by the determination of an initial plume radius, r0, depending of the initial plume density (air/gas mixture). It is assumed that enough air is mixed to the gas such that all liquid is vaporized and initial temperature of the cloud (air/gas mixture) is assumed to be equal to chlorine boiling point at atmospheric pressure.
Air entrainment assessment is deduced from the calculation of mass (Rm) and volume (Rv) ratios air/chlorine (Wheatley, Crabol, Carpenter, Jagger, Nussey, Cleaver, R, Fitzpatrick & Byrne, 1988):
with :Ma : air entrained (kg),
MCl: chlorine quantity (kg),
Lv: chlorine vaporisation heat (J/kg),
Ti: chlorine initial temperature and ambient air temperature (K),
Tb: chlorine boiling point at atmospheric pressure (K),
: specific heat of ambient air at constant pressure (J/kg.K),
: specific heat of liquefied chlorine at constant pressure (J/kg.K),
WCl: chlorine molecular weight (kg/mol),
Wa: ambient air molecular weight (kg/mol).
Air entrainment is an important parameter as it determines the cloud radius and therefore its concentration.
3.2.3. Assessment of the coefficient catm
The catm coefficient allows taking in account the importance of atmospheric stability in atmospheric dispersion of gas plumes. In order to consider catm, concentrations in open field dispersion are equalled to Gaussian concentrations, estimated with original Pasquill-Turner standard deviations coefficients (Turner, 1994) for short distances (20 m) which is scarcely studied and corresponds specially to the problem of small clouds.
Generally, estimation of standard deviations (and so of atmospheric dispersion) is based on greater distances (hundreds of meters) which do not allow studying dispersion for short distances and therefore for small plumes.
The catm coefficient calculation assumes that the plume is passive with specific limits (homogenous and constant wind …) (Turner, 1994). Experiments showed that the plume quickly behaves as a passive one (Dimbour, 2003), which is enhanced by the obstacle.
For memory, Pasquill-Turner original dispersion coefficient are calculated by the following formula (Turner, 1994)
Where: y and z: lateral and vertical standard deviation coefficient (m),
x: distance from the source (m),
T: half angle corresponding to angular spreading of the cloud (Pasquill, 1961) (rad),
a et b: coefficients (dimensionless)
Then, catm can be assessed for each stability class and for different distances, as shown for example in table 1.
3.2.4. Assessment of wind profile in the wake of the obstacle
A particularity of this study lies in the presence of the storage shed which disrupts the wind field by creating recirculation zones (Hussein & Martinuzzi, 1996), (Iaccarino & Durbin, 2000). The wind profile in the disrupted zone which is included in the model is given in the figure 3. It was deduced from experimental values (Hussein & Martinuzzi, 1996) obtained in conditions similar to those of the study, imposing a non disrupted wind at a downwind longitudinal distance of 6.5 H (height of the obstacle) as given by Ogawa & Oikawa (1982).
In RED model wind speed is limited to values higher than 0.5m/s, to avoid divergence in concentrations assessment. Moreover, the wind speed profile was obtained halfway of the obstacle, whereas concentrations can be measured at ground level or at higher heights.
All these modifications are included in the model. Moreover, the sensibility of the model to several parameters such as the modification of wind speed profile, the atmospheric stability coefficient catm, was studied (Dimbour, 2003).
Now, the dilution model predictions must be compared to chlorine field experiments for open field and forced dispersion, i.e. without and with water sprays.
3.2. Statistic parameters of performance assessment
The performances evaluation of an atmospheric dispersion model requires the use of statistic parameters which assess the difference between simulations and observations (Mohan, Panwar & Singh, 1995).
For a strict evaluation of the performances of a model, the comparison between simulations and observations should be based not only on the maximum concentrations but also on the cloud dimensions (Duijm, Ott & Nielsen, 1996). Nevertheless, this study aims at identifying if these tools are well adapted to the problematic of small releases. Therefore, only maximum concentrations in the cloud centreline will be investigated(Hanna & Paine, 1989).
Various indexes of performance evaluation exist (Hanna, Strimaitis & Chang, 1991; Duijm, Ott & Nielsen, 1996). However, it is recommended to select indexes which indicate if the model over or underestimates the observed concentrations, and which measure the dispersion of the predicted concentrations values around this over or underestimation (Duijm, Ott & Nielsen, 1996):
Thus, for this study, three indexes are examined, the Factor-of-2 (Fa2), the Mean Relative Bias (MRB), and the Mean Relative Square Error (MRSE).