Generalized mathematical modelling of spray barriers

Chemical Engineering Journal xxx (xxxx) xxx–xxx

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Generalized mathematical modelling of spray barriers Bruno Fabianoa, , Fabio Curròa, Andrea Reverberib, Emilio Palazzia ⁎

a b

DICCA Civil, Chemical & Environmental Engineering Department, Polytechnic School – University of Genoa, Via Opera Pia, 15, 16145 Genoa, Italy DCCI Chemistry and Industrial Chemistry Department, University of Genoa, via Dodecaneso, 31, 16145 Genoa, Italy

HIGHLIGHTS

general model of water/reacting spray barriers is developed. • AA comprehensive analytical description of the curtain both under still and windy conditions. • Theunified is validated with chlorine releases in a laboratory scale wind tunnel. • The model • approach can be applied to different hazardous gas releases. ARTICLE INFO

ABSTRACT

Keywords: Absorption Hazardous gas Post-release mitigation Reacting curtain Water spray

In this paper, experimental and theoretical investigations on liquid spray curtains are presented, in the context of absorbing and dispersing hazardous gaseous releases. The problem of release mitigation by absorption, either in pure water or in aqueous solution, was investigated or analytically solved by developing a general approach. The structure of the model includes a fluid-dynamic model describing air entrainment rate both in still air and in windy conditions, an absorption model, predicting spray efficiency and a mixing-dispersion model for the evaluation of the overall barrier effectiveness in environmental control. The model was validated by means of replicated experimental runs in a wind tunnel equipped with spray nozzles suitable to create a two-blade barrier. The model agreement with experimental data was fairly good in both cases of water and reacting curtain, which is promising for short-cut design purposes. The developed framework can be applied to more complex situations and different gas, allowing, as well, the attainment of a more generalized approach for the design of a curtain, once given the release parameters, the site layout and the sensitive target specifications.

1. Introduction As demonstrated by recent statistical analysis on process accidents [1], releases of hazardous gases still represent a serious concern in the chemical and petrochemical industries, notwithstanding the available accurate modelling techniques and the achievement of acceptable preventive risk limits. This empirical evidence suggests that there is still much to develop and improve in the field of post-release risk mitigation. Water spray curtains are considered among the most common devices suitable to mitigate the risk connected to accidental flammable or toxic releases and jets. When dealing with flammable gases of low solubility and reactivity, as saturated hydrocarbons, the primary purpose of the barrier is a fast dilution of the released substances, so that the possible contact of the cloud with ignition sources occurs by far below the lower flammable limit (LFL). In this respect, inert vapour or gas curtains located nearest as possible the release can often represent

⁎

the best technical solution [2]. Depending on the mechanism binding the gas compounds in the liquid, one can distinguish between physical and chemical (or reactive) absorption. The role of reactive absorption as a core environmental protection process has grown up significantly, as the current EU legislation imposes tighter restrictions aimed at reduction of the environmental impact of process industries [3]. The development of effective science-based research on release abatement by water curtain still represent an emerging safety research topic, as recently reported in a recent study on the dominant design parameters of water curtain as an LNG vapour cloud mitigation system [4]. When dealing with a toxic release, liquid spray curtains, possibly with chemicals, are to be preferred [5], so to ensure a partial abatement of the released compound by physical and chemical absorption, in addition to the dilution effect [6]. In this regard, it was recently demonstrated how a properly designed and maintained reacting curtain would have effectively contained MIC downwind concentration thus limiting sharply

Corresponding author. E-mail address: [email protected] (B. Fabiano).

https://doi.org/10.1016/j.cej.2018.10.045

1385-8947/ © 2018 Elsevier B.V. All rights reserved.

Please cite this article as: Fabiano, B., Chemical Engineering Journal, https://doi.org/10.1016/j.cej.2018.10.045

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Nomenclature a0 aC aD aE ag ai aT aU aOC aij aXY b bj Cr Cr,eq Cs Cs0 Cs Da DOHDr F g H h hf ho hr ht Kg

Kg k ke kg kl L l ln Ma Mr mD mC mR mU

mXY

mass flow rate of air at still air conditions, kg·s−1 mass flow rate of air entrained into the curtain, kg·s−1 mass flow rate of air circulating downwind the curtain, kg·s−1 total mass flow rate of air circulating in regions d and u, due to curtain action, kg·s−1 mass flow rate of air entrained by gravity effect at distance z from the nozzles, kg·s−1 mass flow rate of air entrained by inertial effect at distance z from the nozzles, kg·s−1 total mass flow rate of air entrained by the curtain at distance z from the nozzles, kg·s−1 mass flow rate of air circulating upwind the curtain, kg·s−1 mass flow rate of air by-passing over the curtain, kg·s−1 mass flow rate of air entrained by inertial effect at the transition point, kg·s−1 mass flow rate of air from compartment X to compartment Y in Fig. 3, kg·s−1 curtain width at distance z from the nozzles, m curtain width at the transition point, m concentration of chlorine in the absorbing solution at distance z from the nozzles, kmol·m−3 concentration of dissolved chlorine in equilibrium with the air leaving the curtain, kmol·m−3 concentration of absorbing solution at distance z from the nozzles, kmol·m−3 concentration of fresh absorbing solution, kmol·m−3 concentration of absorbing solution defined by Eq. (62), kmol·m−3 diffusion coefficient of air in the atmosphere, m2·s−1 diffusion coefficient of OH− in the liquid-phase, m2·s−1 diffusion coefficient of released gas in the liquid-phase, m2·s−1 mass force acting on the curtain, N acceleration of gravity, m⋅s−2 Henry constant relative to absorption of released gas in water, atm⋅m3⋅kmol−1 curtain height, m height of the region F, m height of the obstacle, m height of release, m tunnel height, m overall mass transfer coefficient in gas phase, kmol·m−2·s−1⋅atm−1 modified overall mass transfer coefficient in gas phase, Table 4, kmol·m−2·s−1⋅atm−1 kinetic constant of the first order irreversible reaction, s−1 entrainment constant mass transfer coefficient for gas-phase, kmol·m−2·s−1⋅atm−1 mass transfer coefficient for liquid-phase, m·s−1 length of the tunnel, m width of tunnel and curtain, m nozzle pinch, m mean molar mass of air, kg·kmol−1 molar mass of gas kg·kmol−1 mass flow rate of released gas circulating downwind the curtain, kg·s−1 mass flow rate of released gas entrained into the curtain, kg·s−1 mass flow rate of released gas, kg·s−1 mass flow rate of released gas circulating upwind the

mabs Nn Np nC p qx r rσ s T tp tr V Va VC Vp Vs Vr v va vj vx vz v0 v∞ vbc Xc x xr y yC yCU w wcr w* wcr winv z zj

curtain, kg·s−1 mass flow of released gas from compartment X to compartment Y in Fig. 3, kg·s−1 mass flow of released gas absorbed by the curtain, kg·s−1 number of nozzles number of droplets in the curtain molar flow rate of released gas entrained into the curtain, kmol·s−1 atmospheric pressure, atm horizontal component of momentum flux of the jet, kg·m⋅s−2 rate of released gas absorption, kmol·m−3·s−1 rate of released gas absorption for unit interfacial surface, kmol·m−2·s−1 mass flow rate of the sprays, kg·s−1 temperature, K drop falling time, s release duration, s volume of curtain up to the distance z from the nozzles, m3 volume of air in the curtain, m3 volume of the curtain, m3 drop volume, m3 volume of liquid phase in the curtain, m3 volumetric release rate, l⋅s−1 fluid velocity at distance z from the nozzles, m·s−1 velocity of air flows aDC and aUC approaching the curtain, m·s−1 free fall velocity in the curtain, m·s−1 horizontal component of jet velocity at the transition point, m·s−1 vertical component of jet velocity at the transition point, m·s−1 liquid velocity at the nozzle exit, m·s−1 drop terminal velocity, m·s−1 mean velocity of the overcoming air flow, m·s−1 intrinsic absorption efficiency of released gas distance of the curtain from the tunnel inlet section, m distance of the curtain from a generic release, m molar fraction of released gas at distance z from the nozzles molar fraction of released gas entrained into the curtain molar fraction of released gas leaving the curtain wind velocity, m·s−1 critical wind velocity, m·s−1 adimensional wind velocity, defined by Eq. (38) critical value of the adimensional wind velocity inversion wind velocity, m·s−1 curtain axial coordinate, m curtain axial coordinate at the transition point, m

Greek letters α β δ γ η υa μ θ θc ρc ρa ρs σ 2

parameter defined by Eq. (71) parameter defined by Eq. (78) mean droplet diameter, m parameter defined by Eq. (54) overall absorption efficiency of released gas air kinematic viscosity, m2·s−1 parameter defined in Table 4 tilt of the curtain critical tilt of the curtain mean density of the curtain, kg·m−3 air density, kg·m−3 density of the sprayed solution, kg·m−3 interfacial surface per absorption volume unit, m2·m−3

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σp ωf ωDg

droplet surface, m2 mass fraction of released gas leaving the curtain downwind released gas concentration, ppm (w/w)

ωgU Ψ ζ

the severity of Bhopal gas tragedy [7]. The effectiveness of a liquid barrier suitable to face with toxic gaseous releases can be evaluated on the basis of several items, related to its ability in reducing the amount of the dangerous substances dispersed into the environment, in enhancing its dilution and in slowing down the rate of the aforesaid dispersion, so as to permit the adoption of proper additional protective measures. The first effect, related to the physical and chemical absorption of toxic vapours by the liquid solution, also contributes to reducing its downwind concentration, whatever the release duration may be. With respect to the simple atmospheric dispersion, the additional dilution of the released gas due to air entrainment by the liquid sprays can be very effective, above all in case of stable atmospheric conditions and low ventilation. The third effect, particularly important in the case of emissions of gases heavier than air, depends on the curtain capacity of partially contain the release, so as to avoid a rapid contact with sensible targets. The containment action is also related to the effectiveness of the adsorption and dilution, allowing to recycle many times a significant fraction of the toxic gas to the curtain, before its ultimate release into the external environment. The curtain effectiveness in removing water soluble gases (e.g. ammonia, hydrofluoric acid, chlorine) was investigated either theoretically, or experimentally by several researchers [8–11]. A recent improvement was proposed, by Diaz Ovalle et al. [12] who modelled air, water and curtain mitigation systems as a box type, starting from the SLAB mathematical approach, allowing a better estimation of dispersion characteristics and the proper selection of the mitigation system, in the absence of chemical reaction. A comprehensive CFD approach was presented as an effective but time-consuming numerical tool, to model water spray enhancement of dispersion, by entrainment of the surrounding ambient air [13–14]. In this paper, we present the results obtained during a long-term program, aiming at developing a generalized mathematical model suitable to be adopted as a design tool for reacting spray curtains mitigating accidental hazardous releases. On the basis of a large number of experiments on chlorine releases in wind tunnel, we developed a mathematical model

upwind released gas concentration, ppm (w/w) parameter defined in Eq. (62) parameter defined by Eq. (16)

suitable to be adopted as a real-scale design tool of a barrier, including both under still air and windy conditions. The key difference of this analytical model compared to other studies and to the extensive research by Rulkens [2] is that it presents a unified approach coupling fluid dynamics, spray efficiency, mixing-dispersion and absorption calculation (two-film model), accounting as well for the wind effects on the curtain. A further contribution of this work relies on the derivation of technical constraints for optimal design at the full scale. The mitigation model can be applied to releases of other dangerous gases, provided that proper modifications on the absorption and reaction kinetics be taken into account. 2. Experimental 2.1. Experimental apparatus The experimental set-up, schematised in Fig. 1, consisted of a glass wind tunnel, with a rectangular section (lt = 0.80 m; ht = 0.90 m) and a length of 5 m and properly equipped as described in [15]. Chemical analyses of chlorine concentration in air were performed according to standard methods [16], based on sampling air/chlorine mixture, absorbing sodium hydroxide solution and analysis by UV spectrophotometry (Carlo Erba, Milan, Italy). As already proposed by [17], chlorine concentration was also measured with PID-photo ionisation detector (RAE Systems, USA). A high-speed digital imaging system (Matrox, USA) was used to acquire images with rate of 250 frame s−1. Diffused light from a stroboscope with a maximum frequency of 500 Hz was used in the backlighting mode. The digitised images were analysed using image analysis software to study spray behaviour, determining the boundaries of the spray trajectories, the extension of the jet region and possible break-up effect due to wind cross flow (see Fig. 2). A complete fluid dynamic analysis was carried out, by varying barrier height, h, from 0.49 to 0.67 m, mean wind speed above the curtain, w, between 0 and 3 m·s−1, and liquid velocity at the nozzle exit, v0, in the

Fig. 1. Experimental set-up: A. Gas release; B. Honeycombs; C. Interception valve; D. Flow-meter; E. Height adjustable pipe; F. Stainless-steel nozzles; G. Helical suction fan; s. Water/solution inlet. 3

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described by means of a semi-empirical model [19], accounting separately for the inertial and gravitational effects due to the liquid sprays. These effects were respectively connected to the air entrained into the sprays and externally to them. More precisely, three regions were distinguished in the curtain behaviour, namely:

• a jet region, J, in which water droplets entrain all the air within the • •

Although providing good correlations for the whole set of experimental data, the model cannot be considered satisfactory at all. Its major drawback consists in the definition of the transition point from J to F region in terms of the observed parameters bj and zj, not easily quantifiable in scaling-up problems. As an example, the model does not indicate as the jet spreading and, consequently, the ratio between the curtain width and the extent of the J region, bj / zj, vary as a function of the drop mean diameter, which generally depends on the system size. In this paper, the problem is faced from a more general point of view. Firstly, by means of a fundamental approach, a model giving the global amount of air entrained by the curtain is developed. According to this approach, the correlations among the main parameters are expressed by means of theoretical formulae, suitable to be used in scaling problems. Secondly, the inertial and gravitational contributes to air entrainment are separately calculated, as limiting situations of the model. At last, we show how the expressions proposed in [19] to calculate the air entrained into the curtain and the air circulating around it, be theoretically supported by the model and provide conservative results. The system here studied is depicted in Fig. 3 with reference to the most general situation of windy conditions. The system is considered as a three compartments model, including the curtain, C, the release region, U, and the volume immediately downwind the curtain, D. The above mentioned Fig. 3 also shows the air flows connecting the different compartments and the atmospheric environment, A, mainly determined by the spray actions. The mathematical representation of the system, based on a careful analysis of the main aspects and of the reciprocal correlations of the single subsystem, required the development and the assembling of some specific models, as:

Fig. 2. Spray digital image (spray nozzle CBN series 065, nozzle pitch 0.04 m; spray angle 110°, fluid exit velocity 9 ms−1).

range 7–13 m·s−1. Absorption tests were carried out with four different release rates, Vr = 4.8, 6, 9, 12 and 15 l·h−1, and spraying tap water or water solutions of NaOH at three different concentrations, Cs,0 = 0.0625 M, 0.125 M and 0.25 M. 2.2. Experimental design The whole experimental design includes the following steps:

• preliminary runs, ended to select a curtain of adequate capacity of • •

curtain, whose width linearly increases up to the distance zj, defined as “transition point”; a region, F, of constant fall velocity, in which only outside the barrier some more air is entrained and the curtain width, bj = b(zj), remains constant; a region, G, in which the air, partially decontaminated, spreads upwind and downwind the barrier, near the ground.

containment and air entrainment, mainly by means of qualitative observations [18]; fluid-dynamic runs, aimed to quantify the air entrainment as a function of curtain characteristics and of the operative conditions (entrainment model) [15,18]; absorption runs, for determining the efficiency of the safety device in abatement and dilution of the gaseous release.

The results obtained in experimental steps were used for planning in optimal way the next step of the research. A summary of the operating values of the experimental parameters during the whole set of fluid dynamic and absorption runs is shown in Table 1. 3. Model development

Table 1 Range and reference values of experimental parameters in fluid dynamic and absorption runs.

3.1. Curtain physical model

Parameter

3.1.1. General considerations The mathematical description of the curtain behaviour and of the air entrainment rate can follow different approaches. In the case of steam or gas curtains, where the inertia of the sprays is the only relevant parameter in determining the amount of entrained air, a simple and elegant model was proposed in [2], according to which the jet width, b, linearly increases with respect to the distance from the nozzles, z. The model is not applicable without modifications to liquid sprays since the density difference with respect to the surrounding air modifies the entrainment coefficient and makes gravity effects not negligible. Experimental observations indicate that the sprays and gas curtains similarly behave only up to a certain distance from the nozzles, where the drag forces, related with the inertia of sprays, prevail over the gravity ones. Increasing the mass or the air entrained into the curtain, these forces become comparable and sprays tend to reach a constant fall velocity. As a first attempt, the curtain behaviour was

Nn ln s v0 ρs δ x h l w T ρa θc mR tr Cs0 ρs

4

Operating value [m] [kg·s−1] [m·s−1] [kg·m3] [m] [m] [m] [m] [m·s−1] [K] [kg·m3] [°] [kg·s−1] [s] [kmol·m−3] [kg·m3]

19 0.04 0.11–0.22 7–13 103 2·10-4 0.90 0.49–0.67 0.80 0–3 298 1.2 15 4.8·10-6-1.2·10-5 300 0–0.25 103–1.01·103

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Fig. 3. Physical model of the curtain with water/reacting spraying (J = jet region; F = region of constant fall velocity; G = flow spreading region; U = upwing; D = downwind; C = curtain).

• a fluid-dynamic model, describing the rate of air entrainment and the flow-field, either in still air or under windy conditions; • an absorption model, for evaluating the spray absorption efficiency; • a mixing-dispersion model, predicting the overall efficiency of the

daT v 2dv = 3 aT + s v j v3 where the parameter vj, defined as

barrier in release mitigation.

vj =

3.1.2. Global rate of air entrainment An approximated description of the whole air entrained by the sprays is given by the mono-dimensional models considering a finite element dz of the barrier:

daT = ke·2l· a v dz

C

a ) g · dV

aT aT

sg s g ·b ·l· dz = dz bl v v

a

+s s +

(

a

s 1 a

g·dV =

s

aT a

s

+

s

aT = s

sg v

(7)

v 30

v 3j

v3

v 3j

1/3

1

(8)

Substitution of the last expression into Eq. (4) yields:

dv = dz

(v 3

g v 3j (v 30

v 3j)1/3

v 3j) 4/3 v

(9)

Eqs. (8) and (9) indicate that both aT(z) and v(z) depend on the single parameter vj (or ke), once the sprays characteristic are given. Since Eq. (9) is not integrable in elementary way, the values of vj and ke connected to each experiment are obtained by means of the numerical iteration considering actual operating conditions and the corresponding reference values listed in Table 2 and obtained from the whole series of experimental runs detailed in [15]. Once chosen a value of vj < v0, Eq. (9) is numerically integrated so as to get the behaviour of v(z) and then of aT(z), by means of Eq. (8). The corresponding trends of the total mass flow rate of air and of the vertical component of the jet velocity, both as a function of the curtain axial coordinate, are depicted in Fig. 4. As already remarked, by increasing the liquid flow-rate above 0.17 l⋅s−1, the air entrainment does not increase further, since ke rapidly decreases, owing to the beginning of sprays interference. For the

) g·dV

s

(3)

Combining Eqs. (1) and (2), it follows:

sg 2ke l a v 3 dv = dz v(aT + s )

(6)

a

Integrating Eq. (5) under the condition aT(v0) = 0, we obtain:

(2)

=

1/3

2ke a l v 2 =

Eq. (1) defines the global air entrainment. The balance of vertical momentum, Eq. (2), is based on the assumptions that drops and entrained air are characterized by the same velocity, uniformly distributed on each horizontal section of the curtain. In particular, the right hand side represents the force per unit length acting on the volume element dV ≅ b·l·dz of the curtain, being dF the force acting on dV:

dF = (

sg 2ke l

represents the value of v which makes equal the drag and gravity forces acting on the curtain:

(1)

d s [(aT + s )v] = g dz v

(5)

(4)

On combining Eqs. (1) and (4), one obtains: 5

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contributes to air entrainment are separately estimated, as limiting situations of the model itself.

Table 2 Reference value obtained from fluid dynamic experimental runs. Parameter

Reference value from experimental runs −1

aT aC aE vj ke winv wcr

[kg·s ] [kg·s−1] [kg·s−1] [m s−1] [m s−1] [m s−1]

3.1.3. Air entrained by inertial effect As already remarked, within a certain distance from the sprayers, the action of gravity can be neglected in comparison with the effects of jet inertia. Then, the curtain can be considered as a plane jet [2] and Eq. (1) can be rewritten as:

1.0 0.50 0.50 1.7 0.16 2.5 1.0

d [(ai + s )v] = 0 dz which expresses the momentum conservation and directly gives:

next developments, it is useful to underline some features of the model. First of all, it seems rather realistic, from a physical point of view, in that it accounts for the inertial and gravity effects along the whole curtain. Nevertheless, according to the experimental flow visualization investigations similarly to [20], Fig. 3 indicates that the air entrainment due to the inertia of the sprays is very effective only within a narrow distance from the nozzles (0.20–0.30 m), until v ≫ vj, i.e., in the J region, where the gravity effects are less important. Moreover, increasing z, the velocity v decreases asymptotically to the value vj, or, alternatively, the ratio between the drag and gravity forces decreases asymptotically to the value 1, so that, from Eqs. (4) and (2), it results:

dv dz daT dz

0

ai = s

sg = cost v j2

v0 v

1

(13)

As expected, Eq. (13) is the limiting form of Eq. (8), when v ≫ vj. The combination of Eqs. (1) and (2) yields:

dai s = ke·2l· a v0 dz ai + s

(14)

Integrating Eq. (14) under the condition ai(0) = 0, we obtain

a i (z ) = s

(10)

ke·2l· a vj =

(12)

1+

z

1/2

1

(15)

where (11)

=

Then, the air flow rate increases nearly linearly, according to the distance from the nozzles, relatively far from these ones. Eqs. (10) and (11) approximately characterize the region F identified in [19]. In this way, the model allows an indirect evaluation of aT, even if no information on the amounts of air entrained into the curtain and externally to it is obtained. This deficiency represents a serious drawback, to the end of practical applications. Indeed, the air entrained into the curtain and subjected to absorption of the release must be well distinguished from the circulating one, which only contributes to the dilution effect. Nevertheless, the previously discussed features of the model suggest to overcome this difficulty by the simplified approach presented in the following, where the inertial and gravitational

v 3j (16)

2g v0 Moreover, from Eqs. (13) and (15), one can write

v = v0 1 +

z

1/2

(17)

Eqs. (15) and (17) represent a refinement of the models of gas or steam curtain by Rulkens et al. [2] and of the jet phase of sprays curtain [19], both relying on the hypothesis that s be negligible with respect to ai. We assume the validity of the aforesaid Eqs. until gravitational forces become comparable to passive drags. Then, v = vj at the transition point, where Eqs. (13) and (17) respectively give:

Fig. 4. Fluid velocity and total mass flow rate entrained by the fluid curtain, as a function of the curtain axial coordinate, z. 6

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v0 vj

aij = s

1

(18)

2

v0 vj

zj =

Eqs. (27) and (28) show the same dependence of the air flows on z obtained in [19], but are based on a more sound definition of the transition point, where it results:

1

aC (z j ) = aE (zj ) =

(19)

zj) =

sg (z v j2

zj )

(20)

As already said, the linear dependence of the air flow-rate on z is just the limiting form of Eq. (8), when v ≅ vj. 3.1.5. Simplified expressions of the global air flow- rate According to the simplified model, the global air entrainment is obtained by adding the inertial and gravitational contributes, so that:

(1 + )

z 1/2

s aT (z ) = s

(

)

v0 vj

1 +

sg (z v 2l

1

(z

zj )

z j ) (z

zj )

a i (z ) = s

aij = s

zj =

aT =

(24)

s

v0vj

=

2g

()

z 1/2

1 v0 s 2 vj

+

sg z v 2j

(25)

(z

zl )

(z

zl)

(26)

Additionally, Eq. (26) gives conservative results also far from the nozzles, just where the hypothesis of uniform velocity of all flowing air is more questionable, so that Eq. (8) represents an over estimation of the total air entrained by the curtain (aT). 3.1.6. Air entrained into the curtain and externally to it According to the previous discussion, we assume that the behaviour of air flow-rates entrained into the curtain and circulating externally to it can be respectively calculated from Eqs. (27) and (28):

aC (z ) =

aE (z ) =

s

()

z 1/2 1 v0 s 2 vj

sg z v 2j

sg z v 2j

(z

zl )

(z

z l)

sg h v j2

(31)

aC 2

(32)

aE 2

(33)

When dealing with windy situations, it was observed that, as w increases, the air flow generated in the downwind region D slows down to vanish in connection with the wind velocity corresponding to the here defined “inversion velocity”, winv. Extensive experiments were performed to investigate the dependence of the inversion velocity on the barrier height and liquid flow rate: the results are summarized in Table 3. It can be noticed a slight increase of the inversion velocity as the liquid flow rate increases: in fact the vortex induced in D region by the barrier is directly correlated to the liquid flow rate. The inversion velocity slightly slows down as the barrier height increases, probably due to the increasing of the compression effect exerted by the wind tunnel ceiling in the U region, contrasting the opposite flow aDC. To practical purposes, we assume that the average value of the inversion velocity in tunnel be winv = 2.5 m·s−1. Moreover, as wind speed increases, the curtain tends to tilt, hindering the effectiveness of its protective action, owing to increased spray interactions and drop coalescence, which reduce air entrainment and inter-phase mass transfer. Experimental runs indicated that, as wind velocity increases up to wcr, the whole air flows entrained by the curtain does not change noticeably. However, the singular flows slightly vary according to the following:

(23)

2

aE =

aU = aD =

1/2

v0 vj

(30)

aUC = aDC = aCU = aCD =

1/2

v0 vj

1 v0 s 2 vj

3.2.1. Air flows As indicated in [19] and confirmed by the here presented experimental runs, in case of wind absence, the air flows near the two sides of the curtain are symmetric, so that one can write:

(21)

(22)

z

v = v0

aC =

3.2. Flow field characterization

Compared with the values of aT calculated from Eq. (8), Eq. (21) provides a conservative estimate since it accounts for both mechanisms of air entrainment along the whole curtain that are not considered in the simplified model. If, as reported in [2,19], s is neglected with respect to ai, Eqs. (15), (17)–(19) and (21) simplify respectively as:

z

(29)

Considering the reference values in Table 1, from Eqs. (16), (25) and (29) one calculates: ζ ≅ 0.025; zj ≅ 0.87 m; aC(zj) = aE(zj) = 0.5 kg⋅s−1. The values of the air flows are comparable with those reported in Table 2, confirming that J phase practically exhausts in the tunnel space, as observed in the experimental runs. In dealing with practical applications, where usually hC ≫ zj, the whole entrained flow-rates can be calculated from Eqs. (27) and (28) as:

3.1.4. Air entrained by gravitational effect Assuming that v = vj after the transition point, the integration of Eq. (1) under the boundary condition ag(zj) = 0 yields:

ag (z ) = 2ke l a vl (z

1 v0 s 2 vj

aDC =

aC (1 2

w )

(34)

Table 3 Inversion velocity. h [m]

(27) (28)

0.49 0.55 0.61 0.67

It can be noticed that in particular, Eq. (28) is no more than an extension of Eq. (20) to the entire curtain, so that it accounts also for the gravity effects acting in J region. 7

s [kg s−1] 0.11

0.14

0.16

0.19

0.22

2.65 2.56 2.57 2.17

2.72 2.56 2.47 2.13

2.79 2.62 2.55 2.23

2.85 2.67 2.62 2.33

2.87 2.69 2.68 2.41

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Table 4 Values of the parameters K g and μ, in Eq. (57), for different absorption mechanisms.

aC (1 + w ) 2

aUC =

a aD = E (1 2 aU =

w *)

aE (1 + w ) 2

w winv

(36)

In particular, when w = wc, we obtain, considering also the reference values in Table 2:

(37)

tan

(38)

in fairly good agreement with the experimental observations. The air flow rates coming out of the curtain can be calculated by means of the Eqs.:

According to flow field measurements, Fig. 2 and Eq. (35) indicate that aUC is composed partly by an invariable term, aC/2, corresponding to the air entering the curtain directly from the compartment U, and partly by a wind dependent term:

a = Cw 2

aOC

(39)

=w

a C (w +

aOC )

aD

aT vx

(40)

w 1 aC (w + va ) + aE va aT 2

0.29

c

0. 28 rad

(44)

aCD vj + aCU ( vj ) = aC vx

(45)

aCD + aCU = aC

(46)

aCU =

aC 1 2

vx a = C (1 vj 2

aCD =

aC v a 1 + x = C (1 + tan ) 2 vj 2

tan )

(47)

(48)

3.3.1. Absorption model Independently of the liquid composition, the region F of the curtain acts as an absorption column of height hF, fed with the molar flow rate of chlorine entrained into the sprays, nC. Since, in practical applications, zj ≪ hF ≅ h, and taking into account that the abatement is not realized only in F region, we assume that the height of the column involved in gas absorption be h. The chlorine balance for a volume element dV of curtain can be written:

(41)

On combining Eqs. (40) and (41), we obtain:

vx =

wcr 1 aC (wc + va ) + aE va vj aT 2

In this section, a rather general model is developed for the absorption of a toxic gaseous component into reacting or non-reacting solutions. The particular case of chlorine abatement is then considered, both as an example of application of the absorption model and to the end of subsequent validation of the model itself.

On the other hand, by definition, we can write:

qx

=

3.3. Spray absorption efficiency

aDC ] va + aOC vOC

1 va ) + aE va 2

c

(43)

From the last two Eqs. one obtains, taking also into account Eq. (43):

due to the air by-passing over the curtain and, subsequently, entrained into it in the downwind region D. The measured air flow rates coming out of the curtain show an opposite and non linear behaviour, if compared with the previous ones. Owing to the asymmetry of the flow field in wind presence, all entrained air acquires a horizontal component of momentum, qx, increasing with w. According to the experimental measurements, the mean velocity of the overcoming air flow, vOC, resulted nearly 2w, while the velocity of the air flows approaching the curtain resulted nearly constant with w. Then, taking into account Eqs. (34)–(37), the horizontal component of the air flow momentum can be written as:

qx = [aU + (aUC

=

vx w 1 = aC (w + va ) + aE va vj vj aT 2

tan

where

w =

vx vz

(35)

(42)

The curtain tilt can be written as: 8

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aC dz a vj

nC dX = rdV = r b ·l· dz = r

where X is the fraction of nC completely absorbed in the volume V, r the absorption rate, rσ the absorption rate for unit interfacial surface and σ the interfacial surface for unit volume. With reference to drops of equal size, and taking into accounts Eq. (29), the interfacial surface for unit volume can be approximately calculated as: p Np

=

VC

=

p Vs VC Vp

p Vs Vp Va

6

a s

s 12 = aC

a s

vl v0

r =

r =

HCr

= K g (py

HCr )

HCr cosh H tanh kl

py 1 kg

H kl

+

µ=1+ (51)

Xc =

(64)

1 1 kg

+

H kl

(65) (66)

1 1+

1H s 2 p Ma

v0 vl

1

exp

6

h Ma 1 H s v0 Kg p 1 + v 2 p Ma vl 0 s

(67)

In order to identify the role of the parameters determining the release mitigation efficiency, we refer to a curtain provided of effective containment capacity, so that the relevant chlorine mass flows are those indicated in the previously mentioned Fig. 3. In this general representation, a fraction of the chlorine escaping downwind the curtain is recycled to the curtain itself, while the remaining one is dispersed into the external environment. The whole system can be considered as a recycle absorber characterized by an intrinsic absorption efficiency of the curtain, Xc, and an overall absorption efficiency of the safety device in chlorine abatement, η. In the following, the flows of chlorine are calculated as a function of Xc, η, and of the air flows deriving from the interaction of the sprays with the surrounding regions U and D. Under steady-state conditions, the chlorine balances for the compartments u and d and the whole system can be written respectively as follows:

(54)

y = yc (1

X)

Ma nc (1 ac

X)

n Cr = c s X s

(55) (56)

rσ can be written as:

nc Ma K g p (1

µX ) (57)

ac

where the proper expressions of K g and μ are reported in Table 4. Using Eqs. (50) and (57), the integration of Eq. (49) yields: Xc

nc a vl dX

0

r ac

1 s v0 = ln 12Ma K g pµ 1 µXc

(58)

from which, in case of physical absorption:

Xc =

h Ma kg p s v0

3.4. Release mitigation

Eqs. (51) and (53) are directly applicable to our experiments. Taking into account that in all the considered situations

h=

12

H s ac 1 H s v0 =1+ p s Ma 2 p Ma vl

(53)

kDr kl

r =

(63)

Then, Eq. (59) can be rewritten:

where

=

exp

K g = Kg =

(52)

r = k g py

+

If no reaction takes place, i.e., dealing with water spray curtain, the absorption rate for interfacial surface unit is provided by Eq. (51), so that, from Table 4 and Eq. (30):

The corresponding absorption rate for unit interfacial surface can be respectively expressed as [21]:

+

1 kg

Xc = 1

rather concentrated solution.

1 kg

DOH Dr H kl

py + HCs

As shown in the discussion section, in all our experiments it resulted Cs ≫ C*s , so that rσ can be expressed in any case by Eq. (52). From Table 4, it follows: K g = kg and μ = 1, so that Eq. (59) can be rewritten as:

(50)

• purely physical absorption; • absorption followed by a first order non-reversible reaction; • absorption followed by an instantaneous non-reversible reaction in a

py

(62)

On the contrary, if Cs ≤ C*s , the absorption rate is calculated as:

On the other hand, rσ depends on the way in which the gas absorption is realized. The following situations are particularly significant, as regarding the abatement of toxic gaseous compounds:

r =

k g p Dr y= y kl DOH

C*s =

(49)

1 1 µ

exp

12

h Ma K g pµ s v0

mUC = mR + mCU

(68)

mCD = mDA + mDC

(69)

mR = mDA + mabs

(70)

Taking into account the composition of the flows leaving the curtain, Eqs. (46) and (47) and the definitions of Xc and η, the following further relations can be written:

(59)

mCU a 1 tan = CU = mCD aCD 1 + tan

In the case of chlorine abatement by means of sodium hydroxide solutions, the absorption rate is significantly enhanced by the reaction: (60) which removes a part of chlorine absorbed in the liquid phase. The kinetic of the whole process is then determined by the rate of the step: (61)

=

(71)

mabs = (mUC + mDC ) Xc

(72)

mDA = mR (1

(73)

)

On combining Eqs. (68)–(73), we obtain the expressions of all chlorine flows:

which can be considered as an instantaneous and non-reversible reaction [21–22], provided that the concentration of the solution of sodium hydroxide, Cs = COH−, exceeds everywhere the limiting value:

mCD = mR 9

(1 Xc ) Xc (1 + )

(74)

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mCU = mR

mDC = mR

(1 Xc ) X c (1 + ) (1 + Xc ) Xc (1 + )

mUC = mR 1 +

(75)

1

(76)

(1 Xc ) X c (1 + )

On assuming that the flows entering the curtain and the circulating ones have the same composition, taking into account Eqs. (35)–(38), we can write: (78)

so that:

mD = mR

(1 + Xc ) X c (1 + )

1

(80)

kg p =

4. Model validation

mf

mf af

Ug

Xc )

(87)

(82)

mCU + mU aCU + aU

(83)

Ma

1/3

a

2 + 0.6

1/2

v

Da

1.5·10 2kmol·m 2s

1

(88)

a

Dg

m (1 + ) 1 Xc m 1 Xc = R = R aC + aE Xc aC X c

Ug

mR = aC + aE

Xc

m 1 = R aC

s

s

X

Chlorine flow

mabs

(89)

General case

mR (1

mCD

mUC

1

Xc 1 + (85)

mD

In case of absence of chlorine recycle downwind the curtain, taking into account Eqs. (33), (46), (47), and Table 5, one can write:

mU

10

mR Xc

0

)

mR

1

Xc 2Xc

mR

1

Xc 2Xc

1

mR

1

Xc 2Xc

(1 X c ) Xc (1 + )

mR

1 + Xc 2Xc

(1 + Xc ) Xc (1 + )

mR 1 + mR

(1 + Xc ) Xc (1 + )

mR 1 +

1

(1 Xc ) X c (1 + )

mR

mR

1

Absence of chlorine recycle downwind the curtain ( =

,min

mR

=

1 1+ 1 mR 1+

mR

2Xp

Xc Xc Xc Xc

(1 Xc ) 1 + Xc

0

mR

1+ 1 + Xc

0

Xc 2Xc

1 + Xp

X c (1 + ) ) 1 + Xc

Xc (1 + ) 1 + Xc

mR

mR

(1 Xc ) Xc (1 + ) (1 Xc ) mR Xc (1 + )

mR

mCU mDC

Absence of wind ( = 0)

(mUC + mDC ) Xc

mDE

(84)

Xc

2nc

Table 5 Analytical formulae of the chlorine flows under different conditions.

In case of wind absence, Eqs. (82) and (83) respectively give, taking into account Eqs. (32) and (33) and Table 5:

(1 + X c ) + 1 Xc

a

By virtue of the Eqs. (55) and (89), the previously mentioned

(81)

m + mD = CD aCD + aD =

Da

Cs = Cs0

On assuming that the circulating flows perfectly mix with those emerging from the curtain, one can write: Dg

(1 + ) + (1 1 + Xc

tan ]

being v ≅ 0.65 m·s the drop terminal velocity. Even though the discrepancy in the mass transfer coefficient estimates obtained by experimental data and theoretical method is nearly 35%, this value can be considered reasonable, in consideration of the number and the kind of variables affecting the results. In order to verify the hypothesis on which the spray absorption efficiency was derived obtaining the previously mentioned Eq. (64), i.e.: Cs Cs , we remark in the following that this condition is verified in any point of the liquid solution. In fact, taking into account Eq. (56) and the stoichiometry of the whole absorption process, Eq. (60), the concentration of alkaline solution corresponding to the fraction X of gas absorbed can be calculated as:

In this section we explore the predictions of the general model, by comparing the calculated values of chlorine concentrations with those obtained by experimental runs in wind tunnel, covering both simple physical absorption (water spray curtain) and combined chemical absorption (spray curtain with NaOH solution at different concentrations). In order to validate the model, the theoretical expressions of the concentration of chlorine in compartments D and U are also needed. Dealing with a curtain exerting an effective protective action, so that mf ≪ af, in connection with any flow f, the corresponding mass fraction of chlorine is calculated as:

m f + af

2mR aE (1 + w ) + aC [1

−1

4.1. Experimental and theoretical values of chlorine concentrations

=

=

(86)

In case of chlorine absorption followed by chemical reaction, the intrinsic abatement efficiency of the curtain is provided by the already mentioned Eq. (64). A fairly good agreement between the calculated and measured chlorine concentrations upwind and downwind the curtain is obtained as shown in the parity plot of Fig. 5. The calculated correlation coefficient for the whole range of experimental runs corresponds to 0.79, with kgp = 2.0⋅10−2 kmol m−2 s−1, evidencing that the fluid-dynamic conditions well approached the optimal ones. According to [23], a theoretical estimate of kg p can be obtained as follows:

(79)

These equations rest on the assumption that chlorine release does not modify the air flows. Since the mitigating action of a curtain could be effective only on releases of moderate strength [17], we can indeed neglect the effects related to momentum and density of the release. Table 5 summarizes the chlorine flows, corresponding to all the discussed situations, i.e., general case, wind absence, no recycle in the downwind region.

f

Ug

2mR 1 Xc w ) + aC [1 + tan ] 1 + Xc

aE (1

4.2. Curtain absorption efficiency with conversion in alkaline solution

(1 X c ) Xc (1 + )

mU = mR 1 +

=

Considering the independency of aE and aE on w, taking into account as well that all laboratory experiments were performed under operative conditions not too far from the optimal ones, we assume in the following calculations that, in the various runs, the values of parameters appearing in aforesaid expressions be close to the reference values reported in Table 2. Since in our experiments, h < zl, the intrinsic abatement efficiency will be calculated by substitution of h/2 for h in Eqs. (64) and (67), in consideration of the different residence times of the chlorine entering the curtain.

(77)

mD a a m a = D = U = U = E = mDC aDC aUC mUC aC

Dg

mR

1+ 1 + Xc

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B. Fabiano et al.

Assuming that, during the experiments with water spray curtain, the value of the transport coefficient kg be comparable with the one corresponding to chemical reaction spray curtains, from Eq. (65) one sees that, under the operating conditions adopted, the resistances to mass transfer in the liquid and in the gaseous phases are comparable, since:

kl = H

1 1 Kg

1 kg

1.1·10 2kmol·m 2s 1atm

1

Additionally kl 1.1·10 4 . According to the penetration theory, which gives numerical results comparable to those obtained by the film theory [21], the following relationship can be adopted to evaluate kl:

kl = 2

Dr · tp

1/2

(92)

Assuming Dr 1.5 × 10 [24] and tp ≅ 0.2 s, we calculate kl ≅ 1.0⋅10−4 m·s−1, a value that agrees fairly well with the previous one. 9

5. Discussion

Fig. 5. Parity plot of downwind and upwind chlorine concentration for the whole range of experiments with curtain height 0.55 and 0.67 m. Experiments with reacting spray curtain compared to Eqs. (86) and (87), with intrinsic abatement efficiency of the curtain provided by Eq. (64).

It must be remarked that the correlation between experimental and calculated values seems fairly good to the purpose of this study, in that it considers all experimental runs. Nevertheless, a more general approach to the chlorine dilution scheme was numerically explored, by taking into accounts also the following items:

condition can be rewritten as:

Cs0

2n c

s

s

Ma nc (1 ac

X+

X)

• a flow of chlorine by-passing over the barrier without any abatement; • the presence of chlorine in the downwind circulating flow; • the progressive dilution of the flows involved in the vortexes, due to

(90)

where 0 ≤ X ≤ Xc and, from Eq. (62):

=

Dr kg p DOH kl

22 kmol· m

m2s 1

3

the mixing with the surrounding air.

One immediately sees that, in the performed experiments, the most stringent constraint on Cs0 is obtained when X = Xc = 1, as:

m m Cs0 > 2 s nc = 2 s UC = 2 s R s s MR s MR

1.2·10 3kmol· m

3

However, the slight improvement of the correlation coefficient so obtained does not justify the model complications due to the introduction of the new variables. Moreover, the model predictions on the release mitigation do not vary significantly. In particular, the overall abatement efficiency of the curtain and, consequently, the chlorine

(91)

Then, the solutions of sodium hydroxide used in all the experimental runs (Cs0 ≥ 0.0625 M) were suitable to ensure the reagent excess in the sprays, so as to attain the theoretical abatement efficiency. 4.3. Physical absorption efficiency of the curtain In order to evaluate mass transfer coefficient kgp from Eq. (67), at least a rough estimate of the parameter μ(H) is firstly needed. Although the Henry constant varies with the molar fraction of the chlorine in the gas phase, for the sake of simplicity we assume that H = 10−2 atm m3 kmol−1, on the basis of experimental results obtained in wind absence, where mabs = mR. With reference, for example, to the conditions still air, curtain height 0.55 m, release rate = 7.2 mg s−1, water flow rate 800 kg h−1 it results:

H=

pyCU Cr , eq

pyCU Cr

p

CU

2, 9 mabs s MR s

<

p

ug MR s

2.9mR

2.2·10 2m3·atm ·kmol

1

s

Fig. 6 shows the parity plot of both upwind and downwind chlorine concentrations under physical absorption conditions. Considering the complex mechanism and the large number of parameters involved, the overall correlation coefficient between experimental and calculated values of chlorine concentration is fairly good and corresponds to 0.83, with the value Kgp = 7.4⋅10−3 kmol m−2 s−1. The corresponding values of the intrinsic absorption efficiency of the curtain, calculated by means of Eq. (67) and comparing the different absorption mechanisms are summarized in Table 6.

Fig. 6. Parity plot of downwind and upwind chlorine concentration for the whole range of experiments with curtain height 0.55 and 0.67 m. Experiments with water spray curtain compared to Eqs. (86) and (87), with intrinsic abatement efficiency of the curtain provided by Eq. (67). 11

Chemical Engineering Journal xxx (xxxx) xxx–xxx

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solution flow rate s, the barrier height h and the barrier location. This item is relevant in presence of obstacles characterized by significant geometrical dimensions (e.g. storage tanks), possibly affecting the fluiddynamic behaviour in the upwind region. According to the condition tested in the wind tunnel, the transition from non-interaction to interaction, between obstacle and vortex, was verified in the range 1.30 < x/h < 1.45. Thus, as a conservative approach, a curtain designed and located according to the conditions h/hr > 2 and xr/ h > 1.5 can effectively minimize the by-pass overcoming of the toxic release, under situations characterized by wind speed lower than the critical one. The solution flow rate can be increased by increasing the spray number and, therefore, the total length of the curtain, possibly installing two barriers “in series”. In dealing with the curtain height and location, we can observe that the increasing of h affects favourably both air entrainment and absorbing efficiency. The spray barrier, on the other hand, must be located in close vicinity of the potential gaseous release source, as mechanical dilution effect decreases as distance from the source increases [23]. At last, it should be noted that the values of some parameters in Eq. (93), as δ, kgp and vl (or ke), can vary remarkably in full-scale installations. The subject which is outside the purpose of the current modelling study, is approached in [19] and is extensively treated in [25], where appropriate scaling criteria are suggested to obtain values of the aforesaid parameters suitable for practical applications.

Table 6 Intrinsic absorption efficiency of the curtain, Xc, in different operating conditions. h

Xc

[m]

Absorption in alkaline solution

Absorption in water

0.55 0.67

0.46 0.53

0.29 0.32

fraction released into the environment, remain nearly the same. This remark is consistent with the observation that the limited chlorine fractions by-passing the curtain are somewhat compensated by the recycle and the partial abatement of the chlorine circulating in the region D. Bearing in mind these considerations, the model here presented, including a simplified approach neglecting chlorine recycle in the downwind region and chlorine by-pass, can be adopted to predict the behaviour of the phenomena here investigated. As already said, the model developed in this work rests on the hypothesis that the vortex in region u be able to entrain completely the gaseous release and mix with it, without formation of any dense cloud. The application of the model to these situations could require some refinements. 5.1. Design problem approach

6. Conclusions

The model here presented can be conveniently adopted to design a fluid curtain suitable to mitigate a curtain release, both under still and windy conditions. In facing a design problem, the formulae in Table 5 and Eq. (86) represent an effective tool, since they respectively give the global efficiency in chlorine abatement, η, the flow-rate of chlorine reaching the external environment, mDA, and the resulting concentration of the toxic cloud released into the atmosphere, ωDg, as a function of the wind intensity and of the intrinsic absorption efficiency of the curtain. According to the aforesaid expressions, the curtain effectiveness slowly decreases when the wind increases from 0 to wcr. A conservative approach to safely design the curtain will refer to the worst situation, where w = wcr. On the other hand, the curtain effectiveness depends on some design parameters, i.e., h, l, s, and v0, which can be chosen in an optimal way, in connection with the problem to be solved. As an example, a typical design problem is the dimensioning of a curtain equipped with an alkaline solution, so that the target chlorine concentration released into the atmosphere be contained into a fixed acceptable level ωlim. Taking into account Eqs. (30), (31) and (71), Eq. (86) can be rewritten as: Dg

=

2mR sv wcr* ) + 2 v0 [1 + tan

sg h (1 v 2l

l

c ] (1 +

c)

(

1

exp 12

)

h Ma kg p s v0

In this paper, a general design methodology is presented for reacting spray curtains suitable to mitigate the risk connected to chlorine releases. In order to evaluate the process, a simple but realistic mathematical model was developed. A fairly good agreement was verified between model results and wind tunnel experimental data obtained simulating a chlorine release mitigated by a liquid spray curtain. The major contribution of this work is a unified analytical description of the complex system of transport and reaction, under both still air and windy conditions. The model can provide a direct input to the design of chemical spray curtain for chlorine abatement, and more generally, the same approach can be equally used for other reactive spray curtain systems. However, in order to obtain more reliable results and a broader possibility of application, there is the need to further refinement the model, accounting in particular for the wind effects at the fullscale and for the influence of scale-up on the different coefficients. References [1] B. Fabiano, F. Currò, From a survey on accidents in the downstream oil industry to the development of a detailed near-miss reporting system, Process Saf. Environ. Prot. 90 (2012) 357–367. [2] P.F.M. Rulkens, A.J.P. Bongers, G.P. Ten Brink, C.P. Guldemond, The application of gas curtains for diluting flammable gas clouds to prevent their ignition, Loss Prevention and Safety Promotion in the Process Industries IV, EFCE Publication Series n. 33, Pergamon Press, U.K., 1983, pp. F15–F25. [3] A.A. Kiss, N. Hüser, K. Leßmann, E.Y. Kenig, Reactive absorption in chemical process industry: a review on current activities, Chem. Eng. J. 213 (2012) 371–391. [4] R. Qi, K.P. Prem, D. Ng, M.A. Rana, G. Yun, M.S. Mannan, Challenges and needs for process safety in the new millennium, Process Saf. Environ. Prot. 90 (2012) 91–100. [5] V.M. Fthenakis, D.N. Blewitt, Mitigation of hydrofluoric acid releases: simulation of the performance of water spraying systems, J. Loss Prevent. Process Ind. 6 (1993) 209–217. [6] M. St-Georges, J.M. Buchlin, M.L. Riethmuller, J.L. Lopez, J. Lieto, F. Griolet, Fundamental multidisciplinary study of liquid sprays for absorption of pollutant or toxic clouds, Trans IChemE 70 (1992) 205–213. [7] E. Palazzi, F. Currò, B. Fabiano, A critical approach to safety equipment and emergency time evaluation based on actual information from the Bhopal gas tragedy, Process Saf. Environ. Prot. 97 (2015) 37–48. [8] X. Shen, J. Zhang, M. Hua, Experimental research on decontamination effect of water curtain containing compound organic acids on the leakage of ammonia, Process Saf. Environ. Prot. 105 (2017) 250–261. [9] M. Hua, X. Shen, J. Zhang, X. Pan, Protective water curtain ammonia absorption efficiency enhancement by inorganic and surfactant additives, Process Saf. Environ. Prot. 116 (2018) 737–744. [10] K.W. Schatz, R.P. Koopman, Water spray mitigation of hydrofluoric acid releases, J.

c

(93) where c

=

1 tan 1 + tan

c

0.55

c

(94)

Eq. (93) shows that the safety condition: Dg

lim

(95)

can be satisfied with different choices of the technical parameters. Nevertheless, it is important to underline that the last ones can be grouped into two classes. The former includes those parameters that can be selected only within a narrow range, outside of which a sharp reduction of the mitigation efficiency is verified (e.g., v0, affecting air entrainment, is to be fixed in proximity of the optimum value resulting from experimental runs). The latter class of design parameters is subjected to less stringent constraints. As an example, we can mention the 12

Chemical Engineering Journal xxx (xxxx) xxx–xxx

B. Fabiano et al. Loss Prevent. Process Ind. 3 (1990) 222–233. [11] J.P. Dimbour, A. Dandrieux, D. Gilbert, G. Dusserre, The use of water sprays for mitigating chlorine gaseous releases escaping from a storage shed, J. Loss Prevent. Process Ind. 16 (2003) 259–269. [12] C. Diaz-Ovalle, R. Vazquez-Roman, R. Lesso-Arroyo, M.S. Mannan, A simplified steady-state model for air, water and steam curtains, J. Loss Prevent. Process Ind. 25 (2012) 974–981. [13] R.N. Meroney, CFD modeling of water spray interaction with dense gas plumes, Atmos. Environ. 54 (2012) 706–713. [14] M. Siddiqui, S. Jayanti, T. Swaminathan, CFD analysis of dense gas dispersion in indoor environment for risk assessment and risk mitigation, J. Hazard. Mater. 209–210 (2012) 177–185. [15] E. Palazzi, F. Currò, B. Fabiano, Mathematical modeling of fluid spray curtains for mitigation of accidental releases, Chem. Eng. Commun. 194 (2007) 446–463. [16] Unichim, M.U. 607:83, UNICHIM ed., Milano, Italy, 1983. [17] J.P. Dimbour, A. Dandrieux, G. Dusserre, Reduction of chlorine concentrations by using a greenbelt, J. Loss Prevent. Process Ind. 15 (2002) 329–334. [18] E. Palazzi, F. Currò, B. Fabiano, n-Compartment mathematical model for transient

[19] [20] [21] [22] [23] [24] [25]

13

evaluation of fluid curtains in mitigating chlorine releases, J. Loss Prevent. Process Ind. 20 (2007) 135–143. E. Palazzi, F. Currò, B. Fabiano, From laboratory simulation to scale-up and design of spray barriers mitigating toxic gaseous releases, Process Saf. Environ. Prot. 87 (2009) 26–34. H. Zhang, B. Bai, L. Liu, H. Sun, J. Yan, Droplet dispersion characteristics of the hollow cone sprays in crossflow, Exp. Therm Fluid Sci. 45 (2013) 25–33. G.F. Froment, K.B. Bischoff, Chemical Reactor Analysis and Design, second ed., John Wiley & Sons, New York, 1990. L.K. Doraiswamy, M.M. Sharma, Heterogeneous Reactions: Analysis, Examples and Reactor Design, Wiley & Sons, New York, 1984, pp. 86–89. J.-M. Buchlin, Mitigation of problem clouds, J. Loss Prevent. Process Ind. 7 (1994) 167–174. S. Foust, L.A. Wenzel, C.W. Clump, L. Manz, L.B. Anderson, Principles of Unit Operations, second ed., John Wiley & Sons, New York, 1980, pp. 482–491. K. Hald, J.-M. Buchlin, A. Dandrieux, G. Dusserre, Heavy gas dispersion by water spray curtains: a research methodology, J. Loss Prevent. Process Ind. 18 (2005) 509–511.