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A theoretical study of absorption of toxic gases by spraying
A theoretical study of absorption gases by spraying
of toxic
V. M. Fthenakis and V. Zakkay* Brookhaven National Laboratory, Upton, NY, USA :l;New York University, New York, NY, USA
The feasibility of controlling toxic gases by absorption using liquid sprays has been examined previously. In this paper the physical and chemical phenomena taking place in a gas-spray environment are described in more detail, and a mathematical model of the interactions is developed. The model was implemented in the PSI-Cell computer code and numerical solutions were obtained for a number of different configurations and spray patterns (i.e. vertical and horizontal co-current and counter-current flow, upwards and downwards cross-flow). The effects of several spray parameters (e.g. flow rate, location and drop-size distribution) and gas parameters (e.g. solubility, chemical reaction rate) were considered. Several simulations of water spraying of specific gases (l-IF, NH3, SO2 and H&) were carried out. The effectiveness of gas removal estimated by the numerical model was found to compare favourably with HF laboratory tests. Favourable agreement was also shown with qualitative field data on NH3 and SO2 spraying. Absorption using water spraying provided an effective means of control for highly water soluble gases with fast ionization reactions in the liquid phase (e.g. HF, NHJ, but it did not result in substantial gas removal when the gases were only moderately water soluble (e.g. SOz). (Keywords:
toxic; gas; ammonia)
It has been shown that unconfined releases of hydrotluoric acid’ and ammonia’ can be effectively controlled in the field by absorption using water sprays. The feasibility of using this type of control for several water soluble gases has been examined theoretically via a simple mass transfer model’. In this paper. the physical and chemical phenomena taking place in a gas-spray environment are described in more detail, and a mathematical model of momentum, mass transfer and chemical reaction in the liquid phase is developed. The model is implemented in the PSI-Cell computer code’. which solves the fundamental gas-phase and drop equations and allows easy integration of the mass transfer model. Simulations of water spraying of specific gases (i.e. HF. NH,, SO2 and HIS) are carried out.
Basics of gas absorption reaction
with chemical
Reactions of gases in liquid drops are important for removal of toxic gases accidentally released in the atmosphere. Solubilities of gases dissolved in a liquid without chemical transformations are usually low, and
mass transfer is controlled by the liquid phase resistance. However, if a rapid chemical reaction occurs in the liquid phase, the rate of absorption can increase to the extent that mass transfer becomes limited only by the gas-phase resistance. A fast, irreversible chemical reaction results in high gas solubility, since it ‘drives’ gas inside the liquid by consuming it. Therefore, it increases the liquid phase mass transfer coefficient and also increases the maximum amount of gas that the liquid can absorb. In stagnant drops, very fast (in comparison to mass transfer) chemical reactions take place in a thin liquid layer at the drop-gas interface (mass transfer controlling mechanism); srow reactions can take place at the bulk of the drop (reaction rate mechanism). However, drops moving in relation to the gas-phase develop internal circulation. which speeds-up the transfer of material to the interior of the drop. This allows, even for fast reactions, development of an almost uniform composition of dissolved species within the drop. Two absorption-related criteria apply to liquid solutions for controlling toxic gas releases: l
l
Rewived 31 August 1989; revised 6 December 1989 Presented at ‘Control of Accidental Releases of Hazardous Gases’, AlChE meeting, Philadelphia, PA, USA, August 1989 095&4230/90,‘020197-10 0 1990 Butterworth &Co.
(PublishersI
Relatively high absorption capacity of the liquid as defined by the ratio of equilibrium concentrations in the liquid and the gas phase. Rapid attainment of equilibrium or a considerable extent towards equilibrium, as defined by the masstransfer coefficients and a characteristic reaction time.
Ltd
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Absorption
of toxic gases by spraying:
V. M. Frhenakis and V. Zakkay
For water soluble species that undergo chemical transformations in the aqueous-phase, both physical and chemical equilibria must be considered to calculate the total removal of species from the gas-phase. Tabulated values for solubility, or Henry’s law coefficients, usually give only the equilibrium amount of the non-ionized dissolved gas. These values should not be used directly to predict the amount of dissolved gas for gases that react rapidly in the aqueous-phase; to evaluate overall mass-transfer for these gases, additional considerations must be made. For rapid reversible reactions (e.g. ionization) this is done by determining a pseudo-Henry’s law coefficient that encompasses the totality of the dissolved speciess. For rapid and irreversible reactions an additional ‘sink’ of species A is estimated from the rate equation of the chemical reaction. Henry’s law equilibrium Many expressions and units of Henry’s law coefficients are found in the literature and there is some confusion as to exactly what these coefficients represent. Most sources do not state whether the reported values correspond to only non-ionized or to total dissolved species. Some clarification is therefore attempted by correlating the two types of coefficients and the different expressions used. Following the work of Schwartz>, pseudo-Henry’s law coefficients were determined by considering physical and chemical equilibria separately. Thus. for a gaseous acid HA (e.g. HF. HCl, HNO,, HCN). physical absorption and hydrolysis are described by the Henry’s law coefficient, H HA(g)&
HA(l)
where H = PHA /[HA (I)]. A pseudo-Henry for the total dissolved species [HA(l)] defined as
coefficient + [A-]. is
H* = ([HA(l);:
H* = Pn,,/]Al =
pw/W,Al
+ [HA -I+ LA=I) [H+]’
=H
( [H+]’ + K,[H+]
+
K,K2
1
As shown in the above expressions, dissolution of these gases in aqueous solutions is strongly affected by the solution pH. Pertinent values of Henry’s law and equilibrium coefficients are shown in Table I. The pseudo-Henry’s law coefficients for these gases are shown in Figure I as a function of the solution pH; it is assumed that the solutions are sufficiently buffered so that their pH does not change during gas absorption.
Table 1 Henry coefficients
and equilibrium
constants
for speci-
fic water soluble gases Equilibrium
Constant” at 25 “C
HF(g) = HFII) HF(I) = H’ + F
H = 2.0 E-6 K = 6.9 E-4
6 6
HNOJg) = HNO,(I) HNOJI) = H. + NOJ=
H = 3.0 E-4 Ic= 15
7 7
NH,(g) = NH,OH NH,OH = NHI’ + OH
H = 0.9 x - 1.87 E-5
9 10
SO,(g) = SO,.H,O SO>.H,O = H * + HSO, HSOJ ; H’ + SO,-
H = 29.0 K, = 1.7 E-Z ~~ = 6.5 E-8
6 6 6
Hz+(g) = &S(I) H,S(I) = HS + HHS =S+H,
H = 540 K, = 1.3 E-7 K~ = 7.1 E-15
8 8 8
CO,(g) = CO,.H,O CO,.H,O = H - + HCO, HCO, = H’ + C03=
H = 1633 I, = 4.3 E-7 up = 1.0 E-14
9 11 11
Ref.
“The Henry’s law coefficient, H, is defined as the ratio of the molar fraction in the gas phase to the molar fraction in the liquid phase, Y/X. The concentration units in the equilibrium constant aremoll ’
P [A-])
From the chemical equilibrium HA(l) - x’ H++A-
a pseudo-Henry’s law coefficient for the total dissolved species [A] = [H,A] + [HA -1 + [A=], is estimated in the same way:
equation
WI
W=KI[H+I
and the pseudo-Henry’s
law coefficient
becomes
LH+]
H*;H
KI +
[H+l
Similarly, for a weak base (e.g. NHj) the equilibrium of water ionization H* = H
kw
k, + KI[H+] For acidic gases of the form H2A. steps (e.g. H2S, H2Se, SOZ, CO?) HzA(g) H?A(I) HA-
198
by considering
which
ionize
in two
$ H,A (1)
-2
2 H++HA$H++A=
J. Loss Prev. Process Ind.,
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4
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Figure 1 Pseudo-Henry’s function of solution pH
1990,
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8
law coefficients
9
10
11
12
of certain gases as a
Absorption As shown for acidic gases in alkaline environment or weak bases in low pH environment, these coefficients can be several orders of magnitude higher than the coefficients based on physical equilibrium only. In these calculations, a dimensionless (volume based) pseudo-Henry’s law coefficient, defined as Y/X (the ratio of molar fractions in the gas and the aqueousphase) was used. Values of H estimated in such a way are numerically equal to values given as atm/X, assuming ideal gas law for the gas phase. Chemical reaction The mass transfer submodel is based on Henry’s law solubility of total dissolved species (as defined by H*), followed by liquid-phase irreversible chemical reaction. Given the relatively short times of interaction between gas and drops, it is important to distinguish several types of chemical reactions based on their speed. A useful measure of this parameter is a characteristic reaction time (t,), as estimated by the ratio of the aqueous-phase concentration of species A to the steady-state flux of the chemical ‘removal’ of A /dc ,
tr = CA/-g
which for a pseudo-first
dc, ___= dt
order
rate equation
of the form
KICA
time reduces to t, = K, -I. To obtain the characteristic of the overall mass-transfer, characteristic times of pertinent physical processes must be considered. Such sample ‘characteristic times are given in Tubfe2. In relation to such times, ionization reactions are so fast that chemical equilibrium can be assumed during the entire time of interaction, as confirmed by data on HF absorption in drops’“. The times in Table2 also indicate that absorption and chemical reaction take place to significant extents when internal circulation and fast chemical reaction take place. A model of fluid dynamics is required to describe this dynamic interaction and also to allow study of several spray parameters (e.g. location, orientation, angle) as well as ambient conditions (e.g. wind speed).
Table 2 Characteristic into aqueous droplets
times pertinent to mass transfer of gases
Process
Characteristic time
Gas-phase diffusion Convective mixing with internal circulation Fast pseudo lSt order rxn Fast irrev. 2nd order rxn Drop free-fall from h = 0.7 m from h = 1.9 m
d2/1 2 D, 25d/u, K, I (K,&) h/cl,
1
Ref.
Equivalent timea (s)
5
10-q
12
0.005 10 5 10 4 0.7 1.9
“Assumed values: D, = 0.23E-04 m*s I; D, = 1.5E-09 mzs 1; d = 2.OE-04 m; II, = (4000d) s ‘; Ce (concentration of reagent B) = 1 M
of toxic gases by spraying:
V. M. Fthenakis and V. Zakkay
Models of spray dynamics In a spray, the drops travel downstream, and drag along the ambient gas inducing a gas motion that then modifies the original drop motion. Subsequent behaviour is governed by the equations of fluid dynamics of a two-phase mixture. The dispersed-drop phase can be handled either as a continuous medium (Eulerian approach) or as individual drops (Lagrangian approach). The models that describe spray fluid dynamics fall into three general categories: single-phase flow; two-phase continuous flow; and fluid-drops separated-phase flow. These models are either based entirely on fundamental equations (e.g. continuity and Navier-Stokes equations). or on empirically derived formulae specific to a particular problem. Simple, one-phase models have been used to describe the spray fluid dynamics in plane (flat, or fan) sprays where the velocity profiles follow similarity laws, but these models are not suitable for mass-transfer and chemical reaction analysis, which requires momentum and mass coupling between two phases. Both twophase and separated-flow models can describe this coupling between the two phases. In two-phase models, drops are described as a continuous fluid interpenetrating and interacting with the gas phase, and only one drop size is considered. This limitation can be removed by using several fields, each representing a class of particle sizes, to describe the spray. However, this dramatically increases the computer requirements. An assumption of similarity leads to a system of ordinary differential equations that are much easier to solve than the original Navier Stokes equations. Yeung14 obtained similarity solutions for plane (flat, or fan) twodimensional sprays by following the turbulent jet analysis of Schlichting”. Van Doornlh also assumed similarity for flat sprays and introduced a semiempirical model for the velocity and shear stress fields in the spray. Both these models showed good agreement with velocity field experimental results. However, similarity solutions have not been established for solid-cone and hollow-cone axisymmetric sprays, which are of practical importance in this study; thus, numerical solutions are required for these cases. Separated-phase flow models treat the liquid drops by a Lagrangian approach, according to which the movement of each drop (from a group of drops representing the spray) within the gas is explicitly followed. This approach allows use of the significant volume of data on gas absorption and chemical reaction in a single drop in greater detail, given the same computational requirements. than two-phase models. Single and multiple drop relationships Single-drop relationships assume that the drops do not perturb the flow velocity field, which is reasonable for studies of gas scavenging by rain, but not for spray systems. Momentum In sprays, drops
carry sufficient
momentum
to entrain
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Absorption
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by spraying:
V. M. Fthenakis
and
V. Zakkay
and set into motion the surrounding gas. In turn, the motion of the gas in the vicinity of the particles reduces the resistance to their motion and allows higher velocities than in the case of a single drop. Another way to describe this effect is by visualizing a wake after each drop, within which the following drop experiences less that drops falling drag. Kleinstreuer et al. I7 estimated in a stream have 15% higher terminal velocity than that of a single drop. In this model, this change in the gas velocity field is described by the relative velocity
circulation pattern. This effect decreases with decreasing drop size and can completely cease when various surfactants are in solution. Several models of drop internal mass transfer predict quite different results. In this study the model proposed by AngeloI was used. since it matches better than other models the recent experimental data of Altwicker and Lindhjem’?.
u,(r) = I*CJ(t) - ug(r) Its effect on the drag coefficient is given corresponding dynamic Reynolds number.
‘Gas-spray’
by
the
Mass transfer
The following considered:
coupled
mass transfer
sub-processes
are
Gas-phase mass transfer to the gas-liquid interface (i.e. forced convection and diffusion); described by a gas-phase mass transfer coefficient (as a function of Sherwood number). Interfacial mass transfer; approximated by Henry’s law equilibrium. Liquid-phase mass transfer coupled with chemical reactions; described by a liquid phase coefficient, k,, and the chemistry inside the drop. Desorption of gas into the gas-phase, if the saturation concentration is exceeded; described by Henry’s law coefficient. The Sherwood number using an expression Pruppacherlx
for the gas-phase proposed by
is estimated Beard and
Sh = 1.61 + 0.718Rei/ZSc’/3 where Sh = k,dfD,p. This expression was foundlY to be valid for drop diameter up to 5 mm. Several other formulae exist for the gas transfer coefficient. but they do not differ considerably. None of these relationships account for the enhancement of mass transfer due to the drop induced turbulence in the air field, which can be about 30% (Ref. 20). Wakes also have an effect on mass transfer, by reducing the concentration each drop ‘meets’ in the wake of the following drop. This is described by a reduced interfacial area estimated from the separation angle of the boundary layer. Drop
internal
These considerations were incorporated into the appropriate fundamental equations of fluid flowZh.“, to derive a model of fluid dynamics and mass transfer for the considered gas-spray systems. The gas-spray model comprises two sets of equations, one describing the gas-phase and another describing the drop-phase. The gas-phase is modelled, by an Eulerean approach, as a continuous fluid with properties changing with space coordinates. The liquid-phase is modelled according to a Lagrangian approach by considering a finite number of particles of varying size and trajectory4. A twodimensional steady-state model was adopted. In parallel flows of gas and drops, two-dimensional cylindrical (x, r) coordinates which describe the axi-symmetric nature of the problem are used; in cross-flow, rectangular coordinates are used to model a non-stagnant gas. Turbulent flow is approximated by the equations of laminar flow with effective properties (i.e. viscosity, thermal conductivity and diffusivity) which vary from place to place”. Gas-phase equations Conservation of mass.
-$-(pu) +f-$(rpu) where M is the change volume and unit time. Conservation
= M
in the mass of the drops per unit
of momentum.
x-component
circulation
When drops move in relation to a surrounding gas medium, internal circulation is induced as a result of external viscous shear forces due to the relative velocity and density. It is known M.*~that water drops falling in air exhibit a vigorous internal circulation. Internal circulation can increase the rate of mass transfer across the interface and into the interior of a drop 5-10 times over that of a non-circulating drop22.23. Although a stagnant drop absorbs a solute gas in a radially symmetric pattern, internal circulation in a moving drop accelerates this transfer by carrying the gas along the drop surface to the rear of the drop, where it is injected into the interior of the drop by the return
200
model description
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The terms F, and F, are the components of the total force which account for the distribution of momentum from the drops, per unit volume. The spatial distribution of these force components is obtained from the solution of the drop-phase equations.
Absorption Conservation
of energy.
+ _k_
a’?
-+Q
cpg ax2 where k is thermal conductivity, cpc is the specific heat of the air mixture and Q is the term representing rate of heat exchange with drops in a unit volume. The gas-phase equations reBoundary conditions. quire boundary conditions. In cylindrical coordinates, the solution regime is bounded by the axis of symmetry and a polar boundary sufficiently away from the origin. In planar coordinates, (cross-flow) bottom wall conditions are used instead of symmetry conditions. At the axis of symmetry (r = 0), both the conditions of symmetry and mass conservation apply: o=O,anddr.-
au a/~,,,a~ ar
-
’ ar’
ak,ff
-=0
ar
The free boundary is taken to be far from the spray region; under this assumption the velocity tangential to the boundary is small and it is set equal to zero. The boundary conditions for the velocity normal to the boundary are obtained from the continuity equation. At the horizontal boundary, r = R,. u = 0, a(ro)/Sr = 0. At the vertical boundary, x = X,, u = 0, au/ax = 0. The turbulent viscosity, pEII. is estimated from the solution of the equations of kinetic turbulent energy and dissipation rate under the assumption that all derivatives &i
by spraying:
V. M. Frhenakis
and
V. Zakkay
equations. For Re numbers greater than 400, experimental dataz8 are used; for lower Re numbers the following equations proposed by Beard and Pruppacherls are used.
of species.
where Y is the molar fraction of transported species A, and W is the sink term representing absorption of A into the drops contained per unit volume. Transport of water vapour in the gas-phase is described by a second equation -of this type. The sum of W terms in the species equations is equal to the source term, M. of the continuity equation. Conservation
of toxic gases
Co = (24/Re)(l
+ 0.11 ReOR1)
Re<21
Co = (24/Re)(l
+ 0.189 Re0.632)
21 < Re < 400
These equations, although derived for drops falling at terminal velocity. also accelerating/ apply to decelerating drops since the effect of acceleration on the drag coefficient is negligibleZR. Mass transfer. The mass sink terms in the gas-phase equations are determined from calculations based on an individual drop. The molar flux of a gas A passing through the surface of a drop is denoted by N,, where
N,
= K,(Y
and the diameter reference
-
Y”)
amount of gas A absorbed by a drop of d during its time of passage (AZ) through the volume is Ai
w
ird?
=
c0
Ks( Y -
Y*)dt
where the superscript * indicates phase equilibrium conditions. K, is the overall mass transfer coefficient based on the gas-phase, and is related to the individual gas and liquid mass-transfer coefficients, k, and k,, by l/K,
= l/k,
+ m/k,
where m denotes the slope of the equilibrium the region between X and Xi: m = (Y*
-
Yi)/(X
curve in
- X,)
Henry’s law describes the equilibrium concentration of gas A within a well-mixed drop. Henry’s law, however, can also be used to describe the concentration jump at the drop-gas interface even for non-equilibrium conditionsLZ. and therefore m = H*. The term W is the total absorption by all drops in the reference volume and is estimated from the double sum over trajectory segments and drops in each segment: nt “p wzCCwil~
1 I
The number of drops of size k, per unit time along trajectory i, is estimated by n 1.k
=
a
(mk/md.k)/nt
where mk is the fraction assigned to size k, and
of the initial
mass flow rate
mj,k = m (total liquid flow rate) k I The build-up of average concentration of the dissolved gas A into the drop can be determined as nt cc
-0 -
The pressure boundary conditions are derived from the momentum equations, by ignoring the viscous terms as relatively small in comparison with the pressure terms.
c,$ 19’ = w
I/**
Droplet-phase equations Momentum transfer. The
described in detail by Crowe tion, the drag coefficients
where trajectory
equations are et ~1.~. For this applicawere changed in these
V = drop volume
= ad3/6. This concentration is depleted reaction with reagent B, according the form (for a second order rate)
J. Loss Prev.
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Ind.,
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1990,
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201
Absorption
of toxic gases by spraying:
V. M. Fthenakis and V. Zakkay
dc, - = K,[A][B] dr
where K, is the reaction rate constant and [A] and [B] the concentrations in the liquid phase of species A and B respectively. This reduction of concentration cA subsequently causes a reduction of Y* and enhances the absorption ofgasA. After each computational step At during which a species A was transferred within the drop according to the liquid-phase mass-transfer submodel, the chemical reaction submodel is called, a new sink source is calculated, and then new gas-phase concentration fields are calculated from the species equation.
Model implementation computer code
in the PSI-Cell
The equations were solved using the PSI-Cell code developed at Washington State University4.‘“, which is based on the single-phase code TEACH originally developed by Gosman and Punx’. The gas-phase differential equations are represented by algebraic equations based on finite differences. The drop trajectories and concentrations were obtained by analytical solutions of the drop momentum and mass transfer equations. Each drop on the computation represents a number of physical drops as determined from the liquid flow rates and the number of computed trajectories and drop sizes. The sums of the drop sink terms were evaluated by the number of drops within each trajectory segment transversed during the integration time interval. and the number of such trajectory segments within each cell. PSI-Cell predictions of the drop induced gas flow fields have shown agreement with both laboratory experimental data” and large scale data3i. In principle, this scheme of computational solution allows tracking of the spatial evolution of drops as they exchange mass, momentum and energy with the gas-phase flow-field, regardless of the direction of drop flow. It allows, therefore, the simulation of several patterns of flow (e.g. cross-flow, upwards and downwards; parallel flow, co-current and counter-current). as well as several sprays in series. On implementing the gas-spray model, changes were made to facilitate such patterns. Other changes include the drag coefficient equations, the floor boundary equations in the cross flow, free-stream boundary conditions and facilitation of outputs that allow 2-D and 3-D graphics. The absorption and chemical reaction submodels were added in subroutine CALPMM and the new subroutines CALCMT and CHEMRXN.
Comparison
of model
estimates
Results of comparison The HF laboratory data used in this comparison were obtained by down-flow of water with one or two sprays in a 1.01 m long, 0.305 m high chambers’. These tests were modelled in a two-dimensional (length-height) configuration (see Figure2). The effectiveness of HF Outlet
Inlet Boundary
Y
k
Figure2 tests
I
I
i
I
Boundary
1
Floor
X Geometry
,ooEffecti,tieness
used for simulation
of the HF laboratory
(%)
:;lFI
with HF data
Simulation of spray nozzle The type of nozzles used in the HF tests were pressure atomizing full cone nozzles. The nozzle parameters used in these simulations were: the nozzle angle; volumetric size distribution; and initial drop velocities.
202
Sets of data for the first two parameters and exit velocities of nozzles were supplied by the manufacturer (Bette-Fog Nozzle Inc). The nozzle velocity data were adjusted for specific test conditions, using the Bernoulli equation. Initial drop velocities were then derived from the nozzle exit velocities assuming that all drops acquire the same tangential initial velocity regardless of their size. For computational purposes the volume-size distribution was discretized to four sizes. In establishing the initial trajectory position the nominal spray angle was used. However, the trajectory angle changes with time due to gravitational and drag effects and interaction with entrained air; these are different for each drop size. Drops of different size move in different trajectories, the bigger drops moving to the outer and the smaller to the inner part of the spray. as described by the momentum equation. It was found that for the small geometrical scale of the HF laboratory tests”’ simulation results were quite sensitive to changes of the drop initial velocity, emphasizing the need for accurate evaluation of nozzle parameters.
J. Loss Prev. Process Ind., 1990, Vol3, April
10
20
30
40
Water / HF ?atlo
50
60
(vol/vol)
Figure3 Effectiveness of water spraying on HF releases as a function of water flow rate. Base case: down-flow; mean volume drop diameter 160 pm; wind speed 1.4 m s ’
Absorption removal was estimated from the change of HF mass rate (kgs-I) from the inlet to the outlet cross section. The results of the laboratory scale simulations are shown in Figures 3-9. Figure 3 shows data and model estimates for different ratios of water volume to liquid HF volume. ‘Gas-Spray A’ corresponds to the actual predictions of the model. ‘Analytical A’ corresponds to the predictions of the previously reported analytical Height
of toxic gases by spraying:
100
Effectiveness
:::
V. M. Fthenakis and V. Zakkay
C%)
n-1
70
(m\
0.3 0.25
-
32
-
30
40
50
60
Water / HF Ratio (vol/vol) 0 15 -X-O 01
Figure 7 Effectiveness of water spraying function of water flow rate for several diameters at wind speed of 1.4 m 5-l
-
00.5
-
on HF releases as a mean volume drop
0 0
31
I? d
0
2
‘)
1
02
Figure4 water/HF diameter
Height
Concentration
volume
profiles
01
0
HF mass
02
0
01
02
fraction
at several
axial
distances
ratio of 13. Base case: mean volume
for drop
’
160 pm; wind speed 1.4 m s
(m)
03
0.25 02 015
,
-
__--__--
X.0.93
-x-o
0' c.1
I
13
-
20
3c
40
i
~A
50
60
Water i HF Ratio jvol/vol) o.c.5
-
0
0
0.1
0.2
0
0.1 0.2 HF mass
0
0.1
0.2
0
0.1
0.2
fractldn
Figure8 Effectiveness of water spraying on HF releases as a function of water flow rate for different wind speeds with mean volume drop diameter of 160 pm
Figure 5 Concentration profiles at several axial distances for waterjHF volume ratio of 26.3. Base case: mean volume drop diameter 160&m; wind speed 1.4 m s ’
Height
Effectiveness so -
(mj
80 70
-
60
-
50
-
-
(%)
L=25
-i-1
40 30
-
20
-
-:::
10
I
0
I
0.1
\
,
0.2
0
0.1
0.2
HF mass
0
01
\
II
0.1
0.2
0
10
0.1
0.2
20
30
43
50
8”
Water / HF Ratlo (d/vol)
fraction
Figure 6 Concentration profiles at several axial distances for water/HF volume ratio of 60. Base case: mean volume drop diameter 160 pm; wind speed 1.4 m s ’
Figure9 Effectiveness of water spraying on HF releases as a function of water flow rate for different nozzle to outlet distances: mean volume drop size 160~m: wind speed 1.4 ms~’
J. Loss Prev. Process Ind., 1990, Vol3, April
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Absorption
of toxic gases by spraying:
V. M. Fthenakis and V. Zakkay
models. Although both models correctly predict the increase of HF absorption effectiveness with increasing model seriously water/liquid HF ratio, the analytical underestimates the experimental data. Using an enhancement factor of 1.3 for the gas-phase mass-transfer coefficient in the gas-spray model, an almost perfect fit of the experimental data was obtained (Gas-Spray B). Sensitivity analysis of all other influential parameters, within their limits of uncertainty, showed that only the gas-phase mass transfer coefficient could have produced such an effect. This k, enhancement could be explained by turbulence in the gas field that is not accounted for in the formula of gas-phase mass-transfer coefficient. Thus, an enhanced k, was used in the rest of the simulations. The analytical model required a mass-transfer enhancement factor of 6 to match the magnitude of the experimental data (Analytical B), which is in agreement with previous results3. b Figures 4-6 show concentration profiles, at several distances in the chamber, for three specific water/HF ratios. It is evident in these plots that the action of the spray extends more in both the horizontal and lateral direction with increasing water flow, although the nozzle angle and drop velocity were the same. Figure 7 shows the effect of varying drop size. The model predicts greater effectiveness for both the 120 pm and 100 pm size drops. The experimental data for 120 pm drops were inconclusive whereas this effect was clear from the 100 pm drops. Figure 8 shows a decreasing effectiveness with increasing wind speed; this effect, however, was not as significant in longer chambers. Figures 9 and 10 show that the absorption effectiveness increases with chamber length, or distance from the nozzle to the exit of the chamber, since the smaller drops are carried by air for considerable distances downwind, while absorbing the gas. This effect may give one possible explanation for the higher effectiveness obtained in the field tests, where a 140 ft long chamber was used32. However, this effect may not be observed in spraying of less water soluble gases
,oc Fffectiveness
where drop saturation may diminish absorption downwind. Preliminary analytical results on spray effectiveness for different gases, as described by their pseudoHenry’s law coefficient and molecular transport properties, are shown in Figure 11. Absorption by water spraying can provide an effective means of control for highly water soluble gases with fast ionization reactions in the liquid phase (e.g. HF, NHs), whereas it is only marginally effective in removing gases that are moderately or slightly water soluble (e.g. SOZ and HIS). For such gases, however, when in gas-phase concentrations high enough that absorption is practically liquidphase controlled, adding a chemical reagent to the water can significantly enhance the effectiveness of absorption. These model estimates depend not only on the parameters examined so far, but on other parameters as well (e.g. initial gas concentration and velocity). The effectiveness of absorption was found to decrease with decreasing initial gas concentration, increasing thickness of the gas layer, and increasing gas velocity. The concentration fields of Figure 12 show this latter effect; in Figures I2a and 12b the ambient air has the same velocity (1.4 ms-I), while the gas layer velocity changes from 1.4 to 5 m s-r. The effect of all parameters can only be studied with exhaustive numerical simulations covering the whole range of parameter values. Several simulations of upwards, co-current, and counter-current flows were also made; these simulations indicate lower absorption effectiveness in these configurations than in down-flow. In co-axial flows the absorption effectiveness was localized around the nozzle (see Figures 13 and 14). However, no general conclusions can be made at this time. Typical simulations of these tests using a 40 x 20 computational grid, 50 trajectories and 4 drop sizes, were taking about 2 min of CPU time on a VAX6340, without Including the energy calculations. evaporation/condensation and gas-phase energy calculations, the total time was ~10 min.
(%) 90 80 70-
6C
60 -
---I-
50 -
t
40.
l-.-
20 4c 0
1
1lJ
22
30 -
---
---
--.
x
25
Distwoe
30
34
from Entrance
(in)
10
38
Figure 10 Effectiveness of water spraying on I-IF releases as a function of nozzle location: chamber length 1.1 m; water/HF ratio 23; mean volume drop size 160 pm; wind speed 1.4 ms-’
204
20
/-1
J. Loss Prev. Process lnd., 1990, Vol3, April
Figure 11 Effectiveness of water soravina on HF releases as a fukction of water flow rate for several g&&: mean volume drop diameter 160 pm; wind speed 1.4 m s-’
of t‘ oxic gases by spraying:
Absorption
Figure 12 Concentration fields in down-flow for two different volume drop size 160 pm; wind speed 1.4 m s ’
Height
gas stream
0.3
a, 1.4 m 5-l; b, 5 ms-‘.
velocities:
Height
(m)
V. M. Fthenakis and V. Zakkay
Water/HF
ratio 30; mean
(m) 0.3
o’z6~s !_; x-cc?
0.25
x-0.I
0.2
0.2
0 15
0.15
4”
0.1
0.1
0.05
0.05
- __
0
0 0
0.1
0.2
0
H;
0.1
mass
0.2
0
0.1
0
0.2
0.2
0
0.1
HF mass
fraction
Figure 13 Co-current flow. Concentration profiles at several axial distances for water/HF volume ratio of 13: mean volume drop diameter 160 pm: wind speed 1.4 m s-’
0.1
0.2
0
0.1
0.2
fraction
Figure 14 Co-current flow. Concentration profiles at several axial distances for water/HF volume ratio o: 26.3: mean volume drop diameter 160 pm; wind speed 1.4 m s-l
Conclusions
Acknowledgements
The effectiveness of absorption of toxic gases by water spraying was analysed for several spray parameters (flow rate. orientation, drop-size distribution). and gas parameters (solubility, chemical reaction rate). For gases that ionize in the liquid phase, water spraying provides an effective means of control, whereas this effect is only marginal for moderately soluble gases. The presented gas-spray model correctly predicts the effects determined in the HF laboratory experimentG. The effectiveness of HF removal increases with increasing water flow rate, decreasing drop size, and decreasing wind speed. There are. however. several more parameters that have an influence on this effectiveness. More exhaustive parametric studies are required to enable comparisons between different configurations, gases and chemical reagents.
The authors wish to thank C. T. Crowe of Washington State University for providing the PSI-Cell program, K. W. Schatz of Mobil R&D Corp. for providing the HF data, T. Bassett of Bette-Fog Nozzle Inc. for supplying nozzle data, and S. Morris, P. Moskowitz and L. D. Hamilton for helpful comments. One of the authors (V.F.) gratefully acknowledges partial support from the Photovoltaic Energy Division, Conservation and Renewable Energy, US Department of Energy.
References I
Blewitt, D. N., Yohn. J. F., Koopman, R. P., et al. P ‘ roceedings of the International Conference on Vapour Cloud Modelling’, (Ed. J. Woodward), AIChE, USA, 1987. pp. 155-171 2 Greiner. M. L.. Plant/Operations Progress 1984,3(2), 66 3 Ahenakis. V. M. Chem. Eng. Comm. 19X9,83,173
J. Loss Prev. Process Ind., 1990, Vol3, April
205
Absorption
of toxic gases
by spraying:
V. M. Fthenakis
4 Crow. C. T.. Sharma, M. P. and Stock. D. E. J. Fluid Eng. 1977,99(2), 325 S Schwartz, S. E. ‘Chemistry of Multiphase Atmospheric Systems’. (Ed. W. Jaeschke), NATO ASI Series, Volume Gh, SpringerVerlag, Berlin. FRG, 1986 6 Sillen. L. G. and Martell, A. E. ‘Stability constants of metal ion complexes’ Chem. Sot. Land. Spec., 1964. publ. no 17 7 Schwartz, S. E. and White, W. H. in ‘Adv. in Envir. SC. & Eng.‘. (Eds. J. R. Pfafflin and E. N. Ziegler), Volume 4, Gordon & Breach, 1981 8 Perry, R. H.. and Green, D. W. in ‘Perry’s Chemical Engineers’ Handbook’. 61h Edition, 1984 9 Morgan. 0. M. and Maas, 0. Can. J. Res. 1931.5, 162 10 Robinson. R. A. and Stokes, R. H. in ‘Electrolytic Solutions’ 2nd edition. Butterworth Scientific, Guildford. UK. 1970 11 Pinsent, B. R. W., Pearson, L. and Roughton, F. _I. W. Trans. Far. Sm. 1956.52. 1.512 12 Slinn. W. G. N. ‘Atmospheric Science and Power Production’. DOE/TIC-276UI. 1984 13 ‘Gmelin Handbook of Inorganic Chemistry, Fluorine Supplement’ Volume 3, Springer-Verlag, Berlin. FRG, 1982. p. 246 14 Yeung, W.-S. .I. Applied Mechanics 1982.49,687 15 Sihlichting, H. in ‘Boundary Layer Theory’. 7”’ Edition. McGraw Hill. New York, USA, 1979 16 Van Doom. M. Ph.D. Thesis Delft University of Technology, Netherlands. 1981 17 Kleinstreuer. C., Ramachandran. R. S. and Altwicker. E. R. Chew. Eng. J. 1985.30.45 18 Beard, K. V., and Pruppacher, H. R. J. Amos. SC. 1971, 28. 1455 19 Walcek. C. J. and Pruppacher, H. R. _I. Atmr,s. Chemi.vtry 1984, 1.269 20 Clift. R.. Grace. J. R. and Weber. M. E. in ‘Bubbles. Drops and Particles’. Academic Press, NY. USA. 1978 21 LeClair. B. P., Hamielec, A. E.. Pruppacher. H. R. and Hall. W. D. J. Amos. SC 1972.29.728 22 Harriet. P. Canadian .I. of Chem. Eng. 1962. April. 60 23 Tyroler. G. A.. Hamielec. E.. Johnson. A. 1. and Leclair. B. P. Gun. J. Chew. Eng. 1971.49.56 24 Angelo. J. B.. Lightfoot. E. N.. and Howard. D. W. AlChE J. 1966. 12(4), 751 2.5 Altwickcr, E. R.. and Lindhjem. C. E. AIChE 1. 1980.34(2), 329 26 Bird. R. B.. Stewart. W. E.. and Lightfoot, E. ?1. in ‘Transport Phenomena’. Wiley. NY, USA, 1960 27 Zakkay. V.. Krause. E. and Woo. S. D. L. AIAA J. 1964.2( II). 1939 28 Buzzard. J. L.. and Nedderman. R. M. Chem. Eng. Sri. 1967.22. I577 29 Crowe. C. T. in ‘Advances in Drying’. (Ed. A. Mujumdar) Volume I. Hemisphere. NY. USA. 1980, p. 63 31) Gosman. A. D.,.and Pun. W. M. ‘Calc&ation of Recirculating Flows’. Imperial College of Science and Technology. London, UK. 1973
206
J. Loss Prev.
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Ind.,
1990,
Vol3,
April
and
V. Zakkay
31 Albert. R. L. and Mathews. M. K. ‘Polyphase Flow and Transport Technology’ ASME. NY, USA, 1980. pp. 1 IS- 128 32 Schatz. K. W. and Koopman, R. P. ‘Industry Cooperative HF Mitigation/Assessment Program’, final draft, Volume 1. June 1989
Nomenclature a
zi D H
k, k, K, m M P RC SC Sh t 0 x X v Y Y* x Kw !r Y P
interfacial area per unit volume (mm’) ‘bulk’ gas concentration (kg mol m -“) drop median diameter (m) diffusivity (m?s-‘) Henry’s law coefficient gas-phase mass-transfer coefficient (kg mol m-? s-l) liquid-phase mass-transfer coefficient (kgmol m-I s-l) overall mass-transfer coefficient based on the gas-phase driving force (kg mol m -I s -I) slope of equihbrium curve mass rate (kgm-” s-l) pressure (kgrn-‘~-~) Reynolds number Schmidt number Sherwood number gas-drop contact time (s) drop velocity (m s-l) denotes horizontal direction molar fraction of component A in the liquid-phase denotes vertical direction molar fraction of component A in the gas-phase molar fraction of component A in the gas-phase in equilibrium with A m the liquid-phase equilibrium constant equilibrium constant of water ionization viscosity kinematic viscosity (m’s_‘) air/gas density (kg rnmJ)
Subscripts A eff i :! 1 2 nt “P
denotes denotes denotes denotes denotes denotes denotes number number
gaseous component effective interface gas-phase liquid-phase forward reaction reverse reaction of trajectories of drops
A
of toxic
V. M. Fthenakis and V. Zakkay* Brookhaven National Laboratory, Upton, NY, USA :l;New York University, New York, NY, USA
The feasibility of controlling toxic gases by absorption using liquid sprays has been examined previously. In this paper the physical and chemical phenomena taking place in a gas-spray environment are described in more detail, and a mathematical model of the interactions is developed. The model was implemented in the PSI-Cell computer code and numerical solutions were obtained for a number of different configurations and spray patterns (i.e. vertical and horizontal co-current and counter-current flow, upwards and downwards cross-flow). The effects of several spray parameters (e.g. flow rate, location and drop-size distribution) and gas parameters (e.g. solubility, chemical reaction rate) were considered. Several simulations of water spraying of specific gases (l-IF, NH3, SO2 and H&) were carried out. The effectiveness of gas removal estimated by the numerical model was found to compare favourably with HF laboratory tests. Favourable agreement was also shown with qualitative field data on NH3 and SO2 spraying. Absorption using water spraying provided an effective means of control for highly water soluble gases with fast ionization reactions in the liquid phase (e.g. HF, NHJ, but it did not result in substantial gas removal when the gases were only moderately water soluble (e.g. SOz). (Keywords:
toxic; gas; ammonia)
It has been shown that unconfined releases of hydrotluoric acid’ and ammonia’ can be effectively controlled in the field by absorption using water sprays. The feasibility of using this type of control for several water soluble gases has been examined theoretically via a simple mass transfer model’. In this paper. the physical and chemical phenomena taking place in a gas-spray environment are described in more detail, and a mathematical model of momentum, mass transfer and chemical reaction in the liquid phase is developed. The model is implemented in the PSI-Cell computer code’. which solves the fundamental gas-phase and drop equations and allows easy integration of the mass transfer model. Simulations of water spraying of specific gases (i.e. HF. NH,, SO2 and HIS) are carried out.
Basics of gas absorption reaction
with chemical
Reactions of gases in liquid drops are important for removal of toxic gases accidentally released in the atmosphere. Solubilities of gases dissolved in a liquid without chemical transformations are usually low, and
mass transfer is controlled by the liquid phase resistance. However, if a rapid chemical reaction occurs in the liquid phase, the rate of absorption can increase to the extent that mass transfer becomes limited only by the gas-phase resistance. A fast, irreversible chemical reaction results in high gas solubility, since it ‘drives’ gas inside the liquid by consuming it. Therefore, it increases the liquid phase mass transfer coefficient and also increases the maximum amount of gas that the liquid can absorb. In stagnant drops, very fast (in comparison to mass transfer) chemical reactions take place in a thin liquid layer at the drop-gas interface (mass transfer controlling mechanism); srow reactions can take place at the bulk of the drop (reaction rate mechanism). However, drops moving in relation to the gas-phase develop internal circulation. which speeds-up the transfer of material to the interior of the drop. This allows, even for fast reactions, development of an almost uniform composition of dissolved species within the drop. Two absorption-related criteria apply to liquid solutions for controlling toxic gas releases: l
l
Rewived 31 August 1989; revised 6 December 1989 Presented at ‘Control of Accidental Releases of Hazardous Gases’, AlChE meeting, Philadelphia, PA, USA, August 1989 095&4230/90,‘020197-10 0 1990 Butterworth &Co.
(PublishersI
Relatively high absorption capacity of the liquid as defined by the ratio of equilibrium concentrations in the liquid and the gas phase. Rapid attainment of equilibrium or a considerable extent towards equilibrium, as defined by the masstransfer coefficients and a characteristic reaction time.
Ltd
J. Loss Prev. Process Ind., 1990, Vol3. April
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Absorption
of toxic gases by spraying:
V. M. Frhenakis and V. Zakkay
For water soluble species that undergo chemical transformations in the aqueous-phase, both physical and chemical equilibria must be considered to calculate the total removal of species from the gas-phase. Tabulated values for solubility, or Henry’s law coefficients, usually give only the equilibrium amount of the non-ionized dissolved gas. These values should not be used directly to predict the amount of dissolved gas for gases that react rapidly in the aqueous-phase; to evaluate overall mass-transfer for these gases, additional considerations must be made. For rapid reversible reactions (e.g. ionization) this is done by determining a pseudo-Henry’s law coefficient that encompasses the totality of the dissolved speciess. For rapid and irreversible reactions an additional ‘sink’ of species A is estimated from the rate equation of the chemical reaction. Henry’s law equilibrium Many expressions and units of Henry’s law coefficients are found in the literature and there is some confusion as to exactly what these coefficients represent. Most sources do not state whether the reported values correspond to only non-ionized or to total dissolved species. Some clarification is therefore attempted by correlating the two types of coefficients and the different expressions used. Following the work of Schwartz>, pseudo-Henry’s law coefficients were determined by considering physical and chemical equilibria separately. Thus. for a gaseous acid HA (e.g. HF. HCl, HNO,, HCN). physical absorption and hydrolysis are described by the Henry’s law coefficient, H HA(g)&
HA(l)
where H = PHA /[HA (I)]. A pseudo-Henry for the total dissolved species [HA(l)] defined as
coefficient + [A-]. is
H* = ([HA(l);:
H* = Pn,,/]Al =
pw/W,Al
+ [HA -I+ LA=I) [H+]’
=H
( [H+]’ + K,[H+]
+
K,K2
1
As shown in the above expressions, dissolution of these gases in aqueous solutions is strongly affected by the solution pH. Pertinent values of Henry’s law and equilibrium coefficients are shown in Table I. The pseudo-Henry’s law coefficients for these gases are shown in Figure I as a function of the solution pH; it is assumed that the solutions are sufficiently buffered so that their pH does not change during gas absorption.
Table 1 Henry coefficients
and equilibrium
constants
for speci-
fic water soluble gases Equilibrium
Constant” at 25 “C
HF(g) = HFII) HF(I) = H’ + F
H = 2.0 E-6 K = 6.9 E-4
6 6
HNOJg) = HNO,(I) HNOJI) = H. + NOJ=
H = 3.0 E-4 Ic= 15
7 7
NH,(g) = NH,OH NH,OH = NHI’ + OH
H = 0.9 x - 1.87 E-5
9 10
SO,(g) = SO,.H,O SO>.H,O = H * + HSO, HSOJ ; H’ + SO,-
H = 29.0 K, = 1.7 E-Z ~~ = 6.5 E-8
6 6 6
Hz+(g) = &S(I) H,S(I) = HS + HHS =S+H,
H = 540 K, = 1.3 E-7 K~ = 7.1 E-15
8 8 8
CO,(g) = CO,.H,O CO,.H,O = H - + HCO, HCO, = H’ + C03=
H = 1633 I, = 4.3 E-7 up = 1.0 E-14
9 11 11
Ref.
“The Henry’s law coefficient, H, is defined as the ratio of the molar fraction in the gas phase to the molar fraction in the liquid phase, Y/X. The concentration units in the equilibrium constant aremoll ’
P [A-])
From the chemical equilibrium HA(l) - x’ H++A-
a pseudo-Henry’s law coefficient for the total dissolved species [A] = [H,A] + [HA -1 + [A=], is estimated in the same way:
equation
WI
W=KI[H+I
and the pseudo-Henry’s
law coefficient
becomes
LH+]
H*;H
KI +
[H+l
Similarly, for a weak base (e.g. NHj) the equilibrium of water ionization H* = H
kw
k, + KI[H+] For acidic gases of the form H2A. steps (e.g. H2S, H2Se, SOZ, CO?) HzA(g) H?A(I) HA-
198
by considering
which
ionize
in two
$ H,A (1)
-2
2 H++HA$H++A=
J. Loss Prev. Process Ind.,
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4
5
Figure 1 Pseudo-Henry’s function of solution pH
1990,
Vol3, April
6
8
law coefficients
9
10
11
12
of certain gases as a
Absorption As shown for acidic gases in alkaline environment or weak bases in low pH environment, these coefficients can be several orders of magnitude higher than the coefficients based on physical equilibrium only. In these calculations, a dimensionless (volume based) pseudo-Henry’s law coefficient, defined as Y/X (the ratio of molar fractions in the gas and the aqueousphase) was used. Values of H estimated in such a way are numerically equal to values given as atm/X, assuming ideal gas law for the gas phase. Chemical reaction The mass transfer submodel is based on Henry’s law solubility of total dissolved species (as defined by H*), followed by liquid-phase irreversible chemical reaction. Given the relatively short times of interaction between gas and drops, it is important to distinguish several types of chemical reactions based on their speed. A useful measure of this parameter is a characteristic reaction time (t,), as estimated by the ratio of the aqueous-phase concentration of species A to the steady-state flux of the chemical ‘removal’ of A /dc ,
tr = CA/-g
which for a pseudo-first
dc, ___= dt
order
rate equation
of the form
KICA
time reduces to t, = K, -I. To obtain the characteristic of the overall mass-transfer, characteristic times of pertinent physical processes must be considered. Such sample ‘characteristic times are given in Tubfe2. In relation to such times, ionization reactions are so fast that chemical equilibrium can be assumed during the entire time of interaction, as confirmed by data on HF absorption in drops’“. The times in Table2 also indicate that absorption and chemical reaction take place to significant extents when internal circulation and fast chemical reaction take place. A model of fluid dynamics is required to describe this dynamic interaction and also to allow study of several spray parameters (e.g. location, orientation, angle) as well as ambient conditions (e.g. wind speed).
Table 2 Characteristic into aqueous droplets
times pertinent to mass transfer of gases
Process
Characteristic time
Gas-phase diffusion Convective mixing with internal circulation Fast pseudo lSt order rxn Fast irrev. 2nd order rxn Drop free-fall from h = 0.7 m from h = 1.9 m
d2/1 2 D, 25d/u, K, I (K,&) h/cl,
1
Ref.
Equivalent timea (s)
5
10-q
12
0.005 10 5 10 4 0.7 1.9
“Assumed values: D, = 0.23E-04 m*s I; D, = 1.5E-09 mzs 1; d = 2.OE-04 m; II, = (4000d) s ‘; Ce (concentration of reagent B) = 1 M
of toxic gases by spraying:
V. M. Fthenakis and V. Zakkay
Models of spray dynamics In a spray, the drops travel downstream, and drag along the ambient gas inducing a gas motion that then modifies the original drop motion. Subsequent behaviour is governed by the equations of fluid dynamics of a two-phase mixture. The dispersed-drop phase can be handled either as a continuous medium (Eulerian approach) or as individual drops (Lagrangian approach). The models that describe spray fluid dynamics fall into three general categories: single-phase flow; two-phase continuous flow; and fluid-drops separated-phase flow. These models are either based entirely on fundamental equations (e.g. continuity and Navier-Stokes equations). or on empirically derived formulae specific to a particular problem. Simple, one-phase models have been used to describe the spray fluid dynamics in plane (flat, or fan) sprays where the velocity profiles follow similarity laws, but these models are not suitable for mass-transfer and chemical reaction analysis, which requires momentum and mass coupling between two phases. Both twophase and separated-flow models can describe this coupling between the two phases. In two-phase models, drops are described as a continuous fluid interpenetrating and interacting with the gas phase, and only one drop size is considered. This limitation can be removed by using several fields, each representing a class of particle sizes, to describe the spray. However, this dramatically increases the computer requirements. An assumption of similarity leads to a system of ordinary differential equations that are much easier to solve than the original Navier Stokes equations. Yeung14 obtained similarity solutions for plane (flat, or fan) twodimensional sprays by following the turbulent jet analysis of Schlichting”. Van Doornlh also assumed similarity for flat sprays and introduced a semiempirical model for the velocity and shear stress fields in the spray. Both these models showed good agreement with velocity field experimental results. However, similarity solutions have not been established for solid-cone and hollow-cone axisymmetric sprays, which are of practical importance in this study; thus, numerical solutions are required for these cases. Separated-phase flow models treat the liquid drops by a Lagrangian approach, according to which the movement of each drop (from a group of drops representing the spray) within the gas is explicitly followed. This approach allows use of the significant volume of data on gas absorption and chemical reaction in a single drop in greater detail, given the same computational requirements. than two-phase models. Single and multiple drop relationships Single-drop relationships assume that the drops do not perturb the flow velocity field, which is reasonable for studies of gas scavenging by rain, but not for spray systems. Momentum In sprays, drops
carry sufficient
momentum
to entrain
J. Loss Prev. Process Ind., 1990, Vol3, April
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Absorption
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by spraying:
V. M. Fthenakis
and
V. Zakkay
and set into motion the surrounding gas. In turn, the motion of the gas in the vicinity of the particles reduces the resistance to their motion and allows higher velocities than in the case of a single drop. Another way to describe this effect is by visualizing a wake after each drop, within which the following drop experiences less that drops falling drag. Kleinstreuer et al. I7 estimated in a stream have 15% higher terminal velocity than that of a single drop. In this model, this change in the gas velocity field is described by the relative velocity
circulation pattern. This effect decreases with decreasing drop size and can completely cease when various surfactants are in solution. Several models of drop internal mass transfer predict quite different results. In this study the model proposed by AngeloI was used. since it matches better than other models the recent experimental data of Altwicker and Lindhjem’?.
u,(r) = I*CJ(t) - ug(r) Its effect on the drag coefficient is given corresponding dynamic Reynolds number.
‘Gas-spray’
by
the
Mass transfer
The following considered:
coupled
mass transfer
sub-processes
are
Gas-phase mass transfer to the gas-liquid interface (i.e. forced convection and diffusion); described by a gas-phase mass transfer coefficient (as a function of Sherwood number). Interfacial mass transfer; approximated by Henry’s law equilibrium. Liquid-phase mass transfer coupled with chemical reactions; described by a liquid phase coefficient, k,, and the chemistry inside the drop. Desorption of gas into the gas-phase, if the saturation concentration is exceeded; described by Henry’s law coefficient. The Sherwood number using an expression Pruppacherlx
for the gas-phase proposed by
is estimated Beard and
Sh = 1.61 + 0.718Rei/ZSc’/3 where Sh = k,dfD,p. This expression was foundlY to be valid for drop diameter up to 5 mm. Several other formulae exist for the gas transfer coefficient. but they do not differ considerably. None of these relationships account for the enhancement of mass transfer due to the drop induced turbulence in the air field, which can be about 30% (Ref. 20). Wakes also have an effect on mass transfer, by reducing the concentration each drop ‘meets’ in the wake of the following drop. This is described by a reduced interfacial area estimated from the separation angle of the boundary layer. Drop
internal
These considerations were incorporated into the appropriate fundamental equations of fluid flowZh.“, to derive a model of fluid dynamics and mass transfer for the considered gas-spray systems. The gas-spray model comprises two sets of equations, one describing the gas-phase and another describing the drop-phase. The gas-phase is modelled, by an Eulerean approach, as a continuous fluid with properties changing with space coordinates. The liquid-phase is modelled according to a Lagrangian approach by considering a finite number of particles of varying size and trajectory4. A twodimensional steady-state model was adopted. In parallel flows of gas and drops, two-dimensional cylindrical (x, r) coordinates which describe the axi-symmetric nature of the problem are used; in cross-flow, rectangular coordinates are used to model a non-stagnant gas. Turbulent flow is approximated by the equations of laminar flow with effective properties (i.e. viscosity, thermal conductivity and diffusivity) which vary from place to place”. Gas-phase equations Conservation of mass.
-$-(pu) +f-$(rpu) where M is the change volume and unit time. Conservation
= M
in the mass of the drops per unit
of momentum.
x-component
circulation
When drops move in relation to a surrounding gas medium, internal circulation is induced as a result of external viscous shear forces due to the relative velocity and density. It is known M.*~that water drops falling in air exhibit a vigorous internal circulation. Internal circulation can increase the rate of mass transfer across the interface and into the interior of a drop 5-10 times over that of a non-circulating drop22.23. Although a stagnant drop absorbs a solute gas in a radially symmetric pattern, internal circulation in a moving drop accelerates this transfer by carrying the gas along the drop surface to the rear of the drop, where it is injected into the interior of the drop by the return
200
model description
J. Loss Prev.
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The terms F, and F, are the components of the total force which account for the distribution of momentum from the drops, per unit volume. The spatial distribution of these force components is obtained from the solution of the drop-phase equations.
Absorption Conservation
of energy.
+ _k_
a’?
-+Q
cpg ax2 where k is thermal conductivity, cpc is the specific heat of the air mixture and Q is the term representing rate of heat exchange with drops in a unit volume. The gas-phase equations reBoundary conditions. quire boundary conditions. In cylindrical coordinates, the solution regime is bounded by the axis of symmetry and a polar boundary sufficiently away from the origin. In planar coordinates, (cross-flow) bottom wall conditions are used instead of symmetry conditions. At the axis of symmetry (r = 0), both the conditions of symmetry and mass conservation apply: o=O,anddr.-
au a/~,,,a~ ar
-
’ ar’
ak,ff
-=0
ar
The free boundary is taken to be far from the spray region; under this assumption the velocity tangential to the boundary is small and it is set equal to zero. The boundary conditions for the velocity normal to the boundary are obtained from the continuity equation. At the horizontal boundary, r = R,. u = 0, a(ro)/Sr = 0. At the vertical boundary, x = X,, u = 0, au/ax = 0. The turbulent viscosity, pEII. is estimated from the solution of the equations of kinetic turbulent energy and dissipation rate under the assumption that all derivatives &i
by spraying:
V. M. Frhenakis
and
V. Zakkay
equations. For Re numbers greater than 400, experimental dataz8 are used; for lower Re numbers the following equations proposed by Beard and Pruppacherls are used.
of species.
where Y is the molar fraction of transported species A, and W is the sink term representing absorption of A into the drops contained per unit volume. Transport of water vapour in the gas-phase is described by a second equation -of this type. The sum of W terms in the species equations is equal to the source term, M. of the continuity equation. Conservation
of toxic gases
Co = (24/Re)(l
+ 0.11 ReOR1)
Re<21
Co = (24/Re)(l
+ 0.189 Re0.632)
21 < Re < 400
These equations, although derived for drops falling at terminal velocity. also accelerating/ apply to decelerating drops since the effect of acceleration on the drag coefficient is negligibleZR. Mass transfer. The mass sink terms in the gas-phase equations are determined from calculations based on an individual drop. The molar flux of a gas A passing through the surface of a drop is denoted by N,, where
N,
= K,(Y
and the diameter reference
-
Y”)
amount of gas A absorbed by a drop of d during its time of passage (AZ) through the volume is Ai
w
ird?
=
c0
Ks( Y -
Y*)dt
where the superscript * indicates phase equilibrium conditions. K, is the overall mass transfer coefficient based on the gas-phase, and is related to the individual gas and liquid mass-transfer coefficients, k, and k,, by l/K,
= l/k,
+ m/k,
where m denotes the slope of the equilibrium the region between X and Xi: m = (Y*
-
Yi)/(X
curve in
- X,)
Henry’s law describes the equilibrium concentration of gas A within a well-mixed drop. Henry’s law, however, can also be used to describe the concentration jump at the drop-gas interface even for non-equilibrium conditionsLZ. and therefore m = H*. The term W is the total absorption by all drops in the reference volume and is estimated from the double sum over trajectory segments and drops in each segment: nt “p wzCCwil~
1 I
The number of drops of size k, per unit time along trajectory i, is estimated by n 1.k
=
a
(mk/md.k)/nt
where mk is the fraction assigned to size k, and
of the initial
mass flow rate
mj,k = m (total liquid flow rate) k I The build-up of average concentration of the dissolved gas A into the drop can be determined as nt cc
-0 -
The pressure boundary conditions are derived from the momentum equations, by ignoring the viscous terms as relatively small in comparison with the pressure terms.
c,$ 19’ = w
I/**
Droplet-phase equations Momentum transfer. The
described in detail by Crowe tion, the drag coefficients
where trajectory
equations are et ~1.~. For this applicawere changed in these
V = drop volume
= ad3/6. This concentration is depleted reaction with reagent B, according the form (for a second order rate)
J. Loss Prev.
Process
Ind.,
because of chemical to a rate equation of
1990,
Vol3,
April
201
Absorption
of toxic gases by spraying:
V. M. Fthenakis and V. Zakkay
dc, - = K,[A][B] dr
where K, is the reaction rate constant and [A] and [B] the concentrations in the liquid phase of species A and B respectively. This reduction of concentration cA subsequently causes a reduction of Y* and enhances the absorption ofgasA. After each computational step At during which a species A was transferred within the drop according to the liquid-phase mass-transfer submodel, the chemical reaction submodel is called, a new sink source is calculated, and then new gas-phase concentration fields are calculated from the species equation.
Model implementation computer code
in the PSI-Cell
The equations were solved using the PSI-Cell code developed at Washington State University4.‘“, which is based on the single-phase code TEACH originally developed by Gosman and Punx’. The gas-phase differential equations are represented by algebraic equations based on finite differences. The drop trajectories and concentrations were obtained by analytical solutions of the drop momentum and mass transfer equations. Each drop on the computation represents a number of physical drops as determined from the liquid flow rates and the number of computed trajectories and drop sizes. The sums of the drop sink terms were evaluated by the number of drops within each trajectory segment transversed during the integration time interval. and the number of such trajectory segments within each cell. PSI-Cell predictions of the drop induced gas flow fields have shown agreement with both laboratory experimental data” and large scale data3i. In principle, this scheme of computational solution allows tracking of the spatial evolution of drops as they exchange mass, momentum and energy with the gas-phase flow-field, regardless of the direction of drop flow. It allows, therefore, the simulation of several patterns of flow (e.g. cross-flow, upwards and downwards; parallel flow, co-current and counter-current). as well as several sprays in series. On implementing the gas-spray model, changes were made to facilitate such patterns. Other changes include the drag coefficient equations, the floor boundary equations in the cross flow, free-stream boundary conditions and facilitation of outputs that allow 2-D and 3-D graphics. The absorption and chemical reaction submodels were added in subroutine CALPMM and the new subroutines CALCMT and CHEMRXN.
Comparison
of model
estimates
Results of comparison The HF laboratory data used in this comparison were obtained by down-flow of water with one or two sprays in a 1.01 m long, 0.305 m high chambers’. These tests were modelled in a two-dimensional (length-height) configuration (see Figure2). The effectiveness of HF Outlet
Inlet Boundary
Y
k
Figure2 tests
I
I
i
I
Boundary
1
Floor
X Geometry
,ooEffecti,tieness
used for simulation
of the HF laboratory
(%)
:;lFI
with HF data
Simulation of spray nozzle The type of nozzles used in the HF tests were pressure atomizing full cone nozzles. The nozzle parameters used in these simulations were: the nozzle angle; volumetric size distribution; and initial drop velocities.
202
Sets of data for the first two parameters and exit velocities of nozzles were supplied by the manufacturer (Bette-Fog Nozzle Inc). The nozzle velocity data were adjusted for specific test conditions, using the Bernoulli equation. Initial drop velocities were then derived from the nozzle exit velocities assuming that all drops acquire the same tangential initial velocity regardless of their size. For computational purposes the volume-size distribution was discretized to four sizes. In establishing the initial trajectory position the nominal spray angle was used. However, the trajectory angle changes with time due to gravitational and drag effects and interaction with entrained air; these are different for each drop size. Drops of different size move in different trajectories, the bigger drops moving to the outer and the smaller to the inner part of the spray. as described by the momentum equation. It was found that for the small geometrical scale of the HF laboratory tests”’ simulation results were quite sensitive to changes of the drop initial velocity, emphasizing the need for accurate evaluation of nozzle parameters.
J. Loss Prev. Process Ind., 1990, Vol3, April
10
20
30
40
Water / HF ?atlo
50
60
(vol/vol)
Figure3 Effectiveness of water spraying on HF releases as a function of water flow rate. Base case: down-flow; mean volume drop diameter 160 pm; wind speed 1.4 m s ’
Absorption removal was estimated from the change of HF mass rate (kgs-I) from the inlet to the outlet cross section. The results of the laboratory scale simulations are shown in Figures 3-9. Figure 3 shows data and model estimates for different ratios of water volume to liquid HF volume. ‘Gas-Spray A’ corresponds to the actual predictions of the model. ‘Analytical A’ corresponds to the predictions of the previously reported analytical Height
of toxic gases by spraying:
100
Effectiveness
:::
V. M. Fthenakis and V. Zakkay
C%)
n-1
70
(m\
0.3 0.25
-
32
-
30
40
50
60
Water / HF Ratio (vol/vol) 0 15 -X-O 01
Figure 7 Effectiveness of water spraying function of water flow rate for several diameters at wind speed of 1.4 m 5-l
-
00.5
-
on HF releases as a mean volume drop
0 0
31
I? d
0
2
‘)
1
02
Figure4 water/HF diameter
Height
Concentration
volume
profiles
01
0
HF mass
02
0
01
02
fraction
at several
axial
distances
ratio of 13. Base case: mean volume
for drop
’
160 pm; wind speed 1.4 m s
(m)
03
0.25 02 015
,
-
__--__--
X.0.93
-x-o
0' c.1
I
13
-
20
3c
40
i
~A
50
60
Water i HF Ratio jvol/vol) o.c.5
-
0
0
0.1
0.2
0
0.1 0.2 HF mass
0
0.1
0.2
0
0.1
0.2
fractldn
Figure8 Effectiveness of water spraying on HF releases as a function of water flow rate for different wind speeds with mean volume drop diameter of 160 pm
Figure 5 Concentration profiles at several axial distances for waterjHF volume ratio of 26.3. Base case: mean volume drop diameter 160&m; wind speed 1.4 m s ’
Height
Effectiveness so -
(mj
80 70
-
60
-
50
-
-
(%)
L=25
-i-1
40 30
-
20
-
-:::
10
I
0
I
0.1
\
,
0.2
0
0.1
0.2
HF mass
0
01
\
II
0.1
0.2
0
10
0.1
0.2
20
30
43
50
8”
Water / HF Ratlo (d/vol)
fraction
Figure 6 Concentration profiles at several axial distances for water/HF volume ratio of 60. Base case: mean volume drop diameter 160 pm; wind speed 1.4 m s ’
Figure9 Effectiveness of water spraying on HF releases as a function of water flow rate for different nozzle to outlet distances: mean volume drop size 160~m: wind speed 1.4 ms~’
J. Loss Prev. Process Ind., 1990, Vol3, April
203
Absorption
of toxic gases by spraying:
V. M. Fthenakis and V. Zakkay
models. Although both models correctly predict the increase of HF absorption effectiveness with increasing model seriously water/liquid HF ratio, the analytical underestimates the experimental data. Using an enhancement factor of 1.3 for the gas-phase mass-transfer coefficient in the gas-spray model, an almost perfect fit of the experimental data was obtained (Gas-Spray B). Sensitivity analysis of all other influential parameters, within their limits of uncertainty, showed that only the gas-phase mass transfer coefficient could have produced such an effect. This k, enhancement could be explained by turbulence in the gas field that is not accounted for in the formula of gas-phase mass-transfer coefficient. Thus, an enhanced k, was used in the rest of the simulations. The analytical model required a mass-transfer enhancement factor of 6 to match the magnitude of the experimental data (Analytical B), which is in agreement with previous results3. b Figures 4-6 show concentration profiles, at several distances in the chamber, for three specific water/HF ratios. It is evident in these plots that the action of the spray extends more in both the horizontal and lateral direction with increasing water flow, although the nozzle angle and drop velocity were the same. Figure 7 shows the effect of varying drop size. The model predicts greater effectiveness for both the 120 pm and 100 pm size drops. The experimental data for 120 pm drops were inconclusive whereas this effect was clear from the 100 pm drops. Figure 8 shows a decreasing effectiveness with increasing wind speed; this effect, however, was not as significant in longer chambers. Figures 9 and 10 show that the absorption effectiveness increases with chamber length, or distance from the nozzle to the exit of the chamber, since the smaller drops are carried by air for considerable distances downwind, while absorbing the gas. This effect may give one possible explanation for the higher effectiveness obtained in the field tests, where a 140 ft long chamber was used32. However, this effect may not be observed in spraying of less water soluble gases
,oc Fffectiveness
where drop saturation may diminish absorption downwind. Preliminary analytical results on spray effectiveness for different gases, as described by their pseudoHenry’s law coefficient and molecular transport properties, are shown in Figure 11. Absorption by water spraying can provide an effective means of control for highly water soluble gases with fast ionization reactions in the liquid phase (e.g. HF, NHs), whereas it is only marginally effective in removing gases that are moderately or slightly water soluble (e.g. SOZ and HIS). For such gases, however, when in gas-phase concentrations high enough that absorption is practically liquidphase controlled, adding a chemical reagent to the water can significantly enhance the effectiveness of absorption. These model estimates depend not only on the parameters examined so far, but on other parameters as well (e.g. initial gas concentration and velocity). The effectiveness of absorption was found to decrease with decreasing initial gas concentration, increasing thickness of the gas layer, and increasing gas velocity. The concentration fields of Figure 12 show this latter effect; in Figures I2a and 12b the ambient air has the same velocity (1.4 ms-I), while the gas layer velocity changes from 1.4 to 5 m s-r. The effect of all parameters can only be studied with exhaustive numerical simulations covering the whole range of parameter values. Several simulations of upwards, co-current, and counter-current flows were also made; these simulations indicate lower absorption effectiveness in these configurations than in down-flow. In co-axial flows the absorption effectiveness was localized around the nozzle (see Figures 13 and 14). However, no general conclusions can be made at this time. Typical simulations of these tests using a 40 x 20 computational grid, 50 trajectories and 4 drop sizes, were taking about 2 min of CPU time on a VAX6340, without Including the energy calculations. evaporation/condensation and gas-phase energy calculations, the total time was ~10 min.
(%) 90 80 70-
6C
60 -
---I-
50 -
t
40.
l-.-
20 4c 0
1
1lJ
22
30 -
---
---
--.
x
25
Distwoe
30
34
from Entrance
(in)
10
38
Figure 10 Effectiveness of water spraying on I-IF releases as a function of nozzle location: chamber length 1.1 m; water/HF ratio 23; mean volume drop size 160 pm; wind speed 1.4 ms-’
204
20
/-1
J. Loss Prev. Process lnd., 1990, Vol3, April
Figure 11 Effectiveness of water soravina on HF releases as a fukction of water flow rate for several g&&: mean volume drop diameter 160 pm; wind speed 1.4 m s-’
of t‘ oxic gases by spraying:
Absorption
Figure 12 Concentration fields in down-flow for two different volume drop size 160 pm; wind speed 1.4 m s ’
Height
gas stream
0.3
a, 1.4 m 5-l; b, 5 ms-‘.
velocities:
Height
(m)
V. M. Fthenakis and V. Zakkay
Water/HF
ratio 30; mean
(m) 0.3
o’z6~s !_; x-cc?
0.25
x-0.I
0.2
0.2
0 15
0.15
4”
0.1
0.1
0.05
0.05
- __
0
0 0
0.1
0.2
0
H;
0.1
mass
0.2
0
0.1
0
0.2
0.2
0
0.1
HF mass
fraction
Figure 13 Co-current flow. Concentration profiles at several axial distances for water/HF volume ratio of 13: mean volume drop diameter 160 pm: wind speed 1.4 m s-’
0.1
0.2
0
0.1
0.2
fraction
Figure 14 Co-current flow. Concentration profiles at several axial distances for water/HF volume ratio o: 26.3: mean volume drop diameter 160 pm; wind speed 1.4 m s-l
Conclusions
Acknowledgements
The effectiveness of absorption of toxic gases by water spraying was analysed for several spray parameters (flow rate. orientation, drop-size distribution). and gas parameters (solubility, chemical reaction rate). For gases that ionize in the liquid phase, water spraying provides an effective means of control, whereas this effect is only marginal for moderately soluble gases. The presented gas-spray model correctly predicts the effects determined in the HF laboratory experimentG. The effectiveness of HF removal increases with increasing water flow rate, decreasing drop size, and decreasing wind speed. There are. however. several more parameters that have an influence on this effectiveness. More exhaustive parametric studies are required to enable comparisons between different configurations, gases and chemical reagents.
The authors wish to thank C. T. Crowe of Washington State University for providing the PSI-Cell program, K. W. Schatz of Mobil R&D Corp. for providing the HF data, T. Bassett of Bette-Fog Nozzle Inc. for supplying nozzle data, and S. Morris, P. Moskowitz and L. D. Hamilton for helpful comments. One of the authors (V.F.) gratefully acknowledges partial support from the Photovoltaic Energy Division, Conservation and Renewable Energy, US Department of Energy.
References I
Blewitt, D. N., Yohn. J. F., Koopman, R. P., et al. P ‘ roceedings of the International Conference on Vapour Cloud Modelling’, (Ed. J. Woodward), AIChE, USA, 1987. pp. 155-171 2 Greiner. M. L.. Plant/Operations Progress 1984,3(2), 66 3 Ahenakis. V. M. Chem. Eng. Comm. 19X9,83,173
J. Loss Prev. Process Ind., 1990, Vol3, April
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Absorption
of toxic gases
by spraying:
V. M. Fthenakis
4 Crow. C. T.. Sharma, M. P. and Stock. D. E. J. Fluid Eng. 1977,99(2), 325 S Schwartz, S. E. ‘Chemistry of Multiphase Atmospheric Systems’. (Ed. W. Jaeschke), NATO ASI Series, Volume Gh, SpringerVerlag, Berlin. FRG, 1986 6 Sillen. L. G. and Martell, A. E. ‘Stability constants of metal ion complexes’ Chem. Sot. Land. Spec., 1964. publ. no 17 7 Schwartz, S. E. and White, W. H. in ‘Adv. in Envir. SC. & Eng.‘. (Eds. J. R. Pfafflin and E. N. Ziegler), Volume 4, Gordon & Breach, 1981 8 Perry, R. H.. and Green, D. W. in ‘Perry’s Chemical Engineers’ Handbook’. 61h Edition, 1984 9 Morgan. 0. M. and Maas, 0. Can. J. Res. 1931.5, 162 10 Robinson. R. A. and Stokes, R. H. in ‘Electrolytic Solutions’ 2nd edition. Butterworth Scientific, Guildford. UK. 1970 11 Pinsent, B. R. W., Pearson, L. and Roughton, F. _I. W. Trans. Far. Sm. 1956.52. 1.512 12 Slinn. W. G. N. ‘Atmospheric Science and Power Production’. DOE/TIC-276UI. 1984 13 ‘Gmelin Handbook of Inorganic Chemistry, Fluorine Supplement’ Volume 3, Springer-Verlag, Berlin. FRG, 1982. p. 246 14 Yeung, W.-S. .I. Applied Mechanics 1982.49,687 15 Sihlichting, H. in ‘Boundary Layer Theory’. 7”’ Edition. McGraw Hill. New York, USA, 1979 16 Van Doom. M. Ph.D. Thesis Delft University of Technology, Netherlands. 1981 17 Kleinstreuer. C., Ramachandran. R. S. and Altwicker. E. R. Chew. Eng. J. 1985.30.45 18 Beard, K. V., and Pruppacher, H. R. J. Amos. SC. 1971, 28. 1455 19 Walcek. C. J. and Pruppacher, H. R. _I. Atmr,s. Chemi.vtry 1984, 1.269 20 Clift. R.. Grace. J. R. and Weber. M. E. in ‘Bubbles. Drops and Particles’. Academic Press, NY. USA. 1978 21 LeClair. B. P., Hamielec, A. E.. Pruppacher. H. R. and Hall. W. D. J. Amos. SC 1972.29.728 22 Harriet. P. Canadian .I. of Chem. Eng. 1962. April. 60 23 Tyroler. G. A.. Hamielec. E.. Johnson. A. 1. and Leclair. B. P. Gun. J. Chew. Eng. 1971.49.56 24 Angelo. J. B.. Lightfoot. E. N.. and Howard. D. W. AlChE J. 1966. 12(4), 751 2.5 Altwickcr, E. R.. and Lindhjem. C. E. AIChE 1. 1980.34(2), 329 26 Bird. R. B.. Stewart. W. E.. and Lightfoot, E. ?1. in ‘Transport Phenomena’. Wiley. NY, USA, 1960 27 Zakkay. V.. Krause. E. and Woo. S. D. L. AIAA J. 1964.2( II). 1939 28 Buzzard. J. L.. and Nedderman. R. M. Chem. Eng. Sri. 1967.22. I577 29 Crowe. C. T. in ‘Advances in Drying’. (Ed. A. Mujumdar) Volume I. Hemisphere. NY. USA. 1980, p. 63 31) Gosman. A. D.,.and Pun. W. M. ‘Calc&ation of Recirculating Flows’. Imperial College of Science and Technology. London, UK. 1973
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April
and
V. Zakkay
31 Albert. R. L. and Mathews. M. K. ‘Polyphase Flow and Transport Technology’ ASME. NY, USA, 1980. pp. 1 IS- 128 32 Schatz. K. W. and Koopman, R. P. ‘Industry Cooperative HF Mitigation/Assessment Program’, final draft, Volume 1. June 1989
Nomenclature a
zi D H
k, k, K, m M P RC SC Sh t 0 x X v Y Y* x Kw !r Y P
interfacial area per unit volume (mm’) ‘bulk’ gas concentration (kg mol m -“) drop median diameter (m) diffusivity (m?s-‘) Henry’s law coefficient gas-phase mass-transfer coefficient (kg mol m-? s-l) liquid-phase mass-transfer coefficient (kgmol m-I s-l) overall mass-transfer coefficient based on the gas-phase driving force (kg mol m -I s -I) slope of equihbrium curve mass rate (kgm-” s-l) pressure (kgrn-‘~-~) Reynolds number Schmidt number Sherwood number gas-drop contact time (s) drop velocity (m s-l) denotes horizontal direction molar fraction of component A in the liquid-phase denotes vertical direction molar fraction of component A in the gas-phase molar fraction of component A in the gas-phase in equilibrium with A m the liquid-phase equilibrium constant equilibrium constant of water ionization viscosity kinematic viscosity (m’s_‘) air/gas density (kg rnmJ)
Subscripts A eff i :! 1 2 nt “P
denotes denotes denotes denotes denotes denotes denotes number number
gaseous component effective interface gas-phase liquid-phase forward reaction reverse reaction of trajectories of drops
A