This document discusses methodologies for modeling the evaporation rates and downwind dispersion of accidental releases of chlorine dioxide (ClO2) and ammonia (NH3) aqueous solutions. It presents a heat and mass transfer model to calculate time-dependent evaporation rates that considers variables such as liquid temperature, vapor pressure, and concentration. Example calculations show that this model estimates lower evaporation rates than the EPA guidance method. Three dispersion models (DEGADIS, ALOHA, SLAB) are applied to benchmark example releases of ClO2 and NH3, with ClO2 modeled as a dense gas and NH3 as neutrally buoyant. The maximum distances to toxic endpoints are reported.

1. Environmental solutions delivered uncommonly well
Accidental Releases Analysis for Toxic
Aqueous Solutions
Paper No. 98-TP50A.05
Prepared By:
Hung-Ming (Sue) Sung, PhD, PE ▪ Director - Quality & Technology
TRINITY CONSULTANTS
12700 Park Central Drive
Suite 2100
Dallas, TX 75251
+1 (972) 661-8881
trinityconsultants.com
June 1998

2. 1
ABSTRACT
As a result of the cluster rule for the control of the hazardous air pollutants, pulp and paper mills
are in the process of further substituting chlorine with aqueous chlorine dioxide for their
bleaching operations. In addition, ammonia aqueous solutions are applied by paper mills in
various processes. An evaporation model including both heat and mass transfer for aqueous
solutions has been developed to quantify chemical evaporation rates. Chemical and physical
properties for chlorine dioxide and ammonia aqueous solutions have been analyzed to allow
plants to perform a dynamic analysis for various accidental release scenarios. This paper
provides a detailed discussion of the methodologies for quantifying source parameters and
modeling downwind concentrations from liquid spills of chlorine dioxide and ammonia aqueous
solutions.
INTRODUCTION
Under 40 CFR Part 68, a process, which stores or handles an aqueous solution with a
concentration greater than or equal to the de minimis concentration and a total quantity greater
than or equal to the threshold quantity, is regulated by the Risk Management Program (RMP)
Rule. Chlorine dioxide (ClO2) and ammonia (NH3) aqueous solutions are commonly applied in
pulp and paper mills. The de minimis concentration for ClO2 and NH3 are 1% and 20% by
weight, respectively; while the threshold quantity for ClO2 and NH3 are 1,000 lb and 20,000 lb,
respectively.
The Off-Site Consequence Analysis Guidance1
(OCA Guidance) provides a simple mass transfer
method for calculating evaporation rates from liquid spills. During a spill of a toxic aqueous
solution, the evaporation rate of the toxic chemical is a function of many variables, such as liquid
pool temperature, vapor pressure, solution concentration. Studies2,3
have shown that both mass
and heat transfer mechanisms must be considered in the calculation method in order to accurately
quantify evaporation rates. As the key input parameters to the subsequent dispersion modeling,
accurate evaporation rates will lead to accurate downwind concentrations to determine a
reasonable impact radius . Therefore, a heat and mass transfer model has been developed in this
study to better quantify evaporation rates for spills of the ClO2 and NH3 aqueous solutions. This
paper provides a complete overview of the modeling methodologies for the two aqueous
solutions.
SOURCE PARAMETERS
In the RMP rule, the basic definition of the worst case release scenario provides general guidance
for the determination of source parameters. For a toxic liquid, the worst case scenario is defined
as:
“…the quantity in the largest vessel or pipe is spilled instantaneously to form a liquid pool. The
surface area of the pool shall be determined by assuming that the liquid spreads to 1 centimeter
deep unless passive mitigation systems are in place that serve to contain the spill and limit the
surface area……The volatilization rate shall account for the highest daily maximum temperature
occurring in the past three years, the temperature of the substance in the vessel, and the
concentration of the substance if the liquid spilled is a mixture or solution.”

3. 2
To conduct an accidental release analysis at a pulp bleaching facility, the largest storage tank for
a ClO2 aqueous solution (aq) is typically over 100,000 gallons. The ClO2(aq) is normally chilled
under 10 °C with a concentration lower than 15 grams per liter (g/L) or 1.5% by weight.
ClO2(aq) storage tanks are normally placed near the bleaching process, which is confined with
other structures. Therefore, a ClO2(aq) release is normally contained in a dike (confined) area to
reduce the evaporation surface. In a paper mill, NH3(aq) storage tanks are typically smaller than
those for ClO2(aq) and are not chilled (i.e., ambient temperature). A typical concentration of
NH3(aq) is 29% by weight.
Chemical/Physical Properties
Evaporation rates for a chemical contained in an aqueous solution are calculated based on the
chemical/physical properties of the chemical/water mixture. The first key parameter for
evaporation rate calculations is the partial vapor pressure of a chemical over the aqueous solution
at different concentrations and temperatures. An equation for calculating the partial vapor
pressure of ClO2 above solutions at variable temperatures is shown as follows:4
( )T
ClOClO eCP
3102717.10
22
5.7
−
××= (1)
where
PClO2 = partial vapor pressure of ClO2 (mm-Hg)
CClO2 = ClO2 concentration in water (g/L)
T = absolute temperature (K)
For NH3(aq), the partial vapor pressure data5
for mixtures with a NH3 concentration less than
30% and a temperature less than 25 °C are best fit by the following equation:
( ) ( )3
3
526.10263.5
254.10072.0736.51 NHC
NH eTP
×
×−××= (2)
where
PNH3 = partial vapor pressure of NH3 (mm-Hg)
CNH3 = NH3 molar fraction in water
In addition, liquid densities and heats of vaporization for NH3(aq) as functions of temperatures
and concentrations are also derived or obtained based on data contained in Perry’s Chemical
Engineers’ Handbook.5
Other applicable chemical/physical properties for NH3 and ClO2
aqueous solutions are available in References 5 and 6, respectively.
Evaporation Rates
The Off-Site Consequence Analysis Guidance4
(OCA Guidance) uses a method modified from
the approach developed by Mackay and Matsugu.7
The evaporation rate by this simple mass
transfer method is shown as follows:
T82.05
PAMU0.284
=E v
0.78
×
××××
3
2
(3)

4. 3
where:
E = evaporation rate (lb/min)
U = wind speed (m/sec)
M = molecular weight (lb/lb-mol)
A = surface area of pool (ft2
)
Pv = vapor pressure (mm-Hg)
The OCA Guidance methods can be applied as a screening approach for calculating evaporation
rate from a liquid spill pool. For refined evaporation rate calculations, a heat and mass transfer
model has been developed in this study that applied a modified version of the Surface
Temperature (Ts) method developed by Kawamura & Mackay.2
The evaporation rate applied by
this method is based on the original Mackay and Matsugu7
approach shown as follows:
TR
PMk
E v
×
××
= (4)
where
k = mass transfer coefficient (m/h)
M = molecular weight (g/gmol)
Pv = vapor pressure (Pa)
R = gas constant (Pa m3
/mol K)
To calculated evaporation from an aqueous solution spill, both liquid phase and gas phase mass
transfer were evaluated. During the first hour after a spill, the mass transfer from the surface is
much slower than the mass transfer through the bulk liquid since the chemical concentration in
the solution is high enough to assume that mass evaporated from the surface is replaced
instantaneously with mass from the bulk liquid. In addition, liquid spills are normally drained to
a sewer system before a quiescent pool can be formed. Therefore, the bulk liquid mass transfer
coefficient is not included in this model. The surface mass transfer coefficient can then be
calculated as follows:7
67.011.078.0
029.0 −−
Χ= ScUk (5)
where
U = wind speed at 10 meter height (m/h)
X = effective pool diameter (m)
Sc = Schmidt Number by Equation (6)
ABD
Sc ν= (6)
where
ν = kinematic viscosity of air (cm2
/s)

5. 4
DAB = chemical diffusivity in air (cm2
/s)
DAB of toxic chemicals in air can be calculated using methods included in Liquid and Gas
Properties.8
In this study, DAB for ClO2 and NH3 are estimated to be 0.12 cm2
/s and 0.19 cm2
/s,
respectively.
To calculate evaporation rates using Equation (4), the Schmidt number, vapor pressure, and
temperature are all based on the liquid pool surface temperature, which can be solved by the
Kawamura & Mackay model2
shown as follows:
evsursengrdatmsol QQQQQQ +=+++ (7)
where
Qsol = net solar insolation (kJ/m2
h K)
Qatm = long-wave radiation from the atmosphere (kJ/m2
h K)
Qgrd = conduction energy (kJ/m2
h K)
Qsen = sensible heat from the air (kJ/m2
h K)
Qsur = long-wave radiation emitted by the pool (kJ/m2
h K)
Qev = evaporation energy (kJ/m2
h K)
Detailed calculations of each energy term presented in Equation (7) can be obtained from
Reference 2.
If a liquid is stored under ambient temperature, the surface temperature of a liquid spill is lower
than the ambient temperature due to heat loss from vaporization of liquid compounds. For an
NH3(aq) spill, the surface temperature of the liquid pool can be significantly lower than the
atmosphere temperature due to the rapid vaporization of NH3. Furthermore, the condensation of
ambient water vapor into the pool as a heat input source to the evaporating liquid is significant
enough that it cannot be ignored.3
Therefore, a modified model of the steady state thermal
balance equation is presented in Equation (8):
evsurconsengrdatmsol QQQQQQQ +=++++ (8)
where
Qcon = heat input to the pool from condensation of water vapor (kJ/m2
h K)
An earlier study for NH3(aq) spills3
measured Qcon as a function of liquid surface temperatures.
Based on Reference 3, a water condensation rate of 665 g/m2
-hr for NH3(aq) release is applied in
this study for calculating NH3 evaporation rates within the first hour of a spill. For ClO2(aq)
releases, the evaporation/condensation of water is relatively insignificant comparing with ClO2.
Therefore, Qcon is assumed to be zero for a ClO2(aq) liquid spill. To calculate transient
evaporation rates, all time dependent parameters are recalculated for each assigned time step
within a release duration.

6. 5
Example Calculations of Evaporation Rates
Evaporation rates for example spills are calculated using both the OCA Guidance method and the
modified Ts method. For the ClO2(aq) spill case, 100,000 gallons of ClO2 solution containing
10 g/L of ClO2, stored at less than 45 °F, was released into a 70 ft by 70 ft diked area. For the
NH3(aq) spill case, 15,000 gallons of NH3 solution containing 29% (by weight) NH3 stored in an
8 feet diameter tank at ambient conditions is released to a 36 ft by 36 ft diked area.
The worst case meteorological parameters defined by the RMP rule (1.5 m/s wind, F stability
class) and a typical ambient temperature of 25 °C (77 °F) are used in the calculations. Although
F stability class conditions can only exist under a clear sky with very low solar insolation (i.e.,
night time period), a release time of 7:00 am (Eastern Standard Time 6:00 am) is selected for the
demonstration of the Ts method. The time and location selected for calculations of the solar
angle are the 180th
Julian Day and Lansing, Michigan , respectively.
For each new time step, evaporation rates were recalculated based on heat and mass balances.
Since the first hour evaporation is the worst hour for downwind exposure, all parameters were
calculated for each 10-minute interval for the first hour of a spill. For each time step, the
evaporation rate was recalculated using Equations (3) and (4) with new vapor pressures
calculated using Equations (1) and (2). For NH3 aqueous spills, the OCA guidance provides an
average first hour vapor pressure of 332 mm-Hg for a 30% NH3 aqueous solution. However, to
demonstrate calculations for broader applications, time dependent evaporation rates are
calculated using Equation (2). Using the Ts model, the liquid surface temperature is recalculated
for each time step using the thermal balance method presented by Equation (8). In Equation (8),
Qev, Qsen, Qsur, and Qgrd are functions of surface temperature, which was solved by an iterative
approach using a spreadsheet. The spill temperature remains constant as the storage temperature
when evaporation rates are calculated using the OCA guidance equation.
Table 1 summarizes the first hour average evaporation rates calculated by the two methods
discussed above. Figures 1 and 2 illustrate the calculated time dependent evaporation rates for
ClO2 and NH3, respectively.
For the ClO2 spill case, the OCA guidance allows evaporation rates be calculated based on the
solution storage temperature (45 °F). However, the liquid pool surface temperatures increase
with time since the ambient temperature is higher than the storage temperature. Based on the
modified Ts model, the surface temperatures for the example spill initially dropped, then
increased from 276 K to 289 K within the first hour of spill. As shown in Figure 1, the first hour
average evaporation rate calculated by the modified Ts model is only slightly less than the rate
calculated in accordance with the OCA guidance using the storage temperature.
For the NH3 spill case, the evaporation rates calculated using the OCA guidance are based on the
ambient temperature (77 °F) since the aqueous solution is stored under ambient temperature.
The modified Ts model calculated surface temperatures for the first hour to be approximately
272 K, which is consistent with temperatures observed by Reference 3. As a result of the low
surface temperature, the evaporation rates calculated by the modified Ts model are significantly
less than the rates calculated using the OCA guidance (see Figure 2).

7. 6
DISPERSION MODELING ANALYSIS
Based on the source parameters calculated above, various dispersion models may be applied to
determine downwind concentrations caused by these spills. The vapor cloud behavior must be
examined in order to select the most appropriate model. For the NH3 spill case, the evaporating
NH3 vapor cloud is a neutrally buoyant release that can be modeled with models such as,
SCREEN39
, ALOHA10
, and SLAB.11
For the ClO2 spill case, the evaporating ClO2 may be
neutrally buoyant under turbulent atmospheric conditions; or may be heavier than the ambient air
under a very stable condition. Therefore, the dense gas behavior of a ClO2 release must be
evaluated for selecting an appropriate model to calculate downwind concentration. For a
continuous vapor cloud from a ground level spill, the following Richardson Number (Ri)
equation can be applied:12
5.0
2
*
2
8.9




















= −
u
Q
u
Ri
i
i
a
ai
ρρ
ρρ
(9)
where:
ρi = density of released material (kg/m3
)
ρa = ambient air density (kg/m3
)
Qi = mass emission rate (kg/s)
u = wind speed (m/s)
u* = friction velocity, usually 0.1×u (m/s)
The resulting Ri for the example evaluated above is 178, which indicates that the ClO2 release is
slightly heavier than the ambient air under the slow wind condition and can be modeled as a
dense gas release using DEGADIS13
, ALOHA, and SLAB.
As a benchmark analysis, three dispersion models were applied to calculate downwind
concentrations for each of the release cases. The NH3 release case was modeled by SCREEN3,
ALOHA, and SLAB; while ClO2 release case is modeled by DEGADIS, ALOHA, and SLAB.
The impact distances determined using the lookup table contained in the OCA Guidance are also
included for comparison. For DEGADIS, ALOHA, and SLAB models, the example mill is
modeled with a 0.2 meter surface roughness. The site was considered as a rural area for applying
the SCREEN3 model and the OCA lookup tables. As defined in the RMP rule, the endpoints for
ClO2 and NH3 are 1 ppm, and 200 ppm, respectively. The resulting maximum distances to the
endpoints are summarized in Table 2.
For the ClO2 spill case, the distance of endpoint (DOE) determine by the OCA Guidance was
greater than 10 miles. Using dense gas dispersion models with the evaporation rate calculated by
the modified Ts model, the shortest DOE, 3.13 miles, was calculated by DEGADIS.
For the NH3 spill case, the DOE determine by applying the evaporation rate equation and lookup
table contained in the OCA Guidance was approximately 0.8 miles. Using the evaporation rate
calculated by the modified Ts model, the DOE determined by the OCA lookup table provided the
shortest DOE, 0.31 mile. Using the three neutrally buoyant dispersion models with the

8. 7
evaporation rate calculated by the modified Ts model, the shortest DOE, 0.40 mile, was
calculated by SLAB.
SUMMARY
The Risk Management Program rule requires modeling analysis for both worst case and more
likely alternative release scenarios. The worst case scenarios are the major concern when the
information is presented to the general public. Accurate source parameters will provide more
reasonable impact distance. This paper presented various technical methods that can be applied
to determine downwind concentrations from aqueous solution spills. A heat and mass transfer
emission model has been developed to better quantify transient evaporation rates from aqueous
solution spills. As a benchmark analysis, three dispersion models, all recognized by experts in
the area, were applied to calculate the endpoint distances for each chemical spill case. All results
are compared to the values obtained by applying the screening methods provided in the OCA
Guidance. As shown, different methods and models can lead to significantly different results.
Therefore, selecting the best approach that meets a mill’s specific needs is the key step to prepare
a successful Risk Management Plan.
ACKNOWLEDGE
The author would like to thank Mr. David Bryer of Mead Corporation for his suggestions and
review of this paper.
REFERENCES
1. U.S. EPA, RMP Off-Site Consequence Analysis Guidance, U.S. Environmental Protection
Agency, Research Triangle Park, North Carolina, 1996.
2. Kawamura P., and Mackay, D., “The Evaporation of Volatile Liquids”, Journal of Hazardous
Materials, pp. 343-364, Vol. 15, 1987.
3. Mikesell, J.L.; et al; “Evaporation of Contained Spills of Multicomponent Nonideal
Solutions”, Proceedings of International Conference and Workshop on Modeling and
Mitigating the Consequences of Accidental Releases of Hazardous Materials, CCPS of the
AICHE, 1991.
4. Kirk-Othmer, Encyclopedia of Chemical Technology, 4th
ed., Wiley, New York, 1991.
5. Perry, R.H.; Green, D.W.; Perry’s Chemical Engineers’ Handbook, 7th
ed., McGraw Hill,
New York, 1997.
6. Leach, J.; Chlorine Dioxide - Environmental and Technical Information, Beak Pacific Inc.,
prepared for Industrial Hazardous Chemical Handling Task Force and Council of Forest
Industries, Canada, 1996
7. Mackay, D. and Matsugu, R., “Evaporation Rate of Hydrocarbon Spill on Water and Land”,
Canadian Journal of Chemical Engineering, p. 434, Vol 5., 1973.
8. Reid, R. C., Prausnitz, J.M., and Poling, B.E., The Properties of Gases and Liquids, 4th
ed.,
McGraw-Hill, New York, 1987.

9. 8
9. U.S. EPA, SCREEN3 Model User’s Guide, EPA-454/B-95-004, U.S. Environmental
Protection Agency, Research Triangle Park, North Carolina, 1995.
10. U.S. EPA, National Oceanic and Atmospheric Administration, Areal Locations of Hazardous
Atmospheres, (ALOHA), Washington, D.C., National Safety Council, 1995.
11. Ermak, D.L, User’s Manual SLAB: An Atmospheric Dispersion Model for Denser-than-Air
Release, Lawrence Livermore National Lab., Livermore, CA, 1990.
12. Havens, J. A., and Spicer, T. O. Development of an Atmospheric Dispersion Model for
Heavier-than-Air Gas Mixtures. Report No. CG-D22-85 for the U.S. Coast Guard, Univ. of
Arkansas, 1985.
13. Spicer, T. O., and Havens, J. A., User’s Guide for the DEGADIS 2.1 Dense Gas Dispersion
Model, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina,
EPA-450/4-89-019, 1989.

10. 9
Table 1. The first hour average evaporation rates.
Calculation Method
ClO2
Evaporation Rate
(lb/min)
NH3
Evaporation Rate
(lb/min)
OCA Guidance 59.68 67.87
Modified Ts Model 46.19 16.66
Table 2. Maximum distances to the RMP endpoints.
Dispersion
Model
ClO2 Endpoint
1 ppm
(mile)
NH3 Endpoint
200 ppm
(mile)
OCA Evaporation rate/Lookup Table ~11 0.81
OCA Lookup Table ~10 0.31
SLAB 6.83 0.40
ALOHA 4.60 0.57
DEGADIS 3.13
SCREEN3 0.45

11. 10
Figure 1. Time dependent ClO2 evaporation rates since initial spill.
0
10
20
30
40
50
60
70
80
0 10 20 30 40 50 60
Time Since Initial Spill (min)
EvaporationRate(lb/min)
Modified Ts Model OCA Guidance

12. 11
Figure 2. Time dependent NH3 evaporation rates since initial spill.
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50 60
Time Since Initial Spill (min)
EvaporationRate(lb/min)
Modified Ts Model OCA Guidance