About the Calculator

Use the Evaporation Calculator to estimate the evaporation rate of any of seven toxic chemicals from aqueous solution (a mixture of the chemical and water). The evaporation rate estimate made by Evaporation Calculator represents the rate at which the toxic chemical evaporates out of the solution into the air; the evaporation rate of the water component of the solution is ignored.

To obtain a rate estimate, you need to know:

• the concentration of the chemical in solution, by weight.
• the ambient temperature (the temperature of the air, ground, and puddle).
• the wind speed.
• the alongwind length and crosswind width of the puddle.

The calculator also displays the partial pressure of the selected chemical at the temperature you choose.

Three Caveats

• The calculator estimates only the initial evaporation rate of the toxic chemical from the solution. This rate may decline over time as the puddle temperature drops by evaporative cooling, or as the concentration of the chemical within the solution declines (this will happen if the toxic chemical evaporates at a faster rate than the water). For volatile chemicals near saturation concentration, the decline in rate caused by the decline in concentration may be fast.
• It doesn't account for some factors that may substantially affect evaporation, such as the impedance of wind flow across a puddle by adjacent terrain features.
• Any evaporation rate estimate from the calculator is appropriate only for non-boiling puddles. A puddle is non-boiling when its boiling point is above ambient temperature.

INSTRUCTIONS

To Estimate Evaporation Rate

1. Select a chemical from the chemical menu.
2. Type a wind speed in the Wind Speed box, then select wind speed units.
3. Type the weight percent concentration of the chemical in the Concentration box.
4. Type the ambient temperature of the puddle, air, and ground in the Ambient Temperature box, then select temperature units.
5. Type the alongwind length of the puddle in the Alongwind Puddle Length box, then choose length units. This should be the length of the puddle measured in the alongwind direction.
6. Type the crosswind width of the puddle in the Crosswind Puddle Width box, then choose width units. This should be the width of the puddle measured in the crosswind direction.
7. Check "Adjust for high volatility" if you want the Evaporation Calculator to correct for the high volatility of a chemical (as explained below). If you leave this box unchecked, the correction will not be made. When the chemical's partial pressure approaches or exceeds atmospheric pressure, the correction becomes invalid. If this happens, you will be alerted that the calculator cannot estimate an evaporation rate using the correction. In this case, uncheck "Adjust for high volatility" to see an uncorrected evaporation rate.
8. Click Calculate.

The calculator reports two estimates:

• Evaporation rate. The predicted rate of evaporation of the chemical you selected.
• Partial pressure. Depending on the temperature and concentration you enter, this value is either a pressure derived from laboratory measurements or a linearly-interpolated estimate lying between two measured partial pressure values.

For each of the six chemicals, the calculator can estimate evaporation rate only within a range of temperatures and concentrations--it will alert you if it can't make an estimate for you because temperature or concentration is outside that range.

To Use an Evaporation Estimate in ALOHA

To use an evaporation rate estimate obtained from the calculator in ALOHA:

1. Start ALOHA and choose a location, time and date for your release scenario.
2. Choose Chemical from ALOHA's SetUp menu. Find the name of the solute in the scrolling list of ALOHA chemicals, click on this name to highlight it, then click Select (the "solute" is the toxic component in the solution--for example, hydrogen chloride is the solute in the solution hydrochloric acid). In the case of oleum, choose sulfur trioxide from the list, since it's the component of concern. Oleum itself is not included in the list because it's not a pure chemical. Because formaldehyde is not included in ALOHA's library of chemicals, you'll need to add it; check your ALOHA manual to learn how to do so.
3. Enter the weather conditions for your release scenario.
4. In the SetUp menu, point to Source, then Direct.
5. Type in the estimated evaporation rate as a continuous source strength. To do this, click Continuous source, then choose source strength units, then type to evaporation rate estimate in the box for the amount of pollutant.
6. Select a level of concern (LOC). You can choose to use the IDLH of the solute (this is the default LOC in ALOHA), or a different toxic threshold. Enter your value into ALOHA by choosing Options... from the Display menu.
7. Choose Footprint from the Display menu to see a footprint for this scenario. (Choose Concentration... from the Display menu to view a concentration or dose graph.)

Points to Consider

If you model a solution of a toxic chemical in ALOHA using an evaporation rate estimate from the calculator as your source strength value, consider the following points:

• ALOHA's results are likely to be less accurate than if you were modeling evaporation and dispersion of a pure chemical. This is because you must use a constant evaporation rate as your estimate of source strength. In reality, evaporation rate of a chemical in solution usually changes over time as the concentration of the chemical changes, and as the puddle's temperature rises or falls and its radius changes.
• ALOHA mathematically treats a Direct source as a point source. Its results are less accurate when a puddle is very large and/or the location for which you'd like to produce a concentration graph is very close to the puddle. Consider using another method or model in such a case.

BACKGROUND INFORMATION

Vapor pressure and partial pressure

Vapor pressure is the most important property determining a liquid's evaporation rate. A chemical in a solution or mixture won't display the same vapor pressure that it does when it's in pure form. When the chemical exists in a mixture or solution, its vapor pressure is called its partial pressure. The Evaporation Calculator uses tables of measured partial pressures to estimate evaporation rate.

Computations made by the Evaporation Calculator

The calculator uses the following equation (Kawamura and Mackay 1985) to estimate evaporation rate:

E = A * Km * (Mw * Pv)/(R * T) (kg/s)

where E = evaporation rate, in kg/s, A = area of the evaporating puddle, in m^2, Km = mass transfer coefficient, in m/s, Mw = molecular weight of the selected chemical, in kg/kmol, Pv = vapor pressure, in Pa (from the partial pressure table for the selected chemical), R = the gas constant (8314 J/(kmol K)), and T = ambient temperature, in K. The evaporation of the fraction of the solution that is water is ignored since water isn't a hazardous chemical.

It uses the following equation (Mackay and Matsugu 1973) to calculate Km, the mass transfer coefficient:

Km = 0.0048 * U^(7/9) * Z^(-1/9) * Sc^(-2/3) (m/s)

where U = wind speed at a height of 10 m, in m/s, Z = the pool diameter in the along-wind direction (m), and Sc = the laminar Schmidt number for the selected chemical.

It estimates the Schmidt number, which is a unitless ratio, as:

Sc = (v/Dm)

where v = the kinematic viscosity of the air, assumed to be 1.5 x 10^-5 m^2/s, and Dm = the molecular diffusivity of the selected chemical in air, in m^2/s.

It uses Graham's Law to approximate the molecular diffusivity of the selected chemical in air, in m^2/s^-1 (Thibodeaux 1979) as:

Dm = D(H2O) * [Mw(H2O)/Mw(chem)]^(1/2) (m^2/s)

where D(H2O) = the molecular diffusivity of water (2.4 x 10^-5 m^2/s at 8°C), Mw(H2O) = the molecular weight of water (18 kg/kmol), and Mw(chem) = the molecular weight of the selected chemical, in kg/kmol.

A Correction for Volatility

A volatile chemical is one that has a relatively high vapor pressure at environmental temperatures, and therefore evaporates readily. When you check the "Adjust for high volatility" checkbox, the calculator uses the following correction term (Brighton 1985, 1990; Reynolds 1992) in the evaporation equation, as shown below. This correction method is appropriate only for a chemical at a temperature below its boiling point.

The calculator estimates the correction term as:

C = -(Pa/Pv) * ln [1 - (Pv/Pa)]

where Pa = atmospheric pressure, in Pa (101,325 Pa at sea level), and Pv = vapor pressure of the solute, in Pa.

For chemicals that are not very volatile, the value of C will be about 1.0. It will increase in magnitude as the vapor pressure of the chemical increases.

The corrected evaporation rate is calculated as:

Ec = C * E (kg/s)

where Ec = the evaporation rate corrected for volatility.

REFERENCES

Revised: August 20, 2003
Office of Response and Restoration, National Ocean Service, National Oceanic and Atmospheric Administration