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 calculator also displays the partial pressure of the selected chemical at the temperature you choose.
The calculator reports two estimates:
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 rate estimate obtained from the calculator in ALOHA:
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:
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.
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 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.
Brighton, P. W. M. 1985. Evaporation from a plane liquid surface into a turbulent boundary layer. J. Fluid Mechanics 159:323-345.
Brighton, P. W. M. 1990. Further verification of a theory for mass and heat transfer from evaporating pools. J. Hazardous Materials 23:215-234.
Daubert, T. E. and R. P. Danner. 1989. Physical and thermodynamic properties of pure chemicals. Design Institute for Physical Property Data, American Institute of Chemical Engineers. Hemisphere Publ. Co. New York.
Kawamura, P. I., and D. Mackay. 1987. The evaporation of volatile liquids. J. Hazardous Materials 15:343-364.
Mackay, D., and R. S. Matsugu. 1973. Evaporation rates of liquid hydrocarbon spills on land and water. Can. J. Chem. Eng. 51:434-439.
Mackay, D., S. Paterson, and S. Nadeau. 1980. Calculation of the evaporation rate of volatile liquids. Pp. 361 - 368 In Control of hazardous material spills. Proceedings of the 1980 National Conference on Control of Hazardous Material Spills, May 13 - 15, 1980, Louisville, KY. Sponsored by U. S. Environment Protection Agency, U. S. Coast Guard, and Vanderbilt University.
Reynolds, R. M. 1992. ALOHA (Areal Locations of Hazardous Atmospheres) 5.0 theoretical description. NOAA Tech. Memo. NOS ORCA-65. National Oceanic and Atmospheric Administration/Hazardous Materials Response and Assessment Division. Seattle, WA.
Thibodeaux, L. G. 1979. Chemodynamics: environmental movement of chemicals in air, water, and soil. New York, John Wiley and Sons.