# How can I calculate the evaporation rate for a hazmat spill?

I was given formulas for general evaporation, for a spill calculator I am building.

These are formulas, that are supposed to approximate evaporation, are for a number of different chemicals. Molecular weight is pulled from the chemical itself, same with vapor pressure.

We have a number of different spills at this location. Some spills will go directly onto asphalt/gravel or soil. We do have a number of different areas that have secondary containment, which is referred to as a "Berm", so that is the reason we have two formulas below.

Here are some of them:

### General Evaporation Rate Formula From Asphalt

$$E =\frac {0.284 v^{0.78} M^{0.667}AP}{82.05T}$$ Where:

• $E$ is Evaporation in pounds per minute
• $v$ is the average windspeed
• $M$ is the molecular weight in g/mol
• $A$ is the surface area in feet squared
• $P$ is the vapor pressure in mmHg
• $T$ is the temperature in Kelvin

### Evaporation Rate from Berm

$$E =\frac {0.284 \cdot \text{MW}^{0.667}(\text{Average windspeed})^{0.78}(\text{Surface Area})(\text{vapor pressure})}{82.05 \cdot \text{temperature in K}}$$

Surface Area Equations:
Scenario 1:
$l$ = Length of the liquid spilled
$w$ = Width of liquid spilled
$l \cdot w = A$
$A - (\pi \cdot (\frac {\text{Diameter of tank in berm}}{2})^2 \cdot (\text{How many tanks in berm}))$

Scenario 2: If we have 3 tanks in the berm
$l$ = Length of the liquid spilled
$w$ = Width of liquid spilled
$l \cdot w = A$ $A - (\pi \cdot ((\frac {\text{Diameter of tank in berm}}{2})^2)) \cdot (\text{Number of tanks of that diameter in berm}))-\pi (\frac{(\text{Diameter of tank in berm})}{2})^2 \cdot (\text{Number of tanks of that diameter in berm}))- \pi(\frac{(\text{Diameter of tank in berm})}{2})^2 \cdot (\text{Number of tanks of that diameter in berm}))$

I don't trust the formulas given, because they were given by another student assigned to this task. These formulas are not found in any workbook, website, etc. I am always skeptical about using other people's work without documentation making sure they have proof to backup their claims that this stuff will work.

I am asking precisely this: are these formulas suitable to use as an approximation for evaporation? If not, what would be a better formula?

I am not an engineer, I am a computer science/mathematics major. This project has nothing to do with school though. It is a work project.

Research
The closest thing I can find to an equation I can use is from here, but I am unable to decipher the characteristics it is asking since it is extremely technical in that field. I'm willing to do some research but I still have yet to find an acceptable formula/equation I can implement in this program. Another example is here where equation #7 is the formula it says to use for spills but I have no idea how it works.

• There are still some things you need to clarify. I edited your post with an example of how to present these equations so they can be easily read and understood. However, the definitions of variables should generally be more specific than what I've given here (which molecular weight, what surface area, etc.); your "from berm" equation has both $A$ and "surface area" but doesn't define $A$; and you haven't explained to us why you have a "from berm" equation in the first place. Please explain the scenario to which you mean to apply these equations so that we don't have to guess.
– Air
Aug 18 '16 at 15:08
• All that said, this is very close to being a great question for the site, in my opinion - once those issues are resolved.
– Air
Aug 18 '16 at 15:10
• This can be put into many different scenarios, "Worst Case Scenarios" as it is just a knee jerk reaction to someone reporting a spill. Surface Area is the Spill itself, so a liquid spilling onto asphalt or concrete, what is the surface area of the spill itself. Vapor Pressure is going to be a list of chemicals that can be put into that place holder. It's the Vapor pressure of whatever has been spilt. As I said before, My first time posting onto these boards with equations, so I am greatly appreciative of the help getting into a format that is easier to read for the masses.
– Duck
Aug 18 '16 at 15:16

The evaporation formula you have is a modification of the EPA method for calculating the evaporation rate. See here:

Technical Guidance for Hazards Analysis

look at Appendix G. The modified form I found in a paper by John Barry in CEP magazine. Somebody took the time to scan it and has it posted on the internet:

Estimating Rates of Spreading and Evaporation of Volatile Liquids

Search for the title for a freely available version. Note that your berm and non-berm equations are essentially the same, just with careful calculations of the surface area. Unfortunately, I don't know enough about the equations to gauge their accuracy or expected error. They seem to be based on basic theories defining the evaporation rate as: $$ER=kAP^*$$ where $k$ is the mass transfer coefficient, $A$ is the surface area of the spill, and $P^*$ is the vapor pressure. Calculation of the mass transfer coefficient typically requires an empirical correlation and is where the molecular weight, wind speed, and temperature dependence comes in. Note also that the vapor pressure is temperature dependent and you should treat it appropriately.