the science of storage tanks emissions calculations

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Fixed-roof tanks are the most common form of tank, and if you have tanks in your

facility it is likely that they are of the fixed roof variety.

Chemical makeup of the stored liquid

Like other air emission sources that process chemicals, the type and amount of

emissions generated will vary by the type of chemicals used. Some of the information

you will need to know about your liquid’s chemical makeup include:

%by Weight Chemical Composition of the liquid

Molecular weight

Chemical density

Atmospheric Conditions

The temperature of the tank’s physical location also influences the rate at which the

stored liquid will volatilize. Two identical tanks storing identical mixtures but in

different states will generate different air emissions. Before you can begin to calculate

your tank’s emissions you will need to know the surface temperature of the liquid in

your tank based on correct meteorological data for your location.

Whenever possible use actual recorded temperature data for the period you are

reporting, as that will ensure your results are accurate and won’t be under or over

reported. In some cases you can use average temperatures without significantly affecting

accuracy. However, as we’ll explore later on, relying on annual averages for yearly

reports has been shown to greatly impact the accuracy of emissions accounts.


Amount of liquid moving through the tank

You will also need to know the liquid height of the liquid stored in your tank and how

many times the tank was filled or emptied (turnovers) for the period that you are

accounting emission for. It is more accurate to know the exact liquid height at any given

moment, but you are usually able to calculate emissions using the 2/3 height of tank for

the reporting period if the exact data is unknown.

This set of data is important because the more empty air-filled space there is in a tank,

the greater the standing loss emissions. The liquid height will tell you how much empty

space is in your tanks for the reporting period. Working losses will be affected by

movement through the tank.

Timeframe for standing time

The longer your stored liquid stands in a tank, more evaporation takes place and

generate air emissions. You will need to know how long a liquid was stored before it was

transferred into another tank, a product, or a package.


Standing losses, also known as breathing losses, are the result of evaporated

vapor escaping the tank due to the normal temperature fluctuations that occur

throughout the day. Standing loss occurs without any change in the tank’s liquid

level.

As the temperature increases, usually at it’s highest in the early afternoon, the

vapor buildup in the tank increases, and must be vented out through a vent. As

the temperature cools, the vapor space in the tank shrinks and external air gets

vacuumed into the tank.

Working losses are all the emissions from a tank that are the result of

performing an operation on the tank’s liquid. Essentially, these losses are all the

emissions that occur for any other reason than the standard temperature

fluctuations of the day.

The below calculation can be used to determine the working and standing losses

from a tank, known as the total loss. One exception is loading operations

(loading or unloading a mobile tank or truck), which uses a different equation.

We’ll go over this separate equation later.

When calculating air emissions for any type of tank, the most basic logic at work

can be summed up in one equation, outlined in the U.S. document AP-42,


chapter 7 (available online at

http://www.epa.gov/ttnchie1/ap42/ch07/final/c07s01.pdf):

Lt (Total losses) = Ls (Standing storage loss) + Lw (Working losses)

Lt, the total amount of product lost in the form of emissions is the combined amounts of

the losses due to standing evaporation in the tank (Ls) and the total amount lost from

forced expelling when the tank is being filled with liquid (Lw).

LS = Days x Wv x Vv x KE x Ks

Where:

Days is the number of days you are reporting for, for the liquid (365 for

one year)

*** A note about this variable: be sure to keep accurate daily records of

your tank’s throughput. Some tanks may only hold a specific liquid for half

a day while others hold a liquid for much longer. If you don’t keep track of

processes that happen in less than one full day’s time your results could be

less accurate.***

Wv is stock vapor density

Vv is vapor space volume, ft3

KE is vapor space expansion factor

Ks is vented vapor saturation factor

Lw = 0.0010 x Mv x PvA x Q x KN x Kp

Where:

http://www.epa.gov/ttnchie1/ap42/ch07/final/c07s01.pdf


Mv is the molecular weight of vapor

*** A note about molecular weight: if you are unable to determine the

molecular weight of one or more chemical components of your liquid,

assuming an AVERAGE value of 150 will help avoid under-reporting

emissions. However, this assumption should only be made when absolutely

necessary. ***

PVA is vapor pressure at daily average liquid temperature

Q is the flow (amount of liquid processed)

KN is the working loss turnover factor

KP is the product factor for the specific liquid

This above core equation provides the basis for calculating air emissions from

tanks. However, each of the above variables will differ based on the 5 main

components of tanks calculations. You will need to calculate the unique values for

each of the basic variables for each tank before you can apply this general

equation.

As stated above, the core calculation is merely the base – depending on the type

of tank parameters in place, you will need to modify the equation. For example, if

you use the most common form of tank, a fixed-roof tank, you should refer to the

AP-42 Ch. 7 section 7.1.3.1, which outlines how to specifically calculate the

variables to be used in the core calculation in regards to a fixed-roof. The method

you use for estimating emissions will be different if you had a floating roof, or if

you used a heated tank.


To see one set of differences:

Fixed Roof Tanks Emissions

LT = LS + LW

Floating Roof Tank Emissions

LT = LR + LWD + LF + LD

Where:

LR = rim seal loss, lb/year

LWD = withdrawal loss, lb/year

LF = deck fitting loss lb/year

LD = deck seam loss

EHS Professionals often have the most questions about hot and heated tanks.

The actual emission estimation calculations for these tanks are not much

different than other tanks, but the temperature variables will vary from tank to

tank.

Heated tanks are those tanks that keep a mixture heated to a certain temperature,

higher than the ambient air temperature, in order to preserve its fluidity. Hot

tanks are tanks in which liquids that are already at a higher temperature than the

ambient air temperature are poured in order to eventually cool.


You can calculate emissions from hot and heated tanks using the same core

equation for working losses for unheated tanks. The EPA guidelines assume that

heated and hot tanks will have no breathing losses because the internal

temperature of the tank will be kept at a constant temperature, and the tank is

well insulated from ambient heat loss or gain. Therefore, for hot and heated

tanks, LS = 0.

Be aware of which temperature variables to use in your calculations. The

temperature variable will be based on the temperature at which you keep liquid

in the tanks heated to. This temperature could vary from liquid to liquid,

depending on each one’s chemical properties.

Here’s the basic working loss formula, adjust for hot and heated tanks:

Lw = 0.0010 x Mv x PvA x Q x KN x Kp

Where:

Mv is the molecular weight of vapor

*** A note about molecular weight: if you are unable to determine the

molecular weight of one or more chemical components of your liquid,

assuming an AVERAGE value of 150 will help avoid under-reporting

emissions. However, this assumption should only be made when absolutely

necessary. ***

PVA is vapor pressure at the fixed/constant liquid temperature at

which your hot/heated tank stores liquids.

*** Note: you will need to know the vapor pressure at the temperature your

liquid is stored at, based on its chemical properties. If this data is unknown


or missing, you will need to contact your vendors or perform testing to get

this information.***

Q is the amount of liquid processed.

KN is the working loss turnover factor.

KP is the product factor for the specific liquid.

Hot and heated tanks can become difficult to manage if you have constantly

changing stored liquids and are constantly changing the temperature at which

they are stored. The key in this situation is careful recordkeeping and keeping

your emission estimations on the right schedule – if you see daily

product/temperature changes you’ll need daily records of all those variables to

ensure you have the data you need to report properly.

That’s one main reason why many users of hot and heated tanks are using

sophisticated emissions management systems and monitoring devices to keep

them ahead of all this data management.

In some cases you may have to calculate the vapor pressure of a mixture on your

own, if no data has been provided for you. Use the following logic to calculate

vapor pressures that you can use in the tank calculations in this section.

A chemical’s vapor pressure can be calculated using one of the four following

methods. Which method you use will depend on the data you have available for

each component of the liquid, and the type of liquid:


For Organic chemical Mixtures

For organic chemical mixtures, the total vapor pressure can be estimated to be

the sum of all the partial vapor pressures of all components within the stored

mixture, by Applying Raoult’s Law:

A) If the component’s Antoine constants (A, B, and C) are known, use the

Antoine Equation:

log10(P) = A – (B / (T + C))

B) If that data is not available, check if the Riedel constants A, B, C, D and N,

are available. If so, use the Riedel Equation:

ln(P) = A + B/T + C ln(T) + D TN

C) If that data is not available, use published or empirical data, like copies of

the MSDSs or SDSs containing the pure component measurement at a

given location.

D) If that data is unavailable approximate using this set of assumptions:

All substances that are salts are assigned a vapor pressure of 0

psia.

All substances that are polymers and copolymers are assigned a

vapor pressure of 1 mm Hg (0.01938158 psia).

All remaining unknown components are assigned a vapor

pressure of 0 psia.

For Petroleum Products

The AP42 section 7 provides a specific equation to use for determining the Vapor

Pressure of petroleum products. Instead of Raoult’s Law use equation 3-24:

http://www.epa.gov/ttnchie1/ap42/ch07/bgdocs/b07s01.pdf


Where A and B are calculated from the equations displayed in figure 3-5 of the

same AP42 section. To use this equation you must know the S (distillation slope)

and RVP (Reid Vapor Pressure):

For Crude Oil

The vapor pressure of crude oil products is determined using the equation in

AP42 section 7 figure 3-1b. To use this equation you must know the liquid’s Reid

Vapor Pressure (RVP) variable:


For Further Help with Vapor Pressure Data

The American Petroleum Institute (API) has compiled documentation and data

about various select petroleum and crude oil products and their properties. Table

2 “Typical Properties of Selected Petroleum Liquids” of API Chapter 19.4

provides vapor pressure constants, molecular weight, TVP, etc.

It is available for purchase from the API at www.api.org.

Whenever you move chemical mixtures from one tank into a mobile tank or into

a transportation vehicle like a truck, some air emissions are released during the

process.

http://www.api.org/


The calculation for determining losses from loading operations from mobile

sources is different than the methods used for breathing losses. To calculate the

emissions from your mobile source loading operations use the following formula:

Where:

LL is the loading loss rate, measured as pounds per 1000 gallons of liquid

loaded

S is the applicable saturation factor taken from table 5.2-1 (see below). This

table taken from EPA AP-42 document.

P is the True Vapor Pressure of the liquid loaded, in pounds per square

inch absolute (psia).

M is molecular weight of vapors, in pounds per pound-mole (lb/lb-mole).

T is the temperature of the loaded liquid in degrees R (degrees Fahrenheit

+ 460).

***Note: the final, bracketed segment of the equation is only used if you

have any sort of control devices in place.***


Let’s see that calculation at work:

In this example you are loading 8000 gallons worth of gasoline into a cargo truck

using the dedicated vapor balance service mode of operation. The gasoline is

stored at 80 °F, with a Reid vapor pressure of 9 psia. You have a vapor recovery

efficiency of 95% and a vapor collection efficiency of 98.7%.


Step 1: Calculate the correct variables for use in the loading loss

equation.

In this case:

S = 1.00 (from table 5.2-1)

P = true vapor pressure is 6.6 psia

M = molecular weight of gasoline vapors 66

T = 540°R (80°F + 460)

eff = overall efficiency rating (98.7% collection X 95% recovery) = 94% overall

Step 2: Apply the variable to the equation and find emission rate for

the operation.

= 0.60 lb/103 gallons.

Step 3: Multiply the emission rate by the total amount of liquid

loaded.


= 0.60 lb/103gal x 8000 gallons

= 4.8 lbs of emissions released.


Loading operations at marine terminals do not use the same equation as trucks

and tanks, as outlined in the example above. Instead, the EPA has developed a

table of emission factors that you should use in place of the equation. We’ve

included the table below, taken from the EPA’s AP-42 document:


Because tanks calculations are particularly dense, the United States EPA has

created an online software tool that can be used to more easily calculate

emissions from some types of tanks. This tool is known as TANKS.

You can access TANKS from the EPA’s website here:

http://www.epa.gov/ttnchie1/software/tanks/

However, some regulatory agencies have recently made the decision

to not accept reports done using TANKS for all heated tanks, tanks

that store warm products, and tanks with significant variations in

throughput.

This decision was made because TANKS does not accurately calculate the effects

of temperature on vapor pressure variables and because it relies solely on annual

average liquid temperatures. In situations like heated tanks where temperature

becomes a more complex issue, TANKS fails to accurately report emissions.

Some problem scenarios include:

TANKS underestimates emissions from intermediate process tanks with

floating roofs that store materials at a warmer-than-ambient temperature.

For heated tanks, TANKS incorrectly assumes that vapor-space and liquid-

surface temperature ranges are equal, when this is not always the case.



TANKS cannot calculate emissions for some high molecular weight

petroleum distillates if the storage temperature is over 100 degrees

Fahrenheit.

TANKS does not incorporate temperature as a variable when determining

unheated, fixed-roof tank working losses. Instead it just assumes a fixed

vapor-space temperature of 63 degrees Fahrenheit.

Because TANKS uses the annual average liquid bulk temperature, it uses

incorrect data when computing monthly emissions.

If you are using a heated tank, storing heated liquids, or your tank experiences a

significant amount of throughput, you must use the AP-42 Ch. 7 core

calculation.


Get access to ERA’s 20 years of compliance experience. Meet with one of ERA’s

Subject Matter Experts, to personally discuss how to tackle your specific tanks

compliance issue in a cost effective manner.

Get a 45 minute Technical Overview to personally discuss the specific air

emissions EHS challenges, what systems and processes can be implemented

to reliably solve the problem, and how to make your EHS Department

profitable.

To arrange for this Technical Overview, please contact Brian Haney at (256) 232-

4437 or [email protected] – or alternatively go to:

http://lando.era-environmental.com/tanks-technical-overview

mailto:[email protected]

http://lando.era-environmental.com/tanks-technical-overview


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http://www.era-environmental.com/


AP-42 Chapter 7 (online PDF):


U.S. EPA TANKS software: http://www.epa.gov/ttnchie1/software/tanks/

TANKS Software FAQ: http://www.epa.gov/ttn/chief/faq/tanksfaq.html

Canadian meteorological data from Environment Canada:

http://climate.weather.gc.ca/index_e.html

International meteorological data: https://eosweb.larc.nasa.gov/cgi-

bin/sse/sse.cgi?+s01#s01



http://www.epa.gov/ttn/chief/faq/tanksfaq.html

http://climate.weather.gc.ca/index_e.html

https://eosweb.larc.nasa.gov/cgi-bin/sse/sse.cgi?+s01#s01

https://eosweb.larc.nasa.gov/cgi-bin/sse/sse.cgi?+s01#s01

the science of storage tanks emissions calculations

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