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This report was prepared by the engineering firm, RMT/Four Nines of Plymouth Meeting, Pennsylvania. Although it was prepared for finishers in Pennsylvania, it may be applicable to many finishers across the country who want to calculate their maximum allowable VOC content.

The Pennsylvania code gives the maximum allowable content of VOCs in surface coatings by process. The values in Table I are in lbs of VOC per gal of coating (minus water). These values are based on a standard solvent density of 7.36 lb/gal. Not all solvents have this density, however. To determine the allowable VOC content, corrected for non-standard solvent density, one must use Equation 1.

## Equation 1:

Pct reduction=100{1-[y(1-(x÷z_{1}))÷x(1-(y÷z_{2}))]}

Where:

x=lb VOC÷gal of coating minus water

for the present coating. (Maximum allowable VOC content at coating's solvent density.)

y=lb VOC÷gal of coating minus water

(Found in Table I. Maximum allowable VOC content at standard solvent density.)

z

_{1}=lb VOC÷gal of solvent

(Or density of VOC for present coating)

z

_{2}lb VOC (standard)÷gal of standard solvent

(Or standard solvent density of 7.36 lb/gal)

Equation 1 is formulated to solve for the pct reduction required by a control method when using a coating with VOC content greater than that specified in Table I. However, it is possible to use this equation to solve for x, the maximum allowable VOC content for a coating with non-standard solvent density. By setting the pct reduction to zero in the equation and arranging the equation, one can determine x as follows.

## Equation 2:

y{1-(x÷z

_{1})} = x{1-(y÷z_{2})}

As a practical example for air-dry coatings, the VOC limit in Table I is 3.5 lb/gal. The following analysis will be limited to coatings containing no water and no exempt solvents. A coating with a VOC content reported by the manufacturer as 3.44 lb/gal is selected for use in a dip tank. The coating also has a reported volatile solvent content of 52.37 pct by volume, which implies a solids content of 100 - 52.37 = 47.63 pct by volume. To determine whether or not this is a compliant coating, first solve for the present coating's solvent density:

3.44 (lb VOC (solvent) ÷ gal of coating) x (1 gal of coating ÷ 0.5237 gal of solvent) = 6.569 lb/gal of solvent

Note that this solvent density is less than the standard of 7.36 lb/gal.

Next, place these values in Equation 3 and solve for x: z_{1} = 6.569, y = 3.50 and z_{2} = 7.36. The result is a value of 3.31 lb/gal, the maximum allowable VOC content for the present coating adjusted for its solvent density.

## Equation 3:

x=y{1-x/z

_{1})÷(1-x/z_{2})}

The actual reported VOC content of 3.44 lb/gal is greater than this result and the coating is non-compliant for its intended application as an air-dry coating. Even though the actual VOC content of the coating is less than 3.50 lb/gal value, it is not a compliant coating because it does not meet the adjusted maximum allowable VOC content of 3.31 lb/gal.

To understand Equation 3 more fully, it is helpful to rearrange it in this way.

{x÷(1-x/z

_{1})} = {y÷(1- y/z_{2})}

Substituting units into Equation 4 results in this:

## Equation 4:

{(lb VOC÷gal coating)÷(1-((lb VOC÷gal coating)÷(lb VOC÷gal solvent))} = {(lb VOC÷gal coating)÷(1-((lb VOC÷gal coating)÷(lb VOC÷gal solvent))}

This can be simplified into

(lb VOC÷gal solids) = (lb VOC÷gal solids)

The right-hand side of Equation 4 may be regarded as the maximum allowable VOC content of a coating divided by the minimum required volume fraction of solids in a standard coating. For all coatings used in air-dry applications,

(1-(y÷z

_{2})) = 1-(3.5÷7.36) or 0.5245

Thus, the minimum required volume percentage of solids in a standard coating for air-dry application is 52.45 pct. The right-hand side of Equation 4 becomes

3.5 lb VOC 0.5245 =6.673 gal solids

This is the maximum amount of VOC per unit volume of solids that the standard air-dry coating may contain. The left-hand side of Equation 4 represents the lbs of VOC per gal of solids allowable in the present coating that has non-standard solvent density (and also non-standard solids volume fraction).

Equation four can now be rewritten as:

x (1 + 6.673/ z

_{1}) = 6.673x=(6.673÷ (1+ 6.673/z

_{1}Setting z

_{1}= 6.569 lb/gal as before the solvent density of the present coating, x again evaluates to 3.31.The term (1 - x/z

_{1}) is equal to 0.4961.This means that the solids volume percentage in the coating would have to be at least 49.61 pct in order to be in compliance. Since the solids content of the coating is only 47.63 pct, this coating is not in compliance.

A second coating has a reported VOC content of 3.45 lb VOC/gal of coating, which is slightly greater than the first coating. However, this coating has a volatile content of 47.05 pt by volume and a solids content of 52.95 pct by volume. The solvent density is 3.45/0.4705 = 7.33 lb/gal.

According to Equation 3, the maximum allowable VOC content for this particular coating is 3.49 lb VOC/gal of coating. Since this coating's VOC content of 3.45 lb VOC/gal is less than the allowable value of 3.49 lb VOC/gal, this coating complies with the requirements for air-dry coatings.

The foregoing discussion primarily serves to make the following point. In the world of VOCs the number on the product label or MSDS does not always tell the whole story. It is possible to switch to a lower VOC coating from a higher VOC coating only to find you have moved from a compliant coating to a non-compliant coating. Check solvent density and/or solids volume ratio as well as VOC content then evaluate the compliance status of a coating.

TABLE I--Allowable Content of VOCs in Surface Coatings by Process (in Pennsylvania)Coating Processlbs/galCoil coating 2.60 Automotive/light duty truck a.Prime coat 1.92 b.Topcoat 2.84 c.Repair 4.84 Metal furniture 3.00 Large appliance coating 2.84 Miscellaneous metal parts a.Topcoats for heavy duty trucks 3.50 b.Hopper car and tank car interiors 3.50 c.Pail and drum interiors 4.30 d.Clear coatings 4.30 e.Air-dry coatings 3.50 f.Extreme performance coatings 3.50 g.All others 3.00

TABLE II--Allowable Content of VOCs in Surface Coatings by Process (in Pennsylvania)Coating ProcessVOC allowed per gal of solidCoil coating 4.02 Automotive/light duty truck a.Prime coat 2.60 b.Topcoat 4.62 c.Repair 14.16 Metal furniture 5.06 Large appliance coating 4.62 Miscellaneous metal parts a.Topcoats for heavy duty trucks 6.67 b.Hopper car and tank car interiors 10.34 c.Pail and drum interiors 10.34 d.Clear coatings 6.67 e.Air-dry coatings 6.67 f.Extreme performance coatings 5.06 g.All others 5.06