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EXHIBIT 4-6: Uncerta<strong>in</strong>ty Example for Statistical Sampl<strong>in</strong>g, cont<strong>in</strong>ued<br />

o<br />

The <strong>uncerta<strong>in</strong>ty</strong> associated with this value is calculated by apply<strong>in</strong>g Equation 4-4, us<strong>in</strong>g the absolute<br />

uncerta<strong>in</strong>ties for each molar compound.<br />

∑<br />

U 2<br />

( abs ) = ( )<br />

( % )<br />

mole%<br />

MW<br />

∑<br />

U abs mole × MW<br />

×<br />

2 2 2<br />

(0.0104× 14.93538) + (0.1585× 0.900847) + (0.3286×<br />

0.841325)<br />

= + (0.0871× 0.324503) + (0.0537× 0.059573) + (0.0507×<br />

0.078946)<br />

2 2<br />

+ (0.1040× 0.029461) + (0.1378× 0.022246) + (0.5266×<br />

0.058172)<br />

2 2 2<br />

2 2 2 2 2 2<br />

(0.1559) + (0.1428) + (0.2765) + (0.0283) + (0.0032) + (0.0040)<br />

= = 0.350567<br />

2 2 2<br />

+ (0.0031) + (0.0031) + (0.0306)<br />

Urel 0.350567<br />

( ) = × 100% = 2.03%<br />

∑( mole% × MW )<br />

17.25045<br />

The weight percent carbon of the average composition is calculated by apply<strong>in</strong>g the follow<strong>in</strong>g equation:<br />

Wt% C<br />

∑<br />

lbmole x lbmole C 12 lb C 1<br />

i<br />

Total<br />

= × × ×<br />

100 lbmoletotal lbmole<br />

i<br />

lbmole C MWTotal<br />

This equates to 73.00041% C, as shown <strong>in</strong> Table 4-9. The <strong>uncerta<strong>in</strong>ty</strong> associated with this value is calculated<br />

by apply<strong>in</strong>g Equation 4-1, us<strong>in</strong>g the absolute uncerta<strong>in</strong>ties for the weight percent carbon of each molar<br />

compound.<br />

o The <strong>uncerta<strong>in</strong>ty</strong> associated with this value is calculated by apply<strong>in</strong>g Equation 4-1, us<strong>in</strong>g the absolute<br />

uncerta<strong>in</strong>ties for each molar compound:<br />

2<br />

U ( abs) = U ( abs)<br />

( %)<br />

wt %<br />

∑ wt ∑<br />

2 2 2<br />

(0.0228× 64.7728) + (0.1598× 4.168007) + (0.3292×<br />

1.32982)<br />

=<br />

2 2 2<br />

+ (0.0894× 1.535612) + (0.0574× 0.28521) + (0.0546× 0.377961) = 1.693261<br />

2 2 2<br />

+ (0.1060× 0.142025) + (0.1393× 0.107244) + (0.5270×<br />

0.281732)<br />

o<br />

o<br />

1.693261<br />

Urel ( ) = × 100% = 2.32%<br />

∑( wt%)<br />

73.00041<br />

The average annual CO 2 emissions factor is then calculated by apply<strong>in</strong>g the follow<strong>in</strong>g equation:<br />

6<br />

lb CTotal 44lb CO<br />

2/lbmole CO<br />

2<br />

lbTotal lbmoleTotal<br />

10 scf tonne CO2<br />

× × × × ×<br />

lbTotal 12lb C/lbmole C lbmoleTotal 379.3 scf MMscf 2204.62 lb CO2<br />

=55.2180 tonnes CO 2 /MMscf.<br />

The <strong>uncerta<strong>in</strong>ty</strong> for this quantity is calculated by apply<strong>in</strong>g Equation 4-6 for the relative uncerta<strong>in</strong>ties<br />

of MW Total <strong>and</strong> wt% C Total<br />

2<br />

2 2<br />

⎛UX<br />

⎞ ⎛UY<br />

⎞<br />

Urel ( ) = ⎜ ⎟ + ⎜ ⎟ = 2.03 + 2.32<br />

⎝ X ⎠ ⎝ Y ⎠<br />

2 2<br />

= 3.08%<br />

Pilot Version, September 2009 4-26

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