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Reference Method for Source Testing: Measurement of Releases of Selected Semi-volatile Organic Compounds from Stationary Sources

Section 7: Calculations

To simplify recording during a test, field data may be entered in the units for which the sampling equipment is designed. These values must be converted, if necessary, to the metric units specified in the applicable equations.

7.1 Equations (see Section 7.2 for Nomenclature)

7.1.1 Dry Gas Meter Volume

The total sample volume measured by the dry gas meter is corrected to reference temperature and pressure conditions (25°C and 101.3 kPa) using Equation 1. For a temperature-compensated dry gas meter (Tm)avg should be substituted by the temperature specified by the manufacturer.

Equation 1

Dry Gas Meter Volume Equation

7.1.2 Volume of Water Vapour

The volume of water vapour in the sack gas sample expressed at reference conditions (25°C and 101.3 kPa) is calculated by using Equation 2.

Equation 2

Volume of Water Vapour Equation

7.1.3 Moisture Content

The volumetric fraction of water vapour in the stack gas expressed at reference conditions (25°C and 101.3 kPa) is calculated using Equation 3.

Equation 3

Moisture Content Equation

For a saturated or suspersaturated stack, use a psychrometric chart to determine Bwo.

7.1.4 Absolute Stack Gas Pressure

The absolute stack gas pressure is calculated using Equation 4.

Equation 4

Absolute Stack Gas Pressure Equation

7.1.5 Stack Gas Molecular Weight

The stack gas molecular weight on a wet basis is calculated using Equation 5.

Equation 5

Stack Gas Molecular Weight Equation

7.1.6 Stack Gas Velocity

The stack gas velocity measured at each traverse point is calculated using Equation 6.

Equation 6

Stack Gas Velocity Equation

The average stack gas velocity ((Us)avg) and stack gas temperature ((Ts)avg) for the test run are determined by averaging the velocities and temperatures respectively measured at the traverse points.

7.1.7 Volumetric Stack Gas Flow Rate

The average volumetric stack gas flow rate expressed on a dry basis and at reference conditions (25°C and 101.3 kPa) is calculated using Equation 7.

Equation 7

Volumetric Stack Gas Flow Rate Equation

7.1.8 Isokinetic Variation

The isokinetic variation for each traverse points is calculated using Equation 8.

Equation 8

Isokinetic Variation Equation

A test shall be considered valid when no more than 10% of the isokinetic values fall outside the range 90% to 110% and the average for all the traverse points Iavg falls within the range 90% to 110%.

7.1.9 Correction Factor

The pollutant concentrations expressed in this method must be corrected to a basis of 11% O2. The correction factor to express concentrations at 11% O2 is calculated using Equation 9.

Equation 9

Correction Factor Equation

7.1.10 Polychlorinated Biphenyl Emission Rates

The emission rate of polychlorinated biphenyls is calculated using Equation 10.

Equation 10

Polychlorinated Biphenyl Emission Rates Equation

7.1.11 Concentrations of 2,3,7,8-TCDD Equivalent PCDDs and PCDFs

The concentration of 2,3,7,8-TCDD equivalent PCDDs and PCDFs corrected to 11% O2 is calculated using Equation 11. The weight of 2,3,7,8-TCDD equivalent PCDDs and PCDFs is determined from Figure 5.

Equation 11

Concentrations of 2,3,7,8-TCDD Equivalent PCDDs and PCDFs Equation

Figure 5: Calculation of 2,3,7,8-T4CDD Equivalent PCDDs and PCDFs
Calculation of 2,3,7,8-T4CDD Equivalent PCDDs and PCDFs

7.2 Nomenclature

As
inside cross-sectional area of stack or duct, m2

Bwo
volumetric fraction of water vapour in the stack gas, dimensionless

C2,3,7,8-T4CDD'
concentration of 2,3,7,8-T4CDD equivalent PCDDs and PCDFs on a dry basis at reference temperature and pressure conditions corrected to 11% O2, ng/m3 at 11% O2

CP
S-type pitot tube coefficient, dimensionless

ERPCBs
emission rate of polychlorinated biphenyls, μg/h

ΔHavg
average pressure drop across orifice meter, kPa

ΔH
pressure drop across orifice meter for each traverse point, kPa

Iavg
average isokineticity for the test, (%)

I
isokineticity i.e., the ratio of the sampling velocity through the nozzle to the velocity of the undisturbed gas stream at each traverse point, dimensionless, (%)

j
traverse point number, dimensionless

Md
molecular weight of stack gases on a dry basis, kg/kmol

Ms
molecular weight of stack gases on a wet basis, kg/kmol

MH2O
molecular weight of water, 18 kg/kmol

Nd
inside diameter of the sampling nozzle, mm

f11% O2
correction factor to convert concentrations at dry and reference temperature and presure conditions to 11% O2, dimensionless

%O2
concentration of oxygen in the stack gas (dry basis), % by volume

Ps
absolute stack gas pressure, kPa

Pbar
barometric pressure at the sampling site, kPa

ΔP
pitot-tube velocity pressure reading at each traverse point, kPa

Pref
reference pressure, 101.3 kPa

ΔPs
static pressure of the stack gas, kPa

Qs
volumetric stack gas flow rate on a dry basis at reference temperature and reference pressure conditions, m3/h

R
universal gas constant, 8.31 kPa m3(kmol·K)-1

t
sampling duration for each traverse point, min

(Ts)avg
average of the absolute stack gas temperatures, K

Ts
absolute stack gas temperature at each traverse point, K

(Tm)avg
average of the absolute dry gas meter temperatures, K

Tmi
absolute temperature at the dry gas meter inlet for each traverse point, K

Tmo
absolute temperature at the dry gas meter outlet for each traverse point, K

Tref
reference temperature, 298 K

(Us)avg
average stack gas velocity, m/s

Us
stack gas velocity measured at each traverse point, m/s

Vm
volume of stack gas sample at dry gas meter conditions, m3

(Vm)j
volume of stack gas sample at dry gas meter conditions for each traverse point, m3

(Vm)ref
volume of stack gas sample at reference conditions, m3

As
volume of water vapour in the stack gas sample at reference conditions, m3

WH2O
weight of water vapour condensed in the impingers, g

WPCBs
weight of polychlorinated biphenyls collected in the semi-volatile organics sampling train, mg

W2,3,7,8-T4CDD'
weight of 2,3,7,8-TCDD equivalent PCDDs and PCDFs collected in the semi-volatile organics sampling train, ng

γ
dry gas meter calibration factor (ratio of the wet test meter volume to the dry test meter volume) dimensionless

128.95
proportionality constant (m/s)(K-1·kg/kmol)½
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