Reference method to measure releases of lead in particulate from stationary sources: chapter 5

Section 3: Calculations

• 3.1 Equations
  • 3.1.1 Volume of Stack Gas Sample
  • 3.1.2 Volume of Water Vapour
  • 3.1.3 Moisture Content of Stack Gas
  • 3.1.4 Absolute Stack Gas Pressure
  • 3.1.5 Stack Gas Molecular Weight
  • 3.1.6 Stack Gas Velocity
  • 3.1.7 Volumetric Stack Gas Flow Rate
  • 3.1.8 Weight of Particulate Sample
  • 3.1.9 Weight of Lead in Sample
  • 3.1.10 Concentration of Particulate Matter
  • 3.1.11 Concentration of Lead
  • 3.1.12 Mass Emission Rate of Particulate Matter
  • 3.1.13 Mass Emission Rate of Lead
  • 3.1.14 Percentage of Lead in Particulate Matter
  • 3.1.15 Isokineticity
• 3.2 Nomenclature

To simplify record keeping 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 equations where they are used.

3.1 Equations (see Section 3.2 for nomenclature)

3.1.1 Volume of Stack Gas Sample

Correct the sample volume measured by the dry gas meter to reference temperature and reference pressure conditions (25°C and 101.3 kPa) by using:

Note: For a temperature-compensated dry gas meter, the average dry gas meter temperature, (T_m)_avg, should be substituted by a constant value as specified by the manufacturer.

3.1.2 Volume of Water Vapour

Calculate the volume of water vapour in the stack gas sample at reference conditions using:

3.1.3 Moisture Content of Stack Gas

Calculate the volumetric fraction of water vapour in the stack gas at reference conditions using:

For saturated stack gas, use a psychrometric chart to determine B_wo.

3.1.4 Absolute Stack Gras Pressure

Calculate the absolute stack gas pressure using:

3.1.5 Stack Gas Molecular Weight

Calculate the stack gas molecular weight on a wet basis by using:

Note: Use procedures in Method C of Reference Method EPS 1/RM/8 to calculate M_d.

3.1.6 Stack Gas Velocity

Calculate the stack gas velocity measured at each traverse point using:

3.1.7 Volumetric Stack Gas Flow Rate

Calculate the average volumetric flow rate of the stack gas on a dry basis and at reference conditions using:

3.1.8 Weight of Particulate Sample

Determine the weight of the particulate sample, W_p, from the sum of the particulate weights obtained from Containers No. l and 2 less the acetone blank, as shown in the Particulate Analytical Data sheet (Figure 4).

3.1.9 Weight of Lead in Sample

Determine the total weight of lead collected, W_L, from the Lead Analytical Data Sheet (Figure 5).

3.1.10 Concentration of Particulate Matter

Calculate the concentration of particulate matter in the stack gas using:

3.1.11 Concentration of Lead

Calculate the concentration of lead in the stack gas using:

3.1.12 Mass Emission Rate of Particulate Matter

Calculate the mass emission rate of particulate matter using:

3.1.13 Mass Emission Rate of Lead

Calculate the mass emission rate of lead using:

3.1.14 Percentage of Lead in Particulate Matter

Calculate the percentage of lead in particulate matter using:

3.1.15 Isokineticity

Calculate the isokineticity for each traverse point using:

A test shall be considered valid with respect to isokineticity (or isokinetic variation) providing that:

1. 90% or more of the isokineticity values, I, calculated for all traverse points are within the range 90 to 110%, i.e., 90 % ≤ I ≤ 110 %, and
   
2. the arithmetic average of all the isokineticity values is within the 90 to 110% range, i.e., 90 % ≤ I_avg. ≤ 110 %.

3.2 Nomenclature

A_s

inside cross-sectional area of the stack, duct or flue, m ²

B_wo

volumetric fraction of water vapour in the stack gas, dimensionless

C_L

concentration of lead in the stack gas on a dry basis at reference temperature and pressure conditions, mg/m ³

C_p

S-type pitot tube coefficient, dimensionless

C_s

concentration of particulate matter in the stack gas on a dry basis at reference temperature and pressure conditions, mg/m ³

ER_L

mass emission rate of lead, kg/h

ER_p

mass emission rate of particulate matter, kg/h

ΔH_avg

average pressure drop across orifice meter, kPa

ΔH

pressure drop across orifice meter for each traverse point, kPa

I_avg

the arithmetic average of all the isokineticity values 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), %

j

the j ^th traverse point, dimensionless

10^-3

conversion factor, kg/g

128.95

dimensional constant (m/s) [(kg/kmol/K)] ^½

3600

conversion factor, seconds/hour

10^-6

conversion factor, kg/mg

6 × 10^-5

conversion factor, (m ²/mm ²)(s/min)

M_d

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

M_s

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

M_H2O

molecular weight of water, 18 kg/kmol

N_d

inside diameter of the sampling nozzle, mm

%P_L

percentage of lead in particulate matter,

P_s

absolute stack gas pressure, kPa

P_bar

barometric pressure at the sampling site, kPa

P_ref

reference pressure, 101.3 kPa

Δp_s

static pressure of the stack gases, kPa

Δp

pitot tube velocity pressure at each traverse point, kPa

Q_s

volumetric stack gas flow rate on a dry basis at reference temperature and pressure conditions, m ³/h

R

universal gas constant, 8.31 (kPa)(m ³)(kmol ^-1)(K ^-1)

t

sampling duration for each traverse point, min

( T_m )_avg

arithmetic average of the dry gas meter temperatures, K

T_mi

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

T_mo

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

T_ref

reference temperature, 298 K

( T_s )_avg

arithmetic average of the stack gas, temperatures, K

T_s

stack gas temperature at each traverse point, K

U_s

stack gas velocity at each traverse point, m/s

( U_s )_avg

arithmetic average of the stack gas velocities, m/s

( V_w )_ref

volume of water vapour in the stack gas sample at reference temperature and pressure conditions, m ³

V_m

volume of stack gas sample at dry gas meter conditions, m ³

( V_m )_j

volume of stack gas sample at dry gas meter conditions for the j ^th traverse point, m ³

( V_m )_ref

volume of stack gas sample at reference temperature and pressure conditions, m ³

W_H2O

weight of water vapour condensed in the impingers, g

W_L

total weight of lead collected during the test run, mg

W_p

total weight of particulate samples collected during the test run, mg

γ

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