Reference methods for measuring particulate matter and lead emissions from secondary lead smelters: section 3

Section 3: Calculations

• 3.1 Dry Gas Volume
• 3.2 Moisture Content
• 3.3 Average Volumetric Flow Rate
• 3.4 Total Weight of Particulate Malter
• 3.5 Total Lead Weight
• 3.6 Concentration of Particulate Matter
• 3.7 Concentration of Lead
• 3.8 Emission Rate of Particulate Matter
• 3.9 Emission Rate of Lead
• 3.10 Calculation of Percentage of Lead in Sample
• 3.11 Isokinetic Variation

3.1 Dry Gas Volume

Correct the sample volume measured by the dry gas meter to reference conditions (25°C and 760 mm Hg) using Equation 1.

• (V_m)_ref = volume of gas sample through dry gas meter at reference conditions, m³
• V_m = volume of gas sample through dry gas meter at meter conditions, m³
• T_ref = reference temperature, 298°K
• T_m = average absolute dry gas meter temperature, °K
• P_bar = barometric pressure at the sampling site, mm Hg
• P_ref = reference pressure, 760 mm Hg
• 0.392 = T_ref/P_ref', °K/mm Hg
• ΔH = average pressure drop across orifice, mm Hg

3.2 Moisture Content

Calculate the moisture content of the stack gas using Equations 2 and 3.

• (V_w)_ref = volume of water vapour in the gas stream at reference conditions, m³
• V_lc = total increase in volume of water in impingers (Figure 3), ml
• R = gas constant, 0.0624 mm Hg m³/g-mole °K
• M_H2O = molecular weight of water, 18 g/g-mole
• B_wo = proportion by volume of water vapour in the gas stream

3.3 Average Volumetric Flow Rate

Use Equation 4 to calculate the volumetric flow rate:

• Q = average volumetric flow rate on a dry basis at reference conditions, m³/h
• U_avg = average gas velocity, m/s
• A = stack cross-sectional area, m²
• B_wo = proportion by volume of water vapour in the gas stream, Equation 3, dimensionless
• T_ref = reference temperature, 298°K
• T_avg = average stack gas temperature, °K
• P_s = absolute stack gas pressure, mm Hg
• P_ref = reference pressure, 760 mm Hg
• 3600 = conversion factor, s/h

Note: U_avg is calculated by averaging the gas velocities measured at each traverse point across the stack using the methods of Report EPS 1-AP-74-1 in Method B. Convert the average velocity to metres per second.

3.4 Total Weight of Particulate Matter

Determine the total particulate catch (M_p) from the sum of the weights on the particulate matter analysis data sheet (Figure 4).

3.5 Total Lead Weight

Determine the total lead catch, M_L, from the sum of the weights on the lead analysis data sheet (Figure 5).

3.6 Concentration of Particulate Matter

Determine the concentration of particulate matter in the stack gas using Equation 5.

• C_s = concentration of particulate matter in stack gas on a dry basis at reference conditions, mg/m³
• M_p = total weight of particulate matter collected (see Figure 4), mg
• (V_m)_ref = volume of gas sample through dry gas meter at reference conditions (see Equation 1), m³

3.7 Concentration of Lead

Determine the concentration of lead in the stack gas using Equation 6.

• C_L = concentration of lead in stack gas on a dry basis at reference conditions, mg/m³
• M_L = total weight of lead collected (from Figure 5), mg
• (V_m)_ref = volume of gas sample through dry gas meter at reference conditions (see Equation 1), m³

3.8 Emission Rate of Particulate Matter

Calculate the emission rate of particulate matter using Equation 7.

• ER_p = emission rate of particulate matter from the stack on a dry basis at reference conditions, kg/h
• C_s = concentration of particulate matter in stack gas on a dry basis at reference conditions, mg/m³
• Q = volumetric stack gas flow rate on a dry basis at reference conditions (see Equation 4), m³/h
• 10^-6 = conversion factor, kg/mg

3.9 Emission Rate of Lead

Calculate the lead emission rate using Equation 8.

• ER_L = mass emission rate of lead from source, kg/h
• C_L = concentration of lead on a dry basis at reference conditions, mg/m³
• Q = average volumetric gas flow rate on a dry basis at reference conditions, m³/h
• 10^-6 = conversion factor, kg/mg

3.10 Calculation of Percentage of Lead in Sample

Determine the percentage of lead in the sample using Equation 9.

• P_L = percentage of lead in sample
• M_L = weight of lead in sample, mg (see Figure 5)
• M^p = weight of particulate in sample, mg (see Figure 4)

3.11 Isokinetic Variation

The isokinetic variation (I), calculated for each sample point using Equation 10, should fall within the range 90% ≤ % I ≤ 100%

• % I = ratio of the sampling velocity through the nozzle to stack gas velocity, %
• V_m = volume of gas sampled through gas meter at meter conditions for each point sampled, m³
• t = sampling time for each point sampled, min
• B_wo = proportion by volume of water vapour in the gas stream (see Equation 3)
• P_s = absolute stack gas pressure, mm Hg
• T_s = absolute stack gas temperature for each point sampled, °K
• T_mi = dry gas meter inlet temperature for each point sampled, °K
• T_mo = dry gas meter outlet temperature for each point sampled, °K
• P_bar = barometric pressure at the sampling site, mm Hg
• U_s = stack gas velocity at each point sampled, m/s
• N_d = inside diameter of sampling nozzle, cm
• ΔH = pressure drop across orifice meter for each point sampled, mm Hg

Note: U_s, the stack gas velocity at each point sampled, is calculated using Equation B-1, Method B of Report EPS 1-AP-74-1.