ppmvd can be converted to mg/dscm through the following equation.

mg/dscm = P × ppmvd × MW

R × (273 + C)

For standard conditions: 

MW = molecular weight

PV = nRT

for n = 1.0

V = RT/P

R = 0.0821 (L·atm)/(mol·K)

P = 1.0 atm

T = 20.0 C

V = 24.04 L/mol

Simplified expression for standard conditions:

Theoretical Calculation Method for Kiln Gas Diversion to Alkali By-pass and Coal Mill

NOTE: THIS CALCULATION ONLY REQUIRED IF ALKALI BY-PASS OR COAL MILL EXCEED 24 PPM.

NOTE: FOR THE PURPOSES OF THIS CALCULATION, APPLICABLE VALUES ARE ASSUMED TO BE AT OR CORRECTED TO 7 % O2.

mg/dscm = ppmvd × MW

V (24.04 l/mol)

Due to the fact that V can vary, a referenced conversion value will be used for calculation. 

Referencing 40 CFR 60.45(f)(2)

mg/dscm = ppmvd × MW × 41,500.0

 1,000,000.0

Conversions and other data

THC as propane, MW = 44.0 g/mol

Conversion = 453,592.4 mg/lb

Conversion = 35.3 dscf/dscm

6/28/2012 1 of 4
Theoretical Calculation Method for Kiln Gas Diversion to Alkali By-pass and Coal Mill

NOTE: THIS CALCULATION ONLY REQUIRED IF ALKALI BY-PASS OR COAL MILL EXCEED 24 PPM.

NOTE: FOR THE PURPOSES OF THIS CALCULATION, APPLICABLE VALUES ARE ASSUMED TO BE AT OR CORRECTED TO 7 % O2.

Step 1: Determine the allowable mass emissions of THC based on 24 ppmvd @ 7% O2 standard.

Max Kiln gas flow rate = 54,000.0 dscf/ton feed

Max hourly production = 151.5 ton clinker/hr

Conversion = 1.6 ton of feed/ton of clinker

Hourly max kiln gas flow rate = 13,090,909.1 dscf/hr

Hourly max kiln gas flow rate = 370,742.3 dscm/hr

THC Standard = 24.0 ppmvd @ 7% O2

Concentration = 43.82 mg/dscm

Allowed mass emissions rate = 35.8 lb/hr

Step 2: Determine the actual mass emissions of THC leaving the alkali by-pass.

Actual alkali by-pass flow rate = 37,074.2 dscm/hr Example assumes 10 % of max kiln gas. Normally determine by stack test.

Determine THC concentration = 56.0 ppmvd Determined by stack test.

Concentration = 102.26 mg/dscm

Actual mass emissions rate = 8.4 lb/hr

Step 3: Determine the actual mass emissions of THC upstream of the coal mill.

Actual coal mill flow rate = 55,611.3 dscm/hr Example assumed 15 % of max kiln gas. Normally determine by stack test.

Determine THC concentration = 56.0 ppmvd Determined by stack test.

Concentration = 102.26 mg/dscm

Actual mass emissions rate = 12.5 lb/hr

Step 4: Back Calculate allowable limit to be measured by CEMS using mass and flow data

Kiln stack flow rate = 278,056.7 dscm/hr Example assumes max kiln gas minus bypass and coal mill. Normally determine by CEMS.

Allowable mass emission rate = 14.9 lb/hr Calculated as max allowable emission rate minus actual mass from by-pass and coal mill. 

Allowable concentration = 24.3 mg/dscm

Allowable concentration as ppmvd = 13.3 ppmvd Allowable concentration as ppmvd at 7 % O2

6/28/2012 2 of 4
Theoretical Calculation Method for Kiln Gas Diversion to Alkali By-pass and Coal Mill

NOTE: THIS CALCULATION ONLY REQUIRED IF ALKALI BY-PASS OR COAL MILL EXCEED 24 PPM.

NOTE: FOR THE PURPOSES OF THIS CALCULATION, APPLICABLE VALUES ARE ASSUMED TO BE AT OR CORRECTED TO 7 % O2.

Step 5: Check data against total limit

Total concentration = 24.0 ppmvd assumes all values are based on 7% O2.

Calculates as: (Qab × Cab) + (Qcm × Ccm) + (Qks × Cks)

(Qab + Qcm + Qks)

Step 6: Simplify expression for quick calculation method of required CEMS value.

(Qab × Cab) + (Qcm × Ccm) + (Qks × Cks) ≤ 24

(Qab + Qcm + Qks)

(Qab × Cab) + (Qcm × Ccm) + (Qks × Cks) ≤ (24 × (Qab + Qcm + Qks))

(Qks × Cks) ≤ (24 × (Qab + Qcm + Qks)) - (Qab × Cab) - (Qcm × Ccm)

Cks ≤ (24 × (Qab + Qcm + Qks)) - (Qab × Cab) - (Qcm × Ccm)

Qks

Cks ≤ 13.3 ppmvd Allowable concentration as ppmvd at 7 % O2

6/28/2012 3 of 4
kiln stack (ks) exhaust 9,818,181.8 dscf/hr = Qks

 278,056.7 dscm/hr = Qks

 14.9 lb/hr = Calculated Mks

 24.3 mg/dscm = Dks

 13.3 ppmvd = Cks

alkali by-pass (ab) exhaust

APCD

CEMS

Theoretical Calculation Method for Kiln Gas Diversion to Alkali By-pass and Coal Mill

NOTE: THIS CALCULATION ONLY REQUIRED IF ALKALI BY-PASS OR COAL MILL EXCEED 24 PPM.

NOTE: FOR THE PURPOSES OF THIS CALCULATION, APPLICABLE VALUES ARE ASSUMED TO BE AT OR CORRECTED TO 7 % O2.

alkali by-pass (ab) exhaust

Qab = 1,309,090.9 dscf/hr

Qab = 37,074.2 dscm/hr

Cab = 56.0 ppmvd

Dab = 102.3 mg/dscm

Mab = 8.4 lb/hr

coal mill (cm) exhaust

 1,963,636.4 dscf/hr = Qcm

 55,611.3 dscm/hr = Qcm

 56.0 ppmvd = Ccm

 102.3 mg/dscm = Dcm

kiln gasses 12.5 lb/hr = Mcm

6/28/2012 4 of 4
ppmvd can be converted to mg/dscm through the following equation.

mg/dscm = P × ppmvd × MW

R × (273 + C)

For standard conditions: 

MW = molecular weight

PV = nRT

for n = 1.0

V = RT/P

R = 0.0821 (L·atm)/(mol·K)

P = 1.0 atm

T = 20.0 C

V = 24.04 L/mol

Simplified expression for standard conditions:

Actual Calculation Method for Kiln Gas Diversion to Alkali By-pass and Coal Mill

NOTE: THIS CALCULATION ONLY REQUIRED IF ALKALI BY-PASS OR COAL MILL EXCEED 24 PPM.

NOTE: FOR THE PURPOSES OF THIS CALCULATION, APPLICABLE VALUES ARE ASSUMED TO BE AT OR CORRECTED TO 7 % O2.

mg/dscm = ppmvd × MW

V (24.04 l/mol)

Due to the fact that V can vary, a referenced conversion value will be used for calculation. 

Referencing 40 CFR 60.45(f)(2)

mg/dscm = ppmvd × MW × 41,500.0

 1,000,000.0

Conversions and other data

THC as propane, MW = 44.0 g/mol

Conversion = 453,592.4 mg/lb

Conversion = 35.3 dscf/dscm

6/28/2012 1 of 4
Actual Calculation Method for Kiln Gas Diversion to Alkali By-pass and Coal Mill

NOTE: THIS CALCULATION ONLY REQUIRED IF ALKALI BY-PASS OR COAL MILL EXCEED 24 PPM.

NOTE: FOR THE PURPOSES OF THIS CALCULATION, APPLICABLE VALUES ARE ASSUMED TO BE AT OR CORRECTED TO 7 % O2.

Step 1: Determine the actual mass emissions of THC leaving the alkali by-pass.

Actual alkali by-pass flow rate = 38,232.8 dscm/hr Determine by stack test.

Determine THC concentration = 56.0 ppmvd Determined by stack test.

Concentration = 102.26 mg/dscm

Actual mass emissions rate = 8.6 lb/hr

Step 2: Determine the actual mass emissions of THC upstream of the coal mill.

Actual coal mill flow rate = 57,349.2 dscm/hr Determine by stack test.

Determine THC concentration = 56.0 ppmvd Determined by stack test.

Concentration = 102.26 mg/dscm

Actual mass emissions rate = 12.9 lb/hr

Step 3: Determine the actual total flow of kiln gas and calculate actual allowable mass emissions of THC based on 24 ppmvd @ 7% O2 standard.

Actual kiln stack flow rate (at CEMS) Actual kiln stack flow rate (at CEMS) = 286,746.0 286,746.0 dscm/hr dscm/hr Determined by CEMs. Determined by CEMs.

Total actual kiln gas flow rate = 382,328.0 dscm/hr Sum of alkali by-pass, coal mill, and kiln stack CEMS.

THC Standard = 24.0 ppmvd @ 7% O2

Concentration = 43.82 mg/dscm

Actual allowed mass emissions rate = 36.9 lb/hr

Step 4: Back Calculate allowable limit to be measured by CEMS using mass and flow data

Actual kiln stack flow rate (at CEMS) = 286,746.0 dscm/hr Determined by CEMs.

Allowable mass emission rate = 15.4 lb/hr Calculated as actual allowable emission rate minus actual mass from by-pass and coal mill. 

Allowable concentration = 24.3 mg/dscm

Allowable concentration as ppmvd = 13.3 ppmvd Allowable concentration as ppmvd at 7 % O2

6/28/2012 2 of 4
Actual Calculation Method for Kiln Gas Diversion to Alkali By-pass and Coal Mill

NOTE: THIS CALCULATION ONLY REQUIRED IF ALKALI BY-PASS OR COAL MILL EXCEED 24 PPM.

NOTE: FOR THE PURPOSES OF THIS CALCULATION, APPLICABLE VALUES ARE ASSUMED TO BE AT OR CORRECTED TO 7 % O2.

Step 5: Check data against total limit

Total concentration = 24.0 ppmvd assumes all values are based on 7% O2.

Calculates as: (Qab × Cab) + (Qcm × Ccm) + (Qks × Cks)

(Qab + Qcm + Qks)

Step 6: Simplify expression for quick calculation method of required CEMS value.

(Qab × Cab) + (Qcm × Ccm) + (Qks × Cks) ≤ 24

(Qab + Qcm + Qks)

(Qab × Cab) + (Qcm × Ccm) + (Qks × Cks) ≤ (24 × (Qab + Qcm + Qks))

(Qks × Cks) ≤ (24 × (Qab + Qcm + Qks)) - (Qab × Cab) - (Qcm × Ccm)

Cks ≤ (24 × (Qab + Qcm + Qks)) - (Qab × Cab) - (Qcm × Ccm)

Qks

Cks ≤ 13.3 ppmvd Allowable concentration as ppmvd at 7 % O2

6/28/2012 3 of 4
kiln stack (ks) exhaust 10,125,000.0 dscf/hr = Qks

 286,746.0 dscm/hr = Qks

 15.4 lb/hr = Calculated Mks

 24.3 mg/dscm = Dks

 13.3 ppmvd = Cks

alkali by-pass (ab) exhaust

Actual Calculation Method for Kiln Gas Diversion to Alkali By-pass and Coal Mill

NOTE: THIS CALCULATION ONLY REQUIRED IF ALKALI BY-PASS OR COAL MILL EXCEED 24 PPM.

NOTE: FOR THE PURPOSES OF THIS CALCULATION, APPLICABLE VALUES ARE ASSUMED TO BE AT OR CORRECTED TO 7 % O2.

CEMS

APCD

alkali by-pass (ab) exhaust

Qab = 1,350,000.0 dscf/hr

Qab = 38,232.8 dscm/hr

Cab = 56.0 ppmvd

Dab = 102.3 mg/dscm

Mab = 8.6 lb/hr

coal mill (cm) exhaust

 2,025,000.0 dscf/hr = Qcm

 57,349.2 dscm/hr = Qcm

 56.0 ppmvd = Ccm

 102.3 mg/dscm = Dcm

kiln gasses 12.9 lb/hr = Mcm

6/28/2012 4 of 4