# Coal Calculations

Accurate and precise calculations are vital to the success of your coal operation. These calculations are used to calculate various skeleton parameters including ash and calorific value that let you determine the grades of your coal.

SGS global teams of chemists and experts use a range of coal analytical calculations and indexes to arrive at the calorific values, total hydrogen, Coke Reactivity Index (CRI) and Coke Strength after Reaction (CSR) of your coal sample. Our third party test results and calculations provide you with reliable data that complies with international standards.

The following are some of the interesting protocols and calculations regularly used by SGS coal and coke specialists. These calculations are provided for your information, but SGS cannot guarantee that all data or formulas match the most current standards. Clients trading coal must familiarise themselves with the current standards being used in contracts.

*** Net CV calculation - refer to ASTM D5865-12 / ISO 1928-2009
*** Moisture conversion to different bases - refer to ASTM D3180 / ISO 1170

1. Bases Conversion Factors:
Ref: ASTM D3180 / ISO 1170 - Conversion to different moisture bases

3. AR factor (converts Dry to AR): (100-TM)/100
AR = Dry x ((100-TM))/100)

4. DAF factor (converts Dry to DAF): (100-Dry Ash)/100
DAF = Dry / ((100-Dry Ash)/100)

2. Where:
TM is Total Moisture
ADM is Air Dried Moisture (Moisture in the Analysis Sample)
NM is Nominated Moisture
AD is As Determined (Air Dried) Basis
Dry is Dry Basis
DAF is Dry Ash Free Basis

3. Two Stage Total Moisture Formula (Refer to ASTM D3302 section 10)
Two stage total moisture determination is used when the coal sample is too small mass or too wet to divide or crush without the potential of losing significant amounts of moisture.
TM = Total moisture; Fm = Free Moisture; Rm = Residual moisture

4. Calorific Value Conversion Factors Ref: ASTM 5865-12  X1.4. & ISO 1928-9 10.5
J/g = kcals/kg divided by 0.238846 OR multiplied 4.1868
J/g = Btu/lb multiplied by 2.326 OR divided by 0.429923
kcal/kg = J/g multiplied by 0.238846 OR divided by 4.1868
kcal/kg = Btu/lb divided by 1.8 or multiplied by 0.555556
Btu/lb = J/g divided 2.326 OR multiplied by 0.429923
Btu/lb = kcals/kg multiplied by 1.8 or divided by 0.555556

5. CO2 Emission Factor (Directive 2003/87/EC)  Directive 2007/589/EC
CO2 Emission Factor  tCO2/TJ =
= As Received Carbon x 3.667 x [10,000/NCV(p)] in kJ/kg
= As Received Carbon x 3.667 x [2388.46/NCV(p)] in kcal/kg

Standard Uncertainty of CO2 Emission Factor (tCO2/TJ)
As part of new European Commission (EC) reporting requirements for CO2 emissions, the analyzing laboratory is asked to report “Standard Uncertainty of CO2 Emission Factor”, attributed to laboratory analysis, expressed as a standard deviation.

ISO reproducibility values for C(db) 1.00% and GCV(db) 300J/g, converted to as-received basis, are used in the calculation of Uncertainty.

6. Fuel Ratio
= Fixed Carbon / Volatile Matter

Ballast
= Ash(ar) + Total Moisture

7. Hydrogen in Coal: Refer to ASTM 3180 / ISO 1170
In as much as hydrogen values may be reported on the basis of containing or not containing the hydrogen in water (moisture) associated with the sample, alternative conversion procedures are defined below.

Use the following conversions to report H including or excluding H in moisture:

Total Hydrogen as-determined (ad): includes H in the analysis moisture

1. Hydrogen (excluding H in moisture)
H(dry base) = [Total Hydrogen(ad)-(AMx0.1119)] x (100/(100-AM))

2. Hydrogen (including H in moisture)
H(ar) = [Total Hydrogen(db) x ((100-TM)/100)]+(0.1119*TM)

3. ISO 1170 reports H air-dried basis excluding H in the as analyzed moisture.
H(air-dried) = Total Hydrogen(as-determined) - (Analysis Moisture x 0.1119)

Hydrogen and Oxygen Factors based on the atomic weight of H20
Hydrogen = Moisture X 0.1119
Oxygen = Moisture X 0.8881

8. DMMF Calculations
Dry Mineral Matter Free calculations (Reference ASTM D388)

9. Empirical Formula for estimation of Gross Calorific Value using Ultimate Analysis
(Ref: COAL Typology - Physics - Chemistry - Constitution; author D.W Krevelen; third edition 1993, page 528). All data is on a Dry Basis (DB) expressed as % weight.
 DULONG (1820)  =  (80.8 x C) + (344.6 x H) – (43.1 x O) + (25 x S) BOIE (1953) =  (84 x C) + (277.7 x H) – (26.5 x O) + (15.0 x N) + (25 x S) SEYLER (1938) = (123.9 x C) + (388.1 x H) + (25 x O2) - 4269 NEAVEL (1986) =  (81.05 x C) + (316.4 x H) – (29.9 x O) + (23.9 x S) - (3.5x Ash) MOTT & SPOONER (1940) OXYGEN < 15% = (80.3 x C) + (339 x H) - (34.7 x O) + (22.5 x S) GIVEN (1986) =  (78.3 x C) + (339.1 x H) – (33.0 x O) + (22.1 x S) + 152 MOTT & SPOONER (1940) OXYGEN > 15% = (80.3 x C) + (339 x H) - (36.6 x O) + (0.17 x O2) + 22.5 x S   NOTE: these formulas are not valid for coal blends. Refer to above Note for Seylers Formula.

Extract from COAL - D.W. Krevelen. (page 529) "All the empirical equations are modifications of the original Dulong equation with "some theoretical foundation", and are, by adaption to empirical CV data of coal, de facto empirical relationships. The correlations given by GIVEN (1986) and NEAVEL (1986) are the most reliable."

10. Net Calorific Value (NCV) Calculations and Conversion Factors
Ref: Net Calorific Value (ASTM D5865-12)
The heat produced by combustion of a substance at a constant pressure of 0.1 Mpa (1 Atm), with any water formed remaining as vapour.

ASTM D5865-12 / D3180 at constant pressure
Qh = 0.01 * Hvap * (Had / 2.016)
Qmar = 0.01 *Hvap * (Mar / 18.0154)
Qpar(net) = ( Qvad(gross) + Qv-p - Qh) * (100 - Mar) / (100 - Mad) – Qmar

Where:
Qv-p = The energy associated with this change in the volume of the gaseous phase for the combustion reaction
R = the universal gas constant [8.3143 J/(mol *K)]
T = the standard thermochemical reference temperature (298.15 K)
Hvap = heat of vaporization of water at constant pressure (43985 J/mol)
Qh = heat of vaporization of hydrogen content in the sample
Qmad = heat of vaporization of water content in the analysis sample
Qmar = heat of vaporization of total moisture content in the sample
Atomic Weights:  O2 = 31.998 / N2 = 28.0134 / H2 2.016 / H2O = 18.0154

ISO 1928-2009 at constant volume
Qv, net,m,J/g =( Q gr,v,d - 206.0 [ wHd ] ) x (1-0.01xMT) - (23.05x MT)
Qv, net,m,kcal/kg = ( Q gr,v,d - 49.20 [ wHd ] ) x (1-0.01xMT) - (5.51x MT)

ISO 1928-2009 at constant pressure
Qp, net,m,J/g =
{ Q gr,v,d - 212.2 [ wHd ] - 0.8 x [wOd + wNd] } x (1- 0.01MT) - 24.43 x MT
Qp, net,m,kcal/kg =
{ Q gr,v,d - 50.68 [ wHd ] - 0.191 x [wOd + wNd] } x (1- 0.01MT) - 5.84 x MT

[ wHd ] = H content of the sample less Hydrogen present in the moisture
w(H)d = w(H) x 100/100-MT
MT = Total Moisture

11. Seyler’s Formula
Various parameters of coal can be estimated from the Ultimate Analysis and Calorific Value determinations, using Seyler's formula, and other similar calculations (e.g. Dulong's formula).

ISO 1928 2009 Determination of Gross Calorific Value
The ISO standard is the only international standard that allows for the estimation of hydrogen content to be calculated using Seyler’s Formula.

Seyler’s calculation is only valid for most bituminous coals.
Note 1. NOT valid when the estimated Hdb is less than 3%
Note 2. NOT valid when the Odaf content is greater than 15%
Note 3. NOT valid for estimation of H if coal shipments are a blend of low rank coal, or anthracite, or petcoke, and bituminous coals
Note 4. NOT valid for low rank coal, anthracite, petcoke, or coke

ISO 1928 2009 Part E.3.3
wH = 0.07 x w(V) + 0.000165 x qv,gr,m - 0.0285 x [ 100 - MT - w(A) ]
w(H)  - is the H content of sample less H contained in moisture, as % mass
w(V) - is the VM content of sample with moisture content MT, as % mass
w(A) - is the ash content of sample with moisture content MT, as % mass
qv,gr,m - is the gross CV of sample with moisture content MT, in joules/g

12. MEAN SIZE OF COKE (reference ISO 728 Annex A)
= (B(a-c)+C(b-d)+…+J(h-k) +100j)/200

Where: a,b,c,d…h,j,k are the hole sizes, in mm., of successive sieves; 'A,B,C,D…H,J,K are the cumulative percentage oversizes for each of the sieves.

Note: The sieve with hole size 'a' is the smallest size through which all coke passes (i.e. A = 0%). The sieve with hole size "k" is the hypothetical sieve through which no coke will pass (k=0mm, K=100%).

### Coke Reactivity Index (CRI) and Coke Strength after Reaction (CSR)

When coke descends in the blast furnace, it is subjected to reaction with countercurrent CO2 and abrasion. These concurrent processes weaken the coke and chemically react with it to produce excess fines that can decrease the permeability of the blast furnace burden. SGS conducts CRI and CSR testing to provide high accuracy results with good turnaround times. CRI and CSR tests determine how much energy your coal will produce when being burned in the furnace.

The CRI/CSR test measures coke reactively in carbon dioxide at elevated temperatures and its strength after reaction by tumbling. In the test, duplicate 200g samples of ⅞” x ¾” (19 x 22 mm) sized coke are extracted from a minimum 1kg parent sample and reacted in a vessel with CO2 gas for two hours at 1100°C. The weight loss after the reaction equals the CRI. The reacted coke is then tumbled in an I-shaped tumbler for 600 revolutions at 20 rpm and is then weighed. The weight percent of the + ⅜” coke equals the CSR. Most blast furnaces will require a coke with a CSR greater than 60 and CRI less than 25.SGS is committed to providing accurate, cost effective blast furnace coke analysis for your operation.

SGS is the world leader in coal and coke analysis and testing. The data resulting from our analytical processes ensures optimal recovery rates and performance of your coal or coke.

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