Parr formulas

The Parr formulas, Eqs. (27-1) to (27-3), or the approximation formulas, Eqs. (27-4) and (27-5), are used for classifying coals according to rank. Tne Parr formulas are employed in htigation cases. 

Analyses and calorific values are determined on a mineral-matter-free basis by the Parr formulas (ASTM D-388), with corrections for pyrite and other mineral matter. The amount of pyrite is taken to be that equivalent to the total sulfur of the coal, which despite the potential error has been found to correlate well in studies of mineral matter. The remaining mineral matter is taken to be 1.08 times the weight of the corresponding (iron-oxide-free) ash ... 

In the Parr formula for moist, mineral-matter-free calorific value, the moisture basis used is that of the inherent moisture of the coal in the seam (natural bed moisture, capacity moisture) ... 

Thus, to classify coal, the calorific value and a proximate analysis (moisture, ash, volatile matter, and fixed carbon by difference) are needed. For lower-rank coals, the equilibrium moisture must also be determined. To calculate these values to a mineral-matter-free basis, the Parr formulas are used (ASTM D-388). 

Several formulas have been proposed for calculating the amount of mineral matter originally in the coal using data from ashing techniques as the basis of the calculations. Of these formulas, two have survived and have been used regularly to assess the proportion of mineral matter in coal the Parr formula and the... 

In the Parr formula, the mineral matter content of coal is derived from the expression... 

Because of the changes that occur in mineral matter during the ashing procedure, a number of formulas have been devised to allow calculation of the mineral matter content from various parameters determined during analyses of the coal. Minimally, this involves a calculation based on total content of ash and sulfur. The two formulas most commonly used are the Parr formula and the King-Maries-Crossley formula. 

The Parr formula is the one most often used in the United States and requires only ash and sulfur values as determined in routine analysis ... 

The classification of coal (ASTM D-388) depends on calculation of the volatile matter yield and fixed carbon values on a dmmf basis. Calorific values are calculated on a moist, mineral-matter-free basis. The Parr formula is used in the classification system to calculate the mineral matter from ash and sulfur data. 

One can also generalize the Berkowitz-Parr formula of Eqs. (16) and (55) into the following form, valid for the constrained equilibrium in MG ... 

The values on a dry, mineral matter-free basis (dmmf) were obtained by using the modified Parr formula to calculate the mineral matter (m.m.) content ... 

The ASTM system is based on proximate analysis in which coals containing less than 31% volatile matter on the mineral matter-free basis (Parr formula) are classified only on the basis of fixed carbon, i.e., 100% volatile matter. Coal is divided into five groups (1) >98% fixed carbon, (2) 98%-92% fixed carbon, (3) 92%-86% fixed carbon, (4) 86%-78% fixed carbon, and (5) 78%-69% fixed carbon. The first three of these groups are anthracites, and the last two are bituminous coals. 

Source Considine, D.M., Ed.. Energy Technology Handbook, McGraw-Hill, New York, 1977. M, equilibrium moisUrre, % VM, volatile matter, % FC, fixed carbon, % A, ash, % S, sulfur, Btu/lb rank Btu, moist mineral matter-free Btu/lb all calculations by Parr formulas. 

The Parr formula (which has been widely used in the United States) is obviously considerably simpler than the King-Mavies-Crossley formula (which has been in common use in Great Britain and Europe) and requires less analytical data. However, the King-Mavies-Crossley formula will, because of the detail, provide more precise mineral matter values. It is, however, a matter of assessing whether the slight improvement in precision is justifiable on the basis of the additional analytical effort. 

The most commonly used system of classification refers to the American standard (ASTM D-388 [13]) using fixed carbon combined with volatile matter on a dmmf basis for higher-rank coals and higher heating value (HHV) on moist mineral matter-free (mmmf) basis for lower-rank coals. The moisture used should be as close as possible to the natural bed moisture content and is obtained by exposing the sample to 30 °C and a relative humidity of 97%. To convert the analysis data to the mentioned reference state, the Parr formulas must be used assuming that a part of the ash sulfur leaves with the volatile matter ... 

The produced ash is not always applicable to identification of ash constituents. For determination of the composition of high-alkaline ashes, for example, it is suggested to lower the ashing temperature to 575 °C [15]. The Parr formulas, which are used to calculate the mineral-matter-free basis involving the ash content, have been already introduced by Equations (3.7) to (3.9). 

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