Graham's Ratio

Problems With Determining Oxygen Deficiencies in Ratios Used for Assessing

Spontaneous Combustion Activity

Darren Brady

Manager OHECC

Simtars

Department of Mines and Energy

Spontaneous Combustion Ratios

Several ratios commonly used to indicate spontaneous combustion, compare products of oxidation with the amount of oxygen consumed.


These ratios are used to measure the intensity of any oxidation of the coal that may be occurring. As the coal gets hotter the oxidation reaction becomes more efficient and more of the oxygen is converted to products of oxidation, such as carbon monoxide and carbon dioxide.


Ratios such as Graham’s, Young’s and Jones-Trickett’s all divide products of combustion by the amount of oxygen consumed to give a quantifiable measure of how much oxygen was used to generate the amount of combustion products measured.

DC2.CAD

Oxygen Deficiency

Oxygen deficiency is the term given to the amount of oxygen used (consumed/removed) from the inlet air stream by any activity as it undergoes reactions and interactions with the coal.

What Can Go Wrong?

• More than one source of oxygen depletion

What Can Go Wrong?

• Equation used for calculating the oxygen consumed by any oxidation/absorption-adsorption

What Can Go Wrong?

• The measurement technique

What Can Go Wrong?

• Instrument inaccuracies

What Can Go Wrong?

• Unreliable for samples where oxygen deficiencies are less than 0.3%

More Than One Source of Oxygen Depletion

• If there is more than one source of oxygen depletion then these ratios will be under estimated as it appears that more oxygen was used to produce the products than was really the case

Equations

Graham’s ratio is often expressed as

Where:

= Graham’s ratio

= final carbon monoxide concentration (%)

= final nitrogen concentration (%)

= final oxygen concentration (%)

ff ONCO

GRf

22265.0100

GR

fCOfN 2

fO2

Equation 1

Equations

• Enables calculation without actually knowing what the initial gas concentrations were.

• The denominator in Equation 1 is the oxygen deficiency.

Initial Oxygen Calculation

fi NO 22 265.0

iO2

fN 2

If initial gas entering an area has a fresh air ratio of 20.95% O2 to 79.02% N2 (20.95/79.02 = 0.265), Equation 2 can be used to calculate the initial O2 concentration by using the amount of N2 determined to be present in the sample

Where:= initial oxygen concentration (%) = final nitrogen concentration (%)

Equation 2

Initial Oxygen Calculation

• Based on the assumption that nitrogen, being an inert gas, will not be consumed or created.

• Only valid for samples where the initial gas has the same O2 to N2 ratio as fresh air and where N2 and Ar results are combined (79.02%).

• Eliminates most problems with dilution because the measured N2 will also been diluted.

Oxygen Deficiency

ff ONOD 22265.0

Where:= oxygen deficiency (%)

= final nitrogen concentration (%) = final oxygen concentration (%)

OD

fN 2

fO2

Equation 3

The measured oxygen concentration in the sample is then subtracted from the calculated initial oxygen to give the oxygen deficiency

Equations

• Problems when the oxygen deficiency is large. • Analysis is done on a percentage volume basis, if O2

is being consumed/removed and nothing replaces it, the nitrogen concentration increases.

• The elevated nitrogen concentration results in over estimation of initial oxygen concentration and therefore oxygen deficiency.

Equations

O2

(%)

N2(+ Ar)

(%)

Initial O2

(%) Eq 2

OD( %)Eq 3

OD (%)O2 *(%)

2.3 81.8 21.7 19.4 18.65

9.2 80.4 21.3 12.1 11.75

15.7 83.1 22.0 6.3 5.25

8.1 89.1 23.6 15.5 12.85

*calculated assuming initial oxygen 20.95%.

Equations

GR

fi OO

COCOGR

if

22

100

Where:= Graham’s ratio= final carbon monoxide concentration (%)= initial carbon monoxide concentration (%)= initial oxygen concentration (%)= final oxygen concentration (%)

fCO

iO2

fO2

iCO

Equation 4

If initial gas results are available Graham’s ratio is often calculated using;

Equations

• Used when a tube bundle sampling point located in an intake

• Problems with calibration or drift of the oxygen analyser are negated as they are common to both measurements.

• Any dilution with seam gas between locations is seen as oxygen deficiency and over estimates oxygen deficiency.

Equations

Graham’s ratio calculations using Equation 4

CH4

(%)

O2i

(%)

O2f

(%)

COf

(%)

GR

0 20.95 20.8 0.0005 0.333

3% 20.95 20.8x0.97 = 20.18

0.0005x0.97=0.00049

0.063

6% 20.95 20.8x0.94= 19.55

0.0005x0.94=0.00047

0.034

Equations

fi

i

fOO

N

NOD 22

2

2

OD = oxygen deficiency (%)

fN 2 = final nitrogen concentration (%)

iN 2 = initial nitrogen concentration (%)

iO2 = initial oxygen concentration (%)

fO2 = final oxygen concentration (%)

Where:

Equations

Where:

= Graham’s ratio

= final carbon monoxide concentration (%)

= initial carbon monoxide concentration (%)

= final nitrogen concentration (%)

= initial nitrogen concentration (%)

= initial oxygen concentration (%)

= final oxygen concentration (%)

GR

fi

fi

i

f

ONNO

NNCOCO

GRif

22

22

2

2100

fCO

iCOfN 2

iN 2

iO2

fO2

Equations

Graham’s ratio calculations using Equation 6

CH4

(%)

N2f

(%)

O2f

(%)

COf

(%)

GR

0 78.8 20.8 0.0005 0.55

3 78.8x0.97 =76.44

20.8x0.97 =20.18

0.0005x0.97 =0.00049

0.55

6 78.8x0.94 =74.07

20.8x0.94 =19.55

0.0005x0.94 =0.00047

0.55

Equations

• The use of the fresh air N2 concentration of 79.02% includes 0.9% Ar in the amount and is used for techniques that are unable to differentiate the two gases.

• If the two are reported separately, the fresh air ratio is 20.95% oxygen to 78.1% nitrogen (20.95/78.1=0.268).

Equations

• GC analysis determines Ar and N2 separately• Equations 1, 2 and 3 must be modified for GC results

Equations

• Equation 1 becomes:

ff ON

COGR

f

22268.0

100

Equation 7

Equations


fi NO 22 268.0 Equation 8

Equations


ff ONOD 22268.0 Equation 9

Equations

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

24/03/2006 0:00 13/05/2006 0:00 2/07/2006 0:00 21/08/2006 0:00 10/10/2006 0:00 29/11/2006 0:00 18/01/2007 0:00 9/03/2007 0:00 28/04/2007 0:00 17/06/2007 0:00

Oxygen Deficiency calculated using Nitrogen as 79.02%

Oxygen Deficiency calculated with Nitrogen as 78.1%

Measurement Technique

• Tube bundle and real time systems don’t measure N2

• It’s calculated by subtracting the sum of the measured gases from 100.

• GC actually measures N2

• Influences which equation must be used

Real Time vs Tube Bundle Oxygen Measurements

20.3

20.4

20.5

20.6

20.7

20.8

20.9

21

21.1

21.2

21.3

16/ 07/ 2006 21:36 17/ 07/ 2006 0:00 17/ 07/ 2006 2:24 17/ 07/ 2006 4:48 17/ 07/ 2006 7:12 17/ 07/ 2006 9:36 17/ 07/ 2006 12:00

Time

Oxy

gen

Co

nce

ntr

atio

n(%

)

Realtime Tube

Real Time vs Tube Bundle Oxygen Deficiencies

-0.6-0.5

-0.4-0.3

-0.2-0.1

00.1

0.20.3

0.40.5

0.60.7

16/ 07/ 2006 0:00 16/ 07/ 2006 4:48 16/ 07/ 2006 9:36 16/ 07/ 2006 14:24 16/ 07/ 2006 19:12 17/ 07/ 2006 0:00 17/ 07/ 2006 4:48 17/ 07/ 2006 9:36 17/ 07/ 2006 14:24

Oxy

gen

Def

icie

ncy

(%

)

Real Time Tube Bundle

Real Time vs Tube Bundle Graham’s Ratio

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

7/07/2006 0:00 7/07/2006 12:00 8/07/2006 0:00 8/07/2006 12:00 9/07/2006 0:00 9/07/2006 12:00 10/07/2006 0:00 10/07/2006 12:00 11/07/2006 0:00

Time

Gra

ha

m's

Ra

tio

Real Time Tube

Fresh Air Oxygen as Measured by Tube Bundle

20.45

20.5

20.55

20.6

20.65

20.7

20.75

20.8

20.85

20.9

3/03/2007 0:00 4/03/2007 0:00 5/03/2007 0:00 6/03/2007 0:00 7/03/2007 0:00 8/03/2007 0:00 9/03/2007 0:00

% O

xyg

en

Tube Bundle 1 Tube Bundle 2

Tube Bundle

• Measurement of oxygen using paramagnetic analysers is flow rate dependent so flows from all tubes must be balanced.

Tube Bundle

• Two locations with the same oxygen concentration could read differently because more resistance in one of the tubes results in a slower flow and subsequently a lower reading than a location with the same concentration but flowing through the instrument at a faster rate.

Instrument Inaccuracies

• Slight inaccuracies in all measurements no matter how well the analysis is done and how good the instrument performing the analysis is.

• These slight variations can cause problems in samples with no significant oxygen deficiency whenever we get a slightly higher O2 (or slightly lower N2 measurement by GC analysis), and apply the known fresh air O2 to N2 ratio to determine the oxygen deficiency.


O2

(%)

N2

(%)

Oxygen Deficiency

(%)

20.61 76.63 -0.07

20.55 76.73 0.01


• It can appear that oxygen has actually been created (very unlikely underground).

• Really indicates that the ratio has stayed the same. • Difference comes totally from the acceptable

inaccuracies (tolerance) of the measurement technique.


• Calibration gas suppliers certify each component as the likely concentration within limits eg the O2 concentration in a recently supplied certified calibration gas is 19.6±0.5%.

• The true concentration may be as low as 19.1% or as high as 20.1%.

• When used to calibrate an instrument to 19.6% any difference will result in all oxygen measurements being high or low, but analytically acceptable.

• A change in calibration gas can lead to a step change in values measured by the sensor/instrument calibrated with that gas.


Oxygen analysers, at best, are accurate to 1% of full

scale. Thus a measured value of 20.7% for O2 would

be +/- 0.2%

A sample measured as: 10 ppm CO, 0.1% CO2,

20.7% O2 and 79.2% N2 (by difference) could thus

vary between 20.5% and 20.9% O2 and conversely

N2 would be between 79.4 and 79.0%

Thus Graham’s Ratio would range between:

GR =100 x 0.001 / (0.265 x 79.4 - 20.5)

= 0.1 / (21.04 - 20.5)

= 0.1 / 0.54 = 0.18

and

GR = 0.001 x 100 / (0.265 x 79.0 -20.9)

= 0.1 / (20.94 - 20.9)

= 0.1 / 0.04 = 2.86


Oxygen Deficiencies Less Than 0.3%

• When oxygen deficiencies are less than 0.3% the variation between readings can significantly affect the calculated ratios.

Oxygen Deficiencies Less Than 0.3%

Measured O2

(%) O2 Def

(%) CO (%)

Graham’s Ratio

20.94 0.01 0.0003 3.00 20.92 0.03 0.0003 1.00 20.90 0.05 0.0003 0.60 20.88 0.07 0.0003 0.43 20.86 0.09 0.0003 0.33 20.84 0.11 0.0003 0.27 20.82 0.13 0.0003 0.23 20.80 0.15 0.0003 0.20 20.78 0.17 0.0003 0.18 20.76 0.19 0.0003 0.16 20.74 0.21 0.0003 0.14 20.72 0.23 0.0003 0.13 20.70 0.25 0.0003 0.12 20.68 0.27 0.0003 0.11 20.66 0.29 0.0003 0.10 20.64 0.31 0.0003 0.10 20.60 0.35 0.0003 0.09 20.58 0.37 0.0003 0.08

Conclusions

• Despite the problems, ratios incorporating oxygen deficiencies can still be useful but anyone doing interpretation must be aware of all of these implications.

Conclusions

• Care must be taken when calculating oxygen deficiencies to ensure that the calculation is correct and representative for the sample and analysis technique.

Conclusions

• Interpretation of data is best done looking at trends rather than one off samples. Even if the ratio is being underestimated, any increase in intensity should result in an increase in the trend although the rate of change may not match the increase in intensity.

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Graham's Ratio