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NBSIR 81-2427-1

Calculations of the Heat Release

Rate by Oxygen Consumption for

Various Applications

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

Issued March 1 982

-QC EPARTMENT OF COMMERCE

100

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yAL BUREAU OF STANDARDS

1001

MATIONAL BUMAO

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LIBRABT

NBSIR 81-2427-1

CALCULATIONS OF THE HEAT RELEASE

RATE BY OXYGEN CONSUMPTION FOR

VARIOUS APPLICATIONS

MAY 1 7 1982

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6 . *3-

W. J. Parker

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

Issued March 1 982

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
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TABLE OF CONTENTS

Page

LIST OF TABLES Iv

Abstract 1

1. INTRODUCTION 2

2. GENERAL FORMULA FOR RATE OF HEAT PRODUCTION ^

3. OXYGEN DEPLETION 9

4. EFFECT OF NEGLECTING CARBON MONOXIDE PRODUCTION 12

5. RELATIVE HUMIDITY 14

6. VOLUME FLOW RATE INTO SYSTEM 15

7. WATER VAPOR ANALYZER IN AIR FLOW DETERMINATION 21

8. TRACER GAS IN AIR FLOW DETERMINATION 23

9. COMPLETELY DEPLETED AIR 24

10. HIGH TEMPERATURE OXYGEN CELL 28

11. SIMPLIFICATIONS 30

12. SUMMARY . 32

13. REFERENCES 35

14. NOMENCLATURE 36

ill
LIST OF TABLES

Table 1. Equations to be Used for Various Applications

Page

. 38

iv
CALCULATIONS OF THE HEAT RELEASE RATE BY

OXYGEN CONSUMPTION FOR VARIOUS APPLICATIONS

W. J. Parker

Abstract

The oxygen consumption technique is emerging as a

powerful tool for determining the heat release rate in

a number of diverse fire test applications, including

room fire tests, fire endurance tests, the ASTM E 84

tunnel test, and various heat release rate calorimeters.

Depending upon the constraints of the test, the accuracy

required, the availability of instrumentation and computational facilities, and the willingness to put up with

experimental inconveniences, a number of instrumentation

options have been considered—each of which require different calculational procedures. The purpose of this

report is to develop the equations in a general way and

show how to adapt them to various applications such as:

closed systems versus open systems; trapping carbon

dioxide before it reaches the oxygen analyzer, measuring

it, or assuming that it is equal to the reduction in

oxygen concentration; ignoring carbon monoxide or measuring

it; accounting for the density of the exhaust gases or

assuming that it is the same as for air; using a high

temperature oxygen cell which measures the oxygen concentration in the exhaust duct directly or a paramagnetic analyzer

1
for which corrections must be made for water vapor trapping;

taking into account or ignoring the ambient concentration

of water vapor and carbon dioxide; and improving the accuracy

for open systems by monitoring the water vapor in the

exhaust duct. The equations developed here should be

useful to anyone setting up a new system and will provide

a means of calculating the errors which might be expected when simplified procedures are used.

Key Words: calorimeters; fire tests; heat release rate;

oxygen consumption; room fires.

1 . INTRODUCTION

Experiments in the Steiner tunnel by Parker [1]^, in reduced- and

full-scale room fire tests by Sensenig [2], and in the OSU Heat Release

Rate Calorimeter by Krause and Gann [3] have demonstrated the usefulness

of oxygen consumption measurements for determining the heat release rate

of burning materials in a variety of applications. It has been established

that, to a reasonable engineering approximation, the burning of the

materials normally used in the construction and furnishing of rooms

will yield a nearly constant value, E, of heat produced per unit mass

of oxygen consumed, where E = 13.1 MJ/kg. This value is based on calculations on a large number of polymeric and natural materials by Huggett [A]

.

By measuring the rate of oxygen consumption in a room fire, we have at

^Numbers in brackets refer to the literature references listed at the

end of this report. 2
disposal for the first time a practical method of determining the total

rate of heat production. To the first approximation, the rate of

oxygen consumption is determined by the product of the volumetric flow

rate in the exhaust duct reduced to standard conditions and the decrease

in the oxygen concentration. However, the standard volume flow rate in

the duct which carries off the exhaust gases from the room or the

» calorimeter is in general larger than the standard volume flow rate of

air into the system because of the combustion reactions (e.g., +

6 ©2 ^ 6 €©2 + 5 H2O) which generally increase the molar flow rate.

Furthermore, the oxygen concentration in the exhaust duct may not be

the same as that in the oxygen analyzer because of the trapping out of

species such as water and CO2 in the sampling line. This report serves

to establish a second order of approximation for the calculation of

heat release by oxygen consumption by taking into account these two

factors, as well as the effects of CO production, variation in density

of the exhaust gases, and the relative humidity and vitiation of the

incoming air. Also developed are the equations to be used when a high

temperature oxygen cell or a water vapor analyzer is used to monitor

the exhaust gases.

The equations fot heat release rate by oxygen consumption are

developed in a general way which accounts for vitiated and humid incoming

air and with H2O, CO2, CO, and N2 as well as water soluble gases such

as HC£ and HCN as the combustion products. It is then shown how these

equations can be simplified for specific applications. For example,

there are open systems in which the combustion products along with

3
their entrained air are collected by a canopy hood and the total amount

of air flowing into the system must be estimated from the volume flow

rates measured in the exhaust duct. In addition there are closed

systems in which the combustion takes place in a chamber with an exhaust

duct and an air supply duct where the rate of air inflow can be accurately

measured. In some cases, the CO in the exhaust duct and water vapor

and CO^ in the incoming air can be neglected. Carbon dioxide may be

trapped out of the sampling line or it may be measured. While water

vapor measurements in the exhaust duct are not normally made, they

would improve the accuracy of the technique. There are oxygen analyzers

which operate at high temperature which can measure the actual concentration of oxygen in the exhaust gases, while most of the analyzers

measure oxygen in a cold gas from which the water and sometimes the CO

2 are removed. This report addresses all of these applications.

2. GENERAL FORMULA FOR RATE OF HEAT PRODUCTION

While the equations will be developed for the open system, the

equations for the closed system will appear as a special case. For the

room fire, which exemplifies the open system, it will be assumed that

the hood will collect all of the exhaust gases from the room plus an

arbitrary amount of entrained air. The total volume flow rate of air

into the system (i.e., the airflow into the room plus the air entrained

into the exhaust duct) will be designated as V and will be referred to

standard conditions. The volume flow rate of combustion products and

external air through the exhaust duct, referred to standard conditions.

4
will be designated V^. It is assumed that the water, as well as HC^-,

HCN, and other gases soluable in water, are trapped out in the sampling

line, and that N^, 0^, CO, and CO^ are the only gases that reach the

oxygen analyzer. It is assumed that the components of the incoming air

are nitrogen, oxygen, carbon dioxide, and water vapor. The concentrations

of all other species such as argon will be included in the concentration

of nitrogen.

Let n° , n° , n° , and n° be the molar flow rates of nitrogen,

^2 ^2 ^^2 ^2 ^

s oxygen, carbon dioxide, and water vapor into the system. Let n , ^2

’ ^CO’ ^CO ’ ^

0

molar flow of oxygen, nitrogen, carbon

monoxide, and carbon dioxide in the exhaust duct. The mole fractions

of the incoming gases are:

n.

X

CO,

n;; + n° + n° + n

° N

2 O2 CO2 H2 O

“«2

^2^

’^C02

^2 ^02 ^C02 ’^H20

^H20

’^N2 O2 CO2 ^2°

( 1 )

( 2 )

( 3 )

( 4 )

5
Since all of the gases are represented

( 5 )

If it is assumed that the molar flow rates of N

2

, 0^, CO^, and CO are

in the same ratio to each other in the analyzer as they are in the

exhaust duct, the mole fractions in the analyzers are:

n

=

CO,

C0„ o . S , s . S

2 ^2 ""02

( 6 )

= \o

nCO

o , s , s , s "Nj "O2 "cOj ^

"co

(7)

n

= ^2

Oo o.S.S ,S 2 n^ + n,, + n^,, + n

0,, CO, CO

( 8 )

2 2 2

Making use of equation 1, the volume flow rate of air into the system

referred to standard conditions is given by

W

n \ ^^^N2 ^^02 ''' ^^002 ^^

2°^ AIR °2 \lR

X,

(9)

where is the mass of one gram mole of air and is the density of

air under standard conditions. The oxygen depletion can be defined by

’^O,, ’^0, 0 =

n,.

( 10 )

6
The rate of heat production Is given by

Q - E ( 11 )

where W_ is the mass of one gram mole of oxygen. Combining equations

(9) and (11)

W,

( 12 )

Let the net heat of combustion per unit volume of oxygen consumed be

E’ E Ep = 17.2 MJ/m'

o O

2 AIR

where E = 13.1 MJ/kg, where the reactants and products are at 25°C,

W = 0.032 kg/mole, W = 0.0290 kg/mole based on normal dry air, and

vJ/^ AXK

^ 3 = 1.19 kg/m at 25°C, 760 mm Hg based on normal dry air.

Then the formula for the rate of heat production in the case of

complete combustion is given by

0V

A

(13)

Now consider the case of incomplete combustion where a fraction, f,

of the oxygen consumed goes into CO production. In order to burn off

the CO to CO

2 an additional fraction, f, of the original oxygen consumed

would be required. Then the total rate of oxygen consumption for

7
complete combustion would have had to increase by the factor (1 + f)

and the heat release rate would have been

comp

= E'(l + f) 0 X! V,

where 0 and are the actual measured values. Since the additional

heat produced by burning the CO to CO

2

would have been

^co

=

the actual heat release rate during incomplete combustion would be

^ = %omp - ^CO

= ' = =^0/^

Q - U' - f(E"-E')] XJ (14)

The difference in the heat of formation of CO and CO^ is 283 kJ/

mole. Therefore, there is a heat release of 566 kJ/mole of O

2

consumed

in the burning of CO. The heat release per volume of O

2 consumed in the

3 burning of CO, E", is 23.1 MJ/m referred to 25°C.

The fraction f is given by

f

s

n; - n.

(15)

8
Using equations (7), (8), and (10),

f = 1-0 ^0

( 16 )

Substituting equation (16) into equation (14) , the general formula for

the rate of heat release is given by

which reduces to equation (13) when X = 0,

(17)

The Indeterminate (1-0) /X^ which occurs in equation (17) when the

oxygen is completely consumed will be discussed in section 9.

3 . OXYGEN DEPLETION

In this section, the expression for the oxygen depletion, 0, to be

substituted into equations (13) or (17) will be derived.

Adding equations (6) and (7)

,

“cO

o , S . S , S ^2 ^02 \02 ’"cO

(18)

9
Eliminating n + n from equations (8) and (18)

,

n°

°2 ^2

1 _ - Y^ _ Y^

^ \o

( 19 )

Equation (10) can be written

1 - X“ - X

CO,

0 = 1 - ^,0

( 20 )

Combining equations (19) and (20)

0

= 4o^

-

,A /(I -

CO.

( 21 )

The initial concentrations X° and X° refer to the incoming air.

u

2 ^ ^2 However, the initial (baseline) values in the analyzer prior to the test

are generally for dry air since the water vapor has been trapped out.

A° A°

Let XI and X be the initial concentrations in the analyzer

^2 ^^2

n.

X'0., n° + TL° + n°

0, -

“N, -"CO,

( 22 )

n

X^°'

^CO.

CO.

"0, "

"N, "

"CO,

(23)

10
Combining equations (1) , (3) , (4) , (22) , and (23)

( 24 )

(25)

Equations (24) and (25) should be substituted into equation (21)

for 0 and into equations (13) and (17) for Q when water vapor is trapped

and carbon dioxide is not. In some applications of the oxygen consumption technique, carbon dioxide is also trapped so that

X (26)

In that case, equation (26) should be substituted into equations (13),

(17), and (21).

When €©2 is trapped, equation (26) can be substituted into

equation (21) where = 0 to yield

°2

0 = ®2 ^ ^CO

X^

vA

^0,

(27)

1 -

2 \ 1-X^CO

11
When CO

2 is not trapped equations (24) and (25) can be substituted

into equation (21) to get

0

=

4

°

> X^° _

2 2

°2 (1 -

i?

A- °2

(28)

Thus if the initial values of the 0^ and CO

2 concentrations in the

analyzer are used it is not necessary to know the actual concentrations

of CO

2 and H2 O in the incoming air to determine 0. However, in order

to calculate Q by equations (13) or (17) it is necessary to determine

X° from (1) either equation (24) or (26) depending on whether C0„ is

O2 Z trapped or not trapped or (2) directly from the analyzer prior to the

test with the water vapor and CO

2 traps bypassed.

The percentage error in the calculated heat release rate by

ignoring the effect of water and carbon dioxide in the incoming air and

setting X° = X^ is by equation (24) and (26) equal to 100 X^ and

^2 ^2 ^2^ 100 (X^

Q

+ X°Q ) depending on whether CO

2 is trapped or not trapped.

For a relative humidity of 50% at 20°C the error due to the neglect of

ambient water vapor is only about 1%.

4. EFFECT OF NEGLECTING CARBON MONOXIDE PRODUCTION

The oxygen depletion is given by equation 21. When the moisture

and vitiation of the incoming air are neglected and the CO

2 is trapped,

12
this equation reduces to

X'A

X'

1 - X' 0 = CO

2 1-X

CO

If the CO is neglected

0

* = "o,

-

^0

, (1 -

The fraction of the depleted oxygen going into CO production is

given by

f 1

2 (29)

Equation 14 gives the rate of heat production. If Q* is the

calculated rate of heat production ignoring carbon monoxide then

5

Q*

[1 - fC

E"

0

* (30)

13
The percentage error is then given by

e = 100 [1 - (l-0.343f) ( 31 )

In a severe room fire f can be 0.3 while X is 0.1. Hence e~40%.

If 14% is taken to be the lowest permissable value for the oxygen concentration in the fire effluent and the CO is about 1% then f = 0.07

and e ~5%.

5 . RELATIVE HUMIDITY

The volume fraction of water vapor in the incoming air is given by

H^O

760

H

100 (32)

where P„ _ is the vapor pressure of water in mm Hg at the ambient

H2O

temperature and H is the relative humidity in percent. The vapor pressure of water is given as a function of temperature in the Handbook of

Chemistry and Physics. A partial table is reproduced here.

14
Temperature (°C) Water Vapor Pressure (mm Hg)

0 4.58

5 6.54

10 9.21

15 12.79

20 17.55

25 23.78

30 31.86

35 42.23

40 55.40

6. VOLUME FLOW RATE OF AIR INTO SYSTEM

If the volume flow rate of air into the system,

measured, the volume flow rate in the exhaust duct, V , s and a relationship between V and V must be found. V

S A. S

V = (1-0) V, + a0V,

s A A

so that

cannot be

must be measured

is given by

15
\ + (ot - 1) 0) (33)

where a is the expansion factor for the fraction of the air that was

depleted of its oxygen.

1 - (34)

where 3 is the ratio of the moles of combustion products formed to the

moles of oxygen consumed. The value of $ is determined from the general

reaction:

=a«b°c‘'d='e - f

- f> °2

(a-g) CO2 +

b-e H^O + eHX + gCO "2 N

2 (35)

4a + 2b + 2e + 2d

4a + b - e - 2c - 2g

(36)

It is assumed that the nitrogen contained in the fuel is released as

molecular nitrogen. The s3mibol X represents any of the halogens -

fluorine, chlorine, or bromine. From equation (35) it is seen that if

CO

2

in the incoming air can be neglected

g =

a (37)

provided that CO

2

is not trapped, so that equation (36) can be written

16
6 4a + 2b + 2e + 2d

(38) e - 2c

Equation (38) allows one to correct 3 for carbon monoxide production

during the test based on CO and CO

2

measurements in the gas sampling

line if the stoichiometric coefficients, a, b, c, d and e are known.

If equation (35) is expanded to include the unreacted components

such as N

2

, CO

2

, and H

2

O in the incoming air, the effect of CO

2

in the

incoming air can be accounted for by the expression

which reduces to equation (37) when the ambient CO

2

concentration X°

drops to zero. Since CO

2

is not trapped

g (39)

and

8 (40)

17
Let g* be the approximate value given by equation (37) neglecting

ambient CO

2

. Then

g ^ g*

1 +

JL

a0

[a +

b-e

4 (41)

where the last term represents the fractional error in g that would

occur. Although this fraction could be large for a small depletion 0,

g is itself very small for low 0 so that equation (37) for g should be

quite adequate.

Some 3 and a values are listed for a few common materials

undergoing complete combustion in normal dry air to the products, CO^

,

H^O, and HCS-

:

3 a Carbon 1.0 1.00

Hydrogen 2.0 1.21

Cellulose 1.83 1.175

CH, 1.5 1.105

4

C^Hg 1.4 1.084

-CH^- 1.33 1.069

C2HgCil 1.6 1.126

If we know what is burning, we can specify a. If not, we can set

a = 1.1 which is approximately its value for methane. The largest

error encountered would then be 10 percent if pure carbon, or charcoal,

were burning and the oxygen in the stack were completely consumed (0 = 1)

.

18
At the stage of the fire where charcoal was burning one would not

expect the depletion in the stack to be large. It should be noted that

if charcoal is formed it implies a larger a earlier in the fire due to

the water formed in the char-forming process. During vigorous burning

the materials would more likely lie between cellulose and -CH

2 - and the

stack should be required to entrain enough uncombusted air to insure

that all of the combustion products are pulled into the stack. Let the

maximum value of 0 be 0.5 and consider the error for cellulose and

-CH

2-. For a - 1 = 0.175 but using an assumed value of 0.10 the error

would be 4 percent. This was determined from the ratio of the air flows

in equation (33). For a - 1 = 0.069 the error would be 2 percent.

If the gas velocity in the exhaust duct is measured with a pitot

static tube or a bidirectional probe, the standard volume flow rate is

given by:

where is the gas temperature in the duct in K and AP is the pressure

differential across the pitot static tube in Pa, A is the cross sectional

2 area of the duct in m , k is the ratio of the average mass flow rate per

unit area to the centerline mass flow rate per unit area, and j is a

calibration factor equal to unity for a pitot static tube and 0.926 for

a bidirectional probe [5].

19
In measuring the volume flow rate in the exhaust duct with a pitot

static tube, it is assumed that the density of the exhaust gas is

the same as the density of air when both are referred to standard

conditions. In order to correct for the density difference, the right1/2 hand side of equation (42) should be multiplied by (p /p ) . Let W

o s AIR

and W be the molecular weight of the incoming air and the exhaust gas

in g/mole so that — = ——

.

p W

s s

The weight of one gram mole of the exhaust gases is determined

from equation (35)

.

= (1-0) + 0 [44(a-g) + 18

^

+ 36.4 e + 28 (g + |) +

1 - X

28

°

2 ^

0 ,

(a - 8 +

t>-e 1-X!

1 , r I b , d , e , 2)1 - U + 2+2 +2 + X

0,

(aU _ g24+ ^ 1 2

^^ (43)

and = 0.028 ( 1-X'

AIR \ 0, + 0.032 / X,‘°2)’

It is assumed that the halogen

is chlorine. If X°_ = 0.21, = 0.029 kg/mole,

U2 AiK

For complete burning of cellulose to CO^ and H

2 O and 0=1,

1.001 which is negligible correction.

Equation (43) assumes the inert component of the air is nitrogen and

does not account for humidity.

/ Po \l/2

W = 0.02907. Hence,! _£

Pg

20
7. WATER VAPOR ANALYZER

The quantity 3 in equation (34) represents the expansion of the

gases in the exhaust duct due to chemical reactions. If a water vapor

analyzer is used to measure the water vapor concentration in the exhaust

duct, this concentration along with the oxygen, carbon dioxide, and

carbon monoxide measurements in the sampling line where water is trapped

can be used to calculate 3 without any assumption concerning the chemical composition of the burning materials. The water vapor concentraQ tion Xg

Q

is measured in the presence of all of the exhaust duct gases

while the other concentrations , X^ , and X^ are measured in the

absence of the water vapor. However, for the purposes of the derivation,

it is necessary to express all of these concentrations in terms of their

values in the exhaust duct.

^^0

"h^o

o.S.S .S,S

^2 ^^°2 ^ ^2°

(44)

n.

x: "O.S.S ,s,s

n

2 "°2 “2 ““2°

(45)

n

CO,

CO o.S.S ,s,s

'^2 "O2 "CO2 “co +

“h^o

(46)

nCO

CO + + n

CO

2 ^ "^CO ^^2°

(47)

21
The expansion factor g is given by

^2° ^C02 ’^CO

n.

2

(48)

which with the use of equation (10) can be written

Using equation (6), (7), (8), (44), and (45)

From equation (8) , (44) , and (45)

(49)

(50)

Therefore,

= ^

(51)

(52)

Then from equations (33) , (34) , and (52) the volume flow rate into the

system is given by

^0

V = V I 1 - X° 0 + X° '-T

--- f x^^ + x^^ +

^ -1

A s “2 “ 1-x;; (53)

'2 \ 2

which should be substituted into equations (13) or (17)

0

22
8. TRACER GAS IN AIR FLOW DETERMINATION

When the oxygen consumption technique is applied to large existing

systems such as fire endurance test furnaces or to large scale test

facilities, accurate volumetric flow measurements in the exhaust stack

are often difficult. One technique that might be used to overcome this

is to introduce a tracer gas into the exhaust duct far enough upstream

that mixing is complete by the time that it reaches the gas sampling

point.

Let the gas be introduced at a volumetric flow rate of so that

its concentration in the analyzer is X^. The concentration of nitrogen

in the analyzer is given by

4, 1 - - X^^ - X^ W 1 - x^ - x^^ - x^

0^ CO^ CO T O

2

CO

2 CO

Then the volume flow rate of nitrogen into the system is given by

4

The volume flow rate of oxygen into the system is given by

X

O,

°2 \ \ ^ x„

23
The volume flow rate of 0

^ in the duct after combustion is complete is

V

°2 °2

v„ 4

The heat release rate Q is given by

Q

= E'(V° - ) = E'

^T

O- (1 - X' - X^. - xl) - X'A

0^ CO^ CO' 0

Q

= E' 4T

^0^

- X.

1 - X

0 ,

9. COMPLETELY DEPLETED AIR

In the case of complete consumption of the oxygen in the incoming

air, equations (17) and (53) are indeterminate since 0=1 and X =0.

In that event, it is necessary to solve equation (21) for (1 - 0)/X in

A

2 the limit where X goes to zero. Hence,

^2

1 -

’'S - "^,0

-

2 2

O V©

CO, 1-0 ^ 4^ ^0^ - 4o^ - 4o^

(55)

for fully depleted air.

Substitution into equation (17) where 0=1 yields

24
( 56 )

and assuming for now that there is no other unburned fuel than CO,

substitution into equation (53) yields

+

(57)

when a water vapor analyzer is used. There are some inaccuracies to be

expected in application of the oxygen consumption technique to a ventilation limited fire due to partial oxidation of the pyrolysis products

where the heat release per kg of oxygen consumed may deviate from

13.1 MJ.

If only a fraction X of the fuel vapor is burned in a ventilation

limited system and (1-1) escapes, as would be the case in a postflashover room fire, it is necessary to determine a new volume expansion

factor a.

25
a =

'2 °2 ^ ^2 ^2 ° "'^''2 '' ''°2 (58)

where all of the incoming oxygen has been converted to combustion

g products and n^ is the molar flow rate of the unburned fuel in the

exhaust duct.

X

(59)

a=l-X° + B+ -T-

°2 \ ^0,

The fraction of the fuel vapor burned is given by

o s nf n^

A o n. (60)

where n° is the molar flow rate of fuel into the system. Also,

_ 0 -n Tt ^ nf - nf - R n^^ (61)

where R is the molar ratio of the fuel to oxygen consumed,

The combination of equations (60) and (61) yields

n. 1 - X R (62)

26
so that equation (34) should be replaced by

a +

1-A

A R

when there is unburned fuel in the exhaust.

( 63 )

For a fuel limited fire, where A = 1, equation (63) reduces to

equation (34). For a ventilation limited fire, where 0=1, equation

(33) reduces to

V = V /a A s (64)

The quantity A could be determined by the relationship

A ^ -

<5co

(65)

where is the product of the volumetric flow rate in the stack, V^,

and the heat of combustion per unit volume as determined by a hydrocarbon

analyzer, and is the product of the heat of combustion of CO, the

concentration of CO in the exhaust duct, and the volumetric flow rate of

the exhaust gases.

Since depends on A this determination may require several

iterations. It is also important to recognize that in the case of zero

or near zero concentrations that additional errors can come about due to

27
partially oxidized pryolysis products which, like CO, may not release

13.1 MJ/kg of oxygen consumed.

10. HIGH TEMPERATURE OXYGEN CELL

If a high temperature oxygen cell is used in conjunction with a

high temperature sampling line and no filtering, so that the concentration of oxygen in the cell is equal to that in the duct, then the oxygen

depletion is given by

0 =

X° V

A

( 66 )

Eliminating V /V from equations (33) and (66) , the depletion is given

S A. by

X® - X?

0 = (67)

Substituting equation (33) into equation (13) yields

E'X° V

°2 ® ^ 1/0 + a-1 ( 68 )

for the open system when the volume flow rate must be measured in the

exhaust duct.

Substituting equation (67) into (68) yields

28
^ - (69) ^0^^ ''s/“

In a closed system where V. is measured directly, equation (67) can be

A. substituted into equation (13) to yield

Q

= X” + (a-1)

(70)

If CO production were taken into account, it would be necessary to

substitute equation (33) into equation (17) rather than equation (13)

.

Then equation (68) would become

n = 11 - E" - E' 1 _ 1 fco

^ E' 0-^2^!

E’X° V

0^ s

+ a - 1

(71)

for the case where the volumetric flow rate was measured in the exhaust

duct. Substitution of equation (67) into equation (71) yields

Q

= _ / E"-E'\

2E' )

ax: X^

^co

x^

E’/X° - X® \ V

V °2 °2 j

^ a

(72)

In a closed system where V. is measured directly, equation (67) can be

A

substituted into equation (17) to yield

Q

=

ax:

1 - E"-E‘

2E’

X^

^0 - ^2 2 I 4

/ 2

E’/X° - X" \X° V.

( O2 Oj O2 A

(73)

The concentration of oxygen X„ in the gas sampling line to the CO

2 analyzer appears in both equations (72) and (73) . Combining equations

(8), (44), and (45) we find that

29
1 (74) ^

0 , ^^0

Unless the water vapor concentration is measured in the exhaust

duct, it is best to assume /X^ is equal to unity. The error incurred

^2 2

in the small correction term in equations (71) and (72) would not be

expected to exceed 10 percent during expected operating conditions.

Hence, the error in the heat release rate would be much less than 10

percent

.

11. SIMPLIFICATIONS

Under some circumstances it is adequate to neglect CO and trap out

the C0„ so that these two analyzers can be eliminated. Then X ^

= A

^ X^_ = 0. If it is further assumed that the ambient concentrations of

H

2 O and CO

2 can be neglected, equations (17) and (21) can be combined to

yield

(75)

Equation (75) was used by Krause and Gann [3] in obtaining measurements

of the heat release rate by oxygen depletion in the OSU calorimeter.

When CO^ is trapped, CO is neglected and the system is open, such as in

the bench top calorimeter with a canopy collection hood or for measurements of the heat developed by a room fire, it is necessary to determine

30
V. by equation (33). Assuming (a - 1) = 0.10, with the above

assumptions

/X° - \E'V

^1-X^ y

1+0. 10)

( 76 )

In some cases, particularly in the burning of cellulosic materials

in an adequate air supply where the production of CO can be neglected,

the number of moles of oxygen consumed is approximately equal to the

number of moles of CO

2 produced. Hence

n. and = 0 (77)

in the analyzer, provided that CO^ is not trapped, so that equation (8)

can be written

(78)

Taking equations (1), (2), and (78) into account, equation (10) can be

written

"o,

- "o,

0 TrO (79) X

0,

Substituting this into equation (17) with the assumption that X^^ =

^CO^ " ^2° " ° yields

Q

= E' (80)

31
This approximation was used in the investigation of the rate of heat

release in room fires by Sensenig [2] where it was also assumed that the

molar flow rate of air into the system was the same as that in the

exhaust duct (i.e., = Vg)

.

Table 1 provides a guide to finding the pertinent equations to be

used for the various combinations of operating conditions.

12. SUMMARY

If O^, CO

2

, and CO concentrations are measured in the gas sampling

lines and all other gases, vapors, and particulates except for nitrogen

are trapped out, equation (17) can be used to calculate the rate of heat

release.

(17)

where E' = 17.2 MJ/m , E" =23.1 MJ/m'

( 21 )

and the ambient air concentrations of oxygen and carbon dioxide are

determined from the equations

32
( 24 )

H^O'

(25)

if CO^ is not trapped, and by

^0^ ^oO (26)

A® A°

if C0_ is trapped. The concentrations XV and X are measured in the

I ^2 ^2

analyzers prior to test and account for the water vapor, and in the

latter case, the CO

2 trapped in the sampling line. In many cases, the

ambient concentration of CO

2 can be neglected so that X°^ = 0.

The formula for the ambient water vapor concentration

X

H2O

H

2O 760 (iSo) (32)

is discussed in section V.

If the incoming air is fully depleted of its oxygen, equation (56)

should be substituted for equation (17) in order to determine the heat

release based on the CO and CO

2

concentrations. If a high temperature

oxygen cell is used, then equation (17) should be replaced by equations

(73) and (74).

33
For closed systems, such as an enclosed calorimeter or the ASTM

E 84 tunnel, where the inflow of air can be measured, V, can be obtained

directly. For open systems such as the bench top heat release rate

calorimeter or the standard room fire test, it should be determined from

equation (33)

V

A

V

s 1 + (a-l)0 (33)

The quantity, a, can be calculated using equations (34), (36), (37), or

(38) and (39) if the chemical composition of the pyrolysis products are

known. This is usually not the case, however, so that an average value

of a = 1.1 should normally be used. If a water vapor analyzer is used

to measure the concentration of water vapor in the exhaust duct

equation (53) can be used to determine V unless the oxygen is completely

consumed, in which case equation (57) should be used. Equation ' (42) can

be used to calculate V^. If it is necessary to correct for the density

of the exhaust gases being different than that of air, the right-hand

side of equation (42) should be multiplied by where is the

mass per mole of the incoming air and is the mass per mole of the

exhaust gas given by equation (43) . If there is unburned fuel other

than CO in the exhaust gas, then equation (63) rather than (34) should

be used to calculate a.

If CO can be neglected and CO

2 is trapped, equation (75) can be

used to calculate the heat release rate. For those cases where it can

be assumed that the number of moles of O

2 consumed is equal to the

34
number of moles of CO

2 produced (e.g. complete combustion of cellulose),

the heat release rate can be calculated from equation (80) . CO

2 does

not need to be measured in this case but it must be permitted to flow

through the oxygen analyzer.

13 . REFERENCES

[1] Parker, W. J,, An Investigation of the Fire Environment in the

ASTM E 84 Tunnel Test, NBS Technical Note 945, August 1977.

[2] Sensenig, D. L., An Oxygen Consumption Technique for Determining

the Contribution of Interior Wall Finishes to Room Fires, NBS

Technical Note 1128, July 1980.

[3] Krause, R. F. and Gann, R. G., Rate of Heat Release Rate

Measurements Using Oxygen Consumption, Journal of Fire and

Flammability, Vol. 12, 117-130 (1980).

[4] Huggett, C., Estimation of Rate of Heat Release by Means of Oxygen

Consumption Measurements, Fire and Materials, Vol. 4, No. 2, 61-65

(1980).

[5] McCaffrey, B. J. and Heskestad, G., Combustion and Flame, Vol. 26,

125-127 (1976).

35
14 . NOMENCLATURE

Cross sectional area of the exhaust duct (m )

stoichiometric coefficient for carbon

stoichiometric coefficient for hydrogen

stoichiometric coefficient for oxygen

stoichiometric coefficient for nitrogen

net heat of combustion per unit mass of oxygen consumed

(E = 13.1 MJ/kg) assuming carbon goes to carbon dioxide

net heat of combustion per unit volume of oxygen consumed

referred to 20°C (E' = 17.2 MJ/m^) assuming carbon goes to

carbon dioxide

net heat of combustion per unit volume of oxygen consumed

referred to 20°C (E" = 23.1 MJ/m^) in the burning of carbon

monoxide

stoichiometric coefficient for halogens

fraction of depleted oxygen going into the formation of CO

number of moles of carbon monoxide produced per mole of

reactant consumed

relative humidity of the ambient air (%)

calibration factor equal to 1.00 for pitot static tube and

0.926 for bidirectional probe

ratio of average mass flow rate to centerline mass flow rate

in duct

molar flow rate of species i

vapor pressure of water at ambient temperature (mm Hg)

total rate of heat production (kW)

product of the heat of combustion of exhaust gases and their

flow rate (kW)

molar ratio of fuel to oxygen consumed

temperature of gas (K)
volume flow rate of air into the system referred to standard

conditions (m^/s)

•V volume flow rate of air in exhaust duct referred to standard

conditions (m^/s)

mass of one gram mole of species i (kg/mole)

volume fraction of species i

a molar expansion factor for the fraction of the air that was depleted of its oxygen

6 ratio of the moles of combustion products formed to the

moles of oxygen consumed

AP pressure drop across bidirectional probe (Pa)

e error (%)

0 fraction of oxygen depleted

X fraction of fuel vapor produced that is burned in the system

3 density of air under standard conditions (kg/m )

stoichiometric coefficient for species i

SUBSCRIPTS AND SUPERSCRIPTS

A analyzer

A° analyzer prior to test (baseline values)

f fuel

o incoming air

s exhaust duct or stack

* approximate value

37
Table

1.

Equations

to

be

Considered

for

Various

Applications

ml cN cvj

• > I ^ -cr

<31 fo n • > 1 cn ro

COm

vO

•> CO

<1- m #> csi CO

v£)

e^l CN CN

• O'! cn

CO

r*^ CN

#k cyv

v£)

vO

CNlA

CN

CN

CN

vO

CNm

CN

m

d u o o •H m CN 4-1 d < o CJ 0) X! CU m m rH d

C 1—

1

1 d

o 0) <u O

•H d o CN CJ •U d 0 O

•H •u 0) X! X

X) cO d 4-1 d d d II d d d •H o 0) 4-1 O O •H m o a CO CN M-l 14-1 cO d

0 d O cu 00 tu d u xt X) X) X

d +j D- X cu cu CU 1—

1

0

•H 0 X) X) XI 4-1 4-1 +J cu 4J CU •U 4-1 CL) T3 (U (U cu X) cu d d CU d o 4-1 cO d 4-1 0) d 0 4J cu d d d 1—

1

X d m

d <u d, d d o d d o o & X Xi

<U •H jd a m m cu d m CJ o CU X m

d. 00 CO cO m !—

1

m cO u a X cu 4-1 o' 0 d cu cO 00 cO cu cO cO d m X

d 4J 0 s—

'

0) CU 0 X d d cu

'—

d 0 o o rH d CO m

CN CN CN O o CN tH rQ -d o

CN CN o O o o O CN CN O d d X 1—

1

o o CJ o o u CO Pd X CO pl-l X Cx3 CO

38

closed

system,

V

should

be

measured

directly

in

the

inflow.
U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report NoJ 3. PubI ication Date BIBLIOGRAPHIC DATA

REPORT NO. SHEET (See instructions) NBSIR 81-2427-1 March 1982

4. TITLE AND SUBTITLE

Calculations of the Heat Release Rate by Oxygen Consumption for Various Applications

5. AUTHOR(S)

W. J. Parker

6. PERFORMING ORGANIZATION (If joint or other than MBS. see instructions)

national bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

3. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City. State. ZIP)

10.

SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

The oxygen consumption technique is emerging as a powerful tool for determining the

heat release rate in a number of diverse fire test applications, including room fire

tests, fire endurance tests, the ASTM E 84 tunnel test, and various heat release rate

calorimeters. Depending upon the constraints of the test, the accuracy required, the

availability of instrumentation and computational facilities, and the willingness to

put up with experimental inconveniences, a number of instrumentation options have been

considered—each of which require different calculational procedures. The purpose of

this report is to develop the equations in a general way and show how to adapt them to

various applications such as: closed systems versus open systems; trapping carbon

dioxide before it reaches the oxygen analyzer, measuring it, or assuming that it is

equal to the reduction in oxygen concentration; ignoring carbon monoxide or measuring

it; accounting for the density of the exhaust gases or assuming that it is the same

as for air; using a high temperature oxygen cell which measures the oxygen concentration in the exhaust duct directly or a paramagnetic analyzer for which corrections

must be made for water vapor trapping; taking into account or ignoring the ambient

concentration of water vapor and carbon dioxide; and, improving the accuracy for open

systems by monitoring the water vapor in the exhaust duct. The equations developed

here should be useful to anyone setting up a new system and will provide a means of

calculating the errors which might be expected when simplified procedures are used.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) Calorimeters; fire tests; heat release rate; oxygen consumption; room fires

13. AVAILABILITY

[~x1 Unlimited

( I For Official Distribution. Do Not Release to NTIS

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

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15. Price

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