Combustion Gas Concentrations in Enclosures Containing Unvented Appliances

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Publisher’s version / Version de l'éditeur:

Technical Note (National Research Council of Canada. Division of Building Research), 1967-02-01

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Combustion Gas Concentrations in Enclosures Containing Unvented

Appliances

Mitalas, G. P.

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DIVISION OF BUILDING RESEARCH

NATIONAL RESEARCH COUNCIL OF CANADA

'f

ECIHI]V II CAlL

NOTlE

No.

481

PREPARED BY G. P. Mitalas CHECKED BY APPROVED BY N. B. H.

DATE February 1967

PREPARED FOR

SUBJECT

•

ｾ

Information and inquiry

COMBUSTION GAS CONCENTRATIONS IN ENCLOSURES CONTAINING UNVENTED APP LIANCES

Individual, unvented fuel-burning appliances for lighting and minimal or supplementary space heating

were commonly used in North America more than 40 years ago. Electricity is now widely used for lighting and all fixed fuel-burning devices for primary space heating are provided with chimneys or vents to carry off combustion gases. The major exceptions are gas -burning appliances operated either continuously or intermittently at low fuel flow rates. Small unvented heating and lighting appliances are widely used under the somewhat abnormal conditions of frontier, trailer, cottage or camp living, or in emer-gencies.

Combustion products released into an occupied space are potential hazards to life or health. Recently, when considering lighting and heating for emergency fallout shelters, it became necessary to assess these hazards, i. e. to establish the concentration levels of the combustion gCl.ses in r elation to the rate of combustion of fuel and the ventilation of the space. The resulting report is relevant not only to fallout shelter lighting and heating but to the pTeviously mentioned situations in which unvented fuel-burning appliances are used•

(3)

In the combustion of hydro-carbon fuels, the fuel reacts with oxygen to form water, carbon dioxide and a smaller amount of carbon monoxide. _{A CO2 concentration} of 1.5 per cent by volume and CO of approximately 0.01 per cent by volume are the upper limits for safe atmospheric environment in a continuously occupied enclosure (1). An 02 concentration not less than 17 per cent by volume is the safe limit (1). The combustion gas concentrations and 0z depletion in an enclosure depend on the production rates of these gases and on the ventilation rate of the enclosure. There is. therefore. a need to be able to estimate the ventilation rate required to maintain a safe atmospheric environment in an occupied enclosure where an unvented fuel-burning appliance is used.

In this note equations are derived that relate OZ.

COZ and CO concentrations, ventilation rate. 0z consumption rate and combustion gas production rates. In addition. this set of equations indicates the characteristics required for their solution. Several assumptions ar e made to facilitate the theoretical treatment of this problem. These assumptions ar e noted as the equations ar e developed.

In a vented enclosure where a fuel-burning appliance is operating and where gases are thoroughly mixed, the changes of gas concentrations. ventilation rate, and gas production rates can be related by

and dx R Vx

=

-dt W W ｾ R

_Y:i.

=

m-

-dt W W • •. 1 • •• 2 where dz dt

=

r W Vz W · •. 3

x = 0z depletion in an enclosure (i. e. the difference between outside air 0z

concentration and 0z concentration in an enclosure)

(4)

- 3

-y = COZ concentration in an enclosure

z

= CO concentration in an encl08ur e t = time

W = weight of air in ali enclosur e V = enclosure ventilation rate R = consumption rate of 0z

m = weight ratio of COZ produced to 0z

consumed. The value of m for

ordinary hydro-carbon fuel (C HZ +1)

. . I 0 9 n n

18 appr oX1mate y .. r = production rate of CO

Tests carried out at the Division of Building Research, National Research Council on various types of fuel-burning appliances confirm that 0z consumption rate can be related approximately to 0z depletion by a linear equation

and

is

R = ex.

+

ｾｸ

The solution of equation (l) for

R

=

ex.

+

Sx

x= Oatt=O

• .• 4

(5)

When 02 consumption rate is constant (t. e.

$:;

0), and the enclosure is not ventilated (i. e. V

=

0) solution of equation (1) for

x

=

o

when t :: ₀ is

x

=

-2:

t

...

6

W

The solution of equation (2) can be obtained in a similar way. By equations (1) and (2), however, it can be shown that

y

=

mx •.. 7

for all times, provided that the initial ｏｾ depletion and C02 concentration are zero. Thus equations (5) and (6) can be used to calculate C02 concentrations when

a

and $ are substituted by

rna.

and mf3.

The tests on various burners indicate that CO pro-duction rates depend on 02 depletion, type of fuel burned, the temperature of burner parts when combustion takes place (i. e. the CO production rate is significantly increased when a cooking utensil is placed on a burner), and the burner capacity setting. CO production rate, however, can be related approximately to 02 depletion by a linear equation

r

=

6

+

px

when the other conditions ar e constant. The solution of equation (3) for

r

=

6

+

px

a.

V

-@

x

=

V _f3 (I - exp ( - W t

»

and z

=

Oat t

=

°

• .. 8

(6)

- 5 -is z

=

ｾ

_V ( I exp (_ V

_wt

»

+

_v

pa

(!.

-13

v

1

v

-13

na V Q exp ( - W t})

+

ｾ exp ( - -t) IJ

VI3

w

• .• 9

As the manufacturers of small, unvented fuel-burning appliances do not give the values of

a, 13,

6 and p as a part of appliance description, the above equations are not directly applicable to the selection of an appliance or estimation of the minimum ventilation rate to maintain safe atmospheric environment in an enclosure. Because' of this, additional simplifications must be introduced. Assuming that all the fuel is burned (tests show that some appliances lose part of the fuel as unburned fuel vapour) and that fuel consumption rate is constant and independent of 02 depletion in the range of 02 depletion that is safe for habitation (tests show that the fuel consumption of some of the appliances is reduced noticeably even by relatively small increases of 02 depletion), then the 02 consumption rate of a burner can be approximated by

R

=

pF

=

a

...

10

where

p

=

weight ratio of 02 consumed to fuel burned. For common hydro-carbon fuels (C

n H2n

+

l) p ｾ 3.5 F

₌

fuel consumption rate.

The relation between x, a, V, Wand t is given by equation (5) when 02 consumption rate is constant (i. e.

13 •

0). A curve is given in Fig. 1 to facilitate the solution of equation (5) where x

V;13

is plotted against t

V;/.

This curve shows that at steady state (i. e. lar ge t) the value of x V

-13

ｾ

1. 0 and thus the maximum 02 depletion is

a

x

=

(7)

and the maximum COl concentration is

Ymax

=

rna.

V · .. II

The substitution of the maximum allowable limits* for 0l depletion and COl concentration in equations (11) and (1l), respectively, gives

v

₌

pF C,Ol

0.045

and V :: mpF C,C0 2 0.Ol3

where VC

°

and VC CO are the minimum ventilation , 2 ' 2

rates required to maintain safe atmospheric environment at all times with respect to 02 depletion and CO₂ .

concentration.

Equatioh (9), which gives CO concentrations, can be simplified if it is assumed that CO production rate is constant, i. e.

· .. 13

· .• 14

z

=

rV (1 - exp (-

V

Wt

»

• •• 15

An upper value of CO concentration estimate will be given by equation (15) if the maximum CO production rate, r , i s used where r is the maximum CO

max max

production rate for 02 depletion up to the limit for safe atmospher ic envir onm ent.

*

The maximum allowable limits for safe atmospheric environment are 2.3 per cent by weight for CO2 and 4. 5 per cent by weight for 02 depletion.

(8)

- 7

The CO concentration, z. at steady state (large t) is z (from equation (15».

=

r max V • •. 16

The substitution of the maximum allowable CO concentration value* in above equation gives

::

r

max

0.0001 • .. 17 where VC CO is a minimum ventilation rate required to

,

maintain CO concentration within allowable limit at all times. It should be noted that for hydro-carbon fuels m ｾ 0.9; therefore VC CO is greater than VCO. Thus the ventilation

,

Z

'

Z

rate that is adequate to maintain COZ concentration at a safe le\'"el will be mor e than adequate to maintain

0z

depletion at a safe level. It is mor e difficult to determine whether

VC CO or VC CO is greater, as CO production rate

' z

'

depends on other conditions in addition to the type of fuel used. A knowledge of the CO/COZ production ratio for the burner is useful for this purpose. This ratio indicates whether a ventilation rate that is sufficient to maintain COZ concentration at safe level is also adequate to maintain CO concentration at a safe level. For the concentration limits used in this note (i. e. COZ - Z. 3 per cent and CO - 0.01 per cent) the critical CO/COz production ratio is

r

max

mpF :: 0.0044 by weight • •• 18

* The maximum allowable CO concentration for safe

atmospheric environment is approximately 0.01 per cent by weight.

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The equations given in this note were derived assuming that the gas concentration gradients in an enclosure are zero. On the basis of this assumption the gas concentrations in the atmosphere immediately around the burner and from which its air supply is drawn will be the same as those elsewhere in the enclosure and in the air leaking outward from it. Under most practical heating situations there will be a vertical gradient in both temperature and gas concentration, with the conditions at the lower level in the enclosure tending toward those of the entering ventilation air stream. Under these conditions the burning conditions may be unaffected by the gas concen-trations, but the air flowing out of the enclosure, usually somewhere near the top, must have an average gas concen-tration under steady-state conditions which is given by the

ratio of input rates of combustion gas and ventilating air. There may be locations at upper levels of an enclosure at which the gas concentrations ar e higher than those calculated from input ratios where mixing and dilution of the rising gas stream has not yet taken place. This situation will be complex in most practical

situations.

In the absence of contrary evidence it may reasonably be assumed that air inhaled by occupants of such a heated enclosure will be almost completely mixed.

SUMMARY

An estimate of ventilation requirements or an

estimate of the interval of time for gas concentrations to reach specified levels can be made by equations (5), (7) and (9).

An approximate, but safe, estimate of enclosure ventilation rate required to maintain safe atmospheric environment can be made by

v

₌

pF

C,OZ 0.045

V

=

mpF

C,C0

(10)

.:. 9

and V

_{c co}

• =

r max 0.0001

(equations (13), (14) and (l7), respectively), whichever gives the greatest value.

Equations (5) and (9) indicate that for relatively pr ecise estimates of 02 depletion or combustion gas

concentration the constants A.,

13. ()

and p. which define

the characteristics of a burner, must be known.

Equations (13), (14) and (1 7) indicate that for an approximate, but safe, estimate of ventilation requirements all that is needed is the fuel consumption rate of the burner, F, and the maximum CO production rate, r ,at the burner operating conditions. max

REFERENCE

(1) The effect of oxygen depletion and fir e gases on occupants of shelter s. Navy Civil Engineer, V. 3. n. 1. January 1962. p.29. 33 and 50.