8 flammability limits by X P

Chapter 8

Flammability Limits of Flammable Mixtures Table of Contents 1. Introduction.............................................................................. 201 2. State of the Art ........................................................................ 201 3. Flammability Limits of Premixed Flames ................................. 205 3.1 Flammability Limits of Fuel(s)-Air Mixtures at 1.0 atm and 25ยบC........................................................................................... 205 3.2 Influence of the Temperature and the Pressure on the Flammability Limits .................................................................. 206 3.3 Flammability Limits of Fuel(s)-Inert(s)-Air Mixtures in Backdraft Conditions according to Temperature ....................... 209 3.3.1 Correlation between UFL, LFL and Combustion Heat... 213 3.3.2 Adiabatic Flame Temperature........................................ 215 3.3.3 Mapping the Lower Limit Values of Flammable Diagrams ............................................................................................... 217 3.3.4 Exponential Fit of the AFT at Lower Limit Values ....... 218 3.3.5 Limiting Oxygen Concentration and AFTLOC ................. 219

3.3.5.1 List of Fuels Analysed for Obtaining the AFTLOC..... 220 3.3.5.2 Correlation between AFTLFL and AFTLOC................. 221 3.3.5.3 Equivalence Ratio at LOC........................................ 223 3.3.6 Equivalence between Nitrogen and Other Inert Species.. 225 3.3.7 Application Regarding Temperatures Higher than 25ºC and Mixtures of Several Fuels ....................................................... 226 3.4 Comparative Results............................................................ 227 4. Diffusion Flame Limits ............................................................. 228 4.1 Le Chatelier’s Rule............................................................... 228 4.2 Application for Fire Compartments ..................................... 229 5. Validation of the Diffusion Criterion......................................... 230 6. Parametric Study: Influence of Gas Species on Backdraft Probability.................................................................................... 235 7. Influence of Opening Position on the Critical Hydrocarbon Concentration ............................................................................... 237 8. Conclusions............................................................................... 240

8. Flammability Limits of Flammable Mixtures

1. Introduction To predict backdraft, it is imperative to know whether the gaseous mixture inside the compartment is flammable. Having flammable gas species in the mixture does not necessarily mean that the mixture becomes flammable. The other gas species in the mixture as well as the temperature and pressure in the compartment must be taken into account. Much information about the upper and lower flammability limits (UFL and LFL) of gaseous mixtures at 25ºC and 1.0 atm is found in the literature (Zabetakis, 1965; Bureau of Mines-503, 1952). However, less information is available referring to mixtures of several fuels and several inert species in the mixture, and even less information is found when the mixture is at temperatures or pressures other than 25ºC and 1.0 atm. This corresponds to a normal backdraft situation. To predict with certain accuracy the risk of backdraft in a compartment, it is necessary to take into account all of these factors. In this chapter a model is developed for computing the flammability limits of premixed fuel(s)-inert(s)-air mixtures as a function of temperature, the type of fuel(s) and of the inert specie(s) in the mixture. This model, besides being useful for predicting backdrafts, it can also be applied to industrial activities, i.e. to develop strategies for avoiding flammable mixtures and, consequently, industrial fires. A diffusion flame criterion (Le Chatelier’s rule) is also used in this chapter for checking the risk of backdraft in a fire compartment. It also takes into account the different gas species in the mixture and temperatures other than 25ºC. Finally, the validation is carried out with real backdraft experiments using methane as fuel.

2. State of the Art A common practise is to refer to gases or vapour such as methane and propane as flammable; however, their mixture with air will only burn if the fuel concentration lies within a well-defined level of concentration: UFL and LFL. Beyler, 1995 gives a good review of the theory of flammability limits. Here, the flammability limits of both premixed and diffusion flames of gaseous mixtures are discussed. Different criteria are also provided for evaluating the flammability limits depending on the type of flame. In Chapter 2: “Fundamentals of Fire Compartments” the terms “premixed” and “diffusion flame” are commented on in further detail. Flammability limits for diffusion flames were first examined by Simmons and Wolfhard, 1957. In their experiments, they determined the minimum level of

201

8. Flammability Limits of Flammable Mixtures dilution of the oxidant stream necessary to prevent the stabilization of a diffusion flame for a variety of gas and liquid fuels. Ishizuka and Tsuji, 1981 verified Simmons and Wolfhard’s results for methane and hydrogen, and showed that the adiabatic flame temperature at the flammability limit is the small whether dilution is of the fuel or oxidant stream. This conclusion forms the basis of a method for the evaluation of diffusion flame limits for fuel mixtures. In essence, the ability of a fuel and oxidant pair to react in a diffusion flame is evaluated by examining the flammability of a premixed stoichiometric mixture of the fuel and oxidant. Up to now, flammability limits of premixed gases and vapours have been extensively studied. The most extensive review is that of Zabetakis, 1965, which, despite its age, remains the standard reference. It is based largely on a collection of data obtained with an apparatus developed at the US Bureau of Mines. The experimental criterion used to determine whether or not a given mixture is flammable, is its ability to propagate flames. Alternative methods exist, but none has been used extensively enough to provide a challenge to the Bureau of Mines. Figure 8-1 represents the apparatus used by the USBM.

Figure 8-1: Photograph of the US Bureau of Mines apparatus. A list of the methods used to obtain recommended values is given below: •

The USBM method: the explosion vessel is a cylindrical vertical glass tube with an inner diameter of 50 mm and length of 1500 mm. Ignition is made by an electric spark or a pilot flame passed through the lower open end of the tube.

•

The ASTM 681-98 standard: the explosion vessel is a 5 dm3 spherical glass bulb. A central spark igniter of 15 kV (duration of the spark is 0.4 s) initiates combustion.

•

The German standard according to DIN 51 649: the explosion vessel is a cylindrical vertical glass tube with an inner diameter of 60 mm and a length

202

8. Flammability Limits of Flammable Mixtures of 300 mm. The spark igniter of 15 kV is 60 mm above the tube bottom and the spark duration is 0.5 s. •

A German standard according to VDI 2263-1 was developed for measuring the explosion limits of dust in the air but it is also used for gaseous mixtures. The test apparatus is a 20 dm3 spherical closed vessel. Ignition is centrally produced by electric sparks or by fusing wires.

In general, the flammability limits are affected by the apparatus parameters such as the ignition source (type, power, duration and location), the direction of flame propagation, the determination of the procedure (step size, criterion) and the type and size of the ignition vessel (closed, open, dimensions, material). Razus, 2006 analysed the values of LFL and UFL of several fuel-air mixtures measured by some of the above listed methods. Systematic deviations are observed between the limits determined by DIN 51 649 and VDI 2263 and those determined by the US Bureau of Mines method (see Table 8-1).

Fuel CH4 C2H6 C3H8 n-C4H10

DIN 51649 LFL(vol%) UFL(vol%) 4.60 16.2 2.39 14.8 1.82 10.5 1.34 8.9

VDI 2263 LFL(vol%) UFL(vol%) 4.58 15.9 2.46 14.1 1.85 10.2 1.38 8.6

U.S Bureau of mines LFL(vol%) UFL(vol%) 5.0 15.0 3.0 12.4 2.1 9.5 1.8 8.4

Table 8-1: Flammability limits for common gaseous fuels measured by various methods.

The results obtained by any of the experimental methods are usually represented by flammability diagrams. Two types of flammability diagrams are often used: •

A three-axe diagram in which each of the three constituent gases (fuel, inert and air) are explicitly represented, as in Figure 8-2-a.

•

A two-axe diagram in which the third gas concentration is determined by the difference between the sum of the others and 100 percent, as in Figure 8-2-b. These kinds of diagrams only represent mixtures that lie to the right of the air line. They can be considered as a magnification of a portion of the region included in the diagrams in Figure 8-2-a. Both diagrams give the same information.

203

8. Flammability Limits of Flammable Mixtures

LOC LOC

(a)

(b)

Figure 8-2: (a) Flammability diagram for the three-component system methane/oxygen-nitrogen at atmospheric pressure and 25ยบC (Zabetakis, 1965); (b) Flammability diagram for the system propane/inert (CO2 / N2) at atmospheric pressure and 25ยบC (Zabetakis, 1965). It can be observed that when progressive amounts of an inert gas are added to a flammable mixture, the flammable limits (LFL and UFL) converge and merge to become one unique value. This point is known as the LOC (limiting oxygen concentration). The LOC of a fuel-inert-air mixture system is defined as the maximum allowed oxygen concentration of the fuel-inert-air mixture in which an explosion will not occur. The LOC of premixed gaseous systems are usually determined from measurements of explosion limits at progressive levels of dilution. However, this process is a long and cumbersome procedure. Razus, 2006 has recently developed an algorithm for determining the LOC for a fuel-inert-air mixture at atmospheric conditions. The algorithm was tested for fuel-nitrogen-air and fuel-carbon dioxide-air mixtures. The LOC, together with the LFL and UFL, are very important parameters for safety recommendations and loss prevention, especially concerning human activities based on the use of fuel-air or fuel-inert-air mixtures (Schoder, 2005). Concerning the UFL and LFL, the adiabatic flame temperature changes according to the concentration of the mixture at each point. The criterion of a constant adiabatic flame temperature in a limiting mixture was considered to be adequate by many authors, especially when examining the LFL. This criterion was extended to the UFL as well, after a re-examination of adiabatic flame temperatures by including soot among the combustion products. This criterion was maintained over the entire explosion range, including the LOC.

204

8. Flammability Limits of Flammable Mixtures

3. Flammability Limits of Premixed Flames This section is intended to explain the model developed for computing the flammable region of premixed fuel(s)-inert(s)-air mixtures. For that purpose, we have divided the section into three parts: •

The flammability limits of fuel(s)-air mixtures at 1.0 atm and 25 ºC.

•

The influence of pressure and temperature on the flammable range of fuel(s)-air mixtures.

•

The development of the method that makes it possible to calculate the flammability diagrams for fuel(s)-inert(s)-air.

3.1 Flammability Limits of Fuel(s)-Air Mixtures at 1.0 atm and 25ºC Based on the empirical rule developed by Le Chatelier, the upper and lower flammability limits of a mixture of multiple flammable gases with air can be respectively determined according to Eq. (8-1) and Eq. (8-2):

To mix

  100 = ∑ C i  i UFLTo  i

    

(8-1)

To mix

  100 = ∑ C i  i LFLTo  i

    

(8-2)

UFL

LFL

where: • • • •

UFLTio and LFLTio are the upper and lower flammability limit of the fuel species “i” at To ºC, respectively. These values can be found in the literature (Zabetakis, 1965). o o UFLTmix and LFLTmix are respectively the upper and lower flammability limits of the set of flammable fuels at To ºC. To is the atmospheric temperature, at 25 ºC. Ci is the mole fraction of the fuel species “i” in the mixture, in %.

As an example, let’s calculate the lower flammability limit of a mixture of hydrocarbon gases (at 25ºC and 1 atm) containing 50% propane, 40% n-butane and 10% ethane.

205

8. Flammability Limits of Flammable Mixtures Knowing that LFLPropane = 2.1%, LFLN-Butane = 1.8 and LFLEthane = 3.0% and o using Eq. (8-3), the LFLTmix is calculated by: o LFLTmix =

100 = 2.0% 50 40 10 + + 2.1 1.8 3.0

(8-3)

The composition of the lower flammable mixture fuel-air mixture is 1% propane, 0.8% n-butane, 0.2% ethane and 98% air.

3.2 Influence of the Temperature and the Pressure on the Flammability Limits The influence of the temperature and the pressure on the flammable region is summarized in Table 8-2. When the temperature of the mixture increases, the flammability limits widen in such a way that the LFL tends towards zero in the same proportion that the UFL tends towards greater values. An increase of pressure also enlarges the flammable range. In this case, only the UFL is affected as the LFL remains almost constant.

IF Temperature IF Pressure

↑ ↑

Lower flammability limit ↓ ≈

Upper flammability limit ↑ ↑↑

Table 8-2: Tendency of the flammability limits as a function of temperature and pressure. According to Table 8-2, a mixture that is non-flammable under certain conditions may become flammable if the temperature (or pressure) increases. This effect is represented in Figure 8-3, where points A and B represent the same mixture but at different temperatures.

Correlation according to the temperature: The influence of the temperature on the flammability limits is given by Eq. (84) and Eq. (8-5) (Zabetakis, 1965):

LFLTi = LFLTi o (1 − 7.21·10−4 ( T − 25 ) )

UFLTi = UFLTi o (1 + 7.21·10−4 ( T − 25 ) )

(8-4) (8-5)

where: •

T is the temperature at which the flammability limits of the mixture are calculated, in ºC.

206

8. Flammability Limits of Flammable Mixtures •

UFLTi and LFLTi are respectively the upper and lower flammability limits of the fuel species “i” at T ºC.

This equation is obtained by assuming an adiabatic temperature in the LFL and UFL equal to 1300ºC (Zabetakis, 1965). Figure 8-3 shows the influence of temperature on two mixtures: CH4-air and C3H8-air. It is clearly observed that the flammable range widens when the temperature increases. 22.5

Fuel volume % in air

20.0

Non-flammable

17.5

B Flammable

15.0 12.5

UFL CH4 UFL C3H8

10.0 7.5

LFL CH4

5.0

LFL C3H8

2.5 0.0 0

100

150

200

250

300

350

400

Temperature °C

Figure 8-3: Influence of the temperature on the LFL and UFL. Correlation according to the pressure: The influence of the pressure on the flammability limits is given by Eq. (8-6) and Eq. (8-7): UFLPi = UFLTi + 20.6 ( log10 P + 1)

(8-6)

LFLPi ≈ LFLTi

(8-7)

where P is the pressure at which the flammability limits of the mixture are calculated, in MPa. To illustrate this point, let’s calculate the UFL of a gaseous mixture composed of 1% methane, 2% ethane and 3% propane by volume at 50°C and 2 atmospheres. The process to be followed is given below: 1. To correct for temperature for each fuel. 2. To correct for pressure for each fuel. 3. To correct for mixture.

207

8. Flammability Limits of Flammable Mixtures

Fuel volumen [%] in air

70 60

UFL CH4

50 40

UFL C3H8

30 20

UFL CH4

LFL C3H8

0 0

[atm] Figure 8-4: Influence of the temperature on the LFL and UFL.

1- Correct for the temperature for each fuel Taking the values of the USBM of Table 8-1 and using Eq. (8-5): −4 UFL50ºC ( 50 − 25 ) ) = 15.27% Methane = 15 (1 + 7.21·10

−4 UFL50ºC ( 50 − 25 ) ) = 12.72% Ethane = 12.5 (1 + 7.21·10 −4 UFL50ºC ( 50 − 25 ) ) = 9.67% Pr opane = 9.5 (1 + 7.21·10

(8-8) (8-9) (8-10)

2- Correction for pressure According to Eq. (8-6): 50ºC UFL2atm Methane = UFL Methane + 20.6 ( log10 0.202 + 1) = 21.56%

(8-11)

50ºC UFL2atm Ethane = UFL Ethane + 20.6 ( log10 0.202 + 1) = 19.01%

(8-12)

50ºC UFL2atm Pr opane = UFL Pr opane + 20.6 ( log10 0.202 + 1) = 15.96%

(8-13)

3- Correction for mixture According to Eq. (8-1) and Table 8-3:

UFL2atm,50ºC = mix

100 = 17.67% 16.67 33.3 50 + + 21.56 19.01 15.96

(8-14)

208

8. Flammability Limits of Flammable Mixtures

Mixture Methane Ethane Propane

Volume fraction in fuel-air mixture [%] 1 2 3

Volume fraction of fuel mixture [%] 0.167 0.333 0.500

Table 8-3: Volume fraction in the initial fuel-air mixture and volume fraction of a mixture consisting of only fuels.

The upper flammability limit of the mixture at 2.0atm and 50ºC is 17.67%. For higher concentrations the mixture becomes non-flammable. Normally, the pressure reached in a fire is more or less 1.0 atm. Thus, the influence of the pressure during fire conditions on the flammability limits can be neglected. From this point forward, pressure will not be taken into account in this study.

3.3 Flammability Limits of Fuel(s)-Inert(s)-Air Backdraft Conditions according to Temperature

Mixtures

This section explains the development of the model for computing the flammability limits of flammable mixtures (fuel(s)-inert(s)-air) in backdraft conditions according to temperatures. It has been developed for the following reasons: •

•

Flammability diagrams are obtained by experimental tests. This is a relatively hard task that consumes a significant amount of time and economic resources. Furthermore, the results obtained for a certain flammable mixture cannot be extrapolated for any other mixture. Not very much information exists for flammable gaseous mixtures with more than one inert species and even less information exists when referring to temperatures and pressures other than 25ºC and 1atm.

The model is based on the adiabatic flame temperature, assuming the specific heat of the combustion products and diluents to be constant (see Section 3.3.2: “Adiabatic Flame Temperature”). All the correlations developed throughout this chapter refer to C, H, O-consisting fuel, i.e. CH4, (CH3)2CO, with nitrogen as the inert species and oxygen as oxidizer. The strategy of considering inert species other than nitrogen is explained in Section 3.3.6: “Equivalence between Nitrogen and Other Inert Species”. Briefly, this strategy is based on finding the equivalent quantity of inert species that has the same effects as nitrogen on the adiabatic flame temperature.

209

8. Flammability Limits of Flammable Mixtures Some authors have employed a constant adiabatic flame temperature in the limiting mixtures as well as over the entire explosion region. In this model a more realistic approach is used: a variable adiabatic flame temperature as a function of the gas species concentration. Before continuing with the development, a list of the terms used and their signification is given below: • • • • • • • • • • •

LFL LFLinert UFL UFLinert LOC LFC AFT AFTLFL AFTUFL AFTLOC AFTinert

Lower flammability limit when no inert species is in the Lower flammability limit when an inert species is in the Upper flammability limit when no inert species is in the Upper flammability limit when an inert species is in the Limiting oxygen concentration. Fuel concentration at LOC. Adiabatic flame temperature. Adiabatic flame temperature at LFL. Adiabatic flame temperature at UFL. Adiabatic flame temperature at LOC. Adiabatic flame temperature at lower limiting values.

mixture. mixture. mixture. mixture.

The input data necessary for the model to obtain the flammable range of a mixture are the LFL and the UFL. These values can be found in the literature (Drysdale, 1999; SFPE Handbook, second edition) or they can be obtained by using the correlations given in Section 3.3.1: “LFL and UFL vs. Combustion Heat”. Once these data are obtained, the following methodology is applied: The first step consists of two parts: (a) Obtaining the AFTLFL according to Eq. (8-19). (b) Obtaining the AFTLOC according to Eq. (8-27) and the AFTLFL previously calculated. The second step consists of four parts: (c) Giving an initial fuel concentration and obtaining the O2 and N2 concentration according to Eq. (8-29). (d) Obtaining the AFT for the mixture in (c) according to Eq. (8-19). (e) Checking if the AFT obtained in (d) is equal to the AFTLOC obtained in (b). Two possibilities: • •

If not, return to point (c) and give another value for the fuel concentration. If yes, the concentration at LOC has been found. Continue to point (f).

(f) Obtaining the AFTinet according to Eq. (8-22).

210

8. Flammability Limits of Flammable Mixtures The third step consists of two parts: (g) Obtaining the LFL of the lower limiting values according to the AFTinert and Eq. (8-19). (h) Obtaining the UFL of the upper limiting values according to LFLLOC and UFL. A linear equation is assumed. For a visual representation of these steps, see Figure 8-5.

211

First step: AFT equation

LFL

AFTLFL Eq(8-27)

AFTinert

Third step: LFL (exponential fit)

AFTLOC Second step:

UFL (linear fit)

Fuel [%]

LOC

Eq(8-29)

Air [%]

AFT

N2 [%] AFT equation

Figure 8-5: Methodology for computing the flammable region of a premixed mixture with N2

8. Flammability Limits of Flammable Mixtures

3.3.1 Correlation between UFL, LFL and Combustion Heat A representative set of fuels at 25ºC and 1.0 atm is given in Table 8-4. ∆Hc [kJ/mol] 283 800 1423 1411 2044 2650 3891 4505 3259 5104 5734 3680 3120 635 1843

Fuel CO CH4 C2H6 C2H4 C3H8 C4H10 C6H14 C7H16 C5H12 C8H18 C9H20 C6H12 C6H6 CH3OH C3H6

LFL [Vol%] 12.5 5 3 2.7 2.1 1.8 1.2 1.05 1.4 0.95 0.85 1.2 1.3 6.7 2.4

UFL [Vol%] 74 15 12.4 -9.5 8.4 7.4 6.7 7.8 --7.4 7.9 36 11

Table 8-4: Representative set of data referring to fuels. Figure 8-6 shows the UFL and LFL correlations as a function of the combustion heat obtained for the fuels described in Table 8-4. 80

15.00

12.50 LFL = 2179.6·[CombHeat]-0.9095

UFL [%Vol]

LF L [% vol]

10.00

R = 0.9955

7.50 5.00

UFL= 7302.64·[CombHeat]-0.8517

R2 = 0.9476

40 30 20

2.50

0.00

750

1500

2250

3000

3750

4500

Combustion heat [kJ/mol]

(a)

5250

6000

750

1500 2250 3000 3750 4500 5250 6000

Combustion heat [kJ/mol]

(b)

Figure 8-6: (a) UFL vs. Combustion heat; (b) LFL vs. Combustion heat.

213

8. Flammability Limits of Flammable Mixtures Equations for calculating the UFL and LFL are given by Eq. (8-15) and Eq. (816): −0.9095 LFL = 2179.6·∆Hc,fuel

(8-15)

−0.8517 UFL = 7302.64·∆Hc,fuel

(8-16)

It is common practise to obtain the combustion heat of a fuel according to the quantity of reacting oxygen. An average value for the energy release for common fuels is 12.5 kJ/g(O2). Therefore, the combustion heat of a fuel can be expressed as in Eq. (8-17): ∆H c,fuel

 2x+ y 2 -z  = ·MWO2 ·12.5   2  

(8-17)

where the parameter in brackets is obtained from the balanced chemical reaction of combustion, Eq. (8-18), and MWO2 is the molecular weight of oxygen, in g/mol.

 2x+ y -z  2  O → xCO +  y  H O C x H y Oz +    2 2   2 2 2  

(8-18)

With Eq. (8-15), Eq. (8-16) and Eq. (8-17), it is possible to establish the influence on the UFL and LFL of the amount of atoms of carbon (C), hydrogen (H) and oxygen (O) in the fuel. Figure 8-7 represents this influence. 40

UFL [%]

LFL [%]

25 20 15 10

Vol [%] of fuel in air

Vol [%] fuel in air

UFL [%]

LFL [%]

25 20 15 10

8 10 12 14 16 18 20 22 24

Number of atoms of Carbon

0 2 4 6

8 10 12 14 16 18 20 22 24

Number of atoms of Hydrogen

(a) (b) Figure 8-7: Value of UFL and LFL as a function of the number of atoms of C and H in the fuel.

214

8. Flammability Limits of Flammable Mixtures

It can be observed that: • •

The flammable region is wider for fuels with a higher quantity of H (hydrogen). The LFL is lower for fuels with a higher amount of C (carbon). This means that less fuel is needed for a mixture to become flammable.

Therefore, a burning material that releases unburnt products with a greater number of carbon increases the risk of having backdraft in the compartment. Hence, this can be used to evaluate the risk of backdraft in a compartment as a function of the burning material.

3.3.2 Adiabatic Flame Temperature The energy released by a combustion reaction is absorbed by the reaction system itself in the form of unreacted reactants, combustion products and diluents, although this energy will ultimately be lost from the system by various heat transfer processes. By considering a premixed reaction system without no transfer of heat to or from the system, it is possible to discuss adiabatic flame temperature. For future reference, the term “adiabatic flame temperature” is represented as AFT. Assuming the specific heat of the combustion products and diluents to be constant, the adiabatic flame temperature can be expressed as follows:

AFT = To +

∆H c ∑ n j ⋅ Cp j

(8-19)

where To is the initial temperature of the mixture, normally 25ºC; ∆Hc is the combustion heat of the fuel, expressed in J/mol. nj is the number of moles of the combustion product j per mole of reactant. Cpj is the specific heat of the combustion product j, expressed in J/molK. A list of thermal capacity of some common combustion products and inert species at 1000 K is shown in Table 8-5.

Products Carbon dioxide (CO2) Carbon monoxide (CO) Water (vapour) (H2O) Nitrogen (N2) Oxygen (O2) Helium (He)

Specific heat of products at 1000 [K] [J/molK] 54.3 33.2 41.2 32.7 34.9 20.8

Table 8-5: Specific heat of common combustion products or inert species at 1000 K.

215

8. Flammability Limits of Flammable Mixtures Taking as an example a flame propagating through a stoichiometric mixture of propane in air, let’s calculate the adiabatic flame temperature, assuming that all the energy released is absorbed by the combustion products. From Table 8-4, ∆Hc(C3H8) = -2044.3 kJ/mol. The oxidation reaction in air is given by Eq. (8-20). The combustion energy raises the temperature of the products CO2, H2O and N2 present, whose final temperatures can be calculated if heat capacities of these species are known. C3 H 8 + 5O2 + 18.8N2 → 3CO2 + 4H2O + 18.8N2

(8-20)

It is assumed that the N2 is not involved in the chemical reaction but rather acts as a thermal ballast, absorbing a major share of the combustion energy. The energy released in the combustion of 1 mole of propane is thus taken up by 3 moles of CO2, 4 moles of H2O and 18.8 moles of N2.

Species

Number of moles

Specific heat at 1000 [K] Cp(J/molK) n·Cp (J/K) 3 54.3 162.9 4 41.2 164.8 18.8 32.7 614.8 Total thermal capacity/mole propane 942.5 [J/K]

CO2 H2O N2

Table 8-6: Specific heat of combustion product (stoichiometric propane/air mixture). The total capacity of the mixture is 942.5 J/k (per mole of propane burnt). Assuming an initial temperature of 25ºC, the adiabatic flame temperature, AFT, is: AFT = To +

∆HC 2044300 = 25 + = 2194º C 942.5 ∑ n jCpj

(8-21)

The result of this calculation is only approximate for the following reasons: • • •

The specific heat of each gas is a function of temperature; for simplicity’s sake the values used here refer to an intermediate temperature of 1000 K. The system is not truly adiabatic as radiation losses from the flame zone and its vicinity will tend to reduce the final temperature and cause the temperature to fall in the post-flame gases. At high temperatures, the products are partially dissociated into a number of atomic, molecular and free radical species. Since dissociation is endothermic (absorbs energy rather than releases it), this will tend to lower the final temperature. This effect of dissociation on the calculated temperature is significant above 1700ºC.

216

8. Flammability Limits of Flammable Mixtures It is important to remark at this time that the objective of this section is not to find the real AFT but the flammable region for C, H, and O-consisting fuels with one or more inert species. The AFT is used only as a tool that allows us to calculate the flammability limits with accurately. Furthermore, in Section 3.3.5.2: “Correlation of AFTLFL vs. AFTLOC”, it is shown how, by considering this way of obtaining the AFT, the correlation obtained for calculating the AFTLOC provides better results than other studies with more realistic approaches. In Annex VI, the means of obtaining the AFTLFL and AFTUFL of gaseous mixtures is explained.

3.3.3 Mapping the Lower Limit Values of Flammable Diagrams The concentration of the fuel, inert species and air of a mixture in its limit values (UFL and LFL) can be obtained by mapping the flammable diagrams found in the literature. Knowing the concentration at each point, the AFT according to Eq. (8-19) and the process explained in Annex VI can be calculated.

2200 2100 2000 1900 1800 1700 1600 1500 1400 1300 1200 1100 1000

12 C6H14 used as Fuel

Nitrogen used as Inert

8 6

[Vol%]

AFT[ºC]

Figure 8-8 is a double axis figure that represents the flammable region of a C6H14-N2-air mixture. This figure has been obtained from the literature. The AFT calculated by Eq. (8-19) is also represented (red points).

4 2 0 0

20 25 Inert [Vol%]

Figure 8-8: Flammability diagram of C6H14-N2-air mixture at 25ºC extracted from Zabetakis, 1965. Other fuels are represented in Figure 8-9.

217

8. Flammability Limits of Flammable Mixtures

3.3.4 Exponential Fit of the AFT at Lower Limit Values Repeating the mapping of the lower limit values for several fuel-N2-air mixtures, one can observe that the AFT could be modelled by an exponential curve (E. (8-22)) Inert   AFTInert =  A + B·e C   

(8-22)

Above the constants A, B and C are a function of the AFTLFL and AFTLOC of the fuel (see Eqs. (8-23), (8-24) and (8-25)). These equations have been obtained by approximation for minimum square error with real flammable diagrams by means of “Excel Solver”. Therefore: A = 0.9995·AFTLFL

(8-23)

C is obtained by Eq. (8-24): C=

InertLOC  2000AFTLOC  Ln  -1999+  AFTLFL  

(8-24)

and B is obtained by Eq. (8-26):

AFTLFL 2000

(8-25)

Figures 8-8 (a), (b), and (c) show the AFT for some fuel-N2-mixtures. The black circles represent the AFTinert obtained from the corresponding flammable diagrams and the blue squares represent the AFT obtained from the exponential curve.

218

8. Flammability Limits of Flammable Mixtures 1600

1800

1500

CH4 used as Fuel

1700

C3H8 used as Fuel

Nitrogen used as Inert

1600

Nitrogen used as Inert

1500

AFT[ºC]

1400 1300 1200

1300 1200

According to diagrams

1100

1400

According to diagrams According to exponential fit

1100

According to exponential fit

1000

10 15 20 25 30 35 40 45

Inert [Vol%]

(a)

(b) 2050 Butane used as Fuel

1900

Nitrogen used as Inert

AFT[ºC]

1750 1600 1450 1300

According to diagrams

1150

According to exponential fit

(c)

1000 0

5 10 15 20 25 30 35 40 45

Inert [Vol%]

Figure 8-9: Exponential fit to the AFTinert for representative fuels.

3.3.5 Limiting Oxygen Concentration and AFTLOC The purpose of this section is to provide a method that allows us to obtain the LOC. In the course of this discussion, the fuels listed in Table 8-7 have been used. The method consists in obtaining two correlations: • •

The AFTLOC according to the AFTLFL. The equivalence ratio at LOC.

219

8. Flammability Limits of Flammable Mixtures

3.3.5.1 List of Fuels Analysed for Obtaining the AFTLOC Table 8-7 and Table 8-8 show the fuel species that has been used for developing the model. In Table 8-7, Column 1 indicates the fuel species; Columns 2 and 5 represent the fuel concentration at the LFL and fuel concentration at the LOC, respectively; the oxygen concentration at LOC is shown in Column 6; Columns 3 and 7 are the AFT obtained at LFL and LOC, respectively, from the German ChemSafe database. Columns 4 and 8 represent the AFT obtained by Eq. (819).

Fuel

CH4 CH4 C2H6 C3H8 n-C4H10 i- C4H10 n- C5H12 n- C6H14 C2H4 C2H4 C2H4 C3H6 n-C4H8 i-C4H8 1,3-C4H6 C2H2 CO C2H5OH c-C3H6 n-C3H7OH

LFL Fuel at LFL [%] 4.4 4.3 2.4 1.7 1.4 1.4 1.4 1.0 2.4 2.6 2.4 1.8 1.2 1.6 2.0 2.1 13.7 3.1 2.4 2.1

AFTLFL [K]

Eq. (8-19)

1366 1347 1327 1335 1396 1392 1604 1434 1271 1343 1271 1341 1226 1482 1685 1130 1497 1407 1654 1446

[K] 1313 1291 1273 1285 1344 1344 1563 1389 1281 1360 1281 1248 1144 1408 1568 1076 1449 1352 1545 1371

AFTLFL

Apex of the flammable range Fuel at Oxygen AFTLOC LOC at LOC [K] [%] [%] 4.7 9.9 1436 4.8 10.7 1461 2.8 8.8 1339 2.1 9.8 1449 2.0 9.6 1319 1.8 10.3 1463 2.2 11.8 1438 1.5 9.1 1185 2.7 7.6 1309 3.4 8.6 1398 2.7 7.6 1309 2.5 9.3 1411 1.9 9.8 1463 2.0 10.6 1543 2.6 10.5 1512 3.7 6.2 1229 23.4 6.2 1462 3.6 10.5 1249 3.7 11.6 1576 2.9 9.1 1268

AFTLOC Eq. (8-19)

[K] 1387 1408 1434 1508 1762 1627 2209 1890 1408 1680 1408 1602 1607 1673 1927 1663 2256 1518 2160 1702

Table 8-7: LFL and LOC of various fuel-air-nitrogen mixtures at ambient initial conditions. Table 8-8 can be interpreted in the same way as Table 8-7. However the data of Columns 2, 3 6 and 7 are obtained from Zabetakis, 1965.

220

8. Flammability Limits of Flammable Mixtures

Fuel

CH4 C2H6 C3H8 n-C4H10 n- C5H12 n- C6H14 C2H4 C3H6 n-C4H8 i-C4H8 1,3-C4H6 C2H2 C2H5OH c-C3H6

LFL Fuel at LFL [%] 5.0 3.0 2.1 1.8 1.4 1.2 2.8 2.4 1.6 1.8 2.0 2.6 3.5 2.4

AFTLFL [K]

Eq. (8-19)

1492 1545 1541 1654 1604 1622 1379 1633 1490 1606 1685 1275 1467 1654

[K] 1445 1501 1500 1619 1563 1589 1438 1544 1408 1538 1568 1258 1476 1545

AFTLFL

Apex of the flammable range Fuel at Oxygen AFTLOC LOC at LOC [K] [%] [%] 6.6 12.0 1653 3.6 11.2 1465 3.1 11.6 1500 2.7 12.3 1511 2.2 11.8 1438 1.8 11.8 1455 3.9 9.9 1537 3.0 11.5 1642 2.7 11.0 1452 2.7 12.0 1577 2.6 10.5 1512 2.6 6.2 1270 5.0 10.6 1354 3.7 11.6 1576

AFTLOC Eq. (8-19)

[K] 1797 1731 2024 2211 2209 2167 1869 1840 1933 1932 1760 1267 1933 1928

Table 8-8: LFL and LOC of various fuel-air-nitrogen mixtures at ambient initial conditions (Zabetakis, 1965).

3.3.5.2 Correlation between AFTLFL and AFTLOC Using the values from Columns 2 and 5 of Table 8-7 and Table 8-8, the AFTLFL and AFTLOC can be obtained according to Eq. (8-19) and the process indicated in Annex VI. Other authors, Razus 2004, use a program called ECHIMAD based on the thermodynamic criterion of chemical equilibrium used by Gibbs: the minimum of free enthalpy, at constant temperature and pressure. In this model, the specific heats of the combustion products and diluents are expressed as a function of the temperature, while also taking dissociation into account. Figure 8-9 shows the correlation between the AFTLFL and AFTLOC according to the calculation carried out by ECHIMAD (Razus, 2004). Figure 8-11 shows the correlation between the AFTLFL and AFTLOC obtained in this study.

221

8. Flammability Limits of Flammable Mixtures

1800

AFT at LOC [K]

1700 1600 1500 1400 1300 1200

y = 0.4952x + 714.73

1100

R = 0.3381

1000 1000

1100

1200

1300

1400

1500

1600

1700

1800

AFT at LFL [K]

Figure 8-10: Calculated adiabatic flame temperature for fuel-air at LFL and for fuel-air-N2 mixture at LOC. From Table 8-7 and Table 8-8, Columns 3 and 7.

2400

AFT at LOC [K]

2200 2000 1800 1600 y = 1.7599x - 712.56 1400

R = 0.6344

1200 1200

1250

1300

1350

1400

1450

1500

1550

1600

1650

AFT at LFL [K]

Figure 8-11: Calculated adiabatic flame temperature for fuel-air at LFL and for fuel-air-N2 mixture at LOC. From Table 8-7 and Table 8-8, Columns 4 and 8.

Taking the specific heat of the combustion products to be constant and neglecting the dissociation process provide an AFTLOC which is always higher than the AFTLFL as well as a better correlation than the one carried out by Razus. 222

8. Flammability Limits of Flammable Mixtures Eq. (8-26) and Eq. (8-27) represent the correlation obtained by Razus and obtained by Eq. (8-19), respectively. AFTLOC = 0.4952·AFTLFL − 714.73 R = 0.33 2

AFTLOC = 1.7599·AFTLFL − 712.56 R = 0.63 2

(8-26)

(8-27)

Note that these correlations are valid for nitrogen as the inert species.

3.3.5.3 Equivalence Ratio at LOC The equivalence ratio for complete combustion to CO2 and H2O is defined as follows:

[Fuel ] ϕ=

[O2 ]

 [ Fuel ]   O [ 2 ] stoichCO2 +H2O 

(8-28)

where ([Fuel]/[O2]) is the ratio fuel to oxygen in the mixture and ([Fuel]/[O2])stoichCO2+H2O is the fuel to oxygen ratio for the stoichiometric mixture defined by combustion to CO2. Razus, 2004 states that the equivalence ratio at LOC is 1.25 for the fuels shown in Table 8-7 and Table 8-8 when mixing with N2 at 25ºC. However, the author here proposes a much better approximation. It is based on the fact that the position of the limiting oxygen concentration is related to the number of carbon, (Beyler, 1995). For fuels with one C, the limiting oxygen concentration is near the stoichiometric limit. For C5 and hydrocarbons of higher content, the LOC is bisected by the stoichiometric line defined by combustion to CO rather than to products of complete combustion. This shift has been attributed to incomplete combustion and to preferential diffusion of reactants. Therefore, the equivalence ratio at LOC proposed is:

ϕLOC

 [ Fuel ]    Fuel ]  − [    [O2 ] stoichCO+H2O  [O2 ] stoichCO2 +H2O  (C − 1)  =1+ · 4  [ Fuel ]    O [ ] 2  stoichCO + H O  2 2

(8-29)

223

8. Flammability Limits of Flammable Mixtures where ([Fuel]/[O2])stoichCO+H2O is the fuel to oxygen ratio for the stoichiometric mixture defined by combustion to CO and C is the number of carbons in the fuel. Figure 8-12 compares the equivalence ratio of fuel to oxygen at LOC obtained with Eq. (8-29) and the real values from Table 8-7 and Table 8-8.

Value from model

1.5 1.4 1.3 1.2 1.1 1 0.9 0.9

1.1

1.2

1.3

1.4

1.5

Experimental Value

Figure 8-12: Eq. (8-21) vs. real values of equivalence ratio of fuel to oxygen at LOC. Figure 8-13 represents the relative deviation by using Eq. (8-29) and Razus assumption. One may clearly observe the improvement obtained by the new equation proposed.

Absolute Relative error [%]

Model

Razus

C 2H 2 C -C 3H 6 C 2H 5O H

C 3H 6 N -C 4H 8 IC 4H 8 1, 3C 4H 6

C 2H 4

C 3H 8 N -C 4H 10 N .C 5H 12 N -C 6H 14

C 2H 6

C H 4

Figure 8-13: Relative deviation. Comparison between Eq. (8-29) and Razus.

224

8. Flammability Limits of Flammable Mixtures

3.3.6 Equivalence between Nitrogen and Other Inert Species All the correlations developed in previous sections have been obtained for N2 as the inert specie. To be able to compute the flammable region with any kind of inert species, the strategy used is to obtain the equivalent quantity of the inert species that has the same effect on the adiabatic flame temperature as N2. This equivalence is obtained by considering two fuel-inert-air mixtures, which only differ in the type of inert specie(s), expressed in Eq. (8-31) and Eq. (8-32). N2 as inert specie a·Cx H yOz + b·( O2 + 3.76·N2 ) + c·N2 → → dCO2 + eH2O + fO2 + ( 3.76·b ) N2 + c·N2 (8-31) Inert species other than N2 a·Cx H yOz + b·( O2 + 3.79·N2 ) + c·Inert → → dCO2 + eH2O + fO2 + ( 3.76·b ) N2 + cInert (8-32) The variables a, b c, d, e, and f represent the moles of each gas species. Applying Eq. (8-19) for each mixture: AFT = To +

dCpCO + eCpH O

∆H c + fCpO + ( 3.76·b ) CpN + cCpN

(8-33)

dCpCO + eCpH O

∆H c + fCpO + ( 3.76·b ) CpN + cCpInert

(8-34)

AFT = To +

Obviously, to obtain the same value of AFT in both cases, Eq. (8-35) for inert species must be fulfilled.

CpN2 mol inert = mol N2 CpInert

(8-35)

Eq. (8-35) gives the quantity of moles of inert species that provoke the same effect as N2. Figure 8-14 represents the flammable diagram of CH4-N2-air and CH4-CO2-air mixture taken from the literature. PI represents the mixture with CO2 and PII represents the equivalent mixture with N2.

225

8. Flammability Limits of Flammable Mixtures

16.0 14.0

10.0

N as inert specie 2

Point I

Point II

8.0

CO as inert specie 2

CH Fuel [%]

12.0

6.0

Point I Point II

4.0 Equivalent points:

2.0

Point I: with CO

Point II: with N

0.0 0

Inert [%] Figure 8-14: Equivalent mixture of methane with CO2 and N2.

3.3.7 Application Regarding Temperatures Higher than 25ºC and Mixtures of Several Fuels Higher temperatures: Once the diagram at 25ºC is created for the mixture under study, Eq. (8-36) and Eq. (8-37) can be applied to obtain the flammable diagram at different temperatures. o LFLTmix = LFLTmix (1 − 7.21·10−4 ( T − 25 ) )

o UFLTmix = UFLTmix (1 + 7.21·10−4 ( T − 25 ) )

(8-36) (8-37)

Mixtures of several fuels: o o o First, LFLTmix , UFLTmix and LOCTmix must be obtained. Eq. (8-1) and Eq. (8-2) are To To o used for LFLmix and UFL mix . Eq. (8-1) can be also used for obtaining LOCTmix To To but substituting UFL i for LOCi .

Figure 8-14 shows the flammable diagram of a mixture with CO and air followed by mixture with CH4 and CO.

226

8. Flammability Limits of Flammable Mixtures

Volume fraction [%]

70 60

Flammable region for t = 20 s Fuel = 100% CO

50 40

Flammable region for t = 70 s

Fuel: 78% CH4 & 22% CO [in vol]

20 10 0 0

Time [s]

Figure 8-15: Computed flammable diagrams of a CO-Air mixture and a 22% CO and 78% CH4-Air mixture.

3.4 Comparative Results Figure 8-16 represents the flammable region of a CH4-N2-air mixture computed using the model and compared with an experimental flammable diagram. The input data are the LFL (5%) and the UFL (15%).

16 14 Fuel [%Vol]

Experimetal flammability diagram

10 8

Computed flammability diagram

6 4

CH4 used as Fuel

Nitrogen used as Inert

0 0

Inert [%Vol]

Figure 8-16: Flammable region of a CH4-N2-air mixture computed and compared with an experimental flammable diagram.

227

8. Flammability Limits of Flammable Mixtures

Propane, C3H8 [%]

Figure 8-17 represents the flammable region of a C3H8-N2-air computed using the model and compared with an experimental flammable diagram. The input data in this case are the LFL (2.1%), the UFL (9.4%) for the blue line and the LFL (2.1%), the UFL (9.4%) and the LOC (11.6%) for the red line.

10 9 8 7 6 5 4 3 2 1 0

C H used us fuel. 3

N2 used as inert specie

Experimental flammability diagram

Computed flammability diagram Input data: LFL & UFL

Computed flammability diagram Input data: LFL & UFL & LOC

20 30 40 Added inert, volume percent [%]

Figure 8-17: Flammable region of a C3H8-N2-air mixture computed and compared with an experimental flammable diagram.

4. Diffusion Flame Limits 4.1 Le Chatelier’s Rule The reaction capacity of a fuel and oxidant in a diffusion flame is checked by examining the flammability limits of a premixed stoichiometric mixture of fuel and oxidant. The following equation is used for this purpose (Beyler, 1995)

(

)

i  CFuel 100 ∆H c  ∑  AFTSL,i n pCp dt  ∫To 

  ≥1  

(8-38)

where CFuel is the percent volume of fuel species i, when the fuel stream is mixed stoichiometrically with the oxidant mixture. AFTSL,i is the adiabatic temperature of the stoichiometric limit mixture for the fuel species (1450 K for carbon monoxide and 1080 K for hydrogen). To is the temperature of the stoichiometric mixture prior to reaction, also expressed in K. ∆H ic is the heat of combustion of the fuel species i (283 kJ/mol for carbon monoxide and 242 kJ/mol for hydrogen). np is the number of moles of combustion products per mole of reactant (stoichiometric mixture of the fuel and oxidant streams). Cp is the specific heat of the combustion products. 228

8. Flammability Limits of Flammable Mixtures If the result of Eq. (8-38) is higher than 1.0, the mixture might become flammable; however, if it is lower than 1.0 the mixture cannot ignite. An example of how to apply Eq. (8-38) in a mixture is given in Annex IV.

4.2 Application for Fire Compartments In this section, Le Chatelier’s rule is applied to two fire compartments. The characteristics are summarized below: Scenarios 1 & 2: • • • • • • • •

Floor area: 9.0 m2 Height: 3.0 m. Partitions: Heavy wood (mass: 720 kg/m2, Conductivity: 0.2 W/mK, specific heat: 1880 J/kgK). Type of combustion: complete combustion of methane with water and carbon dioxide as combustion products. Combustion heat of methane: 800 kJ/mol. Fire load of 511 MJ/m2 and a RHRf of 250 kW/m2. Opening for scenario 1: 0.5 m x 1.0 m (height and width) Opening for scenario 2: 1.0 m x 1.0 m (height and width)

Simulation carried out by OZone assuming NFSC design fire. Figure 8-18-(1)-(2)-a represents the volume fraction of volume of the species accumulated in the compartment for scenario 1. Figure 8-16-(1)-(2)-b represents Le Chatelier’s number for each scenario. 1.4

0.4 Vol HC

1.2

Vol O2

0.3

Le Chaterier's number

Volumen fraction [%]

0.35

Vol CO2

0.25

Vol H2O

0.2 0.15 0.1

1 0.8 0.6 0.4

0.05

0.2

0 0

250

500

750

1000 1250 Time [s]

(a)

1500

1750

2000

250

500

750

1000

1250

1500

1750

2000

Time [s]

(1)

(b)

229

8. Flammability Limits of Flammable Mixtures 0.9

0.4

0.3

Vol HC

0.8

Vol O2

0.7 Le Chaterier's number

Volumen fraction [%]

0.35

Vol CO2

0.25

Vol H2O 0.2

0.15 0.1

0.05

0.6 0.5 0.4 0.3 0.2 0.1

0 0

250

500

750

1000

1250

1500

1750

2000

Time [s]

(a)

250

500

750

1000

1250

1500

1750

Time [s]

(2)

(b)

Figure 8-18: Volume fraction of gas species accumulated inside the compartment and Le Chatelier’s number of scenario 1 (1) and 2 (2) during the fire evolution. It is clearly observed that scenario 2 cannot lead to backdraft since the mixture inside the compartment is not flammable and cannot become flammable even with a new supply of fresh air. However, scenario 1 can lead to backdraft. Note that if the opening is created before 350 s in scenario 2, the mixture inside the compartment is not yet flammable and, therefore, backdraft cannot occur.

5. Validation of the Diffusion Criterion The validity of the diffusion flame limit criterion is checked with the backdraft experiments carried out by W.G.Weng, 2002 and Fleischmann, 1993. A brief description of the experiments is given below. The dimensions of the experimental apparatus used by Weng and Fleischmann are respectively 1.2 m x 0.6 m x 0.6 m and 2.4 m x 1.2 m x 1.2 m (length, width, depth) (see Figure 8-19). A methane burner was placed against the wall opposite to the one with the openings. To ignite the combustible mixture in the compartment, an electrical heated metal wire provided an ignition source. Three different positions were studied in Weng’s experiments: upper slot opening, middle slot opening and lower slot opening (Figure 8-20), and only one position in Fleischmann’s experiments: middle slot opening. All of these opening were placed against the wall opposite the gas burner. In their experiments they recorded the species concentration of hydrocarbon (CH4=HC), carbon dioxide (CO2), carbon monoxide (CO) and oxygen (O2) just before opening the window that would create the gravity current of fresh air. The concentration of nitrogen (N2) and water (H2O) were calculated based on the equation for oxidation of methane. The upper and lower temperatures were also recorded.

230

2000

8. Flammability Limits of Flammable Mixtures

Height

Depth Length

Figure 8-19: Schematic backdraft apparatus used in Fleischmann and Weng’s experiments. 600 cm

200 cm

Upper-slot opening

Middle-slot opening

Lower-slot opening

Figure 8-20: Different openings used in Weng’s backdraft experiments.

Table 8-9 and Table 8-10 summarize Fleischmann and Weng’s backdraft experiments. Columns 1 and 2 give the experimental run number and ambient temperature, Ta. Columns 3 and 4 describe the burner characteristics, i.e. the burner flow rate and the amount of time the burner gas flows. Columns 5-9 give the compartment species concentration at opening for hydrocarbon, HC, carbon monoxide, CO, carbon dioxide, CO2 and oxygen, O2. Column 7 is the sum of Columns 5 and 6. Columns 10 and 11 are the results calculated from the thermocouple tree data for the upper temperature, TU, and lower temperature, TL. Column 12 indicates in which run backdraft occurs, according to the test

231

8. Flammability Limits of Flammable Mixtures results. Column 13 shows Le Chaterlier’s number (Eq. (8-38)) for each case. A Le Chatelier’s number higher than 1.0 means that backdraft may occur. Less than 1 means that backdraft cannot occur. The results of the last column have been obtained by assuming a combustion heat for methane of 800 kJ/mol and an efficiency of 0.8.

Run Ta [K]

Flow Burner [10-3 Time kg/s] [s]

Upper-slot opening 1 297 0.2549 2 297 0.2549 3 296 0.1609 4 297 0.2529 5 294 0.1603 6 297 0.2549 7 295 0.1543 8 294 0.1589 Middle slot opening 9 300 0.1603 10 299 0.1609 11 298 0.3210 12 300 0.1597 13 298 0.3156 14 299 0.3196 15 297 0.3206 16 298 0.1583 Lower-slot opening 17 298 0.3146 18 298 0.3226 19 300 0.2399 20 300 0.2389 21 296 0.3206 22 299 0.2310 23 297 0.3246 24 298 0.2569

Species concentration

Compart. Backdraft Temp. [K] occurrence O2 TU TL Test Eq [%] [K] [K] (8-38)

HC [%]

CO [%]

Fuel CO2 [%] [%]

260 240 300 180 280 160 260 240

11.2 10.4 8.40 7.80 7.60 7.10 7.10 6.80

0.5 0.55 0.18 0.48 0.23 0.51 0.32 0.20

11.7 10.99 8.65 8.36 7.89 7.65 7.42 7.03

0.3 0.2 0.4 0.3 1.0 0.1 0.2 0.2

14.0 15.0 14.5 16.0 14.8 16.8 14.6 14.6

396 381 391 396 373 399 388 384

357 343 353 352 332 352 348 343

Yes Yes Yes Yes Yes Yes No No

1.11 1.12 1.04 1.09 1.01 1.10 0.99 0.97

780 540 210 360 180 160 120 210

19.0 13.4 10.5 9.0 8.7 8.2 5.7 5.3

0.08 0.13 0.75 0.25 0.9 1.1 1.0 0.18

19.11 13.59 11.33 9.31 9.69 9.3 6.75 5.49

2.1 3.1 2.1 2.8 2.2 1.0 2.1 2.1

12.5 13.0 12.0 13.0 11.0 12.5 12.5 13.5

374 374 377 391 399 382 407 388

339 339 337 347 344 335 343 338

Yes Yes Yes Yes Yes No No No

1.19 1.12 1.03 1.01 0.96 0.97 0.87 0.84

260 240 300 240 180 210 160 180

12.67 12.13 11.45 9.31 9.14 8.22 8.06 7.86

0.21 0.70 0.63 0.58 0.80 0.50 1.0 0.6

12.88 12.83 12.08 9.89 9.94 8.72 9.06 8.46

3.1 2.1 1.8 1.5 1.8 0.7 1.9 0.5

12 11.9 14.5 13.8 12.0 14.6 11.0 14.6

378 380 381 382 369 384 380 400

341 337 345 344 327 342 333 335

Yes Yes Yes Yes Yes No No No

1.08 1.07 1.13 1.05 0.98 1.04 0.92 0.99

Table 8-9: Summary of backdraft experiments in the reduced-scale compartment. Weng’s experiments.

232

8. Flammability Limits of Flammable Mixtures Run

Ta Flow Burner [K] [10-3 Time kg/s] [s]

Compart. Temp. Species concentration Backdraft [K] occurrence HC CO Fuel CO2 O2 TU TL Test Eq [%] [%] [%] [%] [%] [K] [K] (8-38)

Middle slot opening (70 kW) P3EXP38 P3EXP36 P3EXP35 P3EXP34 P3EXP33 P3EXP45 P3EXP32 P3EXP42 P3EXP39 P3EXP40 P3EXP43 P3EXP41

297 297 297 297 297 297 297 297 297 297 297 297

72 72 72 72 69 77 69 69 73 71 68 70

295 355 415 475 535 535 555 595 655 715 715 775

10 12 14 16 16 20 19 19 21 20 22 22

0.5 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2

10.5 12.4 14.4 16.3 16.3 20.3 19.3 19.3 21.3 20.3 22.3 22.2

7 6 6 5 5 5 5 4 4 4 4 4

9 11 11 11 11 11 11 12 12 11 12 12

417 390 379 362 377 363 359 363 350 348 347 344

378 361 353 339 356 344 340 346 331 332 332 330

No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

1.02 1.15 1.19 1.19 1.20 1.24 1.22 1.24 1.24 1.21 1.25 1.25

13 10 24 29 29

1.2 1.2 0.9 0.8 0.7

14.2 11.2 24.9 29.8 29.7

9 10 7 6 6

4 4 5 6 6

517 570 474 447 433

445 475 427 408 400

No Yes Yes No Yes

1.13 1.10 1.27 1.30 1.29

Middle slot opening (200 kW) P3EXP26 P3EXP30 P3EXP27 P3EXP28 P3EXP29

297 297 297 297 297

200 200 200 200 200

115 145 175 205 235

Table 8-10: Summary of backdraft experiments in the reduced-scale compartment. Fleischmannâ&#x20AC;&#x2122;s experiments.

Comparing the experimental results with those of Eq. (8-38), the two sets correspond well. However, it would be interesting to check this criterion for gases other than methane in order to verify the true effectiveness of this criterion. The results of P3EXP28 and P3EXP29 show two similar backdraft conditions with two different results. The first one does not reach backdraft but the second one reaches it. Similar cases have been found in the literature. That indicates that backdraft is a stochastic phenomenon. The experiments depicted in Table 8-10 have been simulated by OZone. The results obtained are summarized in Table 8-11. In each case, OZone gives a flammable mixture at opening. Note that the values are close to those obtained in Column 13 of Table 8-10.

233

Run Ta [k]

Flow [kW]

Burner time [s]

Compart. Temp. [K]

HC [%] Middle slot P3EXP38 P3EXP36 P3EXP35 P3EXP34 P3EXP33 P3EXP45 P3EXP32 P3EXP42 P3EXP39 P3EXP40 P3EXP43 P3EXP41 Middle slot P3EXP26 P3EXP30 P3EXP27 P3EXP28 P3EXP29

Species concentration CO Fuel CO2 [%] [%] [%]

O2 [%]

TU [K]

Backdraft occurrence

OZone TL [K] Test Simulation

opening (70 kW) 297 297 297 297 297 297 297 297 297 297 297 297

72 72 72 72 69 77 69 69 73 71 68 70

295 355 415 475 535 535 555 595 655 715 715 775

9.39 11.2 13 14.5 15.3 17.2 17.2 17.2 19 19.6 18.7 20.4

0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

9.42 11.23 13.02 14.52 15.32 17.22 17.22 17.22 19.02 19.62 18.72 20.42

7.8 6.9 6.3 5.3 4.9 5.1 4.8 5 4.5 4.2 4.3 3.9

8.3 9.2 9.8 10.1 10.7 10.3 10.5 11 11.1 11.5 11.6 11.7

422.36 409.75 399.51 391.32 384.01 385.64 382.15 379.46 375.28 370.06 372.5 366.83

No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

1.05 1.08 1.11 1.12 1.12 1.16 1.15 1.15 1.17 1.17 1.16 1.17

13.602 16.673 19.692 23.646 27.689

0.04 0.04 0.03 0.03 0.03

13.642 16.713 19.722 23.676 27.719

9.011 8.094 7.456 6.824 6.354

4.198 4.857 5.236 5.494 5.424

498.77 470.358 453.611 440.655 431.816

No Yes Yes No Yes

1.17 1.2 1.23 1.27 1.31

opening (200 kW) 297 297 297 297 297

200 200 200 200 200

115 145 175 205 235

Table 8-11: Summary of backdraft experiments and OZone simulation.

8. Flammability Limits of Flammable Mixtures

6. Parametric Study: Influence of Gas Species on Backdraft Probability In this section the risk of backdraft is established according to the type of gas species accumulated in the compartment. For that purpose, a general mixture is considered which consists of C-H-O constituent fuel, hydrogen, carbon dioxide, oxygen, nitrogen and water (Eq. (839)) at opening. a·CxHyOz + b·CO2 + c·O2 + d·N2 + e·H2O

(8-39)

Le Chatelier’s rule, Eq. (8-38), is the criterion used to evaluate the risk of backdraft. It is important to remark that the Le Chaterier rules only inform us if the mixture under research might become flammable and not really if it is flammable at the moment of study. The studied parameters examine the influence of varying: • • • • • • • •

the the the the the the the the

moles of fuel (HC). number of atoms of C of HC. number of atoms of H of HC. number of atoms of O of HC. moles of H2O. moles of N2. moles of O2. moles of CO2.

The reference case is defined in Table 8-12. A single parameter is modified at a time whereas the other parameters remain unchanged.

Fuel CxHyOz; (x: 1; y: 4; z : 0) CO2 O2 N2 H2 O

Molecular W [g/mol] 16.0 44.0 32.0 28.0 18.0

Moles in mixture 1.7 1.0 0.4 8.0 0.5

Molar Fraction [%] 0.146 0.086 0.034 0.689 0.043

Table 8-12: Reference mixture inside the compartment just before ignition. Figure 8-21 shows the influence on the risk of backdraft of increasing the moles of a gas species, while the other ones remains unchanged.

235

8. Flammability Limits of Flammable Mixtures 1.8

Le Chatelier's number

1.6

FLAMMABLE

1.4 1.2 1 0.8 0.6

MOL MOL MOL MOL MOL

NON FLAMMABLE

0.4 0.2

HC CO2 O2 N2 H2O

0 0

0.5

1.5

2.5

3.5

4.5

Moles of gas species

Figure 8-21: Effect of increasing the gas species on flammability. It can be observed that by increasing the amount of moles of oxygen and/or hydrocarbon, the risk of having a flammable mixture also increases. The opposite effect is observed for water, nitrogen and carbon dioxide. In these cases, a higher amount means a lower risk of having a flammable mixture. According to this figure, to become inert a flammable mixture should use CO2 or H2O as the inert species since a lower quantity of moles is needed than in the case when N2 is used. The reason lies in the specific heat. CpCO2 > CpH2O > CpN2

(8-40)

The same kind of study is carried out as a function of the number of atoms of C, H and O in the fuel. Changing the number of C, H or O also entails a change in the combustion heat of the fuel examined. Figure 8-22 shows the results. Increasing the number of C and H, Le Chatelier’s number increases; therefore, the risk of having a flammable mixture also increases. The opposite effect is obtained with atoms of O. The reason for the tendency found for O is simply that if the oxygen content in the fuel is increased, the oxygen needed for the stoichiometric combustion decreases until the moment it becomes zero or less than zero. The physical representation of this idea could be explained by one of the following: • •

The fuel does not exist in reality. The fuel is not combustible.

236

8. Flammability Limits of Flammable Mixtures 1.4

Le Chatelier's number

FLAMMABLE Atoms of Carbon

1.2 1 0.8

Atoms of Hydrogen

0.6

NON FLAMMABLE

0.4 0.2

Atoms of Oxygen

0 0

4 6 Number of atoms

Figure 8-22: Effect of the number of atoms of C, H and O on the possibility of having backdraft.

According to Figure 8-21, having a fuel with higher number of atoms of C is more dangerous than having a fuel with a higher number of atoms of H. In terms of risk, nine atoms of H (hydrogen) are equivalent to two atoms of C (carbon).

7. Influence of Opening Position on the Critical Hydrocarbon Concentration The influence of the position of the opening in the fire compartment on the critical concentration of hydrocarbon is studied according to the parametric study carried out in the previous section and the tests performed by W.G.Weng, 2004. Weng, after carrying out the experiments shown in Table 8-9, concluded that the position of the opening influenced the critical concentration of hydrocarbon in such a way that the higher the opening is, the lower the amount of hydrocarbon is needed for backdraft to occur. Figure 8-23 represents the critical concentration extracted from Wengâ&#x20AC;&#x2122;s experiments for the upper-side opening, middle-slot opening and lower-slot opening. Black circles represent the cases in which backdraft has occurred. White circles represent the cases in which backdraft has not occurred.

237

8. Flammability Limits of Flammable Mixtures

Mass fraction of Hydrocarbon

20 18 16

Upper-slot opening

Critical hydrocabon value = 7.14

(a)

12 10 8 6 4 0

4 5 Test number

Mass fraction of Hydrocarbon

20 18 16

Middle-slot opening

Critical hydrocabon value = 8.79

(b)

12 10 8 6 4 0

4 5 Test number

Mass fraction of Hydrocarbon

20 18 16

Lower-slot opening

Critical hydrocabon value = 9.14

(c)

10 8 6 4 0

4 5 Test number

Figure 8-23: Mass fraction of unburnt fuel determining the occurrence of backdraft (solid circles) and non-occurrence (hollow circles) of backdraft with (a) upper (b) middle and (c) lower-slot opening.

238

8. Flammability Limits of Flammable Mixtures His conclusion was made without considering the rest of the gas species present in the compartment (CO2, O2, N2 and H2O). Figure 8-24 represents the mass fraction of the equivalent fuel (hydrocarbon + CO), the equivalent nitrogen obtained from the mass fraction of CO2, H2O and N2 and the equivalent oxygen for the cases listed in Table 8-10. The x-axis represents the test number and the y-axis represents the mass fraction in [%]. The green line represents the oxygen concentration, the red one is the fuel concentration and the black one is the inert species concentration. Taking the gas concentration of the upper-slot opening case and comparing with the other slot-opening cases, it is observed that there is a: • •

Higher amount of inert species in the middle and lower slot opening cases than in the upper slot opening. Lower amount of oxygen in the middle and lower opening cases than in the upper-slot opening

Based on the results obtained in the parametric study of Section 6: “Parametric Study: Influence of Gas Species on the Backdraft Probability”, having more inert species decreases the risk of having a flammable mixture and having a lower amount of oxygen also decreases the risk of having a flammable mixture. Following this relationship, it is normal that a higher quantity of hydrocarbon is needed for backdraft to occur in the middle and lower-slot opening cases than in the upper-slot opening cases. 90

Upper-slot opening

Middle-slot opening Lower-slot opening

80 70

[%]

60 50

Fuel Oxygen N2 equivalent

40 30 20 10 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Run number

Figure 8-24: Mass fraction representation of Weng’s backdraft experiments.

239

8. Flammability Limits of Flammable Mixtures Thus, it may be concluded that the position of the openings is not the parameter that determines the critical concentration of hydrocarbon, but rather it is the global composition inside the compartment.

8. Conclusions A model for predicting the flammable diagrams of premixed mixtures (fuel(s)inert(s)-air) has been developed. It is based on the adiabatic flame temperature assuming the specific heat of the combustion products to be constant. A comparison with real diagrams found in the literature reveals an excellent correlation. This model, implemented in OZone, can be used to estimate the duration of the most dangerous period for backdraft to occur when an opening is created. In addition, the model can be used to obtain the flammable range of a mixture in a more complex calculation such as CFD. Besides being useful in predicting backdrafts, this model can be also applied to industrial activities, i.e. to develop strategies for avoiding flammable mixtures and, consequently, industrial fires. Also a diffusion flame criterion is used in this chapter to evaluate the risk of having backdraft in a compartment. This criterion has been validated with 41 backdraft tests, which have provided good predictions. Among these backdraft tests, several cases have been found to give different results (backdraft or no backdraft) even if the conditions just before the opening time are the same. Consequently, this reveals that backdraft is a stochastic phenomenon. In this chapter several parametric studies for establishing the influence of the composition of the flammable mixture on the risk of backdraft have been carried out. The results, in addition to give us knowledge about the backdraft phenomenon that can be used for fire fighting, have been used to correct the following conclusion: the position of the openings is the parameter that determines the critical concentration of hydrocarbon (Weng, 2004). In fact, it is not the position of the openings but the global composition of the mixture inside the compartment.

240

8. Flammability Limits of Flammable Mixtures

241