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ACCOMPLISHMENTS IN THE COMBUSTION SCIENCE IN THE LAST DECADE

STUDY OF THE FIRE RETARDING MECHANISM

OF NITROGEN AND PHOSPHORUS CONTAINING

INHIBITORS IN NATURAL COMBUSTIBLE MATERIALS

V. Bogdanova1, O. Kobets1, and V. Kirlitsa2

1Research Institute for Physical Chemical Problems

Belarusian State University

Minsk 220050, Belarus

e-mail: Bogdanova@bsu.by

2Belarusian State University

Minsk 220030, Belarus

1 Introduction

From an economic point of view, nitrogen and phosphorus containing §ame re-

tardants (FR) are the most perspective ¦re extinguishing agents for natural com-

bustible materials (wood, peat). Due to the fact that the speci¦city of burning

of solid combustible materials (SCM) in the presence of FR consists in occur-

rence of several concurrent transformations of the combustible material, §ame

retardant, products of their decomposition interacting both in the condensed and

gas phases, up to the present time, there is no information in literature about

the mechanism of the synergistic inhibitory action of nitrogenphosphorus FR.

This, in turn, impedes directed development of extinguishing agents and SCM

¦re suppressants meeting the contemporary requirements.

To understand why the developed §ame retardants exhibit di¨erent §ame

protective properties, the present authors have previously investigated evolution

of volatile §ame retardants (nitrogen and phosphorus) into the gaseous phase

and properties of the pre§ame zone formed in the condensed phase melts and

foam protective structures [14].

In order to obtain more information about the role of the factors that in-

troduce the dominant contribution to inhibition of burning natural polymeric

combustible materials (wood, peat), the mathematical models that adequately

describe the FR and ¦re-extinguishing e©ciency have been developed using the

mathematical apparatus of optimal experiment planning [58].

2 Experimental Technique

Fire extinguishing e©ciency of FR with respect to peat was determined by the

method, described in [9], according to which the relative weight loss of a peat

82 V. Bogdanova et al.

Filtration and Heterogeneous Combustion

sample (in %) after ¦ring tests was measured. The ¦re retardant e©ciency with

respect to wood was assessed, following the State Standard 16363, by weight

loss (in %) by a ¦re protected wood sample displaced in a ¤ceramic pipe¥ over

a gas burner §ame. Flame retardant composition (FRC) is considered to be

e©cient when –m≤25%. To assess the adequacy of the obtained observations

to mathematical models, the criterion of adequacy of the models was applied to

repeated observations at each full factorial experiment (FFE) point [8]:

(N−n)mY ′Y−Nk

θk2

(n−p)Y′Y−mY ′Y≤Fα;n−p,N−n(1)

where nis the the number of di¨erent points in the FFE; mis the the number

of repeated observations at each point of FFE; pis the the number of unknown

model parameters; Yis the vector of the mean observed values at each point in

the spectrum of FFE; and Fα;n−p,N −nis the quantile of signi¦cance level αof

Fischer distribution with n−p,N−nbeing the degrees of freedom. In case of

implementation of inequality (1), the model was deemed adequate to obtained

observations at the level of signi¦cance α. Signi¦cance of coe©cients in the

mathematical models was determined with the use of Student£s tcriterion [8].

Coe©cient θjis a signi¦cant factor if

θj

s√cjj

> tα,N−p

where tα,N−pis the quantile of the level αof Student distribution with N−p

degrees of freedom; cj j is the jth diagonal element of the inverse matrix (X′X)−1;

and s2is the unbiased estimate of the variance of equally accurate observations.

For FFE, cj j = 1/N; the value s√cjj , counts on the appropriate aggregate

function Excel; and tα,N −pis the quantile of the αlevel of Student distribution

with N−pdegrees of freedom.

3 Results and Discussion

The synthetic dispersion of ammonium-metalphosphate (bi- and trivalent met-

als) which has a complex ¦re-retarding e¨ect (peat ¦re-extinguishing and wood

¦re-protection) was selected as an object of research. Natural metallosilicate

(bentonite) was used as one of the synthesis starting reagents [10]. Previously,

it was found that during thermolysis of ¦re-retarded wood and peat at tempera-

tures realized in the pre§ame zone of condensed phase (200500 ◦C), formation

of foam structures preventing further SCM pyrolysis and evolution of volatile

combustible products into the gas phase were observed. Therefore, such vari-

able factors as the contents of phosphorus (factor x1), bentonite (factor x2), and

V. Bogdanova et al. 83

ACCOMPLISHMENTS IN THE COMBUSTION SCIENCE IN THE LAST DECADE

nitrogen (factor x3) in the formulation of FRC were selected as the main compo-

nents that can signi¦cantly a¨ect the ¦re-retarding properties of extinguishing

and §ame retardant compositions for wood and peat. Numerical values of these

components (g/100 g) for the best FRC e©ciency are as follows: x(0)

1= 6.09,

x(0)

2= 2.8, and x(0)

3= 6.09. The e©ciency of peat extinguishing (vpeat) and

the e©ciency of wood ¦re-protecting (vwood) were selected as response functions

that characterize the e¨ectiveness of ¦re-resistant, ¦re-extinguishing means for

peat and wood burnout (FRC).

In ¦re tests, averaged data on extinguishing and ¦re-protecting properties of

FRC were obtained: y(0)

peat = 1.825% and y(0)

wood = 4.22%. In order to determine

the in§uence of the FRC chemical composition on its ¦re-extinguishing e©ciency

with respect to peat, the FRC analyzed was chosen as the center of the type 23

FFE plan. As a phenomenological model of the FRC ¦re-extinguishing e©ciency

with respect to peat, the regression model with pairwise interaction coe©cients

was chosen:

E{y}=a0+a1x1+a2x2+a3x3+a12x1x2+a13 x1x3+a23x2x3(2)

where E{y}is the average expected value of extinguishing e©ciency y.

In the coded variables Xiwith given variation interval of x(0)

i, equal to 10%,

the regression equation (2) takes the form:

E{y}=b0+b1X1+b2X2+b3X3+b12X1X2+b13 X1X3+b23X2X3.(3)

In order to estimate the unknown parameters of the model (3) in accordance

with the FFE, in each of the eight corners of a cube in coded variables X(1)

= (−1,−1,−1), X(2) = (−1,−1,1), X(3) = (−1,1,−1), X(4) = (−1,1,1),

X(5) = (1,−1,−1), X(6) = (1,−1,1), X(7) = (1,1,−1), and X(8) = (1,1,1)

double observations have been performed, results are presented in Table 1.

In the matrix form, the model of observation (3) can be written as

E{Y}=Xθ

where Yis the observations vector of dimension 16; Xis the experiment plan-

ning matrix of dimension 16 ×7; and θis the vector of unknown parameters of

dimension 7.

Since the experiments were conducted in accordance with the FFE, the ex-

periment planning matrix Xis a matrix with mutually orthogonal columns; in

this case, the e¨ect of multicollinearity factors vanishes and the best linear un-

biased estimator [8] is equal to

θ=X′Y N−1

where X′is the transposed matrix X; and Nis the total number of experiments.

84 V. Bogdanova et al.

Filtration and Heterogeneous Combustion

Table 1 Plan 23FFE and the results of experiments to optimize FRC formulations

for peat

No.

of

Factors in the

natural scale

Factors in the

coded variables Response function, ypeat , %

experiment x1x2x3X1X2X3

1 5,48 2,52 5,48 −1−1−1y11 = 3.62; y12 = 3.98; y13 = 3.80

2 5,48 2,52 6,7 −1−1 1 y21 = 2.71; y22 = 3.06; y23 = 2.89

3 5,48 3,08 5,48 −1 1 −1y31 = 2.68; y32 = 3.13; y33 = 3.10

4 5,48 3,08 6,7 −1 1 1 y41 = 1.35; y42 = 1.17; y43 = 1.18

5 6,7 2,52 5,48 1 −1−1y51 = 3.51; y52 = 2.61; y53 = 2.80

6 6,7 2,52 6,7 1 −1 1 y61 = 2.51; y62 = 2.37; y63 = 2.48

7 6,7 3,08 5,48 1 1 −1y71 = 1.64; y72 = 1.91; y73 = 1.70

8 6,7 3,08 6,7 1 1 1 y81 = 1.06; y82 = 0.83; y83 = 0.94

Using the statistical functions of Excel spreadsheets, the estimates of the

parameters of the model (3) were obtained:

E{y}= 2.3838 −0.3288X1−0.663X2−0.501X3−0.033X1X2

+ 0.1388X1X3−0.118X2X3.(4)

In determining the adequacy of the observation model obtained (4), after

veri¦cation of the signi¦cance of its coe©cients, it has been established that

the model is adequate on the level of signi¦cance α= 0.05 and the coe©cients

X12,X13 , and X23 are not signi¦cant at the 0.05 level. If they are not taken

into account, the model (4) will be very simpli¦ed and poorly describe the real

phenomenological e¨ect of extinguishing e©ciency due to a small number of ex-

periments (N= 16), which does not allow all the seven signi¦cant coe©cients of

model (4) to be evaluated. Therefore, to get more information for estimating the

unknown parameters, at each range of FFE, another additional experiment has

been conducted and data for y13y83 obtained (see Table 1). After revaluation

of model (4) coe©cients, determining the new model adequacy at a signi¦cance

level α= 0.05, and removing the insigni¦cant coe©cient of X12, the adequate

observation model with all relevant coe©cients was received:

E{y}= 2.3763 −0.3463X1−0.6521X2−0.4971X3+ 0.1654X1X3

−0.1388X2X3.(5)

Upon transition to natural variables, model (8) looks as follows:

E{y}= 19.95178 −3.27493x1−4.60345x2−7.31x3+ 0.4455x1x3

−0.81235x2x3.(6)

V. Bogdanova et al. 85

ACCOMPLISHMENTS IN THE COMBUSTION SCIENCE IN THE LAST DECADE

Model (6) describes the phenomenological e¨ect of changing the composition

of initial ¦re-resistant, ¦re-extinguishing mixture in the vicinity of points with

values x(0)

1= 6.09, x(0)

2= 2.8, and x(0)

3= 6.09 on changes in the average expected

value of FRC e©ciency in peat extinguishing. Because peat and wood are the

solid combustible materials of di¨erent nature and it is quite di©cult to ¦nd

a combination of values of the in§uencing factors which provide extremums of

both response functions of interest, therefore, to improve the ¦re-extinguishing

and protective properties of FRC simultaneously with respect to peat and wood,

the following approach was used. Initially, an adequate mathematical model was

built that describes the in§uence of the selected factors on the e¨ectiveness of

FRC ¦re extinguishers for peat, then, this response function was minimized by

the BoxWilson method [6, 8], with additional condition of increasing the FR

e©ciency for wood.

Models (5) or (6) were used to increase the ¦re-protective and ¦re-

extinguishing e©ciency of the original FRC with respect to peat and wood

by the BoxWilson method of steepest descent [8]. According to the condi-

tion, the e¨ectiveness of a ¦re-resistant, ¦re-extinguishing FRC is the higher,

the smaller E{y}. To formulate a new FRC composition, more e©cient simul-

taneously to the two combustible materials studied, the present authors have

assumed that antigradient function (5) at the FFE center is three-dimensional

vector g= (0.3463; 0.6521; 0.4971) and made a transition from the plan center to

a new point (X(i)=αigat i= 1,2,3,...where αi>0 is the setting step motion)

in the direction of vector g. In the chosen direction g, a consistent displacement

was performed at step α1= 0.2 and then at step α2= 0.4 with transition to the

¦rst point with coordinates: X(1)

1= 0.0693, X(1)

2= 0.1304, and X(1)

3= 0.0994

(in natural variables: x(1)

1= 6.13, x(1)

2= 2.84, and x(1)

3= 6.15) and then to

a point with coordinates X(2)

1= 0.1385, X(2)

2= 0.2608, and X(2)

3= 0.1988 (in

natural variables: x(2)

1= 6.17, x(2)

2= 2.87, and x(2)

3= 6.21).

For each of the two new FRC pertaining to the coordinates in the nat-

ural variables, ¦ve experiments were conducted to determine the e©ciency of

§ame-retarding and ¦re-extinguishing of peat and wood and which furnished the

experimental results, as well as average values of vectors ypeat and ywood listed

in Table 2. Thus, the new recipe made it possible to improve extinguishing

and ¦re-resisting properties of FRC for both peat and wood. Inasmuch as fur-

ther displacements in the selected direction gat α3= 0.6 has led to an FRC,

¦re tests of which showed lower ¦re-extinguishing and ¦re-protection e©ciencies

(see Table 2), the previous FRC with parameters x(2)

1= 6.17, x(2)

2= 2.87, and

x(2)

3= 6.21 was adopted as the best formulation. Application of the mathemat-

ical method of experiment planning allowed to optimize the FRC and increase

its ¦re-retardant and ¦re-extinguishing e©ciency with respect to both peat and

wood as compared to the initial recipe. The conclusions about the in§uence of the

86 V. Bogdanova et al.

Filtration and Heterogeneous Combustion

Table 2 Values of the vectors of observations (¦re retardant and ¦re-extinguishing

e©ciency of FRC) changing with transition from central plan FFE in direction of

vector gwith increments α

α

Factors

in positive

integer

variables

Values of the vectors of observations

x1x2x3ypeat, % ywood, %

0.2 6.13 2.84 6.15 y(1)

peat = (0.78; 1.55; 0.78; 1.15; 0.85)

y(1)

peat = 1.02

y(1)

wood = (3.09; 3.85; 3.75; 2.5; 5.84)

y(1)

wood = 3.81

0.4 6.17 2.87 6.21 y(2)

peat = (0.40; 0.41; 0.01; 0.31; 0.04)

y(2)

peat = 0.23

y(2)

wood = (2.55; 2.52; 2.25; 3.07; 3.87)

y(2)

wood = 2.85

0.6 6.22 2.91 6.27 y(3)

peat = (3.37; 1.53; 2.89; 2.22; 1.83)

y(3)

peat = 2.37

y(3)

wood = (5.41; 5.92; 4.61; 4.27; 4.67)

y(3)

wood = 4.97

selected factors x1,x2, and x3on ¦re-protection and ¦re-extinguishing e©ciency

for peat and wood were drawn based on the adequate model (6). Coe©cients of

these factors determine how fast the FRC ¦re-extinguishing and ¦re-protective

e¨ectiveness changes. Absolute values of the regression coe©cients (6) indicate

that the nitrogen content in the formulation (x3) exerts the greatest e¨ect on the

FRC ¦re-extinguishing and protective e¨ectiveness. Preemptive e¨ect of nitro-

gen on FRC ¦re-extinguishing and ¦re-protective properties is also con¦rmed by

the fact that the model includes nitrogen additionally in pair interactions with

phosphorus (x1) and bentonite (x2).

This fact con¦rms the present authors£ experimental data [11] that metal

phosphate ammonium-containing FR systems exhibit a complex mechanism of

¦re-¦ghting action, slowing down the thermolysis reaction of material in the

condensed phase and simultaneously inhibiting the combustion processes in the

gas phase. Thus, the dominant role in ¦re-retardant action of basically belongs to

the volatile nitrogenous products of their thermolysis, which correlates with the

experimental data on the quantitative admission of volatile nitrogen compounds

in the gas phase [13].

4 Concluding Remarks

Application of the mathematical experiment planning method to ¦nd the factors

that exert the decisive e¨ect on the ¦re-resistive and ¦re-extinguishing e¨ective-

ness of the synthetic nitrogen and phosphorus containing FR for wood and peat

allowed to con¦rm and re¦ne the mechanism of their action. It is found that the

dominant process in termination of burning of natural materials is the inhibition

of radical processes in the gas phase by volatile nitrogen-containing products. It

V. Bogdanova et al. 87

ACCOMPLISHMENTS IN THE COMBUSTION SCIENCE IN THE LAST DECADE

is shown that the synergism of nitrogen-, phosphorus-containing FR is due to

their complex action: phosphorus is mainly involved in formation of organic min-

eral structures in the condensed phase, and nitrogen is an inhibitor for reactions

in the gas phase.

References

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