Explosion-Hazard Region of a Single Triple Dynamic Gas System

V. E. Lanin, Yu. A. Zakharov, V. B. Neimirovskii, L. K. Parfenov, A. V. Melnik

(Presented by the scientific seminar of the Department of Radiation Chemistry)

In developing measures to ensure the explosion safety of the atmospheres of certain objects of new technology, as well as explosion-hazardous gaseous media encountered in chemical production, the question of developing reliable methods for assessing the explosion hazard of multicomponent dynamic gas systems is an urgent one.

By dynamic we shall understand gas systems formed in closed volumes through the continuous inflow of gaseous components—in the general case, combustibles, oxidizers, inert, inhibiting, and catalyzing components—from internal sources, which, to a first approximation, may be assumed to be uniformly distributed over the closed volume; this eliminates the need to take into account the possible nonuniformity of the distribution of components under the real conditions of the object.

The question of a reliable assessment of the explosion hazard of a dynamic gas system is exhausted by establishing a reliable concentration boundary between the regions of explosion-hazardous and explosion-safe concentrations—for all possible ratios between the component contents and levels of the total pressure, and for all possible conditions in the system (thermal, gravitational, electromagnetic and similar effects and conditions).

It seems expedient to begin consideration of the problem with the simplest case, with a triple system whose formation occurs under normal conditions; in doing so, the energy of potential ignition pulses is assumed sufficient to form a flame kernel of critical dimensions [1] and so forth, in mixtures approaching limiting ones.

Let us consider, from the standpoint set forth, the concentration limits of explosibility of the dynamic system \(H_2 - O_2 - N_2\), within the range of possible total pressures in the system of \(100 \div 1300\) mm Hg, with ignition from below.

The concentration limits of explosibility of the system have been studied by many authors, mainly at atmospheric pressure. For the most part, hydrogen–air mixtures have been investigated in the region of the lower concentration limit with respect to hydrogen. The generally accepted values for this system are the following C.L.: in the absence of nitrogen in the mixture, the LCL\(_{H_2}\) is 4.0 vol.%, the UCL\(_{H_2}\) is 94 vol.%; for a hydrogen–air mixture, 4.0 vol.% and 74 vol.%.

A broad review of materials on the system is given in [2]. Of interest for the present work is the dependence, presented in [2], of the CL of the hydrogen–air system on dilution of the air with nitrogen, at atmospheric pressure, Fig. 1. For analysis of the explosion hazard of the system it is more convenient to use the data of Fig. 1 recalculated to the absolute nitrogen content.

The results of the recalculation are given in Table No. 1; the corresponding oxygen contents in the mixture are also given here.

In Fig. 2 the dependence of LCL\(_{H_2}\) on the nitrogen content in the system, obtained as a result of the recalculation, is presented, up to 90 vol.% \(N_2\), when the system becomes explosion-safe (the value of LCL\(_{H_2}\), equal to 93.9 vol.%, is also taken from [2]). Construction of this dependence exhausts the question of the explosion-hazard region for systems under normal conditions. By comparing any composition formed in a closed volume with the explosion-hazard region, it is easy to estimate whether it is explosion-hazardous.

One of the conclusions of such an analysis of the data of [2] is the conclusion that the oxygen content in the system affects the pre-

Fig. 1. On recalculating the curve of the concentration limits of ignition in a mixture of hydrogen with air diluted with nitrogen, [2], into the limit curve of the system
\(H_2 - O_2 - N_2\).

Fig. 2. Dependence of \(K_{\mathrm{LFL}}\) on the nitrogen content in the hydrogen–oxygen–nitrogen system, \(P_{\mathrm{tot}} = 760\) mm Hg (recalculation of the data of Coward G. F. and Jones G. W., [2]).

hydrogen explosion limit, which is illustrated by Fig. 3, curve 1, whence it follows that \(KPN_2\) remains almost unchanged up to an oxygen content of \(\sim 42\) mm Hg (about \(5.5\%\) by volume). A further decrease in the oxygen content while maintaining an explosion-hazardous situation is possible only with an increase in the hydrogen content; however, the decrease in the \(O_2\) content is insignificant, to \(\sim 4.95\%\) by volume. If it is necessary to ignite mixtures containing more than \(30\%\) by volume of \(H_2\), the \(O_2\) content should again be increased, up to \(6.1\%\) by volume when nitrogen is completely replaced by hydrogen.

Thus, on the basis of the foregoing, one can quite definitely speak of \(KPN_2\) for a system with any of the possible \(O_2\) contents and, in particular, of the maximum explosion-hazardous oxygen content (MEOK), equal to \(\sim 4.95\%\) by volume.

In addition, the analysis carried out of the data in [2] substantially facilitates the search for the explosion-hazard region of systems at other pressures—from the practically important interval \(10^3 \div 10^2\) mm Hg. (We note preliminarily that, in order to rationalize the search for the concentration boundary at different gas pressures, it is advisable to obtain dependences \(KPN_2 = f(P_{\text{tot}};\ O_2\%\ \text{by vol.} = \text{const})\) over the entire interval of explosion-hazardous concentrations of \(H_2\) in the system: from \(\sim 4\%\) by volume to \(\sim 93.9\%\) by volume. The explosion-hazard region for other pressures can then be determined by simple recalculation.

Indeed, in accordance with the data of Table No. 1, for example, the dependence \(KPN_2 = f(P_{\text{tot}};\ O_2\%\ \text{by vol.} = 1.75)\) at \(P_{\text{tot}} = 760\) mm Hg must pass through the value \(KPN_2 = 4.25\%\) by volume, etc., as follows from Fig. 4. Thus, there are “reference points” (points b, c, e—Fig. 4; points b and 3—Fig. 5) for the experimental determination of the dependences \(KPN_2 = f(P_{\text{tot}};\ O_2\%\ \text{by vol.} = \text{const})\) for different oxygen contents in the mixture. The shape of the curves in Fig. 4 is approximate and corresponds to the proposition that, at pressures

Fig. 3. Dependence of \( \mathrm{KPN}_2 \) on the oxygen content in the \( \mathrm{H}_2-\mathrm{O}_2-\mathrm{N}_2 \) system. 1 — according to the data of [2]; 2 and 3 — calculation; \(P_{\mathrm{tot}} = 1300\) and \(500\) mm Hg.

Fig. 4. Explanation of the “reference points” of the experiments on the initial curves

\[ \mathrm{KPN}_2 = f\!\left(P_{\mathrm{tot}};\ \mathrm{O}_2,\ \%\ \mathrm{vol}=\mathrm{const}\right). \]

Point б corresponds to \(\mathrm{KPN}_2,\% = 4.25\) and an \(\mathrm{O}_2\) content, \(\%\ \mathrm{vol}\), equal to \(12.75\); point в — \(4.5\) and \(5.5\); point е — \(10\) and \(4.95\), respectively (see Table No. I).

Fig. 5. Presumed course of the dependences

\[ \mathrm{KPN}_2 = f\!\left(P_{\mathrm{tot}};\ \mathrm{O}_2,\ \%\ \mathrm{vol}=\mathrm{const}\right). \]

Curve I — according to the data of [4].

pressures lower than the critical pressure \((P_{\mathrm{cr}})\), the flame does not propagate in the mixture, [3].

In [4] experimental data are presented that make it possible to speak more definitely about the form of the graphs

\[ \mathrm{KPN}_2 = f(P_{\mathrm{tot}};\ O_2\ \mathrm{vol}=\mathrm{const}) \]

for oxygen contents of 96 and 16 vol.%; the dependences

\[ \mathrm{KPN}_2 = f(P_{\mathrm{tot}}) \]

in the pressure interval \(10^3 \div 10^2\) mm Hg are represented practically by a straight line, Fig. 5, graph 1, below point a. If it is assumed that at other \(O_2\) contents the graphs \(\mathrm{KPN}_2=f(P_{\mathrm{tot}})\) also remain straight lines, Fig. 5, graphs \(2 \div 8\), then it becomes possible simply to determine the explosion-hazard region for any total pressure. Table No. 2, for example, gives the results of calculating the \(O_2\) contents along the concentration boundary for \(P_{\mathrm{tot}}=1300\) and \(500\) mm Hg; the corresponding graphs (2, 3) are given in Fig. 3.

It is obvious that, on the basis of the indicated assumption, in particular, it is easy to establish the MVSK for any pressure in the system. Fig. 6 gives the graph

\[ \mathrm{MVSK}=f(P_{\mathrm{tot}}), \]

from which it follows that

\[ \mathrm{MVSK}\simeq 0.049\,P_{\mathrm{tot}}. \]

To implement the method described above for assessing the explosion hazard of dynamic gas systems, it is important to know not only the extreme values characteristic of the system under consideration (MVSK, the lower limit with respect to hydrogen, etc.). It is necessary to delineate the entire explosion-hazard region, i.e., to indicate the whole field of explosion-hazard concentrations. For a given level \(P_{\mathrm{tot}}\), this region may be represented in the form of the curves in Fig. 2, in Fig. 3, etc.

It is obvious that, for problems in which the flowing components are \(H_2\) and \(O_2\), it is more expedient to depict the explosion-hazard region in a coordinate system with axes \(O_2\) and \(H_2\), and in volume percent, since within certain pressure intervals in the system the percentage contents of the components along the concentration boundary may remain unchanged.

Fig. 6. Predicted dependence \(MBSK = f(P_{\mathrm{total}})\); 1 — point corresponding to the data of [2].

Fig. 7. Explosion-hazard regions of the \(\mathrm{H_2}-\mathrm{O_2}-\mathrm{N_2}\) system at different levels of total pressure: 1 — for 760 mm Hg, according to [2]; 2 and 3 — for 500 and 200 mm Hg, estimated.

Such a graph is shown in Fig. 7, curve 1 (see also Table No. I).

Verification of the admissibility of the indicated assumption can most simply be carried out as follows: using the “points” features, Fig. 4 and Fig. 5, experimentally establish the nature of the dependences \(KPN_2=f(P_{\text{tot}})\) for several low \(O_2\) contents (see Table No. I). If the dependence of \(KPN_2\) on the total pressure is established (at \(O_2\%\ \text{vol.}=\text{const}\)), then, having taken a sufficient number of dependences, it will be possible to construct explosion-hazard regions for any pressures in the system.

The explosion-hazard regions in Fig. 7, curves 2, 3 \((P_{\text{tot}} = 500\) and \(200\ \text{mm Hg})\), give an idea of the nature of the shift of the explosion-hazard limits when the pressure in the system is lowered in the case where, for unchanged (in % vol.) \(O_2\) contents in the mixture, the value of \(KPN_2\) is assumed to depend on pressure, Fig. 5, graphs 3–7.

It follows from Fig. 7 that in this case the broadest is the explosion-hazard region for \(P_{\text{tot}} = 760\ \text{mm Hg}\), as well as for pressures greater than atmospheric, where \(KPN_2\) remains at the same level. This region, characterized in this way by the very lowest \(KPN_2\) and \(MVSK\), Fig. 7, should be regarded as the main explosion-hazard region for the pressure interval \(10^3 \div 10^2\ \text{mm Hg}\) and should be used first of all in assessing the explosion hazard of the given gas system under normal, except for pressure, conditions.

The use of this region for systems with reduced pressures will somewhat “tighten” the requirements for them—in the event that \(KPN_2\) depends noticeably on pressure—however, this will increase the reliability of the assessment and raise the “safety factor for explosion hazard.”

Let us note, in conclusion, that in the general case of the problem of establishing the explosion-hazard region of a system, it is necessary, as was noted, to study and take into account all possible actions and conditions affecting the K.P.

Table No. 1

Table No. 2

References

1. Ya. B. Zel’dovich, I. N. Semenov, Zh. Eksp. Teor. Fiz., 23, No. II, 1949.

2. Coward H. F. and Jones G. W., U.S. Bureau of Mines Bull., 503, 1952.

3. L. N. Khitrin, Physics of Combustion and Explosion, 1957, Moscow State University Press.

4. V. R. Panin, D. A. Zakharov, V. A. Marasanov, V. B. Nemirovskii, L. K. Parfenov, “Investigation of the lower concentration limits of flammability of hydrogen–oxygen and hydrogen–air mixtures at reduced pressures,” see the present collection.