A Mathematical Model of the Change of Hydrogen Concentration. Sample Computations for a Real-Life Situation in a Ventilated Room
Journal Title: Safety & Fire Technology - Year 2018, Vol 49, Issue 49
Abstract
Objectives: The aim of this article is to analyse the change of concentration of hydrogen in the atmosphere of large closed spaces with a constant but small emission of hydrogen. The analysis has been conducted for a room equipped with a ventilation system where, in order to retain heat, a significant portion of the exhaust air is recycled and turned back into the room. Thus, fresh air makes up only a part of the air blown into the room. Moreover, it is BITP VOL. 49 ISSUE 1, 2018, pp. 66–74, doi: 10.12845/bitp.49.1.2018.6 SAFETY & FIRE TECHNIQUE 67 RESEARCH AND DEVELOPMENT assumed that there are no sources of harmful substances in the room. In our analysis, we consider the entire room and not only the spaces near the source of emission. Our investigation allowed us to describe how the concentration of hydrogen changes in time and to relate these results to the explosive limits. In particular, we were able to determine the time after which the hydrogen concentration would reach a critical level. Methods: A calculation model was developed for the purposes of this paper. This model takes into account the efficiency of the source of emission, the efficiency of the ventilation system, the volume of the room and the portion of the exhaust air which is recycled. In order to obtain formulas describing how the content of hydrogen (or other emitted substance) changes, differential equations were used in the room. These equations determine the relationship between an unknown function and its derivatives. Currently, a number of studies are being conducted to develop further models for solving differential equations, as they have many practical applications. Results: Once the mathematical model was developed, a set of representative diagrams has been plotted using data from a real-life situation. The graphs which we obtained make it possible to predict how hydrogen concentration changes as a function of time, and to determine when the concentration reaches a critical level. The methods presented here can be useful in assessing the explosion hazard, and in many cases could clarify many doubts related to this issue. The mathematical model is applicable without restrictions for substances that form explosive mixtures with air; air containing harmful substances should not be recycled. Conclusion: Based on the analysis of the obtained data, we drew conclusions regarding current legal regulations in Poland. We recommend that the existing regulation regarding the fire protection of buildings and other structures and areas. Based on the presented model, supported by calculations for the example under consideration, the final conclusions were formulated. The proposed mathematical model is a useful engineering tool and can be useful in determining the maximum amount of substance with air density ≤ 1 in room atmosphere and allows the critical volume Hkr to be linked to ventilation efficiency. The model can also be used to determine the time after which Hkr will be exceeded; this is important for the estimation of the response time. The presented figures confirm that the model is correct.
Authors and Affiliations
dr Anna Zielicz, mł. bryg. dr inż. Tomasz Drzymała, dr inż. Sylwester Kieliszek, Aneta Łukaszek-Chmielewska
Keywords
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- EP ID EP359706
- DOI 10.12845/bitp.49.1.2018.6
- Views 42
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