Abstract:

The application for the theoretical calculations of Jet Fire based on Yellow book was developed on JAVA platform and tested in NetBeans IDE 7.4. Model calculates the size and shape of a jet for gaseous releases from pipelines, tanks and two-phase releases from tanks. Chamberlain empirical formulas for vertical and inclined burns in a horizontal wind are used to describe the geometry of the flame. The model returns the ground level distance for each of the heat radiation level of concern (tested for 5, 8, 10 kW/m2). The model was used to calculate the heat radiation as a function of distance for a) CnH2n+2 (alkanes, n = 1-4), b) CnH2n (alkenes, n = 2-4), c) CnH2n+1OH (alcohols, n = 1-4) and hydrogen. The main benefit of presented model is that it allows a quick and fast estimation of the heat radiation from Jet Fire and could be further developed according to actual needs. It allows understanding the basic connections and the key parameters of Jet Fire phenomena from both the mathematical and physical point of view that make it primarily suitable for academic purposes.

Abstrakt:

Na základě Yellow book byla vytvo?ena aplikace k teoretickému v?po?tu tepelného toku z Jet Fire zalo?ená na platformě JAVA a testována v prost?edí NetBeans IDE 7.4. Modelem je mo?né spo?ítat velikost a tvar tryskového po?áru pro úniky plyn? z potrubí, zásobník? a dvou-fázové úniky ze zásobník?. K popisu geometrie plamene je pou?it Chamberlain?v vztah pro vertikální a horizontální směr vanutí větru. Modelem lze vypo?ítat vzdálenost k cíli pro r?zné hodnoty hustot tepelného toku (testováno pro 5, 8, 10 kW/m2). Model byl pou?it k v?po?tu hustoty tepelného toku jako funkce vzdálenosti pro a) CnH2n+2 (alkany, n = 1-4), b) CnH2n (alkeny, n = 2-4), c) CnH2n (acetylen, n = 2), d) CnH2n+1OH (alkoholy, n = 1-4) a vodík. Hlavním p?ínosem prezentovaného modelu je, ?e umo?ňuje rychlé stanovení hodnoty hustoty tepelného toku z Jet Fire a m??e b?t dále rozvíjen vzhledem k aktuálním in?en?rsk?m a v?ukov?m pot?ebám. Model umo?ňuje porozumět základním vztah?m a klí?ov?m parametr?m jevu Jet Fire jak z matematického, tak z fyzikálního hlediska, co? tento model primárně p?edur?uje pro akademické ú?ely.

**1. Introduction:**

A jet or spray fire is a turbulent diffusion flame resulting from the combustion of a fuel continuously released with some significant momentum in a particular direction or directions. Jet Fires can arise from releases of gaseous, flashing liquid (two phase) and pure liquid inventories. Jet Fires represent a significant element of the risk associated with major accidents on offshore installations. The high heat fluxes to impinged or engulfed objects can lead to structural failure or vessel/pipework failure and possible further escalation. The rapid development of a Jet Fire has important consequences for control and isolation strategies. The properties of Jet Fires depend on the fuel composition, release conditions, release rate, release geometry, direction and ambient wind conditions. Low velocity two-phase releases of condensate material can produce lazy, wind affected buoyant, sooty and highly radiative flames similar to pool fires. Sonic releases of natural gas can produce relatively high velocity fires that are much less buoyant, less sooty and hence less radiative. The main objectives of this contribution are (1) to develop quick and fast estimation of the heat radiation from Jet Fire based on the Yellows book Chamberlain model [1]; (2) to initiate the need to increase knowledge and understanding in areas of Jet Fire effects evaluation for students of technical directions [2].

**2. Previous studies:**

The Yellow book model has been generally accepted since 1997 as the semi-empirical model that provided the most accurate and reliable predictions of the physical hazards associated with Jet Fires, providing its application limited to the validation range of the model. This conclusion essentially remains valid today. The most important consideration when assessing the relevance and applicability of mentioned model is the range of data used in its derivation. This model has been developed in several years of research and has been validated with wind tunnel experiments and field tests both onshore and offshore. An in-depth description of the model is reported in Chamberlain [3]. Chamberlain’s model was selected over the alternative point source model since the latter is known to be insufficient within one to two flame lengths for short-term radiation levels although sufficiently accurate in the far field. The Chamberlain better mimics the actual size and shape of a flare. In the literature [4],[5] could be identified two versions of the model, [3] and [6], both of which approximated the geometry of a flare as a frustum of a cone. While Kalghatgi’s used small burners in a wind tunnel, the main focus of Chamberlain’s work was on field trials at onshore oil and gas production installations. Both models used empirically fit equations to describe the flame shape. In fact, Chamberlain uses empirical equation to derive the flame length. Because Chamberlain’s work was more recent and involved larger scale testing, the Chamberlain model was selected to describe thermal radiation hazards for Jet Fire.

**3. Mathematical model:**

The model represents the flame as a frustrum of a cone, radiating as a solid body with a uniform surface emissive power. Correlation describing the variation of flame shape and surface emissive power under a wide range of ambient and flow conditions. The input parameters for chemicals are taken from DIPPR database [8].

We can see at Figure 1a that there is a simple increasing trend going from the C1 to the C4 species (24.0 kW/m2, 26.4 kW/m2, 30.2 kW/m2, 33.7 kW/m2). The calculated theoretical values of heat radiation curve have its maximum at approximately 9.7 m as a distance of the flame to the object. The lethal value of radiation taken as 10 kW/m2 corresponds to 31.5 m (C1), 34.5 m (C2), 38.2 m (C3) and 42 m (C4), respectively. Similarly, we can see at Figure 1b that there is also a simple trend going from the C1 to the C4 species (26.4 kW/m2, 25.3 kW/m2, 32.8 kW/m2). The calculated theoretical values of heat radiation plot have its maximum at approximately 5.2 m as a distance of the flame to the object. The lethal value of radiation taken as 10 kW/m2 corresponds to 31.5 m (C1), 34.5 m (C2), 38.2 m (C3) and 42 m (C4), respectively. For further comparison we divide the plots from Figures 1a,b into two parts from the point of view of distance. First part will be from 0 mto 5.2 m and the second part will be from 5.2 mto approximately 60 m. If we compare the theoretical calculated results for the first part we can recognize that the line for CnH2n+2 (alkanes, n = 1-4) is less increasing than that for CnH2n (alkenes, n = 2-4). If we compare the theoretical calculated results for the second part for both tested systems we can see that the line for CnH2n+2 (alkanes, n = 1-4) is less decreasing than that for CnH2n (alkenes, n = 2-4). As a conclusion both results show that the profile shape factor of CnH2n+2 (alkanes, n = 1-4) is more sharp than that of CnH2n (alkenes, n = 2-4). These basic facts concerning the heat radiation as a function of distance for the species with different bonds orders could be recognized and could be further analyzed by comparing them with the species substituted by hydroxyl chemical functional group. In both cases, the theoretical calculations of hydrogen heat radiation as a function of distance (denoted by the red color in Figures 1a,b) have been used for scaling (from 0 m to 150 m). As in the case of alkanes and alkenes, we can see at Figure 2a the value of acetylene heat radiation (24.7 kW/m2). The calculated theoretical value of heat radiation curve has its maximum at approximately 5.2 m as a distance very similar to that obtain for alkenes. The lethal value of radiation taken as 10 kW/m2 corresponds to approximately 24.7 m which is slightly lower than 25.3 kW/m2 for C2H4. For further comparison we divide the plots from Figures 1a,b into two parts from the point of view of distance. We can see at Figure 2b that there is also a simple trend in alcohol substituted species going from the C1 to the C4 species (11.2 kW/m2, 17.8 kW/m2, 22.8 kW/m2, 24.3 kW/m2). This may be related to the fact that the molecular structure of the OH· moiety change under substitution heat radiation value much more than in CnH2n+2, as shown by presented theoretical calculation, confirmed by results of experimental studies CnH2n+1OH. Apart from the trends investigated in different number of carbon and different bonds order aspects, the study of calculated jet, fire and heat flux parameters and for calculation used constants are of importance.

All jet, fire and heat flux parameters used for calculation of the heat radiation as a function of distance were established during the present investigation for the first time, and the values of alkanes, alkynes and acetylene could be compared with those of their alcohols analogues. The present gas phase (alkanes, alkenes, alkynes) and two-phase (alcohols) investigation has started the series of studies by mathematical modelling of the substituted hydrocarbons. The calculated values of parameters characterizing the jet, fire and heat radiation have been accurately determined for methane, and they compare well with the theoretical calculations listed in [1]. These values are typical of the hydrocarbons of non-multiple bonds. The mass fraction of fuel in a stoichiometric mixture with air, W, together with gas constant, Rc, and specific heat capacity, Cp, was effectively transformed into ratio of specific heat - Poisson constant, γ. The value of Poisson constant γ = 1,306 has been of comparable value with the value γ Y = 1,307 published in [1]. The Mach-number, Mj ,for chocked flow of an expanding jet has been determined in this investigation. The Mach-number is estimated from the temperature of the expanding jet, Tj, and the static pressure, Pc, at the hole exit plane [N/m2]. The value of the Mach-number Mj = 3,95 has been of slightly higher value than the value MjY= 3,55 published in [1]. The further parameters values are in good agreement with the values published in.

**5. Conclusion**

(1) exit velocity of expanding jet [m/s]; (2) angle between hole and flame axis [°]; (3) frustum lift-off height [m]; (4) width of frustum base [m]; (5) width of frustum tip [m]; length of frustum (flame) [m]; (6) surface area of frustum [m2]; (7) maximum surface emissive power [kW/m2]; (8) atmospheric transmissivity [%] and view factor [-]. Further parameters could be implemented based on actual needs. In the near future we are planning to compare the results of the CnH2n+2 (alkanes, n = 1-4), CnH2n (alkenes, n = 2-4), CnH2n-2 (acetylene, n = 2), CnH2n+1OH (alcohols, n = 1-4) calculations with the results obtained by procedure Jet Fire (Chamberlain model) implemented as a part of the program Effects version 9.0.8 that will be possible to use a tour department. This model could be further developed according to present engineering knowledge and can make a contribution towards solving the problems facing the flammable liquefied fuels in industrial practice in assessment of jet fire hazards comprises (1) identification of areas of uncertainty in the characterization of jet fires; (2) identification where the jet fire hazard is significant in relation to other hydrocarbon hazards; (3) initiation of research to increase knowledge and understanding in ill-defined areas of Jet Fire evaluation and (4) promote the use of a consistent methodology for evaluation of jet fire hazards. Furthermore, the model application and development could support the practice of the Department of Major Accidents Prevention of Occupational Safety Research Institute.