# An experimental study on the heating and burning of a binary liquid mixture in a pool fire

En Xie, Rabah Mehaddi, Lucas Terrei, Tarek Beji

► To cite this version:

En Xie, Rabah Mehaddi, Lucas Terrei, Tarek Beji. An experimental study on the heating and burning of a binary liquid mixture in a pool fire. Journal of Physics: Conference Series, 2024, 2885, 10.1088/1742-6596/2885/1/012042. [hal-04823613](https://hal.science/hal-04823613v1)

HAL Id: hal-04823613

https://hal.science/hal-04823613v1

Submitted on 6 Dec 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

PAPER • OPEN ACCESS

# An experimental study on the heating and burning of a binary liquid mixture in a pool fire

To cite this article: En Xie *et al* 2024 *J. Phys.: Conf. Ser.* **2885** 012042

View the [article online](#) for updates and enhancements.

You may also like

- *Experimental study of synthesis of N-2-Hydroxypropyltrimethylammonium chloride chitosan and carboxymethyl chitosan nanoparticles by ultrasonic microreactor*
  Chang Qu, Xiuzheng Zhao, Zheng Jin et al.

- *The feasibility and efficiency of fly ash as an absorbent for phosphate removal*
  O Juntarasakul, J Vercruysee, P Roongcharoen et al.

- *Preparation and performance verification of calcium silicate composite electrical fireproof materials*
  Yin Wang, Yu Wang, Dedong Yang et al.

<figure><img src="image_3.png" /></figure>
# An experimental study on the heating and burning of a binary liquid mixture in a pool fire

En Xie¹, Rabah Mehaddi², Lucas Terrei² and Tarek Beji¹

¹Ghent University, Department of Structural Engineering and Building Materials, Ghent, Belgium

²University of Lorraine, CNRS, LEMTA, F-54000, Nancy, France

E-mail: En.Xie@UGent.be

**Abstract.** The paper presents experimental measurements for the transient profiles of burning rates and liquid temperatures (at different depths below the surface) in pool fires. Steel square burners with two different side lengths are selected: 10.5 and 15.0 cm. The burner is 5 cm deep and the initial fuel height is about 4.6 cm. At 10°C, the fuel is a mixture of cyclohexane and methanol with a molar composition of about 50%-50%. Under these conditions, there is a top cyclohexane-rich layer and a bottom methanol-rich layer. In the initial transient and steady-state periods, the burning is slightly lower than that of pure cyclohexane due to the presence of methanol in the top layer. Then, a sudden more intense burning occurs due to the expansion of methanol vapor reaching the surface. A semi-empirical model is proposed to predict the onset of this event, assuming that it corresponds to the interface between the two layers reaching the azeotropic point of the blend. A second steady-state period is subsequently established, corresponding to the burning of a well-mixed blend of both liquids at the azeotropic point, as measured by the thermocouples immersed into the liquid.

## 1. Introduction

There are a variety of liquid mixtures that are stored and used, for instance, for power generation devices [1]. Common examples are petrol, kerosene, and fuel oil [2]. As mentioned in [2], 'a hazard associated with some hydrocarbon liquid blends [...] is that of a formation of hot zone' which propagates at a higher rate than the surface regression. The hot zone may encounter a layer of water (commonly present in storage tanks), leading to explosive vaporization of water, thus ejecting, for instance, hot burning oil [2]. This is a clear indication of the need to further understand heat transfer within the liquid in a pool fire, in addition to the ongoing efforts on the gas phase combustion, e.g. the development of multi-component surrogates for petroleum-derived fuels [1]. Heat transfer within pure liquids during a pool fire has been examined theoretically, experimentally, and numerically in several studies, e.g. [3-5]. It has been shown, for example, that convective motion occurring within the liquid due to surface tension or in-depth radiation effects can be modelled using the effective conductivity concept. In this approach, the internal Nusselt number, i.e. the ratio of the effective to the actual thermal conductivity, reflects the enhanced heat transfer due to convective motion. This work is believed to be relevant for the understanding of the heating and burning of blended fuels, especially in the case of immiscible or partially miscible liquids with a layered structure, as examined in [6] and in this work. In [6], a mixture of immiscible n-heptane and methanol is considered in six square pools with a side length ranging from 5 cm to 20 cm. In all cases, there is initially a layer of n-heptane (less dense) on top of a layer of methanol. However, different temporal profiles of the burning are observed, depending on the initial

<figure><img src="image_4.png" /></figure>
blend ratio. Generally speaking, these profiles exhibit quasi-steady state periods of pure liquid burning and/or well-mixed liquid burning at the azeotropic point, a temperature of 59.1°C (for an n-heptane-methanol mixture) that is 'lower than the either boiling point of n-heptane and methanol, which leads to smaller mass loss rates'. The quasi-steady state periods are intercut by short events such as an abrupt increase in the burning rate, which is explained by 'a sudden expansion of vapor at the interface of the two-layered fuels' [6]. The theory of vapor-liquid equilibria (VLE) theory is introduced in [7] to analyse the surface temperature of blends, to describe the variations in the molar fraction of the two components, and to understand the subsequent burning mechanisms in blends [7]. The results show that, as long as the initial proportion is close to the azeotropic ratio, the composition and boiling temperature near the surface are steady. However, in the other proportions, the burning process gradually transits to pure liquid combustion.

In this paper, we do not describe the different burning regimes, depending on the initial blend ratio of a binary mixture. We consider only one blend ratio, but provide a more quantitative analysis of, for example, the time for the onset of the explosive vaporization. Furthermore, in contrast to [6], we are considering here two liquids, namely cyclohexane and methanol, that are initially partially miscible.

## 2. Theoretical background on miscibility and temperature composition diagrams

The first step towards understanding the burning process of a binary mixture of liquid fuels is to determine their liquid-liquid phase and vapor-liquid phase equilibria. The data is displayed in a so-called temperature-composition phase diagram. Figure 1 shows such a diagram for the binary system of interest in this paper, which is a mixture of cyclohexane ($C_6H_{12}$) and methanol ($CH_3OH$). The x-axis gives the molar fraction of cyclohexane and the y-axis gives the temperature of the mixture.

<figure><img src="image_5.png" /><figcaption>Figure 1. (a) Temperature-composition phase diagram for a blend of cyclohexane and methanol at 1 bar [8]; the long vertical (resp. curved) arrow denotes the distillation (resp. dissolution) process. (b) A sketch of the two layers before ignition; the red dots represent the thermocouples.</figcaption></figure>

### 2.1. Liquid-liquid phase equilibrium

The first part of the diagram is the liquid-liquid phase equilibrium, which is given by the dissolution line in figure 1 (a). In the region under the dissolution line, called the two-phase region, the two liquids are partially miscible. Outside this region, they are miscible. For example, let us consider a mixture of 5.0 mol of cyclohexane and 5.0 mol of methanol in a vessel (e.g. a square steel burners as in this study) at 10°C, corresponding to the initial ambient temperature in this study. The overall molar fractions are $X_{\text{methanol}} = X_{\text{cyclohexane}} = 0.50$. The system is in the two-phase region. This means that there will be a cyclohexane-rich layer and a methanol-rich layer. The cyclohexane-rich layer is composed of 93% cyclohexane and 7% methanol in molar proportions (as indicated by point L in figure 1 (a)). The methanol-rich layer is composed of 13% cyclohexane and 87% methanol (as shown by point M in figure 1 (a)). As methanol is denser than cyclohexane, the methanol-rich layer will be at the bottom and the cyclohexane-rich layer will be at the top. The Lever rule can be used to determine the molar fraction of
each layer. If the same molar proportions are kept (50%-50% in this example) and the temperature is raised above the upper critical solution temperature (UCST), which is about 48°C in this case, the two components will become fully miscible. However, in a pool fire, the composition will change because of the evaporation process. Therefore, the miscibility gap does not follow a straight vertical line in figure 1(a).

## 2.2. Vapor-liquid phase equilibrium

The second part of the temperature-composition phase diagram in figure 1 (a) is about the vapor-liquid phase equilibrium (VLE) determined by the liquid and vapor lines meeting at the boiling points of each of the pure liquids, that is 64.7°C for methanol and 80.7 °C for cyclohexane. The liquid and vapor lines meet at another specific point, i.e. the azeotropic point (as shown by point E in figure 1), which can be explained as follows. Suppose the composition of the cyclohexane-rich layer initially corresponds to point L in figure 1 (a). After ignition, if the increase in temperature (due to burning) follows the long vertical solid arrow in figure 1, the intersection with the liquid line indicates a point that corresponds to a more methanol-rich vapor (see the horizontal dashed line in figure 1). This latter vapor is consumed during the burning process, leading to a higher molar fraction of cyclohexane in the liquid phase (the upper layer). This is shown in figure 1 (a) by the transition from point L to point L₁. That is the reason why the surface temperature might increase to the boiling point of cyclohexane, as will be shown later in the results. This process, which we shall name ‘distillation burning’, can be repeated until the azeotropic point is reached. However, it is also important to note that when the liquid mixture is heated (by convection and conduction), the methanol dissolves more easily into cyclohexane. This process leads to a change in the composition from point L to point L₂, as shown by the curve arrow in figure 1 (a). It is called here ‘dissolution transfer’. After that, azeotropic burning occurs. It is noted that distillation burning and dissolution transfer do not start at the same time. In the top layer, the molar fraction of cyclohexane decreases due to dissolution transfer but increases due to the distillation burning.

## 3. Experimental tests

The same experimental set-up as in [4] was used in this study. The tests were carried out using stainless steel square burners with two different side lengths: 10.5 and 15.0 cm. As shown in figure 1 (b), nine type K thermocouples (Chromel/Alumel) of 0.2 mm diameter each and with 5 mm spacing were installed inside the burner. Both burners were 5.0 cm deep and nearly fully filled at the start of each test to ensure that all thermocouples were submerged. Methanol (the denser liquid) is poured first before cyclohexane. Then, the mixture is left at rest for 20 to 30 minutes, yielding a layered structure (as explained in the introduction) prior to ignition. A reference test with pure cyclohexane has been carried out in this study, in addition to the test results with pure methanol already published in [4]. Table 1 provides the list of tests considered in this study.

<table><caption>Table 1. List of test cases. Component A is cyclohexane and component B is methanol.</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Burner length (cm)</th><th colspan="2">Mass fraction (g/g)</th><th colspan="2">Molar fraction (mol/mol)</th><th colspan="2">Heights (cm)*</th><th rowspan="2">Reference</th></tr><tr><th>Y<sub>A</sub></th><th>Y<sub>B</sub></th><th>X<sub>A</sub></th><th>X<sub>B</sub></th><th>H<sub>A</sub></th><th>H<sub>B</sub></th></tr></thead><tbody><tr><td>Test 1</td><td>15.0</td><td>0.73</td><td>0.27</td><td>0.51</td><td>0.49</td><td>3.60</td><td>1.32</td><td>This work</td></tr><tr><td>Test 2</td><td>15.0</td><td>1.00</td><td>0.00</td><td>1.00</td><td>0.00</td><td>5.00</td><td>0</td><td>This work</td></tr><tr><td>Test 3</td><td>10.5</td><td>0.73</td><td>0.27</td><td>0.50</td><td>0.50</td><td>3.70</td><td>1.36</td><td>This work</td></tr><tr><td>Test 4</td><td>10.5</td><td>1.00</td><td>0.00</td><td>1.00</td><td>0.00</td><td>5.00</td><td>0</td><td>This work</td></tr><tr><td>Test 5</td><td>15.0</td><td>0.00</td><td>1.00</td><td>0.00</td><td>1.00</td><td>0</td><td>4.70</td><td>[4]</td></tr><tr><td>Test 6</td><td>10.5</td><td>0.00</td><td>1.00</td><td>0.00</td><td>1.00</td><td>0</td><td>4.70</td><td>[4]</td></tr></tbody></table>

## 4. Results and discussion

The main results are displayed in figure 2 for the transient profiles of the burning rate and liquid temperatures. The burning rate can be divided into five stages which are closely related to the liquid

<footnote>* Depths of, respectively, the top layer that is component A-rich and the bottom layer that is component B-rich.</footnote>
temperatures. The first and the second stages correspond, to the initial transient stage and the quasi-steady state burning of the cyclohexane-rich upper layer, respectively. This can be seen from the temperature recordings of the four top thermocouples (Tcp. 1 to Tcp. 4) which show values stabilizing around the boiling point of cyclohexane (BPC) before a sudden increase because they become immersed in the gas phase [4]. At the end of the second stage, as in [6], an abrupt increase in the burning rate is observed, followed by a decay (third stage) during which the recorded liquid temperatures are between the BPC and the azeotropic point (AP). The fourth stage corresponds to azeotropic burning, as shown by the saturated liquid temperatures around the AP. Finally, extinction occurs due to the completed consumption of the fuel.

<figure><img src="image_6.png" /><figcaption>Figure 2. Results for the burning rates and the liquid temperatures.</figcaption></figure>

A quantitative analysis of the data is proposed for (i) the initial transient and first quasi-steady state stages, (ii) the onset of the abrupt increase, and (iii) the azeotropic steady burning.

### 4.1. Initial transient and first quasi-steady state stages

The temperature profiles in the initial transient stage, i.e. burning of the cyclohexane-rich layer, are analyzed as explained in [4] to estimate the effective thermal diffusivity of cyclohexane and under the assumption of 1D in-depth heat transfer. The analysis is based on the analytical solution for the temperature within a semi-infinite slab, initially at a temperature $T_0$, whose surface is suddenly increased to $T_\infty$ [2]. The solution is as follows:

$$ \theta = \frac{T-T_0}{T_\infty-T_0} = 1 - \operatorname{erf}\left(\frac{z}{2\sqrt{\alpha t}}\right) \quad (1) $$

where $z$ is the depth below the surface, $\alpha$ is the thermal diffusivity of the material and $t$ is the time. The depth below the surface is taken as $z = L_{th}$ where $L_{th}$ is the depth of a thermocouple positioned inside the liquid and measuring the temperature $T$. As described in [4], with pure liquids, the thermocouple
considered in the analysis is the one positioned just above the bottom of the burner. The same procedure is applied by selecting the lowest thermocouple located within the top cyclohexane-rich fuel layer (Tcp.7). Assuming that the surface temperature, $T_∞$, rises quickly to the boiling point $T_b$ of cyclohexane and takes a critical threshold of $θ_{crit} = ε = 0.16$, a thermal penetration time, $t_p$, can be, based on equation (1), defined as:

$$α_{eff} = L_{th}^2/4t_p \qquad (2)$$

The thermal penetration time is estimated experimentally from the temperature measurements. Therefore, the thermal diffusivity of cyclohexane can be estimated from equation (2), given that $L_{th}$ is known. The obtained thermal diffusivity, called the effective thermal diffusivity, is typically higher than the actual thermal diffusivity of the liquid [4]. It is linked to the effective thermal conductivity of the liquid, $k_{eff}$, through $α_{eff} = k_{eff}/ρc$ where $ρ$ and $c$ are, respectively, the density and specific heat of the liquid, assumed to be constant. The liquid Nusselt number, $Nu = k_{eff}/k$, represents the enhanced heat transfer within the liquid due to convective motion. Based on the data displayed in figure 2 (b) and (d), the Nusselt number is estimated to be $Nu = 4.8$ for the 15.0 cm burner and $Nu = 5.7$ for the 10.5 cm burner. These measurements are in the same order of magnitude as the values for heptane ($Nu = 11.8$) and methanol ($Nu = 6.2$) [4].

In addition to the temperature analysis, it is interesting to note from figure 2 (a) and (c) that, in the initial stages, the burning rate of the cyclohexane-rich upper layer is lower than that of pure cyclohexane. This is partially attributed to the fact that the small fraction of methanol increases the overall gasification of the binary mixture.

## 4.2. Onset of ‘explosive vaporization’

The sudden increase in the burning rate is similar to the ‘boilover’, which occurs when the temperature of the fuel/water interface reaches some critical value [2, 9]. Although there is no water in our case, a similar phenomenon is observed in our experiments. The top layer is cyclohexane-rich with a boiling point of about 80.7°C. The denser bottom layer is methanol-rich with a lower boiling point of 64.7°C. Therefore, during the heating process in the initial burning stage, methanol can relatively quickly reach conditions close to boiling. As mentioned in [9], a sudden expansion of vapor at the interface of the two layers may cause a substantial pressure increase, leading to an abrupt increase in mass loss rate. Based on the above, an attempt is made to predict the time for onset of (what we will call hereafter) explosive vaporization, $t_{ev}$, for the cases at hand.

Thermal analysis is carried out using equation (1) to find the time at which the temperature of the top layer/bottom layer interface reaches a critical value, as explained above for a fuel/water system. In the case of a binary fuel mixture, the obvious choice for such a critical value is the azeotropic point. In our case, $T_{AZ} = 55°C$. Thus, in equation (1), we take $T = T_{AZ}$, $T_∞ = T_b$ (boiling point of cyclohexane, i.e. 80.7°C) and $T_0 = 10°C$ (initial condition). On the other hand, $α$ can be taken as the effective thermal diffusivity (previously calculated according to the procedure explained above). The one unknown remaining, besides $t_{ev}$, is the depth $z$. In fact, the initial interface depth is known. However, during the burning process, the liquid surface continuously regresses, making the interface get closer to the surface. It is proposed here to consider this aspect in equation (3), by taking:

$$z = L_0 - (\dot{m}''/ρ)t_{ev} \qquad (3)$$

where $L_0$ is the initial interface height (taken here as $L_0 = 0.03$ m), $\dot{m}''$ is the quasi-steady state fuel mass loss rate per unit area before the onset of explosive vaporization (the values are 0.022 kg/m²/s and 0.018 kg/m²/s, for the 0.15 m and 0.10 m burners, respectively), and $ρ$ is the density of cyclohexane. Equation (1) becomes:

$$\frac{T_{AZ}-T_0}{T_{b,A}-T_0} = 1 - \operatorname{erf}\left[\frac{L_0-\left(\frac{\dot{m}''}{\rho}\right)t_{ev}}{2\sqrt{\alpha_{eff,A}\times t_{ev}}}\right] \qquad (4)$$

with only $t_{ev}$ as unknown. Equation (4) is solved numerically and gives $t_{ev} = 670$ s for the 15.0 cm burner and $t_{bo} = 747$ s for the 10.5 cm burner, which is in good agreement with the experimental data of 600 s and 800 s respectively, as shown in figure 2 (a) and (c).
### 4.3. Azeotropic steady burning

The azeotropic burning, as shown in figure 2 (a), occurs for the 15.0 cm burner at a rate of 16.89 g/m²/s. This is an intermediate value between the burning rate of pure cyclohexane (28.9 g/m²/s) and that of pure methanol (14.2 g/m²/s) [4]. Azeotropic burning is 0.58 times that of pure cyclohexane. For azeotropic burning, the composition is well known, that is 40% cyclohexane – 60% methanol as shown in figure 1, which corresponds to 64% – 36% in mass proportions. It is (highly) unlikely that a simple mixing rule can be applied to make the link between azeotropic burning and pure liquid burning. Instead, the reasoning should be carried out in terms of heat balance; the burning rate is equal to the net heat flux at the liquid surface divided by the heat of gasification (i.e. the sum of the latent heat of vaporization and the sensible enthalpy). The mixing rule (based on mass fractions) gives a latent heat of vaporization, $L_v$, of the azeotropic mixture that is 1.74 times the $L_v$ of pure cyclohexane. If the sensible enthalpy is neglected (because the liquid is preheated at this stage IV as shown in figure 2), which can be translated into an azeotropic burning that is 0.57 times the burning of pure cyclohexane. The change in $L_v$ appears thus to be sufficient to find the azeotropic burning rate based on the burning rate of pure cyclohexane. However, other aspects are likely to be involved, such as the change in the heat of combustion, the change in the flame luminosity, and the subsequent radiative heat fluxes at the liquid surface.

### 5. Conclusion

This paper investigates the burning rates and liquid temperatures of pool fires with binary liquid mixtures. Methanol and cyclohexane are poured into square burners of 15.0 cm and 10.5 cm side lengths with mass fractions of, respectively, 0.27 and 0.73. Prior to burning, there is a methanol-rich layer at the bottom and a cyclohexane-rich layer at the top. Based on mass loss rate measurements (which are consistent with liquid temperature measurements), the whole burning process could be divided into five stages. Most importantly, there is a stage of (almost pure) cyclohexane burning followed by azeotropic burning. The transition is initiated after the occurrence of ‘explosive vaporization’ of methanol (analogous to boilover), which is translated into a sharp peak in the MLR measurements. A model has been developed to predict the onset of this event. The model is based on heat transfer in a semi-infinite slab. In the steady azeotropic burning stage, due to a higher latent heat of vaporization and a reduced flame luminosity, the burning rate of the mixture is only 0.57 times that of pure cyclohexane, which is equal to the ratio of the latent heat of vaporization between methanol and cyclohexane. The main objective of this work was to highlight the difference in burning behavior between pure liquids and binary mixtures. Different fuel types, fuel compositions and larger pan sizes will be studied in the future.

### 6. Reference

[1] Ra Y and Reitz RD 2015 A combustion model for multi-component fuels using a physical surrogate group chemistry representation (PSGCR) *Combustion and Flame* **162** 3456-81.

[2] Drysdale D 2011 *An introduction to fire dynamics* (West Sussex: John wiley & sons).

[3] Beji T 2019 Analytical Modelling of the Effect of In-Depth Radiation Within a Liquid Layer in the Case of a Pool Fire *Proc. of the 9th Int. Seminar on Fire and Explosion Hazards* (Saint Petersburg)

[4] Beji T, Lafdal B and Mehaddi R 2024 Transient heating of liquids in pool fires *Fire Safety Journal* **142** 104044.

[5] Sikanen T and Hostikka S 2016 Modeling and simulation of liquid pool fires with in-depth radiation absorption and heat transfer *Fire Safety Journal* **80** 95-109.

[6] Gao Z, Wan H and Ji J 2021 The effect of blend ratio on the combustion process of mutually stratified blended fuels pool fire *Proc. of the Combustion Institute* **38** 4995-5003.

[7] Xuehui W, Qinpei C, Zhou T, Li H, Ding C and Wang J 2019 In-depth analysis of burning process of binary blended fuel pool fires based on liquid-vapor equilibria *Fuel* **256** 115918.

[8] Waldner P and Gamsjäger H Thermodynamic 2000 Analysis of Phase Equilibria in the System Cyclohexane—Methanol *Journal of solution chemistry* **29** 505-20.

[9] Garo J, Vantelon J and Fernandez-Pello A. 1994 Boilover burning of oil spilled on water *Symp. (Int.) on Combustion* **25** 1481-88.