Pool Boiling Heat Transfer in Dilute Water/Triethyleneglycol Solutions

S. A. Alavi Fazel, A. A. Safekordi and M. Jamialahmadi

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Pool Boiling Heat Transfer in Dilute Water/Triethyleneglycol Solutions

S. A. Alavi Fazel1,*, A. A. Safekordi2and M. Jamialahmadi3

1Islamic Azad University, Mahshahr, Khoozestan, Iran2Sharif University of Technology, Tehran, Iran3University of Petroleum Industry, Ahvaz, Iran

Boiling of water/triethyleneglycol (TEG) binary solution has a wide-ranging application in the gas processing engineering. Design, operation and optimization of the involved boilers require accurate prediction of boiling heat transfer coefficient between surface and solution. In this investigation, nucleate pool boiling heat transfer coefficient has been experimentally measured on a horizontal rod heater in water/TEG binary solutions in a wide range of concentrations and heat fluxes under ambient condition. The present experimental data are correlated using major existing correlations. In addition a correlation is presented for prediction of pool boiling heat transfer for the system in which the vapour pressure of one component is negligible. This model is based on the mass transfer rate equation for prediction of the concentration at the bubble vapor/liquid interface. Based on this prediction, the temperature of the interface and accordingly, the boiling heat transfer coefficient could be straightforwardly calculated from the known concentration at the interface. It is shown that this simple model has sufficient accuracy and is acceptable below the medium concentrations of TEG when the vapor equilibrium concentration of TEG is almost zero. The presented model excludes any tuning parameter and requires very few physical properties to apply.

pool boiling, heat transfer coefficient, water/triethyleneglycol

1 INTRODUCTION

The boiling of heat sensitive liquids is complicated by the high temperature decomposition or the dangerous situations of fire and explosion. In such case, it is conventional to heat the heat sensitive liquids indirectly, through a heating bath. A variable boiling point liquid solution such as water/TEG solution with different compositions is widely used as the intermediate heating medium. Indirect water/TEG boilers have a wide variety of successful applications in the oil and gas production, gas processing and gas distribution industry.

Indirect boilers are comprised of three basic components: (1) shell, (2) the boiling section and (3) the heating coil. The optimum design of the boiling section allows for a rapid transfer of heat from the fuel flame to the water/TEG solution. The heat is transferred from the water/TEG bath to the coil and then safely to the heating fluid. Fig. 1 presents a typical scheme of water/TEG bath unit. Because of high difference between boiling temperatures of water and triethyleneglycol (100oC. 288.39oC), water evaporates while triethyleneglycol remains non-vaporized on the boiling section. Design, operation and optimization of such boiler units require an accurate prediction of boiling heat transfer coefficient between surface and the boiling liquid. Clearly, the temperature of the heating surface is a strong function of heat transfer coefficient, bulk temperature and heat flux. Interestingly, mass transfer mechanism in boiling of the binary water/triethyleneglycol solution provides a more complicated condition, by elective evaporation of water which establishes a concentration gradient through bubble formation stage at the vapor/liquid interface. Accordingly, back diffusion of water from vapor inside the bubble to the bulk liquid establishes a mass transfer gradient and consequently a heat transfer resistance. This phenomenon directly affects the amount of heat transfer and also affects the bubble dynamics; consequently the boiling heat transfer coefficient is indirectly but significantly affected. Many experiments in the literature confirm that the heat transfer coefficients of mixtures were lower than the interpolated heat transfer coefficients between pure components [1, 2].

Figure1 Illustration of a typical process flow diagram of the water/TEG bath unit

There are many existing correlations for prediction of boiling heat transfer coefficient in liquid mixtures. Schlünder [3] has derived a semi-theoretical model including only one tuning parameter based on SF6-CF2Cl2mixtures. This correlation corresponds particularly well with the experimental observation that the heat transfer coefficient is less dependent on heat flux density and the pressure. Jungnickel. [4] measured the boiling heat transfer on a horizontal copper plate for refrigerant mixtures and proposed a new correlation with a unique definition for ideal boiling heat transfer coefficient. Stephan and K?rner [5] equation is the most popular empirical correlation which has an inclusive tuning parameter. For boiling liquid mixtures with high heat of solutions this correlation over-predicts the data over all ranges of fractions, which has the same characteristic as Schlünder [3] correlation. Inoue. [6] measured the pool boiling heat transfer coefficients of ammonia/water mixture and its pure components on a horizontal platinum wire (diameter of 0.3 mm, 37 mm length, heated using a direct electric current) at pressure of 0.4 and 0.7 MPa. Based on the boiling range, the temperature difference between dew and bubble points at a given concentration, as a parameter in reducing the available driving temperature, these authors developed a new model including a tuning parameter which is implicitly independent of mixture physical properties. Thome and Shakir [7] proposed another predicting correlation based on the assumption that the bubble point temperature near the heating surface is not constant. Fujita and Tsutsui [8, 9] used a vertical tube to measure the boiling heat transfer of binary mixtures of CF3CH2F/CHCl2CF3and proposed two different correlations based on a model that the drop of effective temperature difference is a main reason for heat transfer reduction in mixtures. Fujita and Tsutsui [9] also showed that the diminution is most considerable in mixtures with higher gliding temperature. The larger decrease occurs for the higher heat flux condition, higher mole fraction difference between liquid and vapor and consequently larger boiling range. Calus and Rice [10] reported data on boiling under free convection for isopropanol/water and acetone/water binary mixtures and for the three pure components and proposed a new correlation including mass and heat diffusivity coefficients. Unal [11] proposed a correlation based on an empirical procedure of dimensional analysis that allowed to him to obtain a new correlation. Vinayak and Balakrishnan [12] obtained heat transfer coefficient data in nucleate pool boiling of acetone/isopropanol/water and acetone/MEK/water systems and developed a correlation involving thermal and mass diffusivity coefficients. The development of the experimental researches of mixture nucleate boiling has also been reviewed by Fujita and Bai [1].

A summary of main existing correlations for pool boiling heat transfer coefficient for mixtures are given in Table 1.

In this investigation, the boiling heat transfer coefficient for water/triethyleneglycol solution at a wide range of heat flux and concentrations are experimentally measured. These data are correlated to the main existing models. It is shown that all existing correlations are subject to a significant extent of error. Moreover, calculating some of the involved parameters including the diffusivity coefficient, which appears in some of the above mentioned models, is not easy to accomplish. Also a correlation is proposed to predict the concentration at the bubble vapor/liquid interface. This derivation is an extension of the mass transfer rate equation for binary electrolyte solutions [13]. The temperature of the interface, accordingly the boiling heat transfer coefficient could be directly calculated from the concentration at the interface. It is shown that this simple model has a superior performance in comparison to main existing correlations at medium-low concentrations of triethyleneglycol, where the vapor pressure of triethyleneglycol is approximately zero. This model excludes any tuning parameter and is expected to be applicable to other binary systems in which two constituents have very different vapor pressures.

Table 1 Some existing correlations for prediction of pool boiling heat transfer coefficient in liquid mixtures

Note:cis the critical pressure of more volatile component.

2 EXPERIMENTAL

2.1 Experimental setup

Figure 2 presents schematically the experimental equipment used in the present study. This boiling vesselis a vertical hollow cylinder of stainless steel containing 38 L of test liquid connected to a vertical condenser to condense and recycle the evaporated liquid. The whole system is heavily isolated for better control and reduction of the heat loss. The temperature of the liquid inside the tank is constantly monitored and controlled to any set point by a thermal regulator which is involved with thermocouples and a band heater covering the outside of the tank. Before any experiment, the liquid inside the tank is preheated to the saturation temperature using the mentioned band heater. The pressure of the system is monitored and regulated continuously. A safety pressure relief valve is also installed. The test section is a horizontal rod heater with a diameter of 10.67 mm and a heating length of 99.1 mm which can be observed and photographed through observation glasses. This heater consists of an internally heated stainless steel sheathed rod and four stainless steel sheathed thermocouples with an exterior diameter of 0.25 mm are entrenched along the circumference of the heater close to the heating surface. Some details of the rod heater are given in Fig. 3. One thermocouple inside the rod heater was used as a protection trigger to cut off the electric power if the temperature exceeds the maximum limit. The test heater is manufactured by Drew Industrial Chemicals Co. according to specifications by Heat Transfer Research Incorporated (HTRI).

A PC-based data acquisition system was used to record all measuring parameters. The input power to the rod heater is precisely equal to the heat flux and could be calculated by the product of electrical voltage, current and cosine of the difference between electrical voltage and current. The average of five readings was used to determine the difference between heating surface and the bulk temperature of each thermocouple. To calculate the real surface temperature by correcting the minor temperature drop due to the small distance between surface and thermocouple location, the Fourier’s conduction equation is used as follows:

whereis the distance between the thermocouple location and heat transfer surface andis the thermal conductivity of the heater material. The value ofis determined for each thermocouple by calibration of the test heater. The average temperature difference was the arithmetic average of the four thermocouple locations. The boiling heat transfer coefficient,, is calculated by

For each experiment, picture of boiling phenomena was taken using a high speed camera. A high speed video recorder was also used to record the formation and growth of the bubbles at the heat transfer surface. These recordings are used to determine the bubble generation frequency, nucleation site density and also the bubble diameter as function of time.

Figure2 The schematic diagram of the experimental apparatus

Figure3 A schematic of rod heater

2.2 Experimental procedure

Initially, the entire system including the rod heater and the inside of the tank were cleaned and the test solution was introduced. The vacuum pump is then turned on and the pressure of the system is kept low approximately to 10 kPa for 5 h to allow all the dissolved gases especially the dissolved air be stripped from the test solution. Following this, the tank band heater was switch on and the temperature of the system allowed rising to the saturation temperature. This procedure presents a homogeneous medium for boiling heat transfer experiment. Then the electric power was slowly supplied to the rod heater and increased gradually to a predetermined value. Data acquisition system, video equipments including a digital camera were simultaneously switched on to record the required parameters including the rod heater temperature, bulk temperature, heat flux and also all visual information. All experimental runs were carried out with decreasing heat flux to eliminate the hysteresis effect. Some runs were repeated twice and even thrice to ensure the reproducibility of the measurements.

2.3 Physical properties of test solution

Triethyleneglycol is a transparent, moderately viscous, colorless, less volatile and water soluble liquid. Figs. 4 through 6 presents some physical properties including the density, viscosity, latent heat of vaporization and the specific heat of water/triethyleneglycol binary solution as a function of water mole fraction at bubble point condition. This information is predicted by the standard predictive correlations [14]. These physical properties directly affect the boiling heat transfer coefficient.

Figure 7 presents the equilibrium-diagram for water/TEG binary system. These relations are generated by various vapor-liquid-equilibrium (VLE) methods indicated in the figure, including an advanced equation of state method for specifically the modeling of triethyleneglycol/water system for glycol gas dehydration. The activity coefficients for water and triethyleneglycol are calculated using the following equations [15]:

Table 2 The coefficients of Eq. (8)

In addition, the vapor pressure is calculated through the generalized equation as the following mathematical relation:

In above equations, the unit of temperature is K.

The values for constants1to7are calculated by using curve fitting techniques on saturation pressure- temperature data which the results are given in Table 2 [16]. Fig. 7 indicates that for TEG mole fraction lower than about 0.4, the equilibrium water vapor mole fraction is predicted to be equal to 1.0 by any existing equation of states. This means that during the boiling of water/TEG at the mentioned range of concentration, the vaporized bubbles contains only water and the mass diffusion of TEG between interface and bulk liquid may be ignored.

3 RESULTS AND DISCUSSION

3.1 Boiling heat transfer coefficient

Figure 8 indicates higher heat transfer coefficient at higher concentrations of water in the range of TEG mole fraction from0.3 to 0.1. However, at intermediate concentrations, fluctuations make the trends indistinct.

Figure 8 also presents an approximately smooth enhancement of boiling heat transfer coefficient as concentration increases at any constant heat flux. However, major fluctuations are significant at high heat fluxes, which are also related to the chaos and the hysteresis effect in the boiling phenomenon. Interestingly, at low heat fluxes, the boiling heat transfer coefficient is a very weak function or even independent of concentration. This is due to weak role of bubbles dynamics in total amount of heat transfer; free convection is dominant.

Generally, it is well recognized that lower boiling heat transfer coefficient of mixtures in comparison to pure liquids is due to the diffusion resistance of the more volatile component (water in this case) at the vapor-liquid interface during bubble generation. Evaporation of water means increase of the concentration of the less volatile component (TEG in this case) at the vapor-liquid interface; as a result, the local bubble temperature increases at this location. Subsequently, the thermal driving force between surface and the exposed area will drop off.

Figure8 Measured pool boiling heat transfer in water/TEG binary solution as a function of heat flux:◆?0.7;■?0.77;▲?0.8; ×?0.9

3.2 Visual records and bubble dynamics

Figures 9 (a) through 9 (d) explicates typically the impact of TEG concentration on the bubble dynamics. The photos are taken using a Canon EOS 300D DIGITAL camera. The specifications of photos are F-stop: f8, exposure time: 1/200 s, ISO speed: ISO-400, focal length: 55 mm, max. aperture: 4.9708 and exposure bias: 0 step. For the boiling solution of around 95% (by mass) of triethyleneglycol [Fig. 9 (a)], the bubbles are uniform and spherical in shape and the diameters are relatively small. Note that at this concentration,as Fig. 5 serves, the viscosity of mixture is very highconcentration. At the mass concentration of 84% of triethyleneglycol [Fig. 9 (b)], the larger bubble size could be observed and the bubbles are still isolated from each other, however, the bubbles are not spherical. At the mass concentrations of 70% of triethyleneglycol [Fig. 9 (c)], interconnected bubbles with variable diameters, which are difficult to identify, appear at the boiling surface. In addition, for the mass concentration of 24% of triethyleneglycol [Fig. 9 (d)], the bubbles are observed at isolated forms with medium in diameters. Fig. 10 presents the measured bubble diameter as a function of heat flux and concentration and a non-uniform relationship between TEG concentration and bubble diameter at any given heat flux. Conversely, the bubble diameter roughly increases as the heat flux amplifies at any given concentration. Similar non-uniform variation of bubble departure frequencyheat flux and concentration could be observed in Fig. 11. The bubble departure frequencies are calculated by the Zuber correlation [17] using experimental bubble diameters:

Figure12 Temperature profile with and without considering mass transfer inside the diffusion shell

4 MODELING OF BOILING HEAT TRANSFER COEFFICIENT

Combination of Eqs. (2) and (10) yields:

4.1 Calculation of the interfacial temperature

During the bubble formation in boiling Water/ triethyleneglycol mixture, a concentration gradient will be established through the vapor/liquid interface causing water to diffuse towards the gas-liquid interface and evaporates there, while triethyleneglycol to diffuse in the reverse direction, as indicated by the concentration profile in Fig. 12. Accordingly, the total pressure gradient causes a bulk motion of water and triethyleneglycol towards the interface in addition to the transfer by diffusion [18]. Therefore, the total mass flux of water toward the interface relative to stationary coordinates is equal to

The mass average velocity,, could be expressed in terms of mass concentration and the velocity of the species to a flux coordinate as [19]:

Combining Eqs. (12) and (13) and using Fick’s first law in mass transfer yields:

For constancy ofwandTEGis valid under the steady state condition, the differential Eq. (14) could solved and the following equation is the results to calculate the interfacial concentration [13]:

with

The valve ofwis approximated by Schlünder [3]based on this assumption that all of the heat is transferred to the bubble interface. Eq. (15) could be noted in the form of latent heat of vaporization as the following:

In this investigation, a constant mass transfer coefficient of 0.0002 m·s－1is used as Schlünder [3] stated.0is the ratio of heat transfer interfacial area to those of mass transfer. This value is assumed to unity by all investigators [1, 18, 21]. In addition, no triethyleneglycol evaporation is assumed, which is valid in a specific wide range of concentration as indicated in Fig. 7.

Figure13 Equilibrium temperatures at bubble point

4.2 Calculation of ideal boiling heat transfer coefficient

The ideal boiling heat transfer coefficient is believed as the heat transfer coefficient of an imaginary fluid without any kinetic mixture effect. Two approaches are reported in the literature for calculating this ideal nucleate pool boiling coefficient [22]. The first one is derived from the characterization of an ideal heat transfer coefficient for the mixture on the basis of a mole fraction-weighted average of the wall superheat for the pure fluids [23, 24]:

This result in the mole average heat transfer coefficients of the pure components,1and2, at the same temperature or pressure as for the mixture as follows which could be extended to multicomponent systems:

The second approach consists of calculating the ideal heat transfer coefficient using a pure component correlation for nucleate pool boiling with mixture properties. This approach is little used in the literature due to the difficulty in determining the thermophysical properties of mixtures. In this investigation, it is found that the second approach has better results and is accordingly applied. The ideal heat transfer coefficient can be calculated using any valid correlation for heat transfer coefficient for pure boiling liquids. The Stephan-Abdelsalam correlation is applied [25]:

The bubble departure diameter,bcan be estimated by a standard correlation such as Fritz [26] if experimental data are not available.

5 MODEL VALIDATIONS

Figures 14 (a)-14 (d) typically compares the experimental data with the pool boiling heat transfer coefficient predicted by the main existing correlations at different heat fluxes.

There is acceptable agreement between all existing correlations at very high concentrations of water as indicated in Fig. 14 (a). However, at higher concentrations of triethyleneglycol, there is no conformity between the predictions of various correlations at all; any existing correlations under-predicts the actual boiling heat transfer coefficient as pointed out in Figs. 14 (b)-14 (d).

Significant errors are anticipated for the presented model [Eqs. (2) and (10)-(17)] when both constituents evaporate during boiling, which turns out at high heat fluxes or high concentrations of triethyleneglycol. Fig. 14 (d) reflects an over-prediction of the presented model at heat fluxes above 100 kW·m－2where the concentration of triethyleneglycol is high to ignore the evaporation of both constituents.

An overall good agreement between predicted and measured boiling heat transfer coefficient is observed through these equations, not including high heat fluxes and also high concentrations of triethyleneglycol. The average absolute errors of the presented model is about 10% in all range of concentration and heat flux.

6 CONCLUSIONS

Pool boiling heat transfer coefficient for water/ triethyleneglycol binary mixture has been experimentally measured at atmospheric pressure. Measured data are correlated to main existing correlations. A model has been presented for such systems which the vapor pressure of one component in negligible in compare to other constituent. This derivation is based on the mass transfer rate equation. This model has been previously derived for boiling of electrolyte solution where the vapor pressure of one component is negligible in compare to other component. It has been shown that this correlation has superior performance in compare to main existing correlations at medium-low concentrations of triethyleneglycol and also medium-low heat fluxes. Moreover, this correlation needs the minority information to perform. This model is expected to be applicable to many other binary systems, which the vapor pressure of one component is significantly lower than the other component.

NOMENCLATURE

area, m2

0ratio of heat transfer interfacial area to that of mass transfer

diffusivity coefficient, m2·s－1

bbubble diameter, m

bubble frequency, Hz

gravity acceleration, m·s－1

Δvheat of vaporization, J.kg-1

molar flux by diffusion, mol·m－2·s－1

thermal conductivity, W·m－1·oC－1

total molar flux, mol·m－2·s－1

satsaturation pressure, Pa

heat transfer rate, W

distance between surface and thermocouple location, m

bbulk temperature, K

iinterfacial temperature, K

ssurface temperature, K

thmeasured temperature by thermocouples, K

Δiinterfacial thermal supersaturation, K

Δ1,2thermal supersaturation for pure components 1 and 2, K

mass average velocity, m·s－1

liquid mole fraction of water

vapor mole fraction of water

boiling heat transfer coefficient, W·m－2·oC－1

idideal boiling heat transfer coefficient, W·m－2·oC－1

1,2boiling heat transfer coefficient for pure components 1 and 2, W·m－2·oC－1

mass transfer coefficient, m-2·s－1

1,2activity coefficients for pure components 1 and 2

surface tension, N·m－1

density, kg·m－3

Superscripts

b bulk

i interface

Subscripts

liquid

TEG triethyleneglycol

vvapor

w water

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2008-12-28,

2009-06-14.

* To whom correspondence should be addressed. E-mail: seyedali.alavifazel@gmail.com