See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/321276679 The energy balance within a bubble column evaporator Article in Heat and Mass Transfer · May 2018 DOI: 10.1007/s00231-017-2234-x CITATIONS READS 4 729 3 authors, including: Chao Fan Muhammad Shahid UNSW Sydney Australian Defence Force Academy 10 PUBLICATIONS 112 CITATIONS 13 PUBLICATIONS 134 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Australian Research Council View project insight of bubble column evaporator and its applications View project All content following this page was uploaded by Muhammad Shahid on 01 March 2018. The user has requested enhancement of the downloaded file. SEE PROFILE The energy balance within a bubble column evaporator Chao Fan, Muhammad Shahid & Richard M. Pashley Heat and Mass Transfer Wärme- und Stoffübertragung ISSN 0947-7411 Heat Mass Transfer DOI 10.1007/s00231-017-2234-x 1 23 Your article is protected by copyright and all rights are held exclusively by SpringerVerlag GmbH Germany, part of Springer Nature. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com”. 1 23 Author's personal copy Heat and Mass Transfer https://doi.org/10.1007/s00231-017-2234-x ORIGINAL The energy balance within a bubble column evaporator Chao Fan 1,2 & Muhammad Shahid 1 & Richard M. Pashley 1 Received: 26 January 2017 / Accepted: 14 November 2017 # Springer-Verlag GmbH Germany, part of Springer Nature 2017 Abstract Bubble column evaporator (BCE) systems have been studied and developed for many applications, such as thermal desalination, sterilization, evaporative cooling and controlled precipitation. The heat supplied from warm/hot dry bubbles is to vaporize the water in various salt solutions until the solution temperature reaches steady state, which was derived into the energy balance of the BCE. The energy balance and utilization involved in each BCE process form the fundamental theory of these applications. More importantly, it opened a new field for the thermodynamics study in the form of heat and vapor transfer in the bubbles. In this paper, the originally derived energy balance was reviewed on the basis of its physics in the BCE process and compared with new proposed energy balance equations in terms of obtained the enthalpy of vaporization (ΔHvap) values of salt solutions from BCE experiments. Based on the analysis of derivation and ΔHvap values comparison, it is demonstrated that the original balance equation has high accuracy and precision, within 2% over 19–55 °C using improved systems. Also, the experimental and theoretical techniques used for determining ΔHvap values of salt solutions were reviewed for the operation conditions and their accuracies compared to the literature data. The BCE method, as one of the most simple and accurate techniques, offers a novel way to determine ΔHvap values of salt solutions based on its energy balance equation, which had error less than 3%. The thermal energy required to heat the inlet gas, the energy used for water evaporation in the BCE and the energy conserved from water vapor condensation were estimated in an overall energy balance analysis. The good agreement observed between input and potential vapor condensation energy illustrates the efficiency of the BCE system. Typical energy consumption levels for thermal desalination for producing pure water using the BCE process was also analyzed for different inlet air temperatures, and indicated the better energy efficiency, of 7.55 kW·h per m3 of pure water, compared to traditional thermal desalination techniques. Nomenclature ΔHvap Cp Te ρv ΔT ΔP C gp Qwater W Taire Vi Enthalpy of vaporization Specific heat capacity of air in units of J·m−3 K−1 under constant pressure Steady state temperature near the top of the column in the units of K water vapor density Temperature difference between the gas entering and leaving the column in the units of K Differential pressure, between the gas inlet into the sinter and atmospheric pressure at the top of the column Specific heat capacity of air in units of J·g−1 K−1 under constant pressure Energy used for the evaporation of the water in the solution Vb Hab ρ nair nw nwater R T Patm Pv Volume of the bubble at temperature T Energy supplied by the bubble from Tin to Te Mass of air (or gas) in gram per cubic meter Moles of air in the bubble Moles of water vapor in the bubble Moles of water vaporized into the bubble Universal gas constant Absolute temperature Atmospheric pressure Water vapor pressure of the solution Abbreviations BCE RO Bubble column evaporator Reverse osmosis Work done the air pump through the colum Initial (dry) bubble volume, Vf Final (wet) bubble volume 1 Introduction * Chao Fan chao.fan1986@hotmail.com 1 School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Canberra 2600, Australia 2 School of Environmental Science and Engineering, Sun Yat-sen University, Guangzhou 510275, People’s Republic of China The bubble column evaporator (BCE) system is a simple and novel process in which warm/hot gas is pumped through a multi-porous sinter into a solution-filled column. A high density of uniform bubbles can be produced throughout the column. This BCE system, due to highly efficient heat and rapid vapor transfer through bubbles contacting the column Author's personal copy Heat Mass Transfer solution, has been studied and developed for a wide range of useful applications [1], such as, evaporative cooling [2], thermal desalination [3–5], thermal sterilization [6–8], solutes thermolysis in aqueous solution [9] and precise determination of thermophysical properties of concentrated salt solutions [2, 3, 10]. Although the potential mechanism of each application has been introduced and studied, the energy balance involved in the BCE process, as a fundamental aspect for the BCE application, is important for analysis. Also, the mass and heat transfer of bubbles are studied in the typical areas of nucleate boiling [11, 12] and flow dynamics [13, 14], and sub-boiling system regarding the use of warm/hot bubbles, say the BCE, also has significant potentials for developing new applications based on the fundamental theory study. Some types of concentrated salt solutions have unexpected effects on the coalescence inhibition of bubbles [15, 16], which has facilitated the BCE process with the controlled production of a high density of fine bubbles produced by pumping warm or hot dry gases through the sinter into a column containing a solute which inhibits bubble coalescence. These 1–3 mm diameter bubbles, due to coalescence inhibition behavior, become rapidly saturated by water vapor within a few tenths of a second [17], which cannot be estimated by the Fick’s law [2]. At the same time, the heat from the bubbles is also transferred for water evaporation, rather than heating of the column solution after reaching the steady state condition. The efficient heat and vapor transfer have been used for the basis of each BCE application, and they encompass the basic physics of bubble rise rates [17–19], vapor collection rate [4] and interactions within the aqueous solution [20, 21]. In this paper, the methodology regarding the BCE experiment procedure and the derived equations was illustrated. The procedure and derived balances were used to determine ΔHvap values of various salt solutions, which were analyzed for the accuracy of the ΔHvap determination and compared with that from different techniques. Based on the physics analysis and ΔHvap determination of balances in the BCE, it is established that originally proposed balance has a wide temperature range for determining ΔHvap values of salt solutions with high accuracy and precision. In addition, the energy consumption using the BCE for desalination was estimated. 2 Methodology The BCE used in the experiment was supplied with dry air following passage through a large amount of fresh silica gel to dehumidify the normal inlet air and an electrical gas heater was then used to obtain the desired inlet temperature. As warm or hot dry air was pumped by a HIBLOW air pump into the column, fine bubbles (around 1–3 mm in diameter) were produced through a glass sinter disc (porosity No.2) and a steady state column temperature (near the column top) can be reached when the heat supplied from the temperature change of the inlet bubbles was balanced by the thermal energy required for evaporation of water vapor from the salt solutions, assuming no heat transfer with the environment and no heat loss. The BCE system is shown schematically in Fig. 1 (left side). The details of the column and a photograph of bubble column are also given in Fig. 1. In the BCE experiment, the inlet gas, steady-state column top temperature and the differential pressure between the inlet and outlet gas were measured to determine ΔHvap values. Earlier works [2, 3, 10] described how the bubble column can be maintained at a steady state condition, where the stable column top temperature is obtained when the heat supplied from bubbles (per unit volume of dry gas) exactly equals the enthalpy of vaporization required to reach the equilibrium water vapor pressure within the bubbles. This method is based on the steady state volumetric balance in the bubble column, which has been used for the determination of ΔHvap values of concentrated salt solutions [3, 10], and is described by the following Eq. (1): ΔT C p ðT e Þ þ ΔP ¼ ρv ðT e Þ ΔH vap ðT e Þ ð1Þ (in units of J·m−3) where Cp(Te) is the specific heat of the gas flowing into the bubble column at constant pressure, in units of J· m−3 K−1; Te is the steady state temperature near the top of the column in the units of K; ρv is the water vapor density at Te, in units of mol·m−3, can be calculated from the water vapor pressure of salt solutions at the steady state temperature, using the ideal gas equation; ΔT is the temperature difference between the gas entering and leaving the column, in units of K; ΔP is the differential pressure between the air enters and leaves column, in units of J·m−3, which represents the work done by the gas flowing into the base of the column until it is released from the solution. This equation was first time reported by Francis and Pashley [2] for low vapor pressures, e.g. low column top temperatures of about 283 K. The equation’s accuracy and precision was further tested in later studies [3, 10], summarized in a review of BCE applications [1] and used for undergraduate teaching of ΔHvap [22]. However, apart from the use of this equation, it is still worth, in details, analyzing the physics behind this thermodynamic process between the bubble and solution and comparing alternatively proposed balances. 3 Analysis and discussion 3.1 Analysis of original balance in the BCE The original equation Eq. (1) was found to be accurate for determination of ΔHvap values of salt solutions over a wide range of temperature. Although Eq. (1) is on the basis of per Author's personal copy Heat Mass Transfer Fig. 1 Schematic diagram of the BCE system (left side), details of the bubble column (right side, upper) and a photograph of a bubble column for 0.5 mol·kg−1 NaCl (right side, lower) volume of gas in the bubble column, the temperature change from the cooling of bubbles does not have effects on the balance. Any given bubble released into the column at high temperature (Tin) will contract until it reaches the column solution steady state temperature Te. The heat supplied by the bubble (of volume Vb at temperature T) to the column, as it contracts, in a very rapid way, is given by the sum of Cp(T) × Vb(T) over the temperature range from Tin to Te, i.e. over temperature range of ΔT. As Cp(T) and Vb(T) are both functions of temperature T, the heat Hb, supplied by the bubble to the column, is given by: Te H b ¼ ∫T in C p ðT Þ V b ðT ÞdT ð2Þ Importantly, Cp(T) is linearly proportional to 1/T (see Fig. 2) and Vb(T), volume of the bubble, is linearly proportional to T, according to the ideal gas equation; so the product of Cp(T) × Vb(T) is constant, and therefore at steady state: H b ¼ C p ðT Þ V b ðT Þ ΔT ð3Þ Throughout the column, there is pressure decrement from the air enters and leaves the column, which corresponds to the mechanical work done on the column by the pump. It is assumed that this work is converted completely into heat, which is absorbed by the column. This component can be directly related to the original work-heat conversion in Joule’s original paddle wheel experiments in 1843. The bubbles mixed well with the solution and there is no hot or cool region in the column. The dry bubbles are saturated rapidly [17] and it is assumed that bubble in the column is always Vb(Te) when it reaches the steady state. So the work is: W Taire ¼ ΔPV b ðT e Þ ð4Þ It is easy and direct to obtain the energy used for the vaporization of nwater mole water in the solution (Qwater). This is: Qwater ¼ nwater ΔH vap Fig. 2 The linear relationship between specific heat capacity values Cp of air and 1/T. Cp values are from CRC Handbook [23] ð5Þ This analysis regarding the supply and consumption of energy in the bubble column presented the basic physics process between the bubble and solution. Volumetric basis, in the form of per volume of the bubble gas, makes the BCE experiment applicable for the ΔHvap determination through the measurements of inlet air temperature, column top temperature and the differential pressure. Author's personal copy Heat Mass Transfer 3.2 Bubble volume expansion during water vapor capture The physical conditions of a bubble in a solution before and after being saturated by water vapor, at the same temperature and under atmospheric pressure, are described in Fig. 3. Based on Fig. 3, dry and wet bubble volume Vi and Vf can be easily obtained using the ideal gas equation and Dalton’s law: Vi ¼ nair RT Patm ð6Þ Vf ¼ ðnair þ nw ÞRT Patm ð7Þ where Vi, Vf are the initial (dry) and final (wet) bubble volumes; nair and nw are the moles of air and water vapor in the bubble; R is the universal gas constant; T is absolute temperature and Patm is atmospheric pressure. Then the mole of gases in saturated bubble is given by: nair þ nw ¼ nair þ ρv V f ¼ nair Vf Vi ð8Þ where ρv is the water vapor density, which is equal to nw/Vf. Then the final bubble volume is given below after rearranging Eq. (8) and using the ideal gas equation: nair RT Vf ¼ Patm −Pv ð9Þ where Pv is the water vapor pressure of the solution. Then the bubble expansion percent before and after being saturated is given by: V f −V i Patm Percentexpansion ¼ 100 ¼ −1 100 ð10Þ Vi Patm −Pv expansion over a range of temperatures is shown in Fig. 4 (vapor pressure data of pure water, NaCl and CaCl2 are from CRC book [23], Clarke et al. [24] and Patil et al. [25]). This expansion may affect the proposed balance Eq. (1), as the water vapor is included in the original balance for bubble heat supply calculation. Hence, a factor θ can be introduced into the Eq. (1) to reduce the contribution from the gas specific heat Cp, in order to account for the presence of saturated water vapor in the bubble: ΔT C p ðT e Þ θ þ ΔP ¼ ρv ðT e Þ ΔH vap ðT e Þ ρ ðT e Þ RT e θ ¼ 1− v P ð11Þ ð12Þ The factor θ is actually the percent that dry air occupied in the bubbles, excluding the component of water vapor, which indicates the heat contribution is all from the dry gas in the BCE. In the same principle of Eq. (11), instead of using the heat capacity per unit volume, Cp, the weight-based unit, i.e. heat capacity per unit weight of gas C gp , is used. This gives another version [1] of the balance equation which produces same results as Eq. (11): h i ΔT C gp ðT e Þ ρa þ ΔP ¼ ρv ðT e Þ ΔH vap ðT e Þ ð13Þ where ρa is the density of air (or gas) in a bubble. This was obtained from the ideal gas equation using the molar mass of air (28.96 g·mol−1) and by subtracting the number of moles of the absorbed water vapor from the total number of moles of gas in the bubble per unit volume at Te and 1 atm pressure. It should be noted that the mass of air or gas in a bubble remains constant as the bubble passes through the column. This new balance equation removes the water vapor in the bubbles from the heat-supply calculation; compared with Eq. (1). This percent can easily be found using above relation if the vapor pressure data are available. For example, in pure water, 0.5 mol·kg−1 NaCl and 5 mol·kg−1 CaCl2, the % Fig. 3 Two situations of the bubble before and after being saturated by water vapor Fig. 4 Individual bubble expansion percent by capturing water vapor in pure water, 0.5 mol·kg−1 NaCl and 5 mol·kg−1 CaCl2 with temperature Author's personal copy Heat Mass Transfer Table 1 Different error percent of ΔHvap measurements using BCE process for various common salt solutions based on different developed energy balances Temperature (°C) 19–26 44–55 Salt solutions Difference percent from different energy balance (%) Eq.(1) Eq.(11) Eq.(13) Eq.(14) NaCl (1.0 m) 1.0 1.2 1.2 1.5 CaCl2 (1.0 m) 1.1 0.8 0.8 0.5 0.8 0.5 1.4 1.9 2.1 1.9 0.8 9.6 0.8 9.6 2.5 3.4 CaCl2 (5.0 m) KCl (4.0 m) NaCl (0.5 m) All literature values were calculated from published vapor pressure values using the Clausius-Clapeyron equation, which was demonstrated [3] to give authentic literature ΔHvap values. NaCl vapor pressure values from [24]; CaCl2 and KCl vapor pressure values from [25] However, ΔHvap term in Eq. (11) and Eq. (13) includes the work done by bubble-vapor expansion in the solution due to water vapor absorption, although the left side of both equations consider removing the effect of the vapor expansion in the bubble. Hence, the balance becomes: ΔT C gp ðT e Þ ρa þ ΔP ¼ ρv ðT e Þ ΔH vap ðT e Þ−PΔV ðT e Þ ð14Þ cases, the bubble expansion had a significant effect on the results and the original equation gives more accurate ΔHvap values. It is established that the original equation Eq. (1) has high accuracy and precision based the above analysis and previous works [3, 4, 10]. 3.3 The accuracy of the original balance of the BCE where PΔV term is the work done by the bubble-vapor expansion. Based on the energy balance summary [1] and previous works data [3, 4, 10], the difference percent of ΔHvap results from Eq. (1), Eq. (11), Eq. (13) and Eq. (14) with the literature ΔHvap values was calculated on average, as given in the Table 1. As can be seen from Table 1, all balance equations give the similar difference percent in the relatively low temperature cases, i.e. 19–26 °C, due to the low percent of vapor expansion in the bubbles (see Fig. 3); while in the high temperature When the BCE reaches steady state, the column top solution temperature can be accurately predicted based on the original equation Eq. (1) through a fixed inlet gas temperature. The experiment BCE temperature data in previous works were found to well fit with this prediction, as shown in Fig. 5. The potential application in terms of the evaporative cooling effect is also presented in this figure. Figure 5 also indicated that a different ΔP value would be revealed as a slight change in the steady-state column Fig. 5 The relationship between inlet gas temperature and column solution temperature at steady state based on Eq. (1) for 0.5 m NaCl in BCE of different ΔP. Experimental temperature data based on BCE from Francis and Pashley [2], Fan et al. [3, 10] and Shahid et al. [1, 4] are on the predicted curve over the wide range of inlet gas temperature. Arrows show the slightly different column top-solution temperatures at a constant inlet-gas temperature, due to the work done by pumped inlet gas to the column Fig. 6 The linear trend of literature ΔHvap of NaCl over 0.5–1.2 m with temperature. Literature ΔHvap values are from Clarke and Glew [24], Hubert [26] based on the calculation using Clausius-Clapeyron equation and Chou [27] calculated from osmotic coefficient, specific heats and solubilities. Experimental data based on BCE are from Francis and Pashley [2] with accuracy of 3% for 0.5 M NaCl at around 10 °C, Fan et al. [3, 10] with accuracy of within 1% for 1 m NaCl over around 20– 25 °C and Shahid et al. [4] with accuracy of 2% for 0.5 m NaCl over around 40–55 °C 1.0–3.8 m, 30 °C b 0–14.2 m, boiling point c 0–1.6 m, boiling point c 0–1.6 m, boiling point c 0–2.7 m, boiling point c 7.9 m (saturated), 109 °C CaCl2 Ca(NO3)2 NiSO4 FeSO4 ZnSO4 KCl Li2SO4 K2CrO4 K2Cr2O8 KNO3 0–25.7 m, 100–115 °C a Boiling point a Chou [27] Shahid et al. [1, 4] Fan et al. [3, 10] Francis and Pashley [2] Topor et al. [31] Gurovich et al. [30] Hunter and Bliss [29] Lunnon [28] Wagner and Pruss [32] Patil et al. [25] Clarke and Glew [24] k j i h g f e d c b a Accuracy on average Less than 10% NaNO3 H2O 4.2 m (saturated), 106.8 °C a 3.3 m (saturated), 104.8 °C a 1.1–2.6 m, 30 °C b 0–33.5 m, 100–116 °C a 2.6–15.4 m, 30 °C b a 6.8 m (saturated), 110 °C a NaCl KSCN NH4NO3 Theoretical technique Less than 5% 1.4–23.2 m, room temperature-boiling point d Less than 3% 11–12 °C e 4.0 m, 20 °C f 1.0–3.0 m, 25 °C f 3.0 and 3.5 m, 25 °C f 0.5 and 5 M, 10 °C e 1.0 m, 20–25 °C f 0.5 m, 40–55 °C g 1.0 and 5.0 m, 20–25 °C f 1.0–4.0 m, less than 70 °C j 1.0–6.0 m, less than 70 °C j 0.5–6.0 m, 0–110 °C i Reasonable agreement with each other f 0.01–373.95 °C k. calculated from the equation of state. 0.9–5.7 m, 0–176 °C h Calorimetric measurement (CM) thermogravimetric analysis (TGA) Bubble column evaporator (BCE) Calculated from specific Calculated from vapor pressures at different heats and solubilities temperatures (Clausius-Clapeyron equation) Experimental technique Comparison of operation temperature and concentration of salt solutions using different experimental and theoretical technique Salt Solutions Table 2 Author's personal copy Heat Mass Transfer Author's personal copy Heat Mass Transfer temperature in the BCE if the inlet-gas temperature was kept constant. That is, as a necessary term (work to the column) for the energy balance in the BCE (Eq. (1)), the increase of this work leads to a slight increase of the solution temperature, as indicated from arrows for the same inlet gas temperature. Also, a summary of determined ΔHvap values using the BCE supported the high accuracy of the original equation with a wide range of temperature, as shown in Fig. 6. It should be noted that literature ΔHvap of 0.5 m and 1.0 m NaCl at same temperature (5–55 °C) has similar values, with less than 0.04%. There are also other techniques to determine ΔHvap of salt solutions, but the BCE method offers a novel and relatively more accurate way for the determination over a wide range of temperature. As can be seen in a summary of different techniques of Table 2, BCE approach opened a new technique for ΔHvap determination with high accuracy compared to the conventional ways. 3.4 Energy utilization analysis of the BCE process In all of the experiments with high inlet-air temperatures, the solution-top temperatures always reached steady state after about 5 mins, as shown in Fig. 7 [4]. It is also worth noting that the observed column-top temperature was unaffected by the presence or absence of C12EO8 surfactant, added to capture more water vapor when using the BCE for desalination [4], and that these steady-state temperatures were very close to those estimated in Fig. 7, based on Eq. (1). Based on this desalination work using the BCE process, as shown in Fig. 8, three types of energy involved in the operation were estimated with different inlet air temperature: & & & the dry air was heated by the heater from room temperature to different inlet-gas temperatures; the hot air supplied heat to the solution in the BCE to evaporate the water; the energy produced from water-vapor condensation over a 25-min period at steady state (see Fig. 7). Fig. 7 Measured 0.5 mol·kg−1 NaCl solution top temperature within a bubble column using different inlet gas temperature (data reproduced from [4]) supply for the inlet air and there would be more energy lost and consumed for providing hot gas at designed inlet gas temperature. (2) The energy supplied by the hot air to the solution for water vaporization was calculated from the weight of water lost during the 25-min period at steady state and the literature ΔH vap value at the steady-state temperature. As in [4], the water weight loss was measured directly from the difference in the weight of the column at the beginning and at the end of the experiment. In the first five minutes of each experimental run (Fig. 7), before steady state was reached, the weight loss was estimated from the water-vapor density at the column temperature and the air flow. The total weight loss during the 25 mins at steady state was then obtained by subtracting the estimated weight loss in the first 5 mins from the weight loss over 30 mins (data from [4]). These three types are explained and analysed as follows: (1) The heat supplied in heating the inlet air from room temperature to the inlet temperature was calculated using the heat capacity of air (J·g−1·K−1), the weight of the air flowing through the flow meter over the 25-min period and the temperature change. In practice, the temperature of inlet air before entering the column normally has to be heated higher than desired value because of the energy loss with room environment. Hence this is the lowest estimation of energy Fig. 8 Comparison of the energy supplied to heat the dry air, the energy used to vaporize water in 0.5 m NaCl and the energy from water-vapor condensation in producing 1 mol of pure water Author's personal copy Heat Mass Transfer (3) Energy recovery rates in industrial reverse-osmosis desalination and thermal desalination can be up to 99% under optimum conditions [33]. Assuming 99% energy recovery here, the energy produced from condensation was estimated using values for the enthalpy of condensation of the salt solution at the steady-state temperature from the literature [23] and the water weight loss during the 25-min period. Acknowledgments We would like to thank the Australian Research Council for funding this project (Grant Number: DP120102385). Compliance with ethical standards Competing interest interest. The authors declare no competing financial References At higher inlet-air temperatures, more pure water can be produced from the BCE system than at lower temperatures using the same amount of electricity, due to the increased water-vapor density and higher vapor supersaturation in the bubbles [4], as shown in Fig. 8. Industrially, even higher inlet-air temperatures from, for example, industrial-waste flue gases could be used, which would save energy for pumping and heating the inlet air. Commercial reverse-osmosis systems typically have an energy usage in the range of 4–6 kW·h·m−3, conventional thermal/evaporative units 14–27 kW·h·m−3 [34, 35] and BCE systems used for thermal desalination 7.55 kW·h· m−3 [1] at an inlet-gas temperature of 550 K. The comparison of energy consumption by different methods was discussed in details in [1]. Higher inlet-gas temperatures could reduce this estimate still further based on the Fig. 8, but the solution temperature must be less than its boiling point. The BCE system uses a non-boiling process which is fairly independent of the concentration of the salt solution and can work effectively at salt concentrations as high as 5 m NaCl or more. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 4 Conclusions The original balance of the BCE gives the high accurate and precise ΔHvap values of salt solutions either in low temperature or high temperature, even it includes the the water-vapor expansion in the bubbles, as ΔHvap term includes the work done by bubble-vapor expansion in the solution due to water vapor absorption. The consideration of the water-vapor expansion in the bubble leads to different BCE balances, which affected much for the accuracy of the high temperature experiments. Based on the original balance equation, the good prediction of the column temperature and relatively higher accuracy of ΔHvap compared to other techniques further supported the validity of the BCE balance for the thermodynamic study. Also, the good agreement between the energy supplied to the inlet dry air and the energy utilized for water vaporization in the BCE demonstrate the efficiency of the system used for thermal desalination. The process could potentially be pursued for higher energy efficiency by using higher inlet air temperatures. 11. 12. 13. 14. 15. 16. 17. 18. 19. Shahid M, Fan C, Pashley RM (2016) Insight into the bubble column evaporator and its applications. Int Rev Phys Chem 35:143– 185 Francis MJ, Pashley RM (2009) Application of a bubble column for evaporative cooling and a simple procedure for determining the latent heat of vaporization of aqueous salt solutions. J Phys Chem B 113:9311–9315 Fan C, Shahid M, Pashley RM (2014) Studies on bubble column evaporation in various salt solutions. J Solut Chem 43:1297–1312 Shahid M, Pashley RM (2014) A study of the bubble column evaporator method for thermal desalination. Desalination 351:236–242 Francis M, Pashley R (2009) Thermal desalination using a nonboiling bubble column. Desalin Water Treat 12:155–161 Xue X, Pashley RM (2015) A study of low temperature inactivation of fecal coliforms in electrolyte solutions using hot air bubbles. Desalin Water Treat 57:9444–9454 Shahid M, Pashley R, Mohklesur RA (2014) Use of a high density, low temperature, bubble column for thermally efficient water sterilization. Desalin Water Treat 52:4444–4452 Shahid M (2015) A study of the bubble column evaporator method for improved sterilization. J Water Process Eng 8:e1–e6 Shahid M, Xue X, Fan C, Pashley RM, Ninham B (2015) Study of a novel method for the thermolysis of solutes in aqueous solution using a low temperature bubble column evaporator. J Phys Chem B 119:8072–8079 Fan C, Pashley R (2015) Precise method for determining the enthalpy of vaporization of concentrated salt solutions using a bubble column evaporator. J Solut Chem 44:131–145 Chen Z, Utaka Y (2015) On heat transfer and evaporation characteristics in the growth process of a bubble with microlayer structure during nucleate boiling. Int J Heat Mass Transf 81:750–759 Utaka Y, Kashiwabara Y, Ozaki M, Chen Z (2014) Heat transfer characteristics based on microlayer structure in nucleate pool boiling for water and ethanol. Int J Heat Mass Transf 68:479–488 Kong L, Gao X, Li R, Han J (2017) Bubbles in curved tube flows– an experimental study. Int J Heat Mass Transf 105:180–188 Yu C, Ye Z, Sheu TW, Lin Y, Zhao X (2016) An improved interface preserving level set method for simulating three dimensional rising bubble. Int J Heat Mass Transf 103:753–772 Craig V, Ninham B, Pashley R (1993) Effect of electrolytes on bubble coalescence. Nature 364:317–319 Craig VS, Ninham BW, Pashley RM (1993) The effect of electrolytes on bubble coalescence in water. J Phys Chem 97:10192–10197 Leifer I, Patro RK, Bowyer P, Study A (2000) On the temperature variation of rise velocity for large clean bubbles. J Atmos Ocean Technol 17:1392–1402 Klaseboer E, Manica R, Chan DY, Khoo BC (2011) BEM simulations of potential flow with viscous effects as applied to a rising bubble. Engineering Analysis with Boundary Elements 35:489–494 Clift R, Grace J, Weber M (1978) Bubbles, drops and particles. Academic Press, New York Author's personal copy Heat Mass Transfer 20. 21. 22. 23. 24. 25. 26. Shahid M, Xue X, Fan C, Ninham BW, Pashley RM (2015) Study of a novel method for the thermolysis of solutes in aqueous solution using a low temperature bubble column evaporator. J Phys Chem B 119:8072–8079 Fan C, Pashley RM (2016) The controlled growth of calcium sulfate dihydrate (gypsum) in aqueous solution using the inhibition effect of a bubble column evaporator. Chem Eng Sci 142:23–31 Fan C, Pashley RM (2016) Determining the enthalpy of vaporization of salt solutions using the cooling effect of a bubble column evaporator. J Chem Educ 93:1642–1646 Lide DR, Bruno TJ (2012) CRC handbook of chemistry and physics. CRC Press, Boca Raton Clarke ECW, Glew DN (1985) Evaluation of the thermodynamic functions for aqueous sodium chloride from equilibrium and calorimetric measurements below 154 °C. J Phys Chem Ref Data 14:489 Patil KR, Tripathi AD, Pathak G, Katti SS (1991) Thermodynamic properties of aqueous electrolyte solutions. 2. Vapor pressure of aqueous solutions of sodium bromide, sodium iodide, potassium chloride, potassium bromide, potassium iodide, rubidium chloride, cesium chloride, cesium bromide, cesium iodide, magnesium chloride, calcium chloride, calcium bromide, calcium iodide, strontium chloride, strontium bromide, strontium iodide, barium chloride, and barium bromide. J Chem Eng Data 36:225–230 Hubert N, Gabes Y, Bourdet J-B, Schuffenecker L (1995) Vapor pressure measurements with a nonisothermal static method between View publication stats 27. 28. 29. 30. 31. 32. 33. 34. 35. 293.15 and 363.15 K for electrolyte solutions. Application to the H2O+ NaCl system. J Chem Eng Data 40:891–894 Chou J, Rowe AM (1969) Enthalpies of aqueous sodium chloride solutions from 32 to 350 F. Desalination 6:105–115 Lunnon RG (1912) The latent heat of evaporation of aqueous salt solutions. Proc Phys Soc Lond 25:180 Hunter JB, Bliss H (1944) Thermodynamic properties of aqueous salt solutions. Ind Eng Chem 36:945–953 Gurovich BM, Zyuzin RA, Mezheritskii SM (1988) Experimental determination of the heat of vaporization of aqueous salt solutions at atmospheric pressure. Chem Pet Eng 24:599–600 Topor N, Logasheva A, Tsoy G (1979) Determination of the heat of evaporation of pure substances and of aqueous solutions of inorganic salts with the derivatograph. J Therm Anal 17:427–433 Wagner W, Pruss A (2002) The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J Phys Chem Ref Data 31:387–536 Francis MJ, Pashley RM (2009) Thermal desalination using a nonboiling bubble column. Desalin Water Treat 12:155–161 Al-Karaghouli A, Kazmerski LL (2013) Energy consumption and water production cost of conventional and renewableenergy-powered desalination processes. Renew Sust Energ Rev 24:343–356 Hoffman AR (2004) The connection: water and energy security. Institute for the Analysis of Global Security. http://www.iags.org/ n0813043.htm