Heat and Mass Transfer

, Volume 54, Issue 5, pp 1313–1321 | Cite as

The energy balance within a bubble column evaporator

  • Chao Fan
  • Muhammad Shahid
  • Richard M. Pashley


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 (ΔH vap) values of salt solutions from BCE experiments. Based on the analysis of derivation and ΔH vap 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 ΔH vap 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 ΔH vap 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.



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

\( {C}_p^g \)

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

\( {W}_{air}^{T_e} \)

Work done the air pump through the colum


Initial (dry) bubble volume


Final (wet) bubble volume


Volume of the bubble at temperature T


Energy supplied by the bubble from T in to T e


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



Bubble column evaporator


Reverse osmosis



We would like to thank the Australian Research Council for funding this project (Grant Number: DP120102385).

Compliance with ethical standards

Competing interest

The authors declare no competing financial interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Chao Fan
    • 1
    • 2
  • Muhammad Shahid
    • 1
  • Richard M. Pashley
    • 1
  1. 1.School of Physical, Environmental and Mathematical SciencesUniversity of New South WalesCanberraAustralia
  2. 2.School of Environmental Science and EngineeringSun Yat-sen UniversityGuangzhouPeople’s Republic of China

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