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Research Papers: Energy Systems Analysis

Effect of Nonideal Solution Behavior on Desalination of a Sodium Chloride Solution and Comparison to Seawater

[+] Author and Article Information
Karan H. Mistry

e-mail: mistry@mit.edu

John H. Lienhard V.

Fellow ASME
e-mail: lienhard@mit.edu
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139-4307

Contributed by the Advanced Energy Systems Division of ASME for publication in the Journal of Energy Resources Technology. Manuscript received August 30, 2012; final manuscript received April 22, 2013; published online June 24, 2013. Assoc. Editor: Kau-Fui Wong.

J. Energy Resour. Technol 135(4), 042003 (Jun 24, 2013) (10 pages) Paper No: JERT-12-1197; doi: 10.1115/1.4024544 History: Received August 30, 2012; Revised April 22, 2013

Proper evaluation of the Gibbs free energy and other properties of seawater and other aqueous solutions is essential in the analysis of desalination systems. Standard seawater has been studied extensively and property data are readily accessible. However, many aqueous solutions requiring desalination have significantly different compositions from seawater and seawater data are generally not accurate for these solutions. Experimental data for a given aqueous solution may be unavailable under the conditions of interest. Therefore, there is a need to model relevant physical properties from chemical thermodynamic principles. In particular, for solutions that are not ideal, the activity and fugacity coefficients must be considered. In this paper, the effect of nonidealities in sodium chloride (NaCl) solutions is considered through a parametric study of the least work of separation for a desalination system. This study is used to determine the conditions under which the ideal solution approximation is valid and also to determine when an NaCl solution is a good approximation to standard seawater. It is found that the ideal solution approximation is reasonable within ranges of salinities and recovery ratios typical of those found in the seawater desalination industry because many of the nonidealities cancel out, but not because the solution behaves ideally. Additionally, it is found that NaCl solutions closely approximate natural seawater only at salinities typically found in seawater and not for salinities found in typical brackish waters.

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Figures

Grahic Jump Location
Fig. 1

Rational activity coefficient for NaCl in H2O evaluated using Debye-Hückel theory for electrolyte solutions and using experimental data. Dots are data from Ref. [18].

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Fig. 2

H2O data for NaCl solution. Dots are data from Ref. [18]. Solid lines are curve fits.

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Fig. 3

A control volume representation of a desalination system is used to derive the least work of separation

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Fig. 4

Least work of separation for an NaCl solution (Eq. (46)) in which activity and fugacity coefficients are evaluated using data from Ref. [18]

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Fig. 5

Ideal part of the least work of separation for an NaCl solution [Eq. (48)]

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Fig. 6

The nonideal part of the least work of separation for an NaCl solution [Eq. (49)] only becomes significant at high feed salinities and high recovery ratios. Activity and fugacity coefficients are evaluated using data from Ref. [18].

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Fig. 7

Relative error between the ideal solution and actual values of least work of separation is large when salinity is either very low or very high

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Fig. 8

Relative error when only NaCl is approximated as ideal goes to zero when the activity coefficients of salt in the feed and brine are equal

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Fig. 9

Relative error when only H2O is approximated as ideal goes to zero when the fugacity coefficients of all the streams cancel

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Fig. 10

The Debye-Hückel limiting law introduces significant error for all but the lowest feed salinities

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Fig. 11

The Güntelberg equation is accurate for low salinities, but even for seawater salinities, the relative error is at least 10%

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Fig. 12

The Davies equation accurately evaluates the salt nonidealities and results in minimal error except at very high salinities

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Fig. 13

The least work of separation for an NaCl solution is greater than the least work of separation for an aqueous solution with seawater composition

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