The
Volumetric
Properties
of
Aqueous
Sodium
Chloride
Solutions
from
0°
to
5()0°C
at
Pressures
up
to
2000
Bars
Based
on
a
Regression
of
Available
Data
in
the
Literature
GEOLOGICAL
SURVEY
BULLETIN
1421-C
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Volumetric Properties of Aqueous Sodium Chloride Solutions: A Regression of Available Data, Summaries of Literature
Densities of various molalities and weight percentages of sodium chloride solutions at temperatures from 25°C to 500°C and pressures up to 2000 bars. The data is summarized in tables and represents a reliable set of internally consistent data for the volumetric properties of aqueous sodium chloride solutions.
What you will learn
- What other thermodynamic properties of sodium chloride solutions are discussed in the document?
- How do the densities of sodium chloride solutions vary with temperature and pressure?
- What sources were used to obtain the data for the densities of sodium chloride solutions presented in the document?
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The Volumetric Properties of Aqueous
Sodium Chloride Solutions from 0° to
5()0°C at Pressures up to 2000 Bars
Based on a Regression of Available Data
in the Literature
GEOLOGICAL SURVEY BULLETIN 1421-C
UNITED STATES DEPARTMENT OF THE INTERIOR
GEOLOGICAL SURVEY
V. E. McKelvey, Director
Library of Congress Cataloging in Publications Data
Potter, Robert W.
The volumetric properties of aqueous sodium chloride solutions from 0° to
500° C at pressures up to 2000 bars based on a regression of available data
in the literature.
(Preliminary steam tables for NaCl solutions)
Geological Survey Bulletin 1421-C
Bibliography: p. 5-6.
Supt. of Docs., no.: I 19.3.1421-C.
1. Thermochemistry-Tables, etc. 2. Salt-Tables.
I. Brown, David Leslie, 1954- joint author. II. Title. III. Series.
IV. Series:
United States Geological Survey Bulletin 1421-C.
QE75.B9 no. 1421-C [QD511.8] 557.3'08s [546'.382'24] 76-
For sale by the Superintendent of Documents, U. S. Government Printing Office
Washington, D. C. 20402
Stock Number 024-001-
CONTENTS
Page
PRELIMINARY STEAM TABLES FOR NaCl SOLUTIONS.
THE VOLUMETRIC PROPERTIES OF AQUEOUS SODIUM CHLORIDE SOLUTIONS FROM 0° TO 500°C AT PRESSURES UP TO 2000 BARS BASED ON A REGRESSION OF AVAILABLE DATA IN THE LITERATURE
By ROBERT W. POTTER n and DAVID L. BROWN
ABSTRACT
The volumetric properties of aqueous sodium chloride solutions from 0° to 500°C at
pressures up to 2000 bars for concentrations ranging from infinite dilution to as high as
8.0 molal have been obtained by a computer regression of the available experimental
data from the literature. The regression was done using (1) the simplest forms of
equations capable of describing the experimental data, (2) unsmoothed data where
possible, and (3) a least-squares regression technique in which the individual data
points were weighted with respect to their relative uncertainty. By following this
procedure, a set of internally consistent data was generated. The results are presented
in 27 tables of density data at various concentrations, temperatures, and pressures.
Two tables of empirical constants capable of generating the tables of density values as
well as interpolating the tabulated values are also given.
INTRODUCTION
Pressure-volume-temperature-composition (P-V-T-X) data for
brines are required to establish optimum operating temperatures,
pressures, and flow rates for the production of geothermal brine
fields, to minimize scaling and corrosion, and to design intelligently
turbines for production of electricity. One of the prerequisites for
successful chemical modeling of geothermal brine systems, as well as
reservoir modeling, is thermodynamic data derived from the vol-
umetric properties of brines, for example, partial and apparent molal
volumes. In view of the critical importance of P-V-T-X data to the
utilization and understanding of geothermal brine systems, a compi-
lation of the available data from the literature and a critical evalua-
tion of these data are required. The compilation of the available data
from the literature has been completed (Potter and others, 1975), and
this chapter presents a critical evaluation of the volumetric data for
aqueous sodium chloride solutions.
Cl
C 2 PRELIMINARY STEAM TABLES FOR NaCl SOLUTIONS
The volumetric properties of aqueous sodium chloride solutions
have been the focus of experimental investigation since 1854. The
experimental data prior to 1928, from a total of 103 published refer-
ences, have been collected, critically evaluated, and published as
smoothed values in the International Critical Tables (National
Research Council, 1928). The data published since 1928 have been
collected and summarized by Potter, Shaw, and Haas (1975). The 119
references covered by them produced a total of 2,453 volumetric meas-
urements as well as 802 smoothed densities. These data and the data
presented in the International Critical Tables served as the data base
used in this critical evaluation of the volumetric properties of aque-
ous sodium chloride solutions.
Prior to the present evaluation, the only fairly extensive tabula-
tions of smoothed volumetric data for aqueous, vapor-saturated
sodium chloride solutions were: International Critical Tables
(National Research Council, 1928) for 0.5-26 weight percent solu-
tions from 0°-100°C; Fabuss and Korosi (1968) for 0.1-3.5 molal (also
given in weight percent and molarity) solutions from 20°-150°C (ta-
bles also in °F); and Haas (1970) for 0-8.0 molal solutions from 75°-
325°C. There are no critical compilations of smoothed data available
for solutions at pressures greater than the saturation vapor pressure
(Potter, 1976). The limited range of critically evaluated numbers is
further evidence of a need for a critical evaluation of all the data over
the whole P-V-T-X space if it is available, despite the fact that ex-
perimental data summarized by Potter, Shaw, and Haas (1975) are
for solutions from 10^-15.8 molal over the temperature range 0°-
770°C at pressures up to 12000 bars.
DATA REGRESSION METHODS
The intent of this critical evaluation of aqueous sodium chloride
solutions is to produce a set of internally consistent densities that
describes the available volumetric data without introducing any
theoretical bias. Hence only the raw experimental values were used
in the regression of the volumetric properties, except for the pre-
data. Since many of these data are unavailable, the smoothed data
from the International Critical Tables (National Research Council,
1928) were used in their place. These data were converted to a com-
mon system of units and were then fit to the simplest form of an
equation that would adequately describe the experimental data. A
minimum amount of data points were rejected using statistical cri-
terion, and the data were then refit to an equation of the same form.
The equations that were finally derived in this fashion were used to
generate the smoothed density values.
The experimental data for the volumetric properties of aqueous
C4 PRELIMINARY STEAM TABLES FOR NaCl SOLUTIONS
±0.005 g/cm3, equation (2) proved adequate to describe the experi-
mental data. The density as a function of temperature at constant
composition and pressure was found to be adequately described by an
equation of the following form:
d=A+BT+CT2 (Composition, P constant) (3)
where A, B, and C are empirical constants.
The smoothed densities were obtained from a computer regression
of the P-V-T-X data base previously described. The regression of
these data was accomplished by using a least-squares method in
which the individual data points were weighted with respect to their
relative uncertainty (Meyer, 1975). The experimental data were first
regressed at constant temperature and pressure as a function of com-
position, then the resulting smoothed densities were regressed as a
function of temperature at constant composition and pressure. After
the initial fit as a function of composition, the experimental data were
evaluated via Chauvenet's criterion and the inappropriate data were
rejected. The remaining data were then refit to either equation (1) or
(2) depending on the temperature, and the subsequent smoothed val-
ues were used in the final regression. This was the only stage in the
regression at which data were rejected.
RESULTS
Table 1 summarizes the densities for the vapor-saturated aqueous
sodium chloride solutions from 0°-500°C for various concentrations
expressed as molality. The densities for vapor-saturated aqueous
sodium chloride solutions with concentration expressed in weight
percent (table 2) were derived by interpolating the expressions for
density as a function of the molality. The densities for various
molalities, 0.5-6.0 molal in 0.5 molal steps, at pressures greater than
the saturation vapor pressure up to 2000 bars from 25°-500°C are
summarized in tables 3-14; the densities for various sodium chloride
solutions with concentration expressed in weight percent, 1-
weight percent in 2 weight percent increments, for the same pressure
and temperature range are summarized in tables 15-27. The regres-
sion constants for the equations used to generate tables 1-27 are
tabulated in tables 28 and 29.
The uncertainties for the densities given in tables 1-27 are the
mean deviation of the experimental values from the final regressed
equations. The extrapolated densities have been assigned an uncer-
tainty of 10 times the mean standard deviation for the final regressed
equations (tables 28 and 29). These assignments were made because
of the simple form of the equations used; for although the equations
VOLUMETRIC PROPERTIES OF SODIUM CHLORIDE SOLUTIONS C 5
fit the data well, they cannot be readily extrapolated with any
certainty. Data is available for higher temperatures, pressures,
and concentrations than those summarized in tables 1-27; how-
ever, in general, these data are not consistent with the lower tem-
perature, pressure, and concentration data or not extensive enough to
allow for a reliable regression that would yield internally consistent
P-V-T-X data.
As has been previously stated, there are three critical compilations
of density data for limited temperature ranges previous to this study:
International Critical Tables (National Research Council, 1928),
Fabuss and Korosi (1968), and Haas (1970). The observed mean
standard deviations between these data sets and the data in this
study are ±0.0003 g/cm3, ±0.0007 g/cm3, and ±0.0036 g/cm3, respec-
tively. The percentages of the smoothed points from the previous
compilations that lie within the error bands determined for this study
are 69.2 percent, 85.7 percent, and 82.0 percent for the International
Critical Tables, Fabuss and Korosi, and Haas, respectively.
The tabulations given here will differ from those given in Chapters
A and B of this Bulletin (Haas, 1976a, b) because these results were
not available when the earlier chapters were prepared. Haas used an
earlier formulation for the density of NaCl solutions to calculate the
density and specific volume of the vapor-saturated solutions and to
estimate the partial molal volumes of the HzO and NaCl components.
As indicated in the foregoing analysis, these differences are minor in
nature when the precision and accuracy of the available data are
considered.
The density data obtained from smoothing all the available ex-
perimental data are in substantial agreement with previous studies
of a similar nature. The smoothed values presented in tables 1-
represent a reliable set of internally consistent data that describes
the available experimental data for the volumetric properties of
aqueous sodium chloride solutions. Their wider scope, both in
temperature-pressure-composition space and in completeness of data
considered, makes these tabulations superior to the previously avail-
able compilations. The data as presented in tables 1-27 appear to be
of significant precision for engineering purposes; however the preci-
sion is such that only preliminary thermochemical data can be ex-
tracted from the data set (Potter, 1976).
REFERENCES CITED
Fabuss, B. M., and Korosi, Alexander, 1968, Properties of seawater and solutions con-
taining sodium chloride, potassium chloride, sodium sulfate, and magnesium sul-
fate: U.S. Office Saline Water, Research Develop. Progress Rept. No. 384, 133 p.
- Introduction _________________________________________ Abstract___________________________________________Cl
- Data regression methods ______________________________
- Results __________________ __
- References cited ________________________ ___________
- TABLE 1. Densities of vapor-saturated NaCl solutions, g/cm3 C TABLES - 2. Densities of vapor-saturated NaCl solutions, g/cm3 ______ ____ - 3. Densities of 0.5 molal NaCl solutions, g/cm3 __ - 4. Densities of 1 molal NaCl solutions, g/cm3 ________________ - 5. Densities of 1.5 molal NaCl solutions, g/cm3 ______________ - 6. Densities of 2 molal NaCl solutions, g/cm3 _____________ __ - 7. Densities of 2.5 molal NaCl solutions, g/cm3 ________________ - 8. Densities of 3 molal NaCl solutions, g/cm3 ________________ - 9. Densities of 3.5 molal NaCl solutions, g/cm3 ______________ - 10. Densities of 4 molal NaCl solutions, g/cm3 ________________ - 11. Densities of 4.5 molal NaCl solutions, g/cm3 __ - 12. Densities of 5 molal NaCl solutions, g/cm3 __ ____________
- Densities of 5.5 molal NaCl solutions, g/cm3 _______________
- Densities of 5 molal NaCl solutions, g/cm3 __________________
- Densities of 1 weight percent NaCl solutions, g/cm3 __________
- Densities of 3 weight percent NaCl solutions, g/cm3 __
- Densities of 5 weight percent NaCl solutions, g/cm3 __________
- Densities of 7 weight percent NaCl solutions, g/cm3 __________
- Densities of 9 weight percent NaCl solutions, g/cm3 ________
- Densities of 11 weight percent NaCl solutions, g/cm3 ______ __
- Densities of 13 weight percent NaCl solutions, g/cm3 ______
- Densities of 15 weight percent NaCl solutions, g/cm3 __
- Densities of 17 weight percent NaCl solutions, g/cm3 _________
- Densities of 19 weight percent NaCl solutions, g/cm3 ________
- Densities of 21 weight percent NaCl solutions, g/cm3 __________
- Densities of 23 weight percent NaCl solutions, g/cm3 ________
- Densities of 25 weight percent NaCl solutions, g/cm3 __________
- Interpolation coefficients for NaCl solutions
- NaCl interpolation formula coefficients _________________
- TABLES 1-
C8 PRELIMINARY STEAM TABLES FOR NaCl SOLUTIONS
tJ <a o a rH
a> o^< rt o
H^ V-f I <-> o
i-H<1f-l.-Hi-H.Hi-HOOOOOOO
i-H-l,-f»-4i-Hi-<OOOOOOOO*
CTl O Lrt
O O O O O O O O O O
TABLE 3. Densities of 0.5 molal NaCl solutions, g/cm
[The uncertainties in the densities are: 3-place figures ±0.005 and ±0.05 for 2-place figures.]
Temp °C
25 SO 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Pressure 700
0.71* 0.66* -- -- -- ~~
(bars) 800
0.69* 0.64* -- -- ~~
CO
"a
o
G
CO
o f
O
CO
'Extrapolated values
VOLUMETRIC PROPERTIES OF SODIUM CHLORIDE SOLUTIONS Cl 1
«'«' ,'_' rt' «' -H' rt ,-. , O O O C> O O O O O O
«',-,' rt' r-,' ,H _.. CD C. C O o' O O O O O O
3 O
oooooaiotCia»oococor*-r-~vOvO i
-HrtVn-
in i-- oo^ in^ o
TABLE 6. Densities of 2 molal NaCl solutions, g/cm
[The uncertainties in the densities are:. 3-place figures ±0.005 and ±0.05 for 2-place figures.]
Temp °C
25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
Pressure 700
0.61*
(bars) 800
0.62*
o
f
Extrapolated values
o ^
M
CO
O
O
w f O
CO
O
O
CO
Oi 1 CO
TABLE 7. Densities of 2.5 molal NaCl solutions, g/cm 3
[The uncertainties in the densities are: 3-place figures ±0.005 and ±0.05 for 2-place figures.]
Temp °C
25 SO 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500
l.OOS
0.75* 0.71* --
Pressure 700
0.72* 0.68* "
(bars) 800
0.74* 0.70* --
fI I
s
CO
W W CO
*J
O
2 M O CO O
r
H
o
CO
Extrapolated values