HokieFlincs_H2O-NaCl: A Microsoft Excel spreadsheet for interpreting microthermometric data from fluid inclusions based on the PVTX properties of H2O–NaCl

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H
OKIE
F
LINCS
_H2O-N
A
C
L
: A Microsoft Excel spreadsheet for interpreting
microthermometric data from fluid inclusions based on the PVTX properties
of H
2
O–NaCl
Matthew Steele-MacInnis
n
, Pilar Lecumberri-Sanchez, Robert J. Bodnar
Department of Geosciences, Virginia Tech, Blacksburg, VA 24061, USA
article info
Article history:
Received 3 December 2011
Received in revised form
29 January 2012
Accepted 30 January 2012
Available online 6 February 2012
Keywords:
H
2
O–NaCl
Fluid inclusions
Microthermometry
PVTX
Isochores
1. Introduction
Sodium chloride (NaCl) is often the most common salt in
natural fluids (e.g., Fyfe et al., 1978). Consequently, phase equili-
brium (PTX) and volumetric data (PVTX) for H
2
O–NaCl are often
used to interpret microthermometric data from aqueous fluid
inclusions (FI), and for modeling natural aqueous electrolyte
fluids. The pressure–volume–temperature–composition (PVTX)
properties of H
2
O–NaCl have been well characterized by numer-
ous experimental and theoretical studies, as summarized in
Bodnar et al. (1985) and Bodnar (2003).
Several numerical models have been developed to represent
the PVTX properties of H
2
O–NaCl, facilitating interpretation of
data from FI. Those models can be categorized as (1) comprehen-
sive models (equations of state) that are not specifically designed
to interpret FI data (e.g., Anderko and Pitzer, 1993;Driesner,
2007;Driesner and Heinrich, 2007); or (2) correlation equations
designed specifically for FI research, with measurable quantities
(dissolution temperature, T
m
, and homogenization temperature,
T
h
) as independent variables (e.g., Bodnar et al., 1989;Bodnar,
1994;Bodnar and Vityk, 1994). Both types of models have
advantages and disadvantages in FI research. The comprehensive
models can be used as stand-alone internally consistent tools to
analyze fluid PVTX properties, but they require iterative calcula-
tions to interpret T
m
–T
h
data, which can make data reduction time
consuming. The FI-specific models compute FI properties (com-
position, density, etc.) directly from T
m
and/or T
h
(without
iteration). However, no single model covers the complete range
of PVTX conditions of interest in most FI studies.
Owing to the piecemeal nature of the FI-specific models, inter-
preting microthermometric data can be tedious, requiring contin-
uous switching between the various models to obtain all the desired
information. To circumvent this issue, several easy-to-use computer
programs have been published that implement various models to
interpret H
2
O–NaCl (and other) microthermometric data (Bakker,
2003;Bodnar et al., 1989;Brown, 1989;Brown and Hagemann,
1995;Driesner, 2007;Driesner and Heinrich, 2007). These programs
have made the numerical models more accessible and applicable to
FI research. The programs provide powerful and adaptable tools for
interpreting FI data and for theoretical modeling (Bakker and Brown,
2003).Adrawbackofsomeoftheseprograms(e.g.,Bakker, 2003;
Driesner, 2007;Driesner and Heinrich, 2007)isthatafterresultsfor
one FI are computed, the program must be re-set before data for
another FI are entered. As a result, entry of large FI datasets is time
consuming, and it is not possible to have all data for an analytical
session saved to a single output file.
The ideal computer model allows the user to input tempera-
tures of phase changes commonly measured in the laboratory
during microthermometry—namely, dissolution temperatures
Contents lists available at SciVerse ScienceDirect
journal homepage: www.elsevier.com/locate/cageo
Computers & Geosciences
0098-3004/$ - see front matter &2012 Elsevier Ltd. All rights reserved.
doi:10.1016/j.cageo.2012.01.022
n
Corresponding author: Tel.: þ1 540 231 8575; fax: þ1 540 231 3386.
E-mail addresses: mjmaci@vt.edu (M. Steele-MacInnis),
pilar@vt.edu (P. Lecumberri-Sanchez), rjb@vt.edu (R.J. Bodnar).
Computers & Geosciences 49 (2012) 334–337

(T
m
) of various phases and homogenization temperature (T
h
)—to
determine the composition, density, and pressure in the inclusion
at homogenization. From this information one can also calculate
the slope of the isochore and estimate the PT conditions of FI
formation, provided that either trapping Tor Pare known
independently and the inclusions are trapped in the single-phase
fluid field.
Here, we assemble the numerical formulae necessary to fully
characterize H
2
O–NaCl FI properties, based only on the tempera-
ture of dissolution of the last solid phase, T
m
, and the liquid-vapor
homogenization temperature, T
h
, obtained during microthermo-
metry. Note that an H
2
O–NaCl FI can exhibit more than two phase
changes during heating from temperatures less than the eutectic
temperature (21.2 1C; Hall et al., 1988) to the total homogeni-
zation temperature, but only the liquid–vapor homogenization
temperature and the temperature of disappearance of the last
solid phase are required to uniquely define the fluid composition
and density. Using these two input parameters, the program
calculates fluid density and salinity, and also estimates the
isochore slope, which allows the user to calculate a pressure
correction. Importantly, the program is designed such that the
user can quickly and easily reduce large datasets.
2. Program HokieFlincs_H2O-NaCl
H
OKIE
F
LINCS
_H2O-N
A
C
L
includes a set of FI-specific equations
(Fig. 1) that describe the PVTX properties of H
2
O–NaCl based only
on the measured T
m
, and T
h
. Depending on the mode of homo-
genization, different models may be required. For H
2
O–NaCl FI in
which the last solid phase to disappear is H
2
O–ice, salinity is
determined using the equation of Bodnar (1993). If the last solid
phase to disappear (in equilibrium with liquid and vapor) is either
hydrohalite or halite, equations from Sterner et al. (1988) are used
to determine the liquid composition. Correlation equations
derived in the present study are used to compute the densities
of liquid and vapor, the vapor composition, and the mass propor-
tions of liquid and vapor. The liquid and vapor compositions and
mass fractions are used to precisely determine the bulk composi-
tion. For homogenization in the absence of solids, pressure at T
h
and liquid density are represented by equations of Atkinson
(2002) and Bodnar (1983), respectively. The dP/dTslopes of
isochores in the liquid field are modeled using equations of
Bodnar and Vityk (1994), allowing direct determination of trap-
ping PT conditions if an independent estimate of either Por Tis
supplied. Note that although the slopes of fluid isochores gen-
erally have slight concave-down curvature, at crustal PT condi-
tions the isochores of H
2
O–NaCl fluids are essentially linear
(Bodnar and Vityk, 1994) and we assumed linearity in the
program. Critical properties are based on the model of Knight
and Bodnar (1989).
The numerical models described above cannot model the PVTX
properties of fluid inclusions for which T
h
oT
m
(i.e., inclusions
homogenize by halite disappearance). Therefore, in cases where
T
h
oT
m
, the salinity, pressure at homogenization, density and dP/
dTslope of the isochore in the liquid field are determined using
the model of Lecumberri-Sanchez et al. (in review), which is a
revision of an earlier model of Becker et al. (2008).
The Excel spreadsheet ‘‘H
OKIE
F
LINCS
_H2O-N
A
C
L
’’ (available in the
online Supporting Information, Appendix A) does not require
iterative procedures to interpret microthermometric data. The
user inputs a value of T
m
(specifying which solid phase, either
H
2
O–ice, hydrohalite or halite, is the last to dissolve) and T
h
,in1C
(Fig. 2). The fluid salinity, density and the isochore slope are
output (Fig. 2). If a pressure correction is required, the user inputs
an estimate of either Por Tof trapping, and the other quantity is
computed using the isochore slope and the slope-intercept
method. We avoided any formulae that require indirect solutions
(iteration) in order to avoid using macros in the program. There-
fore, H
OKIE
F
LINCS
_H2O-N
A
C
L
uses only Excel formulae and does not
employ Visual Basic (VBA) code. The program was designed in
this way because VBA macros are not supported in all versions of
Excel. Thus, because H
OKIE
F
LINCS
_H2O-N
A
C
L
does not use macros,
the program can be implemented using any version of Excel, on
both Mac and PC platforms.
As an example of the use of H
OKIE
F
LINCS
_H2O-N
A
C
L
, consider a FI
that contains liquid and vapor at room T, has final ice melting (in
the presence of vapor) at 10 1C, and homogenizes by vapor
bubble disappearance at 300 1C. To interpret these data, the value
‘‘10’’ is entered into the cell for T
m
(column C), and ‘‘ice’’ is
entered into the adjacent cell in column D(phase) (row 30 in the
screenshot; Fig. 2). Using the equation of Bodnar (1993) gives a
salinity of 13.9 wt% NaCl (column H;Fig. 2). To determine the
density of the FI and Pat homogenization, the homogenization
temperature (‘‘300’’) is entered into the same row in column E
(T
h
), and the program applies the equations of Bodnar (1983) and
Atkinson (2002) to estimate a bulk density of 0.86 g/cm
3
(column
J;Fig. 2) and Pat homogenization of 78 bar (column I;Fig. 2).
Using the equation of Bodnar and Vityk (1994), the isochore dP/dT
slope for this inclusion is 12.1 bar/1C (column K;Fig. 2). The
isochore slope can be used along with an independent estimate of
the trapping Tto determine the trapping P. For example, if
mineral equilibria indicate that the host phase for the FI formed
at 600 1C, the Pof formation would have been 3700 bar.
As another example, consider a FI that contains liquid, vapor
and halite at room temperature, and in which halite dissolves and
the bubble disappears at the same Tof 400 1C (i.e., the FI
homogenizes on the LVH curve). To interpret these microthermo-
metric data, ‘‘400’’ is entered into columns Cand E, and ‘‘halite’’ is
entered into column D(row 30; Fig. 2). Based on the mode of
homogenization, the models of Sterner et al. (1988) and Bodnar
(1983) are used to determine the salinity (47.4 wt% NaCl) and
density (1.09 g/cm
3
) of the FI (Fig. 2). The program uses the
models of Atkinson (2002) and Bodnar and Vityk (1994) to
estimate the P at homogenization (170 bar) and the slope of the
isochore (14.4 bar/1C) (Fig. 2). Note that most natural FI homo-
genize either by dissolution of the halite before the vapor bubble,
l
i
q
u
i
d
-
v
a
p
o
r
-
h
y
d
r
o
h
a
l
i
t
e
/
h
a
l
i
t
e
:
S
t
e
r
n
e
r
e
t
a
l
.
,
1
9
8
8
liquid-vapor-ice:
Bodnar, 1993
locus of critical points:Knight and Bodnar,1989
Atkinson, 2002
halite liquidus: Lecumberri-Sanchez et al., in review
Not shown:
+ liquid density: Bodnar, 1983;
+ isochore slope: Bodnar and Vityk, 1994
Pressure
Tem
p
erature
T = -21.2 to 700 °C
P = LVH to 6000 bar
X = 0 to 70 wt% NaCl
H
2
O liquid-vapor:
Atkinson, 2002
liquid-vapor curves:
Fig. 1. Schematic illustration of H
2
O–NaCl phase boundaries, showing the sources
of the various equations used in the present study. The halite liquidus line and
liquid–vapor curve both represent projections of constant liquid composition,
whereas the other curves represent a range of compositions. For complete
description of these features in PTX space, the reader is referred to Bodnar et al.
(1985) and Driesner and Heinrich (2007).
M. Steele-MacInnis et al. / Computers & Geosciences 49 (2012) 334–337 335

or by disappearance of the vapor bubble before the halite. The
significance of each mode of homogenization has been discussed
by Roedder and Bodnar (1980) and Bodnar (1994), and
Lecumberri-Sanchez et al. (in review) provide a model to interpret
data from FI in which T
h
oT
m
. All three modes of homogenization
can be modeled using (H
OKIE
F
LINCS
_H2O-N
A
C
L
).
For some FI it is not possible to measure the melting tem-
perature. For example, in some liquidþvapor FI the vapor bubble
occupies less than 10% of the inclusion volume and the ice
melts metastably during freezing experiments (Roedder, 1967).
Also, for very small FI the salinity is sometimes determined from
Raman analysis because ice melting cannot be observed during
microthermometry. In these cases, it is useful to have the option
to model the FI properties without entering a measured T
m
and
instead entering an estimate of salinity. H
OKIE
F
LINCS
_H2O-N
A
C
L
allows the user to input salinity directly for those FI for which
T
m
is not known (Column F,Fig. 2).
H
OKIE
F
LINCS
_H2O-N
A
C
L
can be used to determine properties of FI
that homogenize to the liquid phase. The program is generally
valid from 21.2 to 700 1C, the LV curve to 6000 bar and 0 to
70 wt% NaCl for FI that homogenize by vapor bubble disappear-
ance; and from T
h
of 100 to 600 1C, the LVH curve to 3000 bar and
28–75 wt% NaCl for FI that homogenize by halite disappearance.
For additional details, see Bodnar and Vityk (1994) and
Lecumberri-Sanchez et al. (in review). The program includes a
series of ‘‘if/then’’ statements to identify and alert the user to
potentially invalid input data. For example, if the user inputs a
value of 25 1C in the column for ice melting temperature, the
program recognizes that the input T
m
is less than the H
2
O–NaCl
eutectic temperature (21.2 1C; Hall et al., 1988) and a warning
appears in the same row in column ‘‘S’’. Similarly, the program
verifies that T
m
,T
h
and all estimated fluid properties (density,
pressure at homogenization, etc.) are within the ranges of validity
of the various numerical models.
A major advantage of H
OKIE
F
LINCS
_H2O-N
A
C
L
over other avail-
able programs for interpreting FI microthermometric data is the
speed and ease with which the user can interpret large datasets.
The spreadsheet is arranged such that T
m
and T
h
each occupy one
column (Fig. 2), and the maximum number of input data is only
limited by the number of rows available in Excel. An inclusionist
who regularly enters and stores microthermometric data in a
spreadsheet format needs only copy and paste T
m
and T
h
into the
proper columns to reduce the data. Because all computations are
direct, the results are immediately displayed when T
m
and T
h
are
entered. This is a significant advantage compared to previous
computer tools for interpreting FI data, especially in applications
where large numbers of FI are analyzed (e.g, thermal history
reconstructions, or studies of fluid evolution in hydrothermal ore
deposits). H
OKIE
F
LINCS
_H2O-N
A
C
L
is available for download as an
electronic annex to this paper (see Appendix A).
Acknowledgments
We thank Carlos Marques de Sa
´for discussions about inter-
pretation of microthermometric data, which motivated us to
create H
OKIE
F
LINCS
_H2O-N
A
C
L
. John Mavrogenes provided sugges-
tions for the program layout and experimented with an early
version. Two anonymous reviewers provided critical comments
that clarified and improved the manuscript and the program.
Financial support for MS-M was provided by the Institute for
Critical Technology and Applied Science (ICTAS) at Virginia Tech.
This material is based upon work supported by the US National
Science Foundation under grants nos. OCE-0928472 and EAR-
1019770 to RJB.
Appendix A. Supporting materials
Supplementary data associated with this article can be found
in the online version at doi:10.1016/j.cageo.2012.01.022.
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