ARTICLE IN PRESS
Computers & Geosciences 31 (2005) 797–800 www.elsevier.com/locate/cageo
Short note
COH, an Excel spreadsheet for composition calculations in the C–O–H fluid system$ Jan Marten Huizenga Department of Geology, University of Johannesburg, PO Box 524, Auckland Park, 2006 South Africa Received 5 February 2004; received in revised form 7 March 2005; accepted 7 March 2005
1. Introduction Most crustal fluids are mixtures of H2O, CO2, and CH4 (e.g., Touret and Dietvorst, 1983), which can be described in the three-component C–O–H system. This note describes a user-friendly Microsoft Excel spreadsheet, COH, for composition calculations in the C–O–H system for a selected fluid pressure (41 kbar) and temperature (4350 1C), and three optional compositional variables. As such it differs from the Fortran program GEOFLUID (Larsen, 1993), which calculates the fluid composition using one compositional variable. The spreadsheet is illustrated with several examples and is, in particular, useful for the interpretation of fluid inclusion results (e.g., Huizenga, 2001 and references therein). It is available from the IAMG server or the author’s website (http:// general.uj.ac.za/geology/jmh.htm).
2. Basic principles of the C–O–H fluid system A carbon saturated (i.e., graphite present) C–O–H fluid system has six unknowns at a fixed fluid pressure and temperature: X H2 O , X CO2 , X CH4 , X H2 , X CO and f O2 , i.e. the mole fractions of H2O, CO2, CH4, H2, CO and oxygen fugacity, respectively. For such a system, the carbon activity (acarbon) is unity and the variance is one,
i.e. if one compositional variable is fixed, the system is completely determined. In absence of graphite, the carbon activity must be defined ð0oacarbon p1Þ for the system to be completely determined. Four independent chemical equilibriums may be written for the C–O–H fluid system (French, 1966; Ohmoto and Kerrick, 1977): CO þ 12O2 ¼ CO2 ;
(1)
H2 þ 12O2 ¼ H2 O;
(2)
CH4 þ 2O2 ¼ CO2 þ 2H2 O;
(3)
C þ O2 ¼ CO2 ;
(4)
with the following equilibrium constants K1–K4 (assuming ideal mixing), respectively, which are largely temperature dependent (Ohmoto and Kerrick, 1977): K1 ¼
K2 ¼
1=2 gCO X CO f O2
gH2 O X H2 O 1=2
K3 ¼
log10 K 1 ¼
14751 4:535, T kelvin
(5)
,
12510 0:979log10 T kelvin þ 0:483, T kelvin
gCO2 X CO2 g2H2 O X 2H2 O P2fluid
log10 K 3 ¼
0098-3004/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.cageo.2005.03.003
;
gH2 X H2 f O2
log10 K 2 ¼
$
Code available from server at http://www.iamg.org /CGEditor/index.htm, or at http://general.uj.ac.za/geology/ jmh.htm Tel.: +27 11 489 2308; fax: +27 11 489 2309. E-mail address:
[email protected].
gCO2 X CO2
gCH4 X CH4 f 2O2
ð6Þ
,
41997 þ 0:719 log10 T kelvin 2:404, T kelvin
ð7Þ
ARTICLE IN PRESS J. Marten Huizenga / Computers & Geosciences 31 (2005) 797–800
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gCO2 X CO2 Pfluid , acarbon f O2 20586 Pbar 1 log10 K 4 ¼ þ 0:0421 þ 0:0276 , T kelvin T kelvin K4 ¼
ð8Þ
where Xi and gi denote the mole fraction and fugacity coefficient, respectively. Ignoring the very low X O2 , the mass balance constraint yields X H2 O þ X CO2 þ X CH4 þ X CO þ X H2 ¼ 1.
(9)
Having defined five equations for the system, one additional compositional constraint is needed to calculate the fluid composition. Three different options are available in the spreadsheet, which are discussed in the next section.
3. Program structure COH comprises eight worksheets. The first three worksheets, COH-1, COH-2 and COH-3 allow composition calculations using different input variables, which are fluid pressure, temperature, carbon activity, the fugacity coefficients and either the oxygen fugacity (worksheet COH-1), X CO2 =ðX CO2 þ X CH4 Þ (worksheet COH-2) or the atomic H:O ratio (worksheet COH-3). The remaining five worksheets comprise fugacity coefficient data for H2O, CO2, CH4, H2 and CO, respectively for different pressures (1–10, 1 kbar interval) and temperatures (300–1000, 50 1C interval) calculated from virial type equations of state given by Shi and Saxena (1992). The user may, however, use any fugacity coefficient for the different species as input.
Explicit equations for X H2 and X CH4 are derived from Eqs. (6) and (7), respectively: " # gH2 O 1 X H2 O , (12) X H2 ¼ 1=2 K 2 gH2 f C3
" X CH4 ¼
O2
gCO2 g2H2 O P2fluid
#
K 3 gCH4
C4
1=2
2 C 1 C 4 f 1 O2 X H2 O þ ðC 3 f O2
þ C 1 f O2 ð1 þ
1=2 C 2 f O2 Þ
þ 1ÞX H2 O
1 ¼ 0,
ð14Þ
where C1, C2, C3, and C4 are the constants indicated in Eqs. (10)–(13), respectively. If f fluid O2 is buffered, then Eq. (14) will reduce to a quadratic equation for X H2 O whose positive root is the correct answer. The calculations may only be carried out up to a certain maximum temperature, beyond which the oxygen fugacity becomes too high and the fluid becomes pure CO2 as all carbon oxidises (e.g., Huizenga, 2001). This maximum oxygen fugacity is calculated from Eq. (10) by substituting 1 for X CO2 , i.e. max imum f fluid O2 ¼
gCO2 Pfluid . K 4 acarbon
(15)
3.2. COH-2: constant X CO2 =ðX CO2 þ X CH4 Þ The input variables are the fluid pressure (bar), temperature (1C), X CO2 =ðX CO2 þ X CH4 Þ and the fugacity coefficients. The fluid composition may be calculated if X CO and X H2 are ignored. Eq. (10) changes to X gas CO2 ð1 X H2 O Þ ¼ C 1 f O2 ,
The input variables are the fluid pressure (bar), temperature (1C), the oxygen fugacity and the fugacity coefficients. The oxygen fugacity may be chosen relative to the fayalite–magnetite–quartz (FMQ) buffer (in log10 units) as defined by Ohmoto and Kerrick (1977). The calculations proceed as follows. X CO2 is calculated from Eq. (8) as " # acarbon K 4 X CO2 ¼ f O2 , (10) gCO2 Pfluid
and Eq. (13) to
where the parameters within the square bracket (C1) are constant at a fixed Pfluid and T. Eq. (5) gives: gCO2 1 X CO ¼ X CO2 . (11) K 1 gCO C2 f 1=2 O2
(13)
Substitution of Eqs. (10)–(13) into Eq. (9) yields the following expression for X H2 O :
3.1. COH-1: externally buffered oxygen fugacity
C1
1 X CO2 X 2H2 O . f 2O2
X gas CH4 ð1 X H2 O Þ ¼ C 4
1 gas X CO2 ð1 X H2 O ÞX 2H2 O , f 2O2
(16)
(17)
where gas X gas CH4 ¼ ð1 X CO2 Þ.
(18)
Eqs. (16) and (17) may be solved for X H2 O and f O2 : qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gas X gas CH4 X CO2 X H2 O ¼ pffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , (19) gas C 1 C 4 þ X gas CH4 X CO2
f O2
pffiffiffiffiffiffi X gas CO2 C 4 ¼ pffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . gas C 1 C 4 þ X gas CH4 X CO2
(20)
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X CO and X H2 may be calculated from Eqs. (11) and (12), respectively, and the user should check these values in order to confirm the assumption that they indeed could be ignored.
be solved using the worksheet COH-1. The input and output are given in Table 1.
3.3. COH-3: fixed atomic H:O ratio
4.2. Calculation of f O2 and X H2 O at a fixed Pfluid and T for a given X CO2 =ðX CO2 þ X CH4 Þ
The input variables are the fluid pressure (bar), temperature (1C), the atomic H:O ratio and the fugacity coefficients. The H:O ratio is defined as in Connolly and Cesare (1993): nH 2X H2 O þ 4X CH4 þ 2X H2 ¼ , nO X H2 O þ 2X CO2 þ X CO
(21)
where nO and nH are the number of moles of oxygen and hydrogen in the fluid phase. The H:O ratio can vary between infinity and zero. If X CO and X H2 are ignored in Eqs. (9) and (21), an exact root can be found for X H2 O , X CO2 , X CH4 and f O2 using Eqs. (9), (10), (13) and (21). The equations for calculating X H2 O , X CO2 , X CH4 and f O2 are extremely long and, therefore, not displayed but are available on request from the author. X H2 and X CO can be calculated from Eqs. (11) and (12), respectively, and again the user should check these values in order to confirm if X H2 and X CO could be ignored. Alternatively, the output value of the H:O ratio may be verified and should be similar to the user-defined input value.
4. Examples 4.1. Fluid composition calculation at a fixed P and T for f O2 buffered by FMQ Consider a C–O–H fluid that contains graphite at a fluid pressure of 3 kbar and a temperature of 500 1C. What is the composition of this fluid assuming that the oxygen fugacity is buffered by FMQ? This problem may Table 1 Input and output data for calculation of a carbon saturated C–O–H fluid at 3 kbar and 500 1C Input
Output
Consider a situation in which Pfluid and T are 2 kbar and 400 1C, respectively. Graphite-bearing, carbonic and H2O-rich fluid inclusions were trapped under conditions of immiscibility, of which the carbonic fluid inclusions show a constant gas composition: X gas CO2 ¼ 0:8 and X gas ¼ 0:2. What is the equilibrium composition of CH4 this fluid? This problem can be solved with the worksheet COH-2. Input and output are summarised in Table 2. The results justify the assumption that X CO and X H2 may be ignored.
Table 2 Input and output data for composition calculation of a carbon saturated fluid at 2 kbar, 400 1C and X CO2 =ðX CO2 þ X CH4 Þ of 0.8 Input
Output
Pfluid
2000 bar
log10 f fluid O2
28.2 bar
T
400 1C
29.0 bar
acarbon X gas CO2
1.0 0.8
log10 f FMQ O2 X H2 O X CO2
0.2
X CH4
0.02
0.22 1.69 2.59 2.55 1.82
X CO X H2 X CO2 =ðX CO2 þ X CH4 Þ
o103 o103 0.80
X gas CH4 gH2 O gCO2 gCH4 gH2 gCO
0.88 0.09
Table 3 Input and output data for composition calculation of a carbon saturated C–O–H fluid at 3 kbar and 500 1C and an H:O ratio of 2 Input
Output
Pfluid
3000 bar
log10 f FMQ O2
23.9 bar
T
500 1C
Pfluid
3000 bar
log10 f FMQ O2
23.9 bar
1.0 0
log10 f fluid O2 X H2 O X CO2
23.9 bar
acarbon log10 f fluid O2 (rel. to FMQ) gH2 O gCO2 gCH4 gH2 gCO
0.87 0.08
T
500 1C
log10 f fluid O2
24.1 bar
0.37 2.72 3.75 2.09 3.50
X CH4 X H2 X CO X CO2 =ðX CO2 þ X CH4 Þ max. log10 f O2
0.04 o103 o103 0.66 22.9 bar
acarbon H:O ratio gH2 O gCO2 gCH4 gH2 gCO
1.0 2.0 0.37 2.72 3.75 2.09 3.50
X H2 O X CO2 X CH4 X H2 X CO X CO2 =ðX CO2 þ X CH4 Þ H:O ratio
0.88 0.06 0.06 2.0 103 o103 0.50 2.01
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4.3. H2O interaction with graphite
References
Consider a H2O fluid that interacts with graphite in a rock at 3 kbar and 500 1C. What will be the equilibrium fluid composition? This problem can be solved with the worksheet COH-3. The fluid has an atomic H:O ratio of 2 as the only source for hydrogen and oxygen is H2O. The input and output results are shown in Table 3. Inspection of X CO , X H2 and the H:O ratio confirms that ignoring X CO and X H2 was acceptable.
Connolly, J.A.D., Cesare, B., 1993. C–O–H–S fluid compositions and oxygen fugacity in graphitic metapelites. Journal of Metamorphic Geology 11, 379–388. French, B.M., 1966. Some geological implications of equilibrium between graphite and a C–O–H gas at high temperatures and pressures. Reviews of Geophysics 4, 223–253. Huizenga, J.M., 2001. Thermodynamic modelling of C–O–H fluids. Lithos 55, 101–114. Larsen, R.B., 1993. ‘‘GEOFLUID’’: A Fortran 77 program to compute chemical properties of gas species in C–O–H fluids. Computers & Geosciences 19 (9), 1295–1320. Ohmoto, H., Kerrick, D., 1977. Devolatilization equilibria in graphitic systems. American Journal of Science 277, 1013–1044. Shi, P., Saxena, S.K., 1992. Thermodynamic modelling of the C–O–H–S fluid system. American Mineralogist 77, 1038–1049. Touret, J.L.R., Dietvorst, P., 1983. Fluid inclusions in highgrade anatectic metamorphites. Journal of the Geological Society of London 140, 635–649.
Acknowledgements Financial support was provided by the Rand Afrikaans University and the National Research Foundation of South Africa. The paper benefited from comments by Jay Barton. Reviews by Reiner Klemd, Jacques Touret and Fons van den Kerkhof are highly appreciated.
