- https://www.sciencedirect.com/journal/geothermics
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Research output: Contribution to journal › Journal article

Published

**A new theoretical calculation of the equilibrium constant and temperature for the carbon isotope exchange reaction between CH _{4} and CO_{2}.** / Chen, Xiangrui; Tao, Mingxin; Zhou, Zheng; Li, Dandan.

Research output: Contribution to journal › Journal article

Chen, X, Tao, M, Zhou, Z & Li, D 2019, 'A new theoretical calculation of the equilibrium constant and temperature for the carbon isotope exchange reaction between CH_{4} and CO_{2}', *Geothermics*, vol. 79, pp. 140-144. https://doi.org/10.1016/j.geothermics.2019.01.010

Chen, X., Tao, M., Zhou, Z., & Li, D. (2019). A new theoretical calculation of the equilibrium constant and temperature for the carbon isotope exchange reaction between CH_{4} and CO_{2}. *Geothermics*, *79*, 140-144. https://doi.org/10.1016/j.geothermics.2019.01.010

Chen X, Tao M, Zhou Z, Li D. A new theoretical calculation of the equilibrium constant and temperature for the carbon isotope exchange reaction between CH_{4} and CO_{2}. Geothermics. 2019 May 1;79:140-144. https://doi.org/10.1016/j.geothermics.2019.01.010

@article{58e80b8910a44813988376927119c93c,

title = "A new theoretical calculation of the equilibrium constant and temperature for the carbon isotope exchange reaction between CH4 and CO2",

abstract = "The equilibrium isotope fractionations among C–O–H gases in a variety of geological settings are commonly used as isotope geothermometers to evaluate the temperatures of geothermal fluids at depth, subsurface fluid-rock interactions, volcanic-hydrothermal systems and natural gas pools. However, due to limited experimental data and sophisticated theoretical calculations, applications of these geothermometers have been restricted. This study uses the carbon isotope exchange reaction between CH4 and CO2 as a case study to develop theoretical methods that can improve accuracies in calculating harmonic vibrational frequencies for CH4 and CO2, the equilibrium constants and temperatures for the carbon isotope exchange reaction between CH4 and CO2. Results suggest that the Bigeleisen-Mayer equation is sufficient to calculate the equilibrium constants and temperatures associated with the isotope exchange reaction between CH4 and CO2 with an accurate estimation of molecular harmonic vibrational frequencies. Calculations of the harmonic frequencies of CH4 and CO2 are achieved using the B3LYP density functional method with the 6-311+G(d) basis set, and the calculated harmonic frequencies are highly consistent with experimental values. The frequency correction factor is taken as 1.022 which puts the calculated fractionation factors in good agreement with experimental values. The calculated equilibrium constants are comparable to experimental data and a theoretical data set. They are highly consistent. In order to improve the accuracy and efficiency of solving for equilibrium temperatures using the Bigeleisen-Mayer equation, symbol operation and iterative algorithm in the MatLab software have been applied to compute the temperatures instead of using limited theoretical data sets or empirical fit equations. Our calculated results suggest that this algorithm can rapidly and conveniently yield relatively precise equilibrium temperatures. This algorithm can thus provide an important tool to evaluate whether the carbon isotope exchange reaction for CH4 and CO2 has attained equilibrium and estimate the formation temperature of CH4 and CO2 in high temperature geothermal systems.",

keywords = "Equilibrium fractionation, Geothermometers, Isotope exchange reaction, New algorithm, Temperature",

author = "Xiangrui Chen and Mingxin Tao and Zheng Zhou and Dandan Li",

note = "This is the author’s version of a work that was accepted for publication in Geothermics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Geothermics, 79, 2019 DOI: 10.1016/j.geothermics.2019.01.010",

year = "2019",

month = "5",

day = "1",

doi = "10.1016/j.geothermics.2019.01.010",

language = "English",

volume = "79",

pages = "140--144",

journal = "Geothermics",

issn = "0375-6505",

publisher = "Elsevier Ltd",

}

TY - JOUR

T1 - A new theoretical calculation of the equilibrium constant and temperature for the carbon isotope exchange reaction between CH4 and CO2

AU - Chen, Xiangrui

AU - Tao, Mingxin

AU - Zhou, Zheng

AU - Li, Dandan

N1 - This is the author’s version of a work that was accepted for publication in Geothermics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Geothermics, 79, 2019 DOI: 10.1016/j.geothermics.2019.01.010

PY - 2019/5/1

Y1 - 2019/5/1

N2 - The equilibrium isotope fractionations among C–O–H gases in a variety of geological settings are commonly used as isotope geothermometers to evaluate the temperatures of geothermal fluids at depth, subsurface fluid-rock interactions, volcanic-hydrothermal systems and natural gas pools. However, due to limited experimental data and sophisticated theoretical calculations, applications of these geothermometers have been restricted. This study uses the carbon isotope exchange reaction between CH4 and CO2 as a case study to develop theoretical methods that can improve accuracies in calculating harmonic vibrational frequencies for CH4 and CO2, the equilibrium constants and temperatures for the carbon isotope exchange reaction between CH4 and CO2. Results suggest that the Bigeleisen-Mayer equation is sufficient to calculate the equilibrium constants and temperatures associated with the isotope exchange reaction between CH4 and CO2 with an accurate estimation of molecular harmonic vibrational frequencies. Calculations of the harmonic frequencies of CH4 and CO2 are achieved using the B3LYP density functional method with the 6-311+G(d) basis set, and the calculated harmonic frequencies are highly consistent with experimental values. The frequency correction factor is taken as 1.022 which puts the calculated fractionation factors in good agreement with experimental values. The calculated equilibrium constants are comparable to experimental data and a theoretical data set. They are highly consistent. In order to improve the accuracy and efficiency of solving for equilibrium temperatures using the Bigeleisen-Mayer equation, symbol operation and iterative algorithm in the MatLab software have been applied to compute the temperatures instead of using limited theoretical data sets or empirical fit equations. Our calculated results suggest that this algorithm can rapidly and conveniently yield relatively precise equilibrium temperatures. This algorithm can thus provide an important tool to evaluate whether the carbon isotope exchange reaction for CH4 and CO2 has attained equilibrium and estimate the formation temperature of CH4 and CO2 in high temperature geothermal systems.

AB - The equilibrium isotope fractionations among C–O–H gases in a variety of geological settings are commonly used as isotope geothermometers to evaluate the temperatures of geothermal fluids at depth, subsurface fluid-rock interactions, volcanic-hydrothermal systems and natural gas pools. However, due to limited experimental data and sophisticated theoretical calculations, applications of these geothermometers have been restricted. This study uses the carbon isotope exchange reaction between CH4 and CO2 as a case study to develop theoretical methods that can improve accuracies in calculating harmonic vibrational frequencies for CH4 and CO2, the equilibrium constants and temperatures for the carbon isotope exchange reaction between CH4 and CO2. Results suggest that the Bigeleisen-Mayer equation is sufficient to calculate the equilibrium constants and temperatures associated with the isotope exchange reaction between CH4 and CO2 with an accurate estimation of molecular harmonic vibrational frequencies. Calculations of the harmonic frequencies of CH4 and CO2 are achieved using the B3LYP density functional method with the 6-311+G(d) basis set, and the calculated harmonic frequencies are highly consistent with experimental values. The frequency correction factor is taken as 1.022 which puts the calculated fractionation factors in good agreement with experimental values. The calculated equilibrium constants are comparable to experimental data and a theoretical data set. They are highly consistent. In order to improve the accuracy and efficiency of solving for equilibrium temperatures using the Bigeleisen-Mayer equation, symbol operation and iterative algorithm in the MatLab software have been applied to compute the temperatures instead of using limited theoretical data sets or empirical fit equations. Our calculated results suggest that this algorithm can rapidly and conveniently yield relatively precise equilibrium temperatures. This algorithm can thus provide an important tool to evaluate whether the carbon isotope exchange reaction for CH4 and CO2 has attained equilibrium and estimate the formation temperature of CH4 and CO2 in high temperature geothermal systems.

KW - Equilibrium fractionation

KW - Geothermometers

KW - Isotope exchange reaction

KW - New algorithm

KW - Temperature

U2 - 10.1016/j.geothermics.2019.01.010

DO - 10.1016/j.geothermics.2019.01.010

M3 - Journal article

AN - SCOPUS:85060515170

VL - 79

SP - 140

EP - 144

JO - Geothermics

JF - Geothermics

SN - 0375-6505

ER -