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Application of Cubic EOS for Shale Gas Adsorption Study

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Proceedings of the International Field Exploration and Development Conference 2020 (IFEDC 2020)

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Abstract

Cubic equation of state (EOS) is vital to density calculation in shale gas experimental and theoretical adsorption studies. However, plenty of cubic EOSs have been given and their accuracies on density calculation were still uncertain. Therefore, it is necessary to analyze the applications of different types of cubic EOSs on shale gas adsorption study, according to the density calculation accuracy. Seven Peng-Robinson (PR) type EOSs and eight Soave-Redlich-Kwong (SRK) type EOSs were selected due to their application effect on shale gas. With grand canonical Monte Carlo (GCMC) density data and widely recognized Setzmann-Wagner (SW) EOS, these 15 cubic EOSs were compared and analyzed. Furthermore, cubic and SW EOSs were applied to simplified local density (SLD) model, and the effect of calculated density on adsorption simulation was investigated with GCMC adsorption data. Generally, the densities from PR type EOSs are larger than GCMC data. The SRK type EOS modified by Ghanbari and Check (SRKGC) is as accurate as SW EOS with a small error, 0.6%. The SRK type EOS modified by Mørch et al. has the largest error, which is 7.99%, and is inappropriate to shale gas study. The effect of density accuracy on adsorption simulation could not be neglected. With larger bulk density, absolute adsorption value would get larger, while excess adsorption value would be smaller. This research could be a reference to experiment, molecular simulation, density functional theory and SLD methods for shale gas adsorption study, and the calculation accuracy could be improved effectively.

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References

  1. Adisa, O.O., Cox, B.J., Hill, J.M.: Methane storage in molecular nanostructures. Nanoscale 4(11), 3295–3307 (2012)

    Article  Google Scholar 

  2. Qi, R., Ning, Z., Wang, Q., et al.: Sorption of methane, carbon dioxide, and their mixtures on shales from Sichuan basin China. Energy Fuels 32(3), 2926–2940 (2018)

    Article  Google Scholar 

  3. Chen, L., Zuo, L., Jiang, Z., et al.: Mechanisms of shale gas adsorption: evidence from thermodynamics and kinetics study of methane adsorption on shale. Chem. Eng. J. 361, 559–570 (2019)

    Article  Google Scholar 

  4. Gusev, V.Y., O’Brien, J.A., Seaton, N.A.: A self-consistent method for characterization of activated carbons using supercritical adsorption and grand canonical Monte Carlo simulations. Langmuir 13(10), 2815–2821 (1997)

    Article  Google Scholar 

  5. Kowalczyk, P., Tanaka, H., Kaneko, K., Terzyk, A.P., Do, D.D.: Grand canonical Monte Carlo simulation study of methane adsorption at an open graphite surface and in slitlike carbon pores at 273 K. Langmuir 21(12), 5639–5646 (2005)

    Article  Google Scholar 

  6. Tanaka, H., El-Merraoui, M., Steele, W.A., Kaneko, K.: Methane adsorption on single-walled carbon nanotube: a density functional theory model. Chem. Phys. Lett. 352(5–6), 334–341 (2002)

    Article  Google Scholar 

  7. Pang, Y., Tian, Y., Soliman, M.Y., Shen, Y.: Experimental measurement and analytical estimation of methane absorption in shale kerogen. Fuel 240, 192–205 (2019)

    Article  Google Scholar 

  8. Fairen-Jimenez, D., Colón, Y.J., Farha, O.K., Bae, Y.-S., Hupp, J.T., Snurr, R.Q.: Understanding excess uptake maxima for hydrogen adsorption isotherms in frameworks with rht topology. Chem. Commun. 48(85), 10496–10498 (2012)

    Google Scholar 

  9. Huang, L., Xiang, Z., Cao, D.: A porous diamond carbon framework: a new carbon allotrope with extremely high gas adsorption and mechanical properties. J. Mater. Chem. 1(12), 3851–3855 (2013)

    Google Scholar 

  10. Blanco, A.G., de Oliveira, J.A., López, R., et al.: A study of the pore size distribution for activated carbon monoliths and their relationship with the storage of methane and hydrogen. Colloids Surf. Physicochem. Eng. Aspects 357(1–3), 74–83 (2010)

    Article  Google Scholar 

  11. Butz, J., Zimmermann, P., Enders, S.: Impact of the equation of state on calculated adsorption isotherm using DFT. Chem. Eng. Sci. 171, 513–519 (2017)

    Article  Google Scholar 

  12. Delavar, M., Ghoreyshi, A.A., Jahanshahi, M., Khalili, S., Nabian, N.: Equilibria and kinetics of natural gas adsorption on multi-walled carbon nanotube material. RSC Adv. 2(10), 4490–4497 (2012)

    Google Scholar 

  13. Calleja, G., Coto, B., Morales-Cas, A.J.A.: Adsorption energy distribution in activated carbon from grand canonical Monte Carlo calculation. Appl. Surf. Sci. 252(12), 4345–4352 (2006)

    Google Scholar 

  14. Setzmann, U., Wagner, W.: A new equation of state and tables of thermodynamic properties for methane covering the range from the melting line to 625 K at pressures up to 100 MPa. J. Phys. Chem. Ref. Data 20(6), 1061–1155 (1991)

    Article  Google Scholar 

  15. Ekundayo, J., Rezaee, R.: Effect of equation of states on high pressure volumetric measurements of methane-coal sorption isotherms-part 1: volumes of free space and methane adsorption isotherms. Energy Fuels, 33(2), 1029–1036 (2019)

    Google Scholar 

  16. Qi, R., Ning, Z., Wang, Q., et al.: Measurements and modeling of high-pressure adsorption of CH4 and CO2 on shales. Fuel 242, 728–743 (2019)

    Article  Google Scholar 

  17. Chen, G., Lu, S., Zhang, J., et al.: Keys to linking GCMC simulations and shale gas adsorption experiments. Fuel 199, 14–21 (2017)

    Article  Google Scholar 

  18. Xiong, J., Liu, X., Liang, L., Zeng, Q.: Methane adsorption on carbon models of the organic matter of organic-rich shales. Energy Fuels 31(2), 1489–1501 (2017)

    Article  Google Scholar 

  19. Mohammad, S.A., Chen, J.S., Robinson Jr., R.L., Gasem, K.A.: Generalized simplified local-density/Peng−Robinson model for adsorption of pure and mixed gases on coals. Energy Fuels 23(12), 6259–6271 (2009)

    Article  Google Scholar 

  20. Chareonsuppanimit, P., Mohammad, S.A., Robinson Jr., R.L., Gasem, K.A.: High-pressure adsorption of gases on shales: measurements and modeling. Int. J. Coal Geol. 95, 34–46 (2012)

    Article  Google Scholar 

  21. Chareonsuppanimit, P., Mohammad, S.A., Robinson Jr., R.L., Gasem, K.A.: Modeling gas-adsorption-induced swelling and permeability changes in coals. Int. J. Coal Geol. 121, 98–109 (2014)

    Article  Google Scholar 

  22. Chen, M., Kang, Y., Zhang, T., Li, X., Wu, K., Chen, Z.: Methane adsorption behavior on shale matrix at in-situ pressure and temperature conditions: measurement and modeling. Fuel 228, 39–49 (2018)

    Article  Google Scholar 

  23. Jiang, Z., Zhao, L., Zhang, D.: Study of adsorption behavior in shale reservoirs under high pressure. J. Natl. Gas Sci. Eng. 49, 275–285 (2018)

    Article  Google Scholar 

  24. Hasanzadeh, M., Alavi, F., Feyzi, F., Dehghani, M.R.: Simplified local density model for adsorption of pure gases on activated carbon using Sutherland and Kihara potentials. Microporous Mesoporous Mater. 136(1–3), 1–9 (2010)

    Article  Google Scholar 

  25. Fitzgerald, J.E., Robinson, R.L., Gasem, K.A.: Modeling high-pressure adsorption of gas mixtures on activated carbon and coal using a simplified local-density model. Langmuir 22(23), 9610–9618 (2006)

    Article  Google Scholar 

  26. Peng, D.-Y., Robinson, D.B.: A new two-constant equation of state. Ind. Eng. Chem. Fundam. 15(1), 59–64 (1976)

    Article  Google Scholar 

  27. Gasem, K., Gao, W., Pan, Z., Robinson Jr., R.: A modified temperature dependence for the Peng-Robinson equation of state. Fluid Phase Equilib. 181(1–2), 113–125 (2001)

    Article  Google Scholar 

  28. Mathias, P.M., Copeman, T.W.: Extension of the Peng-Robinson equation of state to complex mixtures: evaluation of the various forms of the local composition concept. Fluid Phase Equilib. 13, 91–108 (1983)

    Article  Google Scholar 

  29. Mathias, P.M.: A versatile phase equilibrium equation of state. Ind. Eng. Chem. Process Des. Dev. 22(3), 385–391 (1983)

    Article  Google Scholar 

  30. Stryjek, R., Vera, J.: PRSV: an improved Peng–Robinson equation of state for pure compounds and mixtures. Can. J. Chem. Eng. 64(2), 323–333 (1986)

    Article  Google Scholar 

  31. Twu, C.H., Coon, J.E., Cunningham, J.R.: A new generalized alpha function for a cubic equation of state part 2 Redlich-Kwong equation. Fluid Phase Equilib. 105(1), 61–69 (1995)

    Article  Google Scholar 

  32. Li, H., Yang, D.: Modified α function for the Peng−Robinson equation of state to improve the vapor pressure prediction of non-hydrocarbon and hydrocarbon compounds. Energy Fuels 25(1), 215–223 (2010)

    Article  Google Scholar 

  33. Soave, G.: Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci. 27(6), 1197–1203 (1972)

    Article  Google Scholar 

  34. Soave, G.: Application of equations of state and the theory of group solutions to phase equilibrium prediction. Fluid Phase Equilib. 87(1), 23–35 (1993)

    Article  Google Scholar 

  35. Nasrifar, K., Bolland, O.: Square-well potential and a new α function for the Soave−Redlich−Kwong equation of state. Ind. Eng. Chem. Res. 43(21), 6901–6909 (2004)

    Article  Google Scholar 

  36. Ghanbari, M., Check, G.R.: New super-critical cohesion parameters for Soave–Redlich–Kwong equation of state by fitting to the Joule-Thomson inversion curve. J. Supercrit. Fluids 62, 65–72 (2012)

    Article  Google Scholar 

  37. Mørch, Ø., Nasrifar, K., Bolland, O., Solbraa, E., Fredheim, A., Gjertsen, L.: Measurement and modeling of hydrocarbon dew points for five synthetic natural gas mixtures. Fluid Phase Equilib. 239(2), 138–145 (2006)

    Article  Google Scholar 

  38. Souahi, F., Sator, S., Albane, S.A., Kies, F.K., Chitour, C.E.: Development of a new form for the alpha function of the Redlich-Kwong cubic equation of state. Fluid Phase Equilib. 153(1), 73–80 (1998)

    Article  Google Scholar 

  39. Wu, X., Ning, Z., Qi, R., Wang, Q., Huang, L.J.E.: Pore characterization and inner adsorption mechanism investigation for methane in organic and inorganic matters of shale. Fuels 34(4), 4106–4115 (2020)

    Article  Google Scholar 

  40. Lee, L.L.: Molecular Thermodynamics of Nonideal Fluids. Butterworth-Heinemann, UK (2016)

    Google Scholar 

  41. Subramanian, R., Lira, C.T.: An engineering model for adsorption of gases onto various media. Fundam. Adsorpt. Springer, pp. 873–880 (1996)

    Google Scholar 

  42. Fitzgerald, J., Sudibandriyo, M., Pan, Z., Robinson Jr., R., Gasem, K.: Modeling the adsorption of pure gases on coals with the SLD model. Carbon 41(12), 2203–2216 (2003)

    Article  Google Scholar 

  43. Wu, X.-J., Ning, Z.-F., Cheng, Z.-L., et al.: Simplified local density model for gas adsorption in cylindrical carbon pores. Appl. Surf. Sci. 491, 335–349 (2019)

    Google Scholar 

  44. Graboski, M.S., Daubert, T.E.: A modified Soave equation of state for phase equilibrium calculations. 1. hydrocarbon systems. Ind. Eng. Chem. Process Des. Dev. 17(4), 443–448 (1978)

    Google Scholar 

  45. Chen, X., McEnaney, B., Mays, T., Alcaniz-Monge, J., Linares-Solano, A.: Theoretical and experimental studies of methane adsorption on microporous carbons. Carbon 35(9), 1251–1258 (1997)

    Article  Google Scholar 

Download references

Acknowledgments

The project is supported by National Natural Science Foundation (Number 51774298, 51974330 and U19B6003-03-04).

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Appendix A. Comparison and Discussion

Appendix A. Comparison and Discussion

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Wu, Xj., Ning, Zf., Zhang, Wt., Wang, Q., Huang, L., Lyu, F. (2021). Application of Cubic EOS for Shale Gas Adsorption Study. In: Lin, J. (eds) Proceedings of the International Field Exploration and Development Conference 2020. IFEDC 2020. Springer Series in Geomechanics and Geoengineering. Springer, Singapore. https://doi.org/10.1007/978-981-16-0761-5_300

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  • DOI: https://doi.org/10.1007/978-981-16-0761-5_300

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