Skip to main content
SpringerLink
Log in

A New Method for Estimating Compressibility Factors of Natural Gases Based on Bender Equation of State

  • Conference paper
  • First Online:
Proceedings of the International Field Exploration and Development Conference 2021 (IFEDC 2021)

Part of the book series: Springer Series in Geomechanics and Geoengineering ((SSGG))

Included in the following conference series:

  • 75 Accesses

Abstract

It is highly significant to determine precisely and rapidly the compressibility factor (Z-factor) of natural gases, a commonly used parameter in many engineering calculations concerning oil and gas reservoir development, such as material balance analysis, estimation of oil/gas in place, gas flow theory, numerical reservoir simulation, pipeline design and so on. A new Z-factor correlation, based on the Bender E (1970) equation of state and corresponding state principle, is developed in this paper, and then a new method for estimating gas compressibility factors continuously is proposed with the nonlinear regression analysis technique. The calculated results of DPR, HY, DAK correlations, commonly used in oil and gas reservoir engineering at present, are compared with those of the new method presented here, using standard data of Z-factor modified by the paper. The results of comparative analysis, based on isotherm error statistics and error distribution maps, show that the new method boasts a wider scope of application and a smoother error distribution. For the standard data points of Z-factor within the general pressure-temperature range (i.e., 0.2 ≤ ppr ≤ 15 & 1.05 ≤ Tpr ≤ 3.0) and relatively high-temperature & high-pressure range (i.e., 15 ≤ ppr ≤ 30 & 1.4 ≤ Tpr ≤ 2.8), its average absolute error (AAE) is 0.305% and 0.065% respectively, distinctly superior to the above three methods. Those approaches for determining gas compressibility factors based on correlations avoid the shortcomings of experimental measurements and type curves which are inefficient, time-consuming, and incapable of continuous estimations. Thus, the new method is recommended to determine Z-factor. The pseudo-critical parameters (i.e., ppc & Tpc) should be corrected beforehand in the presence of non-negligible non-hydrocarbon impurities in the gas mixture. The new method for calculating gas compressibility factors based on Bender (1970) equation of state can estimate the Z value quickly, accurately, and continuously under various pressure and temperature conditions through a simple iteration procedure, helpful to provide valuable reference for relevant engineering applications by virtue of its desirable calculation accuracy.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Van der Waals, J.D.: Over de Continuiteit van den Gas-en Vloeistoftoestand. Leiden University, Leiden (1873)

    Google Scholar 

  2. Van der Waals, J.D.: The equation of state for gases and liquids. Nobel Lect. Phys., 254–265 (1910)

    Google Scholar 

  3. Giglio, F., Landolfi, G., Moro, A.: Integrable extended Van der Waals model. Physica D 333, 293–300 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  4. Pennini, F., Plastino, A.: Statistical complexity, virial expansion, and Van der Waals equation. Physica A 458, 239–247 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Wei, Z., Changming, X., Yongkai, Z.: Modified Van der Waals equation and law of corresponding states. Physica A 471, 295–300 (2017)

    Article  Google Scholar 

  6. Redlich, O., Kwong, J.N.S.: On the thermodynamics of solutions. V. An equation of state. Fugacities of gaseous solutions. Chem. Rev. 44(1), 233–244 (1949)

    Article  Google Scholar 

  7. Djordjević, B.D., Mihajlov, A.N., Grozdanić, D.K., et al.: Applicability of the Redlich-Kwong equation of state and its modifications to polar gases. Chem. Eng. Sci. 32(9), 1103–1107 (1977)

    Article  Google Scholar 

  8. Lielmezs, J., Howell, S.K., Campbell, H.D.: Modified Redlich-Kwong equation of state for saturated vapour-liquid equilibrium. Chem. Eng. Sci. 38(8), 1293–1301 (1983)

    Article  Google Scholar 

  9. Soave, G.: 20 years of Redlich-Kwong equation of state. Fluid Phase Equilib. 82, 345–359 (1993)

    Article  Google Scholar 

  10. Markocic, E., Knez, Z.: Redlich-Kwong equation of state for modelling the solubility of methane in water over a wide range of pressures and temperatures. Fluid Phase Equilib. 408, 108–114 (2016)

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Kadhem, O.M.A., Al-Sahhaf, T.A., Hamam, S.E.M.: Parameters of the modified Soave-Redlich-Kwong equation of state for some chlorofluorocarbons, hydrofluorocarbons and fluorocarbons. J. Fluorine Chem. 43(1), 87–104 (1989)

    Article  Google Scholar 

  13. 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 

  14. Janeček, J., Paricaud, P., Dicko, M., et al.: A generalized Kiselev crossover approach applied to Soave-Redlich-Kwong equation of state. Fluid Phase Equilib. 401, 16–26 (2015)

    Article  Google Scholar 

  15. Ghanbari, M., Ahmadi, M., Lashanizadegan, A.: A comparison between Peng-Robinson and Soave-Redlich-Kwong cubic equations of state from modification perspective. Cryogenics 84, 13–19 (2017)

    Article  Google Scholar 

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

    Article  Google Scholar 

  17. Li, C., Peng, Y., Dong, J., et al.: Prediction of the dew point pressure for gas condensate using a modified Peng-Robinson equation of state and a four-coefficient molar distribution function. J. Nat. Gas Sci. Eng. 27(2), 967–968 (2015)

    Article  Google Scholar 

  18. Kou, J., Sun, S.: Unconditionally stable methods for simulating multi-component two-phase interface models with Peng-Robinson equation of state and various boundary conditions. J. Comput. Appl. Math. 291, 158–182 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  19. Acqua, D.D., Terenzi, A., Leporini, M., et al.: A new tool for modelling the decompression behaviour of CO2 With impurities using the Peng-Robinson equation of state. Appl. Energy 206, 1432–1445 (2017)

    Article  Google Scholar 

  20. Lopez-Echeverry, J.S., Reif-Acherman, S., Araujo-Lopez, E.: Peng-Robinson equation of state: 40 years through cubics. Fluid Phase Equilib. 447, 39–71 (2017)

    Article  Google Scholar 

  21. Kamerlingh Onnes, H.K.: The equation of state of gases and liquids as a power series. Archives Néelandaises 6, 874–888 (1901)

    MATH  Google Scholar 

  22. Beattie, J.A., Bridgeman, O.C.: A new equation of state for fluids. Proc. Am. Acad. Arts Sci. 63(5), 229–308 (1928)

    Article  Google Scholar 

  23. Benedict, M., Webb, G.B., Rubin, L.C.: An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures: I. Methane, ethane, propane and n-butane. J. Chem. Phys. 8(4), 334–345 (1940)

    Article  Google Scholar 

  24. Benedict, M., Webb, G.B., Rubin, L.C.: An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures: II. Mixtures of methane, ethane, propane, and n-butane. J. Chem. Phys. 10, 747–758 (1942)

    Article  Google Scholar 

  25. Orye, R.V.: Prediction and correlation of phase equilibria and thermal properties with the BWR equation of state. Ind. Eng. Chem. Process. Des. Dev. 8(4), 579–588 (1969)

    Article  Google Scholar 

  26. Strobridge, T.R.: The thermodynamic properties of nitrogen from 64 to 300 *K between 0.1 and 200 atmospheres, NBS Technical Note No. 129, pp. 1–16. The Office of Technical Services, US Department of Commerce, Washington D.C. (1962)

    Google Scholar 

  27. Strobridge, T.R.: The thermodynamic properties of nitrogen from 114 to 540 R between 1.0 and 3000 psia supplement A (British Units), pp. 1–16. US Department of Commerce, National Bureau of Standards, Washington D.C. (1963)

    Google Scholar 

  28. Vennix, A.J., Kobayashi, R.: An equation of state for methane in the gas and liquid phases. AIChE J. 15(6), 926–931 (1969)

    Article  Google Scholar 

  29. Sandler, S.I.: Models for Thermodynamic and Phase Equilibria Calculations, p. 137. Marcel Dekker Inc., New York (1994)

    Google Scholar 

  30. Hall, K.R., Yarborough, L.: A new equation of state for Z-factor calculations. Oil Gas J. 71(7), 82–85, 90, 92 (1973)

    Google Scholar 

  31. Carnahan, N.F., Starling, K.E.: Equation of state for nonattracting rigid spheres. J. Chem. Phys. 51(2), 635–636 (1969)

    Article  Google Scholar 

  32. Morsy, T.E.: Extended Benedict-Webb-Rubin equation of state. Application to eight fluorine compounds. J. Chem. Eng. Data 15(2), 256–265 (1970)

    Article  Google Scholar 

  33. Starling, K.E., Powers, J.E.: Enthalpy of mixtures by modified BWR equation. Ind. Eng. Chem. Fundam. 9(4), 531–537 (1970)

    Article  Google Scholar 

  34. Cox, K.W., Bono, J.L., Kwok, Y.C., et al.: Multiproperty analysis. Modified BWR equation for methane from PVT and enthalpy data. Ind. Eng. Chem. Fundam. 10(2), 245–250 (1971)

    Article  Google Scholar 

  35. McFee, D.G., Mueller, K.H., Lielmezs, J.: Comparison of Benedict-Webb-Rubin, starling and Lee-Kesler equations of state for use in P-V-T calculations. Thermochim. Acta 54(1–2), 9–25 (1982)

    Article  Google Scholar 

  36. Lielmezs, J.: Comparison of Benedict-Webb-Rubin and starling equations of state for use in P-V-T calculations of binary mixtures. Thermochim. Acta 152(2), 341–358 (1989)

    Article  Google Scholar 

  37. Modisette, J.L.: Equation of state tutorial. In: Pipeline Simulation Interest Group Annual Meeting, Savannah, pp. 1–21 (2000)

    Google Scholar 

  38. Jacobsen, R.T., Stewart, R.B.: Thermodynamic properties of nitrogen including liquid and vapor phases from 63 K to 2000 K with pressures to 10,000 bar. J. Phys. Chem. Ref. Data 2(4), 757–922 (1973)

    Article  Google Scholar 

  39. Lee, B.I., Kesler, M.G.: A generalized thermodynamic correlation based on three-parameter corresponding states. AIChE J. 21(3), 510–527 (1975)

    Article  Google Scholar 

  40. Dranchuk, P.M., Purvis, R.A., Robinson, D.B.: Computer calculation of natural gas compressibility factors using the standing and Katz correlation. In: Petroleum Society of Canada Annual Technical Meeting, Edmonton (1973)

    Google Scholar 

  41. Standing, M.B., Katz, D.L.: Density of natural gases. Trans. AIME 146(1), 140–149 (1942)

    Article  Google Scholar 

  42. Dranchuk, P.M., Abou-Kassem, J.H.: Calculation of Z factors for natural gases using equations of state. J. Can. Pet. Technol. 14(3), 34–36 (1975)

    Article  Google Scholar 

  43. Takacs, G.: Comparisons made for computer Z-factor calculations. Oil Gas J. 74(51), 64–66 (1976)

    Google Scholar 

  44. Takacs, G.: Comparing methods for calculating Z-factor. Oil Gas J. 87(20), 43–46 (1989)

    Google Scholar 

  45. Tiab, D.: Gas Reservoir Engineering, pp. II.37–II.41. University of Oklahoma, Oklahoma (2000)

    Google Scholar 

  46. Li, S.L.: Natural Gas Engineering, 2nd edn., pp. 31–33. Petroleum Industry Press, Beijing (2008)

    Google Scholar 

  47. Zhang, M.L., Hu, J.G., Qu, X.F.: Evaluating the methods of calculating gas deviation factor by use of state equation. Nat. Gas. Ind. 23(2), 69–71 (2003)

    Google Scholar 

  48. Bender, E.: Equations of state exactly representing the phase behavior of pure substances. In: Proceedings of the 5th Symposium on Thermophysical Properties, pp. 227–235. American Society of Mechanical Engineers, New York (1970)

    Google Scholar 

  49. Bender, E.: An equation of state for predicting vapour-liquid equilibria of the system N2-Ar-O2. Cryogenics 13(1), 11–18 (1973)

    Article  Google Scholar 

  50. Bender, E.: Equations of state for ethylene and propylene. Cryogenics 15(11), 667–673 (1975)

    Article  Google Scholar 

  51. Bühner, K., Maurer, G., Bender, E.: Pressure-enthalpy diagrams for methane, ethane, propane, ethylene and propylene. Cryogenics 21(3), 157–164 (1981)

    Article  Google Scholar 

  52. Mohr, P.J., Newell, D.B., Taylor, B.N.: CODATA recommended values of the fundamental physical constants: 2014. J. Phys. Chem. Ref. Data 45(4), 043102-1–043102-74 (2016)

    Google Scholar 

  53. Mohr, P.J., Newell, D.B., Taylor, B.N.: CODATA recommended values of the fundamental physical constants: 2014. Rev. Mod. Phys. 88(3), 035009-1–035009-73 (2016)

    Google Scholar 

  54. Poettmann, F.H., Carpenter, P.G.: The multiphase flow of gas, oil, and water through vertical flow strings with application to the design of gas-lift installations. Drill. Prod. Pract. API-52-257, 280–291 (1952)

    Google Scholar 

  55. Katz, D.L., Cornell, D., Vary, J.A., et al.: Handbook of Natural Gas Engineering, pp. 106–107, 710–717. McGraw-Hill Book Company, New York (1959)

    Google Scholar 

  56. Smith, R.V.: Practical Natural Gas Engineering, 2nd edn., pp. 255–277. Pennwell Publishing Company, Tulsa (1990)

    Google Scholar 

  57. Zhang, L.X., Guo, C.Q.: A calculation method for Z-factor of natural gas based on BWRS equation. Oil Drill. Prod. Technol. 40(6), 775–781 (2018)

    Google Scholar 

  58. Zhang, L.X., Guo, C.Q.: A new method for determining the natural gas compressibility factor. Chem. Eng. Oil Gas 48(1), 91–98 (2019)

    Google Scholar 

  59. Liu, H.Y.: Computational Methods, pp. 15–16. Beijing University of Posts and Telecommunications Press, Beijing (2010)

    Google Scholar 

Download references

Acknowledgments

The project is supported by the National Science and Technology Major Project of China (Grant No. 2016ZX05015002 & 2017ZX05030003). The authors of the paper would like to express heartfelt gratitude to the Department of Middle East E&P and Department of Asia-Pacific E&P, Research Institute of Petroleum Exploration and Development (RIPED), PetroChina.

Author information

Authors and Affiliations

  1. Research Institute of Petroleum Exploration and Development, PetroChina, Beijing, China

    Li-xia Zhang, Yong Li, Xin-min Song, Dan-dan Hu, Yang Yu & Ze-qi Zhao

  2. Xi’an Shiyou University, Xi’an, China

    Ming-xian Wang

  3. Bohai Oilfield Research Institute, Tianjin Branch of CNOOC (China) Limited, Tianjin, China

    Ying-xu He

  4. CNPC Bohai Drilling Engineering Company Limited, Tianjin, China

    Chen-chao Liu

Authors
  1. Li-xia Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xin-min Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ming-xian Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Dan-dan Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ying-xu He
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yang Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Ze-qi Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Chen-chao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li-xia Zhang .

Editor information

Editors and Affiliations

  1. College of Petroleum Engineering, Xi'an Shiyou University, Xi’an, Shaanxi, China

    Jia'en Lin

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Zhang, Lx. et al. (2022). A New Method for Estimating Compressibility Factors of Natural Gases Based on Bender Equation of State. In: Lin, J. (eds) Proceedings of the International Field Exploration and Development Conference 2021. IFEDC 2021. Springer Series in Geomechanics and Geoengineering. Springer, Singapore. https://doi.org/10.1007/978-981-19-2149-0_196

Download citation

Publish with us

Policies and ethics

Search

Navigation