Machine learning methods for precise calculation of temperature drop during a throttling process

  • M. Farzaneh-GordEmail author
  • H. R. Rahbari
  • B. Mohseni-Gharyehsafa
  • A. Toikka
  • I. Zvereva


It is vital for the designers of the throttling facilities to predict natural gas temperature drop along a throttling valve exactly. Generally, direct prediction of the temperature drop is not possible even by employing equations of states. In this work, artificial neural network method, specifically multilayer perceptron, is utilized to predict the physical properties of natural gas. Then, the method is employed for direct calculation of the temperature drop along a throttling process. To train, validate and test the network, a large database of natural gas fields of Iran plus some experimental data (30,000 random datasets) are gathered from the literature. In addition, according to complexity of the multilayer perceptron model, a group method of data handling approach is used to simplify the major trained network. For the first time, an equation is developed for calculating natural gas temperature drop as a function of molecular weight as well as pressure drop. The results show that the multilayer perceptron and group method of data handling methods have the error R2 = 0.998 and R2 = 0.997, respectively. In addition, the results indicate that both developed machine learning methods present a high accuracy in the calculations over a wide range of gas mixtures and input properties ranges.


Throttling process Artificial neural network Multilayer perceptron Group method of data handling Natural gas temperature drop Natural gas compositions effects 

List of symbols


Activation function


Temperature (K)


Pressure (kPa)


Jacobian matrix




Mole fraction


Gas volume


Gas constant (J K−1 mol−1)


Helmholtz free energy


Reduced fluid mixture

\(\beta_{{{\text{v,ij}}}} ,\gamma_{{{\text{T,ij}}}} ,\beta_{{{\text{T,ij}}}} ,\gamma_{{{\text{T,ij}}}}\)

Binary mixtures parameters of GERG2008 EOS


Helmholtz free energy ideal part of gas mixture


Ideal dimensionless Helmholtz free energy of the component i of GERG2008 EOS

\(n_{\rm ij,k} ,d_{\rm ij,k} ,t_{\rm ij,k} ,\eta_{\rm ij,k} ,\varepsilon_{\rm ij,k} ,\beta_{\rm ij,k} ,\gamma_{\rm ij,k}\)

Parameters of GERG2008 EOS


Reduced Helmholtz free energy residual part




Inverse reduced temperature (1/K)


Generalized departure function

\(\omega_{\rm i}\)

Acentric factor of component i

\(a,b,a_{\rm i} ,b_{\rm i} ,a_{\rm ii} ,b_{\rm ii} ,a_{\rm ij} ,b_{\rm ij} ,k_{\rm ij} ,m_{\rm i} ,\alpha_{\rm i}\)

Mixing rules parameters of cubic EOSs


Number of data points


Correlation coefficient


Number of natural gas components, N = 21


Critical pressure for component i


Critical temperature for component i


Pseudo-critical pressure, \(P_{\text{pc}} = \sum\nolimits_{i = 1}^{N} P_{{{\text{c,i}}}} \times X_{\rm i}\)


Pseudo-critical temperature, \(T_{\text{pc}} = \sum\nolimits_{i = 1}^{N} T_{{{\text{c,i}}}} \times X_{\rm i}\)


Pseudo-reduced pressure, \(P_{\text{pr}} = \frac{P}{{P_{\text{pc}} }}\)


Pseudo-reduced temperature, \(T_{\text{pr}} = \frac{T}{{T_{\text{pc}} }}\)


Weights matrix



Critical point





Average absolute percent deviation


Artificial neural network


Equations of state


Group method of data handling


Helmholtz free energy




Natural gas


Multilayer perceptron



This research was partly funded by Iran National Science Foundation (INSF) under the contract no. 96004167 and Russian Foundation for Basic Research (RFBR Grant 17-58-560018). The second author would like to thank support from Ferdowsi University of Mashhad.

Supplementary material

10973_2019_9029_MOESM1_ESM.docx (25 kb)
Supplementary material 1 (DOCX 26 kb)


  1. 1.
    Cengel YA, Boles MA. Thermodyamics an engineering approach. New York: McGraw-Hill; 2002.Google Scholar
  2. 2.
    Sloan ED, Koh CA. Clathrate hydrates of natural gases, third edition. Clathrate Hydrates of Natural Gases. 2007.Google Scholar
  3. 3.
    Parvizi S, Arabkoohsar A, Farzaneh-Gord M. Natural gas compositions variation effect on capillary tube thermal mass flow meter performance. Flow Meas Instrum. 2016;50:229–36.CrossRefGoogle Scholar
  4. 4.
    Kunz O, Wagner W. The GERG-2008 wide-range equation of state for natural gases and other mixtures: an expansion of GERG-2004. J Chem Eng Data. 2012;57:3032–91.CrossRefGoogle Scholar
  5. 5.
    AGA8-DC92 EoS. Compressibility and super compressibility for natural gas and other hydrocarbon gases. Trans Meas Commun Rep 1992.Google Scholar
  6. 6.
    Ahmadi P, Chapoy A, Tohidi B. Density, speed of sound and derived thermodynamic properties of a synthetic natural gas. J Nat Gas Sci Eng. 2017;40:249–66.CrossRefGoogle Scholar
  7. 7.
    Dranchuk PM, Abou-Kassem JH. Calculation of Z factors for natural gases using equations of state. J Can Pet Technol. 1975;14:34–6.Google Scholar
  8. 8.
    Londono FE, Archer RA, Blasingame TA. Correlations for hydrocarbon-gas viscosity and gas density-validation and correlation of behavior using a large-scale database. SPE Reserv Eval Eng. 2005;8:561–72.CrossRefGoogle Scholar
  9. 9.
    AlQuraishi AA, Shokir EM. Viscosity and density correlations for hydrocarbon gases and pure and impure gas mixtures. Pet Sci Technol. 2009;27:1674–89.CrossRefGoogle Scholar
  10. 10.
    Farzaneh-Gord M, Rahbari HR. Developing novel correlations for calculating natural gas thermodynamic properties. Chem Process Eng: Inz Chem I Process. 2011;32:435–52.CrossRefGoogle Scholar
  11. 11.
    Farzaneh-Gord M, Farsiani M, Khosravi A, Arabkoohsar A, Dashti F. A novel method for calculating natural gas density based on Joule Thomson coefficient. J Nat Gas Sci Eng. 2015;26:1018–29.CrossRefGoogle Scholar
  12. 12.
    Farzaneh-Gord M, Arabkoohsar A, Koury RNN. Novel natural gas molecular weight calculator equation as a functional of only temperature, pressure and sound speed. J Nat Gas Sci Eng. 2016;30:195–204.CrossRefGoogle Scholar
  13. 13.
    Cao W, Wang X, Ming Z, Gao J. A review on neural networks with random weights. Neurocomputing. 2018;275:278–87.CrossRefGoogle Scholar
  14. 14.
    Gill J, Singh J, Ohunakin OS, Adelekan DS. Component-wise exergy analysis using adaptive neuro-fuzzy inference system in vapor compression refrigeration system. J Therm Anal Calorim. 2019;136:2111–23.CrossRefGoogle Scholar
  15. 15.
    Ramezanizadeh M, Alhuyi Nazari M, Ahmadi MH, Lorenzini G, Pop I. A review on the applications of intelligence methods in predicting thermal conductivity of nanofluids. J Therm Anal Calorim. 2019;138:827–43.CrossRefGoogle Scholar
  16. 16.
    Ahmadpour J, Ahmadi M, Javdani A. Hydrodesulfurization unit for natural gas condensate. J Therm Anal Calorim. 2019;135:1943–9.CrossRefGoogle Scholar
  17. 17.
    Ahmadi MH, Tatar A, Seifaddini P, Ghazvini M, Ghasempour R, Sheremet MA. Thermal conductivity and dynamic viscosity modeling of Fe2O3/water nanofluid by applying various connectionist approaches. Numer Heat Transf Part A Appl. 2018;74:1301–22.CrossRefGoogle Scholar
  18. 18.
    Baghban A, Pourfayaz F, Ahmadi MH, Kasaeian A, Pourkiaei SM, Lorenzini G. Connectionist intelligent model estimates of convective heat transfer coefficient of nanofluids in circular cross-sectional channels. J Therm Anal Calorim. 2018;132:1213–39.CrossRefGoogle Scholar
  19. 19.
    Maddah H, Aghayari R, Ahmadi MH, Rahimzadeh M, Ghasemi N. Prediction and modeling of MWCNT/Carbon (60/40)/SAE 10W 40/SAE 85W 90(50/50) nanofluid viscosity using artificial neural network (ANN) and self-organizing map (SOM). J Therm Anal Calorim. 2018;134:2275–86.CrossRefGoogle Scholar
  20. 20.
    Ramezanizadeh M, Ahmadi MA, Ahmadi MH, Alhuyi Nazari M. Rigorous smart model for predicting dynamic viscosity of Al2O3/water nanofluid. J Therm Anal Calorim. 2019;137:307–16.CrossRefGoogle Scholar
  21. 21.
    Ahmadi MH, Ahmadi MA, Nazari MA, Mahian O, Ghasempour R. A proposed model to predict thermal conductivity ratio of Al2O3/EG nanofluid by applying least squares support vector machine (LSSVM) and genetic algorithm as a connectionist approach. J Therm Anal Calorim. 2019;135:271–81.CrossRefGoogle Scholar
  22. 22.
    Bagheri H, Behrang M, Assareh E, Izadi M, Sheremet MA. Free convection of hybrid nanofluids in a C-shaped chamber under variable heat flux and magnetic field: simulation, sensitivity analysis, and artificial neural networks. Energies. 2019;12:2807.CrossRefGoogle Scholar
  23. 23.
    Moghadassi AR, Nikkholgh MR, Parvizian F, Hosseini SM. Estimation of thermophysical properties of dimethyl ether as a commercial refrigerant based on artificial neural networks. Expert Syst Appl. 2010;37:7755–61.CrossRefGoogle Scholar
  24. 24.
    Kamyab M, Sampaio JHB, Qanbari F, Eustes AW. Using artificial neural networks to estimate the z-factor for natural hydrocarbon gases. J Pet Sci Eng. 2010;73:248–57.CrossRefGoogle Scholar
  25. 25.
    Al-Anazi BD, Pazuki GR, Nikookar M, Al-Anazi AF. The prediction of the compressibility factor of sour and natural gas by an artificial neural network system. Pet Sci Technol. 2011;29:325–36.CrossRefGoogle Scholar
  26. 26.
    Sanjari E, Lay EN. Estimation of natural gas compressibility factors using artificial neural network approach. J Nat Gas Sci Eng. 2012;9:220–6.CrossRefGoogle Scholar
  27. 27.
    Mohamadi-Baghmolaei M, Azin R, Osfuri S, Mohamadi-Baghmolaei R, Zarei Z. Prediction of gas compressibility factor using intelligent models. Nat Gas Ind B. 2015;2:283–94.CrossRefGoogle Scholar
  28. 28.
    Azizi N, Behbahani R, Isazadeh MA. An efficient correlation for calculating compressibility factor of natural gases. J Nat Gas Chem. 2010;19:642–5.CrossRefGoogle Scholar
  29. 29.
    Mokhatab S, Poe WA. Handbook of natural gas transmission and processing. Burlington: Gulf Professional Publishing; 2012.Google Scholar
  30. 30.
    Farzaneh-Gord M, Arabkoohsar A, Deymi Dasht-bayaz M, Machado L, Koury RNN. Energy and exergy analysis of natural gas pressure reduction points equipped with solar heat and controllable heaters. Renew Energy. 2014;72:258–70.CrossRefGoogle Scholar
  31. 31.
    ISO 20765-2—Natural gas—Calculation of thermodynamic properties—part 2: single-Phase properties (gas, liquid, and dense fluid) for extended ranges of application. 2015.Google Scholar
  32. 32.
    Hagan T, Demuth HB, Beale MH. Neural Network Design. 2002.Google Scholar
  33. 33.
    Kondo T. GMDH neural network algorithm using the heuristic self-organization method and its application to the pattern identification problem. Proceedings of SICE Annu Conference 1998. p. 1143–8.Google Scholar
  34. 34.
    Ernst G, Wirbser H, Keil B, Jaeschke M. Flow-calorimetric results for the massic heat capacity cp and the Joule-Thomson coefficient of CH4 of (0.85 CH4 + 0.15 C2H6) and of a mixture similar to natural gas. J Chem Thermodyn. 2001;33:601–13.CrossRefGoogle Scholar
  35. 35.
    Day C, Stephan M, Oellrich LR. A new flow calorimeter for the measurement of the isobaric enthalpy increment and the isenthalpic Joule–Thomson effect. Results for methane and (methane + ethane). J Chem Thermodyn. 1997;29:949–71.CrossRefGoogle Scholar
  36. 36.
    National Iran Gas Company official website. Available from:

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringFerdowsi University of MashhadMashhadIran
  2. 2.Faculty of Mechanical EngineeringShahrood University of TechnologyShahroodIran
  3. 3.Department of Chemical Thermodynamics and Kinetics, Institute of ChemistrySaint Petersburg State UniversitySaint PetersburgRussia

Personalised recommendations