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

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Abstract

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.

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Abbreviations

f :

Activation function

T :

Temperature (K)

P :

Pressure (kPa)

J :

Jacobian matrix

Z :

Z-factor

X :

Mole fraction

v :

Gas volume

R :

Gas constant (J K−1 mol−1)

α :

Helmholtz free energy

δ :

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

\(\alpha^{0}\) :

Helmholtz free energy ideal part of gas mixture

\(\alpha_{0i}^{0}\) :

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

\(\alpha^{\text{r}}\) :

Reduced Helmholtz free energy residual part

\(\rho\) :

Density

\(\tau\) :

Inverse reduced temperature (1/K)

\(\alpha_{\text{or}}^{\text{r}}\) :

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

n :

Number of data points

R :

Correlation coefficient

N :

Number of natural gas components, N = 21

\(P_{{{\text{c,i}}}}\) :

Critical pressure for component i

\(T_{{{\text{c,i}}}}\) :

Critical temperature for component i

\(P_{\text{pc}}\) :

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

\(T_{\text{pc}}\) :

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

\(P_{\text{pr}}\) :

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

\(T_{\text{pr}}\) :

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

W :

Weights matrix

c:

Critical point

r:

Reduced

AAPD:

Average absolute percent deviation

ANN:

Artificial neural network

EOS:

Equations of state

GMDH:

Group method of data handling

HFE:

Helmholtz free energy

JT:

Joule–Thomson

NG:

Natural gas

MLP:

Multilayer perceptron

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Acknowledgments

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.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    M. Farzaneh-Gord & H. R. Rahbari

  2. Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

    B. Mohseni-Gharyehsafa

  3. Department of Chemical Thermodynamics and Kinetics, Institute of Chemistry, Saint Petersburg State University, Saint Petersburg, Russia

    A. Toikka & I. Zvereva

Authors
  1. M. Farzaneh-Gord
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  2. H. R. Rahbari
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  3. B. Mohseni-Gharyehsafa
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Correspondence to M. Farzaneh-Gord.

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Farzaneh-Gord, M., Rahbari, H.R., Mohseni-Gharyehsafa, B. et al. Machine learning methods for precise calculation of temperature drop during a throttling process. J Therm Anal Calorim 140, 2765–2778 (2020). https://doi.org/10.1007/s10973-019-09029-3

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