Use of artificial neural networks for calculating derived thermodynamic quantities from volumetric property data

doi:10.1016/S0378-3812(03)00172-9

Fluid Phase Equilibria

Volume 210, Issue 2, 15 August 2003, Pages 247-255

https://doi.org/10.1016/S0378-3812(03)00172-9 Get rights and content

Abstract

Thermodynamic and transport property data on environmentally acceptable refrigerant fluids are of the utmost interest for the refrigeration industry and, in particular, for designing and optimising refrigeration equipment: heat exchangers and compressors. Up to now, the simultaneous representation of vapour–liquid equilibria (VLE) and pressure–volume–temperature (PVT) data is not satisfactory enough with respect to experimental accuracies. New models are then highly required. Therefore, an effort has been made to develop an alternative to a classical equation of state. This work deals with the potential application of artificial neural networks to represent PVT data within their experimental uncertainty. The second aim of the work is to obtain, by numerical derivatives, other properties such as enthalpies, entropies, heat capacities, expansion coefficients, speed of sounds, etc. Tests presented here were performed on data corresponding to six refrigerants from 240 to 340 K at pressures up to 20 MPa.

Introduction

Due to severe international regulations (Montreal Protocol (1987), Kyoto Protocol (1997), etc.), on the use of chloro-fluoro-carbons (CFC), it is absolutely necessary to find and select efficient and environmentally acceptable substitutes with zero ozone depletion potential. For these purposes, there is an increasing need of new thermodynamic data not only in the field of refrigeration but also in the insulation industry [1], [2]. The scientific community is well aware about this environment problem and meetings are held to share knowledge between academy, industry and governments [3]. Experimental data are essential during the screening step, to compare efficiencies of the candidates. Fortunately (great choice) and unfortunately (a lot of measurements required), the number of chemical substances proposed to replace CFCs is very high, implying prohibitive experimental work.

The modelling within an acceptable uncertainty of pressure–volume–temperature (PVT) data by conventional thermodynamic models requires the use of many adjusted parameters. The adjustment of these parameters is tedious and it is never certain to get the best set of parameters due to problem of local minima. The development of numerical tools, such as neural networks, able to represent, within the experimental uncertainties, refrigerant properties is highly required. In this paper, we have designed a neural network model not only to represent PVT properties but also to accurately predict thermal and transport properties.

Section snippets

Neural network models

Artificial neural network (ANN) models have large numbers of computational units connected in a massively parallel structure. Neural networks do not need an explicit formulation of the mathematical or physical relationships of the handled problem. They act as a means to introduce scaled data to the network. The data from the input neurones are propagated through the network via interconnections, scalar weights being associated to each connection [4].

An important aspect of a neural network is

Design of the neural models

In this work, and for both vapour and liquid phases, the neural models (see Fig. 1) are devoted to the computation of the compressibility factor (Z) (output neurone) for the vapour phase and the density (ρ) for the liquid phase, in function of temperature (T) and pressure (P) (input neurones) of the input layer. In this way two neural network models are elaborated for vapour and liquid phases separately. In Fig. 1, ∑f is the summation of all transfer functions.

In order to improve the

Derived properties calculations

The objective of this work consists in the optimal elaboration (using a Levenberg–Marquardt algorithm) of neural models for the prediction of compressibility factor (Z) or density (ρ) in desired temperature and pressure ranges. The problem of local minima is solved by numerous initialisations using random initial weight values. The derived properties such as enthalpy (H), entropy (S), and expansion coefficients α and χ are calculated from Z as a function of temperature and pressure through

Results

The refrigerant compounds studied in this work are R125, R143a, R32, R290, R134a and R227ea. An example of three-dimensional representations of calculated thermodynamic properties (Z, H, S and C_p) is displayed in Fig. 2.

With respect to REFPROP 6.0, we can note by examining Table 2 that the quality of representation of the compressibility factors (Z) or the density (ρ) through neural network models is very good, for all of the studied refrigerant compounds for both vapour and liquid phases

Conclusions

In this work, artificial neural network models have been used to represent pressure–temperature–volume (PVT) data of refrigerants from 240 to 340 K and up to 20 MPa. Results on six refrigerant compounds have been presented (R125, R143a, R32, R290, R134a and R227ea).

Neural network parameters are obtained through a learning step, the compressibility factors obtained from REFPROP are considered as the neural model target. Very good results are obtained concerning Z and ρ. The relative average

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Use of artificial neural networks for calculating derived thermodynamic quantities from volumetric property data

Abstract

Introduction

Section snippets

Neural network models

Design of the neural models

Derived properties calculations

Results

Conclusions

Fluid Phase Equilib.

Fluid Phase Equilib.

Fluid Phase Equilib.

Int. J. Thermophys.