# Preference-driven yield-and-quality optimization for high-sulfur gas sweetening process by extreme learning machine model

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## Abstract

Yield and quality, as the two most important output variables of high-sulfur gas (HSG) sweetening process, are affected by the operating parameters. The HSG sweetening process involves more than ten operating parameters, so the relationship between the parameters and output variables is complex, non-linear and strong coupling. This paper tries to use data mining methods to explore this relationship and apply it to optimize the yield and quality. First, a ten (inputs)-to-three (outputs) model is established by extreme learning machine (ELM). Then, a preference-driven multi-objective optimization algorithm is used to maximize the yield while ensuring that the concentration of carbon dioxide (CO_{2}) and the concentration of hydrogen sulfide (H_{2}S) in the treated gas are close to but not exceeding 3% and 4 ppm respectively. The proposed method is validated in a HSG purification plant in southwest China. A set of 3044 production data is collected and randomly divided into 80 and 20% for training and testing. The results show that the established ELM model is in good agreement with the actual operation data. The maximum deviation of mean square error (MSE), mean absolute error (MAE) and average absolute deviation percent (AAD %) of the predictions in three scenarios are 0.2047, 0.3177 and 7.91% respectively. Moreover, the optimization based on the obtained ELM model is also validated. In particular, the H_{2}S concentration and CO_{2} concentration in the treated gas are significantly higher than those before optimization, but have not exceeding the limits. Thus, the consumptions of energy and amine solvents decreased, while the yield increased.

## Keywords

Yield-and-quality optimization High-sulfur gas sweetening process Extreme learning machine Preference-driven multi-objective optimization Data mining## Abbreviations

- HSG
High-sulfur gas

- ELM
Extreme learning machine

- MSE
Mean square error

- MAE
Mean absolute error

- AAD%
Average absolute deviation percent

- MDEA
N-methyldiethanolamine

- AI
Artificial intelligence

- NSGA-II
Non-dominated sorting genetic algorithm-II

- NNs
Neural networks

- SVM
Support vector machine

- SLFNs
Single-hidden layer feedforward neural networks

- PSO
Particle swarm optimization

- PP
Physical programming

- HD
Highly desirable

- D
Desirable

- T
Tolerable

- U
Undesirable

- HU
Highly undesirable

## List of symbols

- \(x_{i} ,t_{i}\)
Arbitrary distinct samples

- \(\beta_{i}\)
Output weight of the

*i*th hidden layer node connected with the output neuron- \(\omega_{i}\)
Output weight of the input neuron connected with the

*i*th hidden layer node- \(b_{i}\)
Bias of the

*i*th hidden layer node- \(o_{j}\)
Output value corresponding to the

*j*th input sample- \(H^{\dag }\)
Moore–Penrose generalized inverse of matrix H

- \(\hat{y}_{i}\)
Model predictions

- \(y_{i}\)
Real production data

- \(n\)
Number of production data

- \(R_{{{\text{lean}} . {\text{tail}}}}\)
Lean amine flowrate to tail gas absorber (t/h)

- \(R_{{{\text{lean}} . 2 {\text{nd}}}}\)
Inlet lean amine flowrate of 2

^{nd}absorber (t/h)- \(F_{\text{feedgas}}\)
Feed gas flowrate (kNm

^{3}/h)- \(R_{\text{semirich}}\)
Semi-rich amine flowrate (t/h)

- \(T_{{{\text{lean}} . {\text{tail}}}}\)
Inlet lean amine temperature of 1

^{st}absorber(^{o}C)- \(T_{{{\text{lean}} . 2 {\text{nd}}}}\)
Inlet lean amine temperature of 2

^{nd}absorber(^{o}C)- \(P_{\text{flash}}\)
Amine flash drum pressure (MPa)

- \(Q_{\text{reboilerA}}\)
Steam flowrate of reboiler A (t/h)

- \(Q_{\text{reboilerB}}\)
Steam flowrate of reboiler B (t/h)

- \(Q_{\text{preheater}}\)
Steam flowrate of preheater (t/h)

- \(C_{H2S}\)
H

_{2}S concentration in the treated gas (ppm)- \(C_{CO 2}\)
CO

_{2}concentration in the treated gas (mol%)- \(F_{\text{treatedgas}}\)
Treated gas flowrate (kNm

^{3}/h)

## Notes

### Acknowledgements

This work was supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China [Grant Number 2016ZX05017004]; the Chongqing National Science Foundation [Grant Number cstc2015jcyjBX0089]; the National Natural Science Foundation of China [Grant Number 51404051] and the Research Foundation of Chongqing University of Science and Technology [Grant Number CK2016Z16].

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