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Research Papers

Estimation of CO2 Diffusivity in Brine by Use of the Genetic Algorithm and Mixed Kernels-Based Support Vector Machine Model

[+] Author and Article Information
Qihong Feng, Zhe Jiang

School of Petroleum Engineering,
China University of Petroleum (East China),
Qingdao 266580, Shandong, China

Ronghao Cui

School of Petroleum Engineering,
China University of Petroleum (East China),
Qingdao 266580, Shandong, China
e-mail: ronghao.cui1993@gmail.com

Sen Wang

School of Petroleum Engineering,
China University of Petroleum (East China),
Qingdao 266580, Shandong, China
e-mail: fwforest@gmail.com

Jin Zhang

School of Petroleum Engineering,
China University of Petroleum (East China),
Qingdao 266580, Shandong, China

1Corresponding authors.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received July 13, 2018; final manuscript received October 6, 2018; published online November 19, 2018. Assoc. Editor: Daoyong (Tony) Yang.

J. Energy Resour. Technol 141(4), 041001 (Nov 19, 2018) (11 pages) Paper No: JERT-18-1524; doi: 10.1115/1.4041724 History: Received July 13, 2018; Revised October 06, 2018

Diffusion coefficient of carbon dioxide (CO2), a significant parameter describing the mass transfer process, exerts a profound influence on the safety of CO2 storage in depleted reservoirs, saline aquifers, and marine ecosystems. However, experimental determination of diffusion coefficient in CO2-brine system is time-consuming and complex because the procedure requires sophisticated laboratory equipment and reasonable interpretation methods. To facilitate the acquisition of more accurate values, an intelligent model, termed MKSVM-GA, is developed using a hybrid technique of support vector machine (SVM), mixed kernels (MK), and genetic algorithm (GA). Confirmed by the statistical evaluation indicators, our proposed model exhibits excellent performance with high accuracy and strong robustness in a wide range of temperatures (273–473.15 K), pressures (0.1–49.3 MPa), and viscosities (0.139–1.950 mPa·s). Our results show that the proposed model is more applicable than the artificial neural network (ANN) model at this sample size, which is superior to four commonly used traditional empirical correlations. The technique presented in this study can provide a fast and precise prediction of CO2 diffusivity in brine at reservoir conditions for the engineering design and the technical risk assessment during the process of CO2 injection.

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Figures

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Fig. 1

Schematic showing the fundamentals of SVM. The square dots represent support vectors. The circular dots are normal points. The full line denotes the hyperplane and the ε-tube is the region between two dotted lines.

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Fig. 2

Function curves of the polynomial kernel (a), the RBF kernel (b), and the mixed kernel (c). x = 0.2 is the test point in three types of kernels. As an example of mixed kernel functions, d = 1 and γ = 10 are set.

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Fig. 3

Computational procedure of the MKSVM-GA technique

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Fig. 4

Mean square error and average uptime of the MKSVM-GA model in different population size and evolutionary generations

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Fig. 5

Illustration of the Williams plot

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Fig. 6

Prediction performance of the proposed MKSVM-GA model: (a) cross plot of the estimated results versus experimental diffusion coefficients of CO2 in brine; (b) comparison of each experimental and predicted data points

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Fig. 7

Distribution of the residuals between predicted and experimental diffusion coefficients of CO2. The columns are instances and the solid curve is the normal distribution curve. Std Dev represents the standard deviation of residuals.

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Fig. 8

Williams plot used for the detection of outliers

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Fig. 13

Absolute error curves of the MKSVM-GA model, the ANN model, and four empirical correlations

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Fig. 12

Comparison of the prediction performance between the MKSVM-GA model and the ANN model

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Fig. 11

Comparison of the training performance between the MKSVM-GA model and the ANN model

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Fig. 10

The minimum MSE with variation of number of neurons in the hidden layer

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Fig. 9

Illustration of the structure of a typical three-layered feed forward ANN model

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Fig. 14

Comparison of the prediction performances between the MKSVM-GA model and four empirical correlations: (a) Othmer and Thakar; (b) Wilke and Chang; (c) Lu et al.; (d) Cadogan et al. Squares and triangles represent the values predicted using the MKSVM-GA model and empirical correlations, respectively.

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