Spatial-Temporal Separation Based on the Dynamic Recurrent Wavelet Neural Network Modelling for ASP Flooding

Shurong Li; Yulei Ge

doi:doi:10.11648/j.ajam.20170506.12

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Spatial-Temporal Separation Based on the Dynamic Recurrent Wavelet Neural Network Modelling for ASP Flooding

Shurong Li, Yulei Ge

Published in American Journal of Applied Mathematics (Volume 5, Issue 6)

Received: 13 December 2017 Accepted: 27 December 2017 Published: 10 January 2018

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Abstract

In this paper, a three-dimensional spatial-temporal decomposition modelling method is proposed to build the alkali-surfactant-polymer (ASP) flooding model, in which a new dynamic recurrent wavelet neural network (DRWNN) is presented to identify the temporal coefficients. At first, the detailed mathematical model of ASP flooding is described which is a complex distributed parameter system. Then a three-dimensional spatial-temporal modelling method is inferred based on Karhunen-Loeve (K-L) decomposition to decompose the water saturation of reservoir into a series of spatial basis functions and corresponding temporal coefficients. Furthermore, the recurrent wavelet neural network is used to acquire the identification model, in which the injection concentrations of ASP flooding and temporal coefficients are taken as the input and output information. In order to improve the capability of dynamic modelling, DRWNN is proposed through adding feedback layers and setting the different weights with time to achieve dynamic memory of the past information. Considering the gradient descent method for the neural networks training easily leads to local minimum and slow convergence speed, the spectral conjugate gradient method is introduced to optimize the weights of DRWNN. At last, DRWNN is used to build the relation between the moisture content of production wells and the water saturation of the corresponding grids. Thus, the final approximate model of ASP flooding is finished. The accuracy is proved by model with four injection wells and nine production wells through data from the mechanism model.

Published in	American Journal of Applied Mathematics (Volume 5, Issue 6)
DOI	10.11648/j.ajam.20170506.12
Page(s)	154-167
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

ASP Flooding, Karhunen-Loeve Decomposition, Dynamic Recurrent Wavelet Neural Network, Spectral Conjugate Gradient Method

References

[1]	E. Verheyen. Oil extraction imperils Africa's Great Lakes. Science. 354. 6312 (2016) 561-562.
[2]	Y. Zhu, Q. Hou, W. Liu, et al. Recent Progress and Effects Analysis of ASP Flooding Field Tests. Canadian Psychiatric Association Journal, 10 (5) (2012) 387-392.
[3]	F. Abadli. Simulation Study of Enhanced Oil Recovery by ASP (Alkaline, Surfactant and Polymer) Flooding for Norne Field C-segment. Department of Petroleum Engineering & Applied Geophysics, (2012).
[4]	Y. L. Ge, S. R. Li, S. L. Lu, et al. Spatial-Temporal ARX Modelling and Optimization for Polymer Flooding. Mathematical Problems in Engineering, (2014).
[5]	G. Prando, A. Chiuso, G. Pillonetto. Maximum Entropy vector kernels for MIMO system identification. Automatica 79 (2017) 326-339.
[6]	D. Coca, S. A. Billings. Identification of finite dimensional models of infinite dimensional dynamical systems. Automatica, 38 (11) (2002) 1851-1865.
[7]	H. Deng, H. X. Li, G. Chen. Spectral-approximation-based intelligent modelling for distributed thermal processes. IEEE Transactions on Control Systems Technology, 13 (5) (2005) 686-700.
[8]	C. K. Qi, H. X. Li. A time/space separation-based Hammerstein modelling approach for nonlinear distributed parameter processes. Computers & Chemical Engineering, 33 (7) (2009) 1247-1260.
[9]	C. Wan, M. Pan, et al. Performance improvement of magnetic anomaly detector using Karhunen–Loeve expansion. Iet Science Measurement & Technology. 11 (5) (2017) 600-606.
[10]	N. Hamilton, M. Tutkun, R. B. Cal. Low-order representations of the canonical wind turbine array boundary layer via double proper orthogonal decomposition. Physics of Fluids. 28 (2) (2016) 683-739.
[11]	F. Y. Zhao, Z. Y. Ma. Nonlinear dynamical system simulation based on recurrent wavelet neural network. Journal of System Simulation, 19 (7) (2007) 1453-1539.
[12]	N. Yu. Universal gradient methods for convex optimization problems. Mathematical Programming, 152 (1-2) (2015) 381-404.
[13]	F. Rothlauf. Optimization Methods. Design of Modern Heuristics. Springer Berlin Heidelberg, 2011, 45-102.
[14]	Y. H. Dai, Y. X. Yuan. The Nonlinear Conjugate Gradient Method. Shanghai: Shanghai Science and Technology Press, 2001.
[15]	L. Zhang. An improved Wei-Yao-Liu nonlinear conjugate gradient method for optimization computation. Applied Mathematics & Computation, 215 (6) (2009) 2269-2274.
[16]	Z. Q. Li, P. R. Lin, Z. X. Wei. A New Spectral Conjugate Gradient Method for Solving Unconstraints Minimization Problem. Journal of Southwest University (Natural Science Edition), 38 (7) (2016) 115-120.
[17]	C. Hua, N. Li, S. Y. Li. Time-space ARX modelling and predictive control for distributed parameter system. Control Theory & Applications, 28 (12) (2011) 1711-1716.
[18]	C. K. Qi, H. X. Li. Nonlinear dimension reduction based neural modelling for distributed parameter processes. Chemical Engineering Science, 64 (19) (2009) 4164-4170.
[19]	S. R. Li, X. D. Zhang. Optimal control of polymer flooding for enhanced oil recovery, Dongying: China university of petroleum press, 2013, 19-23.
[20]	C. Z. Yang, et al. Enhanced oil recovery for chemical flooding, Beijing: Petroleum Industry Press, 2007.10, 328-344.
[21]	Y. L. Ge, S. R. Li, K. X. Qu. A Novel Empirical Equation for Relative Permeability in Low Permeability Reservoirs. Chinese Journal of Chemical Engineering, 22 (11) (2014) 1274-1278.
[22]	F. M. F. El-Sousy, K. A. Abuhasel. Adaptive Nonlinear Disturbance Observer Using Double Loop Self-Organizing Recurrent Wavelet-Neural-Network for Two-Axis Motion Control System. IEEE Transactions on Industry Applications 99 (2017).
[23]	Z. Wan, C. Hu, Z. Yang. A spectral PRP conjugate gradient methods for nonconvex optimization problem based on modified line search. Discrete and Continuous Dynamical Systems - Series B (DCDS-B). 16 (4) (2017) 1157-1169.

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Shurong Li, Yulei Ge. (2018). Spatial-Temporal Separation Based on the Dynamic Recurrent Wavelet Neural Network Modelling for ASP Flooding. American Journal of Applied Mathematics, 5(6), 154-167. https://doi.org/10.11648/j.ajam.20170506.12

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ACS Style

Shurong Li; Yulei Ge. Spatial-Temporal Separation Based on the Dynamic Recurrent Wavelet Neural Network Modelling for ASP Flooding. Am. J. Appl. Math. 2018, 5(6), 154-167. doi: 10.11648/j.ajam.20170506.12

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AMA Style

Shurong Li, Yulei Ge. Spatial-Temporal Separation Based on the Dynamic Recurrent Wavelet Neural Network Modelling for ASP Flooding. Am J Appl Math. 2018;5(6):154-167. doi: 10.11648/j.ajam.20170506.12

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@article{10.11648/j.ajam.20170506.12,
  author = {Shurong Li and Yulei Ge},
  title = {Spatial-Temporal Separation Based on the Dynamic Recurrent Wavelet Neural Network Modelling for ASP Flooding},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {6},
  pages = {154-167},
  doi = {10.11648/j.ajam.20170506.12},
  url = {https://doi.org/10.11648/j.ajam.20170506.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170506.12},
  abstract = {In this paper, a three-dimensional spatial-temporal decomposition modelling method is proposed to build the alkali-surfactant-polymer (ASP) flooding model, in which a new dynamic recurrent wavelet neural network (DRWNN) is presented to identify the temporal coefficients. At first, the detailed mathematical model of ASP flooding is described which is a complex distributed parameter system. Then a three-dimensional spatial-temporal modelling method is inferred based on Karhunen-Loeve (K-L) decomposition to decompose the water saturation of reservoir into a series of spatial basis functions and corresponding temporal coefficients. Furthermore, the recurrent wavelet neural network is used to acquire the identification model, in which the injection concentrations of ASP flooding and temporal coefficients are taken as the input and output information. In order to improve the capability of dynamic modelling, DRWNN is proposed through adding feedback layers and setting the different weights with time to achieve dynamic memory of the past information. Considering the gradient descent method for the neural networks training easily leads to local minimum and slow convergence speed, the spectral conjugate gradient method is introduced to optimize the weights of DRWNN. At last, DRWNN is used to build the relation between the moisture content of production wells and the water saturation of the corresponding grids. Thus, the final approximate model of ASP flooding is finished. The accuracy is proved by model with four injection wells and nine production wells through data from the mechanism model.},
 year = {2018}
}

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TY  - JOUR
T1  - Spatial-Temporal Separation Based on the Dynamic Recurrent Wavelet Neural Network Modelling for ASP Flooding
AU  - Shurong Li
AU  - Yulei Ge
Y1  - 2018/01/10
PY  - 2018
N1  - https://doi.org/10.11648/j.ajam.20170506.12
DO  - 10.11648/j.ajam.20170506.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 154
EP  - 167
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20170506.12
AB  - In this paper, a three-dimensional spatial-temporal decomposition modelling method is proposed to build the alkali-surfactant-polymer (ASP) flooding model, in which a new dynamic recurrent wavelet neural network (DRWNN) is presented to identify the temporal coefficients. At first, the detailed mathematical model of ASP flooding is described which is a complex distributed parameter system. Then a three-dimensional spatial-temporal modelling method is inferred based on Karhunen-Loeve (K-L) decomposition to decompose the water saturation of reservoir into a series of spatial basis functions and corresponding temporal coefficients. Furthermore, the recurrent wavelet neural network is used to acquire the identification model, in which the injection concentrations of ASP flooding and temporal coefficients are taken as the input and output information. In order to improve the capability of dynamic modelling, DRWNN is proposed through adding feedback layers and setting the different weights with time to achieve dynamic memory of the past information. Considering the gradient descent method for the neural networks training easily leads to local minimum and slow convergence speed, the spectral conjugate gradient method is introduced to optimize the weights of DRWNN. At last, DRWNN is used to build the relation between the moisture content of production wells and the water saturation of the corresponding grids. Thus, the final approximate model of ASP flooding is finished. The accuracy is proved by model with four injection wells and nine production wells through data from the mechanism model.
VL  - 5
IS  - 6
ER  -

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Author Information

Shurong Li

Automation School, Beijing University of Posts and Telecommunications, Beijing, China
Yulei Ge

College of Information and Control Engineering, China University of Petroleum (East China), Qingdao, China

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APA Style

Shurong Li, Yulei Ge. (2018). Spatial-Temporal Separation Based on the Dynamic Recurrent Wavelet Neural Network Modelling for ASP Flooding. American Journal of Applied Mathematics, 5(6), 154-167. https://doi.org/10.11648/j.ajam.20170506.12

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ACS Style

Shurong Li; Yulei Ge. Spatial-Temporal Separation Based on the Dynamic Recurrent Wavelet Neural Network Modelling for ASP Flooding. Am. J. Appl. Math. 2018, 5(6), 154-167. doi: 10.11648/j.ajam.20170506.12

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AMA Style

Shurong Li, Yulei Ge. Spatial-Temporal Separation Based on the Dynamic Recurrent Wavelet Neural Network Modelling for ASP Flooding. Am J Appl Math. 2018;5(6):154-167. doi: 10.11648/j.ajam.20170506.12

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@article{10.11648/j.ajam.20170506.12,
  author = {Shurong Li and Yulei Ge},
  title = {Spatial-Temporal Separation Based on the Dynamic Recurrent Wavelet Neural Network Modelling for ASP Flooding},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {6},
  pages = {154-167},
  doi = {10.11648/j.ajam.20170506.12},
  url = {https://doi.org/10.11648/j.ajam.20170506.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170506.12},
  abstract = {In this paper, a three-dimensional spatial-temporal decomposition modelling method is proposed to build the alkali-surfactant-polymer (ASP) flooding model, in which a new dynamic recurrent wavelet neural network (DRWNN) is presented to identify the temporal coefficients. At first, the detailed mathematical model of ASP flooding is described which is a complex distributed parameter system. Then a three-dimensional spatial-temporal modelling method is inferred based on Karhunen-Loeve (K-L) decomposition to decompose the water saturation of reservoir into a series of spatial basis functions and corresponding temporal coefficients. Furthermore, the recurrent wavelet neural network is used to acquire the identification model, in which the injection concentrations of ASP flooding and temporal coefficients are taken as the input and output information. In order to improve the capability of dynamic modelling, DRWNN is proposed through adding feedback layers and setting the different weights with time to achieve dynamic memory of the past information. Considering the gradient descent method for the neural networks training easily leads to local minimum and slow convergence speed, the spectral conjugate gradient method is introduced to optimize the weights of DRWNN. At last, DRWNN is used to build the relation between the moisture content of production wells and the water saturation of the corresponding grids. Thus, the final approximate model of ASP flooding is finished. The accuracy is proved by model with four injection wells and nine production wells through data from the mechanism model.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Spatial-Temporal Separation Based on the Dynamic Recurrent Wavelet Neural Network Modelling for ASP Flooding
AU  - Shurong Li
AU  - Yulei Ge
Y1  - 2018/01/10
PY  - 2018
N1  - https://doi.org/10.11648/j.ajam.20170506.12
DO  - 10.11648/j.ajam.20170506.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 154
EP  - 167
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20170506.12
AB  - In this paper, a three-dimensional spatial-temporal decomposition modelling method is proposed to build the alkali-surfactant-polymer (ASP) flooding model, in which a new dynamic recurrent wavelet neural network (DRWNN) is presented to identify the temporal coefficients. At first, the detailed mathematical model of ASP flooding is described which is a complex distributed parameter system. Then a three-dimensional spatial-temporal modelling method is inferred based on Karhunen-Loeve (K-L) decomposition to decompose the water saturation of reservoir into a series of spatial basis functions and corresponding temporal coefficients. Furthermore, the recurrent wavelet neural network is used to acquire the identification model, in which the injection concentrations of ASP flooding and temporal coefficients are taken as the input and output information. In order to improve the capability of dynamic modelling, DRWNN is proposed through adding feedback layers and setting the different weights with time to achieve dynamic memory of the past information. Considering the gradient descent method for the neural networks training easily leads to local minimum and slow convergence speed, the spectral conjugate gradient method is introduced to optimize the weights of DRWNN. At last, DRWNN is used to build the relation between the moisture content of production wells and the water saturation of the corresponding grids. Thus, the final approximate model of ASP flooding is finished. The accuracy is proved by model with four injection wells and nine production wells through data from the mechanism model.
VL  - 5
IS  - 6
ER  -

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