Parameter estimation for nonlinear diffusion problems by the constrained homotopy method
This paper studies a parameter estimation problem for the non-linear diffusion equation within multiphase porous media flow, which has important applications in the field of oil reservoir simulation. First, the given problem is transformed into an optimization problem by using optimal control framew...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2023
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| Online Access: | https://hdl.handle.net/10356/171714 |
| _version_ | 1826123494634553344 |
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| author | Liu, Tao Ding, Zijian Yu, Jiayuan Zhang, Wenwen |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Liu, Tao Ding, Zijian Yu, Jiayuan Zhang, Wenwen |
| author_sort | Liu, Tao |
| collection | NTU |
| description | This paper studies a parameter estimation problem for the non-linear diffusion equation within multiphase porous media flow, which has important applications in the field of oil reservoir simulation. First, the given problem is transformed into an optimization problem by using optimal control framework and the constraints such as well logs, which can restrain noise and improve the quality of inversion, are introduced. Then we propose the widely convergent homotopy method, which makes natural use of constraints and incorporates Tikhonov regularization. The effectiveness of the proposed approach is demonstrated on illustrative examples. |
| first_indexed | 2024-10-01T06:05:36Z |
| format | Journal Article |
| id | ntu-10356/171714 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:05:36Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-10356/1717142023-11-10T15:40:39Z Parameter estimation for nonlinear diffusion problems by the constrained homotopy method Liu, Tao Ding, Zijian Yu, Jiayuan Zhang, Wenwen School of Electrical and Electronic Engineering Science::Mathematics Non-linear Diffusion Problem Inversion This paper studies a parameter estimation problem for the non-linear diffusion equation within multiphase porous media flow, which has important applications in the field of oil reservoir simulation. First, the given problem is transformed into an optimization problem by using optimal control framework and the constraints such as well logs, which can restrain noise and improve the quality of inversion, are introduced. Then we propose the widely convergent homotopy method, which makes natural use of constraints and incorporates Tikhonov regularization. The effectiveness of the proposed approach is demonstrated on illustrative examples. Published version This research was funded by the Natural Science Foundation of Hebei Province of China (A2020501007), the Fundamental Research Funds for the Central Universities (N2123015), the Open Fund Project of Marine Ecological Restoration and Smart Ocean Engineering Research Center of Hebei Province (HBMESO2321), the Technical Service Project of Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration (KJ2022-021). 2023-11-06T03:25:58Z 2023-11-06T03:25:58Z 2023 Journal Article Liu, T., Ding, Z., Yu, J. & Zhang, W. (2023). Parameter estimation for nonlinear diffusion problems by the constrained homotopy method. Mathematics, 11(12), 2642-. https://dx.doi.org/10.3390/math11122642 2227-7390 https://hdl.handle.net/10356/171714 10.3390/math11122642 2-s2.0-85164120495 12 11 2642 en Mathematics © 2023 The authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). application/pdf |
| spellingShingle | Science::Mathematics Non-linear Diffusion Problem Inversion Liu, Tao Ding, Zijian Yu, Jiayuan Zhang, Wenwen Parameter estimation for nonlinear diffusion problems by the constrained homotopy method |
| title | Parameter estimation for nonlinear diffusion problems by the constrained homotopy method |
| title_full | Parameter estimation for nonlinear diffusion problems by the constrained homotopy method |
| title_fullStr | Parameter estimation for nonlinear diffusion problems by the constrained homotopy method |
| title_full_unstemmed | Parameter estimation for nonlinear diffusion problems by the constrained homotopy method |
| title_short | Parameter estimation for nonlinear diffusion problems by the constrained homotopy method |
| title_sort | parameter estimation for nonlinear diffusion problems by the constrained homotopy method |
| topic | Science::Mathematics Non-linear Diffusion Problem Inversion |
| url | https://hdl.handle.net/10356/171714 |
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