Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow
On the basis of similar structure of solution for a second-order linear differential equation's boundary value problem, and our analysis of the relationship between this similar structure and its kernel function, the differential equation, and the boundary conditions, we propose a new simple so...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/219218 |
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| _version_ | 1832567345248206848 |
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| author | Cui-Cui Sheng Jin-Zhou Zhao Yong-Ming Li Shun-Chu Li Hu Jia |
| author_facet | Cui-Cui Sheng Jin-Zhou Zhao Yong-Ming Li Shun-Chu Li Hu Jia |
| author_sort | Cui-Cui Sheng |
| collection | DOAJ |
| description | On the basis of similar structure of solution for a second-order linear differential equation's boundary value problem, and our analysis of the relationship between this similar structure and its kernel function, the differential equation, and the boundary conditions, we propose a new simple solution—similar constructive method of solution (SCMS)—and sum up its detailed steps. We set up a porous media model under three kinds of outer boundary conditions (infinite, constant pressure, and closed), in which the influences of fractal dimension, spherical flow, skin effect, and storage are taken into consideration. And then we use SCMS to solve it. The SCMS is a straightforward method for differential equation's boundary value problems with complex boundary conditions, especially for solving the reservoir models in petroleum engineering. |
| format | Article |
| id | doaj-art-ed2cb4569d33442789f31ebacf33250f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-ed2cb4569d33442789f31ebacf33250f2025-02-03T01:01:47ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/219218219218Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical FlowCui-Cui Sheng0Jin-Zhou Zhao1Yong-Ming Li2Shun-Chu Li3Hu Jia4State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, ChinaState Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, ChinaState Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, ChinaInstitute of Applied Mathematics, Xihua University, Chengdu 610039, ChinaState Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, ChinaOn the basis of similar structure of solution for a second-order linear differential equation's boundary value problem, and our analysis of the relationship between this similar structure and its kernel function, the differential equation, and the boundary conditions, we propose a new simple solution—similar constructive method of solution (SCMS)—and sum up its detailed steps. We set up a porous media model under three kinds of outer boundary conditions (infinite, constant pressure, and closed), in which the influences of fractal dimension, spherical flow, skin effect, and storage are taken into consideration. And then we use SCMS to solve it. The SCMS is a straightforward method for differential equation's boundary value problems with complex boundary conditions, especially for solving the reservoir models in petroleum engineering.http://dx.doi.org/10.1155/2013/219218 |
| spellingShingle | Cui-Cui Sheng Jin-Zhou Zhao Yong-Ming Li Shun-Chu Li Hu Jia Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow Journal of Applied Mathematics |
| title | Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow |
| title_full | Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow |
| title_fullStr | Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow |
| title_full_unstemmed | Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow |
| title_short | Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow |
| title_sort | similar construction method of solution for solving the mathematical model of fractal reservoir with spherical flow |
| url | http://dx.doi.org/10.1155/2013/219218 |
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