Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media
Numerical simulation of two-phase flow in fractured porous media is an important topic in the subsurface flow, environmental problems, and petroleum reservoir engineering. The conventional model does not work well in many cases since it lacks the memory property of fracture media. In this paper, we...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2013/429835 |
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| _version_ | 1832556358739689472 |
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| author | Wenwen Zhong Changpin Li Jisheng Kou |
| author_facet | Wenwen Zhong Changpin Li Jisheng Kou |
| author_sort | Wenwen Zhong |
| collection | DOAJ |
| description | Numerical simulation of two-phase flow in fractured porous media is an important topic in the subsurface flow, environmental problems, and petroleum reservoir engineering. The conventional model does not work well in many cases since it lacks the memory property of fracture media. In this paper, we develop a new numerical formulation with fractional time derivative for two-phase flow in fractured porous media. In the proposed formulation, the different fractional time derivatives are applied to fracture and matrix regions since they have different memory properties. We further develop a two-level time discrete method, which uses a large time step for the pressure and a small time step size for the saturation. The pressure equation is solved implicitly in each large time step, while the saturation is updated by an explicit fractional time scheme in each time substep. Finally, the numerical tests are carried out to demonstrate the effectiveness of the proposed numerical model. |
| format | Article |
| id | doaj-art-c52d560e4ba6430584c481c881fa6814 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-c52d560e4ba6430584c481c881fa68142025-02-03T05:45:46ZengWileyAdvances in Mathematical Physics1687-91201687-91392013-01-01201310.1155/2013/429835429835Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured MediaWenwen Zhong0Changpin Li1Jisheng Kou2Department of Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaSchool of Mathematics and Statistics, Hubei Engineering University, Xiaogan, Hubei 432000, ChinaNumerical simulation of two-phase flow in fractured porous media is an important topic in the subsurface flow, environmental problems, and petroleum reservoir engineering. The conventional model does not work well in many cases since it lacks the memory property of fracture media. In this paper, we develop a new numerical formulation with fractional time derivative for two-phase flow in fractured porous media. In the proposed formulation, the different fractional time derivatives are applied to fracture and matrix regions since they have different memory properties. We further develop a two-level time discrete method, which uses a large time step for the pressure and a small time step size for the saturation. The pressure equation is solved implicitly in each large time step, while the saturation is updated by an explicit fractional time scheme in each time substep. Finally, the numerical tests are carried out to demonstrate the effectiveness of the proposed numerical model.http://dx.doi.org/10.1155/2013/429835 |
| spellingShingle | Wenwen Zhong Changpin Li Jisheng Kou Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media Advances in Mathematical Physics |
| title | Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media |
| title_full | Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media |
| title_fullStr | Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media |
| title_full_unstemmed | Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media |
| title_short | Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media |
| title_sort | numerical fractional calculus model for two phase flow in fractured media |
| url | http://dx.doi.org/10.1155/2013/429835 |
| work_keys_str_mv | AT wenwenzhong numericalfractionalcalculusmodelfortwophaseflowinfracturedmedia AT changpinli numericalfractionalcalculusmodelfortwophaseflowinfracturedmedia AT jishengkou numericalfractionalcalculusmodelfortwophaseflowinfracturedmedia |