A Green’s Function Construction Method of the Single Well Seepage Model for Asymmetric Fractures

JI Anzhao; WANG Yufeng; ZHANG Guangsheng

doi:10.21656/1000-0887.420237

Volume 43 Issue 4

Apr. 2022

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Article Navigation > Applied Mathematics and Mechanics > 2022 > 43(4): 424-434

JI Anzhao, WANG Yufeng, ZHANG Guangsheng. A Green’s Function Construction Method of the Single Well Seepage Model for Asymmetric Fractures[J]. Applied Mathematics and Mechanics, 2022, 43(4): 424-434. doi: 10.21656/1000-0887.420237

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A Green’s Function Construction Method of the Single Well Seepage Model for Asymmetric Fractures

doi: 10.21656/1000-0887.420237

School of Energy Engineering, Longdong University, Qingyang, Gansu 745100, P.R.China

Received Date: 2021-08-09
Rev Recd Date: 2021-10-19

Available Online: 2022-03-16

Publish Date: 2022-04-01

Abstract

Abstract

The seepage law for asymmetric fractures can be solved by the Green’s function method. According to the basic seepage theory, the point source mathematical model for asymmetric fractures was established. The dimensionless point source mathematical model differential equation in the Laplacian space was obtained through the dimensionless transformation and the Laplacian transformation. By means of the unknown Green’s function combined with the point source differential equation, and in view of the homogeneous boundary conditions for the point source differential equation and the characteristics of the point source differential equation, a general construction method for Green’s function was given to meet the homogeneous boundary conditions for the point source differential equation and the solution of the unknown objective function. According to the symmetry and continuity of spatial Green’s function, the Green form of the asymmetric fracture point source model was obtained. Finally, through the seepage mathematical model for the asymmetric-fracture vertical well, it was verified that the 2 forms of Green’s function are consistent with the results calculated in references and with the commercial well test analysis software Saphir.
- Green’s function,
- asymmetric fracture,
- fractured well,
- unequal-spacing grid

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References

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