Pseudo-Steady-State Productivity Formula for a Partially Penetrating Vertical Well in a Box-Shaped Reservoir
For a bounded reservoir with no flow boundaries, the pseudo-steady-state flow regime is common at long-producing times. Taking a partially penetrating well as a uniform line sink in three dimensional space, by the orthogonal decomposition of Dirac function and using Green's function to three-di...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2010-01-01
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| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2010/907206 |
| Summary: | For a bounded reservoir with no flow boundaries, the pseudo-steady-state flow regime is common at long-producing times. Taking a partially penetrating well as a uniform line sink in three dimensional space, by the orthogonal decomposition of Dirac function and using Green's function to three-dimensional Laplace equation with homogeneous Neumann boundary condition, this paper presents step-by-step derivations of a pseudo-steady-state productivity formula for a partially penetrating vertical well arbitrarily located in a closed anisotropic box-shaped drainage volume. A formula for calculating pseudo skin factor due to partial penetration is derived in detailed steps. A convenient expression is presented for calculating the shape factor of an isotropic rectangle reservoir with a single fully penetrating vertical well, for arbitrary aspect ratio of the rectangle, and for arbitrary position of the well within the rectangle. |
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| ISSN: | 1024-123X 1563-5147 |