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...
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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2010/907206 |
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doaj-9728bfcb3f3a4276a3dfdcbec3984abf2020-11-24T22:55:05ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472010-01-01201010.1155/2010/907206907206Pseudo-Steady-State Productivity Formula for a Partially Penetrating Vertical Well in a Box-Shaped ReservoirJing Lu0Djebbar Tiab1Department of Petroleum Engineering, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, UAEMewbourne School of Petroleum and Geological Engineering, The University of Oklahoma, T-301 Sarkeys Energy Center, 100 East Boyd Street, Norman, OK 73019-1003, USAFor 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.http://dx.doi.org/10.1155/2010/907206 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Jing Lu Djebbar Tiab |
spellingShingle |
Jing Lu Djebbar Tiab Pseudo-Steady-State Productivity Formula for a Partially Penetrating Vertical Well in a Box-Shaped Reservoir Mathematical Problems in Engineering |
author_facet |
Jing Lu Djebbar Tiab |
author_sort |
Jing Lu |
title |
Pseudo-Steady-State Productivity Formula for a Partially Penetrating Vertical Well in a Box-Shaped Reservoir |
title_short |
Pseudo-Steady-State Productivity Formula for a Partially Penetrating Vertical Well in a Box-Shaped Reservoir |
title_full |
Pseudo-Steady-State Productivity Formula for a Partially Penetrating Vertical Well in a Box-Shaped Reservoir |
title_fullStr |
Pseudo-Steady-State Productivity Formula for a Partially Penetrating Vertical Well in a Box-Shaped Reservoir |
title_full_unstemmed |
Pseudo-Steady-State Productivity Formula for a Partially Penetrating Vertical Well in a Box-Shaped Reservoir |
title_sort |
pseudo-steady-state productivity formula for a partially penetrating vertical well in a box-shaped reservoir |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2010-01-01 |
description |
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. |
url |
http://dx.doi.org/10.1155/2010/907206 |
work_keys_str_mv |
AT jinglu pseudosteadystateproductivityformulaforapartiallypenetratingverticalwellinaboxshapedreservoir AT djebbartiab pseudosteadystateproductivityformulaforapartiallypenetratingverticalwellinaboxshapedreservoir |
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