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Non-Darcian flow in a single confined vertical fracture toward a well |
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| Authors: | Zhang Wen Guanhua Huang Hongbin Zhan |
| Institution: | aDepartment of Irrigation and Drainage, College of Water Conservancy and Civil Engineering, China Agricultural University, Beijing 100083, PR China bChinese–Israeli International Center for Research in Agriculture, China Agricultural University, Beijing 100083, PR China cDepartment of Geology and Geophysics, Texas A&M University, College Station, TX 77843-3115, USA |
| Abstract: | Non-Darcian flow towards a well which fully penetrates a confined single vertical fracture is presented in this paper on the basis of the Izbash equation. We have obtained semi-analytical solutions for non-Darcian flow by using the Boltzmann transform and developed the non-Darcian flow well functions for cases with and without the effect of wellbore storage. The results show that the non-Darcian flow type curves are more or less deviated from the Darcian flow type curve. The non-linear effect is mainly attributable to the turbulent factor, v, a dimensionless parameter related to the pumping rate, the fracture aperture, the fracture thickness, and two constants k′ and n used in the Izbash power-law. The non-linear effect appears to be less sensitive to the power-law index, n. When excluding wellbore storage, the well function at early times is proportional to v−1/(n−1)u−n/(n−1), where u is a dimensionless term inversely proportional to time; whereas the well function at late times is approximated as |
| Keywords: | Non-Darcian flow Type curve Wellbore storage Well function Power-law |
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