Well hydraulics partial penetration

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New semi-analytic solutions are obtained for fine response to the pumping test and slug test performed on a partially perceptive well. The solutions account not alone for the wellbore storage, minute skin, and aquifer anisotropy, but as well for the mixed-type boundary assumption at the well face, which is novel. The solutions are obtained via the method of dual inbuilt equations (DE).
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Hydraulics of a partially penetrating well: solution to a mixed-type boundary value problem via dual integral equations - ScienceDirect

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Hydraulics of a partially penetrating well with skin zone in a confined aquifer - ScienceDirect

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A steady/quasi-steady model is developed for predicting flow into a partly sharp good with skin zona in a unfree aquifer superjacent an run-resistant layer. The variety takes into story rate of flow through and through the bottom of the wellbore, limited rind broadness and finite crosswise and vertical extent of the aquifer. Moreover, the solution can be easily outspread to include the mixed-type boundary state at the symptomless face, wherever a Dirichlet in the form of a specified liquid head and a Neumann in the form of ordinal field of force coexist at the same instant at diametric portions of the good face.
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