Abstract
This study analyzes the unsteady groundwater flow to a real well (with wellbore storage and the skin effect) that fully penetrates the confined aquifer. The well is located within an infinite system, so the effect of boundaries is not considered. The Laplace-domain solution for a partial differential equation is used to describe the unsteady radial flow to a well. The real space solution is obtained by means of the numerical inversion of the Laplace transform using the Stehfest algorithm 368. When wellbore storage and the skin effect dominate pumping test data and testing is conducted for long enough, two semilogarithmic straight lines are normally obtained. The first straight line can be identified readily as the line of the maximum slope. The correlation of the dimensionless drawdown for the intersection time of this first straight line, with the log time axis as a function of the dimensionless wellbore storage and the skin factor, is shown. This paper presents a new method for evaluating the skin factor from the early portion of a pumping test. This method can be used to evaluate the skin factor when the well-known Cooper–Jacob semilogarithmic method cannot be used due to the second straight line not being achieved in the semilogarithmic graph drawdown vs. the log time. A field example is presented to evaluate the well rehabilitation in Veselí nad Lužnicí by means of the new correlation.
Highlights
A pumping test is a field test in which a well is pumped at a constant rate, and “drawdown” is measured and analyzed
The new method for evaluating the skin factor in a single well fully penetrating the confined aquifer from the early portion of a pumping test is derived under the following assumptions: non zero additional resistance at the pumping well, a finite well radius, and the well being situated in an infinite aquifer
We derived a correlation of the dimensionless drawdown for the intersection time tD * of the first straight-line of the pumping test in a semilogarithmic graph as a function of the dimensionless wellbore storage, CD, and the skin factor, SF (Equation (12))
Summary
Pumping tests are widely used for the evaluation of aquifer hydraulic parameters, including transmissivity, T, and the storage coefficient of the aquifer, S These tests have wide applications in the field of petroleum engineering and groundwater hydraulics based on the Theis analytical solution [1] for drawdown at the well caused by pumping at a constant rate from a full well in a homogeneous, uniform, and confined aquifer with a negligible well radius, as well as when the flow to the well is not influenced by the outer boundaries and additional resistances in a well and in its surroundings. The new method for evaluating the skin factor in a single well fully penetrating the confined aquifer from the early portion of a pumping test is derived under the following assumptions: non zero additional resistance at the pumping well, a finite well radius (wellbore storage effect), and the well being situated in an infinite aquifer (where no observation well is available). This new method to evaluate the skin factor from the early portion of a pumping test is not intended to replace any of the approaches presented in the literature but rather to supplement them
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