# Software for Evaluating Pumping Tests on Real Wells
## 1 Introduction  
Pumping tests are conducted for the purpose of determining not only aquifer parameters (hydraulic conductivity, transmissivity and storativity), but also well parameters (e.g., the coefficient of additional resistance, known as the skin factor, and well storage). In 1935, [PERSON] [1], on the basis of idealized conditions, published a solution to a basic equation describing an unsteady, radially symmetric flow to an ideal well in a saturated aquifer. [PERSON] used an analog equation describing thermal conduction in a solid environment to describe groundwater flow through a permeable environment [2]. His solution is used to determine an aquifer's transmissivity and storativity in the case of a well without additional resistances and with a negligibly small radius, and is known as the Theis type-curve method. [PERSON] and [PERSON] [3] built on this work by simplifying the Theis well function, generating a straight section for longer pumping test times when plotting drawdown vs. the logarithm of time and incorporating only the first two elements of the Theis well function, while omitting the others (the error in the calculations for the argument of the Theis function is less than 0.01-0.25%). Pumping tests on actual wells are influenced first by additional resistances (expressed by the skin effect). [PERSON] [4] and [PERSON] [5] were the first to incorporate additional resistances in a well and its close surroundings in calculations for oil wells. [PERSON] [6] inserted additional resistances into calculations in the form of a zone around a well with altered hydraulic conductivity (K). In the initial phase of a pumping (and drawdown) test, the well volume (well storage (WBS)) has a significant effect on drawdown over time. [PERSON] and [PERSON] [7] were the first to take this into account in underground hydraulics, while [PERSON] [8] and others [9, 10] first incorporated this factor in the oil sector. [PERSON] and [PERSON] [11] addressed the issue of the impact of a well's volume on pumping tests in elliptical coordinates. [PERSON] and [PERSON] [12]expanded upon [PERSON] and [PERSON]'s solution by factoring in well storage and horizontal anisotropy. [PERSON] et al. (2013) and others (2014, 2015) investigated this method in the Laplace domain. In 1970, [PERSON] et al. (2016) published a basic solution to the equation for unsteady, radially symmetric flow of a liquid to a complete well, taking into account additional resistances and the effect of well volume. Subsequent authors derived various approaches and methods, such as type curves, for determining additional resistances and well storage using a pumping test (1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977,  
is used for the straight-line section (red line), as seen in Figure 1, where the WBS represents well storativity and W represents the skin effect.  
The final equation for drawdown in an ideal well is [3]  
\[s_{w}=\frac{Q}{4\pi T}ln\left(\frac{2.246 Tt}{r_{w}^{2}S}\right) \tag{1}\]  
where \(S_{W}\) is drawdown at a well (m), \(Q\) is the pumped amount of water (m\({}^{3}\) s\({}^{-1}\)), \(T\) is aquifer transmissivity (m\({}^{2}\) s\({}^{-1}\)), \(t\) is time (s), and \(S\) is aquifer storativity (-).