The solution of the governing equation representing the drawdown in a
horizontal confined aquifer, where groundwater flow is unsteady, is provided in
terms of the exponential integral, which is famously known as the Well
function. For the computation of this function in practical applications, it is
important to develop not only accurate but also a simple approximation that
requires evaluation of the fewest possible terms. To that end, introducing
Ramanujan's series expression, this work proposes a full-range approximation to
the exponential integral using Ramanujan's series for the small argument (u
\leq 1) and an approximation based on the bound of the integral for the other
range (u \in (1,100]). The evaluation of the proposed approximation results in
the most accurate formulae compared to the existing studies, which possess the
maximum percentage error of 0.05\%. Further, the proposed formula is much
simpler to apply as it contains just the product of exponential and logarithm
functions. To further check the efficiency of the proposed approximation, we
consider a practical example for evaluating the discrete pumping kernel, which
shows the superiority of this approximation over the others. Finally, the
authors hope that the proposed efficient approximation can be useful for
groundwater and hydrogeological applications.Comment: 10 page