Q

known as the Theis solution. Ei is the exponential integral, and u is a dimensionless variable defined by

Ssr2

or or

S/ 4Tt for confined flow

The exponential integral Ei(u) is referred to as the well function W(u). Ei(u) can be approximated by

u2 u3 0.577216 - (n u + u - —— + —— 2.2! 3.3!

Using the well function W(u), the Theis solution can be written as

rQr 4r

The drawdown s is obtained by

Values of W(u) for different values of u are shown in Table 9.7.2. The drawdown s at a given distance r from the well at given time t can be calculated from Equation 9.7(20) and Table 9.7.2.

Figure 9.7.2, accompanied by Table 9.7.3, shows an example of drawdown versus a time curve for a transient radial flow in a confined aquifer with T = 1000 m2/d and S = 0.0001 for a pumping rate of Q = 1000 m3/d. The figure shows that even in a transient flow, the rate of drawdown (As) achieves a steady state after a short period of pumping, two days in this example.

If u is small (e.g., less than 0.01), only the first two terms of the brackets in Equation 9.7(17) are significant. Equation 9.7(19) can be simplified to u =

TABLE 9.7.2 VALUES OF W(U) FOR DIFFERENT VALUES OF U

\ u N \

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