## Cooper Jacob Method

Cooper and Jacob (1946) showed that when u becomes small (u << 1), the drawdown equation can be represented by Equation 9.7(22) as

On semilog paper, this equation represents a straight line with a slope of 2.3Q/4 ttT. This equation can be plotted in three different ways: (1) s versus logt, (2) s versus log r, or (3) s versus log t/r2 or log r2/t.

DRAWDOWN-TIME ANALYSIS (s VERSUS logt)

The drawdown measurements s at a constant distance r are plotted against time as shown in Figure 9.8.3. The slope of the line is 2.3Q/4^T and is equal to

If a change in drawdown As is considered for one log cycle, then log (t2/t1) = 1, and this equation reduces to or

When the straight line intersects the x axis, s = 0 and the time is to. Substituting these values in Equation 9.8(12) gives

2.3Q 2.25Tto

2.25Tto and

2.25Tto

Example: Figure 9.8.3 shows that to = 1.6 X 10~3 days and slope As = 0.181. These values yield T = 1011 m2/d and S = 0.00009, which agree with the values for T and S obtained by the Theis solution.

DRAWDOWN-DISTANCE ANALYSIS (s VERSUS log r)

The drawdown measurements s are plotted against distance r at a given time t as shown in Figure 9.8.4. From similar considerations as in drawdown-time analysis

2.25Tt

m so