Question $2(25$ marks$)$: A large production well has been installed in a confined aquifer to supply water for a municipality in Nova Scotia. A series of observation wells have been installed $($see Figure $1$ below$)$ in the same aquifer at distances of $3\mathrm{.}4,22,57,$ and $167m$ from the pumping well. A pumping test was conducted over a $24$ hour period, but you are hesitant to analyze the drawdown data because fluctuations in the pumping rate caused water levels to fluctuate in the observation wells. Fortunately, you were able to record the total drawdown in all wells at the end of the $24$ hour pumping period and you also recorded the water level recovery in the pumping well for an additional $24$ hour period. These data points are shown in Tables $1$ and $2$ below.

a$)$ Plot a graph of drawdown versus distance using data from the four observation wells at the end of the pumping period $($i$.$e$.,$ distance$-$drawdown method$).$ Using an average pumping rate of $120\frac{L}{m}in$ over the pumping period, estimate the transmissivity and storativity of the aquifer from this method. Given that the aquifer thickness is $4\mathrm{.}2m,$ estimate the horizontal hydraulic conductivity using the calculated transmissivity, and speculate on the geological material that the aquifer is comprised of$.(10$ marks$)$

b$)$ Calculate the drawdown in the pumping well at the end of the $24$ hour pumping period. Assume the pumping well has an effective radius of $0\mathrm{.}10m.$ Would you expect the actual drawdown in the pumping well to be greater than or less than the theoretical value you calculated? Explain your answer. $(5$ marks$)$

c$)$ Using the recovery data from the pumping well, plot a graph of residual drawdown versus time ratio $(\frac{t}{t^{\text{'}}}).$ Using the plotted data, estimate the transmissivity of the aquifer. $(5$ marks$)$

d$)$ Comment on the shape of the recovery curve at large recovery times $($i$.$e$.,$ small values of $\frac{t}{t^{\text{'}}}).$ What does it suggest about the hydraulic response of the aquifer? $(5$ marks$)$

Figure $1.$ Plan view map of pumping and observation wells $($not to scale$).$

Table $1.$ Drawdown in observation wells at the end of the $24-$hour pumping period

$\backslash$table$[[$Well$,\backslash$table$[[$Distance from$],[$pumping well$],[(m)$