Well Hydraulics: Equations and Analysis Methods

Well Hydraulics: Equations and Analysis Methods: The determination of well capacity and flow has great practical significance due to its prevalence in both the private and commercial sectors. There has also been great concern over the emergence of contaminants in groundwater, and knowledge of groundwater movements allows us to predict the appearance of these contaminants in our water supply. The rate of replenishment in a well is largely a function of soil porosity but is also dependent on the piezometric head and geologic substrata present.

The basic eq. for an unconfined aquifer with uniform radial flow is

Q=(P_t \times K(h_2^2 - h_1^2))/ In(\frac{r_2}{r_1})

By converting K to $gkld/ft^2,$ Q to gpm, h and r in ft, and ln to log the eq. becomes.

K=\frac{1055 \:Q \:log(r_2/r_1)}{h_2^{2}-h_1^{2}}

Where,

Q = well discharge
$r_1$ = dist. from well to closest observation well
$r_2$ = dist. from well to farthest observation well,
$h_1$ = ht of original water table minus the amount of drawdown at $r_1$
$h_2$ = ht of original water table minus the amount of drawdown at $r_2$

For a well drilled into a confined aquifer, a separate equation is required. must be used, this equation. takes into account the aquifer thickness, m:

K=\frac{528 \:Q \:In(r_2/r_1)}{m(h_2-h_1)}

Where,
m = ht. of confined aquifer

It is also necessary to be able to analyse well with unsteady flow. Without a computer, this is traditionally done by a graphical solution developed by Theiss. His method is used to find out the transmissibility of soil and its storage coefficient. The storage coefficient is the volume of water an aquifer takes in or releases per unit surface area of aquifer per unit change in head normal to the surface. The method consists of using drawdown, radius, and time measurements from the start of pumping. The eq relates these.

D_e=\frac{L_e}{Ce^{1.85}}(\frac{\Sigma (CL^{1.85}D^{4.87}}{L})^{(1/4.87)}

And since,

C = Ce

D_e= 300(\frac{12^{4.87}}{2000}+\frac{16^{4.87}}{1000})^{(1/4.87)}

= $12.73^\circ$

Next, a plot of the well function W(u) is superimposed on a log-log plot of observed values for $r_2$ /t vs. S, the drawdown. To determine T and S, simply place the well function plot over the data plot with the u and $r_2$ /t as the X-axis and move them around until the 2 match closely, yielding a pt. with the necessary data. It is then an easy procedure to plug values from this point into the equations. r_2/t as the X-axis and move them around until the 2 match closely, yielding a pt. with the necessary data. It is then an easy procedure to plug values from this point into the equations.

T=\frac{114.6Q}{s}(W(u)

S=\frac{\mu T}{1.87(r^2/t)}