Fig. 15.3 Control volume in case of confined aquifer

 

Consider the control volume shown in figure 15.3.

The inflow to the control volume is Q_r

The outflow from the control volume is

The net inflow to the control volume is        (15.1)

Applying principle of mass conservation on the control volume

Inflow - outflow = Time rate of change in volumetric storage

Time rate of change in volumetric storage                      (15.2)

                                                                                                 (15.3)

where S_o is the specific storage

Replacing V by 2πrdrb, we have

                                                                       (15.4)

                                                                      (15.5)

Where S_s is the aquifer storativity which is equal to S_o / b

Putting (15.5) in (15.3), we have

                                                                            (15.6)

As per Darcy's law

             (15.7)

Putting in equation (15.6)

                                                                (15.8)

Simplifying,

                                                                                     (15.9)

                                                                                        (15.10)

This is the flow equation for radial flow into a well for confined homogeneous and isotropic aquifer.

In case of steady state condition, the governing equation becomes,

                                                                                            (15.11)