3.2 Water Balance

Conservation of mass is a basic principle for understanding groundwater flow. Combining this principle (as a continuity equation) with Darcy’s Law yields a partial differential equation describing changes in head and flux through a groundwater system in response to stresses and boundary conditions. This is discussed in another Groundwater Project book that describes the principles of groundwater flow, including the groundwater flow equations. We can also present a simpler but useful algebraic equation that describes a water balance in an aquifer. A quantitative global water balance statement for a groundwater system can be expressed as Equation 1:

 ∆V/∆t = (R0 + ∆Rt) – (D0 + ∆Dt) – Qt (1)

where:

 ∆V = change in the volume of water in storage in the aquifer (L3) ∆t = length of a time increment of interest (T) ∆V/∆t = global (aquifer-wide) rate of change in storage (L3/T) R0 = total recharge rate into the undisturbed natural system (the virgin recharge) (L3/T) ΔRt = global change in recharge caused by the pumping (L3/T) D0 = total discharge rate from the undisturbed system (prior to development) (L3/T) ΔDt = global change in discharge caused by the pumping (L3/T) Qt = global rate of pumping during the time period, t (L3/T)