Consider a steady-flow system. The mass balance equation describing the time variation of average concentration in an aquifer under constant recharge from the surface soil can be written as (Appelo and Postma, 1993; Gelhar, 1993)

where n is the effective porosity of the aquifer, H is the average thickness of the aquifer, C is the average concentration in the aquifer, q is the volumetric recharge rate per unit horizontal area, C_in is the inflow concentration, and t is time. Solving the differential equation above for an initial concentration of C₀ yields

where C(t) is the average concentration in the aquifer at time t.

The aquifer is viewed as a ideal mixer .

Water enters the aquifer at a constant recharge rate , q, and constant concentration C_in .

Discharge from the aquifer is equal to the recharge and the aquifer is a steady-flow system.