Solution Exercise 5
1. Impact Time for a Hydraulic Head Change at the Community Spring
The time to observe a hydraulic head response at the community springs can be approximately by:
t = (L2Ss)/K
where L is the distance from the pumping center to the springs, Ss is specific storage of the limestone and K is hydraulic conductivity.
t = (3000 m) (3000 m) (1×10–4 m–1) / (5×10–6 m/s) ≅ 6 years
2. Solute Arrival Time to the Community Spring
The time for a solute released in the pit, which then bypasses the capture zone of the pumping wells, and migrates to the springs can be approximated using the equation for groundwater velocity (v):
v = (K / θ) dh/dL
where θ is the effective porosity and dh/dL is the hydraulic gradient. The hydraulic gradient can be estimated in a simple way as the vertical distance between the pit floor and the springs divided by the distance from the pit to the springs. The water table at the open pit will likely be controlled by pumping at an elevation a small distance below the pit floor.
v = [(5×10–6 m/s) / 0.05] * [200 m / 2800 m]
v = 7x 10–6 m/s
The solute arrival time by advective transport, assuming a linear horizontal flow path to the springs (that is, 2800 m) and steady state flow, travel time is distance/velocity.
time = distance/v = 2800 m / (7×10–6 m/s) thus, the estimated travel time is about 12 years.
The calculation of both the head response time and the travel time should be viewed as initial estimates. If more accurate values were required in an impact assessment, standard practice would be to construct a three-dimensional hydrogeological simulation model to take into proper account the influence of domain geometry on pressure propagation and groundwater flow paths. Given the minimal time required to calculate an analytical solution, the results are valuable to a numerical modeler who can compare the values and, while qualitatively compensating for the simplifications of the analytical solution, can investigate the numerical model setup more carefully if the analytical and numerical results are strikingly different.