02 Exercises Pumping Test

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Sustainable Use of Underground Energy Resources 2023-2024 Pumping test exercises Exercise 1 Groundwater is withdrawn at a constant rate by a fully-penetrating well (PW) from a confined aquifer of infinite lateral extent, constant thickness b = 20 m and homogeneous and isotropic permeability k = 4 × 10-11 m2 . In steady-state conditions, the hydraulic head values measured at two piezometers P1 and P2 are h1 = 35 m and h2 = 38 m. The coordinates of pumping well and piezometers are reported in Table 1. The hydraulic head before pumping is h0 = 40 m. • Determine the rate of withdrawal Q1 from pumping well PW (use water density ρ = 1000 kg m-3 ; gravity acceleration g = 9.8 m s-2 ; water viscosity µ = 10-3 Pa s). Table 1. Pumping well and piezometers coordinates x[m] y[m] PW 0 0 P1 3 4 P2 5 -12 Exercise 2 A pumping test satisfying all conditions of the Cooper and Jacob’s equation is performed with a pumping rate Q = 788 m3 /day. The hydraulic head measured at an observation borehole located at distance r = 30 m from the pumping well is h1 = 9.32 m at t1 = 18 min and h2 = 9.13 m at t2 = 95 min. Calculate the value of transmissivity, T, and storativity, S, of the aquifer that can be inferred from these data knowing that the hydraulic head before the start of pumping was 10 m. Note: all hydraulic head data are given with respect to the same reference system (z = 0).