Energy Engineering - Sustainable use of underground energy resources

02 - Exercises Pumping Test

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Sust ai nable U se of Unde rgro und Ene rgy R es ources 2023 -2024 Pum ping test exercises Exercise 1 Ground water is withd rawn at a constant rate by a fully-pen etrating well (PW) from a confined aqu ifer of infinite lateral extent, constant thickness b = 20 m and homo gene ous and isotropic per meab ility k = 4 × 10-11 m2 . In stead y-state cond itions, the hydraulic head values measured at two piezometers P1 and P2 are h1 = 35 m a nd h2 = 38 m. The coordinates of p ump ing well a nd pi ezom eters are rep orted in Table 1. The hydraulic head b efore pump ing is h0 = 40 m. • Determine the rate of withdrawal Q1 from pump ing well PW (use water dens ity ρ = 1000 kg m-3 ; gravity accele ration g = 9.8 m s-2 ; water viscosity µ = 10-3 Pa s). Table 1. Pumping well and piezom eters coo rdinates x[m] y[m] PW 0 0 P1 3 4 P2 5 -12 Exercise 2 A pump ing test satisfying all cond itions of the Cooper and Jacob’s eq uation is performed with a pump ing rate Q = 788 m3 /day. The hydraulic head measu red at an observation bo rehole located at distance r = 30 m from the pump ing well is h1 = 9.32 m at t1 = 18 min and h2 = 9.13 m at t2 = 95 min. Calc ulate the value of transmiss ivity, T, and storativity, S, of the aquifer that can be inferred from these data kn owing that the hydraulic head before the start of pump ing was 10 m. Note: all hydraulic head d ata a re given with respect to the same referen ce syst em (z = 0).