AG0 exam TP 24 01 22

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24-01-2022 Transport Phenomena in Petroleum Reservoirs Professor Alberto Guadagnini 1. PUMPING TEST A pumping test is performed withdrawing water in an ideal, confined reservoir of constant thickness 𝐵 (unknown) and characterized by a specific storage 𝑆𝑠 = 0.00001 [𝑐𝑚−1]). The pumping well discharges at a constant flow rate equal to 10[ 𝑚3 𝑠 ], is fully penetrating and has an infinitesimal radius. The measured drawdown s [m] at a borehole well located at a distance 𝑟𝑂𝐵𝑆 =30 [m] from the pumping well is plotted for two observations of times 𝑡𝐴 and 𝑡𝐵 (see the available values, marked by red crosses, in Figure 1). It is asked to: i) Estimate the system transmissivity T and thickness 𝐵 using the late time approximation of the Theis solution by relying on the two above cited data (describe in detail the adopted procedure, highlighting the underlying hypotheses, and check their validity). ii) Re-estimate the system properties using the Theis Type curve method on the basis of Figure 1. Compare the estimates of storativity and transmissivity obtained at the previous step against the estimates obtained employing the graphical method and provide comments (see also point (iv) below). iii) Predict (analytically, according to the late time solution ) the drawdown measured at the observation well at two times, namely 𝑡𝐶 and 𝑡𝐷, such that 1 𝑢𝐶 = 100 and 1 𝑢𝐷 = 10. Then, compare these values against those which are actually measured and displayed in Figure 1 (see circles in the figure; hint: comment and motivate the discrepancy, if any, exhibite d at the two instants of time here considered). iv) Is there any advantage in employing the Theis Type curve method to estimate aquifer properties on the basis of the available data? v) Describe the concept of diagnostic plot and list the…