AG exam TP 11 02 22

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02-11-2022 Transport Phenomena in Petroleum Reservoirs Professor Alberto Guadagnini 1. PUMPING TEST A pumping test is performed withdrawing water in a homogeneous, confined reservoir of constant thickness 𝐵 (unknown) and characterized by a specific storage 𝑆𝑠 = 10−6 [𝑐𝑚−1]). The pumping well 𝑃𝑊1 discharges according to the stepwise variable flow rate (schedule depicted in the chart ), is fully penetrating and has an infinitesimal radius. Drawdown is observed at a borehole (located at a distance 𝑟0 =90 [m] from the pumping well ) at times 𝑡1 = 1[ℎ] (drawdown 𝑠1 = 19.8182[𝑚]) and 𝑡2 = 1.8[ℎ] (drawdown 𝑠2 = 20.4936[𝑚]). It is asked to: i) Estimate hydraulic conductivity and thickness of the aquifer (describe in detail the procedure, highlighting the underlying hypotheses and check ing their validity). ii) A second pumping well, namely 𝑃𝑊2, located at distance 𝑟02 = 110[𝑚] from the monitoring borehole (see picture) , starts pumping at time 𝑡𝑃2 = 𝑡2 with constant flow rate 𝑄3 = 20[𝑚3/𝑠]. Evaluate drawdown at the monitoring well at 𝑡3 = 2[ℎ] from the beginning of pumping of the first pumping well (hint: consider superimposition of effects). iii) Briefly describe strengths and limitations of collecting drawdown measurements directly at the pumping well for system characterization. iv) Briefly describe the main concepts associated with the Bear and Jacobs model for (single) well catchment regions. 2. TRACER EXPERIMENT A pulse of conservative tracer is injected in a column (of length 𝐿 of 70 [𝑐𝑚]) filled with porous material. The porous medium is characterized by a hydraulic conductivity 𝐾 = 2.34 [𝑚/ℎ], effective porosity Φ = 13% and uniform head gradient J = 0.02. The total injected solute mass is 𝑀𝑖𝑛𝑗 = 25 [𝜇𝑔]. The following measurements of concentration are available at 𝑥 =…