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HW10Key (323K)

# HW10Key (323K) - Homework#10 Key PGE323k 1 Associating a...

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Homework #10 Key PGE323k 1. Associating a Time Scale. The figures below show the rate and pressure history of the primary depletion of a small reservoir to its economic limit. The total compressibility is 3 GPa -1 . The produced fluid is a slightly compressible undersaturated single-phase oil. 0 2 4 6 8 10 12 0 50 100 150 200 250 300 350 Time, days 22.5 23 23.5 24 24.5 25 25.5 0 50 100 150 200 250 300 350 Time, days Average Well a. (5 points) Give values for the plateau rate, the length of time of the constant rate period, the length of time required to attain stabilized flow, the limiting pressure, and the value for the economic limit. These are read directly from the graph. Plateau rate = 10 m 3 /day 1

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Constant rate length = 105 days Time to attain stabilized flow = about 10 days (time for pressure decline to be straight) Limiting pressure = 23 MPa Economic limiting rate = 1.5 m 3 /day b. (10 points) Estimate the productivity index and the time constant. The productivity index is based on the drawdown during stabilized flow in the constant rate period. J = q P - P wf ( 29 = 10Ź m 3 day 1ŹMPa = 10Ź m 3 day - MPa The time constant follows from the exponential decline during the depletion phase. λ = - ln q q plat t - t 1 ( 29 Substituting in values for a particular time and rate λ = - ln q q plat t - t 1 ( 29 = - ln 4 10
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