PGE 331 Final Exam Key
Unique 19320
Open book, notes.
Show all work and read each problem carefully.
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 singlephase 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.
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Plateau rate = 10 m
3
/day
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
Grading:
1 point each
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
=
θ
Π Π
ϖφ
(
29
=
10
μ
3
δαψ
1 ΜΠα
= 10
μ
3
δαψ ΜΠα
The time constant follows from the exponential decline during the depletion phase.
λ = 
λν
θ
θ
πλατ
τ τ
1
(
29
Substituting in values for a particular time and rate
λ = 
λν
θ
θ
πλατ
τ τ
1
(
29
= 
λν
4
10
200 105
(
29
δαψσ
= 0.0096 δαψσ
1
Grading:
5 points each
c.
(10
points)
Estimate the pore volume drained, and the maximum possible cumulative
oil recovered.
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 Spring '08
 Lake
 Fluid Dynamics, 3rd millennium, constant rate

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