PETE 311
Spring2009
Homework #5
Problem 3.
Oil (5 cp) is being produced from a 50md permeability reservoir at rate of 40,000
bbl/day. The pressure at the well, P
w
, is measured to be 2000 psia. Given that the
reservoir radius, r
e
, is 2000 ft, the wellbore radius, r
w
, is 0.5 ft, and the reservoir
thickness, h, is 30 ft. Find the pressure at the boundary of the drainage area, P
e
.
Start from Darcy’s law for radial geometry
And integrate from a poit r to the well,
to the expression for pressure as a function of r
as shown below Note the constant appears due to conversion of units and the (2Pi), as we
saw before for linear case):
1. Use the differential form of Darcy’s equation to derive the flow equation for spherical
flow
of incompressible liquid in a hemispherical shaped reservoir, with a well that
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 Spring '08
 Staff
 Drainage basin, 50md permeability reservoir, hemispherical shaped reservoir

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