PGE 331
Exam 2 Key
Open book, notes.
Read each problem carefully and show all work, including units.
One
hour time limit.
Indicate your class unique number on the first page below your name:
19320
1011 am
19325
1 2 pm
1.
Derivations.
(5 points each).
Begin with the following conservation equation.
1
r
d
dr
k
ρ
μ
r
dp
dr
=
0
1
The symbols have the meanings that we used in class.
The permeability k is constant in
all cases.
Answer or derive the following:
a.
What type of conservation equation is this?
What are the assumptions involved?
This is a steadystate, microscopic conservation equation for a single phase fluid in one
dimensional radial coordinates.
The phase need not be slightly compressible.
b.
Write Eq. 1 for the special case of an incompressible fluid with constant viscosity.
For incompressible flow the density is constant.
Eq. 1 becomes
1
r
d
dr
r
dp
dr
=
0
c.
Derive the right side of Eq. 756
in the text.
The viscosity is constant.
Cancel out the mobility terms from Eq. 1 to give
1
r
d
dr
k
ρ
μ
r
dp
dr
=
0
=
1
r
d
dr
ρ
dp
dr
0
= ρ
d
dr
dp
dr
+
dp
dr
d
ρ
dr
0
= ρ
d
2
p
dr
2
+
dp
dr
2
d
ρ
dp
1
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0
=
d
2
p
dr
2
+
dp
dr
2
1
ρ
d
ρ
dp
0
=
d
2
p
dr
2
+
dp
dr
2
c
which is the equation.
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 Fall '07
 Lake
 Trigraph, Incompressible Flow, Dr Dr Dr Dr, dr dp dp

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