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NAME
___________________
SIGNATURE _____________________
UT EID ___________________
MIDTERM EXAM
PGE 421K
SPRING 2010
Open book and open notes.
Answer all
five
questions on the exam paper; use your own engineering paper only if you
need more space.
Put your name and EID on any engineering paper you turn in.
If you think you need more information to solve a problem, make a plausible assumption,
write it down, and continue working.
No credit
for answers with inappropriate units.
1)
Two immiscible, incompressible fluids are flowing in the control volume
pictured below. Each mass flow rate
and
refers to the combined rate of
both fluids. There are exactly two components
A
and
B
in system. For
t
1
<
t
<
t
2
,
the rate of generation of component
A
in the control volume is negative.
Which
of the following
must be true
during the interval
t
1
<
t
<
t
2
?
Circle all that apply.
10 pts
a.
Net rate of accumulation of
A
in the CV
is positive.
b.
Net rate of accumulation of total mass in the CV is positive.
c.
Net rate of accumulation of
A
in the CV
is negative.
d.
Net rate of generation of
B
in the CV is positive.
e.
Net rate of transport of
B
across the CV boundaries is negative.
We have
,
and during the
time interval in question we also have
.
Since
, where
w
A
is the mass
fraction of
A
in the streams flowing across the CV boundaries, it follows that the rate of
accumulation of
A
in the CV is negative. Thus (a) cannot be true and (c) must be true.
For the total mass in the CV, we have
, because the
rate of generation of total mass must be zero. Therefore (b) cannot be true. Because there
are exactly two components in the system, the rate of destruction of
A
must
equal the rate
of creation of
B
.
That is,
,
, so
. Therefore (d) must
be true. The rate of transport of component
B
across the CV boundaries is
, so (e) must be true.
2
0
m
Control Volume
1
0
m
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View Full Document2)
Work all
four
parts (a)  (d).
Vast quantities of brine in deep, overpressured
formations in south Texas contain dissolved methane. The binary system (CH
4
– H
2
O)
phase diagrams for two temperatures are shown below (one set with linear xaxis, the
other with logarithmic).
Your company has acquired rights to a formation that is 12,000
ft deep. The aquifer conditions are 11500 psia and 280°F.
A sample of the brine has been
retrieved. Laboratory measurements indicate its bubble point is 5000 psia; its density,
heat capacity and viscosity at reservoir conditions are 1100 kg/m
3
, 4.25 J/g/K and 0.44 cP.
30 points
a) Estimate the concentration of CH
4
in the brine at aquifer conditions. Give
your answer as a mole fraction.
The bubble point tells you the pressure at which first bubble of gas forms from the
brine at reservoir temperature. The intersection of P = 5000 psia and the bubble point
curve (left hand curve on the Px diagrams) shows the mole fraction of CH
4
would be
0.01 if the aquifer temperature were 250 F and 0.004 if the aquifer were at 300 F.
Note it
is much easier to determine the mole fraction from the log scale curves. Interpolation
indicates that the mole fraction of CH
4
in our 280°F aquifer is about 0.007.
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 Spring '11
 BRYANT

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