Homework #6
Do problems 12.1, 12.3 on page 265 & 15.6 on page 337.
CBEN 408 Spring 2016
-1-
April 21, 2016
Solutions
Problem #12.1 (15 points)
For an inlet temperature of 32°F (O°C), compare the cooling obtained from a J-T expansion of
methane from 1000 to 200 psig to that obtained from a turboexpander with an adiabatic efficiency
of 80%. What are the outlet temperatures, and how much work is produced for each expansion?
Solution
The table below shows the results for three separate situations: an isentropic expansion (needed
for the actual turboexpander operation), an expansion at 80% adiabatic efficiency (i.e., the change
of enthalpy is only 80% of that for an isentropic expansion), and an isenthalpic expansion to model
the JT valve. The turboexpander will produce as gas 90°F colder than the JT valve (-102°F vs -30°F);
the JT valve will not produce any work whereas the turboexpander will produce work equivalent to
56 Btu/lb of flow.
Note that the results are highly dependent on how accurately one can read the curves of Figure
B.24.
CBEN 408 Spring 2016
-2-
April 21, 2016
Problem #12.3 (15 points)
In a simple turboexpander plant, similar to that shown in Figure 12.15, the bottom and side reboiler
are heated by exchange with inlet gas. The total inlet gas flow rate is 10,000 lb-mol/hr (4,536 kgmol/hr). The inlet gas, which is at 104°F (40°C), splits into two streams. One portion is cooled by
cold residue gas. The other portion is cooled first in the reboiler and then the side reboiler. The
liquid from the demethanizer to the side reboiler is at 0°F (-18°C). The side reboiler duty is 2.866
MMBtu/h (3.024 GJ/h) and the reboiler duty is 2.397 MMBtu/h (2.529 GJ/h). If the inlet gas has a
molar heat capacity of 11.20 Btu/lb-mol (26.05 kJ/kg-mol) over the temperature range being
considered and the minimum exchanger approach temperature is 10°F (5.6°C), what fraction of the
inlet gas is needed to provide the required demethanizer heating?
Solution
The table below shows the temperature & flow parameters for the heat transfer in the two
exchangers (only considering the feed gas sides as the heating utility). Since the total flow of gas is
10,000 lb.mol/hr then about 50% needs to flow through the reboiler/side exchanger combination.
The diagram below shows the order & configuration of the two exchangers & the feed gas.
Bypass
10,000 lb.mol/hr
104°F
10°F
Reboiler
2.397 MMBtu/hr
Side Reboiler
2.866 MMBtu/hr
The following are the steps to do the analysis:
• The temperature of the gas after the 2nd exchanger (the side reboiler) is implied by the
conditions of the cold fluid in (0°F) and the temperature approach on the exchanger, 10°F.
So the outlet temperature on the hot side will be:
•
Thot ,out = Tcold ,in + ( ∆T )approach = 0 + 10 = 10°F
The flowrate can then be determined by considering the duty required in the two
exchangers:
CBEN 408 Spring 2016
-3-
April 21, 2016
B ˆ (T
=
Q NC
=
NB
p
hot ,in − Thot ,out ) ⇒
=
•
Q
Cˆ p (Thot ,in − Thot ,out )
(2.397 + 2.866 ) ⋅106 Btu/hr
(11.20 Btu/lb.mol °F ) (104 − 10 ) °F 
= 4,999 lb.mol/hr
Though not requested we can calculate the intermediate temperature between the two
exchangers. It will either be the temperature out of the reboiler:
Q
B ˆ (T
Q=
NC
Thot ,in −
p
hot ,in − Thot ,out ) ⇒ Thot ,out =
B
NCˆ p
= 104°F −
= 61.2°F
(2.397 ) ⋅106 Btu/hr
( 4,999 lb.mol/hr )(11.20 Btu/lb.mol °F )
or the temperature into the side reboiler:
Q
B ˆ (T
Q =NC
p
hot ,in − Thot ,out ) ⇒ Thot ,in =Thot ,out +
Bˆ
NC
p
=
2.866 ) ⋅ 106 Btu/hr
(
10°F +
( 4,999 lb.mol/hr )(11.20 Btu/lb.mol °F )
= 61.2°F
CBEN 408 Spring 2016
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April 21, 2016
Problem #15.6 (15 points)
The NGL feed to a fractionator is 100,000 bbl/d. The feed consists of 35% ethane, 30% propane,
10% iC4, 20% nC4 and the balance iC5+ (natural gasoline). The percentages are on a liquid volume
basis. If the fractionator produces an 80/20 (LV%) ethane/propane mix, what are the approximate
product rates (bbl/d, m3/h) for EP mix, propane, iC4, nC4 and natural gasoline?
Solution
The table below shows the results assuming that all splits between streams are essentially perfect,
i.e, there are no “tail” amounts between the streams. Note that ethane product is actually 80%
ethane & 20% propane, so there will be ¼ the amount of propane as ethane in this stream. The
remaining propane will be produced as a separate product stream.
CBEN 408 Spring 2016
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April 21, 2016