Homework #6
Do problems 18.1, 18.2, 18.3, 18.4, 18.5 on page 417.
CBEN 408 Spring 2016
-1-
May 3, 2016
Solutions
Problem #18.1, 18.2, & 18.3 (10 to points)
How much HHV energy (in Btu or PJ) is contained in the cargo aboard a 145,000 m3 LNG carrier?
Assume the LNG has a relative density of 0.45, a molar mass of 18 and a heating value of 1,000
Btu/scf (39.4 MJ/Nm3).
What is the value of the cargo in Exercise 18.1 if the fuel is priced at $5.00 per MMBtu
($4.75/GJ)?
What is the equivalent volume of gas (in scf [Nm3]) of the cargo in Exercise 18.1?
Solution
The table below shows all of the intermediate calculations using U.S. Customary units. The cargo
has an HHV content of 3.0 TBtu (3.0 million MMBtu = 3.01012 Btu), has a value of $14 million, and
is equivalent to 3.0Bscf (3.0109 scf).
The calculation is converting from volume to number of moles. The value of relative density is for
the density at the storage conditions but is related to the density of water its standard conditions
(60°F & 1 atm), 63.3665 lb/ft3). So:


 145000 m3  

  0.45  62.3665 lb  
3 

ft 3  

m  
0.3048
*

 
ft  
V  V   NG w   
N


lb
M
M
18
lb.mol
6
 7.98 10 lb.mol
All other values are derived from here.
CBEN 408 Spring 2016
-2-
May 3, 2016
Problem #18.4 (5 points)
An LNG-receiving terminal sends gas to the pipeline at 1,000 psig (70 barg). The LNG is essentially
pure methane and is stored in a tank at 2 psig. What is the pump energy (hp, MW) required to send
out 400 MMscfd (10.7 × 106 Nm3/d) of gas to the pipeline at 40°F (4.4°C). Assume a pressure drop
through the vaporizer of 20 psi (1.4 bar) and a pump efficiency of 70%. (See Chapter 2 for pumps).
Solution
The BFD for this process is shown below. Note that all of the pressure increase comes from
pumping the cryogenic liquid. Sufficient pressure is required to overcome any of the other process
pressure drops (i.e., the pressure drop across the Revaporizer). The results are shown in the
following table.
Liquid @ 1020 psig
Gas @ 1000 psig
Liquid @ 2 psig
Storage Tank
Revaporizer
Pump
Rather than trying to use the PH diagram for methane to
do these calculations (since following lines for constant
entropy is extremely difficult when dealing with a liquid)
we will use the Bernoulli equation:
P
Wˆ s 

The values for the methane properties were obtained
from Table B.21 of the text book. The actual values were
obtained by linear interpolation of the appropriate values
at the inlet pressure, 2 psig = 16.7 psia.
For this pumping:
lbf  
in2 

1020

2
144



in2  
ft 2 
ft lbf
P 
Wˆ s 

 5590
lb

lbm
26.23 m2
ft
Next, we need the mass flowrate to determine the total pumping power:
CBEN 408 Spring 2016
-3-
May 3, 2016

6 scf 
 400  10 day  
lbm 
lb
lb
  16.042
m  NM  
 16.9  106 m  195.7 m

lb.mol 
day
sec
 379.49 scf 


lb.mol 

So the required power @ 100% efficiency is:
lb  
ft lbf 

Ws  mWˆ s   195.7 m   5590

sec  
lbm 

ft lbf
Btu
 1,094,000
 1,406
 1,989 hp
sec
sec
Since the pump efficiency is 70% then:
Wact 
Ws 1,989 hp

 2,841 hp

0.7
How do these calculations compare to the results for HYSYS? The PFD below shows a simple
simulation using BWRS for the methane properties. The hand calculation is just 0.6% higher than
that calculated in HYSYS. This corresponds to the 0.6% difference in the liquid densities.
CBEN 408 Spring 2016
-4-
May 3, 2016
Problem #18.5 (10 points)
The LNG terminal in Exercise 18.4 uses seawater to heat LNG from storage temperature for send
out. For a gas send out rate of 400 MMscfd (10.7 x 106Nm3/d) and using fresh water properties:
a) What water flow rate (lbm/h, kg/h) is required to heat the LNG, assuming an inlet water
temperature of 50°F (10°C) and an outlet water temperature of 40°F (4°C)?
b) What is the hp (kW) required to lift the water 50 feet (15 m) above sea level to the
vaporizer assuming a pump efficiency of 80%?
Solution
The BFD for this process is shown below. Note that the duty in the Revaporizer will depend on how
hot the methane can be warmed; if we assume that the heat exchanger can be designed with a 10°F
approach temperature then the outlet temperature will be 40°F (i.e., water inlet temperature minus
the approach temperature). The results are shown in the following table.
40°F
50°F
40°F
50 ft
Revaporizer
Pump
Methane: -258°F
Sea water
The methane properties are determined from the P-H
diagram in the textbook, Figure B.24.
We will use the Bernoulli equation to determine the
amount of work required to lift the seawater up 50 ft:
g
Wˆ s  h
gc
The rate of seawater needed is determined form an energy balance around the Revaporizer:
CBEN 408 Spring 2016
-5-
May 3, 2016
Q  mgas
mwater


Hˆ gas,out  Hˆ gas,in  mwaterCˆ p ,water Tin  Tout    mwater 

mgas Hˆ gas,out  Hˆ gas,in

Cˆ p ,water Tin  Tout 

Btu 
6 lb  
 16.9  10 day   365  45 lb 
lb
lb



 541  106
 6,260
day
sec
 Btu 
 1 lb °F  50  40 °F 


For this pumping:
g
Wˆ s  h  50 ft 
gc
ft
sec2  50 ft lbf
lb ft
lbm
32.2 m 2
lbf sec
32.2
So the required power @ 100% efficiency is:
lb   ft lbf 

Ws  mWˆ s   6260 m   50

sec  
lbm 

ft lbf
Btu
 313,000
 402
 569 hp
sec
sec
Since the pump efficiency is 80% then:
Wact 
Ws 569 hp

 712hp

0.8
How do these calculations compare to the results for HYSYS? The PFD below shows a simple
simulation using BWRS for the methane properties & ASME steam tables for the water properties.
The hand calculation is just 0.5% lower than that calculated in HYSYS. This is due to the difference
in the Revaporizer duty; the major contribution to this is that the hand calculation has a duty that is
0.6% lower than that from HYSYS. Further note that HYSYS does not allow one to specify the
hydraulic “head” on the pump; but, we can specify the pressure change necessary to overcome this
head. This will be:

ft
32.2

lb
g 

sec2
P  h   62.40 m3  50 ft  
gc 
ft 
 32.2 lbm ft

lbf sec2

CBEN 408 Spring 2016
-6-

 1

in2

144
 
ft 2



lb
  21.67 2f .
in



May 3, 2016
CBEN 408 Spring 2016
-7-
May 3, 2016