CPE833 Hydrocarbon Production and Processing Tutorial Problems
Property Calculations
1. Using the ideal gas law, the virial equation of state and the Redlich-Kwong equation of
state calculate the specific volume (m3 kg-1) of ethane at 500 K and a range of pressures
between 101.3 kPa and 5000 kPa. Comment on the difference between the values predicted
using each of the three methods. Ethane molar mass (M)= 0.030 kg mol-1
Virial equation of state:
1 Ê RT
V= + Bˆ B = 0.000051 m3 mol-1
M PË ¯
Redlich Kwong equation of state:
RT a
P= - a = 9.869 J m3 mol-1 K0.5 b = 0.0000451 m3 mol-1
(MV - b) MV (MV + b) T
2. Water at 298 K and 101.3 kPa is heated to 350 K. Using the data given below calculate:
(a) The entropy and enthalpy of water at 350 K
(b) The amount of energy required to heat 2.5 kg of water to 350 K
o
S298 = 365 J kg-1 K-1 Ho298 = 104140 J kg-1
C P = 5360 - 7.56T + 0.012T 2 J kg-1 K-1
† Answers
o -1 -1 o
(a) S350 = 1036 J kg K H 350 = 321135 J kg-1 (b) 542488 J
3. Using the data given below calculate the entropy and enthalpy of octane vapour at 101.3
kPa and 450 K. The† octane boils at 400 K.
So298 = 3239 J kg-1 K-1 H o298 = 567000 J kg-1
∆Sv = 736 J kg-1 K-1 ∆Hv = 294700 J kg-1
Cp (liq) = 2231 J kg-1 K-1 Cp(vap) = 1680 J kg-1 K-1
Answers o
S450 = 4830 J kg-1 K-1 H o450 = 1173262 J kg-1
4. 3 m3 of methane are heated from 298 K to 500 K at 101.3 kPa. If the methane behaves as
† gas calculate:
an ideal
(a) The entropy and enthalpy of the methane at 500 K
(b) The amount of energy required to heat the methane.
So298 = 8450.3 J kg-1 K-1 H o298 = 946840 J kg-1
Cp = 1417.4 + 2.879 T J kg-1 K-1 M = 0.016 kg mol-1
Answers (a) So500 = 9765.4 J kg-1 K-1 H o500 = 1465196 J kg-1
(b) Q = 1017 kJ
CPE833 Hydrocarbon Production and Processing Tutorial Problems
5. 10 m3 of propane at 250 K and 1000 kPa are heated to 350 K at 1000 kPa. The PVT
(Pressure Volume Temperature) properties of the propane can be described by the Virial
equation of state. Calculate the energy required for heating.
Molar mass of Propane = 0.044 kg mol-1
At 250 K B = -5.94 x 10-4 m3 mol-1 ∂B/∂T = 5.31 x 10-6 m3 mol-1 K-1
At 350 K B = -2.82 x 10-4 m3 mol-1 ∂B/∂T = 1.81 x 10-6 m3 mol-1 K-1
CoP = 16.4 +0.20 T J mol-1 K-1
Answers 55912 kJ
6. Calculate the enthalpy and entropy of a mixture of gases containing 0.2 kg of carbon
dioxide, 0.4 kg of water, 0.05 kg of methane and 0.01 kg of carbon monoxide, at 600 K and
standard pressure. Assume the mixture behaves as an ideal gas.
Component Molar Mass H o298 So298 Cp
(kg mol-1) (J mol-1) (J mol-1 K-1) (J mol-1 K-1)
Carbon dioxide 0.044 -393794 213.7 28.70+0.033 T
Water (vapour) 0.018 -241993 188.7 30.60+0.010 T
methane 0.016 -74923 186.3 17.86+0.060 T
Carbon monoxide 0.028 -110603 197.6 27.62+0.005 T
o
Answer Smix,600 = 10312 J kg-1 K-1 o
H mix,600 = -10767 kJ kg-1
†7. Calculate the enthalpy and entropy
† of a solution containing 0.8 kg water, 0.1kg ethanol and
0.1 kg methanol at 340 K, and the energy required to heat the solution from 298 K. Assume
the solution is ideal.
Component Molar Mass H o298 So298 Cp
(kg mol-1) (J mol-1) (J mol-1 K-1) (J mol-1 K-1)
Water (liquid) 0.018 -286025 39.8 75.4
Ethanol 0.046 -235160 151.2 120.5
Methanol 0.032 -201440 110.4 80.6
o
Answers Smix,340 = 3123.8 J kg-1 K-1 o
H mix,340 = -13691 kJ kg-1
† †
CPE833 Hydrocarbon Production and Processing Tutorial Problems
Valves, Heat Exchangers Compressors and Expanders
8. Carbon Dioxide at 1000 kPa and 400 K is let down through an adiabatic valve to a pressure
of 200 kPa. Use the data given below to calculate the temperature of the carbon dioxide after
the valve. Assume that:
(a) The carbon dioxide behaves as an ideal gas
(b) The carbon dioxide obeys the Virial equation of state.
For the Carbon dioxide
B = -5.8 x 10-5 m3 mol-1 ∂B/∂T = 4.2 x 10-7 m3 mol-1 K-1
CPo = 37.2 J mol-1 K-1 M = 0.044 kg mol-1
Answers (a) TOUT = 400 K (b) TOUT = 395 K
†
9. Liquid carbon dioxide at its boiling point at 300 K and 6710 kPa is let down to a pressure
of 3203 kPa. Calculate
(a) The vapour fraction after the valve.
(b) The entropy after the valve.
For the carbon dioxide
At 300 K and 6710 kPa
6710
H 300 ( sat.liq.) = 585400 J kg-1
At 270 K and 3203 kPa
3203
†
H 270 ( sat.liq) = 494400 J kg-1 3203
H 270 ( sat.vap.) = 735600 J kg-1
3203
S270 ( sat.liq.) = 3089 J kg-1 K-1 3203
S270 ( sat.vap.) = 3981 J kg-1 K-1
Answers (a) f = 0.377 -1 -1
† † (b) SOUT = 3425 J kg K
† †
10. Steam at 500 kPa is condensed to heat 4 kg s-1 of paraffin from 25 ˚C to 110 ˚C, calculate
the mass flow of steam required for this duty.
For the paraffin CP = 1649 J kg-1 ˚C-1
For the steam at 500 kPa and 150 ˚C ∆HV = 2107420 J kg-1
Answer m˙ steam = 0.266 kg s-1
11. Water at 20˚C is used to cool 10 kg s-1 of crude oil from 150˚C to 40˚C. If the water
cannot be heated to more than 35 ˚C, calculate the mass flow of cooling water required.
†
For the crude oil CP = 2050 J kg-1 ˚C-1
For the water CP = 4180 J kg-1 ˚C-1
Answer m˙ water = 36.0 kg s-1
†
CPE833 Hydrocarbon Production and Processing Tutorial Problems
12. 1.5 kg s-1 of methane are compressed from 280 K and 200 kPa to 1200 kPa in three
stages. The first stage compresses the methane from 200 kPa to 363 kPa. The second stage
compresses the methane from 363 to 600 kPa. The methane is cooled to 305 K between
stages. The isentropic efficiency of each compressor stage is 80%. Calculate the work done in
each stage and plot the process on temperature-entropy coordinates.
For the methane:
M = 0.016 kg mol-1 CPo = 2568 J kg-1 K-1
B = -1.5 x 10-5 m3 mol-1 ∂B/∂T = 1.8 x 10-7 m3 mol-1 K-1
200
S280 = 11484 J kg-1 K-1
†
Answers W1 = 172.4 kW W2 = 156.8 kW W3 = 220.1 kW
†
13. In a gas turbine air is compressed, heated by the combustion of a fuel and then expanded
to gain work from the combustion of the fuel.
2 kg s-1 of air are compressed from 101.3 kPa and 298 K to 1500 kPa. 400 kW of heat is
added to the compressed air by the combustion of natural gas. The air is then expanded to
101.3 kPa. If the isentropic efficiency of the compressor and turbine are 80%, use the data
given below to calculate the net-work done by the gas turbine and the temperature of the gas
after compression, heating and expansion.
M = 0.028 kg mol-1 CPo = 1078 J kg-1 K-1
B = 1.28 x 10-5 m3 mol-1 ∂B/∂T = 5.23 x 10-8 m3 mol-1 K-1
Answers
Net Work = -76 kW !!! This should†be positive, what should be changed to make it positive?
After compression T = 710.6 K, after heating T = 896.6 K, after expansion T = 519.6 K
CPE833 Hydrocarbon Production and Processing Tutorial Problems
Liquid Flows in Pipelines
14. 1.2 kg s-1 of water are pumped from a tank along a pipeline to a heat exchanger where the
water is used to cool a process stream. At the surface of the water in the tank, which is 2 m
above the pump the pressure is 101300 Pa. The diameter of the tank is 2 m.
The inlet to the heat exchanger is 5 m above the pump and the pressure is 175000 Pa. The
pipeline connecting the tank to the heat exchanger is 130 m long and 0.0225 m in diameter,
with an absolute roughness of 0.00004m.
In the pipeline connecting the tank and the heat exchanger there are twelve 90˚ bends, four
fully open gate valves, and a globe valve that is half open.
If the pump has an isentropic efficiency of 90%, calculate the work required to pump the
water from the tank to the heat exchanger. The density of water is 1000 kg m-3 and the
viscosity is 0.001 Pa s.
Answer 1240 W
15. A drain line for water, from an oil-water separator is used to control the level of water.
The oil-water separator is at a pressure of 400000 Pa and the outlet of the drain line is at
101300 Pa. A vertical distance of 1 m separates the inlet and outlet of the drain. The drain line
is 10 m long, has a diameter of 0.01 m and can be considered smooth. In the drain line there is
a bevel seat globe valve. Plot a graph of volumetric flow rate against valve opening.
The density of water is 1000 kg m-3 and the viscosity is 0.001 Pa s.
Flow Rate as a function of Valve Opening for a Bevel Seat Globe Valve
CPE833 Hydrocarbon Production and Processing Tutorial Problems
Compressible flows in Pipelines
16. 0.8 kg s-1 of gas flow isothermally down a pipeline that is 1500 m long. The pipe is
0.0984 m in diameter and the roughness is 0.0001 m. There are six 90˚ bends and a disc check
valve in the pipeline. If the outlet as at a pressure of 350 kPa, calculate the inlet pressure
required.
The temperature is 310 K and the molar mass of the gas is 0.028 kg mol-1. The viscosity of
the gas is 0.00002 Pa s..
Answer PIN = 817.7 kPa
17. Air flows adiabatically down a pipeline 250 m long. The inlet to the pipe line is at 420000
Pa and the outlet is at 340000 Pa. The pipe line is 0.029 m in diameter and has a roughness of
0.00001 m. There are six 90˚ bends and four fully open gate valves in the pipe line.
(a) Calculate the mass flow of air along the pipeline.
(b) Calculate the maximum flow of air along the pipeline.
The air obeys the ideal gas law
M = 0.0288 kg mol-1
The temperature at the inlet is 320 K
Ratio of specific heat capacities g = 1.41
Answers
(a) m = 0.038 kg s-1
(b) Gmax = 102.3 kg m-2 s-1
CPE833 Hydrocarbon Production and Processing Tutorial Problems
Dew Point Control
18. Figure 1 is the Txy diagram for Butane and Pentane at 200 kPa. If 2.5 kg s-1 of a mixture
containing 50 mass% propane is cooled from 330 K to 310 K and passed to a vapour-liquid
separator calculate:
(a) The mass flows of vapour and liquid produced.
(b) The heat load on the cooler
Data
Component CP (liq) J kg-1 K-1 CP (vap) J kg-1 K-1 ∆HV (J kg-1)
Butane 2297 1676.6 383748
Pentane 2146 1666.1 357168
Figure 1 Txy for Butane-Pentane system
Answers
(a) Liquid flow = 1.67 kg s-1 Vapour flow = 0.83 kg s-1
(b) Heat load on the cooler = 701 kW
CPE833 Hydrocarbon Production and Processing Tutorial Problems
19. Figure 2 is a P-xy diagram for methyl butane and di-methyl butane at 340 K. If 0.4 kg s-1
of a mixture containing 60 mass% methyl butane flows through a valve, where the pressure is
reduced from 300 kPa to 230 kPa and then passes to a vapour liquid separator calculate:
(a) The mass flows of vapour and liquid that are produced.
(b) The temperature of the vapour and liquid leaving the separator if the process is
adiabatic.
Data
Component CP (liq) CP (vap) ∆HV Tboil at 101.3
kPa (K)
J kg-1 K-1 J kg-1 K-1 (J kg-1)
methyl butane 2180 1664 354144 301
di-methyl butane 2095 1656 346887 331
Figure 2 – Pxy for Methyl Butane – di Methyl Butane
Answers
(a) Liquid flow = 0.2 kg s-1 Vapour flow = 0.2 kg s-1
(b) T = 251 K
CPE833 Hydrocarbon Production and Processing Tutorial Problems
20. Figure 3 is an xy diagram for the system pentane-dimethyl Butane at 101.3 kPa. 200
kmols per hour of feed containing 25 mol% pentane is to be separated using a distillation
column into a top product containing 90 mol% pentane and a bottom product containing 90
mol% dimethyl butane. If the reflux ratio is 1.5 times the minimum, calculate the number of
stages required.
Pentane - diMethyl Butane at 101.3 kPa
1.0
Mole Fraction Pentane in Vapour
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Pentane in Liquid
Figure 3 xy diagram for pentane di-methyl butane
Answer 12 stages
