## Problems and Solutions

Chapter 14

Practical Applications

### Textbook Examples:

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14.01
Pressure Build-Up in Vessel Filled with Water and Nitrogen
(p.570)

14.02
Outlet Temperature of a Throttle Valve (p. 572)

14.03
Adiabatic Compression of R22 (p.575)

14.04
Choice of Optimal Refrigerant (p. 576)

14.05
Required Size of a Rupture Disk (p.
580)

14.06
Minimum Crossflow Area of a Valve (p. 582)

### Additional Problems:

P14.01 **
Joule-Thomson Coefficient of Nitrogen Using the Virial Equation
and the SRK EOS**

Calculate the Joule-Thomson coefficient of nitrogen at a
temperature of 150 K and a pressure of 10 atm using the

a) virial equation truncated after the second term using a second
virial coefficient

estimated via the Tsonopoulos method.

b) Soave-Redlich-Kwong equation of state.

All required parameters are given in Appendix A.

P14.02
**Work and Temperature Change Upon Isentropic Compression of
Oxygen**

Oxygen at 25°C and a pressure of 1 bar is compressed to 10 bar.
Calculate the required work and the temperature of the compressed gas
assuming isentropic compression

a)
using ideal gas law

b)
using the Soave-Redlich-Kwong equation of
state

All required physical property parameters are given in Appendix A.

P14.03 **Reversible
and Isothermal Compression of Liquid Water**

A water stream (2000kg/h at 25°C and 1 bar) is compressed to 100
bar in a cooled pump. The process can assumed to be reversible and
isothermal. Calculate the required work and heat duty of the cooling
system. The thermal expansion coefficient
α = 0.207·10^{-3}
K^{-1} and compressibility coefficient
χ= 0.46·10^{-4}
bar^{-1 }can assumed to be constant over the relevant
temperature and pressure range. The molar volume of liquid water at feed
conditions is 18.07 cm^{3}/mol.

P14.04 **Heat
Effect Upon Mixing of Methane and Dodecane at Elevated Temperature and
Pressure Using SRK **

A feed stream of 1600 kg/h of methane is adiabatically mixed with
170 kg/h of n-dodecane.
Both streams are at 160°C and a pressure of 20 bar. Calculate the
temperature of the stream leaving the mixer using the
Soave-Redlich-Kwong equation of state with a binary parameter of k_{12}
= 0. Explain the result.

All physical property parameters for methane can be found in Appendix A.
The required values for n-dodecane are: T_{c} = 658.8 K, P_{c}
= 1809.7 kPa,
ω = 0.562, c_{P}^{id} = 379.8
J/mol K.

P14.05 **Required
Power for R134a Compression Using a High Precision Equation of State**

The refrigerant R134a is compressed from
J_{1}
= 5°C, saturated vapor, to P_{2} = 10 bar. The isentropic
efficiency of the compressor is
h_{th}
= 0.7. The mechanical efficiency is
h_{mech}
= 0.7. Calculate the power of the compressor. The mass flow is 3,000
kg/h. Use a high-precision equation of state.

P14.06
**Required Volume for a Gas Storage Tank for Ammonia**

In a 50 m^{3} vessel, liquid ammonia at
J_{1}
= 50°C is stored at P_{1 }= 100 bar. Due to a vessel failure,
the ammonia is collected in a backup vessel. Which is the necessary
volume of the backup vessel, if P_{2} = 10 bar must not be
exceeded?

P14.07
**Liquid Nitrogen Production Via Volume Expansion of the
Compressed Gas **

In a Linde plant, nitrogen at (J
= -104°C, 240 bar) is let down to P = 1 bar through a valve. How much
liquid nitrogen is produced?

P14.08
**Required Compressor Power for Isothermal and Adiabatic
Compression of a Gas Mixture (CO**_{2}**,
O**_{2}**)
Using the Ideal Gas Law**

A mixed stream consisting of 1 kmol/h CO_{2} and 1 kmol/h
O_{2} is compressed from T_{1} = 290 K, P_{1} =
1 bar to P_{2} = 5 bar. Calculate the compressor power for

a)
adiabatic compression

b)
isothermal compression

The mixture should be regarded as an ideal gas. The compression should
be assumed to be reversible in both cases.

P14.09 **
Temperature Change Upon Ethylene Expansion in Throttle Valves Using a
High Precision EOS**

In an LDPE
(Low Density Polyethylene) plant, ethylene is expanded from P_{0}
= 3000 bar, T_{0} = 600 K to P_{1} = 300 bar by a
throttle valve. By a second throttle valve, it is expanded to
environmental pressure P_{2} = 1 bar. Calculate the temperatures
T_{1} and T_{2} by using a high-precision equation of
state. The velocity terms in the First Law should be neglected.

P14.10
**Leakage Rate Change in Vacuum Distillation When Lowering the
Column Pressure**

In vacuum distillation columns, the leakage of ambient air into
the column is always a problem and might lead to an explosive atmosphere
in the condenser. How does the leakage rate rise if the column operating
pressure is lowered from P_{1} = 400 mbar to P_{2} = 100
mbar? The ambient pressure shall be 1.013 bar.

P14.11
**Pressure Rise In a Storage Tank Upon Heating**

A vessel (1 m^{3}) containing 500 kg propylene at
J
= 30°C is exposed to sun radiation. What is the initial pressure? The
safety valves of the vessel actuate at P = 60 bar. Use a high-precision
equation of state to calculate the respective temperature.

P14.12 ** Work
and Temperature Change Upon Adiabatic Compression of Oxygen**

Oxygen (J
= 25°C,
_{1} = 1
bar to P_{2} = 10 bar. Calculate the power of the compressor and
the outlet temperature of the gas using

a) the ideal gas law

b) the Soave-Redlich-Kwong equation
of state

The isentropic efficiency of the compressor is
h_{th}
= 0.75. The mechanical efficiency is
h_{mech}
= 0.95.

P14.13
**Thermodynamic Cycle Calculation Using a High-Precision EOS **

A thermodynamic cycle is operated with water at the following
conditions:

1. Isobaric heating to P_{1} = 100 bar,
J_{1
}= 350°C

2. Reversible and adiabatic expansion of the vapor in a turbine to P_{2}
= 1 bar.

3. Isobaric condensation.

4. Isentropic compression of the liquid in a pump to P_{4} =100
bar.

Calculate the thermal efficiency of the process defined by

Use the high-precision equation of state.

P14.14
**Refrigeration Cycle Calculation Using the Peng-Robinson EOS **

A refrigerator is operated with R12 (dichlorodifluoromethane).
The particular steps of the compression cycle are:

- Isobaric condensation without
subcooling at
J_{1}
= 30°C.

- Adiabatic pressure relief by a
throttle valve to P_{2} = P^{s}(-20°C).

- Complete isobaric evaporation of
the refrigerant at
J_{2
}=
J_{3
}= -20°C

without
superheating

- Isentropic compression of the
saturated vapor to P_{4} = P^{s}(30°C).

Calculate the process data for the steps 1-4 using the Peng-Robinson
equation of state.

P14.15 **Joule-Thomson
Coefficient for Methane Using the Peng-Robinson EOS**

Calculate the Joule-Thomson coefficient for methane at T = 300 K
and P = 30 bar using the Peng-Robinson equation of state. The critical
data and the acentric factor can be taken from App. A.

P14.17 **
Compressor Duty and State Properties after Ammonia Compression**

Gaseous ammonia (100°C, 5 bar) is compressed to P_{2} =
10 bar. The thermal efficiency is
h_{th}
= 0.8, the mechanical efficiency is
h_{mech}
= 0.9. Calculate the compressor duty and the state properties at the
compressor outlet.