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
using ideal gas law
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 cm3/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 k12 = 0. Explain the result.
All physical property parameters for methane can be found in Appendix A. The required values for n-dodecane are: Tc = 658.8 K, Pc = 1809.7 kPa, ω = 0.562, cPid = 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 J1 = 5°C, saturated vapor, to P2 = 10 bar. The isentropic efficiency of the compressor is hth = 0.7. The mechanical efficiency is hmech = 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 m3 vessel, liquid ammonia at J1 = 50°C is stored at P1 = 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 P2 = 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 (CO2, O2) Using the Ideal Gas Law

A mixed stream consisting of 1 kmol/h CO2 and 1 kmol/h O2 is compressed from T1 = 290 K, P1 = 1 bar to P2 = 5 bar. Calculate the compressor power for
adiabatic compression   
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 P0 = 3000 bar, T0 = 600 K to P1 = 300 bar by a throttle valve. By a second throttle valve, it is expanded to environmental pressure P2 = 1 bar. Calculate the temperatures T1 and T2 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 P1 = 400 mbar to P2 = 100 mbar? The ambient pressure shall be 1.013 bar.

P14.11         Pressure Rise In a Storage Tank Upon Heating

A vessel (1 m3) 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, ) is compressed adiabatically from P1 = 1 bar to P2 = 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 hth = 0.75. The mechanical efficiency is hmech = 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 P1 = 100 bar, J1 = 350°C
2. Reversible and adiabatic expansion of the vapor in a turbine to P2 = 1 bar.
3. Isobaric condensation.
4. Isentropic compression of the liquid in a pump to P4 =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 J1 = 30°C.
        - Adiabatic pressure relief by a throttle valve to P2 = Ps(-20°C).
        - Complete isobaric evaporation of the refrigerant at J2 = J3 = -20°C
            without superheating
        - Isentropic compression of the saturated vapor to P4 = Ps(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 P2 = 10 bar. The thermal efficiency is hth = 0.8, the mechanical efficiency is hmech = 0.9. Calculate the compressor duty and the state properties at the compressor outlet.