Download 11.A-1 It is often necessary to prepare a gas mixture with accurately

© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.A-1 It is often necessary to prepare a gas mixture with accurately known composition. Such
mixtures are used to calibrate gas analysis instruments. In the present case, a mixture of
80% ethylene (molar basis) (C2H4) and 20% carbon dioxide (CO2) is prepared in the
following manner. Two uninsulated tanks, each of 4 liter volume, are connected
together. One tank contains ethylene gas at 100 atm, 25°C. The other contains carbon
dioxide 25°C and PCO2,1. The valve connecting the tanks is now opened and remains
open for a long time until a homogeneous mixture at the desired proportions is obtained.
The surroundings are at 25°C, 1 atm.
Answer the following questions assuming that the gas mixture obeys the ideal gas law.
Note that, in EES, ideal gas ethylene is represented with substance C2H4 and ideal gas
carbon dioxide is represented with substance CO2.
a.)
b.)
c.)
d.)
What is the initial CO2 pressure, PCO2,1?
What is the final pressure of the gas mixture?
What is the heat transfer for this process?
What is the total exergy destruction for this process?
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.A-2 A mixture of 80% methane and 20% ethane on a molar basis is contained in an insulated
0.5 m3 tank at 6 bar and 30°C. The value is opened accidentally, and the pressure quickly
drops to 2 bar before the valve is closed.
a.) Calculate the mass of gas mixture that escapes, assuming ideal gas behavior.
b.) Eventually, the gas mixture returns to the temperature of the surroundings, 30°C.
Estimate the tank pressure at this time, assuming ideal gas behavior.
c.) Calculate the heat transferred to gas mixture in part b), assuming ideal gas behavior.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.A-3 A mixture of helium and ethane was prepared as follows. As shown in Figure 11.A-3,
there are separate supply manifolds for helium and ethane. The well-insulated mixing
tank is first evacuated to a very low pressure. Helium from a pipeline at 100°F, 10 atm is
then admitted very rapidly until the pressure in the tank is 2 atm. The helium supply
valve is then closed. Thirty minutes later, the ethane supply valve is opened to allow
ethane from a pipeline at 100°F, 5 atm to flow into the tank. The valve is closed when
the tank pressure reaches 3 atm. A day later, the gas mixture is drawn off through valve
C. The tank is cylindrical with an inner diameter of 1 ft and a height of 1 ft. The walls
are made of aluminum with a uniform thickness of 0.25 in. At these low pressures,
assume helium and ethane to behave as ideal gases.
Helium
100°F, 10 atm
Ethane
100°F, 5 atm
Valve A
Insulated
Aluminum
Tank
Valve B
Height=1 ft
Diameter=1 ft
Thick=1/4 in
Valve C
Figure 11.A-3: Preparation of a gas mixture of helium and ethane
a.) What is the temperature of the helium in the tank when valve A is closed?
b.) What is the temperature of the gas mixture in the tank when valve B is closed?
c.) What is your best engineering estimate of the composition of the mixture removed
through valve C?
d.) What is the total entropy generation for this process?
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.A-4 A mixture of 70% methane and 30% nitrogen (molar basis) enters a compressor at -40°C,
and 10 atm with a mass flow rate of 10 kg/min. Estimate the minimum power required to
compress the mixture to 100 atm, assuming ideal gas behavior.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.A-5 A gas mixture is prepared by steadily mixing carbon dioxide and ethylene, both at 100°C,
175.8 atm, in molar proportions of 69.5% carbon dioxide and 30.5% ethylene. The
mixture exits at 100°C, 175.8 atm. Assuming that the mixture obeys the ideal gas law,
a.) Determine the molar volume of the mixture
b.) Determine the required heat transfer per mole of mixture
c.) Determine the entropy generation per mole of mixture
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.A-6 A binary gas mixture can be prepared by charging one component into a tank of known
volume that contains the other gas. The pressure of the gas that is initially in the tank
must be set so that the desired composition results when the second gas is charged. In a
particular case, a 40 liter tank is available containing nitrogen at 25°C. The tank is
connected to a fill line carrying ethane gas at 25°C and 84 bar is available as shown in
Figure 11.A-6. The valve is opened to allow ethane to enter the tank. The valve remains
open until the gas mixture within the tank returns to 25°C.
Ethane
25°C, 84 bar
valve
40 liters
Nitrogen
Figure 11.A-6: Schematic of the charging process
Assuming ideal gas behavior, determine
a.) The pressure that the nitrogen should be at so as to have an equimolar mixture when
the charging process has completed.
b.) The heat transfer for this process
c.) The entropy generation for this process
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.B-1 The gases in Problem 11.A-1 may not obey the ideal gas law at the pressures occurring in
this problem. However, the gas mixture is still likely to behave as an ideal solution. An
ideal solution, also called Amagat’s rule is defined as a mixture that does not change
volume when the pure gases are mixed isothermally. In an ideal solution, each gas
behaves as if it is pure at the temperature and pressure of the mixture. Answer the
questions posed in problem 11.A-1 using the pure gas properties in EES with substances
ethylene and carbondioxide and ideal solution theory. Compare your results with the
results obtained assuming ideal gas behavior in problem 11.A-1.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.B-2 a.) What will the answers to questions a), b), and c) of problem 11.A-2 be if the gas
mixture is assumed to obey the ideal solution theory (Amagat’s rule) instead of the
ideal gas law?
b.) Repeat the calculations for an initial pressure of 60 bar and a final pressure after the
leak is discovered of 20 bar using the ideal gas law and Amagat’s rule. Compare the
results and comment on the applicability of the ideal gas law at these conditions.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.B-3 Use the Peng-Robinson equation of state to solve problem 11.B-2 in place of ideal
solution theory. You are welcome to use the Peng-Robinson library in EES if you wish.
The binary interaction coefficient between methane and ethane may be assumed to be
zero because of the chemical similarity of ethane and methane. Compare the results with
the results from problem 11.B-2. Which method in your opinion will provide more
reliable answers?
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.B-4 Resolve problem 11.A-5 assuming the mixture obeys
a.) the ideal solution assumption
b.) the Peng-Robinson equation of state
Compare the results with each other and with the results from the ideal gas law.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.B-5 Refrigerant 410A is a mixture of 50% Refrigerant 32 and 50% Refrigerant 125 where the
percentages are on a weight basis. Property information for R32 and R125 are available
in EES. Use the pure fluid property data and Peng-Robinson equation of state for the
mixture to calculate and plot the specific volume, specific enthalpy and specific entropy
of R410A as a function of temperature between 40°C and 100°C for pressures of 5, 10,
and 20 bar. Compare your results with the property data in EES for R410A. However,
note that the specific enthalpy and entropy reference states for R410A are not consistent
with the reference states for R32 and R125 so an offset between the EES values and those
calculated with the Peng-Robinson equation of state can be expected.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.B-6 Nitrogen and hydrogen are mixed at 300 atm and 25°C as the first step in the production
of ammonia. Using the Peng-Robinson equation of state, prepare the following plots as a
function of the mole fraction of hydrogen, ranging from 0 to 1.
a.) the mixture specific volume
b.) the enthalpy change of mixing
c.) the entropy change of mixing
Indicate how the plots would look if the mixture were assumed to be an ideal solution
following Amagat’s rule.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.B-7 A natural gas has the following composition on a weight basis: 85% methane, 5% ethane
and 10% nitrogen. The gas is compressed to 4 MPa for transport though a pipeline at
10°C. The power needed to transport the gas is a function of its density. Estimate the
density of this gas mixture with the following methods and compare the results.
a.) ideal gas law
b.) ideal solution of real gases
c.) Kay’s approximation
d.) Redlich-Kwong-Soave equation of state
e.) Peng-Robinson equation of state
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.B-8 Solve problem 11.A-6 using the Peng-Robinson equation of state for the properties of the
mixture. The EES property data base can be used for the pure fluids.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.B-9 A gas mixture consisting of 70 mole percent methane and 30 mole percent nitrogen at
100 atm and 300 K expands through an insulated nozzle to a final pressure of 35 atm.
The temperature at the nozzle exit is reported to be 255 K. Using the Peng-Robinson
equation of state, determine:
a.) the velocity at the nozzle exit
b.) the rate of entropy generation for this process
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.B-10 A mixture of 60% (by mole) carbon dioxide and 40% nitrogen at 60 bar and 30°C is
prepared in a 5 m3 tank by mixing appropriate amounts of the pure gases, that each enter
the tank at 60 bar and 30°C. The tank is initially evacuated. Assume that the mixture
obeys the Peng-Robinson equation of state.
a.) Determine the mass that has been placed in the tank
b.) Estimate the required heat transfer
c.) What is the entropy generation resulting form this mixing process?
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.B-11 A gas mixture used in a Joule-Thomson expansion cycle consists of 50% R23 and 50%
methane (molar basis). This mixture enters a compressor at 2.5 atm and -40°C with a
mass flow rate of 0.25 kg/s where it is compressed to 92 atm. Estimate the specific
volume of the mixture exiting the compressor, the minimum compressor power, and the
compressor outlet temperature (for the adiabatic case) if the compression process is: a.)
isothermal; b.) adiabatic, using the following three methods:
i.) the ideal solution approximation,
ii.) Kay’s method, and
iii.) the Peng-Robinson equation of state.
You may use the GEN_EOS and Peng-Robinson libraries in EES to simplify the
calculations, if you wish. The interaction coefficient between these gases can be
estimated using Eq. (11-80).
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.B-12 Compare the specific volumes of an equimolar mixture of propane and n-butane at 450 K
and 25000 kPa using:
a.) Dalton's rule;
b.) Amagat's rule;
c.) Kay's rule.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.B-13 A gas mixture is prepared by isothermally mixing ammonia and propane, both at 375 K,
at a constant pressure of 30 bar. Calculate and plot the molar volume of the mixture, the
heat transfer per mole of mixture and the entropy production per mole of mixture as a
function of the ammonia mole fraction determined in the following ways:
a.) Ideal gas approximation;
b.) Kay’s rule;
c.) Redlich-Kwong-Soave equation of state
d.) Peng-Robinson equation of state.
You may use the GEN_EOS and Peng-Robinson libraries in EES to simplify the
calculations, if you wish. The interaction coefficient between these gases can be
estimated using Eq. (11-80).
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.C-1 A mixture of oxygen and helium is prepared as shown in Figure 11.C-1. Helium gas at
25°C and pressure P is bubbled through tank containing liquid oxygen at 125 K. The
pressure in the tank is maintained at P with a pressure regulator. The temperature of the
liquid oxygen is maintained at 125 K by heat transfer to liquid nitrogen coil. The gas
mixture is eventually heated to 25°C and throttled to 1 bar at 0.034 m3/s. The helium has
negligible solubility in the liquid oxygen. Assuming that the gas mixture behaves as an
ideal solution, calculate and plot the mole fraction of the oxygen and the required heat
transfer rate to the liquid nitrogen as a function of the pressure in the tank for pressures
ranging from the saturation pressure of oxygen at 125 K to 120 bar.
Pressure
gauge
Pressure
Regulator Throttle
long pipe
0.034 m3/s
25°C, 1 bar
Oxygen and
Helium gas
liquid N2
Liquid
Oxygen
Helium
25°C, P
Figure 11.C-1: System to generate mixture of helium and oxygen
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.C-2 A mixture of refrigerants R12 and R114 enters the evaporator of a vapor compression
refrigeration system at -25C and 60 kPa. The quality (on a mass basis) of the entering
mixture is 35%. R12 and R114 are chemically similar and it can be assumed that the
mixture obeys Raoult’s law and that specific enthalpy of the liquid and vapor phases can
be determined assuming that they form ideal solutions. Property data for pure refrigerant
R12 and R114 are available in EES.
a.) Calculate the entering mole fractions for the R12 and R114 in the liquid and vapor
phases.
b.) Determine the overall mass ratio of R114.
c.) Determine the temperature of the refrigerant mixture exiting the evaporator as a
saturated vapor at 60 kPa.
d.) Estimate the heat transfer in the evaporator per kg of entering refrigerant for these
conditions.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.C-3 The “propane” tanks that are used for heating and cooking actually contain a mixture of
propane and butane. Some suppliers of the fuel will tailor the composition of the fuel as
a function of local weather conditions. In cold weather, a higher percentage of propane is
used in order to achieve a higher delivery pressure whereas, in summer, the propane
percentage is reduced. Assume that liquid and vapor phases of propane and n-butane
form ideal solutions due to their chemical similarity. Property data for the pure fluids are
available in EES with properties PROPANE and n-BUTANE, respectively, should you need
them.
a.) Suppose that a 0.42 m3 tank is charged on a hot summer day with a saturated mixture
of propane and n-butane to 900 kPa at 40C. The volume fraction of the liquid is
95% after charging. What are the total mass of fuel in the tank and the overall mole
fraction of propane?
b.) What will the pressure be if the tank and its contents are later cooled to -30C without
any of the fuel having been used?
c.) What will be the mass of fuel and overall mole fraction of propane if the 0.42 m3 tank
is charged with a mixture of propane at -30C, 115 kPa so that 80% of the volume is
liquid?
d.) If the tank contents determined in part c) are later heated to 40C without any of the
fuel having been used, what will the pressure be?
e.) Estimate the percent difference in energy content for a fully charged tank for cases a)
and c). The lower heating values of propane and n-butane are 46,327 kJ/kg and
45,348 kJ/kg, respectively.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.C-4 A saturated liquid mixture of propane and n-butane at 40C, 900 kPa is throttled to 125
kPa as it passes from an LPG tank through the piping into the heating appliance.
Assuming that the throttling process is adiabatic, estimate the temperature, the quality on
a mass basis, and the molar composition of the liquid and vapor streams of the fuel just
downstream of the throttle. You may assume Raoult’s law and is applicable for this
mixture. Further, at the low pressure downstream of the throttle, the vapor phase may be
assumed to obey the ideal gas law.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.C-5 The performance of standard vapor compression refrigeration cycles is normally
estimated assuming that the refrigerant is a pure substance. In most refrigeration cycles,
however, the refrigerant is mixed with oil. The presence of oil in the liquid refrigerant
lowers the vapor pressure exerted by the refrigerant at a given temperature, leading to
lower capacity or higher evaporator temperatures than expected based on property data
for pure refrigerants. Consider a specific situation in which refrigerant R22 with 3% (by
mass) mineral oil exits the condenser of a refrigeration cycle as a liquid solution at 35°C
and 1500 kPa. This liquid is adiabatically throttled into the evaporator. The refrigerant
oil mixture exits the evaporator as a two-phase system at -10°C, 300 kPa. The oil-rich
liquid phase returns oil to the compressor crankcase. The compressor is a reciprocating
constant-displacement device that produces a constant volumetric flow. Properties of the
oil are provided below. Assume that the oil and R22 form an ideal solution and that
Raoult’s law is applicable for phase equilibrium.
Data for mineral oil:
Mol. Wt. = 390 [kg/kmol]
Specific heat of oil = 1.75 [kJ/kg-K]
Oil vapor pressure can be represented approximately by
ln(Psat) = 24.56 – 10,510 / T
where Psat [=] mm Hg and T[=] K
a.) What is the quality (mass basis) of the refrigerant-oil mixture exiting the evaporator
at 300 kPa, -10°C?
b.) What is the mass fraction of oil in the liquid phase that exits the evaporator?
c.) What is the evaporator heat transfer per kg of refrigerant-oil mixture passing through
the evaporator? Compare this value with the heat transfer per kg that would occur if
there were no oil in the refrigerant with the same temperatures and pressures.
d.) One problem resulting from the oil is that some of the refrigerant exits the evaporator
as a liquid and it cannot enter the compressor in this condition. Assuming the
pressure remains at 300 kPa, to what temperature must the refrigerant-oil mixture be
heated so that the fraction of refrigerant remaining in the liquid phase is less than
0.001 of the total mass of R22?
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.C-6 Determine the liquid and vapor composition of a mixture that has an overall molar
composition of 60% methane, 20% ethane, and the remainder propane, at –120°F and
250 psia. Compare the results determined in the following ways:
a) using Raoult’s Law
b) assuming the liquid and vapor form ideal solutions
c) using the Peng-Robinson library to determine the fugacity of each fluid in the gaseous
solution. Note that the fugacity of each component in the solution is the product of
the mole fraction in the gas, the partial fugacity coefficient returned by function
PHI_I_PR and the total pressure. Assume that the liquid phase forms an ideal
solution, as in part b.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
11.C-7 Prepare a temperature composition diagram for a mixture of propane and n-butane at
fixed pressures of 1, 5, and 10 bar assuming Raoult’s law is applicable for these
conditions. Label the dew and bubble point curves. Superimpose all the plots on one set
of axes. Explain the trends observed in the plots.