Prob_05

Consider a two-stage cascade refrigeration system operating between the pressure limits of 1.6 MPa

and 180 kPa with refrigerant-134a as the working fluid (Figure 5.5). Heat rejection from the lower

cycle to the upper cycle takes place in an adiabatic counter-flow heat exchanger where the pressure

in the upper and lower cycles are 0.4 and 0.5 MPa, respectively. In both cycles, the refrigerant

is a saturated liquid at the condenser exit and a saturated vapor at the compressor inlet, and the

isentropic efficiency of the compressor is 85%. If the mass flow rate of the refrigerant through the

lower cycle is 0.07 kg/s, (a) draw the temperature–entropy diagram of the cycle indicating pressures;

determine (b) the mass flow rate of the refrigerant through the upper cycle, (c) the rate of heat

removal from the refrigerated space, and (d) the COP of this refrigerator; and (e) determine the

rate of heat removal and the COP if this refrigerator operated on a single-stage cycle between the

same pressure limits with the same compressor efficiency. Also, take the mass flow rate of R-134a

through the cycle to be 0.07 kg/s.

Licuación de Gas Natural

Natural gas at the ambient temperature of 35ºC and 4 bar at a rate of 8500 kg/h is to

be liquefied in a natural gas liquefaction plant. Natural gas leaves the plant at 4 bar and

−150ºC as a liquid. Using methane properties for natural gas determine (a) the rate of heat

removed from the natural gas, and (b) the minimum power input, and (c) the reversible

COP. (d) If the actual power input during this liquefaction process is 13,500 kW, determine

the exergy efficiency and the actual COP of this plant.

Various properties of methane before and after liquefaction process are given as follows:

h_1= 18.69 kJ/kg

h_2= −870.02 kJ/kg

s_1= −0.6466 kJ/kg-K

s_2= −6.3343 kJ/kg-K

For the inlet and exit states of natural gas described above, the heat removed from the natural gas

can be determined from Equation 5.63 to be 823.0 kJ/kg. That is, for the removal of 823.0 kJ/kg

heat from the natural gas, a minimum of 456.8 kJ/kg work is required. Since the ratio of heat

removed to the work input is defined as the COP of a refrigerator, this corresponds to a COP of

1.8.

In this illustrative example, we use numerical values to study multistage cascade refrigeration cycle

used for natural gas liquefaction. A numerical value of the minimum work can be calculated using

typical values of incoming and outgoing natural gas properties. The pressure of natural gas is around 40 bar when entering the cycle. The temperature of natural gas at the cycle inlet can be

taken to be the same as the ambient temperature T_1 = 25 ºC. Natural gas leaves the cycle

liquefied at about 4 bar pressure and at −157ºC. Since the natural gas in the cycle usually consists

of more than 95% methane, thermodynamic properties of methane can be used for natural gas.

Using these inlet and exit states, the minimum work input to produce a unit mass of LNG can be

determined from Equation 5.30 to be 456.8 kJ/kg. The heat removed from the natural gas during

the liquefaction process is determined from

Q = m(h_1 − h_4)

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