When the transportation of natural gas in a pipeline is not feasible for economic reasons, it is first liquefied using nonconventional refrigeration techniques and then transported in super-insulated tanks. In a natural gas liquefaction plant, the liquefied natural gas (LNG) enters a cryogenic turbine at 30 bar and –160°C at a rate of 20 kg/s and leaves at 3 bar. If 120 kW power is produced by the turbine, determine the efficiency of the turbine. Take the density of LNG to be 423.8 kg/m3.

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ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2020-06-24T06:05:30+02:00

Answer:

the isentropic efficiency of turbine is 99.65%

Explanation:

Given that:

Mass flow rate of LNG m = 20 kg/s

The pressure at the inlet [tex]P_1 =30 \ bar[/tex] = 3000 kPa

turbine temperature at the inlet [tex]T_1 = -160^0C[/tex] = ( -160+273)K = 113K

The pressure at the turbine exit [tex]P_2 = 3 bar[/tex] = 300 kPa

Power produced by the turbine W = 120 kW

Density of LNG [tex]\rho = 423.8 \ kg/m^3[/tex]

The formula for the workdone by an ideal turbine can be expressed by:

[tex]W_{ideal} = \int\limits^2_1 {V} \, dP[/tex]

[tex]W_{ideal} ={V} \int\limits^2_1 \, dP[/tex]

[tex]W_{ideal} ={V} [P]^2_{1}[/tex]

[tex]W_{ideal} ={V} [P_1-P_2][/tex]

We all know that density = mass * volume i.e [tex]\rho= m*V[/tex]

Then ;

[tex]V = \dfrac{m}{\rho}[/tex]

replacing it into the above previous derived formula; we have:

[tex]W_{ideal} ={ \dfrac{m}{\rho}} [P_1-P_2][/tex]

[tex]W_{ideal} ={ \dfrac{20}{423.8}} [3000-300][/tex]

[tex]W_{ideal} ={ \dfrac{20}{423.8}} [2700][/tex]

[tex]W_{ideal} =0.04719*[2700][/tex]

[tex]W_{ideal} =127.42 kW[/tex]

However ; the isentropic efficiency of turbine is given by the relation:

[tex]n_{isen} =\dfrac{W}{W_{ideal}}[/tex]

[tex]n_{isen} =\dfrac{120}{120.42}[/tex]

[tex]n_{isen} =0.9965[/tex]

[tex]n_{isen} =[/tex] 99.65%

Therefore, the isentropic efficiency of turbine is 99.65%