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.

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  = 3000 kPa

turbine temperature at the inlet = ( -160+273)K = 113K

The pressure at the turbine exit = 300 kPa

Power produced by the turbine  W = 120 kW

Density of LNG

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

We all know that density = mass * volume i.e

Then ;

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

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

99.65%

Therefore, the   isentropic efficiency of turbine is 99.65%