Question

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.

Answer 1

the isentropic efficiency of turbine is 99.65%

Step-by-step explanation:

Given that:

Mass flow rate of LNG m = 20 kg/s

The pressure at the inlet
`P_1 =30 \ bar` = 3000 kPa

turbine temperature at the inlet
`T_1 = -160^0C` = ( -160+273)K = 113K

The pressure at the turbine exit
`P_2 = 3 bar` = 300 kPa

Power produced by the turbine W = 120 kW

Density of LNG
`\rho = 423.8 \ kg/m^3`

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

`W_(ideal) = \int\limits^2_1 {V} \, dP`

`W_(ideal) ={V} \int\limits^2_1 \, dP`

`W_(ideal) ={V} [P]^2_(1)`

`W_(ideal) ={V} [P_1-P_2]`

We all know that density = mass * volume i.e
`\rho= m*V`

Then ;

`V = (m)/(\rho)`

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

`W_(ideal) ={ (m)/(\rho)} [P_1-P_2]`

`W_(ideal) ={ (20)/(423.8)} [3000-300]`

`W_(ideal) ={ (20)/(423.8)} [2700]`

`W_(ideal) =0.04719*[2700]`

`W_(ideal) =127.42 kW`

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

`n_(isen) =(W)/(W_(ideal))`

`n_(isen) =(120)/(120.42)`

`n_(isen) =0.9965`

`n_(isen) =` 99.65%

Therefore, the isentropic efficiency of turbine is 99.65%