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

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 $P_1 =30 \ bar$  = 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 ;

$V = \dfrac{m}{\rho}$

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

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

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

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

$W_{ideal} =0.04719*[2700]$

$W_{ideal} =127.42 kW$

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

$n_{isen} =\dfrac{W}{W_{ideal}}$

$n_{isen} =\dfrac{120}{120.42}$

$n_{isen} =0.9965$

$n_{isen} =$ 99.65%

Therefore, the   isentropic efficiency of turbine is 99.65%