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 \(-160^{\circ} \mathrm{C}\) at a rate of \(20 \mathrm{kg} / \mathrm{s}\) and leaves at 3 bar. If \(115 \mathrm{kW}\) power is produced by the turbine, determine the efficiency of the turbine. Take the density of LNG to be \(423.8 \mathrm{kg} / \mathrm{m}^{3} .\)

Short answer

Question: Calculate the efficiency of a cryogenic turbine used in a natural gas liquefaction plant given the following information: inlet pressure (30 bar), inlet temperature of LNG entering the turbine, mass flow rate of LNG (20 kg/s), outlet pressure of LNG (3 bar), power produced by the turbine (115 kW), and density of LNG (423.8 kg/m³). Answer: The efficiency of the cryogenic turbine is 75.60%.

Step-by-step solution

Calculate actual work done

The actual work done by the turbine can be calculated by multiplying the power produced by the turbine by the mass flow rate. Given that the power produced is 115 kW and the mass flow rate is 20 kg/s, the actual work done can be calculated as follows: Actual Work = (Power Produced) * (Mass Flow Rate) = 115 kW * 20 kg/s = 2300 kJ/s

Calculate the specific volume of the LNG

The specific volume of the LNG can be calculated by taking the inverse of the density. Given that the density of LNG is 423.8 kg/m³, the specific volume can be calculated as follows: Specific Volume = 1 / Density = 1 / 423.8 kg/m³ = 0.00236 m³/kg

Calculate the isentropic work

The isentropic work can be calculated by finding the enthalpy difference between the inlet and outlet conditions multiplied by the mass flow rate: Enthalpy Difference = Inlet Enthalpy - Outlet Enthalpy We can assume that the properties of LNG are constant since it is liquid. With this assumption, the change in enthalpy is proportional to the change in pressure and specific volume: Enthalpy Difference = Specific Volume * (Inlet Pressure - Outlet Pressure) Isentropic Work = (Mass Flow Rate) * Enthalpy Difference = 20 kg / s * 0.00236 m³ / kg * (30 bar - 3 bar) * 100 kJ / m³ / bar Isentropic Work = 3042.24 kJ/s

Calculate the turbine efficiency

Now we can calculate the efficiency of the turbine using the actual work done and the isentropic work: Efficiency = (Actual Work) / (Isentropic Work) = 2300 kJ/s / 3042.24 kJ/s = 0.7560 The efficiency of the turbine is 75.60%.