A natural gas stream is to be cooled and condensed from 298K to 115K to produce liquetied natural gas (LNG). The total heat duty of the natural gas stream is 25.85MN. The cooling profile is shown in Figure 2. Figure 2 LNG cooling and liquetaction profile It is proposed to perform the required cooling and condensation using a three-level cascade cycle refrigeration system. Each cycle in the cascade features a single stage with a pure component. The lowest temperature cooling uses methane and rejects the heat from the cycle to the ethylene cycle. The ethylene cycle accepts the heat rejected from the methane cycle, periorms the intermediate cooling and rejects its heat to the propane cycle. The propane cycie accepts heat rejected by the ethylene cycle, pertorms the highest temperature cooling and rejects its heat to cooling water, which is at a temperature of 298K. The heat is to be translerred with a minimum temperature ditference of 3K in all the evaporators, and 5 K in the propare condenser to relect heat to cooling woter. The portion of the superheated region of the cooling curve from 298K to 230K can be represented by Equation 1 : H=10.773T1.81 (1) Where AH= enthalpy change per second (MW) T T The portion of the middle section of the cooling curve from 230K to 180K can be represented by Equation 2: T=0.0683H32.7214H2+38.598H+8.5 The portion of the subcooled region from 180K to 115K can be representod by Equation 3 . H=8.4632T13.59 a) Sketch the flowsheet of the relrigeration system. [6 Marks] b) The cooling duties for the three cycles are initially set such that: i) Propane cools the natural gas from 298K to 263K ii) Ethylene cools the natural gas from 263K to 178K iii) Methane cools the natural gas from 178K to 115K Dotermine the cooling dutles for the natural gas, given the above distribution of cooling in the cycles, assuming the cooling duties operate with the minimum permissible temperature difference of 3K. [3 Marks] c) Use the Carnot Efliciency Model to calculate the power input to the refrigeration cycle. Assume a Carnot efficiency of 60% and a minimum temperature difference of 3K in all the evaporators, and 5K in the condenser to reject heat to cooling water with a retum temperature of 298K. [10 Marks] d) The use of 3 stages of cooling is considered to be too inetficient. It is therefore proposed to make the methane and ethylene cycles two stage instead of single stage with two expansions and two evaporators for the natural gas cooling instead of one in both the methane and ethylene cycles. Sketch the flowsheet of the refrigeration system. [8 Marks] e) Assuming that the additional stages are midway between the initial temperature spans sot in Part b) above, use the Camot Elliclency Model to calculate the power input to the refrigeration cycie. Assume a Camot efficiency of 60% and a minimum temperafure ditference of 3K in all the evaporators, and 5K in the condenser to reject heat to cooling water with a retum temperature of 298K. [10 Markn] f) What could be done to improve the performance of the refrigeration system to docrease the power requirement in Parts d) and e) both by changing the process conditiona and the cortiguration? [B Marks] A natural gas stream is to be cooled and condensed from 298K to 115K to produce liquetied natural gas (LNG). The total heat duty of the natural gas stream is 25.85MN. The cooling profile is shown in Figure 2. Figure 2 LNG cooling and liquetaction profile It is proposed to perform the required cooling and condensation using a three-level cascade cycle refrigeration system. Each cycle in the cascade features a single stage with a pure component. The lowest temperature cooling uses methane and rejects the heat from the cycle to the ethylene cycle. The ethylene cycle accepts the heat rejected from the methane cycle, periorms the intermediate cooling and rejects its heat to the propane cycle. The propane cycie accepts heat rejected by the ethylene cycle, pertorms the highest temperature cooling and rejects its heat to cooling water, which is at a temperature of 298K. The heat is to be translerred with a minimum temperature ditference of 3K in all the evaporators, and 5 K in the propare condenser to relect heat to cooling woter. The portion of the superheated region of the cooling curve from 298K to 230K can be represented by Equation 1 : H=10.773T1.81 (1) Where AH= enthalpy change per second (MW) T T The portion of the middle section of the cooling curve from 230K to 180K can be represented by Equation 2: T=0.0683H32.7214H2+38.598H+8.5 The portion of the subcooled region from 180K to 115K can be representod by Equation 3 . H=8.4632T13.59 a) Sketch the flowsheet of the relrigeration system. [6 Marks] b) The cooling duties for the three cycles are initially set such that: i) Propane cools the natural gas from 298K to 263K ii) Ethylene cools the natural gas from 263K to 178K iii) Methane cools the natural gas from 178K to 115K Dotermine the cooling dutles for the natural gas, given the above distribution of cooling in the cycles, assuming the cooling duties operate with the minimum permissible temperature difference of 3K. [3 Marks] c) Use the Carnot Efliciency Model to calculate the power input to the refrigeration cycle. Assume a Carnot efficiency of 60% and a minimum temperature difference of 3K in all the evaporators, and 5K in the condenser to reject heat to cooling water with a retum temperature of 298K. [10 Marks] d) The use of 3 stages of cooling is considered to be too inetficient. It is therefore proposed to make the methane and ethylene cycles two stage instead of single stage with two expansions and two evaporators for the natural gas cooling instead of one in both the methane and ethylene cycles. Sketch the flowsheet of the refrigeration system. [8 Marks] e) Assuming that the additional stages are midway between the initial temperature spans sot in Part b) above, use the Camot Elliclency Model to calculate the power input to the refrigeration cycie. Assume a Camot efficiency of 60% and a minimum temperafure ditference of 3K in all the evaporators, and 5K in the condenser to reject heat to cooling water with a retum temperature of 298K. [10 Markn] f) What could be done to improve the performance of the refrigeration system to docrease the power requirement in Parts d) and e) both by changing the process conditiona and the cortiguration? [B Marks]
