## 20

Dec

### Definition and Calculation of Effective Energy in Cryogenic Air Separation

Nitrogen compressor sellers answer the definition and calculation of effective energy for cryogenic air separation：

All effective energy in cryogenic air separation unit comes from compression work! Compression efficiency is a very important content of the effective energy efficiency of cryogenic air separation. The previous post has explained that the polytropic efficiency and adiabatic efficiency are the effective energy efficiency of the compression process, while the isothermal efficiency is the effective energy efficiency of the compression system (subsystem). In the previous post, we gave the definition and calculation method of the effective energy efficiency of the system (subsystem). The ratio of the pressure energy of the pressure gas to the compression power consumption of the air compression system is obtained from the isothermal efficiency calculation formula. In the effective energy efficiency calculation formula of the system (subsystem), it is the ratio of the added value of pressure energy and the sum of the added value of pressure energy and the difference value of effective energy balance (i.e. the loss amount of effective energy). Since the initial state of the system is the environmental state, the pressure energy of the final state of the system is the added value of the pressure energy. The actual compression power consumption is the sum of the end state pressure energy increase value and the system effective energy balance difference (i.e. the effective energy loss amount)! The calculation of isothermal efficiency has strict preconditions. First, the initial compression pressure and temperature must be consistent with the ambient pressure and temperature. Second, the temperature of the final state of the compression system must be consistent with the ambient temperature. The system (subsystem) effective energy calculation formula is not subject to these preconditions, and is a more general definition and calculation method.

The textbook of cryogenic air separation contains the calculation of the effective energy efficiency of the whole unit of the standard double tower process, which is completely consistent with the calculation result of the effective energy efficiency of the system (subsystem)! This is because the number of liquid products in the standard double tower process plan is zero, and there is no internal compression. If the air separation unit has liquid product output and adopts internal compression process scheme, the calculated effective energy efficiency is meaningless. If the effective energy efficiency of the system (subsystem) is used, there will be three calculated results of effective energy efficiency according to different positioning, which is not of great practical significance.

Now let's discuss the effective energy efficiency of the double tower process distillation system. As mentioned in the previous post, it is very difficult to calculate the effective energy efficiency of the distillation process. Generally, only the effective energy efficiency of the distillation system can be calculated. The boundary of the distillation system in cryogenic air separation can be large or small, the whole air separation unit can be used as the distillation system, and the small can be just the distillation standard part. After the emergence of the calculation software, the effective energy values of each node can be easily obtained, so someone tried to calculate the effective energy efficiency of the distillation system. The calculation scope does not include the air compression system, purifier, main heat exchanger, expander, and the rest belongs to the distillation system. According to the effective energy values of each node of the standard double tower process, the calculation results include that the effective energy efficiency of the upper and lower tower distillation systems is more than 90%, and the lower tower distillation efficiency is more than 95%! According to the effective energy value of each node of the standard double tower process, including the effective energy balance difference of the distillation system of the upper and lower towers, which reaches 40% of the compression power consumption of the air compressor, the effective energy balance difference of the lower tower also reaches 10% of the compression power consumption of the air compressor, and the separation energy of the cryogenic air separation unit is 20% of the compression power consumption of the air compressor (this value is too small). This result is certainly unimaginable.

If the effective energy efficiency definition and calculation method of the system (subsystem) in the previous post are used, the calculation result is that the effective energy efficiency of the distillation system (subsystem) including the upper and lower columns is 30% - 40%!

If the lower tower is positioned as a primary distillation tower, the calculation result is about 50%. If the lower tower is positioned as a one driven two heat pump converter, the calculation result is 70% - 80%!

The definition and calculation of effective energy efficiency are the most difficult contents in thermodynamic theory, but they are also extremely important. A brief summary is as follows.

1、 The value of any effective energy is the value under the determined environmental reference state, and the change of the environmental reference state will inevitably lead to the corresponding change of the effective energy value.

2、 The compression and expansion process is the most important process of thermal work conversion, and the effective energy efficiency of the compression and expansion process is generally described by polytropic efficiency and adiabatic efficiency. Adiabatic efficiency and polytropic efficiency are clearly defined.

3、 The isothermal efficiency of gas compression is not the effective energy efficiency of the compression process, but the effective energy efficiency of the compression system (subsystem). In fact, the isothermal compression process does not exist. The actual compression process is a multi wheat process, but it is very close to the adiabatic compression process and far from the isothermal compression process. The compression system for calculating the isothermal efficiency is actually composed of polytropic compression process (nearly adiabatic compression process), cooling to room temperature and other processes. The calculation of the isothermal efficiency of the compression system is only meaningful if the compressed air inlet state is the environmental reference state and the compressed gas is cooled to the temperature of the environmental reference state. If the above conditions are not met, the isothermal efficiency should not be used.

4、 The definition and calculation of the effective energy efficiency of the system (subsystem) used to be very confused, so there are terms of white box, black box and gray box. Now this situation has changed a lot. The state has formulated technical guidelines for system effective energy analysis, and standardized the technical terms, definitions and calculation formulas of system (subsystem) effective energy efficiency.

5、 The effective energy efficiency of a system is essentially the effective energy input-output rate. The technical guidelines specify two calculation formulas. One is for systems (subsystems) that do not have effective energy conversion (heat energy is converted into separated energy, cold energy is converted into separated energy, etc.), and the effective energy efficiency is the ratio of the sum of the effective energy values of the system (subsystem) out of the system and the effective energy values of the logistics into the system (subsystem). Second, for the system (subsystem) with effective energy conversion, it is the ratio of the added value of effective energy of the conversion target to the reduced value of effective energy other than the effective energy of the target, which of course can also be based on the ratio of the sum of the added value of effective energy of the target, the added value of effective energy of the target and the effective energy loss of the system (subsystem).