## 18

Jan

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

Except for the purifier, the cryogenic air separation process involves pure physical processes, which can be divided into compression expansion process, heat exchange process and distillation (generalized) separation process, respectively corresponding to pressure energy, heat energy (cold energy) and minimum separation work (separation energy)

Before discussing the definition and calculation of the effective energy of cryogenic air separation, first make clear the environmental state. All the definitions and calculations related to the effective energy of cryogenic air separation are carried out under this environmental state. The environmental state is the earth's atmospheric environment, with an ambient temperature of 25 degrees, a pressure of one standard atmospheric pressure, and dry air composition of 20.7% oxygen, 0.9% argon, and 88.4% nitrogen. The above proportions are mole percent or volume percent! The temperature of 25 ℃ is the benchmark of thermal energy and cold energy, a standard atmospheric pressure, the temperature of 25 ℃ is the benchmark of pressure energy, and the dry air composition is the benchmark of minimum separation work (separation effective energy). Of course, the above environmental state is only a standard state. If there is any discrepancy between the actual environmental state and the standard state, it needs to be corrected.

In thermodynamics, all efficiency refers specifically to the effective energy efficiency, namely the so-called isentropic efficiency. If not, it is expressed in other terms, such as coefficient. As for the effective energy efficiency, it can be divided into process effective energy efficiency and system (subsystem) effective energy efficiency. The process effective energy efficiency is relatively simple, while the system (subsystem) effective energy efficiency is extremely complex and difficult to master. Therefore, there are black box, white box and gray box, which means that the definition and calculation conclusion of system (subsystem) effective energy efficiency are not reliable, and there are many problems that can be discussed.

The effective energy involved in deep cold air separation is only pressure energy, thermal energy, cold energy and minimum separation work (separation energy). The basic process also includes compression (expansion) process, heat exchange process and distillation separation process. The heat exchange process is a process of effective energy transfer and loss, while the distillation separation process is a process of effective energy conversion and loss. Neither of them has work input or output, while the compression (expansion) process has work output input!

The actual compression process is a polytropic compression process, and its efficiency is called polytropic efficiency. Of course, it is the effective energy efficiency. The so-called adiabatic compression and isothermal compression process only exist in the thought test, which is actually impossible. However, most of the polytropic compression processes are very close to the adiabatic compression process, which is very different from the isothermal compression process. In fact, adiabatic efficiency is the approximation and simplification of polytropic efficiency. The isothermal efficiency is not the effective energy efficiency of the isothermal compression process, but the effective energy efficiency of the air compression system (subsystem).

The effective energy efficiency of the compression expansion process is called adiabatic efficiency (in fact, it is only the approximation and simplification of the polytropic efficiency). The adiabatic efficiency of the compression process is defined as the ratio of the reversible minimum compression power consumption (i.e. isentropic compression power consumption) to the actual compression power consumption. There is no doubt that its value is between 0 and 100%, which is neither less than zero (that is not a compression process) nor greater than 1! The adiabatic efficiency of the expansion process is defined as the ratio of the actual expansion work output to the reversible maximum work output (i.e. isentropic expansion work output). The value is between zero and 100% for the same reason.

The so-called isothermal efficiency is not the effective energy efficiency of the isothermal compression process, because the isothermal compression process does not actually exist! The so-called isothermal efficiency is actually the effective energy efficiency of the air pressure separation system. Its actual process is to cool to room temperature after polytropic (adiabatic) compression (which can be segmented)! It is a subsystem composed of polytropic (adiabatic) compression process and cooling process. Isothermal efficiency is defined as the ratio of the pressure energy obtained by the air compression system to the actual power consumption. This calculation method of effective energy efficiency has strict preconditions. First, the initial compression state is the environmental state, and the effective energy of the final state is only the pressure energy and there is no other effective energy, that is, the temperature is equal to the environmental temperature! If the precondition is not tenable, the calculation method of the so-called isothermal efficiency is inexplicable! Not to mention the calculation method used to calculate the effective energy efficiency of the cryogenic adiabatic compression process is even more inexplicable!

Kaifeng Kaixing Air Separation Equipment Co., Ltd. is an energy-saving and environmental protection emerging technology service enterprise integrating air separation equipment, cryogenic technology application, energy-saving technology promotion, and contract energy management. The main products are complete sets of air separation plants, dynamic air separation plants, oxygen compressors, nitrogen compressors, turboexpanders, and air compressors.