Performance design of a cryogenic air separation unit for variable working conditions using the lumped parameter model

  • Jinghua Xu
  • Tiantian Wang
  • Qianyong Chen
  • Shuyou ZhangEmail author
  • Jianrong Tan
Research Article
Part of the following topical collections:
  1. Innovative Design and Intelligent Design


Large-scale cryogenic air separation units (ASUs), which are widely used in global petrochemical and semiconductor industries, are being developed with high operating elasticity under variable working conditions. Different from discrete processes in traditional machinery manufacturing, the ASU process is continuous and involves the compression, adsorption, cooling, condensation, liquefaction, evaporation, and distillation of multiple streams. This feature indicates that thousands of technical parameters in adsorption, heat transfer, and distillation processes are correlated and merged into a large-scale complex system. A lumped parameter model (LPM) of ASU is proposed by lumping the main factors together and simplifying the secondary ones to achieve accurate and fast performance design. On the basis of material and energy conservation laws, the piecewise-lumped parameters are extracted under variable working conditions by using LPM. Takagi-Sugeno (T-S) fuzzy interval detection is recursively utilized to determine whether the critical point is detected or not by using different thresholds. Compared with the traditional method, LPM is particularly suitable for “rough first then precise” modeling by expanding the feasible domain using fuzzy intervals. With LPM, the performance of the air compressor, molecular sieve adsorber, turbo expander, main plate-fin heat exchangers, and packing column of a 100000 Nm3 O2/h large-scale ASU is enhanced to adapt to variable working conditions. The designed value of net power consumption per unit of oxygen production (kW/(Nm3 O2)) is reduced by 6.45%.


performance design air separation unit (ASU) lumped parameter model (LPM) variable working conditions T-S fuzzy interval detection 



ai, bi, Ci

Parameter set of the shape-changing degree of the membership function


Total area of the hole (m2)


Specific heat capacity at constant pressure (J · kg−1 · K−1)

C1, C2, C3



Bore diameter (m)


Particle diameter (m)


Diameter of PC (m)


Equivalent diameter of the flowing passage (m)


Friction factor


Friction factor for flow past a single particle


Packing factor of the flooding point (m · s−1 · (kg·m−3)0.5)


Froude number for liquid


Gravitational acceleration (m/s2)


Specific enthalpy (J/kg)


Enthalpy drop (kJ/kg)


Liquid holdup below the loading point


Dynamic liquid holdup of the packing column


Liquid holdup of the packing column


Static liquid holdup of the packing column


Height of MSA (m)

k1, k2



Heat exchanger length (m)

Fluid mass flow rate (kg/s)


Iteration number


Pressure drop (MPa)


Critical pressure (MPa)


Shaft power of AC (kW)

\(\dot Q\)

Heat transfer rate (kW)


Actual cooling capacity of TE (kW)


Reynolds number for the gas


State parameter set


Temperature of fluid (K)


Critical temperature (K)


Mean temperature difference between streams (K)


Fluid flow speed (m/s)


Flooding velocity (m/s)


Actual gas flow velocity (m/s)


Overall heat transfer coefficient (W · m−2·K−1)


Kinematic viscosity (m2/s)


Volume flow rate of fluid under working conditions (m3/s)


Input or variables in premise


Output of the model


Total height of packing (m)


Specific surface area of packing (m2/g)


Truncation error


Compression ratio of the air compressor




Isentropic efficiency


Fuzzy approximation error of ith judgement


Dynamic viscosity (Pa·s)


Fluid density (kg/m3)


Critical density (kg/m3)


Heat transfer efficiency


Degree of variable working condition of PC in ASU



Air compressor


Cold streams


Unirrigated (dry) bed


Evaporator condenser


Gas fluid


Hot streams




Irrigated bed




Liquid fluid


Lower column


molecular sieve adsorber




Packing column


Plate-fin heat exchangers


Turbo expander


Upper column


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This work was funded by the National Natural Science Foundation of China (Grant Nos. 51775494, 51821093, and 51935009), the National Key Research and Development Project (Grant No. 2018YFB1700701), and Zhejiang Key Research and Development Project (Grant No. 2019C01141).


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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Jinghua Xu
    • 1
    • 2
  • Tiantian Wang
    • 1
    • 2
  • Qianyong Chen
    • 1
    • 2
  • Shuyou Zhang
    • 1
    • 2
    Email author
  • Jianrong Tan
    • 1
    • 2
  1. 1.State Key Laboratory of Fluid Power and Mechatronic SystemsZhejiang UniversityHangzhouChina
  2. 2.Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, School of Mechanical EngineeringZhejiang UniversityHangzhouChina

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