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

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Abstract

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%.

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Abbreviations

ai, bi, Ci :

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

A f :

Total area of the hole (m2)

Cp:

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

C1, C2, C3 :

Constants

d :

Bore diameter (m)

d p :

Particle diameter (m)

D :

Diameter of PC (m)

D e :

Equivalent diameter of the flowing passage (m)

f :

Friction factor

f 0 :

Friction factor for flow past a single particle

F f :

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

Fr 1 :

Froude number for liquid

g :

Gravitational acceleration (m/s2)

h :

Specific enthalpy (J/kg)

Δh :

Enthalpy drop (kJ/kg)

h 0 :

Liquid holdup below the loading point

h d :

Dynamic liquid holdup of the packing column

h l :

Liquid holdup of the packing column

h s :

Static liquid holdup of the packing column

H :

Height of MSA (m)

k1, k2 :

Constants

L :

Heat exchanger length (m)

ṁ :

Fluid mass flow rate (kg/s)

N :

Iteration number

ΔP :

Pressure drop (MPa)

P c :

Critical pressure (MPa)

P s :

Shaft power of AC (kW)

\(\dot Q\) :

Heat transfer rate (kW)

\(\rm{\dot{Q}}_{\rm{act}}\) :

Actual cooling capacity of TE (kW)

Re g :

Reynolds number for the gas

S :

State parameter set

T :

Temperature of fluid (K)

T c :

Critical temperature (K)

ΔTm :

Mean temperature difference between streams (K)

u :

Fluid flow speed (m/s)

u f :

Flooding velocity (m/s)

u g :

Actual gas flow velocity (m/s)

U :

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

V :

Kinematic viscosity (m2/s)

V s :

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

x :

Input or variables in premise

y :

Output of the model

Z :

Total height of packing (m)

α p :

Specific surface area of packing (m2/g)

β :

Truncation error

γ :

Compression ratio of the air compressor

ε :

Porosity

η :

Isentropic efficiency

λ i :

Fuzzy approximation error of ith judgement

µ :

Dynamic viscosity (Pa·s)

ρ 1 :

Fluid density (kg/m3)

ρ c :

Critical density (kg/m3)

ψ :

Heat transfer efficiency

ω :

Degree of variable working condition of PC in ASU

AC:

Air compressor

c:

Cold streams

d:

Unirrigated (dry) bed

EC:

Evaporator condenser

g:

Gas fluid

h:

Hot streams

i:

Inlet

irr:

Irrigated bed

k:

Known

l:

Liquid fluid

LC:

Lower column

MSA:

molecular sieve adsorber

o:

Outlet

PC:

Packing column

PFHEs:

Plate-fin heat exchangers

TE:

Turbo expander

UC:

Upper column

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Acknowledgements

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).

Author information

Authors and Affiliations

  1. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, 310027, China

    Jinghua Xu, Tiantian Wang, Qianyong Chen, Shuyou Zhang & Jianrong Tan

  2. Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, School of Mechanical Engineering, Zhejiang University, Hangzhou, 310027, China

    Jinghua Xu, Tiantian Wang, Qianyong Chen, Shuyou Zhang & Jianrong Tan

Authors
  1. Jinghua Xu
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  2. Tiantian Wang
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Corresponding author

Correspondence to Shuyou Zhang.

Additional information

Jinghua XU, born in 1979, is currently an associate professor at Zhejiang University in China. He received his Ph.D. from Zhejiang University, China, in 2009. His research interests include mechanical design.

Tiantian WANG, born in 1995, is currently a Master’s Degree candidate in Mechanical Engineering College, Zhejiang University, China. His research interests include CAD.

Qianyong CHEN, born in 1993, is currently a Ph.D. candidate in Mechanical Engineering College, Zhejiang University, China. His research interests include CAD.

Shuyou ZHANG, born in 1963, is currently a professor at Zhejiang University, China. He received his Ph.D. from Zhejiang University, China, in 1999. His research interests include CAD/CG.

Jianrong TAN, born in 1954, is currently an academician in the Chinese Academy of Engineering and a professor in the Mechanical Engineering College of Zhejiang University, China. He received his Ph.D. from Zhejiang University, China, in 1992. His research interests include product design methodology.

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Xu, J., Wang, T., Chen, Q. et al. Performance design of a cryogenic air separation unit for variable working conditions using the lumped parameter model. Front. Mech. Eng. 15, 24–42 (2020). https://doi.org/10.1007/s11465-019-0558-6

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  • DOI: https://doi.org/10.1007/s11465-019-0558-6

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