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

doi:10.1007/s11465-019-0558-6

Front. Mech. Eng.

2020, Vol. 15

Issue (1) : 24-42 https://doi.org/10.1007/s11465-019-0558-6

RESEARCH ARTICLE

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

Jinghua XU, Tiantian WANG, Qianyong CHEN, Shuyou ZHANG(

), Jianrong TAN

State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China; Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China

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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 Nm³O₂/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/(Nm³O₂)) is reduced by 6.45%.

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

Corresponding Author(s): Shuyou ZHANG

Just Accepted Date: 10 October 2019 Online First Date: 26 November 2019 Issue Date: 21 February 2020

Cite this article:

Jinghua XU,Tiantian WANG,Qianyong CHEN, et al. Performance design of a cryogenic air separation unit for variable working conditions using the lumped parameter model[J]. Front. Mech. Eng., 2020, 15(1): 24-42.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-019-0558-6
https://academic.hep.com.cn/fme/EN/Y2020/V15/I1/24

Fig.1 Typical external compression cryogenic air separation process.

Fig.2 Typical internal compression cryogenic air separation process.

Fig.3 T–S fuzzy interval detection to judge the critical point of ASU.

Fig.4 AC. (a) AC in a factory; (b) digital mockup of the AC; (c) CFD simulation of the work flow in the AC; (d) air temperature change in the AC.

Fig.5 MSA. (a) Two vertical radial flow MSAs; (b) simulation process of MSAs.

Fig.6 TE. Experiment on TE: (a) Expansive end and (b) supercharging end. (c) TE structure. The left part is the expansive end, and the right part is the supercharging end. (d) Simulated flow process of TE.

Fig.7 Vertical brazed aluminum PFHE. (a) Overall structure of the PFHE; (b) a layer of passage.

Fig.8 Feedstock inside PCs. (a) Cold box; (b) CFD simulation process of the upper column; (c) gas–liquid distributor; (d) flow state of the air in PC.

Fig.9 Comparison of

h l

between ω =75% and ω =105% PCs.

Fig.10 SCF experimental platforms for measuring physical properties. (a) Cryogenic fluid; (b) oscilloscope.

Components	Status	$T c$ /K	$P c$ /MPa	$ρ c$ /(kg·m⁻³)	$C p$ /(kJ·kg⁻¹·K⁻¹)	$μ$ /(Pa·s)	$ν$ /(m²?s⁻¹)
Nitrogen (N₂)	Theoretical	126.19	3.3958	313.30	1.1239	5.4400×10⁻⁶	1.7363×10⁻⁸
Nitrogen (N₂)	Experimental	125.32	3.4720	315.60	1.1527	5.3500×10⁻⁶	1.7154×10⁻⁸
Oxygen (O₂)	Theoretical	154.58	5.0430	436.16	1.6994	5.4437×10⁻⁶	1.2481×10⁻⁸
Oxygen (O₂)	Experimental	155.82	5.1020	437.36	1.7503	5.3639×10⁻⁶	1.2583×10⁻⁸
Argon (Ar)	Theoretical	150.69	4.8630	535.60	0.5658	7.1618×10⁻⁶	1.3372×10⁻⁸
Argon (Ar)	Experimental	150.31	4.9240	536.80	0.5762	7.1527×10⁻⁶	1.3518×10⁻⁸

Tab.1 Comparisons of experimental and theoretical critical physical properties of various components in ASU

Fig.11 (a) AC efficiency; (b) pressure drop of MSA.

Fig.12 (a) Main PFHEs’ efficiency; (b) pressure drop of PC.

Products and parameters	Minimum working condition/(Nm³?h⁻¹)	Designed working condition/(Nm³?h⁻¹)	Maximum working condition/(Nm³?h⁻¹)	Purity/ppm	Outlet pressure/MPa
High-pressure oxygen	75375	100500	106550	$≥ 9.96 × 105$ O₂	5.9
High-pressure nitrogen	6850	6850	9250	$≤ 10$ O₂	7.0
Low-pressure nitrogen	69500	69500	78500	$≤ 10$ O₂	1.0
LOX	2500	1500	0	$≥ 9.96 × 105$ O₂	–
LIN	2500	1000	0	$≤ 10$ O₂	–

Tab.2 Products and parameters of 100000 Nm³ O₂/h large-scale ASU

Processes	Units	Status	Performance parameters	Performance before using LPM	Performance after using LPM	Ratio
Adsorption process	AC	Axial flow type	Shaft power	$P s$ =26138 kW	$P s$ =27561 kW	5.44%
		Axial flow type	Isentropic efficiency	$η AC$ =82.6%	$η AC$ =89.6%	8.47%
		Centrifugal type	Shaft power	$P s$ =12894 kW	$P s$ =13195 kW	2.33%
		Centrifugal type	Isentropic efficiency	$η AC$ =84.3%	$η AC$ =87.6%	3.91%
	MSA	Adsorption	Adsorption pressure drop	$Δ P MSA$ =7.26 kPa	$Δ P MSA$ =6.79 kPa	–6.47%
		Regeneration	Regeneration pressure drop	$Δ P MSA$ =7.13 kPa	$Δ P MSA$ =6.74 kPa	–5.47%
		Maximum	Maximum pressure drop	$Δ P MSA$ =14.39 kPa	$Δ P MSA$ =13.53 kPa	–5.98%
Heat transfer process	TE	Expansive end	Isentropic efficiency	$η TE$ =86%	$η TE$ =89%	3.49%
	TE	Supercharging end	Isentropic efficiency	$η TE$ =81%	$η TE$ =82%	1.23%
	PFHEs	Whole	Isentropic efficiency	$η PFHEs$ =86.78%	$η PFHEs$ =88.40%	1.87%
			Total heat transfer coefficient	$U$ =2286 W/(m²·°C)	$U$ =2518 W/(m²·°C)	10.15%
			Heat transfer efficiency	$ψ$ =87.6%	$ψ$ =93.8%	7.08%
			Maximum Pressure drop	$Δ P PFHEs$ =17 kPa	$Δ P PFHEs$ =16 kPa	–5.88%
Distillation process	PC	Whole	Upper column Pressure drop	$Δ P PC$ =3.6 kPa	$Δ P PC$ =3.4 kPa	–5.56%
Distillation process	PC	Whole	Lower column Pressure drop	$Δ P PC$ =4.3 kPa	$Δ P PC$ =4.1 kPa	–4.65%

Tab.3 Comparison of results before and after using LPM in the 100000 Nm³O₂/h large-scale ASU

$a i, b i, c i$	Parameter set of the shape-changing degree of the membership function
$A f$	Total area of the hole (m²)
$C p$	Specific heat capacity at constant pressure (J?kg⁻¹?K⁻¹)
$C 1, C 2, C 3$	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)
$F r l$	Froude number for liquid
$g$	Gravitational acceleration (m/s²)
$h$	Specific enthalpy (J/kg)
$Δ h$	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)
$k 1, k 2$	Constants
$L$	Heat exchanger length (m)
$m ˙$	Fluid mass flow rate (kg/s)
$N$	Iteration number
$Δ P$	Pressure drop (MPa)
$P c$	Critical pressure (MPa)
$P s$	Shaft power of AC (kW)
$Q ˙$	Heat transfer rate (kW)
$Q ˙ a c t$	Actual cooling capacity of TE (kW)
$R e g$	Reynolds number for the gas
$S$	State parameter set
$T$	Temperature of fluid (K)
$T c$	Critical temperature (K)
$Δ T m$	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)
$ν$	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)
$ρ l$	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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