Surrogate model-based optimal design of multi-stage nanofiltration separation system for saline wastewater

doi:10.11949/0438-1157.20200722

Abstract

Abstract:

Based on Donnan steric pore model with dielectric exclusion (DSPM-DE), this work develops a surrogate model for the multi-stage nanofiltration separation of industrial saline wastewater. Firstly, a high-fidelity surrogate model with a high fitting degree is established to describe the DSPM-DE-based nanofiltration process via high dimensional model representation. On this basis, we construct the optimization model of multi-stage nanofiltration separation for minimizing the specific energy consumption (SEC) of unit NaCl separated. The impacts of the changing feed ratio [Cl^-]/[ $S O 4 2 -$ ] on the separation performance and optimal operating conditions of the nanofiltration system are investigated under the given design parameters. The results indicate that an increased feed ratio [Cl^-]/[ $S O 4 2 -$ ] is beneficial to improve the total recovery of NaCl and to reduce the SEC. Under the same investment cost of nanofiltration membranes, the two-stage system is superior in reducing energy consumption, and can save up to 5.84% compared with the single-stage system.

Key words: wastewater, nanofiltration, salts separation, surrogate model, specific energy consumption, optimization, energy saving

摘要：

基于道南细孔-介电DSPM-DE模型，开展了工业含盐废水多级纳滤分离系统的代理模型构建与优化研究。首先，利用高维模型表征的数学建模方法，构建与原有纳滤理论模型有高拟合度的高精度代理模型。基于此代理模型，进一步构建膜法分盐工艺中的多级纳滤分离的数学优化模型，并以分离单位质量NaCl的比能耗为优化目标，讨论在给定设计参数的条件下进料液中[Cl^-]/[ $S O 4 2 -$ ]的变化对不同级数纳滤系统的分盐性能及最优操作条件的影响。优化结果显示，进料[Cl^-]/[ $S O 4 2 -$ ]的增加有利于提高NaCl总回收率和降低分盐比能耗。在相同的纳滤膜投资成本下，双级系统在降低能耗方面更胜一筹，与单级系统相比最高可节能5.84%。

关键词: 废水, 纳滤, 分盐, 代理模型, 比能耗, 优化, 节能

CLC Number:

LU Zhibin, XIE Xing, LU Sida, HE Chang, ZHANG Bingjian, CHEN Qinglin. Surrogate model-based optimal design of multi-stage nanofiltration separation system for saline wastewater[J]. CIESC Journal, 2021, 72(3): 1400-1408.

陆至彬, 谢星, 鲁思达, 何畅, 张冰剑, 陈清林. 基于代理模型的含盐废水多级纳滤系统的过程优化设计[J]. 化工学报, 2021, 72(3): 1400-1408.

Figures/Tables 13

Fig.1 Structural diagram of the pressure vessel of nanofiltration

Fig.2 Flow diagram of multi-stage nanofiltration system

Table 1 Key parameters of the mass transfer model for nanofiltration

Parameter		Unit	Value	Ref.
NF270 properties	S_m	m²	37.16	[26]
	r_pore	nm	0.43	[13]
	?x_e	μm	1.5
	ε_pore	—	42.4	[27]
	X_d	mol/m³	fitting	[12]
Other parameters	temperature, T	K	298
	D_i_,∞( $S O 4 2 -$ /Cl^-/Na⁺)×10⁹	m²/s	1.065/2.031/1.344	[28]
	r_i( $S O 4 2 -$ /Cl^-/Na⁺)	nm	0.231/0.121/0.184	[29]
	ε_b	—	80.4	[16]

Table 1 Key parameters of the mass transfer model for nanofiltration

Parameter		Unit	Value	Ref.
NF270 properties	S_m	m²	37.16	[26]
	r_pore	nm	0.43	[13]
	?x_e	μm	1.5
	ε_pore	—	42.4	[27]
	X_d	mol/m³	fitting	[12]
Other parameters	temperature, T	K	298
	D_i_,∞( $S O 4 2 -$ /Cl^-/Na⁺)×10⁹	m²/s	1.065/2.031/1.344	[28]
	r_i( $S O 4 2 -$ /Cl^-/Na⁺)	nm	0.231/0.121/0.184	[29]
	ε_b	—	80.4	[16]

Table 2 Key parameters and constraints used in optimization process

Parameter	Unit	Value	Ref.
minimum element pressure drop, ?P_drop	bar	0.05
maximum element water recovery, r_e	—	15%	ROSA
maximum applied pressure per element, ?P_e	bar	41	[26]
maximum element feed flow rate, $Q e i n$	m³/h	13.85	ROSA
number of elements in each pressure vessel, Ne	—	4
fluid viscosity, μ	Pa?s	0.936×10^-3	Aspen Plus
high pressure pump efficiency, η_hp	—	0.75	[23]
booster pump efficiency, η_bp	—	0.57	[23]
circulating pump efficiency, η_cp	—	0.8	[23]
energy recovery device efficiency, η_ERD	—	0.9	[23]
total feed rate of waste water, Q_f	m³/h	400
pipeline fluid pressure, P₁	bar	2.0	[23]

Table 2 Key parameters and constraints used in optimization process

Parameter	Unit	Value	Ref.
minimum element pressure drop, ?P_drop	bar	0.05
maximum element water recovery, r_e	—	15%	ROSA
maximum applied pressure per element, ?P_e	bar	41	[26]
maximum element feed flow rate, $Q e i n$	m³/h	13.85	ROSA
number of elements in each pressure vessel, Ne	—	4
fluid viscosity, μ	Pa?s	0.936×10^-3	Aspen Plus
high pressure pump efficiency, η_hp	—	0.75	[23]
booster pump efficiency, η_bp	—	0.57	[23]
circulating pump efficiency, η_cp	—	0.8	[23]
energy recovery device efficiency, η_ERD	—	0.9	[23]
total feed rate of waste water, Q_f	m³/h	400
pipeline fluid pressure, P₁	bar	2.0	[23]

Fig.3 Comparison of simulation data by DSPM-DE model and experiment data under various water fluxes (feed concentration: SO42- 80 mol/m3, Cl- 180 mol/m3)

Table 3 First order coefficients of surrogate model for SO42- concentration in permeate

$A α, θ S O 4 2 -$	θ=1	θ=2
α=1	-0.014436	0.022249
α=1	-0.011062	0.002860
α=3	—	—
α=4	-0.012763	0.003062

Table 3 First order coefficients of surrogate model for SO42- concentration in permeate

$A α, θ S O 4 2 -$	θ=1	θ=2
α=1	-0.014436	0.022249
α=1	-0.011062	0.002860
α=3	—	—
α=4	-0.012763	0.003062

Table 4 Second order coefficients of surrogate model for SO42- concentration in permeate

$B α, β, θ, ω S O 4 2 -$	θ=1, ω=1	θ=1, ω=2	θ=2, ω=1	θ=2, ω=2
α=1, β=2	0.027319	-0.000168	-0.000341	0.000047
α=1, β=3	—	—	-0.002461	0.000884
α=1, β=4	0.011366	-0.002616	-0.004330	0.000888
α=2, β=3	—	—	-0.000704	0.000175
α=2, β=4	0.008873	-0.002153	0.006755	-0.001389
α=3, β=4	—	—	-0.033619	0.007160

Table 4 Second order coefficients of surrogate model for SO42- concentration in permeate

$B α, β, θ, ω S O 4 2 -$	θ=1, ω=1	θ=1, ω=2	θ=2, ω=1	θ=2, ω=2
α=1, β=2	0.027319	-0.000168	-0.000341	0.000047
α=1, β=3	—	—	-0.002461	0.000884
α=1, β=4	0.011366	-0.002616	-0.004330	0.000888
α=2, β=3	—	—	-0.000704	0.000175
α=2, β=4	0.008873	-0.002153	0.006755	-0.001389
α=3, β=4	—	—	-0.033619	0.007160

Table 5 First order coefficients of surrogate model for Cl- concentration in permeate

$A α, θ C l -$	θ=1	θ=2
α=1	21.073186	-3.237781
α=2	82.290331	7.929830
α=3	—	—
α=4	-11.560941	2.654041

Table 5 First order coefficients of surrogate model for Cl- concentration in permeate

$A α, θ C l -$	θ=1	θ=2
α=1	21.073186	-3.237781
α=2	82.290331	7.929830
α=3	—	—
α=4	-11.560941	2.654041

Table 6 Second order coefficients of surrogate model for Cl- concentration in permeate

$B α, β, θ, ω C l -$	θ=1, ω=1	θ=1, ω=2	θ=2, ω=1	θ=2, ω=2
α=1, β=2	9.617871	0.110605	0.163656	-0.031836
α=1, β=3	—	—	1.071423	-0.169995
α=1, β=4	-9.937840	1.888694	2.622338	-0.449131
α=2, β=3	—	—	-2.578999	0.374763
α=2, β=4	-45.992975	8.506330	4.323250	-1.123688
α=3, β=4	—	—	-9.240002	1.694438

Table 6 Second order coefficients of surrogate model for Cl- concentration in permeate

$B α, β, θ, ω C l -$	θ=1, ω=1	θ=1, ω=2	θ=2, ω=1	θ=2, ω=2
α=1, β=2	9.617871	0.110605	0.163656	-0.031836
α=1, β=3	—	—	1.071423	-0.169995
α=1, β=4	-9.937840	1.888694	2.622338	-0.449131
α=2, β=3	—	—	-2.578999	0.374763
α=2, β=4	-45.992975	8.506330	4.323250	-1.123688
α=3, β=4	—	—	-9.240002	1.694438

Fig.4 Comparison of results obtained by HDMR and DSPM-DE models

Fig.5 The optimal SECs in different stage with varied [Cl-]/[SO42-]

Fig.6 The optimal unit operating pressures in different stage with varied [Cl-]/[SO42-] (s1, s2, s3 represent the first, second and third unit of system)

Fig.7 The overall recovery of NaCl in different stage with varied [Cl2-]/[SO42-]

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