A review of CFD simulation in pressure driven membrane with fouling model and anti-fouling strategy

doi:10.1007/s11783-024-1853-y

Front. Environ. Sci. Eng.

2024, Vol. 18

Issue (8) : 93 https://doi.org/10.1007/s11783-024-1853-y

A review of CFD simulation in pressure driven membrane with fouling model and anti-fouling strategy

Shiyong Miao¹, Jiaying Ma¹, Xuefei Zhou^1,², Yalei Zhang^1,², Huaqiang Chu^1,²(

)

¹. State Key Laboratory of Pollution Control and Resource Reuse, Tongji University, Shanghai 200092, China
². Shanghai Institute of Pollution Control and Ecological Security, Tongji University, Shanghai 200092, China

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Abstract

● The numerical realization method of the membrane permeation process is summarized.

● Biofouling, scaling and colloidal particle fouling models are detailed presented.

● Representative CFD-aided simulations of anti-fouling strategies are described.

Pressure-driven membrane filtration systems are widely utilized in wastewater treatment, desalination, and water reclamation and have received extensive attention from researchers. Computational fluid dynamics (CFD) offers a convenient approach for conducting mechanistic studies of flow and mass transfer characteristics in pressure-driven systems. As a signature phenomenon in membrane systems, the concentration polarization that accompanies the permeation process is a key factor in membrane performance degradation and membrane fouling intensification. Multiple fouling models (scaling, biofouling and colloidal particle fouling) based on CFD theory have been constructed, and considerable research has been conducted. Several representative antifouling strategies with special simulation methods, including patterned membranes, vibration membranes, rotation membranes, and pulsatile flows, have also been discussed. Future studies should focus on refining fouling models while considering local hydrodynamic characteristics; experimental observation tools focusing on the internal structure of inhomogeneous fouling layers; techno-economic model of antifouling strategies such as vibrational, rotational and pulsatile flows; and unfavorable hydraulic phenomena induced by rapidly changing flows in simulations.

Keywords Computational fluid dynamics Membrane Fouling model Concentration polarization

Corresponding Author(s): Huaqiang Chu

Issue Date: 14 May 2024

Cite this article:

Shiyong Miao,Jiaying Ma,Xuefei Zhou, et al. A review of CFD simulation in pressure driven membrane with fouling model and anti-fouling strategy[J]. Front. Environ. Sci. Eng., 2024, 18(8): 93.

URL:

https://academic.hep.com.cn/fese/EN/10.1007/s11783-024-1853-y
https://academic.hep.com.cn/fese/EN/Y2024/V18/I8/93

Spacer geometry	Feature size	Flow state &Boundary condition	Mesh & Software	Validation	Significant results or innovation point	Ref.
3D; 3 × 5 cellsnonwoven, 2-layer, nonuniform spacer	$H = 0.78 m m; W = 78 m m;$ $L m = 2.85 m m;$ $D f = 386 − 555 μ m;$ $α = 45 ∘; β = 90 ∘$	$R e = 127$ ; Laminar $u 0 = 0.163 m / s$ nonpermeable membrane	$N = 430000$ Tetrahedron; $S < 200 μ m$ COMSOL 3.5	Not mentioned	First 3D model for biofouling in the feed channel	Picioreanu et al. (2009)
2D(1) Submerged spacer(2) Zigzag spacer(3) Cavity spacer	$D f = 500 μ m; W = 1 m m; L = 15 m m; L m = 4 m m$	$R e = 160;$ Laminar; Steady $u 0 = 0.1 m / s$ permeable membrane	$N = 200000 − 270000$ $S = {5 − 30 μ m 10 μ m f o r b i o f i l m m e s h$ COMSOL 3.5	Literature	Spacer geometry is based on (Schwinge et al., 2002a); Biofouling model is developed based on (Picioreanu et al., 1998a, 2001); Potential biofouling area is suggested.	Radu et al. (2010; 2012)
3D; Sinusoidal spacers	$H = 1.5 m m; W = 6 m m$ Wavelength = 12, 24 mm	$u 0 = 0.148 m / s$ permeable membrane	510?640 elements/mm³COMSOL 4.2	Original experiment	Permeate is enhanced by the sinusoidal channel.	Xie et al. (2014)
3D; 5 cells(1) Commercial spacers(2) 2-layer, nonwoven, nonuniform spacer	$D f = 221 − 563 μ m$ $H = 711 − 1168 μ m$ $L = 2385 − 2788 μ m$ $α = 45 ∘; β = 90 ∘$ Porosity: $0.88 − 0.92$	Re < 200; LaminarStationary in each biomass calculation time step $u 0 = 0.041 − 0.178$ permeable membrane	$N = 1300000$ $S < 90 μ m$ tetrahedral meshCOMSOL 4.3	Original experiment and literature (Araújo et al., 2012; Vrouwenvelder et al., 2009b)	Biofouling model is developed based on (Picioreanu et al., 2009);The influence of the nutrient load, spacer geometry, work condition on biofouling in NF is investigated.	Bucs et al. (2014a; 2014b)
3D; 1 cell2-layer, nonwoven, nonuniform spacer	$α = 45 ∘, 90 ∘; β = 90 ∘$ $H = 800 μ m; L = 4411 μ m$ $W = 4411 μ m$ $D f = 250 − 520 μ m$ $L m ≈ 3100 μ m$	Laminar; Steady $u 0 = 0.14 m / s$ permeable and nonpermeable membrane for different cases	$S < 30 μ m$ TetrahedralCOMSOL 4.2	Original experiments	Particle trajectory is used to determine the potential fouling area, and the cross-velocity has an effect on the deposition area.	Radu et al. (2014b)
3D; 1 cell2-layer, nonwoven, nonuniform spacer	$W = 4.38 m m; L = 4.38 m m$ $H = 787 μ m; β = 90 ∘$	$R e = 70, 160, 300$ Steady; Laminar $u 0 = 74, 163, 294 m m / s$ nonpermeable membrane	$S < 50 μ m$ TetrahedralCOMSOL 4.4	Original experiments	Simulation with different velocities has been induced in SWM modules and exhibits in good agreement with experiments.	Bucs et al. (2015)
2D; zigzag	$L = 15 m m; H = 1 m m$ $L m = 4 m m; D f = 0.5 m m$	Laminar; Steady; $u 0 = 0.07 − 0.2 m / s$ permeable membrane	$S < 5 μ m$ COMSOL 3.5	Not mentioned	A model integrating mineral precipitation and biofilm formation with hydrodynamics and solute transport is developed, and the interactions between biofouling and scaling is investigated.	Radu et al. (2015)
3D; 1 cell(1) 2-layer, nonwoven, uniform spacer(2) 1-layer, uniform, spherical node spacer	$D n o d e / D f = 2$ $L m / D f = 10, 12$ $β = 105 ∘, 120 ∘$	$R e < 200;$ Flow state depended on $R e$ $S c = 1 − 100$ nonpermeable membrane with constant wall concentration	Not mentionedFluent 6.2	Original experiment	Spherical spacer node reduced contact area with membrane significantly.	Koutsou & Karabelas (2015)
3D; five mesh angles(1) Nonwoven spacer; 1 cell(2) Partially woven spacer; 1 cell(3) Middle layer spacer; 1 cell(4) Fully woven spacer; 2 cells	$H = 1 m m; L m = 4.5 m m$ $D f = 0.5, 1 m m$ $α = 30 ∘, 60 ∘, 90 ∘$ $β = 30 ∘, 60 ∘, 90 ∘$	$R e c h = 224$ Laminar; Steady $u 0 = 0.1 m / s$ permeable membrane	$N$ = 1.4–2.9 million TetrahedralCOMSOL 5.0	not mentioned	3D simulations of 20 spacer geometries with considering realistic boundary condition via the solution-diffusion model.	Gu et al. (2017)
3D; 9 cells(1) Zigzag spacer(2) Triple spacer(3) Wavy spacer	$D f = 0.5 m m; H = 1 m m$ $L = W = 4.1 m m$ $(1.5 m m f o r t r i p l e s p a c e r)$ $α = 90 ∘; β = 90 ∘$	$R e = 50 ? 200$ Steady; LaminarNonpermeable membrane with a constant wall concentration of 35% w/w NaCl	Tetrahedral $S > 0.1 μ m$ Fluent 15,16	Li et al., （2004）; Shakaib et al., （2007); Saeed et al., 2012	Correlations of various parameters with Re is developed and compared with other studies;Comparison of spacer geometries based on pressure drop, SCE, SPC, Pn, Sh and other performance indicators.	Kavianipour et al. (2017)
2D; 35 cells; Zigzag spacer	$D f = 0.39 m m; H = 0.78 m m$ $L = 200 m m; L m = 2.85 m m$	LES turbulence modelpermeable membrane	$N = 6.8 × 105$ $S > 0.8 μ m$ Fluent	Original experiment	Time-dependent salt concentration distribution and permeate flux in a vibrating membrane system is obtained	Su et al. (2018)
3D; 1 cell2-layer, nonwoven, uniform spacer	$H = 2 D f; L m / D f = 8$ $α = 45 ∘; β = 90 ∘$	$R e = 60 − 200$ ; Flow state depended on $R e$ $S c = 1 − 100$ DNS (direct numerical simulation)Nonpermeable membrane with constant wall concentration	Not mentionedFluent 6.2	Literature (Koutsou et al., 2007)	Assuming a uniform fouling layer on the membrane surface.	Koutsou et al. (2018)
3D; 2 cells + 2 half cells1-layer, uniform spacer with 0-3 holes;	$H = 1200 μ m$ $L m = 4000 μ m$ $D f = 1000 μ m$ $α = 45 ∘; β = 90 ∘$ Hole diameter $D h o l e = 300, 500 μ m$	$R e = 73 − 375$ $Q 0 = 12 L / h$ nonpermeable membrane	22 million grid pointsFluent	Original experiment with synthetic solution	3D model for 3 novel feed spacers with perforations.	Kerdi et al. (2018)
3D; 3 cells2-layer, nonwoven, nonuniform spacer	$H = 787 μ m$ $L m = 3100 μ m$ $D f = 340 − 610 μ m$ $α = 45 ∘; β = 90 ∘$	steady to unsteady;DNS (direct numerical simulation)nonpermeable membrane	67 million grid pointsFluent 17	Original experiment	Overlap at the intersection of filaments	Qamar et al. (2019)
3D; 3 cellsNonwoven, uniform filament with 2-layer or 3-layer	$H = 1 m m$ $D f / H = 0.4 − 0.6$ $L m / H = 4$ $α = 0 − 60 ∘; β = 90 ∘$	$R e h = 200$ ; Steady $S c = 600$ Permeable membrane	$N$ = 90 millionTetrahedralCFX 16.2nonstructured cells with a maximum size of $3 % – 5 % H$ in main fluid domain prismatic cells with a size of $2 % – 4 % H$ and a minimum number of 20 for the inflated boundary	Literature (Fimbres-Weihs & Wiley, 2007; Schwinge et al., 2002b; 2004)	Multiscale techno-economic model for feed spacer channel in RO system is established	Liang et al. (2019)
3D; 1 × 4 cells(1) Empty(2) Circular spacer(3) Diamond spacer(4) Elliptic spacer	–	$u 0 = 0.1, 0.3, 0.5 m / s$ Standard k?ε model	$N = 3886000$ Hexahedral dominantFluent 6.3	Original experiment	The great potential to mitigate membrane fouling and enhance permeate flux of turbulence promoter, especially the elliptic shape, is confirmed.	Tsai et al. (2019)
3DNonwoven, uniform spacer with standard nodes or column nodes	$H = 1.2 m m$ $D f = {0.5 m m (c o l u m s p a c e r) 1 m m (s t a n d a r d s p a c e r)$ $L m = 4 m m; D n o d e = 1.5 m m$ $α = 45 ∘; β = 90 ∘$	$u 0 = 0.16, 0.18 m / s$ Unsteady;Nonpermeable membrane	$N$ = 30 millionFluent 2018	Original experiment	Better performance such as pressure drop reduction, shear stress reduction and higher specific flux is found for novel column spacer compared to standard spacer.	Ali et al. (2019)
3D; 1 × 3 cells(1) Standard spacer(2) Turbo spacer	–	DNS (direct numerical Simulation)Nonpermeable membrane	Hexahedron dominant	Original experiment	Novel turbo spacer exhibits better performance in facilitating the homogenous distribution of high velocity and shear stress compared to a standard spacer.	Ali et al. (2020)
3D; 3 × 5 cells(1) 2-layer, nonwoven, nonuniform spacer(2) 1-layer, nonuniform spacer	$H = 460 μ m$ $L m = {1770 μ m f o r 2 l a y e r 3140 μ m f o r 1 l a y e r$ $D f = {220 − 320 μ m 2 l a y e r 280 − 460 μ m 1 l a y e r$ $α = 45 ∘; β = 90 ∘$	$u 0 =$ 0.12 m/sSteady; LaminarNonpermeable membrane	2.3 million grids	Original experiment	Nonuniform filament with different thinning zone location $(0, 1 / 3, 1 / 2)$ on filaments.	Lin et al. (2020)
2D(1) Cavity spacer(2) Submerged spacer(3) Zigzag spacer	$L m / D f = 4, 8, 12$ $H = 0.2 − 1.4$	Steady; LaminarPermeable membrane	$N = 9000 − 16200$ COMSOL 5.1	Literature (Schock & Miquel, 1987; Koutsou et al., 2009)	Correlation for CP; pressure drop is concluded.	Gu et al. (2021)
3D; 2 cells1-layer, pillar nodes, uniform filament	$H = 1200 μ m$ $D f = 340, 500, 1000 μ m$ $α = 45 ∘; β = 90 ∘$ $D n o d e = 1000 μ m$	$u 0 = 92, 185, 389, 469 m m / s$ Transient; Laminarnonpermeable membrane	Fluent	Original experiment	Same numerical methodology with (Kerdi et al., 2018).	Kerdi et al. (2021)
3D; 3 cells; Single layer(1) Commercial, nonuniform spacer(2) Pillar node, uniform spacer(3) Hole pillar, uniform spacer	$L = 20 m m; H = 1.2 m m$ $L m = 4 m m; D n o d e = 1 m m$ $D f = 0.5 o r 0.5 − 0.9 m m$ Hole: $0.4 m m × 0.25 m m$ $α = 45 ∘; β = 90 ∘$	$u 0 = 0.185 m / s$ Nonpermeable membrane	hexahedral $S > 50 μ m$ ~2600000 grid pointsFluent 2020	Original experiment	Measuring parameters in intermediate units to avoid inlet and outlet effects.	Qamar et al. (2021)
3D; 1 cell2-layer, fully woven, uniform spacer	$D f = H / 1.8$ $α = 45 ∘; β = 90 ∘$ Porosity: $0.663 − 0.828$	$R e > 400$ ; shear stress transport (SST) turbulence modelnonpermeable membrane	$N = 6000220 − 13714094$ Tetrahedral mainly, with tetrahedra and prisms in the regions surrounding the ﬁlaments. $S / H = 2, 3, 4$	Literature	Flow, mass transfer and heat transfer are simulated;The dependence of $f, N u$ and $S h$ on the Reynolds number shows a double asymptotic trend;The attack angle and filament spacing have significant influence on flow and mass/heat transfer.	Mokhtar et al. (2021)
3D(1) Standard spacer; 1 × 3 cells(2) Honeycomb-shaped spacer; 1 × 2 cells	(1) $α = 45 ∘; β = 90 ∘$ $L m = 2.79 m m; D f = 0.43 m m$ (2) $α = 30 ∘; β = 120 ∘$ $L m = 1.73 m m; D f = 0.4 m m$	$R e = 295.74$ ;SteadyStandard k?ε model	$N =$ 33, 20 million	Original experiment	Honeycomb spacer increases the permeate flux, mitigates CP, and inhibits fouling layer deposition.	Park et al. (2021)
3D; 3 × 5 cells2-layer, nonwoven, uniform filament	$D f = 0.4 − 0.6 m m$ $H = 660 − 864 μ m$ $L m = 2 − 4 m m$ $α = 15 − 37.5 ∘; β = 30 − 90 ∘$ Porosity: $0.630 − 0.882$	Re < 300; Laminar $u 0 = 0.12 m / s$ Nonpermeable membrane	$N =$ 12.9 $−$ 22.7 million	Original experiment	Channel porosity is one of the determinant parameters for spacer performance and the appropriate value is approximately 0.85.	Lin et al. (2022b)
3D; 2 × 6 cells(1) 2-layer, nonwoven, uniform spacer(2) 2-layer, fully woven, uniform spacer(3) 2-layer, nonwoven, uniform, spine ramp spacer	$H = 0.77 m m; W = 3.465 m m;$ $L m = 1.2, 1.5 m m;$ $D f = 385 μ m;$ $α = 45, 60 ∘; β = 90, 60 ∘$	$R e ≈ 300;$ realizable k?ε turbulence model $u 0 = 0.2 m / s$ permeable membrane	$N =$ 3.2 $−$ 5.8 millionTetrahedral $S = 14 − 45 μ m$	Literature	High membrane flux aggravates CP;Water flux, solute flux, CP modulus, pressure drop and wall shear rate are used in spacer performance evaluation.	Bae et al. (2023)

Tab.1 Summary of CFD simulations about SWM modules

Parameter	$κ s p a c e r$	$R s p a c e r$	$ε$
Parameter	Permeability coefficient for the porous spacer	Resistance loss/inertial coefficient for the porous spacer	Porosity for the porous spacer
unit	$m 2$	$m − 1$	–
Lin et al. (2022a)	$2 × 10 − 9$ ⁱ	25775 ⁱ	0.8
Abdelkader & Sharqawy (2022)	0.97 $× 10 − 8$ –64.85 $× 10 − 8$ ⁱⁱ	33–282.9	0.74–0.89
Jeong et al. (2020)	$2 × 10 − 10$	–	0.5

Tab.2 Parameters in the spacer porous domain

Solute	Osmotic pressure?π (bar)	Viscosityµ (Pa·s)	Diffusion coefficientD (m²/s)	Densityρ (kg·m³)	Ref.
1 mg/LMgSO₄	4.97×10⁵ m(49.55−136.7 m+1207 m²)	0.8972×10⁻³(1+3.713 m+26.0614 m²)	0.849×10⁻⁹(1−0.41873 m^0.0872)	997+1036 m	Yang et al. (2023)
< 100 g/LNaCl	77.17 m				Johnston et al. (2023)
$< 0.09 k g / k g$ $N a C l$	$805.1 × 105 m^$	$0.89 × 10 − 3 (1 + 1.63 m^)$	$M a x {(1.61 × 10 − 9 (1 − 14 m) 1.45 × 10 − 9$	997.1×(1.0+0.696 m)	Cao et al. (2018); Guan et al. (2023); Shang et al. (2021)
0.1 < c < 1.5 mol/L NaCl	4.793×10⁶c	10⁻³(1.004+0.08c)	1.45×10⁻⁹	995.7+38.54c	Su et al. (2018)
c < 0.6 mol/L CaCl₂	(62.35c + 13.14c²+8.993c³)×10⁵	10⁻³(1.004 + 0.2981c)	${(1.176 + 107.5 c) / (1 + 95.24 c + 26.03 c 2) f o r c < 0.132 1.134 – 0.3213 c + 0.2319 c 2 – 0.1553 c 3 f o r 0.132 < c < 0.6$	995.7+89.72c
c < 0.6 mol/L $N a 2 S O 4$	(56.29c−28.37c²+23.05c³)×10⁵	10⁻³(1.004+0.4094c)	${(1.08 + 129.3 c) / (1 + 124.5 c + 40.92 c 2) f o r c < 0.108 1.042 – 0.3225 c + 0.1048 c 2 – 0.07547 c 3 f o r 0.108 < c < 0.6$	995.7+11.91c
0.05 < c < 0.5 mol/L $M g S O 4$	(33.08c–178.9c²+942.7c³)×10⁵	10^–3(1.004+0.06092c)	0.7288–0.1929c+0.1517c²–0.9297c³	995.7+11.88c
	$8.48 × 104 m (0.917 + 2.13 ×$ $10 − 4 m + 3.141 × 10 − 6 m 2)$	$− 6.196 × 10 − 10 m 2 +$ $1.968 × 10 − 6 m +$ $9.885 × 10 − 4$	$2.811 × 10 − 20 m 4 − 2.645 ×$ $10 − 17 m 3 + 7.021 × 10 − 15 m 2 − 1.458 ×$ $10 − 13 m + 1.477 × 10 − 9$	−2.179 × 10⁻⁴ m² + 0.692 m + 997.99	Sitaraman & Battiato (2022)
Typical value for brackish desalination and softening	4.872×10⁶c				Zhou et al. (2021)
BSA solution	$π = R T (2 2.5 × 10 − 7 Z 2 c 2 + c s 2 − 2 c s +$ $10 − 3 c + 10 − 6 A 2 c 2 M + 10 − 9 A 3 c 3 M 2)$ Z=−497.512−37.913pH+2896.079pH⁻²+352.129ln(pH)A₂=−5.625×10⁻⁴−2.41×10⁻⁴Z−3.664×10⁻⁵Z²A₃=−2.95×10⁻⁵−1.051×10⁻⁶Z+1.762×10⁻⁷Z²	$μ w e 2.44 × 10 − 11 c 2$	$D i d μ w μ (c) 1 R T ∂ π ∂ c$	Constant	Schausberger et al. (2009)

Tab.3 Calculation correlations of permeation parameters

Fig.1 Schematic of the calculation method of the permeation process and concentration near the membrane: (a) impermeable membrane; (b) impermeable and dissolving membrane; (c) construction of the membrane hole; (d) permeable membrane with direct calculation methods and (e) permeable membrane with the loop-fitting calculation method.

Fig.2 Schematic of the numerical implementation method of scaling model.

Meaning	Attachment rate, $r a t t$	Yield coefficient, $Y S X$	Maximum specific rate, $μ m a x$	Half-saturation coefficient, $K S$	Maximum Biomass concentration, $C X, M$	Biomass mechanical strength, $σ d e t$	Diffusion coefficient for substrate, $D s u b$
	$C m o l / (m 2 ? d)$	$m o l C / m o l b i o m a s s$	d^–1	mol/m³	Cmol/m³	N/m⁻²	m²/s
Picioreanu et al. (2009)	$6 × 10 − 4$	0.52	2.8	0.063	2800	–	2.5×10⁻⁹
Radu et al. (2010)	$5 × 10 − 3$	0.5i	2	0.025	8000	7	10⁻⁹
Radu et al. (2012)	$5 × 10 − 3, 15 × 10 − 3$	0.5	2	0.025	8000	7	10⁻⁹
Bucs et al., (2014a)	$0.06, 0.13, 0.26$	1	1.08	0.05	1400	–	10⁻⁹>
Radu et al. (2015)	$5 × 10 − 3 (C − m o l / (m · d)$	0.5i	2	0.025	`	7	10⁻⁹

Tab.4 Parameters of the in biofilm model

Fig.3 Schematic of the numerical implementation method of the biofouling model (Radu et al., 2010).

Fig.4 Schematic of the artificially established biomass geometry: (a) various concentration of BSA particles in the Monte Carlo box (Petrosino et al., 2023); (b) cylinders represent the EPS layer covering the membrane surface (Luo et al., 2022); and (c) the manually established biomass domain is regularly distributed on filaments (Lin et al., 2023).

Fig.5 Simulation results of patterned membranes. (a) stream lines in the valley (Choi et al., 2015); (b) particle distribution on patterned membrane for different particle diameters and Reynolds numbers (Jung and Ahn, 2019); (c) velocity streamline profile for different patterned membranes: wave tri, rec, and trap (Zhao et al., 2021); (d) velocity streamline profile for conventional membrane and rectangular membrane (Shang et al., 2020a); (e) real-time solute concentration distribution for triangular membrane and cambered membrane (Shang et al., 2021); (f) streamlines for different patterned membranes (Shang et al., 2020b); (g) streamlines for rectangular membranes and triangle membranes (Ilyas et al., 2021); and (h) solute concentration distribution for different patterned membranes, namely, rectangles, trapezoids, prisms, pyramids, cylinders, circles, and polyhedrons (Zhou et al., 2021).

Fig.6 Simulation results of the vibration and rotation membranes. (a) the deposited particle on no-vibration and 60 Hz vibration membranes (Su et al., 2019); (b) the wall shear stress distribution on the membrane surface with a rotating impeller (Xie et al., 2018); (c) wall shear stress distribution on the perforated and nonperforated disk (Kim et al., 2015); (d) the vortex structures visualized by the

λ 2

-criterion for etching disks with the number of etching patterns ranging from 0 to 16 (Park et al., 2023); (e) the shear stress distribution on the surfaces of staggered rotating membranes (Zhang et al., 2022); and (f) the shear stress distribution on basket surfaces (Naskar et al., 2019).

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