CFD simulation of a novel membrane distributor of bubble columns for

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Thermodynamics, Transport, and Fluid Mechanics

CFD simulation of a novel membrane distributor of bubble columns for generating microbubbles Xiaoli Li, Yefei Liu, Hong Jiang, and Rizhi Chen Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b05776 • Publication Date (Web): 24 Dec 2018 Downloaded from http://pubs.acs.org on December 31, 2018

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Industrial & Engineering Chemistry Research

CFD simulation of a novel membrane distributor of bubble columns for generating microbubbles

Xiaoli Li, Yefei Liu*, Hong Jiang, Rizhi Chen* State Key Laboratory of Materials-Oriented Chemical Engineering, College of Chemical Engineering, Nanjing Tech University, Nanjing 210009, China

*Corresponding Author. Tel: +86-25-83172286; Fax: +86-25-83172292; E-mail address: [email protected], [email protected]

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Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Microbubbles have attracted much attention due to their high mass-transfer efficiency. CFD simulations are performed for the flows in a membrane distributor and a bubble column. Gas permeation in the membranes is simulated using Darcy’s law, while the two-fluid model is employed for studying gas-liquid flow in the membrane channel and bubble column. It reveals that the Darcy’s law can describe the gas flow in dry ceramic membranes. For the membrane coated with a skin layer of smaller pore size, more gas permeates into the inner membrane channels. The relative permeability model is capable to predict the gas permeation flow in the membrane partially saturated with water. The water saturation makes membrane pores unavailable and the large pressure drop is caused. Gas holdup is well predicted using the Schiller-Naumann drag coefficient for the spherical microbubbles. In the future work, scaling-up membrane distributor will be guided by the CFD simulations.

Keywords: membrane distributor; bubble column; gas permeation; relative permeability; CFD


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INTRODUCTION Bubble columns are widely employed in chemical, biochemical and petrochemical industries. Gas bubbles are dispersed in liquid and homogeneous bubbly flow is very desirable for achieving high mass transfer efficiency. The bubble column performance highly relies on the design of gas distributors. The distributor configurations are generally classified into two main categories: plate type and pipe type. The class of plate-type distributor mainly includes perforated plate1 and porous plate.2 The plate-type distributors are equipped with a chamber to uniformly supply the gas to all holes in the plate. The distributors with nozzle,3 spider4 and ring5 have been developed as the pipe-type distributors. Gas is supplied to these distributors by a header pipe. Large bubbles are usually generated by these conventional distributors. Microbubbles have excellent gas dissolution ability due to self-compression, large interfacial area and slow rising velocity in the liquid. In recent years, the membrane distributors have attracted great attention in the light of the microbubble generation. 6-10 Success in designing bubble columns requires the fundamental knowledge on the influence of gas distributors. CFD simulations have been employed to perform the investigations on gas-liquid flow in bubble columns. 11,12 Ranade and Tayalia

13

studied

the influence of single- or double-ring spargers in shallow bubble column reactors. Their CFD simulations revealed that the flow behaviors were controlled by the sparger configurations. Dhotre and Joshi

14

studied the influence of the size, location, opening

area and hole diameter of nozzles on the flow pattern of a bubble column with a gas chamber. They found that the effect of nozzle size and its location with respect to the distributor was very important. The flow pattern within the gas chamber was analyzed and the chamber configurations affected the uniformity of gas distribution in the sparger region. Bahadori and Rahimi 15 investigated the influence of the orifice number on gas holdup and liquid velocity in shallow bubble column reactors. They reported that the total gas holdup was increased by increasing the number of orifice in the sparger and each local orifice contributed to the liquid circulation and mixing. Li et al.16 simulated different multiple-pipe gas distributors in a pilot cylindrical bubble column. They found 3 ACS Paragon Plus Environment


that the distributor configurations had strong impact on the asymmetric flow and mixing characteristics in the vicinity of gas distributor. Those CFD efforts have been made to the traditional distributors only generating millimeter-sized bubbles. To the best of our knowledge, numerical simulations of membrane distributors have not been reported. There would be an interest for process engineers aiming at effectively generating microbubbles. In the membrane distributor, the nano- or micro-pores greatly benefit for the in-situ growth of the microbubbles controlled by cross flow. To comprehensively understand the effect of the membrane distributors, it is very necessary to carry out the CFD simulations. There are two main challenges in the simulation of gas-liquid flow influenced by the membrane distributor. The first one is that the direct modeling of pore-scale flow cannot be afforded due to the high complexity of the membrane structure. The Darcy’s law-based method is computationally efficient but the pore-scale information should be provided due to the averaging. The second one is the modeling of microbubble flow in the bubble column. Previous simulation of bubble column flow was targeted on the millimeter-sized or larger bubbles.17,18 The dynamics of large bubbles (> 1mm) has been extensively investigated by both experimental and numerical studies.19-22 For low Eötvös number, the bubble remains spherical, and increasing the value of Eötvös number, the bubble becomes oblate. Differently, the microbubbles behave as spheres with slower rising velocity. The stronger momentum transfer occurs between the different phases. Therefore, the classical interphase force models should be re-examined for the microbubble flow. The objective of this work is to establish the CFD simulation methods for studying the membrane distributor equipped in a bubble column. The Darcy’s law-based simulation method is established for simulating the flows in the multichannel membrane distributor. The gas permeation driven by different pressure drops is studied in the dry and wet membranes. The gas-liquid flow in the bubble column is simulated using the two-fluid model.


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EXPERIMENTAL SETUP The bubble column with a membrane distributor is shown in Figure 1. A vertical cylindrical plexiglas pipe (0.032 m i.d.) with 0.8 m length is fixed downstream of the membrane distributor. The distributor contains a ceramic membrane with 19 channels with 0.5 m length. The diameter of a multi-channel membrane tube is 0.03 m, and the diameter of each membrane channel is 0.004 m. Before the liquid flow, the gas firstly flows though the dry membrane. In order to reduce permeation resistance, ceramic membranes are usually manufactured to have asymmetric structure including a thick support, an intermediate layer and a skin layer, as shown in Figure 1. Large pores exist in the membrane support and small pores in the skin layer. In this work, one membrane only contains the support with a mean pore size of 3000 nm, while the other is prepared by coating a skin layer of 200 nm pores on the support surface.

MATHEMATICAL MODELS Single-phase Flow Model Fluid flow through porous media is usually modeled either at the pore-scale 23 or at the representative elementary volume (REV)

24

. The pore scale approach requires that

the pore geometry be fully resolved and the flow is determined using the Navier-Stokes equations. However, the pore-scale simulation is too expensive to be used in real applications. The REV methods, e.g. Darcy’s law, are computationally economical since the volume averaging is performed with reasonable closure. In this work, it is assumed that the Reynolds number through the membrane is very low and meets the Darcy’s law: p= 

 k

U

(1)

where p is the pressure, Pa; U is the gas velocity, m/s;  is the viscosity, Pas; k is the gas absolute permeability in the membrane, m2. The absolute permeability is the ability of a membrane to allow fluids to flow through its pores, which depends solely on the membrane properties. 5 ACS Paragon Plus Environment


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In the membrane channel, the free flow is governed by the continuity equation and momentum equation: ρ    ( ρU)  0 t

(2)

( ρU)    ( ρUU)  p    τ t

(3)

where  is the gas density, kg/m3, which is calculated using perfect gas law; U is the gas velocity, m/s; p is the pressure, Pa;  is the viscous stress, Pa, which is modeled using Newton’s law of viscosity. Since the laminar flow exists in the channels, no turburblence modeling is needed.

Two-fluid Model for Porous Media and Free Flow In this work, the porou media flow and free flow are simulated by the two-fluid model. The mass continuity and momentum equations of the gas and liquid phases are written as (αi ρi )    (αi ρi Ui )  0 t

(4)

(αi ρi Ui )    (αi ρi Ui Ui )  αi p    (αi τi )  αi ρi g  Mi t

(5)

where i refers to the phase (l for liquid and g for gas); U is the phase velocity, m/s;  is the volume fraction of each phase;  is the phase viscous stress tensor, Pa, which is modeled as 2 T τi  μi Ui   Ui    μi    Ui  I   3

(6)

Since the Reynolds numbers of the flow in membrane pores, membrane channels and bubble column are quite small, the assumption of laminar fow is acceptable. The interfacial momentum transfer term Mi should be modeled differently in the porous media and free flow region. Under the capillary pressure, the porous ceramic membrane is firstly wetted. As the gas pressure increases, the liquid is drained out of the membrane and gas passes through the open pores into the bulk liquid phase. The liquid displacement generates a residual liquid in the pores. To model the flow in the membrane distributor, the momentum transfer term is modeled based on the Darcy’s law as 6 ACS Paragon Plus Environment

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Mi  

i Ki

Ui

(7)

where the apparent permeability Ki is expressed as follows Ki  kkri

(8)

where kri is the relative permeability of phase i, whose value is determined by the saturation of the wetting phase Sw. The relative permeability suggests that the presence of one fluid blocks some pore spaces available, and therefore, reduces the permeability. Due to capillary effects in the porous medium, no equality exists between the averaged pressure fields of each phase. Following the classical multiphase porous medium approach,25 we define a macro-scale capillary pressure pc using the pressure of wetting phase Sw and non-wetting phase Snw: pc  pnw  pw

(9)

The values of pc are usually obtained experimentally and then correlated on a capillary pressure model. As can be seen that the main difficulty in solving the velocity is the modeling of the relative permeability and capillary pressure in the porous membrane. These meso-scale models bridge the pore-scale physics with the Darcy-scale quantities. From the experimental data, the relative permeability of gas in the membrane with 200 nm pore is modeled in this work like the correlation of Brooks and Corey 26 as kr ,nw  1  Sw 

12

kr ,w  Sw12

(10) (11)

The capillary pressure model is modeled in this work as

pc  pc ,0 Sw0.8

(12)

where pc,0 is the entry capillary pressure, which is estimated as 1.0105 Pa. After the microbubble formation at the membrane suface, the microbubbles flow in the membrane channel and bubble column. In this study the drag force is assumed to be dominant and the momentum interfacial transfer term is calculated as



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3 C M D,g  M D ,l   g l D U g - Ul  Ul - U g  4 db

(13)

where db is the mean bubble size, m, which is measured by the experiment; and CD is the drag coefficient. There are several drag models available in the literature.27-30 However, they were originally developed for large bubbles. Figure 1 shows the microbubbles captured in our experimental work. Here, the drag coefficient for the flow past a spherical microbubble is approximated by the Schiller-Naumann correlation 27 as  24 0.687  1  0.15 Re  CD   Re  0.44 

Re  1000

(14)

Re  1000

where the bubble Reynolds number Re is defined as

Re 

ρl d b U g  Ul μl

(15)

SIMULATION DETAILS Gas permeation in the dry membrane distributor is simulated using the OpenFOAM 2.3.1 solver rhoPorousSimpleFoam.31 The governing equations are linearized by finite volume discretization. The Gauss linear scheme with second-order accuracy is used for the gradient term. The convection term is discretized by the Gauss linearUpwindV scheme. Due to the non-orthorganol mesh, the Laplacian term is discretized by the Gauss linear corrected scheme. The pressure-velocity coupling is handled using the SIMPLE algorithm. The steady-state simulation is performed with the under-relaxitation factor, 0.3 for pressure and 0.7 for velocity. The solution is considered converged when the residual for the pressure equation drops to below 10-4. The mass flow rate is used for gas inlet. At the outlet, the pressure is set at 1105 Pa. The two-fluid model for porous media and free flow is implemented in our new solver porousTwoPhaseEulerFoam. Since large pressure difference occurs through the porous membrane, the gas compressibility is considered in this solver. The linear equation systems resulting from the finite volume discretization are also solved in a segregated fashion. Since the transient simulation is performed, the pressure-velocity 8 ACS Paragon Plus Environment

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coupling is handled using the PISO solution algorithm. The interphase drag coupling terms in the phase momentum equations are treated by the semi-implicit method.32 The gradient term is discretized by the Gauss linear scheme. The convection term of phase volume fraction is discretized by the Gauss upwind scheme. The linear upwind scheme is used for the momentum convection terms. To largely reduce the computational time, the bubble column with the membrane distributor is simulated by three steps. First, the porous region is simulated to determine the gas distribution in each membrane channels. Second, the gas-liquid flow in the membrane channels is simulated using the results of the first step as the boundary conditions. Third, the gas-liquid bubbly flow in the bubble column is simulated. The column section of 0.1 m height is selected as the 3D computational domain. The no-slip boundary condition is used for velocity at the column wall. Table 1 lists the mean bubble sizes measured and they are used for the calculation of drag force.

RESULTS AND DISCUSSION Gas Flow in Membrane The simulation is performed for the gas permeation through two dry ceramic membranes. First, grid sensitivity study is carried out using three grids with significantly different resolutions. As shown in Figure 2, three different meshes are compared and Grid 2 is enough to obtain the grid-independent the results. For the dry membranes, only gas permeates through the membranes pores. Figure 3 shows the pressure drops at different gas flow rates through the two membranes. It can be seen that a linear relationship exists between pressure drop and gas flow rate, which indicates that the gas flow in the membranes follows the Darcy’s law. By coating the skin layer on the support, the pressure drop is greatly increased. Interestingly, at the high flow rate, the increase in pressure drop becomes larger for the membrane having the skin layer of 200 nm pore. This is the unique characteristics of the multi-channel ceramic membranes. Figure 4 gives the pressure and velocity distributions of gas flow in the cross section of the two membranes. For the membrane only having 3000 nm pore, the 9 ACS Paragon Plus Environment


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pressure drop mainly occurs at the region around the outermost channels. According to the Darcy’s law, the gas permeation is driven by the pressure drop, and therefore the gas flow is concentrated in the outermost channels. Due to the thin skin layer, the inner channels make contribution to the pressure drop, and the pressure drop drives more gas permeate into the inner channels. The contribution of membrane channels is presented in Figure 5. The contribution of a channel for gas permeation is calculated as

C=

Qr Q

( r  1, 2,3)

(16)

where Qr is the gas permeation quantity flowing out from channels in Ring r, Q is the total gas permeation quantity. For the membrane with 3000 nm pore, most gas flows out from the channels in Ring 1. The channels in Ring 1 are nearest to the gas inlet. From Eq. (1), the larger distance between the channel and gas inlet makes the lower gas permeation flux. When the membrane is coated with the skin layer with 200 nm pore, the contribution of the 2nd-ring channels increases. This is due to the increased portion of pressure drop contributed by the membrane skin layer. Therefore, to increase the gas permeation into the inner channels, the membrane skin layer with smaller pores should be used. This conclusion is the same as that made from the liquid permeation flow reported by Yang et al.24

Gas-Liquid Flow in Membrane The CFD simulations are carried out for the gas flow through the membrane wetted by water. The porous media zone of Grid 2 is used to obtain the grid-independent results. Figure 6(a) shows the experimental values of water saturation measured at different gas pressure drops through the membrane with a skin layer of 200 nm pore. The saturation represents the proportion of pores filled with the residual water in the whole porous region. Increasing the pressure drop leads to more gas permeation and therefore the saturation decreases. Based on the data of water saturation and the corresponding pressure drop, the gas relative permeability is correlated as shown in Figure 6(b). As the water saturation increases, the gas relative permeability reduces quickly, indicating that more membrane pores are blocked by water. 10 ACS Paragon Plus Environment

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By using the gas relative permeability model, the relationship between gas flow rate and pressure drop is predicted as shown in Figure 7. It can be seen that, due to the water saturation, the pressure drops through the wet membranes are much larger than those through the dry ones. The relative permeability model gives acceptable prediction in the large range of pressure drop, which is very helpful for guiding the operation of the membrane distributor. In the membrane partially saturated with water, the pressure drop mainly occurs at the membrane skin layer as shown in Figure 8(a). In Figure 8(b), the gas flow almost has the uniform distribution in the 1st-and 2nd-ring membrane channels. Since the distance is far from the innermost channel to the gas inlet, very little gas permeates into the innermost channel. To qualitatively validate this simulated finding, the bubbles in the different channels are experimentally observed as shown in Figure 8(c). In this experiment, no liquid flows in the channel, and the large bubbles are formed due to the coalescence.

Gas-Liquid Flow in Bubble Column The gas-liquid flow in single membrane channel is shown in Figure 9. The liquid inlet velocity is set to be 0.07 m/s. The gas permeates through the porous region into the membrane channel, while the liquid flows in the membrane channels. The laminar liquid flow provides the shear stress force for controlling the microbubble generation. A small number of bubbles exist at the lower part of the channel. Liquid carries the bubbles upward and the accumulation of the bubbles makes larger gas holdup at the upper part of the channel. When more gas permeates into the membrane, larger gas holdup is found and the dense bubbly flow is formed at the lower part of the channel at the high gas flow rate of 1.2  10-5 kg/s. At the upper part, the bubbles move together and the possibility of bubble coalescence is greatly enhanced. The short membrane channel would benefit for the microbubble generation. In the bubble column section, the global gas holdup is predicted for different superficial gas velocities, as shown in Figure 10. Three grids are used to investigate the influence of cell numers. The cell numbers are 21794, 57166 and 73530 for Grid 1, and 11 ACS Paragon Plus Environment


Grid 2 and Grid 3, respectively. It is found that the results of Grid 2 and Grid 3 have small difference. To save computational time, we use Grid 3 to further study the gas-liquid flow in the bubble column. The gas holdup increases with the increase in the superficial gas velocity. The simulated results have good agreement with our experimental data reported by Han et al.33 The two-fluid modeling method is valid for predicting the bubble column flow with this membrane distributor. More specifically, the Schiller-Naumann drag coefficient is adequate to describe the motion of microbubbles. In Figure 11, by increasing the gas inlet velocity, the bubble Reynolds number is increased, but it is still below 1000. According to Eq. (14), we can infer that the microbubbles flow in the transitional regime where both viscous and inertial effects are important. The smaller bubble Reynolds number results in the larger drag coefficient. In the simulation of millimeter-sized bubbles,34,35 the drag coefficient is smaller than 1.0. However, the microbubble have the drag coefficients larger than 1.0, indicating that the stronger drag force exerted on the microbubbles.

CONCLUSIONS CFD models are proposed for the flows in a bubble column with a membrane distributor. The simulation accuracy can be acceptable from the experiemntal validations. The gas flow in the dry ceramic membranes follows the Darcy’s law. By coating the membrane support with a skin layer of smaller pore size, more gas permeates into the inner channels due to more pressure drop contributed by the skin layer. The relative permeability model and capillary pressure model can be used to predict the gas permeation flow in the membranes partially saturated with water. The larger water saturation makes less membrane pores available, which results in much larger pressure drop. The 1st-and 2nd-ring membrane channels are near to the gas inlet, and uniform gas flow is found around these channels. The bubble column with microbubble flow can be predicted by the two-fluid model. It is reasonable to use the Schiller-Naumann drag coefficient to describe the drag force of spherical microbubbles. In our bubble column, the microbubbles experience several times larger drag force than the millimeter-sized bubbles. 12 ACS Paragon Plus Environment

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Acknowledgements This work is supported by Natural Science Foundation of Jiangsu Province (BK20160978) and the National Natural Science Foundation of China (91534110).

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gas-channeling phenomena in micropacked-bed reactors via catalyst wettability modification. Ind. Eng. Chem. Res. 2018, 57, 84–92. (24) Yang, Z.; Cheng, J. C.; Yang, C.; Liang, B. CFD-based optimization and design of multi-channel inorganic membrane tubes. Chinese J. Chem. Eng. 2016, 24, 1375–1385. (25) Horgue, P.; Soulaine, C.; Franc, J.; Guibert, R.; Debenest, G. An open-source toolbox for multiphase flow in porous media. Comput. Phys. Commun. 2015, 187, 217-226. (26) Brooks, R.H.; Corey, A.T. Hydraulic properties of porous media. Hydrol. Pap. 3. Colo. State Univ., Fort Collins. 1964. (27) Schiller, L.A.; Nauman, Z. A drag coefficient correlation. Ver. Dtsch. Ing. 1935, 77, 138. (28) Ishii, M.; Zuber, N. Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE J. 1979, 25, 843–855. (29) Tomiyama, A.; Kataoka, I.; Zun, I.; Sakaguchi, T. Drag coefficients of single bubbles under normal and micro gravity conditions. JSME Int. J. 1998, 41, 472–479. (30) Zhang, D. Z.; Vanderheyden, W. B. The effects of mesoscale structures on the macroscopic momentum equations for two-phase flows. Int. J. Multiphas. Flow 2002, 28, 805–822. (31) OpenFOAM. The Open Source CFD Toolbox: User Guide. OpenFOAM Foundation, London, UK. 2014. (32) Liu, Y. F.; Hinrichsen, O. Study on CFD-PBM turbulence closures based on k- and Reynolds stress models for heterogeneous bubble column flows. Comput. Fluids. 2014, 105, 91-100. (33) Han, Y.; Liu, Y.F.; Jiang, H.; Xing, W. H.; Chen, R.Z. Large scale preparation of microbubbles by multi-channel ceramic membranes: Hydrodynamics and mass transfer characteristics. Can. J. Chem. Eng. 2017, 95, 2176-2185. (34) Xing, C.T.; Wang, T. F.; Wang, J. F. Experimental study and numerical simulation with a coupled CFD–PBM model of the effect of liquid viscosity in a bubble column. Chem. Eng. Sci. 2013, 95, 313-322. (35) Masood, R.M.A.; Delgado, A. Numerical investigation of the interphase forces and turbulence closure in 3D square bubble columns. Chem. Eng. Sci. 2014, 108, 154-168.



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Table 1. The mean bubble sizes at different superficial gas velocities Ug (m/s)

0.002

0.004

0.006

0.008

0.010

db (m)

3.210-4

3.610-4

4.810-4

5.510-4

6.010-4

Ceramic membrane

Figure 1. Schematic of a bubble column with a membrane distributor.


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(a)

Grid 1: 285300 cells

(b)



250

Exp. Grid 1 Grid 2 Grid 3

200

Pressure drop (Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


150

100 50

3000 nm pore 0 2

4

6

8

10

-6

12 10

Mass flow rate (kg/s) Figure 2. (a)Computational grids and (b) Pressure drop simulated using three grids.



350 Exp. (200 nm pore) Sim. (200 nm pore) Exp. (3000 nm pore) Sim. (3000 nm pore)

300

Pressure drop (Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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250 200 150 100

k3000nm= 4.010

50

-14

m

k200nm = 1.010

-14

m

8

12 10

0 2

4

6

10

2

2

-6

Mass flow rate (kg/s) Figure 3. Pressure drop through two dry porous membranes at different mass flow rates.


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p (Pa)

3000 nm pore

200 nm pore

u(m/s)

Figure 4. Pressure and velocity distributions in the cross section of the membranes.



Ring 1 Ring 2 Ring 3 100 80 -5

mg =1.2  10 kg/s

60

Contribution (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

40 20

2 1 0 Ring3 Ring2 Ring1

Ring3 Ring2 Ring1

3000 nm pore

200 nm pore

Figure 5. Contribution of channels at different positions to the total permeation flux through the two membranes.


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Water saturation (-)

0.58

Membrane: 200 nm pore

(a)

0.57

0.56

0.55

0.54 0.40

0.42

0.44

0.46

0.48

0.50

Pressure drop (MPa)

-4

2.5x10

Gas relative permeability (-)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


k r , nw   1  S w 

(b)

12

-4

2.0x10

Membrane: 200 nm pore -4

1.5x10

-4

1.0x10

-5

5.0x10

0.0 0.50

0.52

0.54

0.56

0.58

0.60

Water saturation(-) Figure 6. (a) Experimental results of water saturation at different pressure drops; (b) The modeling results of gas relative permeability.



-6

16

Mass flow rate of gas (kg/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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10

Exp. Sim.

14 12 10

Membrane: 200 nm pore

8 6 4 2 0.40

0.42

0.44

0.46

0.48

0.50

Pressure drop (MPa) Figure 7. Predictions of the gas flow rates at different pressure drops through the membrane.

(a)

(b)

(c)

p(Pa)

Figure 8. (a) Pressure distribution; (b) Gas flow vector; (c) Experimental observation of bubbles in the membrane channels.


Page 23 of 25

g

gas

gas

liquid 2.410-6 kg/s 7.210-6 kg/s

Membrane distributor

1.210-5 kg/s

Gas mass flow rate

Figure 9. Gas-liquid flows in the single membrane channel.

0.10 0.09 0.08

Global gas holdup (-)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.07 0.06 0.05

Exp. Grid 1 Grid 2 Grid 3

0.04 0.03 0.02 0.01 0.002

0.004

0.006

0.008

0.010

Superficial gas velocity (m/s) Figure 10. Global gas holdup up at different superficial gas velocities.



100

Drag coefficient (-)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

10

1 0

10

20

0.002 m/s

Re

30

40

0.006 m/s

50

60

0.01 m/s

Gas inlet velocity Figure 11. Bubble Reynolds number and drag coefficient in the bubble column.


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CFD simulation of a novel membrane distributor of bubble columns for

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