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Dual-membrane Module and its Optimal Flow Pattern for H2/CO2 separation Bo Chen, Xuehua Ruan, Xiaobin Jiang, Wu Xiao, and Gaohong He Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b04384 • Publication Date (Web): 12 Jan 2016 Downloaded from http://pubs.acs.org on January 15, 2016

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Industrial & Engineering Chemistry Research

Dual-membrane Module and its Optimal Flow Pattern for H2/CO2 separation Bo Chena, Xuehua Ruanb, Xiaobin Jianga, Wu Xiaoa,Gaohong He*a, b State Key Laboratory of Fine Chemicals, Research and Development Center of Membrane Science and Technology, a School of Chemical Engineering, b School of Petroleum and Chemical Engineering, Dalian University of Technology, Dalian, LN 116024, China. *

Corresponding author：： Tel: +86-411-84986291; Fax: +86-411-84986291;

E-mail: [email protected] (Gaohong He) Key words: Process intensification; Dual-membrane module; Hydrogen recovery; Membrane gas separation.

Abstract: Dual-membrane module is able to provide higher separation performance for H2/CO2 gas mixture comparing to conventional single-membrane modules. In this work, the flow patterns of dual-membrane modules are studied, and the results indicate that the co(H2):counter(CO2) flow pattern is the optimal flow pattern for H2 recovery. The co(H2):counter(CO2) flow pattern employs co-current (permeate flow parallel to bulk flow) to the H2-selective membrane and counter-current (permeate flow reverse to bulk flow) to the CO2selective membrane; the flow pattern reduces the permeation flux of CO2 in the H2-selective membrane, resulting in higher H2 separation factor. The evaluations show that the H2 product purity could be raised by 35% (from 62 mol% to 84 mol%), comparing to conventional membrane modules. The results indicate that enhancing the membrane separation performance through flow pattern is a practical and effective method for process engineering.

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1. Introduction Membrane technology has been widely used in hydrogen separation process due to its high efficiency1-4. Traditional fields for membrane hydrogen separation are hydrogen recovery from ammonia purge gases (H2/N2 separation) and refinery gases (H2/hydrocarbon separation). The membrane selectivity of H2/N2 and H2/hydrocarbon could reach 100-200, which enables the membrane process to produce hydrogen with high purity. The steam methane reforming (SMR) and coal gasification processes become widely-used in petroleum industry and power plants. However, the hydrogen recovery in those processes is much difficult due to CO2 issues. The CO2 concentrations in typical SMR processes5 and integrated gasification combined cycle (IGCC) power plants6 vary from 15 mol% to 50 mol%; while the commercial membranes only possess selectivities ranging from 2-15 for H2/CO2 gas pair7-11, which still cannot meet the requirements of industrial applications. Most researches focus on improving the selectivities of membrane materials, some candidate materials for next generation membranes are able to improve the H2/CO2 selectivity significantly12-19; unfortunately, those membranes still require long-term field test on durability before commercialization20, implying that the commercial membranes are still the only choice for H2/CO2 separation. To solve the problem, it is imperative to intensify the membrane hydrogen recovery process through practical methods and current-available membranes. A practical method is to introduce an additional membrane with reversed-selectivity (CO2-selective in this case) into the module; the two kinds of membranes will share the bulk flow, while the permeate channels of them are independent. Such kind of membrane module is denoted dual-membrane module (DMM). The DMM allows bulk CO2 to be removed simultaneously as bulk H2 being recovered, which is able


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to improve the H2 separation performance, comparing to conventional single-membrane modules (SMMs).

Figure 1. Illustrations of dual-membrane modules (DMM) with different flow patterns. a: counter:counter-current; b: co:co-current; c: counter:co-current/co:counter-current. The DMM was proposed by Onho et al21, and further investigated by several resarchers22-24. The flow pattern was found to be the most distinctive and influential configuration for DMM. Industrial gas-separation membrane modules can operate in two flow patterns: counter-current and co-current; the former one was proved to be more efficient at separation than the latter22, 23. It can be easily derived that the DMM can operate in four flow patterns, which are counter:counter-current (counter-current for both membranes, as shown in Figure 1a), co:cocurrent (co-current for both membranes, as shown in Figure 1b), counter:co-current and


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co:counter-current (one membrane operates in counter-current and the other operates in cocurrent, as shown in Figure 1c). The counter:counter-current and co:co-current were analogy from SMMs; the counter:counter has been proved to be the most effective flow pattern for DMMs24, which is conformed to the analogy of SMMs. However, the counter:co-current and co:counter-current haven’t been reported or investigated yet to the best of our knowledge, and those flow patterns may reserve the potentials for further improvements. In this work, the effects of the flow patterns of DMMs are thoroughly investigated. A multicomponent mathematical model for DMMs is proposed for evaluation. The flow patterns, membrane dimensions, permeate pressures, feed compositions and membrane selectivities are investigated to optimize the separation performance of H2/CO2. 2. Modeling of dual-membrane module Several mathematic models for DMM were developed by Sengupta et al.22, 24, 25 and Perrin et al.23,

26

. Those models employed differential method to solve multi-component separation

problems, and provided contributive results and predictions for DMMs. Their works also provided guidelines for DMM modeling, and demonstrated that the mathematical model of DMMs could be derived from SMMs. Coker et al.27 proposed a numerical algorithm for SMM modeling, which treated modules as several cells linking in series. In the algorithm, each cell’s residue is fed to the next cell, and the permeate flow of the cell is a combination of local membrane permeation and the permeate flow from next/previous cell. The model has good accuracy and robustness at all range of stage cut; more importantly, it has good expansibility and can be easily established in simulation environment.


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In this paper, a numerical solution for the DMM is developed based on Coker’s method; the flow succession relationships between cells of different flow pattern DMMs are illustrated in Figures 2a-2d.

Figure 2. Flow successions of the mathematical model. a: co:co-current; b: counter:countercurrent; c: co:counter-current; d: counter:co-current. The transport equation of membrane is , , , ,

(1)

where i, is the component index; j is the cell number; k is membrane index (I or II); Q is the permeate flow rate, mol s-1; J is the membrane permeace, mol s-1 m-2 kPa-1; A is the membrane area, m2; Pf and Pp are residue and permeate pressure, kPa; x and y are the mole fractions of residue and permeate. The permeate and residue flow rates of component i in cell j are , ,

(2)


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, ,

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(3)

The permeate and residue flow rate of cell j is

,

(4)

,

(5)

where c is the component number; v and l is the flow rate of the permeate or residue, mol/s; Fp and Fr are total the flow rates of the permeate and residue, mol s-1. The membrane area ratio is the key parameter to the DMM, which is defined as

(6)

where I and II are the membrane indices. 2.1. Co:co-current and counter:counter-current The co:co-current and counter:counter-current flow patterns have been well investigated and modeled in literatures. Because the modeling and calculation procedure of the two flow patterns are practically the same to co:counter-current, the details of the modeling will be shown in Appendix. 2.2. Co:counter-current The modeling of co:counter-current configuration starts from co-current membrane (membrane index: I) , ,

,

(7)

Substitute Eq. 7 to Eq. 1 and rearrange


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,

(, + 1) ,

,

1

,

,

(8)

where , ,

,

(9)

,

(10)

The local mass balance of cell j for co:counter-current configuration module is , , + ,

, + ,"

, 0

(11)

By substituting Eq. 8, Eq. 11 can be rearranged 1

, ,$ %

& , ,

+, % +, %

, + 1 , ,

, + 1 , ,

( , + 1)(, + 1)

, ,

+

1

& ,

1

& ,

(12)

Then Eq. 11 can be transformed to a set of equations in the following form

 G1,1 H1,2   E2,1 G2,2  D3,1 E3,2  O       

H 2,3 G3,3

H 3,4

O

O

O

D j , j −2

E j , j −1

G j, j

H j , j +1

O

O

O

DN −1, N −3

O

EN −1, N −2 GN −1, N −1 DN , N −2

EN , N −1

  viI,1   Bi ,1    I      vi ,2   0    viI,3   0       ⋅ M  =  M    vI   0    i, j      M   M  H N −1, N  viI, N −1   0       GN , N   viI, N   0 

(13)

where D, E, G and H are the coefficients (the subscripts of D, E, G and H are the row and column index, and the component index “i” is omitted in Eq. 13 for simplicity), where


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', % 1 +,$ ,, -,

, + 1 ,

, + 1 ,

1

+

1

,

+1+

, + 1

, ,"

1

1

λ ,

,

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& ∗ ,*

(14)

1

, ,

(15)

1 1 , + 1 , + 1 + + + , ," , , , , ,

," + 1

," ,"

1

,"

( , + 1)(, + 1)

, ,

(16)

1

, (17)

.,"

( ," + 1)(," + 1)

," ,"

+

1

,

(18)

Notice here that Eq. 13 must be solved for all the components. By solving Eq. 13, the component flow rate profiles of co:counter-current could be calculated, then vi,jII and li,j will be calculated by Eq. 12 and Eq. 8. Through Eq. 2-5, the concentration profiles of the membrane module could be calculated. 2.3. Counter:co-current Co:counter-current and counter:co-current are essentially same to each other. The counter:cocurrent configuration can be simply solved by swapping the membrane indices (I and II) in the co:counter-current’s model, and then perform same procedures as shown in Section 2.2. 3. Model solution and validation 3.1. Model solution The solution to the proposed model requires initial values for module profiles; after the initial calculation, the pressure profiles are revolved for the next iteration until convergence. The solution used in this paper employed cross flow configuration to generate initial profiles for dualmembrane module. The cross flow mass transfer equation is


8

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0 . , , , .

(19)

where yi,jk’ is the cross flow mole fraction 0 .

.

∑ .

(20)

The local mass balance of stage j is . . . 0

(21)

The influence of total cell number (N) has been thoroughly discussed by Coker et al.27 and Thundyil et al.28, they suggested the cell number should be at least 100 for accuracy; therefore all the simulations in this study were performed under N = 100 to save computation resources. The lumen pressure build-up effect has been investigated by several researchers29-33, the lumen pressure calculating protocol of this model is similar to Coker’s method. During initial profile calculation, the lumen pressure drop is neglected; after each iteration, the pressure profile of membrane lumen is recalculated by Hagen-Poiseuille's law34 d 64/6 $ 9 d 28

Counter-current: |;* *

Co-current: |;< * (22) and then the pressure profiles will be revolved. The viscosity of gas mixture is calculated by Wiley’s method35. The convergence of the calculation is determined by Eq. 23a and 23b = =

∆ = ≤ @A6BCDE6

(23a)

= ≤ @A6BCDE6

(23b)

∆


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where △Fr and △Fpk is the flow rate difference of permeate and residue between last two iterations. After one iteration step completes, if the profile of membrane module satisfies Eq. 23a and 23b, the calculation ends; else, the previous calculated profiles are used as initials for next iteration. The tolerance of the simulation is 10-5, which is sufficient for all the cases except the calculations of model validation. 3.2. Model validation Several researchers performed lab-scale gas separation experiments for DMMs. The experimental data reported by Sengupta et al.25 is used to validate the proposed model. The comparisons between simulation results and experimental data are presented in Figures 3a-3b. In the calculations of model validations, the tolerance is changed to 10-10 to provide accurate results.

Figure 3. Comparisons of simulation results and experimental data. CA represents cellulose acetate; SR represents silicon rubber. Symbols: exp. data; lines: simulation. a: co(He):co(CO2)current flow pattern; b: counter(He):counter(CO2)-current flow pattern. The results of the proposed model show good accuracy for most range of stage cut in Figures 3a-3b, indicating that the proposed model is capable of providing reliable predictions for the separation process of DMMs. 4. Results and discussion


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4.1. Effects of flow pattern Before investigating the influences of flow patterns, it is important to review the principles for improving the hydrogen separation performance of DMMs. There are generally four ways to achieve the goal through the perspective of permeation: Method a, increase H2 permeation in H2-selective membrane; Method b, reduce CO2 permeation in H2-selective membrane; Method c, reduce H2 permeation in CO2-selective membrane; Method d, increase CO2 permeation in CO2-selective membrane. The former two are intended to increase the H2 product purity and recovery; the latter two are to reduce the H2 loss rate and CO2 interference. For certain membranes with fixed permeabilities, Method a and d cannot be directly achieved (they can only be maintained as much as possible, e.g., reducing lumen pressure build-ups to maintain driving force); while Method b and c are both achievable through optimizations of module parameters and configurations. The uninvestigated flow patterns of DMM (counter(H2):co(CO2)-current and co(H2):counter(CO2)current) provide the potentials for further improvement, and the following discussions are carried out to investigate the optimization methods. 4.1.1. Ideal condition (neglecting pressure build-up) The DMMs are first investigated under ideal condition (the permeate pressure build-up effects are neglected). Under the ideal condition, the differences between DMMs are completely caused by flow patterns, therefore the influences of can be observed explicitly and separately. PI (H2-selective) and PEO (CO2-selective) are chosen as the membranes. A DMM containing 10 m2 membrane in total (API + APEO) is employed for evaluation; in this scheme36, increase the area of one membrane species, the area of the other membrane will be reduced, enabling it to


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observe the influences of membrane area ratio at a wide range. To preserve the unity of figure appearance, Figure 4 and 7 are both plotted against PI membrane area. The syngas of water-gas-shift reaction is a typical case of H2/CO2 separation, and the gas mixture usually contains H2, CO2, CH4, CO, H2O and hydrocarbons. In the gas mixture, CH4 and CO have similar permeabilities in both membranes, and therefore the composition of CO can be combined to CH4 for simplicity. The concentration of hydrocarbons and H2O is usually less than 1 mol% in the syngas of SMR process, and thus the two components are also neglected. However, the hydrocarbons and H2O have great impacts on membrane permeability and selectivity; the effects can be treated as different-selectivity scenarios, which will be discussed in Section 4.3. Table 1. Properties of dual-membrane module Total membrane Fiber area of DMM length (m2) (m) 10

Permeancea (GPUb) Membranes H2

CO2

CH4

PI

520

195

7

PEO

195

1580

130

1.0

a

Reported by Harlacher et al.37 b 1 GPU = 10-6 cm3 s-1 cmHg-1 cm-2 The compositions of the feed gas for the simulations are set as 75 mol% H2, 15 mol% CO2 and balanced with CH4. The feed gas pressure is 2000 kPa, and the permeate pressure of both membrane is 100kPa. The properties of the module and membranes are listed in Table 1. It is obvious that the DMM must employ shell-side feed configuration according to Figure 1. The evaluations are carried out by comparing the separation indices31, 36 J

/$ / $

(24)


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where xf is mole fraction in feed, and y is the mole fraction in permeate. During the investigations, the H2 and CO2 separation indices are calculated by PI and PEO permeate compositions, respectively.

Figure 4. Influences of membrane area and feed flow rate on separation indices (ideal condition). The total membrane area of PI and PEO is 10 m2 (API + APEO = 10 m2). a: H2 separation index (ωH2I); b: CO2 separation index (ωCO2II). The comparisons of separation indices are shown in Figures 4a-4b. In Figure 4a, the H2 separation index of the co(H2):counter(CO2) DMM is greater than other flow patterns, though the advantages are little; however, the counter(H2):co(CO2) DMM, as the control module to the co(H2):counter(CO2) DMM, has much lower H2 separation index. Figure 4b compares the CO2 separation indices of different flow pattern DMMs. The counter(H2):co(CO2) DMM has similar enhancing effect on the co-current side membrane (PEO), and the CO2 separation index of the counter(H2):co(CO2) DMM becomes highest when PI membrane area is near 10 m2 (i.e., PEO membrane area is approaching zero, and R is approaching infinite). The optimizing effect of the co(H2):counter(CO2) flow pattern is validated in Figure 4a. Method b works here to reduce the CO2 permeation flux in H2-selective membrane. The co-


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current flow pattern of the H2-selective membrane relocates the highest driving force position to the residue outlet, therefore most bulk H2 will be permeated there27; as bulk CO2 being removed by the CO2-selective membrane, the bulk CO2 concentration decreases along bulk flow direction, which enables the H2 to be recovered with less CO2 interference near the residue outlet position. However, such advantages are still insufficient for industrial applications; optimizations are needed to further improve the separation performance. 4.1.2. Non-ideal condition (considering pressure build-up) In real scenarios, the membrane lumen pressure build-up effect is a major disadvantageous effect. However, in the co(H2):counter(CO2) DMM, it could be utilized to reduce CO2 impact (through Method b). The key is to manipulate the permeate pressures and take advantages of the flow pattern. An illustration is presented in Figure 5a to explain the mechanism of the optimizing method. In the co(H2):counter(CO2) DMM, if the permeate pressure at the lumen closed end position of the H2-selective membrane (feed entrance) is raised, the permeation flux at that position will be reduced. The bulk flow has highest CO2 concentration at the feed entrance postition, a reduction of permeation flux implies less CO2 will be permeated into H2 product (as the right hand side picture of Figure 5a shows); according to Method b, the H2 product purity will be increased. This effect suggests that increasing the permeate pressure gradient (higher

KLM K;

) of H2-selective

membrane could further improve the H2 separation performance. Meanwhile, the CO2 removal is the key to realize such effect, therefore Method d is also hoped to provide influences here. To manipulate the permeate pressure gradient of a membrane module, changing the membrane fiber inner diameter (ID) is the most direct method, according to Eq. 22. The effects of the membrane fiber ID (pressure gradient) are shown in Figures 5b-5c. In the figures, the H2


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recovery and membrane area ratio (R) of the modules are kept at 70 % and 3.6, respectively and constantly, and the fiber OD (outer diameter) is kept as twice of fiber ID.

Figure 5. Influences of H2-selective membrane fiber inner diameter (ID) on H2 mole fraction of PI permeate (yH2I). The membrane area ratio (R) is 3.6. Fiber OD/ID ratio is 2; H2 recovery is 70%. a: mechanism for the optimizing method; b: influences of PI fiber ID (diI); c: influences of PEO fiber ID (diII). As Figure 5b shows, when the fiber ID of the H2-selective membrane is reduced (i.e., the permeate pressure gradient is increased), the co(H2):counter(CO2) DMM shows a significant increase in product purity, which is distinct from the counter(H2):counter(CO2)

and

counter(H2):co(CO2). This effect indicates that the high permeate pressure gradient actually benefits co(H2):counter(CO2) DMM greatly by reducing the permeation flux at the lumen closed end of the H2-selective membrane (Method b).


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The co(H2):co(CO2) DMM has similar effect when diI is reduced to 100 µm; however, the H2 product purity is lower than co(H2):counter(CO2) DMM. The reason is because of Method d, since the CO2-selective membrane of the former DMM is operating in co-current, and the CO2 removal efficiency of co(H2):co(CO2) DMM is much worse than co(H2):counter(CO2). The effect indicates that the CO2-selective membrane should operate in counter-current to maximize the separation performance. Following the point of Method d, it is necessary to improve the separation performance of the CO2-selective membrane. An efficient method is to reduce the permeate pressure drops, i.e., the fiber dimensions of the CO2-selective membrane should be as great as possible. Figure 5c shows the impacts of CO2-selective membrane (PEO) ID on H2 separation performance (the data of co(H2):co(H2) and counter(H2):co (CO2) is not shown in Figure 5c for clarity). In Figure 5c, the H2 product purity of the co(H2):counter(CO2) DMM increases significantly with increasing CO2selective membrane ID (diII), and becomes much greater than the counter(H2):counter(CO2) when diII is greater than 150 µm.

Figure 6. Effects of PI permeate pressure (PpI) on H2 product purity (yH2I). The membrane area


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ratio (R) is 3.6; the permeate pressure of PEO is 100kPa. a: the fiber IDs of PI and PEO are both 400µm; b: the fiber IDs of PI and PEO are 75 and 400µm, respectively. Besides changing permeate pressure gradients, the outlet permeate pressure is also influential to the separation performance according to Eq. 22. Normally, increasing permeate outlet pressure of the H2-selective membrane (PpI) will reduce the driving force, and hence reduce the product purity when recovery rates are same. The effect is valid for counter(H2):counter(CO2) DMM as Figures 6a-6b show. In both figures, PpI has no positive influence on the separation performance of the counter(H2):counter(CO2) DMM, regardless of the fiber ID. The co(H2):counter(CO2) DMM has similar effects when PpI is low in Figure 6a; however, when PpI is raised to 800kPa, the H2 product purity starts to increase with increasing PpI. The effect becomes more significant in Figure 6b, in which the product purity of the co(H2):counter(CO2) DMM always increases with increasing PpI. When PpI reaches 1000 kPa (feed/permeate pressure ratio is reduced from 20 to 2), the H2 product purity of co(H2):counter(CO2) DMM is about 2 mol% higher than PpI = 100 kPa. From Figures 5-6, the optimal configurations for DMMs can be determined: the diI and diII are set as 75 and 400 µm, respectively (the fiber OD is twice as ID). The separation indices of the DMMs with optimized configuration are compared in Figures 7a-7b (the total membrane area of the module is 10 m2, and feed/permeate pressures are 2000 and 100 kPa, respectively). A significant increase in ωH2I can be found for co(H2):counter(CO2) DMM comparing to results shown in Figure 7a; the ωCO2II is also improved slightly. Figures 7a-7b also portray the key elements for the DMMs: rational membrane area ratio to remove bulk CO2 effectively (Method d); co(H2):counter(CO2) flow pattern along with less diI to reduce CO2 impact on H2-selective


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membrane (Method b). The two aspects together enable the co(H2):counter(CO2) DMM to achieve optimal separation performances.

Figure 7. Influences of membrane area and feed flow rate on separation indices (non-ideal condition). The total membrane area of PI and PEO is 10 m2 (API + APEO = 10 m2). The feed pressure is 2000 kPa; the permeate pressure of both membrane is 100 kPa. The membrane fiber inner diameters of PI and PEO are 75 and 400µm, respectively. a: H2 separation index (ωH2I); b: CO2 separation index (ωCO2II). However, compromises have to be made to realize the optimal separation performance. Optimizing the separation through membrane dimensions inevitably reduces the permeation flux, especially when PpI is raised (which is the reason that the feed/permeate pressures of Figure 7 are remained 2000/100 kPa); the trade-offs between product purity and membrane flux will increase the demand of membrane area. The effects of reduced membrane diameter are illustrated in Figure 8. The membrane permeation flux is reduced by 50 % approximately, comparing to the ideal condition. Although this increases the cost on membranes for process engineering, the improvement in H2 product purity is not achievable for the membranes employed in this work.


18

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The quality of hydrogen products is the most determinative aspect for hydrogen recovery process; considering the benefits in product purity, the compromise in membrane cost is sustainable.

Figure 8. Influences of membrane dimensions on permeation flux. The membrane is PI, and the membrane outer diameter is kept twice as inner diameter. 4.2. Hydrogen separation performance The hydrogen separation performance can be evaluated by plotting product purity against recovery, as shown in Figure 9a (in which “R = infinite” implies the membrane module only contains PI membrane; “R = 0” implies the membrane module only contains PEO membrane). The results of co(H2):co(CO2) DMM will not be presented for clarity, since it provides worst separation performance for almost all the cases. The CO2 concentration of PEO permeate is presented in Figure 9b to investigate the CO2 separation performance.


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Figure 9. Effects of membrane area ratio (R) on the separation performance of different flow pattern dual-membrane modules. a: H2 permeate mole fraction of PI (yH2I); b: CO2 permeate mole fraction of PEO (yCO2II) In Figure 9a, when R decreases, the co(H2):counter(CO2) DMM shows a significant increase in H2 product purity. The co(H2):counter(CO2) DMM with R = 3.0 provides 94 mol% H2 purity with 72 % recovery, which is 2 mol% and 8 mol% higher than counter (H2):counter(CO2) DMM and SMM, respectively. Figure 9b shows the CO2 mole fractions of PEO permeate versus CO2 recovery for different R. For most range of CO2 recovery, the co(H2):counter(CO2) and counter(H2):counter(CO2)

DMM

provide

higher

CO2

product

purity;

while

the

counter(H2):co(CO2) DMM always provides worst CO2 product concentration. This is because when a low selectivity membrane is implemented in DMM, the separation of both membranes will be exacerbated25. In this case, counter(H2):co(CO2) DMM is employing low selectivity membrane (PI) to enhance the separation of higher selectivity one (PEO), which eventually resulted in the worse separation performance for both membranes. 4.3. Sensitivity analysis In industrial processes, the H2/CO2 composition varies: up to 40 mol% of CO2 exists in the gas mixture (e.g., in IGCC power plants). Therefore, it is important to investigate the influences of


20

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feed gas composition. The sensitivity analysis of feed CO2 concentration is presented in Figures 10a-10b, in which the feed CO2 concentration is raised to 40mol% (the feed compositions of other components are 50 mol% H2, balanced with CH4); the operating conditions are remained as same as in Section 4.2.

Figure 10. The separation performance of different flow pattern dual-membrane modules (DMMs) at elevated feed CO2 concentration. The feed composition is 50 mol% H2, 40 mol% CO2 and balanced with CH4. a: H2 permeate mole fraction of PI (yH2I); b: CO2 permeate mole fraction of PEO (yCO2II). The co(H2):counter(CO2) still provides best separation performance among all the flow patterns in Figure 10a; while the PI SMMs (R = Infinite), counter(H2):counter(CO2) and counter(H2):co(CO2) DMM suffer from high feed CO2 concentration severely. The product purity of co(H2):counter(CO2) DMM is 84 mol%, which is 8 mol% higher than counter(H2):counter(CO2) DMM and 22 mol% higher than SMM. The increase in feed CO2 concentration also improves the separation performance of the CO2-selective membrane. In Figure 10b, the CO2 separation performance of the co(H2):counter(CO2) DMM is always better than the other flow pattern DMMs, especially at high CO2 recovery. Figures 10a-10b imply that, although the case studies employ a membrane with low H2/CO2 selectivity (αH2/CO2I = 2.67), the


21


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Page 22 of 34

separation performance of the co(H2):counter(CO2) DMM is comparable to SMMs with αH2/CO2I = 8-10 membranes. According to Method c and d, the hydrogen separation performance will be improved if αCO2/H2II is increased. Some promising membranes showed excellent separation properties on CO2/H2 separation13,

16, 38-40

; when those membrane materials realize commercialization, the

separation performance of the DMM could be further improved. The influences are shown in Figure 11, in which the permeance and selectivities of PI are remained as same as in Table 1. The CO2/H2 selectivity of the CO2-selective membrane (αCO2/H2II) is changed from 10 to 100 by increasing JCO2II (αH2/CH4II and JH2II is remained as same as PEO).

Figure 11. Influences of CO2-selective membrane selectivity (αCO2/H2II) on H2 product purity (yH2I). The membrane area ratio (R) is 3.6; feed pressure: 2000 kPa; permeate pressure of both membranes: 100 kPa. a: 75 mol% H2, 15 mol% CO2, balanced with CH4; b: 50 mol% H2, 40 mol% CO2, balanced with CH4. In Figures 11a, the co(H2):counter(CO2) DMM shows great superiority comparing to the counter(H2):counter(CO2) one. When feed CO2 concentration is 15 mol%, the product purity of


22

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the co(H2):counter(CO2) DMM increases with increasing αCO2/H2II, and reaches 99 mol% at about 70 % recovery. When the feed CO2 concentration is raised to 40 mol% (Figures 11b), the product purity and recovery of the co(H2):counter(CO2) DMM are 97 mol% and 70 %. The results imply that the co(H2):counter(CO2) DMM is able to provide great H2/CO2 separation performance even without employing high-selectivity membranes. The improvement brought by the high-performance CO2-selective membrane becomes less significant when αCO2/H2II is over 40, indicating that the optimal range of selectivities for the CO2selective membrane is about 20-40. When PI membrane is coupled with such membranes, the DMM is able to provide comparable separation performance to the high-performance H2selective membranes (αH2/CO2I ≥ 20). The effects imply that the co(H2):counter(CO2) flow pattern is a promising approach for membrane gas separation process to solve the H2/CO2 separation problem. 4. Conclusion A mathematical model for dual-membrane module (DMM) is developed to investigate the influences of flow patterns. The co(H2):counter(CO2) flow pattern is found to be the most effective one for H2 separation. Optimization is performed through manipulating membrane permeate pressures; the results indicate that when a DMM employs co(H2):counter(CO2) and high permeate pressure gradient in the H2-selective membrane, the H2 separation performance could be further improved. The separation performance analysis of a typical steam methane reforming syngas shows that the co(H2):counter(CO2) DMM is able to increase the H2 product purity by 8 mol%, comparing to conventional SMMs. When the feed CO2 concentration is raised to 40 mol%, more than 22


23


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Page 24 of 34

mol% increase in H2 product purity has been found, indicating that the improvement of the co(H2):counter(CO2) flow pattern becomes more significant. The sensitivity analysis of membrane selectivity shows that, when the co(H2):counter(CO2) DMM employs a CO2-selective membrane with 20-40 CO2/H2 selectivity, the H2 separation performance is comparable to next generation H2-selective membranes. The results indicate that enhancing membrane gas separation process through flow pattern intensified membrane module is a practical and promising method.


24

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AUTHOR INFORMATION Corresponding Author: Gaohong He Tel.: +86-411-84986291 Fax: +86-411-84986291 E-mail: [email protected] FUNDING SOURCES National Natural Science Foundation of China (21236006) National High Technology Research and Development Program of China (2012AA03A611) National Science Fund for Distinguished Young Scholars of China (21125628) ACKNOWLEDGMENT The authors acknowledged the ﬁnancial support by the National Natural Science Foundation of China (21236006), National High Technology Research and Development Program of China (2012AA03A611) and National Science Fund for Distinguished Young Scholars of China (21125628). SUPPORTING INFORMATION Driving force distribution of the co(H2):counter(CO2) dual-membrane module. Model validation and comparison. Data of residue composition. ABBREVIATIONS SMM, single-membrane module; DMM, dual-membrane module; SMR, steam methane reforming; IGCC, integrated gasification combined cycle; ID, inner diameter; OD, outer diameter.


25


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Page 26 of 34

Nomenclature A

Membrane area, m2;

c

Total component number;

F

Flow rate, mol s-1;

J

Membrane permeance, GPU (10-6 cm3 s-1 cmHg-1 cm-2);

L

Membrane fiber length, m;

l

Flow rate of component in residue side, mol s-1;

M

Equation coefficient;

P

Pressure, Pa;

Q

Permeate flow rate, mol s-1;

R

Membrane area ratio;

v

Flow rate of component in permeate side, mol s-1;

x

Mole fraction of residue;

y

Mole fraction of permeate;

α

Membrane selectivity;

λ

Coefficient;

ω

Separation factor;

φ

Component recovery;

Subscript and superscript f

--

Feed;

i

--

Component index;

j

--

Stage index;

k --

Membrane index;

p

--

Permeate side;

r

--

Residue side.


26

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Appendix The modeling of co:co-current and counter:counter-current DMM is illustrated below. Co:co-current DMM: Co:co-current is relatively simple for modeling, since the profiles of next stage can be calculated directly from previous stage. The local transport equation of membrane k is , ,

,

(A-1)

At the lumen closed end (where vi,0k is zero), i.e., feed entrance position, Eq. A-1 can be rewritten as ,

,

, + 1

, ,

(A-2)

N1

The local mass balance of stage j is , , +

,

,

(A-3)

0

We could deduce an equation for li,j by substituting Eq. A-2 to Eq. A-3 when j = 1: ,

1+

,

,

, + 1

+

, , +

1

,

N1

(A-4)

where li,0 is component feed flow rate. Similar approach could be applied for stage 2-N to get the expression for li,j:

,

, + %1

1 1 & , + (1 ) +1 , + 1 ,

,

, , 1+ + , + 1 + 1

,

,

,

+ 1

, +

, N 2~P

1 , , N 2~P +1

,

(A-5)

(A-6)


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Page 28 of 34

Through the equations, we could calculate all the flow rate profile of co:co-current DMM, and therefore all the concentration profiles can be calculated. Counter:counter-current DMM: The mass balance across the membrane is , ,

,"

(A-7)

Substitute the coefficients, and rearrange ,

(, + 1) ,

,

1

,

(A-8)

,"

The local mass balance of stage j for counter:counter-current configuration module is , , + ,"

, 0

(A-9)

Then we can derive an equation for vi,jII by substituting Eq. A-8 to Eq. A-7 ,

, + 1 , % & , , % +,

1

, ,

+

, + 1 +," ( , ,

, + 1 , + 1

, ,

1

,

+

1

& ,

)

(A-10)

Substituting Eq. A-10 to Eq. A-9  E1,1 G1,2  2 2  Di ,1 Ei ,2  O       

H1,3 Gi2,3

H i2,4

O

O

O

D j , j −1

E j, j O

G j , j +1 O

H j , j+2 O

O

DN −1, N −3

E N −1, N − 2

GN −1, N −1

DN , N − 2

EN , N −1

  viI,1   Bi ,1    I      vi ,2   0    M   M    I     ⋅  vi , j  =  0    M   M       H N −1, N  viI, N −1   0  GN , N   viI, N   0 

(A-11)


28

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where

', % 1 +, ,,

1

,

, + 1 ,

1

& λ ,

, + 1 Q,

, + 1

, ,"

+

∗ ,*

(A-12)

, + 1

Q, Q,

1

, ,

(A-13) , + 1 , + 1 , ,

1

,

1 (A-14)

-,"

1

,

+

1 1 1 ," + 1 ," + 1 , + 1 + + + + + 1 , ," ," ," ," , , ,

(A-15)

.,"$

," + 1

," ,"

1

,

(A-16)

By solving Eq. A-11, we can calculate vi,jI for every stage and every component; when vi,jII and li,j are calculated, all the concentration and flow rate profiles of the module could be derived.


29


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Page 30 of 34

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