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A numerical investigation on H2 separation by a conical palladium membrane
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A numerical investigation on H2 separation by a conical palladium membrane Farangis Mahdizadeh Ghohe, Faramarz Hormozi* Department of Chemical, Petroleum, and Gas Engineering, Semnan University, Semnan, Iran
article info
abstract
Article history:
Separation of hydrogen gas from the outlet of water-gas shift reactor via palladium
Received 16 October 2018
membrane was simulated with a two-dimensional computational fluid dynamic model. To
Received in revised form
study the influence of the geometry of membrane on the separation of hydrogen, four
18 February 2019
various membrane modules with cylindrical shells and cone tubes were considered. The
Accepted 21 February 2019
results showed that the conical membrane module with upper and bottom diameters of
Available online 21 March 2019
2 mm and 16 mm can potentially have the highest average flux across the other studied cases. To investigate the effect of flow pattern, four various flow patterns were applied to
Keywords:
the model and it was found that the counter-current flow pattern has the highest flux
Hydrogen
across the membrane for the case in which the cross section is reduced along with the
Membrane processes
length of the membrane. The results also indicated that the change in the cross section of
Computational fluid dynamics
the membrane module can prevent the intensification of the concentration polarization
Counter-current flow pattern
index within the membrane.
Cone tube
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction The production of hydrogen as an energy source has received particular attention since hydrogen is a clean fuel with lower heating value of 120 MJ/kg. Pure hydrogen is considered to be a future energy carrier [1]. It is also employed in fuel cells which enlists hydrogen amongst the plausible candidates for the future fuel. With the advancement in thermal and process heat, the release of greenhouse gases such as carbon dioxide has led to a new challenge referred to as “global warming” [2]. Therefore, clean fuels such as hydrogen can play a key role in reducing the emission of greenhouse gases. Hence, the production and separation of hydrogen from gaseous mixtures is one of the important research topics [3,4]. Hydrogen gas can be separated from other components of a gas mixture by three main routes including pressure swing
adsorption, cryogenic distillation and membrane separation [5,6]. Membrane technology requires the lowest amount of energy in comparison with other pathways. Membrane processes offer great advantages such as low energy consumption due to lack of phase shift, low space requirement, low pressure drop and high rate of mass transfer [7]. However, this technology has some drawbacks including (but not limited to) concentration polarization, low membrane flow rate and high cost of construction [8]. Notably, the membrane technology is an environmentally friendly technology, which does not produce any greenhouse gases and the separation is also based on the velocity difference of the mixed feed passing through a permeable membrane. Separation factor in membrane technology is the difference in the transmission velocity of different components of a gas mixture from the membrane [9]. Several membranes are suitable for the separation of hydrogen in the industry such as metal, polymer, and ceramic
* Corresponding author. E-mail address: [email protected] (F. Hormozi). https://doi.org/10.1016/j.ijhydene.2019.02.149 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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and zeolite membranes and these membranes can be dense, porous. The ceramic and the dense membranes represent high hydrogen separation as the selectivity of H2 for these membranes is > 1000:1 [10]. Likewise, palladium membranes have the highest hydrogen selectivity value and the largest permeability in the metal membranes [11]. For palladiumbased membrane, the mechanism of hydrogen separation includes the following steps: 1) Molecular adsorption of hydrogen on a membrane surface; 2) Dissociation of atomic hydrogen on a metallic membrane surface; 3) Diffusion of hydrogen atoms into the bulk of the membrane; 4) The penetration of hydrogen atoms from membrane bulk to the other side of surface and the formation of hydrogen molecules; 5) Hydrogen desorption from the membrane surface. Palladium membrane is a dense medium, so the mechanism of hydrogen separation from this membrane is solutiondiffusion. Hydrogen flux across the palladium membranes is obtained with the partial pressure of both side of the membrane. J H2 ¼
k n pr;H2 pnp;H2 l
study on the effect of the membrane thickness and pressure on the amount of hydrogen permeation. In a similar study conducted by Castillo et al. [31], the amount of hydrogen separation from a biogas with a palladium-silver alloy membrane was assessed. Chen et al. [32] examined the effects of parameters such as Reynolds number on the membrane side, feed temperature and the inlet hydrogen concentration on the recovery and the quantity of the hydrogen permeation. Guo et al. [33]offered a method for porous alumina supports with polyvinyl alcohol middle layer and the subsequent deposition of a palladium membrane by electro less plating. In addition, the hydrogen permeation performance and membrane stableness were investigated. In a similar study, Basile et al. [34] were studied the Pd-based membranes on a porous support using the nanozeolites as a middle layer. The efficiency of membranes was investigated in the mixture of hydrogen and nitrogen gases for hydrogen purification. Chen et al. [35] were studied detail of water gas shift reaction in a Pd-based membrane reactor at high-temperatures. Their results reveal when membrane is in the reactor CO conversion can be improved up
(1)
here, k, l, n, pr;H2 and pp;H2 are permeability, membrane thickness, pressure exponent and the hydrogen partial pressure at the retentate and permeate sides of a membrane, respectively [5]. Experimental values of n have been determined in the range 0.5e1. When n ¼ 0.5, the hydrogen flux follows the so-called Sieverts' law which applies only where the hydrogen to metal atomic ratio is quite small (H/Pd ≪ 1) [12e21]. The value of n can be between 0.5 and 1 according to the stage in the separation [22]. This stage shows the competition between the phenomena of transmission [23]. If the adsorption step is rate-limiting, n ¼ 1 in Equation (1), n ¼ 0.5 if the diffusion in the membrane bulk is rate-limiting and n ¼ 1 for the case in which the desorption hydrogen gas molecules from the surface of the membrane is rate limiting [24]. Coroneo et al. [25] simulated the pressure and velocity distribution of the gas mixture containing hydrogen in a membrane using a three-dimensional computational fluid dynamics (3D CFD1) model. They conducted a sensitivity analysis by changing the operating parameters such as pressure, flow rate of feed and temperature of gas mixture were investigated. In another study, Coroneo et al. [26] studied the effect of non-ideal fluid on the hydrogen gas purification. Chen et al. [27] studied the effect of four major factors such as pressure difference, the mole fraction of hydrogen at the inlet stream, Reynolds number and the membrane permeability on the concentration polarization with a two-dimensional model. They investigated the effects of the feed and sweep gas flow pattern on the hydrogen permeation [28]. Ji et al. [29] numerically investigated the separation of hydrogen using high-temperature gas feed. Santucci et al. [30] conducted a 1
Computational fluid dynamics.
Fig. 1 e Schematic representation of experimental test rig used in the present work to validate the model.
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to 83% and the CO conversion increased by palladium membrane higher than thermodynamic equilibrium. This model is surveyed by computational fluid dynamics in 400e700 C to simulate the chemical reaction in a Pd-based membrane reactor. Ma et al. [36] investigated Ethanol steam reforming in a catalytic membrane reactor by computational fluid dynamics. They used nickel-based catalyst and Pd/Au as a membrane in the reactor. They concluded that the Hydrogen was produced in catalytic membrane reactor 122% over fixed bed. Sumrunronnasak et al. [37] examined hydrogen production from the dry reforming reaction of methane and carbon dioxide in palladium-based membrane reactors. They compared the results with a non-membrane reactor. According to their studies, hydrogen selectivity and hydrogen separation efficiency increased. Conical micro reactor for
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hydrogen production has been investigated by one of the author of this paper [38,39]. In this work, separation of hydrogen from the outlet of water-gas shift reaction via palladium membrane is simulated with a 2D computational fluid dynamic. To study the influence of geometrical properties on separation of hydrogen, four various membrane modules with cylindrical shells and cone tubes were considered and a rough comparison was made between the outcomes of the simulations with those of obtained for cylindrical membrane. To investigate the effect of flow pattern, four various flow patterns were applied to the model. In the present work, an effort has been made to improve their model significantly. Also, the detailed assessment of the geometrical properties of the membrane on hydrogen separation is conducted, which further develops a
Fig. 2 e (a)schematic of cylindrical membrane module with cone tube (b) A schematic representation of four various geometries used for the numerical investigation of H2 purification in a conical pd membrane.
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new insight on the separation of hydrogen with conical membranes.
Mathematical formulation In this section, the mass and momentum equations involved in the modelling are presented. The experimental results of Chen et al. [40] were utilized to validate the obtained model. A schematic representation of the model introduced by Chen et al. [40] is shown in Fig. 1. A gaseous feed enters the shell side, while sweep gas enters the tube. Notably, the palladium membrane selectivity is anomalously high against hydrogen. After passing the hydrogen from the membrane in the gas mixture, the rest of the mixture is removed from the retentate outlet. Steam (as a sweeping gas) drives the hydrogen to the outside (permeate side). The membrane module consists of a cylindrical shell and a co-axial cone frustum tube. The schematic representation of the module is shown in Fig. 2a. The thickness of the palladium membrane is 20 mm and its length is 150 mm. A twodimensional model is developed since the geometry is axially symmetric. The length of the membrane module is 200 mm and its width is 18 mm. Hereafter, the domain of gas feed is referred to as the retentate side and the domain that hydrogen is referred to as the permeate side. To investigate the effect of geometry on the hydrogen separation, the four modules with different dimensions were considered and represented in Fig. 2b. In each of them, the diameter of tube varies, while the length of the modules is constant. The hydrogen permeation is an isothermal and steadystate process in which the temperature of the process is 623 K. The experimental results presented by Chen et al. Therefore, the temperature has been selected according to Chen's study, in order to validate and compare numerical results by experimental results [31]. Other assumptions for the modelling include: The flow field in the membrane module is laminar, incompressible and symmetrically axial. The density of the membrane is constant. An ideal gas law is applied into the process because the mixture represents the ideal gas reasonably. There is no chemical reaction during the separation of hydrogen. The membrane selectivity is considered to be infinite to hydrogen and zero to other gas mixture components [41]. Steam is a sweep gas for sweeping hydrogen in the permeate side. For an incompressible fluid and a steadystate flow, the governing transport phenomena equations are as follows [42e44]:
Table 1 e The operating condition used for the modelling [28,40]. Feed gas Feed gas viscosity [pa.s] Feed gas density [kg/m3] Module temperature [ C] Pressure of retentate side [bar] Molar fraction in feed gas Hydrogen gas Carbon dioxide gas Carbon monoxide Membrane properties Membrane Palladium permeance [mol/(m2.S.Pa0.5)] Membrane length [mm] Membrane thickness [mm] Sweep gas properties Sweep gas Sweep gas viscosity [pa.s] Sweep gas density [kg/m3] Pressure of permeate side [bar]
2.628 105 3.2432 350 9 0.6520 0.3460 0.0018 Palladium 3 104 200 20 Water steam 2.2371 105 0.3483 1
Continuity conservation equation . V$ V ¼ 0
(2)
here, V is velocity (m.s1). Given the cross-sectional flow in this model the coordinates of the equations are cylindrical and with this in mind, the equations are expressed as follows. 1 v vV v vV r þ ¼0 r vr vr vz vz Momentum conservation equation
(3)
Fig. 3 e (a) A schematic representation of the model (cylindrical). (b) A comparison between the experimental data and the outcome of the model, %H2 recovery and %H2 concentration at the outlet of the retentate side in three different flow rates in cylindrical module.
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Fig. 4 e Hydrogen concentration contour in the conical membrane for the fourth model.
T . . . . rV: VV ¼ Vp þ V$ mðVV þ VV
Terms of V:
j
(4)
Here, r is the density (kg.m3), p is pressure (Pa) and m is viscosity (Pa.s). . 1 v vui v vvi 1 v vui r r þ ¼ Vp þ V$ m rV r vr vz vz r vr vr vr vuj v vvi 1 v r þ þ vz vz r vr vr v vvj þ vz vz
(5)
0
(6)
0
X 1 v vxj v vxj r þ Dij r vr vz vz vr j 1 . xj wj 1 v xj wj v vp vp r þ þ rwi V A þ r vr vr vz vz p p
.
rV$ V :wi
¼ Si
Si represent the transition of the components in a gas mixture, diffusion of gas components at retentate and permeate side and source term, respectively [43,44]. The mass transfer across the membrane cannot be expressed by Navier-Stoke equations because the membrane indicates discontinuity in the gas flow. This problem is always solved by means of adding a source term [25,45].
Boundary conditions
Species equations 1 X Vp . þ rwi VA ¼ Si V$@ rwi Dij Vxj þ xj wj p j
! . P Vp rwi Dij Vxj þ ðxj wj Þ p , V:ðrwi V Þ and
þ V$@ rwi
The membrane system consists of two different inflows, two downstream outflows, tube centerline and wall. Three solution domains of retentate, membrane and permeate side are considered. The applicable boundary conditions were employed for each region. The difference of flow velocity on the wall and membrane is zero and no-slip velocity condition on the wall and membrane is applied. No hydrogen separation occurs on walls. Hence, following equations are applied: ! V ¼ Vwi ¼ 0
(8)
Inflow: (7)
here, wi is the mass fraction of species i, xj is the mole fraction of species j, Dij is diffusion coefficient (m.2s1) and S is the source term (kg.m3.s1).
! V ¼ Vin ! n and wi ¼ wi;in
(9)
Sievert law is also employed as the boundary condition at both surfaces of membrane. The amount of hydrogen passing
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across the membrane is obtained with the following equation introduced by Sievert: i k h 0:5 pH2;Shell p0:5 H2;mem d
J¼
(10)
Outflow .
vV ¼ Vwi ¼ 0 and P ¼ Ptotal vz
(11)
Physical properties of the gas mixture The physical properties of the gas mixture are obtained with the equations reported. Viscosity of the gas mixture is calculated with Wilke semi-empirical correlation. Thermal conductivity of the gas mixture is also obtained with the correlation developed by Wilke. The binding factor is also used for calculating the viscosity and thermal conductivity in the mixture. The Chapman-Enskog equation is also used for estimating of mixture diffusivity in binary mixture. m¼
N X i¼1
xi m Pn i j¼1 xj Fij
(12)
2 0:5 1 Mi 41 þ Fij ¼ pffiffiffi 1 þ Mj 2 2
k¼
N X i¼1
mi mj
!0:5 32 Mj 0:25 5 Mi
xi ki Pn j¼1 xj Fij
3
Dij ¼ 1:881 10
(13)
The method of solving the governing equations is finite element. Geometry is discretized by orthogonal grid system. The growth rate of the cell size from the membrane to wall equals to 1.1. Transformation equations are solved by SPOOLES solver (stationary linear system solver using Newton's method For symmetric system) as represented the variations of hydrogen flux relative to the mesh number and it was calculated at feed flow rate of 1.0852 103 [mol. s1] and at 350 C. With an increase in the number of elements from about 680442 to 100008, the change in the flux remained unchanged, thereby indicating the independence of the calculation of the number of elements. To validate the model, results were compared with the experimental results reported by Chen et al. [40]. For the validation, the diameter of shell and tube were 18 mm and 9.8 mm respectively. The membrane thickness was 0.02 mm and the rest of the operating conditions are as per Table 1. The mixture is fed from the top of the shell (Fig. 3a). Steam as a sweep gas enters the bottom of the tube and removes hydrogen from the top side. Fig. 3b represents the result of the comparison between the outcome of the model and the experimental data. As can be seen, the simulated data are in a good agreement with the experimental ones [40]. Notably, to calculate the relative error, following equations were used:
(14)
T1:5
1 Mi
þ M1j
ps2ij Ud
0:5 (15)
Please note that the pressure differences is the mass transfer driving force. Also, in a gaseous thermodynamic system, the pressure difference causes a partial concentration difference, which results in the mass transfer in the membrane domain.
Numerical method A laboratory study on hydrogen production and separation is time-consuming and expensive. Hence, a detailed numerical study was conducted to better understand the process and to develop an insight on hydrogen separation using conical membrane. To achieve this, a suitable solution domain for the system was selected and divided into a large number of computational elements. The grid system were regular or irregular according to the type of geometry. The physical and chemical properties of the fluid were determined and analyzed for solving the equations of the model. A numerical solution involving the formulation of algebraic equations was defined with the discretization of the model equations on a grid system and solved for the convergence of the equations. Finally, the results of the modelling were post-processed and analyzed. It was found that the accuracy of the model is highly dependent on the number of elements in the system. The smaller the cells, the more accurate the solution. However, it adds to the time and difficulty of the solution.
Fig. 5 e Average H2 flux in different molar flow rates of (a) sweep gas (b) feed gas.
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Fig. 6 e Hydrogen concentration contours in the conical membrane module at various values of sweeping gas.
Error ¼
X abs Fh2;Numerical Fh2;Exprimental Fh2;Exprimental
100
(16)
F is the quantity used to calculate the error. If F is the H2 recovery, the error value is 8%, and if F is the H2 concentration, the error will be 11%. As can be seen, the H2 recovery obtained from the simulation represents only 8% error against the experimental data. Also, ~11% error for H2 mole fraction was obtained showing that the model is accurate and results for the conical membrane are reliable.2
Results and discussion Hydrogen permeation Fig. 4 presents a schematic diagram of the direction of the hydrogen permeation. As can be seen, the feed enters the shell from the upper side and the red color in this area reflects the high concentration of hydrogen since feed is enriched with hydrogen. While, at the bottom region, the hydrogen concentration is almost zero since it is occupied with steam showing with the blue color. The average hydrogen flux passing through the membrane was 0.247 [mol.m2. s1] which occurred at the fourth model. As can be seen in Fig. 5a, the average value for the hydrogen flux is almost identical amongst all the models. However, the flow velocity increases by a decrease in the cross-section of the membrane. Thus, the fourth and third 2
HTSR(High-temperature temperature shift reaction).
shift
reaction).
LTSR(Low-
models have the highest average of hydrogen flux as represented in Fig. 5a. Fig. 5b shows the variations of the average hydrogen flux with feed flow rate. As can be seen, the amount of hydrogen in the feed increases with an increase in the feed mass flow rate, resulting in the increase in the average hydrogen flux across the membrane. The change in the average hydrogen flux in the second model is similar to the cylindrical membrane module. The hydrogen flux in the first membrane model does not change with the feed flow rate. Also, the fourth membrane module has the highest hydrogen passing through the membrane. This is because this model has the largest change in the cross section area, hence the flow velocity increases along with the membrane. This phenomenon decreases the potential for the accumulation of the mixture in the path of hydrogen passage. Likewise, with an increase in the feed flow rate, the concentration of other components in the gaseous feed increases throughout the membrane. Thus, this phenomenon prevents further hydrogen to enter the membrane. Notably, the decrease in the cross-section in the fourth and third modules is larger than the other modules. Hence, they have the highest increase in velocity along with the membrane (Fig. 5b). The hydrogen concentration contour is also plotted in Fig. 6 at various flow rates of the sweeping gas. The flow pattern is counter-current. The feed enters from the top of the shell into the module and the sweeping gas comes from the bottom of the tube. When the hydrogen passes across the membrane into the tube (in the low flow rate) of the sweeping gas, the partial pressure of hydrogen increases in the permeate side (tube) so the required driving force to transport hydrogen from the membrane decreases. Thus, it can be concluded that all the hydrogen in the feed is not
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Fig. 7 e % H2 recovery for various molar flow rates of (a) feed gas, (b) sweep gas.
separated completely and some of it is removed from the bottom of the shell. Notably, for higher flow rates of the sweeping gas, hydrogen can rapidly be removed from the top of the tube, decreasing the hydrogen partial pressure in this area. Hence, the required driving force to separate hydrogen is met and hydrogen concentration in the retentate side (shell) decreases, (Fig. 6, the domain with blue color). Fig. 7 shows the results of the simulations for the hydrogen recovery and for various molar flow rate of the gaseous feed. As can be seen, the fourth model has the highest hydrogen recovery. The amount of hydrogen permeated from the membrane increases with an increase in the molar flow rate of the inlet feed. In fact, the hydrogen recovery initially increases with an increase in the molar flow rate of the feed mixture, then it reaches a flat region for other flow rates. For a high molar flow rate of the inlet feed, the separated hydrogen reaches the highest quantity, so the hydrogen recovery is maximized. The variation of hydrogen recovery with the flow rate of the sweeping gas has been shown in Fig. 7b, the hydrogen recovery increases with an increase in the sweeping gas flow rate. Here, the fourth model has the highest hydrogen recovery, followed by the third model with the recovery rate over 80%. It can be concluded that the decrease in the cross section leads the velocity to increase along with the membrane, which causes a significant improvement in the mass transfer and the separation process of hydrogen. Thus, the fourth and third models have the highest percentage of hydrogen recovery in the membrane modules. Notably, the first geometry and cylindrical module had a nearly equal recovery rate. As can be seen in Fig. 8, the concentration of hydrogen increases with an increase in the feed flow rate. The sweeping gas enters the tube under a constant flow rate of 0.5 [ml.min1]. Similar to the previous section, the hydrogen transfer increases with an increase in the feed flow rate.
Fig. 8 e Hydrogen concentration contours for the four conical modules and for various feed gas flow rates (m0 ¼ 1.0852 £ 10¡3 [mol.s¡1]).
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Fig. 9 e The studied flow patterns on the fourth model, a) counter-current, b) co-current.
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The effect of flow pattern on mass transfer In this section, the results of modelling for the fourth membrane module are discussed under the counter-current and co-current flow patterns. The effect of the flow pattern on the quantity of hydrogen separation is also investigated. The studied flow patterns for the fourth model have been represented in Fig. 9. For each of the studied patterns, the diameter of the top side of the conical tube is 2 mm and the diameter at the bottom region is 16 mm. The shell diameter is 18 mm and its length is 200 mm. Feed mixture enters to the shell under a constant molar flow rate of 1.0852 103 [mol.s1]. As can be seen in Fig. 10a, the dependence of hydrogen flux on the molar flow rate of feed is not linear. For the first mode, the inlet feed and the sweeping gas flows are counter-current and the cross-section area is reduced in retentate and permeate sides, therefore it is expected that the velocity along with the membrane increases for a constant feed and sweeping gas flow rates. Thus, the accumulation reduces throughout the membrane domain. The partial pressure of hydrogen in the permeate side is reduced and the necessary driving force is provided for the hydrogen separation by the membrane. Hydrogen flows to the permeate side to compensation for the lack of partial pressure in the retentate side. As shown in Fig. 10a, the first flow pattern has the highest mean hydrogen flux passing through the membrane (Fig. 10a).
Fig. 10 e Dependence of average H2 flux on molar flow rates of feed gas for four flow patterns shown in Fig. 9.
In the second mode, the inlet feed and sweeping gas are in a counter-current regimen and the cross-sectional flow increases in the direction of flow in retentate and permeate sides. Thus, the quantity of hydrogen flux passing across the membrane is potentially less than the first mode. Accordingly, under a counter-current flow, the driving force behind the hydrogen separation is higher than the co-current flow. The inlet feed and the sweeping gas in the third and fourth modes are co-current. As the flow rate of the feed increases in the third flow pattern and the cross-sectional area in the downstream decreases in the direction of the feed flow, the feed velocity increases in the direction of the flow and the concentration accumulation is eliminated. In the fourth mode, the cross-sectional flow feed increases in the flow direction, however, the flow rate of the cross-sectional sweeping gas in the permeate zone is reduced. Therefore, the flow rate of the feed decreases along with the length of the membrane and the velocity of the sweeping gas is also increased in the fourth mode. The average hydrogen flux in this flow pattern is less than other modes. This shows that with increasing the molar flow rate of the inlet feed, the average hydrogen flux from membrane changes and the effect of this change on the crosssectional area of the tube and also on the velocity of sweeping gas is low (see Fig. 10b).
Fig. 11 e Dependence of a) average H2 flux b) % H2 recovery on the molar flow rate of sweeping gas.
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Fig. 11 shows the variation of the average hydrogen flux with the flow rate of the sweeping gas. The first countercurrent mode has the highest hydrogen flux. As already discussed, for such a flow pattern, the feed and gas flow velocity increases with a decrease in cross-sectional flow. In the first and fourth flow patterns (cases 1 and 4), the average hydrogen flux increases with an increase in the sweeping gas flow rate. However, it is constant in second and third flow patterns (cases 2 and 3). The sweeping gas velocity is also reduced with an increase in the cross section of the tube. As a result, the case 1 has the highest average hydrogen flux because in the first flow pattern, the sweeping gas and the feed velocity both increased with a decrease in cross-sectional module (see Fig. 11a). Fig. 11b shows the hydrogen recovery for various sweeping gas flow rates. There is a pressure difference (referred to as a driving force of the separation) to the end of the membrane at counter-current flow. Thus, the first and the second flow patterns have the highest hydrogen separation in comparison with the third and the fourth ones. Therefore, these two flow patterns have the highest percentage of hydrogen recovery. Also, the sweeping gas velocity along with the length of the membrane increases with a decrease in the cross-sectional flow for the first and the fourth modes. Hence, hydrogen recovery increases in these two flow patterns. The first flow patterns have the highest recovery rate. The counter-current flow patterns have the highest hydrogen flux from palladium membrane which can be attributed to the residence time of the feed. (See Fig. 11b). In membrane separation processes, the penetrating agent is permeated from the membrane on the other side. The feed components penetrate the membranes at various velocities. In the retentate side, the impervious or low-passive components accumulate near the membrane. Hence, a concentration layer of impurities can be created near the surface of the membrane and the resistance to mass transfer becomes considerable. The quantity of the permeation from the membrane decreases with the creation of concentration polarization on the membrane [46]. In some cases, the hydrogen concentration layer has been developed along with the membrane surface. In such cases, the hydrogen partial pressure is lower in retentate side than the permeate side. Therefore, the flow path is changed and consequently, the hydrogen purification is reduced. This phenomenon can be prevented by optimizing the geometrical properties of the membrane together with the installation of the baffle in retentate side and the use of sweeping gas [24,47,48]. Notably, the concentration polarization is the appearance of the concentration gradients on a membrane interface, which is due to the selective transfer of some species under the effect of the transmembrane driving forces through the membrane [49]. For better understanding, the concentration polarization index (CPI3) is defined to determine the polarization extent as the following [50]: CPI ¼
3
CPIr þ CPIp 2
concentration polarization index.
CPIr ¼ 1
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xH2;m xH2;in
CPIp ¼ xH2;m
(18)
(19)
here, the subscripts r and p show the retentate and permeate sides, respectively. The subscript m denotes the membrane inlet. Fig. 12 shows the dependence of CPI on the length of the membrane for various modes studied in the present work. As can be seen, the Fig. has been plotted for the inlet feed flow rate of 1.0852 103 [mol. s1] and the sweeping gas flow rate of 0.5 [ml.min1]. As can be seen, the third model has the highest polarization density. For all the modules, the accumulation of other components increased by decreasing the amount of hydrogen in the feed, which in turn, leads to the concentration polarization. Therefore, the concentration polarization index reaches a constant value due to the decrease in the cross-sectional flow and the increase in the velocity in the steady flow of the inlet feed and the sweeping gas. The progression of the concentration polarization phenomenon in the cylindrical module initially decreases and then increases along with the length of the membrane. This is due to the fact that the thickness of the concentration boundary layer of
(17) Fig. 12 e The dependence of CPI on length of the membrane for a) four membrane module, b) four flow pattern.
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other components including CO and CO2 increases within the retentate side (shell). Therefore, the intensification of the polarization phenomenon is observed for the cylindrical membrane module in the membrane's length. Also, with the separation of hydrogen, its quantity in the gaseous feed decreases and the flow rate decreases as well. Hence, the concentration polarization index is relatively high. For the second counter-current mode, the highest polarization was obtained, which is due to the increase in the cross sectional area of the sweeping gas in the direction of the flow and also the reduction of both flow rates. (Fig. 12b).
Conclusions The process of hydrogen separation from a synthetic gas with a palladium membrane was modeled to understand the effect of geometry on the degree of the purification for hydrogen. Initially, four membrane modules were simulated with a cylindrical shell and a conical tube with different dimensions. Then numerical results were compared to the cylindrical module. The mechanism of the mass transfer in the palladium membrane was solution-diffusion. To investigate the effect of the flow pattern on hydrogen separation, four different flow patterns have been considered. The velocity of feed and sweeping gas flow increased with a decrease in the cross section of the shell and tube. This also increased the separated hydrogen flux. Changing the cross section of the membrane module prevented the intensification of the concentration polarization index (CPI). It was also identified that the membrane module with a conical tube (fourth geometry) had the highest recovery of 96% with the hydrogen flux of 0.247 [mol.m2. s1]. The counter-current flow pattern had the highest hydrogen flux passing through the palladium membrane with a decreasing the cross-section along with the flow direction.
Acknowledgments The authors of this work gratefully acknowledge the financial supports by Semnan University's Research Councils of for partial financial support.
Nomenclature Cp V C wi Di xi Do z DH
Gas mixture specific heat, [J/kg. K] Velocity [m.s1] Volumetric molar concentration, [mol/m3] Mass fraction of species i Inner diameter, [m] Mole fraction of species i Outer diameter, [m] Axial coordinate Hydraulic diameter, [m]
Subscript Diffusion coefficient [cm.2s1] Dij Hydrogen H2 Activation energy, [J.mol1] Ea
i Species i J Flux, [mol.m2. S1] in Inlet K Permeance, [mol.m1.s1.Pan ] m Membrane Pre-exponential term, [mol.m1.s1.Pan] K◦ P Permeate side Ma Mach number[e] r Retentate side Mixture molecular weight [kg.mol1] Mni s Site Pressure[atm] p R (¼8.314) universal gas constant [m.3 Pa.K1. Mol1] S Source[kg. m3.s1] T Temperature[K]
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A numerical investigation on H2 separation by a conical palladium membrane Farangis Mahdizadeh Ghohe, Faramarz Hormozi* Department of Chemical, Petroleum, and Gas Engineering, Semnan University, Semnan, Iran
article info
abstract
Article history:
Separation of hydrogen gas from the outlet of water-gas shift reactor via palladium
Received 16 October 2018
membrane was simulated with a two-dimensional computational fluid dynamic model. To
Received in revised form
study the influence of the geometry of membrane on the separation of hydrogen, four
18 February 2019
various membrane modules with cylindrical shells and cone tubes were considered. The
Accepted 21 February 2019
results showed that the conical membrane module with upper and bottom diameters of
Available online 21 March 2019
2 mm and 16 mm can potentially have the highest average flux across the other studied cases. To investigate the effect of flow pattern, four various flow patterns were applied to
Keywords:
the model and it was found that the counter-current flow pattern has the highest flux
Hydrogen
across the membrane for the case in which the cross section is reduced along with the
Membrane processes
length of the membrane. The results also indicated that the change in the cross section of
Computational fluid dynamics
the membrane module can prevent the intensification of the concentration polarization
Counter-current flow pattern
index within the membrane.
Cone tube
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction The production of hydrogen as an energy source has received particular attention since hydrogen is a clean fuel with lower heating value of 120 MJ/kg. Pure hydrogen is considered to be a future energy carrier [1]. It is also employed in fuel cells which enlists hydrogen amongst the plausible candidates for the future fuel. With the advancement in thermal and process heat, the release of greenhouse gases such as carbon dioxide has led to a new challenge referred to as “global warming” [2]. Therefore, clean fuels such as hydrogen can play a key role in reducing the emission of greenhouse gases. Hence, the production and separation of hydrogen from gaseous mixtures is one of the important research topics [3,4]. Hydrogen gas can be separated from other components of a gas mixture by three main routes including pressure swing
adsorption, cryogenic distillation and membrane separation [5,6]. Membrane technology requires the lowest amount of energy in comparison with other pathways. Membrane processes offer great advantages such as low energy consumption due to lack of phase shift, low space requirement, low pressure drop and high rate of mass transfer [7]. However, this technology has some drawbacks including (but not limited to) concentration polarization, low membrane flow rate and high cost of construction [8]. Notably, the membrane technology is an environmentally friendly technology, which does not produce any greenhouse gases and the separation is also based on the velocity difference of the mixed feed passing through a permeable membrane. Separation factor in membrane technology is the difference in the transmission velocity of different components of a gas mixture from the membrane [9]. Several membranes are suitable for the separation of hydrogen in the industry such as metal, polymer, and ceramic
* Corresponding author. E-mail address: [email protected] (F. Hormozi). https://doi.org/10.1016/j.ijhydene.2019.02.149 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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and zeolite membranes and these membranes can be dense, porous. The ceramic and the dense membranes represent high hydrogen separation as the selectivity of H2 for these membranes is > 1000:1 [10]. Likewise, palladium membranes have the highest hydrogen selectivity value and the largest permeability in the metal membranes [11]. For palladiumbased membrane, the mechanism of hydrogen separation includes the following steps: 1) Molecular adsorption of hydrogen on a membrane surface; 2) Dissociation of atomic hydrogen on a metallic membrane surface; 3) Diffusion of hydrogen atoms into the bulk of the membrane; 4) The penetration of hydrogen atoms from membrane bulk to the other side of surface and the formation of hydrogen molecules; 5) Hydrogen desorption from the membrane surface. Palladium membrane is a dense medium, so the mechanism of hydrogen separation from this membrane is solutiondiffusion. Hydrogen flux across the palladium membranes is obtained with the partial pressure of both side of the membrane. J H2 ¼
k n pr;H2 pnp;H2 l
study on the effect of the membrane thickness and pressure on the amount of hydrogen permeation. In a similar study conducted by Castillo et al. [31], the amount of hydrogen separation from a biogas with a palladium-silver alloy membrane was assessed. Chen et al. [32] examined the effects of parameters such as Reynolds number on the membrane side, feed temperature and the inlet hydrogen concentration on the recovery and the quantity of the hydrogen permeation. Guo et al. [33]offered a method for porous alumina supports with polyvinyl alcohol middle layer and the subsequent deposition of a palladium membrane by electro less plating. In addition, the hydrogen permeation performance and membrane stableness were investigated. In a similar study, Basile et al. [34] were studied the Pd-based membranes on a porous support using the nanozeolites as a middle layer. The efficiency of membranes was investigated in the mixture of hydrogen and nitrogen gases for hydrogen purification. Chen et al. [35] were studied detail of water gas shift reaction in a Pd-based membrane reactor at high-temperatures. Their results reveal when membrane is in the reactor CO conversion can be improved up
(1)
here, k, l, n, pr;H2 and pp;H2 are permeability, membrane thickness, pressure exponent and the hydrogen partial pressure at the retentate and permeate sides of a membrane, respectively [5]. Experimental values of n have been determined in the range 0.5e1. When n ¼ 0.5, the hydrogen flux follows the so-called Sieverts' law which applies only where the hydrogen to metal atomic ratio is quite small (H/Pd ≪ 1) [12e21]. The value of n can be between 0.5 and 1 according to the stage in the separation [22]. This stage shows the competition between the phenomena of transmission [23]. If the adsorption step is rate-limiting, n ¼ 1 in Equation (1), n ¼ 0.5 if the diffusion in the membrane bulk is rate-limiting and n ¼ 1 for the case in which the desorption hydrogen gas molecules from the surface of the membrane is rate limiting [24]. Coroneo et al. [25] simulated the pressure and velocity distribution of the gas mixture containing hydrogen in a membrane using a three-dimensional computational fluid dynamics (3D CFD1) model. They conducted a sensitivity analysis by changing the operating parameters such as pressure, flow rate of feed and temperature of gas mixture were investigated. In another study, Coroneo et al. [26] studied the effect of non-ideal fluid on the hydrogen gas purification. Chen et al. [27] studied the effect of four major factors such as pressure difference, the mole fraction of hydrogen at the inlet stream, Reynolds number and the membrane permeability on the concentration polarization with a two-dimensional model. They investigated the effects of the feed and sweep gas flow pattern on the hydrogen permeation [28]. Ji et al. [29] numerically investigated the separation of hydrogen using high-temperature gas feed. Santucci et al. [30] conducted a 1
Computational fluid dynamics.
Fig. 1 e Schematic representation of experimental test rig used in the present work to validate the model.
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to 83% and the CO conversion increased by palladium membrane higher than thermodynamic equilibrium. This model is surveyed by computational fluid dynamics in 400e700 C to simulate the chemical reaction in a Pd-based membrane reactor. Ma et al. [36] investigated Ethanol steam reforming in a catalytic membrane reactor by computational fluid dynamics. They used nickel-based catalyst and Pd/Au as a membrane in the reactor. They concluded that the Hydrogen was produced in catalytic membrane reactor 122% over fixed bed. Sumrunronnasak et al. [37] examined hydrogen production from the dry reforming reaction of methane and carbon dioxide in palladium-based membrane reactors. They compared the results with a non-membrane reactor. According to their studies, hydrogen selectivity and hydrogen separation efficiency increased. Conical micro reactor for
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hydrogen production has been investigated by one of the author of this paper [38,39]. In this work, separation of hydrogen from the outlet of water-gas shift reaction via palladium membrane is simulated with a 2D computational fluid dynamic. To study the influence of geometrical properties on separation of hydrogen, four various membrane modules with cylindrical shells and cone tubes were considered and a rough comparison was made between the outcomes of the simulations with those of obtained for cylindrical membrane. To investigate the effect of flow pattern, four various flow patterns were applied to the model. In the present work, an effort has been made to improve their model significantly. Also, the detailed assessment of the geometrical properties of the membrane on hydrogen separation is conducted, which further develops a
Fig. 2 e (a)schematic of cylindrical membrane module with cone tube (b) A schematic representation of four various geometries used for the numerical investigation of H2 purification in a conical pd membrane.
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new insight on the separation of hydrogen with conical membranes.
Mathematical formulation In this section, the mass and momentum equations involved in the modelling are presented. The experimental results of Chen et al. [40] were utilized to validate the obtained model. A schematic representation of the model introduced by Chen et al. [40] is shown in Fig. 1. A gaseous feed enters the shell side, while sweep gas enters the tube. Notably, the palladium membrane selectivity is anomalously high against hydrogen. After passing the hydrogen from the membrane in the gas mixture, the rest of the mixture is removed from the retentate outlet. Steam (as a sweeping gas) drives the hydrogen to the outside (permeate side). The membrane module consists of a cylindrical shell and a co-axial cone frustum tube. The schematic representation of the module is shown in Fig. 2a. The thickness of the palladium membrane is 20 mm and its length is 150 mm. A twodimensional model is developed since the geometry is axially symmetric. The length of the membrane module is 200 mm and its width is 18 mm. Hereafter, the domain of gas feed is referred to as the retentate side and the domain that hydrogen is referred to as the permeate side. To investigate the effect of geometry on the hydrogen separation, the four modules with different dimensions were considered and represented in Fig. 2b. In each of them, the diameter of tube varies, while the length of the modules is constant. The hydrogen permeation is an isothermal and steadystate process in which the temperature of the process is 623 K. The experimental results presented by Chen et al. Therefore, the temperature has been selected according to Chen's study, in order to validate and compare numerical results by experimental results [31]. Other assumptions for the modelling include: The flow field in the membrane module is laminar, incompressible and symmetrically axial. The density of the membrane is constant. An ideal gas law is applied into the process because the mixture represents the ideal gas reasonably. There is no chemical reaction during the separation of hydrogen. The membrane selectivity is considered to be infinite to hydrogen and zero to other gas mixture components [41]. Steam is a sweep gas for sweeping hydrogen in the permeate side. For an incompressible fluid and a steadystate flow, the governing transport phenomena equations are as follows [42e44]:
Table 1 e The operating condition used for the modelling [28,40]. Feed gas Feed gas viscosity [pa.s] Feed gas density [kg/m3] Module temperature [ C] Pressure of retentate side [bar] Molar fraction in feed gas Hydrogen gas Carbon dioxide gas Carbon monoxide Membrane properties Membrane Palladium permeance [mol/(m2.S.Pa0.5)] Membrane length [mm] Membrane thickness [mm] Sweep gas properties Sweep gas Sweep gas viscosity [pa.s] Sweep gas density [kg/m3] Pressure of permeate side [bar]
2.628 105 3.2432 350 9 0.6520 0.3460 0.0018 Palladium 3 104 200 20 Water steam 2.2371 105 0.3483 1
Continuity conservation equation . V$ V ¼ 0
(2)
here, V is velocity (m.s1). Given the cross-sectional flow in this model the coordinates of the equations are cylindrical and with this in mind, the equations are expressed as follows. 1 v vV v vV r þ ¼0 r vr vr vz vz Momentum conservation equation
(3)
Fig. 3 e (a) A schematic representation of the model (cylindrical). (b) A comparison between the experimental data and the outcome of the model, %H2 recovery and %H2 concentration at the outlet of the retentate side in three different flow rates in cylindrical module.
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Fig. 4 e Hydrogen concentration contour in the conical membrane for the fourth model.
T . . . . rV: VV ¼ Vp þ V$ mðVV þ VV
Terms of V:
j
(4)
Here, r is the density (kg.m3), p is pressure (Pa) and m is viscosity (Pa.s). . 1 v vui v vvi 1 v vui r r þ ¼ Vp þ V$ m rV r vr vz vz r vr vr vr vuj v vvi 1 v r þ þ vz vz r vr vr v vvj þ vz vz
(5)
0
(6)
0
X 1 v vxj v vxj r þ Dij r vr vz vz vr j 1 . xj wj 1 v xj wj v vp vp r þ þ rwi V A þ r vr vr vz vz p p
.
rV$ V :wi
¼ Si
Si represent the transition of the components in a gas mixture, diffusion of gas components at retentate and permeate side and source term, respectively [43,44]. The mass transfer across the membrane cannot be expressed by Navier-Stoke equations because the membrane indicates discontinuity in the gas flow. This problem is always solved by means of adding a source term [25,45].
Boundary conditions
Species equations 1 X Vp . þ rwi VA ¼ Si V$@ rwi Dij Vxj þ xj wj p j
! . P Vp rwi Dij Vxj þ ðxj wj Þ p , V:ðrwi V Þ and
þ V$@ rwi
The membrane system consists of two different inflows, two downstream outflows, tube centerline and wall. Three solution domains of retentate, membrane and permeate side are considered. The applicable boundary conditions were employed for each region. The difference of flow velocity on the wall and membrane is zero and no-slip velocity condition on the wall and membrane is applied. No hydrogen separation occurs on walls. Hence, following equations are applied: ! V ¼ Vwi ¼ 0
(8)
Inflow: (7)
here, wi is the mass fraction of species i, xj is the mole fraction of species j, Dij is diffusion coefficient (m.2s1) and S is the source term (kg.m3.s1).
! V ¼ Vin ! n and wi ¼ wi;in
(9)
Sievert law is also employed as the boundary condition at both surfaces of membrane. The amount of hydrogen passing
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across the membrane is obtained with the following equation introduced by Sievert: i k h 0:5 pH2;Shell p0:5 H2;mem d
J¼
(10)
Outflow .
vV ¼ Vwi ¼ 0 and P ¼ Ptotal vz
(11)
Physical properties of the gas mixture The physical properties of the gas mixture are obtained with the equations reported. Viscosity of the gas mixture is calculated with Wilke semi-empirical correlation. Thermal conductivity of the gas mixture is also obtained with the correlation developed by Wilke. The binding factor is also used for calculating the viscosity and thermal conductivity in the mixture. The Chapman-Enskog equation is also used for estimating of mixture diffusivity in binary mixture. m¼
N X i¼1
xi m Pn i j¼1 xj Fij
(12)
2 0:5 1 Mi 41 þ Fij ¼ pffiffiffi 1 þ Mj 2 2
k¼
N X i¼1
mi mj
!0:5 32 Mj 0:25 5 Mi
xi ki Pn j¼1 xj Fij
3
Dij ¼ 1:881 10
(13)
The method of solving the governing equations is finite element. Geometry is discretized by orthogonal grid system. The growth rate of the cell size from the membrane to wall equals to 1.1. Transformation equations are solved by SPOOLES solver (stationary linear system solver using Newton's method For symmetric system) as represented the variations of hydrogen flux relative to the mesh number and it was calculated at feed flow rate of 1.0852 103 [mol. s1] and at 350 C. With an increase in the number of elements from about 680442 to 100008, the change in the flux remained unchanged, thereby indicating the independence of the calculation of the number of elements. To validate the model, results were compared with the experimental results reported by Chen et al. [40]. For the validation, the diameter of shell and tube were 18 mm and 9.8 mm respectively. The membrane thickness was 0.02 mm and the rest of the operating conditions are as per Table 1. The mixture is fed from the top of the shell (Fig. 3a). Steam as a sweep gas enters the bottom of the tube and removes hydrogen from the top side. Fig. 3b represents the result of the comparison between the outcome of the model and the experimental data. As can be seen, the simulated data are in a good agreement with the experimental ones [40]. Notably, to calculate the relative error, following equations were used:
(14)
T1:5
1 Mi
þ M1j
ps2ij Ud
0:5 (15)
Please note that the pressure differences is the mass transfer driving force. Also, in a gaseous thermodynamic system, the pressure difference causes a partial concentration difference, which results in the mass transfer in the membrane domain.
Numerical method A laboratory study on hydrogen production and separation is time-consuming and expensive. Hence, a detailed numerical study was conducted to better understand the process and to develop an insight on hydrogen separation using conical membrane. To achieve this, a suitable solution domain for the system was selected and divided into a large number of computational elements. The grid system were regular or irregular according to the type of geometry. The physical and chemical properties of the fluid were determined and analyzed for solving the equations of the model. A numerical solution involving the formulation of algebraic equations was defined with the discretization of the model equations on a grid system and solved for the convergence of the equations. Finally, the results of the modelling were post-processed and analyzed. It was found that the accuracy of the model is highly dependent on the number of elements in the system. The smaller the cells, the more accurate the solution. However, it adds to the time and difficulty of the solution.
Fig. 5 e Average H2 flux in different molar flow rates of (a) sweep gas (b) feed gas.
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Fig. 6 e Hydrogen concentration contours in the conical membrane module at various values of sweeping gas.
Error ¼
X abs Fh2;Numerical Fh2;Exprimental Fh2;Exprimental
100
(16)
F is the quantity used to calculate the error. If F is the H2 recovery, the error value is 8%, and if F is the H2 concentration, the error will be 11%. As can be seen, the H2 recovery obtained from the simulation represents only 8% error against the experimental data. Also, ~11% error for H2 mole fraction was obtained showing that the model is accurate and results for the conical membrane are reliable.2
Results and discussion Hydrogen permeation Fig. 4 presents a schematic diagram of the direction of the hydrogen permeation. As can be seen, the feed enters the shell from the upper side and the red color in this area reflects the high concentration of hydrogen since feed is enriched with hydrogen. While, at the bottom region, the hydrogen concentration is almost zero since it is occupied with steam showing with the blue color. The average hydrogen flux passing through the membrane was 0.247 [mol.m2. s1] which occurred at the fourth model. As can be seen in Fig. 5a, the average value for the hydrogen flux is almost identical amongst all the models. However, the flow velocity increases by a decrease in the cross-section of the membrane. Thus, the fourth and third 2
HTSR(High-temperature temperature shift reaction).
shift
reaction).
LTSR(Low-
models have the highest average of hydrogen flux as represented in Fig. 5a. Fig. 5b shows the variations of the average hydrogen flux with feed flow rate. As can be seen, the amount of hydrogen in the feed increases with an increase in the feed mass flow rate, resulting in the increase in the average hydrogen flux across the membrane. The change in the average hydrogen flux in the second model is similar to the cylindrical membrane module. The hydrogen flux in the first membrane model does not change with the feed flow rate. Also, the fourth membrane module has the highest hydrogen passing through the membrane. This is because this model has the largest change in the cross section area, hence the flow velocity increases along with the membrane. This phenomenon decreases the potential for the accumulation of the mixture in the path of hydrogen passage. Likewise, with an increase in the feed flow rate, the concentration of other components in the gaseous feed increases throughout the membrane. Thus, this phenomenon prevents further hydrogen to enter the membrane. Notably, the decrease in the cross-section in the fourth and third modules is larger than the other modules. Hence, they have the highest increase in velocity along with the membrane (Fig. 5b). The hydrogen concentration contour is also plotted in Fig. 6 at various flow rates of the sweeping gas. The flow pattern is counter-current. The feed enters from the top of the shell into the module and the sweeping gas comes from the bottom of the tube. When the hydrogen passes across the membrane into the tube (in the low flow rate) of the sweeping gas, the partial pressure of hydrogen increases in the permeate side (tube) so the required driving force to transport hydrogen from the membrane decreases. Thus, it can be concluded that all the hydrogen in the feed is not
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Fig. 7 e % H2 recovery for various molar flow rates of (a) feed gas, (b) sweep gas.
separated completely and some of it is removed from the bottom of the shell. Notably, for higher flow rates of the sweeping gas, hydrogen can rapidly be removed from the top of the tube, decreasing the hydrogen partial pressure in this area. Hence, the required driving force to separate hydrogen is met and hydrogen concentration in the retentate side (shell) decreases, (Fig. 6, the domain with blue color). Fig. 7 shows the results of the simulations for the hydrogen recovery and for various molar flow rate of the gaseous feed. As can be seen, the fourth model has the highest hydrogen recovery. The amount of hydrogen permeated from the membrane increases with an increase in the molar flow rate of the inlet feed. In fact, the hydrogen recovery initially increases with an increase in the molar flow rate of the feed mixture, then it reaches a flat region for other flow rates. For a high molar flow rate of the inlet feed, the separated hydrogen reaches the highest quantity, so the hydrogen recovery is maximized. The variation of hydrogen recovery with the flow rate of the sweeping gas has been shown in Fig. 7b, the hydrogen recovery increases with an increase in the sweeping gas flow rate. Here, the fourth model has the highest hydrogen recovery, followed by the third model with the recovery rate over 80%. It can be concluded that the decrease in the cross section leads the velocity to increase along with the membrane, which causes a significant improvement in the mass transfer and the separation process of hydrogen. Thus, the fourth and third models have the highest percentage of hydrogen recovery in the membrane modules. Notably, the first geometry and cylindrical module had a nearly equal recovery rate. As can be seen in Fig. 8, the concentration of hydrogen increases with an increase in the feed flow rate. The sweeping gas enters the tube under a constant flow rate of 0.5 [ml.min1]. Similar to the previous section, the hydrogen transfer increases with an increase in the feed flow rate.
Fig. 8 e Hydrogen concentration contours for the four conical modules and for various feed gas flow rates (m0 ¼ 1.0852 £ 10¡3 [mol.s¡1]).
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Fig. 9 e The studied flow patterns on the fourth model, a) counter-current, b) co-current.
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The effect of flow pattern on mass transfer In this section, the results of modelling for the fourth membrane module are discussed under the counter-current and co-current flow patterns. The effect of the flow pattern on the quantity of hydrogen separation is also investigated. The studied flow patterns for the fourth model have been represented in Fig. 9. For each of the studied patterns, the diameter of the top side of the conical tube is 2 mm and the diameter at the bottom region is 16 mm. The shell diameter is 18 mm and its length is 200 mm. Feed mixture enters to the shell under a constant molar flow rate of 1.0852 103 [mol.s1]. As can be seen in Fig. 10a, the dependence of hydrogen flux on the molar flow rate of feed is not linear. For the first mode, the inlet feed and the sweeping gas flows are counter-current and the cross-section area is reduced in retentate and permeate sides, therefore it is expected that the velocity along with the membrane increases for a constant feed and sweeping gas flow rates. Thus, the accumulation reduces throughout the membrane domain. The partial pressure of hydrogen in the permeate side is reduced and the necessary driving force is provided for the hydrogen separation by the membrane. Hydrogen flows to the permeate side to compensation for the lack of partial pressure in the retentate side. As shown in Fig. 10a, the first flow pattern has the highest mean hydrogen flux passing through the membrane (Fig. 10a).
Fig. 10 e Dependence of average H2 flux on molar flow rates of feed gas for four flow patterns shown in Fig. 9.
In the second mode, the inlet feed and sweeping gas are in a counter-current regimen and the cross-sectional flow increases in the direction of flow in retentate and permeate sides. Thus, the quantity of hydrogen flux passing across the membrane is potentially less than the first mode. Accordingly, under a counter-current flow, the driving force behind the hydrogen separation is higher than the co-current flow. The inlet feed and the sweeping gas in the third and fourth modes are co-current. As the flow rate of the feed increases in the third flow pattern and the cross-sectional area in the downstream decreases in the direction of the feed flow, the feed velocity increases in the direction of the flow and the concentration accumulation is eliminated. In the fourth mode, the cross-sectional flow feed increases in the flow direction, however, the flow rate of the cross-sectional sweeping gas in the permeate zone is reduced. Therefore, the flow rate of the feed decreases along with the length of the membrane and the velocity of the sweeping gas is also increased in the fourth mode. The average hydrogen flux in this flow pattern is less than other modes. This shows that with increasing the molar flow rate of the inlet feed, the average hydrogen flux from membrane changes and the effect of this change on the crosssectional area of the tube and also on the velocity of sweeping gas is low (see Fig. 10b).
Fig. 11 e Dependence of a) average H2 flux b) % H2 recovery on the molar flow rate of sweeping gas.
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Fig. 11 shows the variation of the average hydrogen flux with the flow rate of the sweeping gas. The first countercurrent mode has the highest hydrogen flux. As already discussed, for such a flow pattern, the feed and gas flow velocity increases with a decrease in cross-sectional flow. In the first and fourth flow patterns (cases 1 and 4), the average hydrogen flux increases with an increase in the sweeping gas flow rate. However, it is constant in second and third flow patterns (cases 2 and 3). The sweeping gas velocity is also reduced with an increase in the cross section of the tube. As a result, the case 1 has the highest average hydrogen flux because in the first flow pattern, the sweeping gas and the feed velocity both increased with a decrease in cross-sectional module (see Fig. 11a). Fig. 11b shows the hydrogen recovery for various sweeping gas flow rates. There is a pressure difference (referred to as a driving force of the separation) to the end of the membrane at counter-current flow. Thus, the first and the second flow patterns have the highest hydrogen separation in comparison with the third and the fourth ones. Therefore, these two flow patterns have the highest percentage of hydrogen recovery. Also, the sweeping gas velocity along with the length of the membrane increases with a decrease in the cross-sectional flow for the first and the fourth modes. Hence, hydrogen recovery increases in these two flow patterns. The first flow patterns have the highest recovery rate. The counter-current flow patterns have the highest hydrogen flux from palladium membrane which can be attributed to the residence time of the feed. (See Fig. 11b). In membrane separation processes, the penetrating agent is permeated from the membrane on the other side. The feed components penetrate the membranes at various velocities. In the retentate side, the impervious or low-passive components accumulate near the membrane. Hence, a concentration layer of impurities can be created near the surface of the membrane and the resistance to mass transfer becomes considerable. The quantity of the permeation from the membrane decreases with the creation of concentration polarization on the membrane [46]. In some cases, the hydrogen concentration layer has been developed along with the membrane surface. In such cases, the hydrogen partial pressure is lower in retentate side than the permeate side. Therefore, the flow path is changed and consequently, the hydrogen purification is reduced. This phenomenon can be prevented by optimizing the geometrical properties of the membrane together with the installation of the baffle in retentate side and the use of sweeping gas [24,47,48]. Notably, the concentration polarization is the appearance of the concentration gradients on a membrane interface, which is due to the selective transfer of some species under the effect of the transmembrane driving forces through the membrane [49]. For better understanding, the concentration polarization index (CPI3) is defined to determine the polarization extent as the following [50]: CPI ¼
3
CPIr þ CPIp 2
concentration polarization index.
CPIr ¼ 1
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xH2;m xH2;in
CPIp ¼ xH2;m
(18)
(19)
here, the subscripts r and p show the retentate and permeate sides, respectively. The subscript m denotes the membrane inlet. Fig. 12 shows the dependence of CPI on the length of the membrane for various modes studied in the present work. As can be seen, the Fig. has been plotted for the inlet feed flow rate of 1.0852 103 [mol. s1] and the sweeping gas flow rate of 0.5 [ml.min1]. As can be seen, the third model has the highest polarization density. For all the modules, the accumulation of other components increased by decreasing the amount of hydrogen in the feed, which in turn, leads to the concentration polarization. Therefore, the concentration polarization index reaches a constant value due to the decrease in the cross-sectional flow and the increase in the velocity in the steady flow of the inlet feed and the sweeping gas. The progression of the concentration polarization phenomenon in the cylindrical module initially decreases and then increases along with the length of the membrane. This is due to the fact that the thickness of the concentration boundary layer of
(17) Fig. 12 e The dependence of CPI on length of the membrane for a) four membrane module, b) four flow pattern.
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other components including CO and CO2 increases within the retentate side (shell). Therefore, the intensification of the polarization phenomenon is observed for the cylindrical membrane module in the membrane's length. Also, with the separation of hydrogen, its quantity in the gaseous feed decreases and the flow rate decreases as well. Hence, the concentration polarization index is relatively high. For the second counter-current mode, the highest polarization was obtained, which is due to the increase in the cross sectional area of the sweeping gas in the direction of the flow and also the reduction of both flow rates. (Fig. 12b).
Conclusions The process of hydrogen separation from a synthetic gas with a palladium membrane was modeled to understand the effect of geometry on the degree of the purification for hydrogen. Initially, four membrane modules were simulated with a cylindrical shell and a conical tube with different dimensions. Then numerical results were compared to the cylindrical module. The mechanism of the mass transfer in the palladium membrane was solution-diffusion. To investigate the effect of the flow pattern on hydrogen separation, four different flow patterns have been considered. The velocity of feed and sweeping gas flow increased with a decrease in the cross section of the shell and tube. This also increased the separated hydrogen flux. Changing the cross section of the membrane module prevented the intensification of the concentration polarization index (CPI). It was also identified that the membrane module with a conical tube (fourth geometry) had the highest recovery of 96% with the hydrogen flux of 0.247 [mol.m2. s1]. The counter-current flow pattern had the highest hydrogen flux passing through the palladium membrane with a decreasing the cross-section along with the flow direction.
Acknowledgments The authors of this work gratefully acknowledge the financial supports by Semnan University's Research Councils of for partial financial support.
Nomenclature Cp V C wi Di xi Do z DH
Gas mixture specific heat, [J/kg. K] Velocity [m.s1] Volumetric molar concentration, [mol/m3] Mass fraction of species i Inner diameter, [m] Mole fraction of species i Outer diameter, [m] Axial coordinate Hydraulic diameter, [m]
Subscript Diffusion coefficient [cm.2s1] Dij Hydrogen H2 Activation energy, [J.mol1] Ea
i Species i J Flux, [mol.m2. S1] in Inlet K Permeance, [mol.m1.s1.Pan ] m Membrane Pre-exponential term, [mol.m1.s1.Pan] K◦ P Permeate side Ma Mach number[e] r Retentate side Mixture molecular weight [kg.mol1] Mni s Site Pressure[atm] p R (¼8.314) universal gas constant [m.3 Pa.K1. Mol1] S Source[kg. m3.s1] T Temperature[K]
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