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ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming
international journal of hydrogen energy xxx (xxxx) xxx
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ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming Grazia Leonzio* Department of Industrial and Information Engineering and Economics, University of L'Aquila, Via Giovanni Gronchi 18, 67100 L'Aquila, Italy
article info
abstract
Article history:
Steam methane reforming is an endothermic reaction and it used to produce hydrogen and
Received 13 January 2019
syngas. In this research, a factorial design is developed for an integrated Pd-based mem-
Received in revised form
brane reactor, producing hydrogen by methane steam reaction. In literature, no analogous
10 March 2019
works are present, because a simple sensitivity analysis is carried out without finding
Accepted 11 March 2019
significant factors for the process. The reactor is modelled in MATLAB software using the
Available online xxx
Numaguchi kinetic. The reactor does not use conventional catalysts, but a Ni(10)/CeLaZr catalyst supported on SSiC ceramic foam. In ANOVA analysis, inlet temperature (550 K-
Keywords:
815 K), methane flow rate in the feed (0.1 kmol/h-1 kmol/h), hydrogen permeability (1000
Anova analysis
m3mmm2hrbar0.5e3600 m3mmm2hrbar0.5), the thickness of membrane (0.003 m-0.02 m)
Integrated membrane reactor
are the chosen factors. The analyzed responses are: hydrogen yield, carbon dioxide con-
Methane steam reforming
version and methane conversion. Results show that only inlet temperature, methane flow
Optimization
rate, their interaction and the thickens of membrane are significant. Also, the optimal
Mathematical model
operating conditions are obtained with inlet temperature, methane flow rate, hydrogen permeability
and
thickness
of
membrane
equal
to
550
K,
0.1
kmol/h,
3600
m3mmm2hrbar0.5 and 0.003 m. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Hydrogen is able to store energy from primary sources then it is an important energy vector [1]. In particular, it is the most desirable energy carriers due to its cleanness and zero emissions property. The high energy density of hydrogen contributes to increase the annual energy demand. Hydrogen is an important chemical feedstock that is employed to produce ammonia, methanol, can be used in Fischer Tropsch synthesis, petroleum hydrogenation,
desulfurization, hydro treating, petroleum refining, metallurgy and in cryogenic industry [2e4]. Furthermore, hydrogen is consumed in fuel cells, achieving an electrical efficiency higher than 90% and it is going to have an important role inside the suitable energy supply chain [5]. Currently, hydrogen is obtained from natural gas with three different technologies: steam reforming, partial oxidation and autothermal reforming [6e8]. However, the steam reforming of natural gas has lower costs than other technologies and it is the most used at commercial scale [9,10]. The highest hydrogen yield per fed methane is ensured [11].
* Corresponding author. E-mail address: [email protected]. https://doi.org/10.1016/j.ijhydene.2019.03.077 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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Overall, about 50 million tons of hydrogen are produced via the reforming of natural gas [2,12]. Methane and steam react in an endothermic catalytic reaction with the range of temperature and pressure between 1073 and 1273 K and 5e35 bar respectively [13]. Hydrogen with high purity can be achieved in membrane reactors, that are getting the attention of researchers in the last years. The use of a membrane permeable to hydrogen ensures lower operating temperatures and pressures with higher methane conversions in a reduced total reactor volume compared to traditional reactors [14]. In fact, thermodynamic equilibrium limitations are present, then high temperatures and pressures are required to have high methane conversion and hydrogen yield. Instead, the use of membrane permeable to hydrogen allows to shift chemical equilibrium towards the products, according to the Le Chatelier's principle, the a reaction temperature between 673 K and 873 K and a pressure about 2.5 bar are allowed [15,16]. In addition, cheaper materials resistant to heat can be used and increasing the durability, total costs are reduced [17,18]. Generally, dense palladium membranes or silver-palladium membranes are used to remove hydrogen due to their high permeability and selectivity [19,20]. The steam reforming reaction is industrially operated over nickel-alumina based catalysts. Catalysts based on nickel have a high activity and low cost, but they are quickly deactivated by coke. To improve the resistance to coke, precious metals (Ru, Rh, Pt, Pd, etc.), alkaline earth metals (Mg, Ca, Ba, Sr, etc.) and rare earth metals (La, Ce, Pr, etc.) are added to the basic catalyst [21]. In membrane reactor, catalysts such as Ru instead of Ni, ensure high performances [22e24]. In the last years, research studies are regarding metallic and ceramic foam catalysts, due to a high thermal conductivity, an uniform thermal dispersion and a high mechanical strength [25,26]. Different researches are present in literature about membrane reactors producing hydrogen by methane steam reforming [27e30]. In these works, different reactor configurations are shown. An external or embedded membrane configuration is analyzed by De Falco et al. [31]. Borgognoni et al. [32] propose a separate membrane module, in a so called “open architecture”. In other configurations of membrane reactor, the solar heat is exploited indirectly through molten salts, a heat transfer fluid improving the thermal transfer [33]. The modeling of membrane reactors is a research field that received a great attention: it can design, evaluate and optimize any reactor. Cruz and da Silva [34] with a two dimensional model show the best performance, in term of hydrogen yield, of membrane reactor compared to a fixed one. Simulation results suggest that methane conversion in traditional and membrane reactor are respectively of 97.21% at 1250 K and of 99.79% at 923 K. Comparing these two different reactors, Silva et al. [15] develop a dynamic mathematical model evaluating the hydrogen yield: a higher value is found for membrane reactor. Sensitivity analysis are carried out to evaluate the effect of operating parameters. In Patel and Sonul [35] the performance of the reactor is numerically investigated for various key operating variables, such as inlet fuel concentration, inlet steam/methane ratio, inlet reformer gas temperature and inlet reformer gas velocity.
Yu et al. [36] model a ceramic membrane reactor for methane steam reforming, evaluating the effect of temperature, pressure and gas reactants flow rate on methane conversion and hydrogen production. The effect of temperature and pressure on hydrogen production is evaluated by Castillo et al. [37]. The positive effect of pressure is found by Kim et al. [38]: a methane conversion of 82% is obtained at 912 kPa. Said et al. [3] analyze the effect of temperature, steam-tocarbon ratio and space velocity on conversion, hydrogen recovery and carbon monoxide selectivity. They also show that the water gas shift reaction is enhanced by the removal of hydrogen; this allows to reduce carbon monoxide concentration that produces coke at low temperature. A high hydrogen recovery is obtained at high space velocities. Marin et al. [39] in their sensitivity analysis find that inlet temperature and space velocity have a higher effect than pressure, steam excess and sweep gas rate in the permeate side. Alamdari [40] consider a packed bed and a catalytic membrane reactor with metal foam catalyst support. The authors evaluate the effect of pressure, reaction temperature, methane to steam in the feed ratio, thickness of membrane and sweep gas on methane conversion and hydrogen production. Results show that higher performances are obtained in membrane reactor. Sensitivity analysis with the aim to optimize the process are also carried out. Chibane and Brahim [41], find the optimal operating conditions with the range of temperature between 853 K and 873 K, steam to methane ratio of 3, the pressure range of 4e6 bar and the sweep gas ratio of 3. Simakov and Sheintuch [42,43] with a sensitivity analysis find the optimal operating conditions for a membrane reactor. De Falco et al. [44] evaluate the influence of inlet temperature, inlet methane flow rate, steam to carbon ratio, ratio between sweeping steam and inlet methane, operating reaction temperature on the total heat power required by the process. In optimal operating conditions, 687.4 kW are needed to convert 2 kmol/h of methane with a conversion of 98%. Anzelmo et al. [45] evaluate the effect of N2 and CO2 as impurities in the feed line and the effect of gas hourly space velocity. The best performance of the Pd-based membrane reactor is obtained at 420 C, 3.0 bar and 100 mL/min of sweepgas. Taji et al. [46] suggest a modeling and a real time optimization of an industrial membrane reactor for methane steam reforming considering catalyst deactivation. The best operating conditions (873 K and 500 kPa) of a membrane reactor at lab scale are also calculated by Di Marcoberardino et al. [47] and are validated by a mathematical model. A comparison with an industrial membrane reactor is also developed by Shigarov et al. [48] using Ni foam catalyst: good performance are obtained due to the relaxation of transport limitations on heat and hydrogen transfer, between catalyst and membrane. From the above literature works, it is evident that a simple analysis, sensitivity analysis and optimization is carried out for a methane steam reforming membrane reactor. In this research, a modeling and an ANOVA analysis for an integrated membrane reactor producing hydrogen by the
Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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reforming of natural gas is developed. Then the novelty of this work is evident, because a different methodology is used to study an integrated membrane reactor. The aim of ANOVA analysis is to optimize the reactor and to find factors influencing the system. These obtained results are verified by the literature. Another innovative point of this research, is that the analyzed reactor is the only integrated membrane reactor (at pilot scale) in Europe. that uses a ceramic foam catalyst (Ni(10)/CeLaZr catalyst supported on SSiC ceramic foam) for methane steam reforming. Molten salts ensure heat for the reaction. In future activities, a response surface methodology should be applied to find more accurate optimal solutions.
Table 1 e Geometric data of analyzed integrated membrane reactor for methane steam reforming. Internal diameter (mm)
External diameter (mm)
10 14 16 42.7 6
14 20 40 48.3 9
Membrane support Palladium membrane Catalyst Stell tube Tube of sweeping gas
Table 2 e Operating conditions of membrane reactor. Feed
Material and methods Integrated membrane reactor The single tube of the analyzed integrated membrane reactor for hydrogen production is presented in Fig. 1. The reactor is constructed with three concentric tubes. Through the membrane tube, sweeping gas flows to drag the permeate hydrogen, then improving driving force. The membrane tube is located inside a steel tube, where reforming reaction takes place. The catalyst is set in the reaction zone defined by annular space. This system ensures a recovery of high-grade hydrogen with high methane conversion, at relative low temperature. Table 1 shows the dimensions of membrane reactor. The membrane area is 1.17 m2, the length is 748 mm and the thickness is 3 mm. The tube number is 10, placed in triangular pitch inside the reactor, while the length is 900 mm. The outside diameter of shell reactor is 273 mm. Table 2 shows the operating conditions of membrane reactor. Natural gas and steam are in the feeding stream, while a retentate at high pressure rich in CO2 and a permeate at low-pressure rich in H2 stream are in the outlet stream. In the feed, steam to carbon (S/C) ratio is equal to 3:1 while methane conversion is 56% [49]. Ni(10)/CeLaZr supported on SSiC ceramic foam is used as catalyst. The catalyst volume is 9.6 L with the bed void fraction of 0.83 and a density of 1910 kg/
Mole Flow (kmol/h) H2 CO CO2 H2O CH4 Mole Fraction H2 CO CO2 H2O CH4 Total Flow (kmol/h) Total Flow (kg/h) Temperature (K) Pressure (barg) Vapor Fraction Enthalpy (cal/mol)
Permeate
Retentate
0 0 0 0.197 0.065
0.114 0.000 0.000 0.088 0.000
0.031 0.002 0.034 0.126 0.029
0.000 0.000 0.000 0.751 0.249 0.262 4.59 773 9 1 43439
0.563 0.000 0.000 0.437 0 0.202 1.81 723 0.4 1 21981
0.138 0.010 0.154 0.568 0.129 0.222 4.36 809 9 1 45218
m3, while the porosity of foam and the pore diameter are 15 ppi and 0.0017 m respectively [50]. The heat of reaction is externally provided by molten salts, a binary mixture of NaNO3/KNO3 (60/40 %w/w), that is able to exploit solar energy. The flow rate of molten salts is 800 kg/h. This system ensures the achievements of nearly isothermal operating conditions: it is a good way to transfer and store heat [3].
Fig. 1 e Analyzed integrated membrane reactor for the methane steam reforming reaction: section view [2]. Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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Modeling of kinetic reactions Methane steam reforming reaction involves the following reactions: the reforming reaction (see Eq. (1)) and the water gas shift reaction (see Eq. (2)): CH4 þ H2 O 4CO þ 3$H2
(1)
CO þ H2 O 4CO2 þ H2
(2)
The enthalpy of reaction 1 and 2 are respectively of 206 kJ/ mol and 41 kJ/mol then reforming process is overall endothermic [44] The reactions are modelled according to the Numaguchi kinetic [51] and not to the common used Xu and Fromant [52] kinetic, because better results are provided as suggested by Leonzio [2]. In fact, the kinetic of Xu and Froment is very fast. According to the Numaguchi kinetic, the surface reaction is the rate-determining step for methane steam reforming reaction. Considering a hybrid rate between Langmuir-Hinshelwood and power law type, the following reaction rates as a function of partial pressures are obtained [58] (See Eqs. (3) and (4)): PCH4 PCH4ðeqÞ ER o $ aR rrf ¼ kR $exp dR R$T PCH4 $PH2O
(3)
PCO PCOðeqÞ Es o $ as rsf ¼ kS $exp s R$T PCH4 $PdH2O
(4)
where rrf is for the steam reforming reaction rate in kmol/m3h, rsf is for the shift reaction rate in kmol/m3h, PCH4(eq) and PCO(eq) are pressures at equilibrium conditions for methane and carbon monoxide respectively in bar, PCH4 and PCO are pressures for methane and carbon monoxide respectively in bar, R is the constant of universal gas in J/molK, T is temperature in K. Table 3 shows the parameter values for the above reaction rates [51,53].
Modeling of integrated membrane reactor A mathematical model is developed in 1-D dimension to carry out an ANOVA analysis, then neglecting radial phenomena. Radial phenomena are considered by Murmura et al. [54] finding a boundary layer in the near membrane region whose extent is independent on reactor aspect ratio, by Murmura et al. [55] developing a model describing the flow across the membrane as a function of main operating parameters and by Murmura et al. [56] showing a radial model
Table 3 e Values of fitted parameters for Namaguchi kinetics. ko R ER (kJ/mol) aR dR ko S Es (kJ/mol) aS dS
92 108 106.87 0 0,596 8.688 105 54.531 0 0
coupling mass and momentum mechanism in the presence of a concentration-dependent density of the gaseous mixture. However, as the aim of this analysis is to evaluate the effect of some factors and not to quantify their value these considerations are neglected. A modeling of membrane reactor is developed according to the material and energy balances, in MATLAB software. The following assumptions are considered: steady state conditions, plug flow, the catalytic bed is isobaric, one dimensional and pseudo-homogeneous model, the foam bed has mechanic, thermic and kinetic equivalence to granular bed, polarization phenomena by concentrations are neglected due the dimension of membrane, as well as for inhibition phenomena due to impurities, ideal gas conditions [40,46,57]. The material balance for each component is according to the following equation (see Eq. (5)): N R ¼3 X dFi ¼ U$ vij $rj $hj dz j¼1
(5)
where U is reactor section in m2, hj is the effectiveness factors of reaction j as the ratio between the actual total rate of reaction and the rate that would exist in the absence of resistance to diffusion [34], rj is the considered reaction rate in kmol/m3h, z is the length of the reactor in m, Fi is the flow rate of component i in kmol/h, vij is the stochiometric coefficient. For methane and carbon dioxide the following material balances are considered (see Eqs. (6) and (7)): dFCH4 ¼ U$ rrf $hrf dz
(6)
dFCO2 ¼ U$ þ rsf $hsf dz
(7)
where U is reactor section in m2, hrf, hsf, are the effectiveness factors of steam reforming reaction and shift reaction respectively considered equal to 1, z is the length of reactor in m, FCH4 and FCO2 are the flow rate of methane and carbon dioxide respectively in kmol/h, rrf is for steam reforming reaction rate in kmol/m3h, rsf is for shift reaction rate in kmol/m3h. Hydrogen flow through membrane is described by the following relation (see Eq. (8)): dFH2;perm ¼ JH2 $2$p$ðr þ dÞ dz
(8)
with ro is the inner radius of membrane in m, d is the thickness of membrane in m, z is the length of reactor in m, FH2,perm is hydrogen flow rate through the membrane in kmol/h, JH2 is hydrogen permeation through the palladium membrane according to the Sieverts' law in m3mmm2hrbar0.5 (the difference between the square root of hydrogen partial pressure in permeate and retentate sides) [14] (see Eq. (9)): JH2 ¼
Qpd 0:5 $ PH2;r P0:5 H2;p d
(9)
where d is the thickness of membrane in m, Qpd is the permeation of hydrogen in m3umhbar0.5/m2, PH2,r and PH2,p are hydrogen pressure in permeate and reaction side in bar. From the above material balances, methane conversion (consumption), carbon dioxide conversion (production) and the hydrogen yield, can be obtained respectively according to
Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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the following relations reported by Roux [58] (see Eq. (10)e(12)): XCH4 ¼
XCO2 ¼
YH2 ¼
FoCH4 FCH4 $100 FoCH4 FCO2 $100 FoCH4
FH2;perm FoCH4
(10)
(11)
(12)
Table 4 e Factors and values of levels chosen in ANOVA analysis. Code
A B C D
Factors
Inlet temperature (K) Methane flow rate (kmol/h) Hydrogen permeability (m3mmm2hr bar0.5) Thickness of membrane (m)
Levels ()
(þ)
550 0.1 1000
815 1 3600
0.003
0.02
where FCH4 is methane flow rate in the feed in kmol/h, XCH4 is methane conversion, XCO2 is carbon dioxide conversion, YH2 is hydrogen yield, FCH4 is methane flow rate in kmol/h, FCO2 is carbon dioxide flow rate in kmol/h. The energy balance providing temperature in reaction and permeation zone is described below (See eq. (13) and (14)): vT ¼ vz
P2 j¼1
DHj $rj $hj $Ac Ac $U$ðT Tw Þ P4 P4 i¼1 cpi $Fi i¼1 cpi $Fi
(13)
where T is temperature in K, Tw is temperature applied on the outer reactor wall, z is the length of reactor, Ac is crosssectional area in m2, U is overall heat transfer coefficient between wall and foam block in J/m2hK, cpi the heat capacity of gas for component i in J/molK, rj is reaction rate for reaction j in kmol/m3h, DHj is the heat of reaction j in J/mol, Fi is the molar flow rate of component is in kmol/h. In the energy balance, it is assumed that reaction and separation zone have the same temperature, then without radial gradient [59]. The ordinary differential equation (ODE) system is numerically solved in MATLAB using the 4th order Runge and Kurta algorithm. The step size of the 4th order Runge e Kurta algorithm is 0.001. The described model is validated by the work of Alamandari [40] and by the work of Leonzio [60] according to Fig. 2 showing the hydrogen partial pressure in retentate side, for experimental and modeling data.
Modeling of ANOVA analysis For considered factors and interaction, the estimation of effects is carried out by ANOVA analysis (analysis of variance) finding if these are significant respect to experimental error (sε). To this scope, Yates's algorithm is used. Interactions and factors are selected or rejected (then are significant or not)
Fig. 2 e Comparison of modeling data with experimental data.
according to the value of their probability that can be lower or higher than 95%. In this work, sε is calculated by the means of mean square (MS) of not significant factors and interactions. Overall, a 24 full factorial design with 16 simulation tests is developed [61]. Then 4 factors with two levels are considered (a level defines a value, status or characteristic that the factor can assume). Significant factors and interactions can be used to find a mathematical model that describes the system and its quality is evaluated by the coefficient of determination R2. The investigated factors are: inlet temperature, methane flow rate, hydrogen permeability, the thickness of membrane. The chosen responses to understand the behavior of the reactor are: hydrogen yield, methane conversion and carbon dioxide conversion.
Results and discussions Results of ANOVA analysis The results obtained in MATLAB for the integrated membrane reactor in different operating conditions are used to carry out an ANOVA analysis. These results related to the mathematical model of the integrated membrane reactor are also reported by Leonzio [2]. Inlet temperature, methane flow rate in the feed, hydrogen permeability through the membrane and the thickness of membrane are the chosen factors. Generally, in industrial processes inlet temperature and methane concentration are used in strategies to improve efficiency and to ensure a fixed production of hydrogen [46]. The analyzed responses are methane conversion and carbon dioxide
Fig. 3 e Results of ANOVA analysis (Factor A: Temperature (K); Factor B: Methane flow rate (kmol/h); Factor C: Hydrogen permeability (m3mmm-2hrbar0.5); Factor D: Thickness of membrane (m)·[10¡4]).
Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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Table 5 e Result of ANOVA analysis (Factor A: Temperature (K), Factor B: Methane flow rate in the feed (kmol/h), Factor C: Hydrogen permeability (m3 mmm-2 hr bar0.5), Factor D: Thickness of membrane (m)∙[10¡4]). Factor
A B AB C AC BC ABC D AD BD ABD CD ACD BCD ABCD
Hydrogen yield
CO2 conversion
CH4 conversion
Effects
F-ratio
Remarks
Effects (%)
F-ratio
Remarks
Effects (%)
F-ratio
Remarks
5,63$101 6,73$101 7,59$101 2,50$105 0 2,50$105 0 7,50$105 5,00$105 2,50$105 5,00$105 2,50$105 0 2,50$105 0
5,07$108 7,25$108 9,22$108 1 0 1 0 9 4 1 4 1 0 1 0
100% 100% 100% 63% 0% 63% 0% 96% 88% 63% 88% 63% 0% 63% 0%
6,05 4,64 1,39$101 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103
5,85$106 3,44$106 3,09$107 1 1 1 1 1 1 1 1 1 1 1 1
100% 100% 100% 63% 63% 63% 63% 63% 63% 63% 63% 63% 63% 63% 63%
1,89$101 2,83$101 1,84$101 7,50$102 1,35$101 7,50$102 1,35$101 9,25$102 1,63$101 9,25$102 1,63$101 3,50$102 2,50$102 3,50$102 2,50$102
4,45$104 9,93$104 4,18$104 6,98$101 2,26 6,98$101 2,26 1,06 3,28 1,06 3,28 1,52$101 7,76$102 1,52$101 7,76$10-2
100% 100% 100% 55% 79% 55% 79% 64% 86% 64% 86% 28% 21% 28% 21%
conversion and hydrogen yield. Among them, methane conversion is the main parameter used to analyze the efficiency of the process [62]. Table 4 presents the selected factors and the values of their levels, signed by þ and e respectively for high level and low level. Fig. 3 and Table 5, with statistical data, show the results of ANOVA analysis with significant factors and interactions (values of probability lower than 0.05 suggest that terms are significant, while values greater than 0.05 are not significant). Results show that inlet temperature has a positive effect on hydrogen yield, due to the endothermic nature of reaction. A higher temperature ensures a more heat for the process, leading the reaction to move forward: a higher amount of hydrogen is produced [63,64]. In addition, a higher reaction
rate improves the hydrogen partial pressure gradient due to the increase of hydrogen partial pressure in reaction side: a higher hydrogen removal and yield are ensured. Methane flow rate in the feed has a negative effect on hydrogen production as also found by Silva et al. [65]. However, hydrogen yield obtained by decreasing methane in the feed is found to be lower than the maximum hydrogen yield obtained by increasing water in the feed [66]. The interaction of factor A (inlet temperature) and B (methane flow rate in the feed) is positive. Interaction AB on hydrogen yield has the highest effect. The thickness of membrane has a negative effect, according to the relation for hydrogen flux through membrane and also reported by Fernandes and Soares [67]: thin membranes can increase conversion even at moderate temperatures.
Fig. 4 e Surface plot of hydrogen yield as function of: a) factor C (hydrogen permeability) and factor D (thickness of membrane); b) factor B (methane flow rate in the feed) and factor D (thickness of membrane); d) factor B (methane flow rate in the feed) and factor C (hydrogen permeability); d) factor A (inlet temperature) and factor D (thickness of membrane); e) factor A (inlet temperature) and factor C (hydrogen permeability); f) factor A (inlet temperature) and factor B (methane flow rate in the feed) (Hold value: factor A ¼ B]C¼D ¼ 0). Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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Fig. 5 e Surface plot of carbon dioxide conversion as function of: a) factor C (hydrogen permeability) and factor D (thickness of membrane); b) factor B (methane flow rate in the feed) and factor D (thickness of membrane); d) factor B (methane flow rate in the feed) and factor C (hydrogen permeability); d) factor A (inlet temperature) and factor D (thickness of membrane); e) factor A (inlet temperature) and factor C (hydrogen permeability); f) factor A (inlet temperature) and factor B (methane flow rate in the feed) (Hold value: factor A ¼ B]C¼D ¼ 0).
For methane conversion, inlet temperature (factor A), has a positive effect. The important role of temperature and its positive effect is also found by Tabrizi et al. [68]. Also, the importance of these factors on methane conversion is reported by Fan et al. [69]. Factor B (methane flow rate in the feed) has a negative effect, as also studied by Silva et al. [65]. In fact, a lower recovery of hydrogen is obtained. In general, a
lower flow rate gives a longer contact time with the catalyst and improves conversion. Mbodji et al. [70] find that methane conversions are higher at higher resident time. Interaction AB, has a positive effect. For carbon dioxide conversion, in term of production, factor A (inlet temperature) has a negative effect (the single reaction is exothermic so is not favorite at higher temperature)
Fig. 6 e Surface plot of methane conversion as function of: a) factor C (hydrogen permeability) and factor D (thickness of membrane); b) factor B (methane flow rate in the feed) and factor D (thickness of membrane); d) factor B (methane flow rate in the feed) and factor C (hydrogen permeability); d) factor A (inlet temperature) and factor D (thickness of membrane); e) factor A (inlet temperature) and factor C (hydrogen permeability); f) factor A (inlet temperature) and factor B (methane flow rate in the feed) (Hold value: factor A ¼ B]C¼D ¼ 0). Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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then to minimaze the amount of greenhouse gas is preferable to operate at higher temperatures [70]. This result is also reported by Giwa and Giwa [66]: a higher temperature favors the reforming reaction than the water gas shift reaction, decreasing CO2 production. Factor B (methane flow rate in the feed) as also reported by Giwa and Giwa [66] has a negative effect: CO2 flow rate should increase at first and then decrease. Interaction AB have a positive effect. Interaction AB has a positive effect, as also found by Hossain et al. [71]. With significant factors and interactions, a mathematical model for hydrogen yield, carbon dioxide and methane conversion is developed like the following relations (see Eq. (14)e(16)): yYH2 ¼ 2:77 þ 0:28$X1 0:336$X2 þ 0:379$X1 $X2 2 0:000038$X4 R ¼ 0:99 yyCO2 ¼ 28:38 3:02$X1 2:31$X2 þ 6:95$X1 $X2
0 level. In the second case, methane flow rate is at low level (0.1 kmol/h), factor C (hydrogen permeability) can assume all value, factor A (inlet temperature) and factor D (thickness of membrane) are at 0 level. In the third case, factor A (inlet temperature) and factor B (methane flow rate in the feed) are at low level, while the other two factors are at 0 level. This should be a better condition because can have energetic and economic advantages and savings.
Results of test of two levels A significative interaction AB is found by ANOVA analysis for the analyzed responses. An accurate analysis for this interaction can be developed with the test of two levels. Considering this interaction and not single factors, it results that the best conditions of the process are obtained with
(14)
R2 ¼ 0:98 (15)
yXCH4 ¼ 85:49þ 9:47$X1 14:14$X2 þ 9:18$X1 $X2
2 R ¼ 0:99 (16)
where X1 is factor A (inlet temperature), X2 is factor B (methane flow rate), X1$X2 is interaction AB, yYH2 is hydrogen yield, yyCO2 is carbon dioxide conversion, yXCH4 is methane conversion. For the three equations, the values of R2 near to unit ensure a good agreement between simulation and predicted data. The mentioned models can be considered as a reliable model for methane steam reforming simulation and optimization in an integrated membrane reactor. The above mathematical models are used to find the respective surface plots. Fig. 4 presents the surface plot of hydrogen yield as function of analyzed factors. It evident that the factor A (inlet temperature), factor B (methane flow rate in the feed), their interaction and in a lower measure factor D (thickness of membrane) are significative factors. It is possible to see as factor A has a positive effect while factor B has a negative effect. The effect of factor D is negative, but it is lower significative than other significative factor and interactions. Fig. 5 presents the surface plot of carbon dioxide conversion as function of analyzed factors. Also, in this case, it results that significative factors are the inlet temperature, methane flow rate in the feed and their interaction. As found, in previous results, inlet temperature and methane flow rate have a negative effect. Considering the interaction AB, a higher CO2 conversion is obtained with the value of factor A and B at low level. Fig. 6 presents the surface plot of methane conversion as function of analyzed factors. As the previous responses, only factor A (inlet temperature) and factor B (methane flow rate in the feed) are significative with positive and negative effect respectively. From Fig. 5b, c and 5f it is possible to see that a methane conversion close to 100% is achieved. In the first case methane flow rate is at low level (0.1 kmol/h), factor D (thickness of membrane) can assume all value, factor A (inlet temperature) and factor C (hydrogen permeability) are at
Fig. 7 e Test of two levels for interaction AB for different responses: a) hydrogen yield, b) carbon dioxide conversion, c) methane conversion.
Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
international journal of hydrogen energy xxx (xxxx) xxx
inlet temperature and methane flow rate in the feed at low level. Considering all analyzed responses, as shown in Fig. 7, it is possible to have a higher efficiency of the process with factor A (inlet temperature) and factor B (inlet methane flow rate) at lower level. The optimal operating conditions of the process are obtained by Minitab software maximizing the composite desirability. It is found that optimum conditions can be achieved with inlet temperature equal to 550 K, methane flow rate equal to 0.1 kmol/h, hydrogen permeability equal to 3600 m3mmm-2hrbar0.5, chosen in order to have the better performances of membrane and a thickness equal to 0.003 m in order to reduce the costs. In these optimal operating conditions, methane conversion, carbon dioxide conversion and hydrogen yield are respectively to 99%, 40% and 3.2.
Conclusions An innovative point of this research, is the development of an ANOVA analysis for an integrated membrane reactor producing hydrogen by methane steam reforming, carried out by using the results obtained by mathematical model. Reactor data are related to the first integrated membrane reactor at pilot plant in Europe. This guarantee novelty to this research study. In anova analysis, inlet temperature, methane flow rate in the feed, hydrogen permeability through membrane and the thickness of membrane are the chosen factors. The analyzed responses are methane conversion and carbon dioxide conversion and hydrogen yield. Compared to other literature work, significant factors for the process are found. In fact, it is concluded that only inlet temperature, methane flow rate, their interaction and the thickness of membrane are the significant factors. However, the thickness of membrane has a very small effect on hydrogen yield. Moreover, it is shown that hydrogen yield is increased at a higher temperatures and at a lower methane flow rate. For methane conversion, inlet temperature has a positive effect, while methane flow rate has a negative effect; their interaction has a positive effect. On the other hand, carbon dioxide conversion is decreased by increasing temperature and methane flow rate in the feed, while the interaction of these factors has a positive effect. After that, the process is optimized and the optimal values of independent variables are reported.
Acknowledgements The author of the study is grateful to the European Commission for the research grant allowing the performance of this study.
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ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming Grazia Leonzio* Department of Industrial and Information Engineering and Economics, University of L'Aquila, Via Giovanni Gronchi 18, 67100 L'Aquila, Italy
article info
abstract
Article history:
Steam methane reforming is an endothermic reaction and it used to produce hydrogen and
Received 13 January 2019
syngas. In this research, a factorial design is developed for an integrated Pd-based mem-
Received in revised form
brane reactor, producing hydrogen by methane steam reaction. In literature, no analogous
10 March 2019
works are present, because a simple sensitivity analysis is carried out without finding
Accepted 11 March 2019
significant factors for the process. The reactor is modelled in MATLAB software using the
Available online xxx
Numaguchi kinetic. The reactor does not use conventional catalysts, but a Ni(10)/CeLaZr catalyst supported on SSiC ceramic foam. In ANOVA analysis, inlet temperature (550 K-
Keywords:
815 K), methane flow rate in the feed (0.1 kmol/h-1 kmol/h), hydrogen permeability (1000
Anova analysis
m3mmm2hrbar0.5e3600 m3mmm2hrbar0.5), the thickness of membrane (0.003 m-0.02 m)
Integrated membrane reactor
are the chosen factors. The analyzed responses are: hydrogen yield, carbon dioxide con-
Methane steam reforming
version and methane conversion. Results show that only inlet temperature, methane flow
Optimization
rate, their interaction and the thickens of membrane are significant. Also, the optimal
Mathematical model
operating conditions are obtained with inlet temperature, methane flow rate, hydrogen permeability
and
thickness
of
membrane
equal
to
550
K,
0.1
kmol/h,
3600
m3mmm2hrbar0.5 and 0.003 m. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Hydrogen is able to store energy from primary sources then it is an important energy vector [1]. In particular, it is the most desirable energy carriers due to its cleanness and zero emissions property. The high energy density of hydrogen contributes to increase the annual energy demand. Hydrogen is an important chemical feedstock that is employed to produce ammonia, methanol, can be used in Fischer Tropsch synthesis, petroleum hydrogenation,
desulfurization, hydro treating, petroleum refining, metallurgy and in cryogenic industry [2e4]. Furthermore, hydrogen is consumed in fuel cells, achieving an electrical efficiency higher than 90% and it is going to have an important role inside the suitable energy supply chain [5]. Currently, hydrogen is obtained from natural gas with three different technologies: steam reforming, partial oxidation and autothermal reforming [6e8]. However, the steam reforming of natural gas has lower costs than other technologies and it is the most used at commercial scale [9,10]. The highest hydrogen yield per fed methane is ensured [11].
* Corresponding author. E-mail address: [email protected]. https://doi.org/10.1016/j.ijhydene.2019.03.077 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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Overall, about 50 million tons of hydrogen are produced via the reforming of natural gas [2,12]. Methane and steam react in an endothermic catalytic reaction with the range of temperature and pressure between 1073 and 1273 K and 5e35 bar respectively [13]. Hydrogen with high purity can be achieved in membrane reactors, that are getting the attention of researchers in the last years. The use of a membrane permeable to hydrogen ensures lower operating temperatures and pressures with higher methane conversions in a reduced total reactor volume compared to traditional reactors [14]. In fact, thermodynamic equilibrium limitations are present, then high temperatures and pressures are required to have high methane conversion and hydrogen yield. Instead, the use of membrane permeable to hydrogen allows to shift chemical equilibrium towards the products, according to the Le Chatelier's principle, the a reaction temperature between 673 K and 873 K and a pressure about 2.5 bar are allowed [15,16]. In addition, cheaper materials resistant to heat can be used and increasing the durability, total costs are reduced [17,18]. Generally, dense palladium membranes or silver-palladium membranes are used to remove hydrogen due to their high permeability and selectivity [19,20]. The steam reforming reaction is industrially operated over nickel-alumina based catalysts. Catalysts based on nickel have a high activity and low cost, but they are quickly deactivated by coke. To improve the resistance to coke, precious metals (Ru, Rh, Pt, Pd, etc.), alkaline earth metals (Mg, Ca, Ba, Sr, etc.) and rare earth metals (La, Ce, Pr, etc.) are added to the basic catalyst [21]. In membrane reactor, catalysts such as Ru instead of Ni, ensure high performances [22e24]. In the last years, research studies are regarding metallic and ceramic foam catalysts, due to a high thermal conductivity, an uniform thermal dispersion and a high mechanical strength [25,26]. Different researches are present in literature about membrane reactors producing hydrogen by methane steam reforming [27e30]. In these works, different reactor configurations are shown. An external or embedded membrane configuration is analyzed by De Falco et al. [31]. Borgognoni et al. [32] propose a separate membrane module, in a so called “open architecture”. In other configurations of membrane reactor, the solar heat is exploited indirectly through molten salts, a heat transfer fluid improving the thermal transfer [33]. The modeling of membrane reactors is a research field that received a great attention: it can design, evaluate and optimize any reactor. Cruz and da Silva [34] with a two dimensional model show the best performance, in term of hydrogen yield, of membrane reactor compared to a fixed one. Simulation results suggest that methane conversion in traditional and membrane reactor are respectively of 97.21% at 1250 K and of 99.79% at 923 K. Comparing these two different reactors, Silva et al. [15] develop a dynamic mathematical model evaluating the hydrogen yield: a higher value is found for membrane reactor. Sensitivity analysis are carried out to evaluate the effect of operating parameters. In Patel and Sonul [35] the performance of the reactor is numerically investigated for various key operating variables, such as inlet fuel concentration, inlet steam/methane ratio, inlet reformer gas temperature and inlet reformer gas velocity.
Yu et al. [36] model a ceramic membrane reactor for methane steam reforming, evaluating the effect of temperature, pressure and gas reactants flow rate on methane conversion and hydrogen production. The effect of temperature and pressure on hydrogen production is evaluated by Castillo et al. [37]. The positive effect of pressure is found by Kim et al. [38]: a methane conversion of 82% is obtained at 912 kPa. Said et al. [3] analyze the effect of temperature, steam-tocarbon ratio and space velocity on conversion, hydrogen recovery and carbon monoxide selectivity. They also show that the water gas shift reaction is enhanced by the removal of hydrogen; this allows to reduce carbon monoxide concentration that produces coke at low temperature. A high hydrogen recovery is obtained at high space velocities. Marin et al. [39] in their sensitivity analysis find that inlet temperature and space velocity have a higher effect than pressure, steam excess and sweep gas rate in the permeate side. Alamdari [40] consider a packed bed and a catalytic membrane reactor with metal foam catalyst support. The authors evaluate the effect of pressure, reaction temperature, methane to steam in the feed ratio, thickness of membrane and sweep gas on methane conversion and hydrogen production. Results show that higher performances are obtained in membrane reactor. Sensitivity analysis with the aim to optimize the process are also carried out. Chibane and Brahim [41], find the optimal operating conditions with the range of temperature between 853 K and 873 K, steam to methane ratio of 3, the pressure range of 4e6 bar and the sweep gas ratio of 3. Simakov and Sheintuch [42,43] with a sensitivity analysis find the optimal operating conditions for a membrane reactor. De Falco et al. [44] evaluate the influence of inlet temperature, inlet methane flow rate, steam to carbon ratio, ratio between sweeping steam and inlet methane, operating reaction temperature on the total heat power required by the process. In optimal operating conditions, 687.4 kW are needed to convert 2 kmol/h of methane with a conversion of 98%. Anzelmo et al. [45] evaluate the effect of N2 and CO2 as impurities in the feed line and the effect of gas hourly space velocity. The best performance of the Pd-based membrane reactor is obtained at 420 C, 3.0 bar and 100 mL/min of sweepgas. Taji et al. [46] suggest a modeling and a real time optimization of an industrial membrane reactor for methane steam reforming considering catalyst deactivation. The best operating conditions (873 K and 500 kPa) of a membrane reactor at lab scale are also calculated by Di Marcoberardino et al. [47] and are validated by a mathematical model. A comparison with an industrial membrane reactor is also developed by Shigarov et al. [48] using Ni foam catalyst: good performance are obtained due to the relaxation of transport limitations on heat and hydrogen transfer, between catalyst and membrane. From the above literature works, it is evident that a simple analysis, sensitivity analysis and optimization is carried out for a methane steam reforming membrane reactor. In this research, a modeling and an ANOVA analysis for an integrated membrane reactor producing hydrogen by the
Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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reforming of natural gas is developed. Then the novelty of this work is evident, because a different methodology is used to study an integrated membrane reactor. The aim of ANOVA analysis is to optimize the reactor and to find factors influencing the system. These obtained results are verified by the literature. Another innovative point of this research, is that the analyzed reactor is the only integrated membrane reactor (at pilot scale) in Europe. that uses a ceramic foam catalyst (Ni(10)/CeLaZr catalyst supported on SSiC ceramic foam) for methane steam reforming. Molten salts ensure heat for the reaction. In future activities, a response surface methodology should be applied to find more accurate optimal solutions.
Table 1 e Geometric data of analyzed integrated membrane reactor for methane steam reforming. Internal diameter (mm)
External diameter (mm)
10 14 16 42.7 6
14 20 40 48.3 9
Membrane support Palladium membrane Catalyst Stell tube Tube of sweeping gas
Table 2 e Operating conditions of membrane reactor. Feed
Material and methods Integrated membrane reactor The single tube of the analyzed integrated membrane reactor for hydrogen production is presented in Fig. 1. The reactor is constructed with three concentric tubes. Through the membrane tube, sweeping gas flows to drag the permeate hydrogen, then improving driving force. The membrane tube is located inside a steel tube, where reforming reaction takes place. The catalyst is set in the reaction zone defined by annular space. This system ensures a recovery of high-grade hydrogen with high methane conversion, at relative low temperature. Table 1 shows the dimensions of membrane reactor. The membrane area is 1.17 m2, the length is 748 mm and the thickness is 3 mm. The tube number is 10, placed in triangular pitch inside the reactor, while the length is 900 mm. The outside diameter of shell reactor is 273 mm. Table 2 shows the operating conditions of membrane reactor. Natural gas and steam are in the feeding stream, while a retentate at high pressure rich in CO2 and a permeate at low-pressure rich in H2 stream are in the outlet stream. In the feed, steam to carbon (S/C) ratio is equal to 3:1 while methane conversion is 56% [49]. Ni(10)/CeLaZr supported on SSiC ceramic foam is used as catalyst. The catalyst volume is 9.6 L with the bed void fraction of 0.83 and a density of 1910 kg/
Mole Flow (kmol/h) H2 CO CO2 H2O CH4 Mole Fraction H2 CO CO2 H2O CH4 Total Flow (kmol/h) Total Flow (kg/h) Temperature (K) Pressure (barg) Vapor Fraction Enthalpy (cal/mol)
Permeate
Retentate
0 0 0 0.197 0.065
0.114 0.000 0.000 0.088 0.000
0.031 0.002 0.034 0.126 0.029
0.000 0.000 0.000 0.751 0.249 0.262 4.59 773 9 1 43439
0.563 0.000 0.000 0.437 0 0.202 1.81 723 0.4 1 21981
0.138 0.010 0.154 0.568 0.129 0.222 4.36 809 9 1 45218
m3, while the porosity of foam and the pore diameter are 15 ppi and 0.0017 m respectively [50]. The heat of reaction is externally provided by molten salts, a binary mixture of NaNO3/KNO3 (60/40 %w/w), that is able to exploit solar energy. The flow rate of molten salts is 800 kg/h. This system ensures the achievements of nearly isothermal operating conditions: it is a good way to transfer and store heat [3].
Fig. 1 e Analyzed integrated membrane reactor for the methane steam reforming reaction: section view [2]. Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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Modeling of kinetic reactions Methane steam reforming reaction involves the following reactions: the reforming reaction (see Eq. (1)) and the water gas shift reaction (see Eq. (2)): CH4 þ H2 O 4CO þ 3$H2
(1)
CO þ H2 O 4CO2 þ H2
(2)
The enthalpy of reaction 1 and 2 are respectively of 206 kJ/ mol and 41 kJ/mol then reforming process is overall endothermic [44] The reactions are modelled according to the Numaguchi kinetic [51] and not to the common used Xu and Fromant [52] kinetic, because better results are provided as suggested by Leonzio [2]. In fact, the kinetic of Xu and Froment is very fast. According to the Numaguchi kinetic, the surface reaction is the rate-determining step for methane steam reforming reaction. Considering a hybrid rate between Langmuir-Hinshelwood and power law type, the following reaction rates as a function of partial pressures are obtained [58] (See Eqs. (3) and (4)): PCH4 PCH4ðeqÞ ER o $ aR rrf ¼ kR $exp dR R$T PCH4 $PH2O
(3)
PCO PCOðeqÞ Es o $ as rsf ¼ kS $exp s R$T PCH4 $PdH2O
(4)
where rrf is for the steam reforming reaction rate in kmol/m3h, rsf is for the shift reaction rate in kmol/m3h, PCH4(eq) and PCO(eq) are pressures at equilibrium conditions for methane and carbon monoxide respectively in bar, PCH4 and PCO are pressures for methane and carbon monoxide respectively in bar, R is the constant of universal gas in J/molK, T is temperature in K. Table 3 shows the parameter values for the above reaction rates [51,53].
Modeling of integrated membrane reactor A mathematical model is developed in 1-D dimension to carry out an ANOVA analysis, then neglecting radial phenomena. Radial phenomena are considered by Murmura et al. [54] finding a boundary layer in the near membrane region whose extent is independent on reactor aspect ratio, by Murmura et al. [55] developing a model describing the flow across the membrane as a function of main operating parameters and by Murmura et al. [56] showing a radial model
Table 3 e Values of fitted parameters for Namaguchi kinetics. ko R ER (kJ/mol) aR dR ko S Es (kJ/mol) aS dS
92 108 106.87 0 0,596 8.688 105 54.531 0 0
coupling mass and momentum mechanism in the presence of a concentration-dependent density of the gaseous mixture. However, as the aim of this analysis is to evaluate the effect of some factors and not to quantify their value these considerations are neglected. A modeling of membrane reactor is developed according to the material and energy balances, in MATLAB software. The following assumptions are considered: steady state conditions, plug flow, the catalytic bed is isobaric, one dimensional and pseudo-homogeneous model, the foam bed has mechanic, thermic and kinetic equivalence to granular bed, polarization phenomena by concentrations are neglected due the dimension of membrane, as well as for inhibition phenomena due to impurities, ideal gas conditions [40,46,57]. The material balance for each component is according to the following equation (see Eq. (5)): N R ¼3 X dFi ¼ U$ vij $rj $hj dz j¼1
(5)
where U is reactor section in m2, hj is the effectiveness factors of reaction j as the ratio between the actual total rate of reaction and the rate that would exist in the absence of resistance to diffusion [34], rj is the considered reaction rate in kmol/m3h, z is the length of the reactor in m, Fi is the flow rate of component i in kmol/h, vij is the stochiometric coefficient. For methane and carbon dioxide the following material balances are considered (see Eqs. (6) and (7)): dFCH4 ¼ U$ rrf $hrf dz
(6)
dFCO2 ¼ U$ þ rsf $hsf dz
(7)
where U is reactor section in m2, hrf, hsf, are the effectiveness factors of steam reforming reaction and shift reaction respectively considered equal to 1, z is the length of reactor in m, FCH4 and FCO2 are the flow rate of methane and carbon dioxide respectively in kmol/h, rrf is for steam reforming reaction rate in kmol/m3h, rsf is for shift reaction rate in kmol/m3h. Hydrogen flow through membrane is described by the following relation (see Eq. (8)): dFH2;perm ¼ JH2 $2$p$ðr þ dÞ dz
(8)
with ro is the inner radius of membrane in m, d is the thickness of membrane in m, z is the length of reactor in m, FH2,perm is hydrogen flow rate through the membrane in kmol/h, JH2 is hydrogen permeation through the palladium membrane according to the Sieverts' law in m3mmm2hrbar0.5 (the difference between the square root of hydrogen partial pressure in permeate and retentate sides) [14] (see Eq. (9)): JH2 ¼
Qpd 0:5 $ PH2;r P0:5 H2;p d
(9)
where d is the thickness of membrane in m, Qpd is the permeation of hydrogen in m3umhbar0.5/m2, PH2,r and PH2,p are hydrogen pressure in permeate and reaction side in bar. From the above material balances, methane conversion (consumption), carbon dioxide conversion (production) and the hydrogen yield, can be obtained respectively according to
Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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the following relations reported by Roux [58] (see Eq. (10)e(12)): XCH4 ¼
XCO2 ¼
YH2 ¼
FoCH4 FCH4 $100 FoCH4 FCO2 $100 FoCH4
FH2;perm FoCH4
(10)
(11)
(12)
Table 4 e Factors and values of levels chosen in ANOVA analysis. Code
A B C D
Factors
Inlet temperature (K) Methane flow rate (kmol/h) Hydrogen permeability (m3mmm2hr bar0.5) Thickness of membrane (m)
Levels ()
(þ)
550 0.1 1000
815 1 3600
0.003
0.02
where FCH4 is methane flow rate in the feed in kmol/h, XCH4 is methane conversion, XCO2 is carbon dioxide conversion, YH2 is hydrogen yield, FCH4 is methane flow rate in kmol/h, FCO2 is carbon dioxide flow rate in kmol/h. The energy balance providing temperature in reaction and permeation zone is described below (See eq. (13) and (14)): vT ¼ vz
P2 j¼1
DHj $rj $hj $Ac Ac $U$ðT Tw Þ P4 P4 i¼1 cpi $Fi i¼1 cpi $Fi
(13)
where T is temperature in K, Tw is temperature applied on the outer reactor wall, z is the length of reactor, Ac is crosssectional area in m2, U is overall heat transfer coefficient between wall and foam block in J/m2hK, cpi the heat capacity of gas for component i in J/molK, rj is reaction rate for reaction j in kmol/m3h, DHj is the heat of reaction j in J/mol, Fi is the molar flow rate of component is in kmol/h. In the energy balance, it is assumed that reaction and separation zone have the same temperature, then without radial gradient [59]. The ordinary differential equation (ODE) system is numerically solved in MATLAB using the 4th order Runge and Kurta algorithm. The step size of the 4th order Runge e Kurta algorithm is 0.001. The described model is validated by the work of Alamandari [40] and by the work of Leonzio [60] according to Fig. 2 showing the hydrogen partial pressure in retentate side, for experimental and modeling data.
Modeling of ANOVA analysis For considered factors and interaction, the estimation of effects is carried out by ANOVA analysis (analysis of variance) finding if these are significant respect to experimental error (sε). To this scope, Yates's algorithm is used. Interactions and factors are selected or rejected (then are significant or not)
Fig. 2 e Comparison of modeling data with experimental data.
according to the value of their probability that can be lower or higher than 95%. In this work, sε is calculated by the means of mean square (MS) of not significant factors and interactions. Overall, a 24 full factorial design with 16 simulation tests is developed [61]. Then 4 factors with two levels are considered (a level defines a value, status or characteristic that the factor can assume). Significant factors and interactions can be used to find a mathematical model that describes the system and its quality is evaluated by the coefficient of determination R2. The investigated factors are: inlet temperature, methane flow rate, hydrogen permeability, the thickness of membrane. The chosen responses to understand the behavior of the reactor are: hydrogen yield, methane conversion and carbon dioxide conversion.
Results and discussions Results of ANOVA analysis The results obtained in MATLAB for the integrated membrane reactor in different operating conditions are used to carry out an ANOVA analysis. These results related to the mathematical model of the integrated membrane reactor are also reported by Leonzio [2]. Inlet temperature, methane flow rate in the feed, hydrogen permeability through the membrane and the thickness of membrane are the chosen factors. Generally, in industrial processes inlet temperature and methane concentration are used in strategies to improve efficiency and to ensure a fixed production of hydrogen [46]. The analyzed responses are methane conversion and carbon dioxide
Fig. 3 e Results of ANOVA analysis (Factor A: Temperature (K); Factor B: Methane flow rate (kmol/h); Factor C: Hydrogen permeability (m3mmm-2hrbar0.5); Factor D: Thickness of membrane (m)·[10¡4]).
Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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Table 5 e Result of ANOVA analysis (Factor A: Temperature (K), Factor B: Methane flow rate in the feed (kmol/h), Factor C: Hydrogen permeability (m3 mmm-2 hr bar0.5), Factor D: Thickness of membrane (m)∙[10¡4]). Factor
A B AB C AC BC ABC D AD BD ABD CD ACD BCD ABCD
Hydrogen yield
CO2 conversion
CH4 conversion
Effects
F-ratio
Remarks
Effects (%)
F-ratio
Remarks
Effects (%)
F-ratio
Remarks
5,63$101 6,73$101 7,59$101 2,50$105 0 2,50$105 0 7,50$105 5,00$105 2,50$105 5,00$105 2,50$105 0 2,50$105 0
5,07$108 7,25$108 9,22$108 1 0 1 0 9 4 1 4 1 0 1 0
100% 100% 100% 63% 0% 63% 0% 96% 88% 63% 88% 63% 0% 63% 0%
6,05 4,64 1,39$101 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103 2,50$103
5,85$106 3,44$106 3,09$107 1 1 1 1 1 1 1 1 1 1 1 1
100% 100% 100% 63% 63% 63% 63% 63% 63% 63% 63% 63% 63% 63% 63%
1,89$101 2,83$101 1,84$101 7,50$102 1,35$101 7,50$102 1,35$101 9,25$102 1,63$101 9,25$102 1,63$101 3,50$102 2,50$102 3,50$102 2,50$102
4,45$104 9,93$104 4,18$104 6,98$101 2,26 6,98$101 2,26 1,06 3,28 1,06 3,28 1,52$101 7,76$102 1,52$101 7,76$10-2
100% 100% 100% 55% 79% 55% 79% 64% 86% 64% 86% 28% 21% 28% 21%
conversion and hydrogen yield. Among them, methane conversion is the main parameter used to analyze the efficiency of the process [62]. Table 4 presents the selected factors and the values of their levels, signed by þ and e respectively for high level and low level. Fig. 3 and Table 5, with statistical data, show the results of ANOVA analysis with significant factors and interactions (values of probability lower than 0.05 suggest that terms are significant, while values greater than 0.05 are not significant). Results show that inlet temperature has a positive effect on hydrogen yield, due to the endothermic nature of reaction. A higher temperature ensures a more heat for the process, leading the reaction to move forward: a higher amount of hydrogen is produced [63,64]. In addition, a higher reaction
rate improves the hydrogen partial pressure gradient due to the increase of hydrogen partial pressure in reaction side: a higher hydrogen removal and yield are ensured. Methane flow rate in the feed has a negative effect on hydrogen production as also found by Silva et al. [65]. However, hydrogen yield obtained by decreasing methane in the feed is found to be lower than the maximum hydrogen yield obtained by increasing water in the feed [66]. The interaction of factor A (inlet temperature) and B (methane flow rate in the feed) is positive. Interaction AB on hydrogen yield has the highest effect. The thickness of membrane has a negative effect, according to the relation for hydrogen flux through membrane and also reported by Fernandes and Soares [67]: thin membranes can increase conversion even at moderate temperatures.
Fig. 4 e Surface plot of hydrogen yield as function of: a) factor C (hydrogen permeability) and factor D (thickness of membrane); b) factor B (methane flow rate in the feed) and factor D (thickness of membrane); d) factor B (methane flow rate in the feed) and factor C (hydrogen permeability); d) factor A (inlet temperature) and factor D (thickness of membrane); e) factor A (inlet temperature) and factor C (hydrogen permeability); f) factor A (inlet temperature) and factor B (methane flow rate in the feed) (Hold value: factor A ¼ B]C¼D ¼ 0). Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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Fig. 5 e Surface plot of carbon dioxide conversion as function of: a) factor C (hydrogen permeability) and factor D (thickness of membrane); b) factor B (methane flow rate in the feed) and factor D (thickness of membrane); d) factor B (methane flow rate in the feed) and factor C (hydrogen permeability); d) factor A (inlet temperature) and factor D (thickness of membrane); e) factor A (inlet temperature) and factor C (hydrogen permeability); f) factor A (inlet temperature) and factor B (methane flow rate in the feed) (Hold value: factor A ¼ B]C¼D ¼ 0).
For methane conversion, inlet temperature (factor A), has a positive effect. The important role of temperature and its positive effect is also found by Tabrizi et al. [68]. Also, the importance of these factors on methane conversion is reported by Fan et al. [69]. Factor B (methane flow rate in the feed) has a negative effect, as also studied by Silva et al. [65]. In fact, a lower recovery of hydrogen is obtained. In general, a
lower flow rate gives a longer contact time with the catalyst and improves conversion. Mbodji et al. [70] find that methane conversions are higher at higher resident time. Interaction AB, has a positive effect. For carbon dioxide conversion, in term of production, factor A (inlet temperature) has a negative effect (the single reaction is exothermic so is not favorite at higher temperature)
Fig. 6 e Surface plot of methane conversion as function of: a) factor C (hydrogen permeability) and factor D (thickness of membrane); b) factor B (methane flow rate in the feed) and factor D (thickness of membrane); d) factor B (methane flow rate in the feed) and factor C (hydrogen permeability); d) factor A (inlet temperature) and factor D (thickness of membrane); e) factor A (inlet temperature) and factor C (hydrogen permeability); f) factor A (inlet temperature) and factor B (methane flow rate in the feed) (Hold value: factor A ¼ B]C¼D ¼ 0). Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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then to minimaze the amount of greenhouse gas is preferable to operate at higher temperatures [70]. This result is also reported by Giwa and Giwa [66]: a higher temperature favors the reforming reaction than the water gas shift reaction, decreasing CO2 production. Factor B (methane flow rate in the feed) as also reported by Giwa and Giwa [66] has a negative effect: CO2 flow rate should increase at first and then decrease. Interaction AB have a positive effect. Interaction AB has a positive effect, as also found by Hossain et al. [71]. With significant factors and interactions, a mathematical model for hydrogen yield, carbon dioxide and methane conversion is developed like the following relations (see Eq. (14)e(16)): yYH2 ¼ 2:77 þ 0:28$X1 0:336$X2 þ 0:379$X1 $X2 2 0:000038$X4 R ¼ 0:99 yyCO2 ¼ 28:38 3:02$X1 2:31$X2 þ 6:95$X1 $X2
0 level. In the second case, methane flow rate is at low level (0.1 kmol/h), factor C (hydrogen permeability) can assume all value, factor A (inlet temperature) and factor D (thickness of membrane) are at 0 level. In the third case, factor A (inlet temperature) and factor B (methane flow rate in the feed) are at low level, while the other two factors are at 0 level. This should be a better condition because can have energetic and economic advantages and savings.
Results of test of two levels A significative interaction AB is found by ANOVA analysis for the analyzed responses. An accurate analysis for this interaction can be developed with the test of two levels. Considering this interaction and not single factors, it results that the best conditions of the process are obtained with
(14)
R2 ¼ 0:98 (15)
yXCH4 ¼ 85:49þ 9:47$X1 14:14$X2 þ 9:18$X1 $X2
2 R ¼ 0:99 (16)
where X1 is factor A (inlet temperature), X2 is factor B (methane flow rate), X1$X2 is interaction AB, yYH2 is hydrogen yield, yyCO2 is carbon dioxide conversion, yXCH4 is methane conversion. For the three equations, the values of R2 near to unit ensure a good agreement between simulation and predicted data. The mentioned models can be considered as a reliable model for methane steam reforming simulation and optimization in an integrated membrane reactor. The above mathematical models are used to find the respective surface plots. Fig. 4 presents the surface plot of hydrogen yield as function of analyzed factors. It evident that the factor A (inlet temperature), factor B (methane flow rate in the feed), their interaction and in a lower measure factor D (thickness of membrane) are significative factors. It is possible to see as factor A has a positive effect while factor B has a negative effect. The effect of factor D is negative, but it is lower significative than other significative factor and interactions. Fig. 5 presents the surface plot of carbon dioxide conversion as function of analyzed factors. Also, in this case, it results that significative factors are the inlet temperature, methane flow rate in the feed and their interaction. As found, in previous results, inlet temperature and methane flow rate have a negative effect. Considering the interaction AB, a higher CO2 conversion is obtained with the value of factor A and B at low level. Fig. 6 presents the surface plot of methane conversion as function of analyzed factors. As the previous responses, only factor A (inlet temperature) and factor B (methane flow rate in the feed) are significative with positive and negative effect respectively. From Fig. 5b, c and 5f it is possible to see that a methane conversion close to 100% is achieved. In the first case methane flow rate is at low level (0.1 kmol/h), factor D (thickness of membrane) can assume all value, factor A (inlet temperature) and factor C (hydrogen permeability) are at
Fig. 7 e Test of two levels for interaction AB for different responses: a) hydrogen yield, b) carbon dioxide conversion, c) methane conversion.
Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077
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inlet temperature and methane flow rate in the feed at low level. Considering all analyzed responses, as shown in Fig. 7, it is possible to have a higher efficiency of the process with factor A (inlet temperature) and factor B (inlet methane flow rate) at lower level. The optimal operating conditions of the process are obtained by Minitab software maximizing the composite desirability. It is found that optimum conditions can be achieved with inlet temperature equal to 550 K, methane flow rate equal to 0.1 kmol/h, hydrogen permeability equal to 3600 m3mmm-2hrbar0.5, chosen in order to have the better performances of membrane and a thickness equal to 0.003 m in order to reduce the costs. In these optimal operating conditions, methane conversion, carbon dioxide conversion and hydrogen yield are respectively to 99%, 40% and 3.2.
Conclusions An innovative point of this research, is the development of an ANOVA analysis for an integrated membrane reactor producing hydrogen by methane steam reforming, carried out by using the results obtained by mathematical model. Reactor data are related to the first integrated membrane reactor at pilot plant in Europe. This guarantee novelty to this research study. In anova analysis, inlet temperature, methane flow rate in the feed, hydrogen permeability through membrane and the thickness of membrane are the chosen factors. The analyzed responses are methane conversion and carbon dioxide conversion and hydrogen yield. Compared to other literature work, significant factors for the process are found. In fact, it is concluded that only inlet temperature, methane flow rate, their interaction and the thickness of membrane are the significant factors. However, the thickness of membrane has a very small effect on hydrogen yield. Moreover, it is shown that hydrogen yield is increased at a higher temperatures and at a lower methane flow rate. For methane conversion, inlet temperature has a positive effect, while methane flow rate has a negative effect; their interaction has a positive effect. On the other hand, carbon dioxide conversion is decreased by increasing temperature and methane flow rate in the feed, while the interaction of these factors has a positive effect. After that, the process is optimized and the optimal values of independent variables are reported.
Acknowledgements The author of the study is grateful to the European Commission for the research grant allowing the performance of this study.
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Please cite this article as: Leonzio G, ANOVA analysis of an integrated membrane reactor for hydrogen production by methane steam reforming, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.03.077