Thesis for degree: Licentiate of Engineering

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The reaction rates for both the steam reforming reaction and the water-gas shift reaction are plotted in Figure 4.9 for Achenbach & Riensche’s (left) and Drescher’s kinetics (right). It should be clearly noted that the reaction rates are only plotted for the entrance region, through 0.01 m. Close to the inlet where the concentration of methane is high the reaction rate for the steam reforming reaction is high. The reaction rate for the steam reforming and the water-gas shift is much higher for Drescher’s kinetics than for both Achenbach & Riensche’s and Leinfelder’s kinetics. Leinfelder’s kinetics is higher than Achenbach & Riensche’s. Close to the inlet in the anode where the carbon monoxide generation is high, the reaction rate for the water-gas shift reaction is at the highest. The high generation of carbon monoxide is due to the steam reforming reaction. Furthermore, more hydrogen is produced when steam is generated due to the fact that the water-gas shift equation is in equilibrium through the process. As hydrogen is consumed, steam is generated thanks to the electrochemical reaction at the TPB. The reaction rate for the water-gas shift reaction reaches a higher value due to the faster reaction rate for the steam reforming reaction of the Drescher’s and Leinfelder’s kinetics compared to Achenbach & Riensche’s. The comparison between the different kinetic models needs to be evaluated on a more detailed level as it cannot be correctly explained by just a few empirical parameters, such as the activation energy and the pre-exponential value. To fully understand the effect and dependence of the parameters, microscale modeling is needed. What can be concluded from this study is that the configuration and geometrical properties of the anode and the chemical composition and catalytic characteristics are important. To draw firm conclusions from the modeling work, it is important to reveal the difference of the kinetic models from experimental work carried out on SOFC and a reformer based on the same properties. A parameter study was carried out for Leinfelder’s kinetics by increasing the inlet temperature by 50 K. The other parameters were kept the same as in the base case. The temperature distributions for both cases result in similar effects but obviously resulted in a higher temperature range. The mole fraction distribution of the fuel gas species was maintained in the same range and trend as the base case at 1000 K. The reaction rates are slightly higher for a higher inlet temperature. Due to the increased inlet temperature the maximum reaction rates are almost doubled compared to the base case at the inlet. Another parameter study was conducted for the active surface area-to-volume ratio (AV) from 10 ∙10 4 to 5 ∙10 5 m 2 /m 3 , which is a frequently used interval in the literature. All the other parameters were kept the same as the base case. The temperature profile and each mole fraction profile were distributed in a similar overall trend as for the base case. The mole fractions reach approximately the same maximum value for different AV but occur at different distances from the inlet. A higher ratio moves in the maximum of all the mole fraction species closer to the inlet. The characteristics of reaction rates for Leinfelder’s kinetics with an increased AV are distributed similarly to the base case, but the maximum value is more or less doubled for an increased active surface area to volume ratio. 4.3.2 Case study: Methane content and steam-to-fuel ratio A case study was performed to simulate biogas as a fuel by varying the amount of methane and SF. Three cases were performed, all with 60% CH 4 content but the SF was varied between 1, 3, and 5. Additionally, three cases with SF equal to 3 but CH 4 varied as 45%, 60% and 75%. For all the cases, a small fraction of hydrogen is added to enable electrochemical reactions close to the inlet as well. CO is also added, similarly as H 2 , to achieve numerical stability. Steam was added to avoid carbon deposition and also to be used in the reforming reactions. The amount of H 2 O was calculated from the relationship SF = [H 2 O]/[CH 4 ] as SF is specified for the different cases. In Table 4.5 the inlet mole fractions are presented for the different cases with varying amount of methane content and SF. 46
Table 4.5: Inlet mole fractions for the different case studies. Case models CH 4 CO 2 H 2 O CH 4 0.45, SF=3 0.191 0.235 0.574 CH 4 0.60, SF=3 0.214 0.143 0.643 CH 4 0.75, SF=3 0.231 0.076 0.692 CH 4 0.60, SF=1 0.375 0.25 0.375 CH 4 0.60, SF=5 0.15 0.1 0.75 Similar to the previous section, the fuel flow rates for the different cases were calculated to keep the fuel utilization at 80 percent. Note that each molecule of methane corresponds to a generation of four molecules of hydrogen by both the steam reforming and water-gas shift reaction and each molecule of carbon monoxide corresponds to one molecule generation of hydrogen. The flow rate of air was kept constant for all cases and the oxygen utilization is set to 20 percent. The inlet temperature was set to 1100 K to ensure functional conversion of the fuel and the current density was kept constant at 3000 A/m 2 . The Knudsen diffusion was neglected in this model to reduce computational cost. For both the steam reforming reaction and the water-gas shift reaction, the equilibrium model is chosen for the kinetic model. Figure 4.10: Mole fraction distribution in the middle of the anode for 45% CH 4 (left) and 75% CH 4 (right). In Figure 4.10, the mole fractions at the centerline of the anode along the whole cell length are presented. The change of H 2 O between the different cases is directly connected to the methane content, in this case, to ensure significant steam at the inlet of the cell. Depending on the inlet fraction a decrease in the mole fraction of water can be observed close to the inlet. The biogas contains no hydrogen in the collected data but for numerical calculations the hydrogen is initially set to have a small inlet value to enable the electrochemical reactions at the inlet of the cell. The variations of the mole fractions are however quite small and it is mostly CO 2 that changes. The reason for this is that CO 2 is linked to the choice of CH 4 and 47
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SOFC modeling from micro to macrosc
Page 3 and 4:
Abstract The purpose of this work i
Page 5 and 6:
katalytisk omvandling av naturgas o
Page 7 and 8: List of publications Journal public
Page 9 and 10: 3.2 Governing equations for the mac
Page 11 and 12: Q source term (heat), W/m3 q heat f
Page 13 and 14: 1 Introduction After some time of d
Page 15 and 16: 2 SOFC modeling at smaller scales T
Page 17 and 18: etween 0.3 and 1.5 mm. In this conf
Page 19 and 20: Volume Method (FVM) which adopt the
Page 21 and 22: 2.3 Lattice Boltzmann method LBM ha
Page 23 and 24: streaming [3]. The concentration ρ
Page 25 and 26: ease the correspondence between the
Page 27 and 28: applicable for a mixture of two spe
Page 29 and 30: Figure 2.6: Effective boundary arra
Page 31 and 32: Table 2.1: Comparison of previous w
Page 33 and 34: Figure 2.7: Schematic illustration
Page 35 and 36: model is presented after the data c
Page 37 and 38: 3.2.1 Mass transport In the electro
Page 39 and 40: where h v is the volume heat transf
Page 41 and 42: Achenbach [43], it was found that t
Page 43 and 44: cathode are assumed to be similar t
Page 45 and 46: (3.48) where, besides the parameter
Page 47 and 48: for an isothermal spherical particl
Page 49 and 50: Velocity carried out to check wheth
Page 51 and 52: Figure 4.4: Velocity field [lu/ts]
Page 53 and 54: Table 4.2: Parameters in the SOFC a
Page 55 and 56: eactions are safely fulfilled. This
Page 57: Figure 4.8: Mole fraction distribut
Page 61 and 62: Figure 4.12: Mole fraction distribu
Page 63 and 64: 5 Conclusions The physics and the t
Page 65 and 66: 7 References [1] Andersson M., Yuan
Page 67 and 68: [25] Latt J., Hydrodynamic Limit of
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Thesis for degree: Licentiate of Engineering

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