Heat Transfer Modeling of Tubular Reforming Reactor

Transcription

1 Heat Transfer Modeling of Tubular Reforming Reactor Carlos Gonçalo Ferreira 1 1 IST Instituto Superior Técnico, Lisbon, Portugal Keywords: Steam reforming, numerical simulation, methane, methanol, temperature, conversion Abstract: With the work developed for the present thesis, a numerical model was prepared to analyze the behavior of a reforming reactor, for methane or methanol as fuels. The developed model is based on the numerical resolution of transport of mass, energy and momentum equations. The steady state is considered and the domain is axissimetric. The resolution of the equations was performed by using a discretization method consisting in finite volumes, with the terms being solved by a hybrid upwind /central differences scheme. The kinetics of reformation was simulated with kinetic models from the literature. The reaction zone, where reforming occurs, was considered to be filled with two types of catalysts: monoliths or fixed-bed of spheres. A study was carried out for these porous media, consisting in the analysis of heat and mass transfer and pressure drop. This analysis was performed using some correlations present in the literature and by estimating those that were not available, with some simplifications. The model validation was made by four test cases. The catalysts characteristics were unknown, so it was used a parameter to represent the internal diffusion in the catalyst particles. This parameter had to be fitted for each test case. The model and results comparison took into account the outlet composition, the conversion of the fuel and temperature profiles. The model proved to be able to calculate consistent results with what was expected. So the model can be used in future investigations in the reforming field, for both methane and methanol. 1. Introduction The World energy requirement is, nowadays, mostly attended using fossil fuels. Fossil fuels are burned to transform their energy into work, heat, electricity and to transport people and goods. This represents tons of carbon dioxide released to the atmosphere, and, besides that, fossil fuels are getting less available for consuming. Countries like China and India are developing very quickly thanks to fuels like coal that is cheap but has larger emissions, including CO 2, contributing to the green house effect. Conjugating these facts, the World needs an alternative to fossil fuels, that doesn t pollute so much and renewable energies is a contribution to this. In this context, fuel cells gain importance (energetic efficiency of ~45%), once this technology can transform hydrogen, the energy carrier, into electricity, which is more difficult to store than hydrogen. So hydrogen is not considered as a fuel resource but rather as an energy carrier that has to be produced, and there are nowadays two main processes: reforming of hydrocarbons or water electrolysis. The present work is about modeling heat transfer of steam reforming of methane and methanol. These two fuels can get conversions above 90% in theory, with actual values up to 75%. Natural gas is

2 widely available due to its distribution in networks while methanol is considered due to its flexibility in transport and handling. Steam reforming of fuels is an endothermic reaction, so it needs an energy input that is usually given by an oven that burns residual fuels. The reaction of reforming produces CO and H 2. One way to prevent de formation of CO is to inject excess of steam that oxidize the CO and enhance the production of H 2 and CO 2. That is called the water gas shift reaction. There are other processes developed to produce hydrogen from hydrocarbon reforming like: partial oxidation and auto-thermal reforming. As mentioned before, this work is about methane and methanol. Methane steam reforming is investigated in a lot of studies based on the kinetics proposed by Xu and Froment (1989). They proposed a mechanism and reaction rates of the steam reforming of methane, including the water gas shift reaction. For methanol there are no comprehensive models for kinetics of steam reforming. For the present work the mechanism presented by Mizsey et al. (2001) was used. Four reactions were considered. The reforming of hydrocarbons is a field of investigation that is gaining importance. Because of that there is a strong investment on research. There are many things to be improved until the best technology is achieved, like: the geometry of the reactors, the type of catalysts, the way the gases are heated, etc. There are three typical types of reactors: fixed-bed reactors, monolith reactors and heat transfer plate reactors. The fixed-bed reactors are very simple, using particles made of or covered by catalyst placed inside tubes and fixed by grids. Monoliths are regular structures of metal or more usually ceramic materials forming channels where the catalyst is deposited. In both the fixed-bed and monoliths heat transfer represents a limitation due to the endothermic characteristics of the reaction. The heat transfer plate reactors try to solve this problem by depositing the catalyst in heat transfer surfaces, including metal structures with fins. Lee et al. (2008) investigated the heat and mass transfer characteristics in a reformer, by numerical and investigation. They also proposed a new conception of the catalyst: layers of inert and catalyst. The new catalyst distribution proposed had the objective of improving the heat transfer in the catalyst medium, enhancing the production of hydrogen. Ventura (2008) developed a numerical simulation of a reactor using natural gas as fuel that includes the burner. The simulations were performed using a commercial program Fluent, for the burner zone, coupled with a UDF (User defined function), written in C++ language (SRP). The reforming reaction was simulated with a single first order rate and the products were considered in chemical equilibrium. For the validation of the SRP model, the results were compared with results obtained by Umicore. 2. Model Description For the present work computer model prepared by Jorge (1995) was used that included mass and energy balances based on a single reforming reaction with products in equilibrium. This model uses the finite volume discretization and was modified to include the new mechanisms and to allow the calculation of the flow. For the implementation of the kinetic mechanisms further than the main fuel

3 mass balance, a new balance was introduced for CO and the other species are obtained from elemental balances. The flow momentum balances are calculated to obtain the velocity in both directions (radial and axial) and the pressure. The pressure is calculated from the continuity equation, using the SIMPLE algorithm, which defines the pressure concerning the pressure in a reference point (in this case is the entry). The catalyst zone is a porous medium and corresponds to a pressure drop. For the pressure drop in porous medium corresponding to the catalyst bed, the friction factor, for the monolith case, was obtained from the correlation for square channels. For the fixed bed reactor was used the Ergun equation, using the friction factor developed presented for Macdonald et al. (1978). The program has the possibility for the user to choose from thermal equilibrium or consider individual energy balance to each phase. The individual energy balance considers heat transfer trough convection, conduction and radiation. For the radiation term, an equivalent conductibility is used. Due to the non-isotropic characteristics of e.g. the monolith properties are defined in the two directions axial and transversal. For the conduction some expressions were derived in the present work, including the radiation in the monolith. The radiation term for the radiation in the fixed bed of spheres was the equation presented by Bauer and Schlünder (1978). The convection for monolith was considered based on constant Nusselt number equal to 2.98 within the channels. For the fixed-bed of spheres, it was used a correlation mentioned in the literature, that uses the Colburn module, the porosity and the Reynolds number, defined by the spheres diameter. Mass transfer was exactly treated as the convection, considering the Sherwood number equal to the Nusselt number, and replacing the Prandtl number by the Schmidt number. Mass transfer rates are considered for the reactants between the bulk gas and surface. There are also mass transfer limitations within the catalyst that can only be quantified knowing its structure and here was considered through an internal mass transfer efficiency. The external mass transfer resistance was considered to be in series with the chemical kinetics with the mechanisms explained below. For the simulation of methane steam reforming, as previously mentioned, the reaction rates were based on the model developed by Xu and Froment (1989). The reactions considered are: And the correspondent rates are: Reaction (2.1): Reaction (2.2):

4 Reaction (2.3): The DEN parameter corresponds to the adsorption/desorption phenomena of reactants considered in the model: For the kinetic constant of each reaction and the adsorption constants present in the parameter DEN, the expression are: Table 1.1. Values for calculation of kinetic constant for reaction i and for calculation of adsorption constants of j specie i E [kjmol - A (k i) j ΔH [kjmol -1 ] A (K j) 1 ] 1 240,1 4, [kmolbar 1/2 kg cath -1 ] CO -70,65 8, [bar -1 ] 2 67,13 1, [kmolbar -1 kg cath -1 ] H 2-82,90 6, [bar -1 ] 3 243,9 1, [kmolbar 1/2 kg cath -1 ] CH 4-38,28 6, [bar -1 ] For the methanol model the considered reaction were the following: H 2O 88,68 1, The reaction rate equations can be expressed by: Reaction (2.10): Reaction (2.11): Reaction (2.12): Reaction (2.13): The reaction constants are also given by the expression (2.9). The necessary values are in table 1.2: Table 1.2. Values for rate constants calculation Reaction A (k r) E a [kjmol -1 ] (I) 1,12 [kmolkg -1 s -1 kpa -1 ] 76 (II) 0,0023 [kmolkg -1 s -1 kpa -1 ] 50 (III) 6,75 [kmolkg -1 s -1 kpa -1 ] 81 (IV) 2040 [kmolkg -1 s -1 kpa -2 ] 117 For the model is based in the following set of balance equations: Continuity Equation:

5 Mass Balance Where the term S i is the mass source for the i specie: For methanol is the same type of equation as 2.20, but the subscript is CH 3 OH. Energy Balance for thermal equilibrium Energy Balance for the solid phase Where S E is the source term for energy, related to reactions enthalpy: Energy Balance for the gas phase Momentum Balance The parameter S QMx/r is the source term of each balance and it is related to the pressure drop in each direction. 3. Results The simulations were performed with a grid of 40x20 elements. This grid resolution was set based on comparisons between successive grids up to 100x50 and small differences were obtained between the calculated flow fields. For the Umicore test case, the space velocity had a range from to h -1. The SCR was 3, the wall temperature was fixed at 1050ºC. The results were obtained, using both energy models: equilibrium and individual balance. For the lower space velocity efficiency was fitted for the internal diffusion of the reactants in the catalyst. The estimated value was 1.9%. Figure 1 represents the molar fraction of CO and CO 2 at the reactor outlet, for and simulation results. Figure 2 represents the molar fraction of CH 4, H 2, in dry basis as in figure 1 and the equivalent H 2 O in the same basis. Conversion is also represented. These results are for the thermal equilibrium model. It can be seen that the results of the model are closer to the ones for lower space velocities, as expected, once the adjustment of the efficiency was for that range of velocity. The figures show that, as the space velocity rise the conversion decrease, and to larger values of methane and water concentration in the products. For carbon monoxide and carbon dioxide the variation with space velocity is lower. Experimental results reveal more carbon dioxide then carbon monoxide. In the simulation results however the opposite occurs.

6 Molar fraction in dry basis Molar fraction in dry basis/conversion Molar Fractionin dry basis 0,12 0,11 0,10 0,09 0, CO CO Modelo CO2 CO2 Modelo GHSV[h -1 ] Figure 1. CO and CO 2 molar fractions for and models results, considering thermal equilibrium 1,00 0,50 0, H2O H2O Modelo Conversão Conversão Modelo H2 H2 Modelo CH4 CH4 Modelo GHSV[h -1 ] Figure 2. H 2 O, CH 4, H 2 and conversion results of thermal equilibrium model The diffusion efficiency was determined for the lower space velocity, where the temperature is higher. This means the sensibility to chemical kinetics is lower. For higher space velocities the temperature decreases and the reaction is further far from the chemical equilibrium, meaning the kinetics is more influent. The kinetics leading to the formation of CO 2 indicates a smaller conversion in the w.g.s reaction. So, CO fraction is calculated by excess, while the CO 2 fraction is calculated by defect. One possibility for a better adjustment of the results is to define de the internal diffusion efficiency for higher space velocities, where kinetics is more influent. That way, for lower space velocities the reaction reached closer to equilibrium and the molar fraction of carbon dioxide would be higher than the carbon monoxide one. An important fact should be considered in this analysis: for SCR=3, at atmospheric pressure, the equilibrium conditions indicate a molar fraction value of CO 2 higher than the CO molar fraction till 650ºC. For higher temperatures that relation inverts. This way, when the space velocity is higher, as the bed temperature is lower, the equilibrium value of CO is lower due to lower conversion of CH 4, and that is what is being predicted by the results. Using the individual calculation of phase temperature, the results are very similar, except for the CO/CO 2 molar fraction presented in the next figure: 0,12 0,10 0, GHSV[h ] CO CO Modelo 2 fases CO2 CO2 Modelo 2 fases Figure 3. CO and CO2 molar fraction for thermal individual balance The efficiency parameter (1.8%) was once again calculated for the lower space velocity. The temperature that is used for all the reactions including the water gas shift rate calculation is the solid

7 Temperature [ C] temperature. When the space velocity rises, the solid temperature decreases. This implies a deviation from the equilibrium. The temperature is enough to produce more carbon dioxide than carbon monoxide. The figure 4 represent two axial profiles of the temperatures, for a radial value of 1.04 mm and two space velocities: the lower and the higher Tequilíbrio Tequilíbrio Tsólido Tsólido Tgás Tgás 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 Axial coordinate[m] Figure 4. Axial Profiles of temperature for solid, gas and equilibrium temperature The figure 4 shows that the temperature has a higher drop for higher space velocities. It also shows that for lower space velocities, the temperature is rapidly recovered due to the smaller quantity of hydrogen formed and the product composition is influenced by the higher temperatures along the reactor as the reforming reaction is almost complete. The gas temperature, in the model of two phase heat transfer, has a slower variation and the difference between the gas and the solid is higher at the entry of the catalyst. Observing the reaction zone, it can be seen that the solid temperature is in average lower than the gas temperature. It also can be seen that the temperature of both phases is higher than equilibrium one, and for that the conversion is slightly higher for the two phase model. This figure justifies, also, the difference seen for the CO and CO 2 evolutions for both models. The temperature of the solid is lower than the equilibrium one, at the reaction zone entry, so for the model of two phase calculation, when the efficiency parameter is calculated, the kinetics is more influent than in the case of equilibrium. For the test case with the conditions of Farinha (2008), we have a reactor with 75 mm entry length, 50 or 100 mm of catalyst, and 25 mm of outlet length. The diameter is 10 mm. The catalyst was tested following a treatment consisting of a reduction preceded or not by an oxidation to eliminate eventual carbon deposits. The internal efficiency was adjusted for the lower space velocity with values of 0.9% without oxidation, while with the oxidation treatment the value rises up to 1.67%. The conversion results from simulations are very close to for the lower space velocities. The value of the efficiency was fitted for lower velocities, so it was expected to occur that fact. For selectivity the values from the simulation are completely different from the results. The results for the simulation are, once again, justified with the relation between chemical kinetics and equilibrium and show a small increase with both space velocity and temperature. The values have much larger variations exceeding what would be expected from chemical equilibrium. The figure 5 shows the difference in conversion, when the simulation uses the alternative placement of catalyst/inert.

8 Conversion [%] Conversion [%] T=800 C, Configuração regular T=800 C, Configuração alternada T=900 C, Configuração regular T=900 C, Configuração alternada GHSV[h -1 ] Figure 5. Comparison of the results for the two catalyst configuration As it can be seen, the conversion enhances when the alternative configuration is used. At 800ºC the conversion is higher 12, 15 and 17% at each space velocity. At 900ºC there is an improvement of 4, 7 and 10%. Once for 900ºC the conversion is already high, it hard to improve much more the conversion. For the results, the conversion for the three space velocities used (12223, 24446, h -1 ) was about 96%, for a temperature of 850ºC. For methanol there is a test case, based on the conditions used in the work of Neto and Azevedo (2008). The reactor had a diameter of 18.3 mm, a length of 280 mm, and reaction zone of 220 mm. It were used two different catalysts, both on fixed-bed: 1 mm spheres of CuZnO on silica and 3 mm spheres of CuZnO on alumina. The parameter for the internal diffusion was set for the lower flow. The results are closer for lower flow, and then diverge. That is due to the results were obtained in series. So the degradation of the catalyst might have influenced the results. The catalyst of 1 mm presents better results, once it has a larger surface area and the coating is the same (CuZnO). The selectivity showed to be high for both results. For a liquid volumetric flow of mlmin -1 the conversion is presented as function of the oven temperature in Figure 6: Figure 6. Conversion vs temperature for two phase temperature calculation for the SiO 2 catalyst The typical S curve was obtained. For higher temperatures the conversion is higher because the kinetic is improved. The 100% conversion, for the model, is achieved at 500ºC. The results shows the 100% is achieved ate 400ºC. The difference between results might be due to the efficiency defined For a different reactor temperature profiles were obtained. The reactor had a 200 mm length, a diameter of 15 mm and a reaction zone of 100 mm. The SCR is 1.5 and the volumetric flow rate is 1,319 mlmin -1. The diffusion efficiency was estimated in 1.42%. The model was tested with two conductivities (0.5 and 0.1 Wm -1 K -1 ). 0 Conversion - Model Conversion - Experimental Oven temperature[ C]

9 % Molar of Hydrogen % Molar of Carbon Monoxide Temperature [ C] ,06 0,11 0,16 Axial Coordinate [m] T externa 440ºC T interna 440ºC T interna 320ºC T externa 320ºC T interna 440ºC modelo, k=0.5 T parede 440ºC modelo T interna 320ºC modelo k=0.5 T parede 320ºC modelo T interna 440ºC modelo, k=0.1 T interna 320ºC modelo, k=0,1 Figure 7. Temperature profiles Figure 7 shows the axial profiles for two different oven temperatures. The profiles were obtained using a tube guide with thermocouples. For the higher furnace higher temperature a temperature drop in the reaction zone can be observed. This happens in the model and in the case. For the higher conductivity the profile is closer to the furnace temperature. The thermal gradient is higher in the 400ºC case, because more heat is transferred to the reaction, achieving 82% of conversion with a 0.1 conductivity. The conversion is about 67%. As it can be seen, the internal profile of temperature is closer to the external for lower temperature, because there is a lower thermal resistance. Another case was tested for methanol reforming, considering the conditions of Nagasaki (2003). The volume of reaction is 4.12x10-7 m 3, the space velocity is 16033h -1 and three temperatures were tested. The figure 8 and 9 shows the evolution of the molar fraction of CO and H 2 along the reaction zone. 0,5 0,4 0,3 0,2 0,1 0 0 Axial 2 coordinate 4 [cm] 6 523K- 573K- 623K- 523K-Modelo 573K- Modelo 623K-Modelo Figure 8. CO distribution along the reaction zone Axial Coordinate [cm] 523K- 573K- 623K- 523K-Modelo 573K-Modelo 623K-Modelo Figure 9. Hydrogen distribution along the reaction length As it can be seen the affinity between and model results is good. The results shows some irregularity and the model results show a less than linear profile along the reactor. An increase of 100 K in the temperature leads to a production of H 2 much higher at the exit of the

10 reactor. Remembering the figure 7, it might be due to that in these temperatures the mechanism is in the ascendant zone of the S curve, with 523 K at the bottom and 623 K ate the top of the curve. 4. Conclusions This work presents a model that can predict with reasonably temperature profiles and the outlet composition of steam reforming in test reactors. The unknown temperature profile in the wall of the reactor was one of the major difficulties to achieve better results. Further the models are limited by the lacking knowledge on internal diffusion. Also, by fitting the efficiency of the internal diffusion to the lower space velocities the results were influenced by the chemical equilibrium. It should be done to higher space velocity where kinetics has more influence. The comparisons of results for CO/CO 2 molar fraction show that the water gas shift reaction is far from equilibrium. For the methane test cases the result were consistent, and differences evidenced are due to unknown information like the wall real temperature, the catalyst characteristics and the real conductivity of both phases. For methanol the results were also good and consistent. For higher space velocities the conversion is lower due to the lower residence time. Higher temperature leads to higher conversion because improves the reaction rates. The heat transfer coefficients for convection showed to be high, once the thermal equilibrium results for temperature are similar to results obtained with the calculation for individual phase. 5. References Bauer R., Schündler E.U., Part I: Effective radial thermal conductivity of packings in gás flow, International Chemical Engineering, Volume 18, 1978, Pages Farinha J., Reformação de Metano com vapor de água em reformador de escala laboratorial, Tese de Mestrado, Instituto Superior Técnico, Setembro Jorge P.A., Dimensionamento, modelação e análise de um reactor para produção de hidrogénio, Course Final Work, Instituto Superior Técnico, Lee S., Bae J., Lim S., Park J., Improved configuration of supported nickel catalysts in a steam reformer for effective hydrogen production from methane, Journal of Power Sources, Volume 180, 2008, Pages Macdonald I. F., El-Sayed M. S., Mow K.; Dullen F. A. L., Flow trough Porous Media the Ergun Equation Revised, Ind. Eng. Chem. Fund., Volume 18, 1978, Page 198. Mizsey P., Newson E., Truong T., Hottinger P., The kinetics of methanol decomposition: a part of autothermal partial oxidation to produce hydrogen for fuel cells, Applied Catalysts A: General, Volume 213, Index 2, May 2001, Pages Neto R., Azevedo J.L.T., Actividade E3- Produção de Hidrogénio, Projecto EDEN, IDMEC, IST, Nagasaki T., Master Dissertation Thesis, Waseda University Graduate School of Science, Dept. Mec. Eng.,2003. Ventura C., Modeling of a Reformer with Integrated Burner, Master Thesis, Instituto Superior Técnico, Xu J., Froment G. F., Methane Steam Reforming, Methanation and Water-Gas Shift: I. Intrinsic Kinetics, American Institute of Chemical Engineers Journal, Volume 35, Index 1, 1989, Pages