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Numerical simulation of a tubular solar reactor for methane cracking
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Numerical simulation of a tubular solar reactor for methane cracking F.J. Valde´s-Parada, H. Romero-Paredes*, G. Espinosa-Paredes A´rea de Ingenierı´a en Recursos Energe´ticos, Universidad Auto´noma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, 09340 Me´xico, D.F., Mexico
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abstract
Article history:
This study addresses the solar thermal cracking of methane for the co-production of
Received 24 August 2010
hydrogen and carbon black as a medium to avoid CO2 emissions from natural gas
Received in revised form
combustion processes. The objective of this work is to numerically simulate the transport
2 November 2010
processes of momentum heat and mass in an indirect heating solar reactor, which is fed
Accepted 5 December 2010
with an argon-methane mixture. The reactor is composed of a cubic cavity receiver, which
Available online 12 January 2011
absorbs concentrated solar irradiation through a quartz window and a graphite reaction tube is settled vertically inside this cavity. A series of numerical experiments were carried
Keywords:
out in order to gain a better understanding of the interaction between the several transport
Hydrogen production
phenomena taking place. The simulations showed that, in general, when the temperature
Solar reactor design
of the reaction chamber is higher than 2000 K, the methane conversion is practically 100%.
Numerical simulation
To validate our simulation results we compared them with available experimental data obtaining good agreement. Moreover, our results clearly evidence that most of the reaction takes place at the bottom of the reactor, which is the zone with the highest temperature profiles. Therefore, we propose modifications in the reactor design to increase conversion. The results of this work can thus serve to improve design and control of solar reactors for light hydrocarbons. Copyright ª 2010, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Efficient solar hydrogen production is a challenge that deserves serious (theoretical and experimental) efforts to make it a viable power alternative. The system is based on the use of concentrated solar radiation as the energy source for achieving high temperatures reactions in order to produce hydrogen [1]. Several paths are possible for this task: from transformation of various fossil and non-fossil fuels via different routes such as natural gas steam reforming, water splitting thermochemical cycles, gasification and/or pyrolysis of biomass that produce syngas and then, hydrogen with separation of carbon dioxide [2e4]directly produce carbon black [5], among others.
Most of the natural gas (NG) composition is methane, thus the study of solar reforming of methane is focused on transforming NG into hydrogen and carbon black as proposed by Lede´ et al. [6]. As a matter of fact, solar cracking of methane has also enabled the production of carbon nanotubes, which have a higher market value [7]. The expectations of the advantages in the syngas production and NG cracking to produce hydrogen with low CO2 emissions have led to work with solar reactors (coupled to solar concentrators) that allow reaching high temperatures [8]. These technologies can be regarded as a transition energy system in the path to sustainability energy production, based on the economy of hydrogen connected to renewable energy [9e14]. The design of solar reactors must establish conditions for momentum,
* Corresponding author. Tel.: þ52 55 5804 4648; fax: þ52 55 5804 4900. E-mail address: [email protected] (H. Romero-Paredes). 0360-3199/$ e see front matter Copyright ª 2010, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2010.12.022
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heat and mass transfer that enable high chemical conversions by efficiently capturing and using concentrated solar energy with high thermal and exergetic performance [13]. A challenge of the solar thermochemical engineering is the optimized design of the solar reactor. Indeed, the design and operation of novel receiver/reactor system capable to efficiently collect the concentrated solar radiation and perform the high temperature reaction is probably the main objective of this field. In order to scale up solar reactors, parameters such as the reactor volume, maximum working temperature, physicochemical properties of the construction materials, the reactants concentrations and temperature distribution have to be optimized. This can be achieved by taking into account the heat transfer characteristics, the reaction rates and the transient phenomena due to incoming concentrated solar flux. Relatively few studies have dealt with solar reactor modeling and simulation e.g. [13,15e21] have been focused onto radiative heat transfer within particle suspension exposed to concentrated solar radiation; these include the use of Monte Carlo (MC) methods, and transient models based on the MC and Rosseland approximations as well as deterministic approaches [22e32]. Other models and simulations have been developed in order to describe the temperature profile in the reactor and to have a method of multiphase flow in the case of solid particle dissociation reaction [17]. Furthermore, a cavity receiver with a tubular absorber using concentrated solar energy was studied for thermochemical processes, in particular for ZnO dissociation [33]. Recently Rodat et al. [5,34e36] have proposed an indirect heating tubular solar reactor for the pyrolysis of methane from natural gas for the co-production of hydrogen and carbon black. For this reactor configuration, Maag et al. [21] formulated a mathematical model that couples radiative heat transfer within the cavity receiver with radiation-convection-conduction heat transfer for reacting flow inside the absorber tubes. The results from the model showed good agreement with experimental data and were used to optimize the design of a 10 MW commercial-
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scale reactor. In this work we use the characteristics of the solar reactor studied by Rodat et al. [5] to perform numerical simulations for a reactor with a capacity up to 10 kW for the thermal dissociation of the methane. The simulated reactor is composed of an insulated cavity receiver that captures the solar concentrate irradiation flow. The cavity behavior approaches a black body. Under this configuration, the solar flux hits the walls of the cavity made of graphite and then the re-radiation hits on the tubular reaction zone composed of two concentric tubes that are settled vertically inside the cavity. The objective of this work is to evaluate the velocity, concentration and temperature profiles inside the reaction zone as a function of the concentration and flow of gas at the entrance of the reactor. To validate our modeling approach we compare our predictions with the experimental data from Rodat et al [5]. In addition, we carry out a detailed analysis at the bottom of the reaction zone, where most of the chemical reaction takes place. The results from this work should motivate more detailed design and optimization studies of this type of reactors.
2.
Solar reactor configuration
A sketch of the solar reactor under consideration is shown in Fig. 1. The reactor is made up of a receiver cavity made of graphite of cubical form and the radiation source is a parabolic dish concentrator (not show in the figure). Each side has 20 cm of length and the opening to the center of one of its faces measures 9 cm where solar concentrated radiation hits on the quartz window and enters the cavity. Within the chamber, four independent tubes of reaction are settled vertically at the center of the cavity, each of them working in parallel. In turn, each tube of reaction is made up of two concentric tubes. The inner tube has an internal diameter of 4 mm and 12 mm of external diameter. Further in this work, we analyze the effects of varying the length of the bottom part of the reactor;
Fig. 1 e Scheme of the tubular solar reactor and the receiver.
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however, as a first approach we consider the same length used in [5]. In addition, the external tube has 18 mm of internal diameter and 24 mm of external diameter. The total length of the external tube is 380 mm. In this way, the length exposed to radiant flux is 178 mm, whereas the rest of the tube has an isolation layer of 150 mm thickness in order to minimize the conduction losses. This isolated layer is composed by 3 different materials: graphite in contact with the cavity, (eg. ¼ 0.05 m), a middle layer made of refractory ceramic fiber (ef ¼ 0.05 m) and the last one of microporous isolation of zirconia-silica and calcium oxide (ea ¼ 0.05 m). A transparent window covers the entrance to the cavity, which aids to conserve an inert atmosphere inside the system in order to prevent graphite oxidation. Both direct concentrated solar radiation and infrared radiation emitted by the hot walls of the interior cavity help warming up the reactive tubes. For the purposes of the simulations that follow, we assume that there is only one reaction tube within the cavity.
3.
System description
In order to describe the physical process of the heat, mass and momentum transfer in the system, a simplified scheme of the physical solar reactor was considered as illustrated in Fig. 2. Here, we identify 5 regions, which are listed below along with the transport processes taking place, Region 1: Inner pipe (r0 r r1). The fluid enters the inner pipe at a specified temperature (Tin) and pressure (Pin). As the fluid passes through the inner pipe, its temperature is determined by the rate of heat transfer by conduction and convection and the heat exchange with the graphite pipe wall.
Region 2: Pipe wall (r1 r r2). The pipe wall temperature at r1 is determined by the rate of heat conduction from r2/r1 and the rate of heat convection between the wall and flow down the pipe and up in the annulus. Region 3: Annulus (r2 r r3). The temperature in this region is determined by the rate of heat conduction and convection into the reaction cavity (Region 5) and the rate of heat exchange between the annulus and the drill pipe wall. The fluid passing through the annulus is a mixture of reactant and products, depending of the reaction conversion and the temperatures reached. Region 4: Annulus wall (r3 r r4). The outer surface of this region is exposed to the radiation provided by the concentrator chamber. In previous studies, it has been assumed that the temperature is sufficiently high to be fixed throughout this surface. However in this work, we propose to abandon this assumption and in its place impose that the heat flux should be fixed at the boundary. This is less restrictive than fixing the temperature value and follows a more physical conception of the heat transfer process. Of course the price to be paid for this modification in the problem statement is that the numerical convergence is more difficult to reach since Neumann-type boundary conditions are known to be less stable than Dirichlet-type boundary conditions. Region 5: Reaction zone (r0 r r4), cz ˛ (z0, zi). In this portion of the system rapid changes in momentum, heat and mass transfer take place. Therefore, the dimensions of this region may determine the performance of the whole system. In the following paragraphs we present results from the numerical simulations considering the dimensions reported in [5] (see Fig. 1). Later on we will explore the influence of modifying the design dimensions of this region on the hydrogen production of the system.
Fig. 2 e Dimensions and regions of the tubular solar reactor.
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4.
Mathematical model
The momentum, heat and mass transfer differential equations that govern transport phenomena in the system are Momentum transfer :
in the g phase V$vg ¼ 0; 0 ¼ Vpg þ rg g þ mg V2 vg ; in the g phase (1a)
Heat transfer :
rg cpg vg $VTg ¼ kg V2 Tg DHRAg ; in the g phase in the k phase 0 ¼ kk V2 Tk ; (1b)
Mass transfer : vg $VcAg ¼ Dg V2 cAg RAg ; in the g phase
(1c)
In the above equations, the g and k-phases represent the gas and solid phases of the system, respectively. From Eq. (1a) we notice that the fluid phase has been assumed to be incompressible and Newtonian. In addition, the analysis has been restricted, as a first approach, to steady-state conditions and all transport properties (viscosity, density, thermal conductivities) are taken to be spatially invariant. The latter is reasonable under the assumption that the g and k-phases are homogeneous. Directing the attention to Eq. (1b), we observe that there is a heat sink term due to the endothermic reaction taking place in the fluid phase, whereas in the solid phase only steady-state heat conduction is considered. Finally, the structure of Eq. (1c) indicates that the methane (species A) is sufficiently diluted in the gas mixture in order for Fick’s law to be applicable. Moreover, it is stressed that methane adsorption and adsorption by particles is not considered in our derivations for the sake of simplicity. In this same expression, RAg is the molar reaction rate (mol/m3 s), and it is given by the following expression EA cAg RAg ¼ k0 exp Rg T
(2)
with k0 being the pre-exponential factor (for the cracking of methane, k0 ¼ 6.6 1013 s1), EA is the activation energy (370 kJ/mol) and Rg is the ideal gases constant (8.314 J/mol K). In this way, the heat transfer equations are coupled (only through the g-phase) with the momentum and mass transport equations, whereas the mass transport equation is coupled to Eqs. (1a) and (1b) through the convection and reaction terms, respectively. Eqs. (1a)e(1c) are subject to the following set of boundary conditions at Ai ; pg ¼ 1095:3 Pa; cAg ¼ 40mol=m3 ; Tg ¼ 298 K
(3a)
at Ao ; pg ¼ 958 Pa; n$DAg VcAg ¼ 0; n$kg VTg ¼ 0
(3b)
at Aw ; vg ¼ 0m=s; n$DAg VcAg ¼ 0; n$kg VTg ¼ n$kk VTk ; Tg ¼ Tk (3c) at AOT ; n$kk VTk ¼ 0
(3d)
at AIT ; n$kk VTk ¼ Q0
(3e)
where Ai, Ao and Aw represent the input, output and inner walls of the reactor, respectively. In addition, AOT and AIT
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denote the outer surface area of the reactor outside and inside the chamber, respectively. As stated in Eqs. (3c) and (3e), the reactor is isolated at AOT, and it is subject to a constant heat flux, Q0 at AIT. Because of the latter boundary condition, one may constrain the analysis only to the tubular reactor and not to the chamber and reactor sketched in Fig. 1. Furthermore, we assume that the system is axially symmetric, so that all the computations can be performed in two dimensions.
5.
Results and discussion
In order to solve the boundary-value problems presented in the previous section, we used the commercial finite-element solver Comsol Multiphysics 3.5a using adaptive mesh refinements to guarantee that the results are independent of the number of computational nodes. The linear system solver UMFPACK (included with the COMSOL package) was used for the computation of the velocity, concentration and temperature fields. Our numerical scheme consisted of solving firstly the momentum transport equations [Eq. (1a)] to determine the velocity field. This solution is later substituted in the heat and mass balance equations [Eqs. (1a) and (1c), respectively], which are in turn coupled through the reaction term. Under this framework, we present our observations for the momentum transport simulations to later discuss the heat and mass transfer processes.
5.1.
Velocity, temperature and concentration profiles
The circulation process in the solar reactor is similar to a heat exchanger system. In such process, the fluid phase moves downward inside the inner pipe (Region 1) and upward through the annulus between the inner and outer pipes (Region 3). From the velocity profiles in Fig. 3, it is evident that the largest velocity values are located at the center of Region 1, i.e., at r ¼ r0. Furthermore, in the reaction cavity (Region 5) located at the bottom of the system, the flow changes direction drastically as shown in Fig. 3. Obviously, the amplitude of the velocity oscillations near the bottom of the reaction cavity increases with the imposed pressure gradient and this, in turn determine the methane residence time in the system. From the previous section, we notice that, aside from the pressure gradient, the only remaining degree of freedom in the model is the heat flux, Q0, that is applied at the external surface of the reactor contained in the chamber (AIT). In Fig. 4, we show temperature distributions in the reactor corresponding to three values of Q0. We notice that the temperature distribution at the external graphite walls is highly sensitive to the variations in Q0. In this way, for Q0 ¼ 50 kW/m2, the outer walls of the reactor can reach a temperature of about 1300 K (Fig. 4a). This temperature can be increased to 2000 K for Q0 ¼ 160 kW/m2 as shown in Fig. 4c. In all cases, the most significant variations of the temperature occur in the annulus and its walls (Regions 3 and 4, respectively). In fact, according to the results shown in Fig. 4, the temperature of the gas mix in the inner pipe (Region 1) is about 1000 K for the three cases here analyzed. This means that the reaction cavity (Region 5) experiences drastic changes of temperatures from the outside
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Fig. 3 e Example of velocity fields at the top and bottom of the reactor for an inlet and outlet pressure values of 1095.3 and 958 Pa, respectively.
to the center of the reactor. This has a direct impact in the methane consumption rate as is explained below. In Fig. 5 we present the methane yield profiles near the reaction cavity for the same heat fluxes considered in Fig. 4. In this work, we define the methane yield in the same way as Rodat et al. (see Eq. (2) in ref. [5]). This figure clearly shows that if the external heat flux, Q0, is not sufficiently high, the conversion of methane to hydrogen and carbon can be severely hindered. In the simulations we fixed the input methane concentration to be 40 mol/m3; notice that the conversion is quite poor through almost all the inner pipe, until approaching the reaction zone. Since the largest temperatures of this region are concentrated in its corners, it is not surprising that they become sinks for the methane transport and reaction process. Despite of this, we observe that for Q0 ¼ 100 kW/m2, the annulus pipes carry a stream with a conversion of about 60%. This value is highly sensitive to variations of the external heat flux and the residence time; in fact, from Fig. 5b, we notice that it decreases to about 20% for Q0 ¼ 50 kW/m2. Finally, for Q0 ¼ 160 kW/m2, complete methane conversion is achieved since there is no methane in the reactor output.
5.2. Average temperature and methane concentration in the annulus While the above results provide a first appreciation about the heat and mass transfer processes taking place near the reaction zone, a more thorough analysis is in order. With this aim, we computed the cross-sectional concentration, methane yield and temperature, T, profiles in the annulus and plotted them for several values of Q0 in Fig. 6. We observe the following: The temperature decreases in a stepwise manner along the reactor. There are two constant-temperature sections: the first one corresponds to the graphite wall that separates Region 5 from the collector chamber (i.e., z ˛ [0,103] m); the second section corresponds to a portion of the annulus that is located outside of the collector chamber and it goes from z ¼ 102 m to z ¼ 101 m. Notice that both temperature decrements have approximately the same magnitude, but they take place over different lengths. Interestingly, the imposition of different values of heat fluxes only affects the first temperature section, while for the second section all
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Fig. 4 e Temperature profiles in the reactor taking a) Q0 [ 50 kW/m2, b) Q0 [ 100 kW/m2 and c) Q0 [ 160 kW/m2.
temperature profiles collapse in a single curve only to be separated again near the reactor output. This means that heat transfer along the annulus is driven mostly by the endothermic chemical reaction taking place. In fact, we observed that if one neglects the sink term in the heat balance equation, the temperature profiles no longer collapse into a single curve. If the incident heat flux is not sufficiently high, the annulus temperature is smaller than 1500 K, thus preventing methane to dissociate in hydrogen and carbon and leading to an almost flat methane conversion profile. As the heat flux is increased, methane cracking is enhanced mainly in the reaction cavity (i.e., for z ˛ [2 103,102] m). This is in agreement with the observations made in Fig. 5. Away from Region 5, there is a competition between mass transfer and reaction that results in a valley in the methane yield profiles at about z ¼ 102 m. This sudden increase in the methane concentration can be attributed to the sudden changes of
Fig. 5 e Methane yield in the reactor taking a) Q0 [ 50 kW/ m2, b) Q0 [ 100 kW/m2 and c) Q0 [ 160 kW/m2.
the velocity (see Fig. 3) that may, in some cases, promote convective mass transfer despite the system high temperatures. Once this transition zone is passed, the methane concentration decreases drastically if the annulus temperature is sufficiently high (i.e, T 1500 K). If this is not the case, methane conversion is reduced and this species may be present in the output despite the high temperatures in the reaction cavity. In this way, the presence of a valley in the yield profiles is attributed to the competition between the transport and reaction processes taking place in the outflow tubes of the reactor. At the bottom of the system we have the reaction zone, where high conversions are achieved, however further
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a
Table 2 of the work by Rodat et al [5]; a detailed explanation of the experimental setup is available in Section 4.2 of the same reference. As explained by these authors, they assumed that the wall temperature of the reactor was practically constant and for this reason they only report one temperature value, which was obtained by a pyrometer. In our formulation we assumed that the heat flux is constant at the external walls of the reactor. For this reason we conveniently modified the value of Q0 in our computer code in order to match the experimental conditions reported by Rodat et al. [5]. In addition, the pressure gradient was modified in each experiment in order to match the reported residence time. The comparison between our theoretical predictions and the experimental data is shown in Fig. 7. Overall, we found good agreement with the experimental results, in fact the largest mean absolute error was found to be smaller than 5%. Nevertheless, a more exigent validation in which the experimental and theoretical temperature and concentration profiles within the system are compared should be performed. The above follows from the observations drawn from Fig. 6b, where it shown that high output conversions can certainly be achieved, but this does not necessarily means that the system is working efficiently. In fact, in order to enhance methane cracking in the reaction zone, in the following paragraphs we present the results that our simulations provide when modifying the length of this part of the system.
b
5.4. Influence of the reaction cavity length over the methane concentration
Fig. 6 e Cross-sectional averaged a) temperature and b) methane yield profiles in the solar reactor annulus as functions of Q0.
on the tubes, convection and diffusion mechanisms compete with the reaction rate. In fact, if the residence time is not sufficient, the transport mechanisms should be expected to overcome the reaction sink. Later on the system, the reaction is still taking place due to the high temperatures reached, thus producing a sigmoidal-like curve after the reaction zone. To the best of our knowledge, the observation of this phenomenon has not been addressed in the literature, since the concentration measurements are typically made at the exit of the system where it is only observed that larger conversions are achieved by providing more heat at the reactor walls, which is also predicted from our simulations. For this reason, the results from Fig. 5b should encourage more detailed experimental measurements that can shed some new light to better understand the transport processes taking place in the system.
5.3.
From the above paragraphs we learned that the reaction cavity is the place where the most drastic changes in momentum, heat and mass transfer occur. We observed that it is necessary to apply relatively large heat fluxes at the external walls of the reactor in order to achieve complete methane conversion. However, it is not hard to reason that there may be applications in which this is not a feasible option. This motivates exploring alternatives that lead to high methane conversions without employing such high heat fluxes. In this work, we propose increasing the length of the
Comparison with experiments
In order to validate our modeling effort, we include in our analysis a comparison with the experimental data reported in
Fig. 7 e Comparison of experimental and theoretical predictions of methane yield.
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Fig. 8 e Decrement of the average methane concentration with the length of the reaction cavity for Q0 [ 100 kW/m2.
reaction zone (L) to achieve such high conversions. With this aim, let us define the average methane concentration in the reaction cavity as
cAg
rc
¼
1 Vrc
Z cAg dV
(4)
Vrc
where Vrc is the volume of the reaction cavity. In Fig. 8, we consider the case in which the reactor walls are exposed to heat flux Q0 ¼ 100 kW/m2. For comparison purposes, we introduce the following dimensionless concentration and reaction zone length, cAg rc L ; z¼ U¼ L0 cAg rc;0
(5)
here we have used the subscript 0 to refer to the design conditions employed by Rodat et al. [5]. In Fig. 8 we present the average methane yield at the reaction zone and at the reactor output for several values of z. While the latter is not significantly affected by the variations of the reaction zone length, the first one is certainly dependent of this length. We observe that triplicating the length of the reaction zone considerably increases the average methane conversion and can be regarded as an optimum value since further modifications did not result in drastic variations. These observations were verified under different operating conditions. This suggests that increasing the bottom conversion can result in a reduction of dead zones in the system and thus an overall performance increment.
6.
Conclusions
In this work we carried out numerical simulations of the momentum, heat and mass transfer phenomena for methane cracking in a solar reactor. Despite the assumptions involved in the mathematical model, the results from this work may serve as guide for future design and optimization efforts. Our simulations evidence the existence of a high reaction zone located at the bottom of the system. In this region, rapid
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variations of the velocity, concentration and temperature take place. For the configuration and operation conditions used by Rodat et al.[5], we notice that the methane concentration is considerably reduced in the reaction cavity when its temperature surpasses 1500 K. However, a high temperature in the reaction cavity does not necessarily guarantee complete methane conversion. We found that for values of the heat flux applied to the reactor walls larger than 100 kW/m2, the (crosssection) average concentration profiles in the annulus increase near the end of the reaction cavity and they decrease along the annulus channel. This behavior is attributed to the competition between the mass transfer and reaction mechanisms that govern the methane concentration values. Interestingly, the sinks of the methane yields profiles occur at the place where the two steps in the temperature profiles join (see Fig. 6a and b). To validate our modeling effort we have compared our predictions with the experimental data from Rodat et al. [5] obtaining good agreement. However, this comparison is constrained at the reactor output, and more rigorous verification is certainly in order. Motivated by the above observations, we studied the influence of increasing the length of the reaction cavity over methane conversion. Our simulations show that significant energy savings can be achieved by simply triplicating the size of this portion of the reactor. This should reduce the formation of dead zones in the system and thus increase the residence time and the overall system performance. Finally, it is worth pointing out that the analysis has been focused to the reactor assuming that its external walls are exposed to a constant heat flux, Q0. This approach departs from previous studies where the temperature is assumed constant at the reactor walls. In addition, it is desirable to relax some of the (physical and geometrical) assumptions involved in the model. For instance, all the results presented here are constrained to steady-state conditions; consequently, relevant transport mechanisms, such as carbon deposition have been disregarded. Obviously, more sophisticated computations result in more expensive and timeconsuming simulations. We are currently working on this type of simulations and a comparison with experimental data will be presented in a future work.
Nomenclature
Ai AIT Ao AOT Aw cAg hcAg i hcAg irc cpg EA g DAg
cross-section area of the inner pipe, m2 area of the reactor inside the collector chamber, m2 cross-section area of the annulus pipe, m2 area of the reactor outside the collector chamber, m2 area of the pipe and annulus walls, m2 molar concentration of methane, mol/m3 cross-sectional averaged molar concentration of methane, mol/m3 averaged molar concentration of methane in the reaction cavity, mol/m3 specific heat of the fluid phase, J/kg K activation energy, J/mol gravity vector, m2/s methane molecular diffusion coefficient, m2/s
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kj k0 pg Q0 RAg Rg r r0 r1 r2 r3 r4 Tj T U Vrc Vrc vg
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thermal conductivity of the j -phase ( j ¼ g, k), W/mK pre-exponential factor, s1 pressure of the fluid, Pa heat flux irradiated to the reactor walls, W/m2 methane consumption reaction rate, mol/m3s ideal gases constant, J/mol K radial direction, m center of the reactor, m radius of the inner pipe, m radius of the pipe wall, m radius of the annulus, m radius of the annulus wall, m temperature of the j -phase ( j ¼ g, k), K cross-sectional averaged temperature, K dimensionless average methane concentration domain occupied by the reaction cavity volume of the reaction cavity, m3 fluid velocity, m/s
Greek symbols fluid density, kg/m3 rg mg fluid viscosity, kg/ms z dimensionless length of the reaction cavity
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[13] Agrafiotis C, Pagkoura C, Lorenzou S, Kostoglou M, Konstandopoulos G. Hydrogen production in solar reactors. Catal Today 2007;127:265e77. [14] Muradov N, Veziroglu T. “Green” path from fossil-based to hydrogen economy: an overview of carbon-neutral technologies. Int J Hydrogen Energ 2008;33(23):6804e39. [15] Meier A, Ganz J, Steinfeld A. Modelling of a novel high temperature solar chemical reactor. Chem Eng Sci 1996;51 (11):3181e6. [16] Palumbo R, Keunecke M, Mo¨ller S, Mo¨ller S, Steinfeld A. Reflections on the design of solar thermal chemical reactors: thoughts in transformation. Energy 2004;29:727e44. [17] Abanades S, Charvin P, Flamant G. Design and simulation of a solar chemical reactor for the thermal reduction of metal oxides: case study of zinc oxide reduction. Chem Eng Sci 2007;62:6323e33. [18] Abanades S, Flamant G. Experimental study and modeling of a high - temperature solar chemical reactor for hydrogen production from methane cracking. Int J Hydrogen Energ 2007;32:1508e15. [19] Petrasch J, Steinfeld A. Dynamics of a solar thermochemical reactor for steam reforming of methane. Chem Eng Sci 2007; 62:4214e28. [20] Kogan A, Israeli M, Alacobi E. Production of hydrogen and carbon by solar thermal methane splitting. IV. Preliminary simulation of a confined tornado flow configuration by computational fluid dynamics. Int J Hydrogen Energ 2007;32:4800e10. [21] Maag, G., Rodat, S., Flamant, G., Steinfeld, A. Heat transfer model and scale-up of an entrained-flow solar reactor for the thermal decomposition of methane. Int J Hydrogen Energ 2010;35:13232e41. [22] Evans G, Houf H, Greif R, Crowe C. Gas particle flow within a high temperature solar cavity receiver including radiation heat transfer. J Sol Energ-T ASME 1987;109:134e42. [23] Miller F, Koenigsdorff R. Theoretical analysis of a hightemperature small-particle solar receiver. Sol Energ Mater 1991;24:210e21. [24] Mischler D, Steinfeld A. Nonisothermal nongray absorbingemitting-scattering suspension of Fe3O4 particles under concentrated solar irradiation. J Heat Trans-T ASME 1995; 117:346e54. [25] Hirsch D, Steinfeld A. Solar hydrogen production by thermal decomposition of natural gas using a vortex flow reactor. Int J Hydrogen Energ 2004;29:47e55. [26] Osinaga T, Olalde G, Steinfeld A. A solar carbothermal reduction of ZnO shrinking packed bed reactor modelling and experimental validation. Ind Eng Chem Res 2004;43:7981e8. [27] Lipinski W, Steinfeld A. Heterogeneous decomposition under direct irradiation. Int J Heat Mass Trans 2004;47:1907e16. [28] Dombrovsky L. Spectral model of absorption and scattering of thermal radiation by diesel fuel droplets. J High Temp 2002;40:242e8. [29] Dombrovsky L, Lipinski W, Steinfeld A. A diffusion-based approximate model for radiation heat transfer in a solar thermochemical reactor. J Quant Spectrosc Ra 2007;103: 601e10. [30] Klein H, Karni J, Ben-vi R, Bertocchi R. Heat transfer in a direct irradiated solar receiver/reactor for solid-gas reactions. Sol Energy 2007;81:1227e39. [31] Mu¨ller R, Steinfeld A. Band approximated radiative heat transfer analysis of a solar chemical reactor for the thermal dissociation of zinc oxide. Sol Energ 2007;81:1285e94. [32] Villafa´n-Vidales H, Arancibia-Bulnes C, Dehesa-Carrasco U, Romero-Paredes H. Monte carlo radiative transfer simulation of a cavity solar reactor for the reduction of cerium oxide. Int J Hydrogen Energ 2009;34:115e24. [33] Melchior T, Perkins C, Weimer A, Steinfeld A. A cavityreceiver containing a tubular absorber for high-temperature
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thermochemical processing using concentrated solar energy. Int J Ther Sci 2008;47(11):1496e503. [34] Rodat, S., Abanades, S., Flamant, G. Co-production of hydrogen and carbon black from solar thermal methane splitting in a tubular reactor prototype. Sol Energ, in press, Corrected Proof, doi:10.1016/j.solener.2010.02.016.
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[35] Rodat S, Abanades S, Flamant G. Experimental evaluation of indirect heating tubular reactors for solar methane pyrolysis. Int J Chem React Eng 2010;8. Article number A25. [36] Maag G, Zanganeh G, Steinfeld A. Solar thermal cracking of methane in a particle-flow reactor for the co-production of hydrogen and carbon. Int J Hydrogen Energ 2009;34(18):7676e85.
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Numerical simulation of a tubular solar reactor for methane cracking F.J. Valde´s-Parada, H. Romero-Paredes*, G. Espinosa-Paredes A´rea de Ingenierı´a en Recursos Energe´ticos, Universidad Auto´noma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, 09340 Me´xico, D.F., Mexico
article info
abstract
Article history:
This study addresses the solar thermal cracking of methane for the co-production of
Received 24 August 2010
hydrogen and carbon black as a medium to avoid CO2 emissions from natural gas
Received in revised form
combustion processes. The objective of this work is to numerically simulate the transport
2 November 2010
processes of momentum heat and mass in an indirect heating solar reactor, which is fed
Accepted 5 December 2010
with an argon-methane mixture. The reactor is composed of a cubic cavity receiver, which
Available online 12 January 2011
absorbs concentrated solar irradiation through a quartz window and a graphite reaction tube is settled vertically inside this cavity. A series of numerical experiments were carried
Keywords:
out in order to gain a better understanding of the interaction between the several transport
Hydrogen production
phenomena taking place. The simulations showed that, in general, when the temperature
Solar reactor design
of the reaction chamber is higher than 2000 K, the methane conversion is practically 100%.
Numerical simulation
To validate our simulation results we compared them with available experimental data obtaining good agreement. Moreover, our results clearly evidence that most of the reaction takes place at the bottom of the reactor, which is the zone with the highest temperature profiles. Therefore, we propose modifications in the reactor design to increase conversion. The results of this work can thus serve to improve design and control of solar reactors for light hydrocarbons. Copyright ª 2010, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Efficient solar hydrogen production is a challenge that deserves serious (theoretical and experimental) efforts to make it a viable power alternative. The system is based on the use of concentrated solar radiation as the energy source for achieving high temperatures reactions in order to produce hydrogen [1]. Several paths are possible for this task: from transformation of various fossil and non-fossil fuels via different routes such as natural gas steam reforming, water splitting thermochemical cycles, gasification and/or pyrolysis of biomass that produce syngas and then, hydrogen with separation of carbon dioxide [2e4]directly produce carbon black [5], among others.
Most of the natural gas (NG) composition is methane, thus the study of solar reforming of methane is focused on transforming NG into hydrogen and carbon black as proposed by Lede´ et al. [6]. As a matter of fact, solar cracking of methane has also enabled the production of carbon nanotubes, which have a higher market value [7]. The expectations of the advantages in the syngas production and NG cracking to produce hydrogen with low CO2 emissions have led to work with solar reactors (coupled to solar concentrators) that allow reaching high temperatures [8]. These technologies can be regarded as a transition energy system in the path to sustainability energy production, based on the economy of hydrogen connected to renewable energy [9e14]. The design of solar reactors must establish conditions for momentum,
* Corresponding author. Tel.: þ52 55 5804 4648; fax: þ52 55 5804 4900. E-mail address: [email protected] (H. Romero-Paredes). 0360-3199/$ e see front matter Copyright ª 2010, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2010.12.022
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heat and mass transfer that enable high chemical conversions by efficiently capturing and using concentrated solar energy with high thermal and exergetic performance [13]. A challenge of the solar thermochemical engineering is the optimized design of the solar reactor. Indeed, the design and operation of novel receiver/reactor system capable to efficiently collect the concentrated solar radiation and perform the high temperature reaction is probably the main objective of this field. In order to scale up solar reactors, parameters such as the reactor volume, maximum working temperature, physicochemical properties of the construction materials, the reactants concentrations and temperature distribution have to be optimized. This can be achieved by taking into account the heat transfer characteristics, the reaction rates and the transient phenomena due to incoming concentrated solar flux. Relatively few studies have dealt with solar reactor modeling and simulation e.g. [13,15e21] have been focused onto radiative heat transfer within particle suspension exposed to concentrated solar radiation; these include the use of Monte Carlo (MC) methods, and transient models based on the MC and Rosseland approximations as well as deterministic approaches [22e32]. Other models and simulations have been developed in order to describe the temperature profile in the reactor and to have a method of multiphase flow in the case of solid particle dissociation reaction [17]. Furthermore, a cavity receiver with a tubular absorber using concentrated solar energy was studied for thermochemical processes, in particular for ZnO dissociation [33]. Recently Rodat et al. [5,34e36] have proposed an indirect heating tubular solar reactor for the pyrolysis of methane from natural gas for the co-production of hydrogen and carbon black. For this reactor configuration, Maag et al. [21] formulated a mathematical model that couples radiative heat transfer within the cavity receiver with radiation-convection-conduction heat transfer for reacting flow inside the absorber tubes. The results from the model showed good agreement with experimental data and were used to optimize the design of a 10 MW commercial-
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scale reactor. In this work we use the characteristics of the solar reactor studied by Rodat et al. [5] to perform numerical simulations for a reactor with a capacity up to 10 kW for the thermal dissociation of the methane. The simulated reactor is composed of an insulated cavity receiver that captures the solar concentrate irradiation flow. The cavity behavior approaches a black body. Under this configuration, the solar flux hits the walls of the cavity made of graphite and then the re-radiation hits on the tubular reaction zone composed of two concentric tubes that are settled vertically inside the cavity. The objective of this work is to evaluate the velocity, concentration and temperature profiles inside the reaction zone as a function of the concentration and flow of gas at the entrance of the reactor. To validate our modeling approach we compare our predictions with the experimental data from Rodat et al [5]. In addition, we carry out a detailed analysis at the bottom of the reaction zone, where most of the chemical reaction takes place. The results from this work should motivate more detailed design and optimization studies of this type of reactors.
2.
Solar reactor configuration
A sketch of the solar reactor under consideration is shown in Fig. 1. The reactor is made up of a receiver cavity made of graphite of cubical form and the radiation source is a parabolic dish concentrator (not show in the figure). Each side has 20 cm of length and the opening to the center of one of its faces measures 9 cm where solar concentrated radiation hits on the quartz window and enters the cavity. Within the chamber, four independent tubes of reaction are settled vertically at the center of the cavity, each of them working in parallel. In turn, each tube of reaction is made up of two concentric tubes. The inner tube has an internal diameter of 4 mm and 12 mm of external diameter. Further in this work, we analyze the effects of varying the length of the bottom part of the reactor;
Fig. 1 e Scheme of the tubular solar reactor and the receiver.
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however, as a first approach we consider the same length used in [5]. In addition, the external tube has 18 mm of internal diameter and 24 mm of external diameter. The total length of the external tube is 380 mm. In this way, the length exposed to radiant flux is 178 mm, whereas the rest of the tube has an isolation layer of 150 mm thickness in order to minimize the conduction losses. This isolated layer is composed by 3 different materials: graphite in contact with the cavity, (eg. ¼ 0.05 m), a middle layer made of refractory ceramic fiber (ef ¼ 0.05 m) and the last one of microporous isolation of zirconia-silica and calcium oxide (ea ¼ 0.05 m). A transparent window covers the entrance to the cavity, which aids to conserve an inert atmosphere inside the system in order to prevent graphite oxidation. Both direct concentrated solar radiation and infrared radiation emitted by the hot walls of the interior cavity help warming up the reactive tubes. For the purposes of the simulations that follow, we assume that there is only one reaction tube within the cavity.
3.
System description
In order to describe the physical process of the heat, mass and momentum transfer in the system, a simplified scheme of the physical solar reactor was considered as illustrated in Fig. 2. Here, we identify 5 regions, which are listed below along with the transport processes taking place, Region 1: Inner pipe (r0 r r1). The fluid enters the inner pipe at a specified temperature (Tin) and pressure (Pin). As the fluid passes through the inner pipe, its temperature is determined by the rate of heat transfer by conduction and convection and the heat exchange with the graphite pipe wall.
Region 2: Pipe wall (r1 r r2). The pipe wall temperature at r1 is determined by the rate of heat conduction from r2/r1 and the rate of heat convection between the wall and flow down the pipe and up in the annulus. Region 3: Annulus (r2 r r3). The temperature in this region is determined by the rate of heat conduction and convection into the reaction cavity (Region 5) and the rate of heat exchange between the annulus and the drill pipe wall. The fluid passing through the annulus is a mixture of reactant and products, depending of the reaction conversion and the temperatures reached. Region 4: Annulus wall (r3 r r4). The outer surface of this region is exposed to the radiation provided by the concentrator chamber. In previous studies, it has been assumed that the temperature is sufficiently high to be fixed throughout this surface. However in this work, we propose to abandon this assumption and in its place impose that the heat flux should be fixed at the boundary. This is less restrictive than fixing the temperature value and follows a more physical conception of the heat transfer process. Of course the price to be paid for this modification in the problem statement is that the numerical convergence is more difficult to reach since Neumann-type boundary conditions are known to be less stable than Dirichlet-type boundary conditions. Region 5: Reaction zone (r0 r r4), cz ˛ (z0, zi). In this portion of the system rapid changes in momentum, heat and mass transfer take place. Therefore, the dimensions of this region may determine the performance of the whole system. In the following paragraphs we present results from the numerical simulations considering the dimensions reported in [5] (see Fig. 1). Later on we will explore the influence of modifying the design dimensions of this region on the hydrogen production of the system.
Fig. 2 e Dimensions and regions of the tubular solar reactor.
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4.
Mathematical model
The momentum, heat and mass transfer differential equations that govern transport phenomena in the system are Momentum transfer :
in the g phase V$vg ¼ 0; 0 ¼ Vpg þ rg g þ mg V2 vg ; in the g phase (1a)
Heat transfer :
rg cpg vg $VTg ¼ kg V2 Tg DHRAg ; in the g phase in the k phase 0 ¼ kk V2 Tk ; (1b)
Mass transfer : vg $VcAg ¼ Dg V2 cAg RAg ; in the g phase
(1c)
In the above equations, the g and k-phases represent the gas and solid phases of the system, respectively. From Eq. (1a) we notice that the fluid phase has been assumed to be incompressible and Newtonian. In addition, the analysis has been restricted, as a first approach, to steady-state conditions and all transport properties (viscosity, density, thermal conductivities) are taken to be spatially invariant. The latter is reasonable under the assumption that the g and k-phases are homogeneous. Directing the attention to Eq. (1b), we observe that there is a heat sink term due to the endothermic reaction taking place in the fluid phase, whereas in the solid phase only steady-state heat conduction is considered. Finally, the structure of Eq. (1c) indicates that the methane (species A) is sufficiently diluted in the gas mixture in order for Fick’s law to be applicable. Moreover, it is stressed that methane adsorption and adsorption by particles is not considered in our derivations for the sake of simplicity. In this same expression, RAg is the molar reaction rate (mol/m3 s), and it is given by the following expression EA cAg RAg ¼ k0 exp Rg T
(2)
with k0 being the pre-exponential factor (for the cracking of methane, k0 ¼ 6.6 1013 s1), EA is the activation energy (370 kJ/mol) and Rg is the ideal gases constant (8.314 J/mol K). In this way, the heat transfer equations are coupled (only through the g-phase) with the momentum and mass transport equations, whereas the mass transport equation is coupled to Eqs. (1a) and (1b) through the convection and reaction terms, respectively. Eqs. (1a)e(1c) are subject to the following set of boundary conditions at Ai ; pg ¼ 1095:3 Pa; cAg ¼ 40mol=m3 ; Tg ¼ 298 K
(3a)
at Ao ; pg ¼ 958 Pa; n$DAg VcAg ¼ 0; n$kg VTg ¼ 0
(3b)
at Aw ; vg ¼ 0m=s; n$DAg VcAg ¼ 0; n$kg VTg ¼ n$kk VTk ; Tg ¼ Tk (3c) at AOT ; n$kk VTk ¼ 0
(3d)
at AIT ; n$kk VTk ¼ Q0
(3e)
where Ai, Ao and Aw represent the input, output and inner walls of the reactor, respectively. In addition, AOT and AIT
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denote the outer surface area of the reactor outside and inside the chamber, respectively. As stated in Eqs. (3c) and (3e), the reactor is isolated at AOT, and it is subject to a constant heat flux, Q0 at AIT. Because of the latter boundary condition, one may constrain the analysis only to the tubular reactor and not to the chamber and reactor sketched in Fig. 1. Furthermore, we assume that the system is axially symmetric, so that all the computations can be performed in two dimensions.
5.
Results and discussion
In order to solve the boundary-value problems presented in the previous section, we used the commercial finite-element solver Comsol Multiphysics 3.5a using adaptive mesh refinements to guarantee that the results are independent of the number of computational nodes. The linear system solver UMFPACK (included with the COMSOL package) was used for the computation of the velocity, concentration and temperature fields. Our numerical scheme consisted of solving firstly the momentum transport equations [Eq. (1a)] to determine the velocity field. This solution is later substituted in the heat and mass balance equations [Eqs. (1a) and (1c), respectively], which are in turn coupled through the reaction term. Under this framework, we present our observations for the momentum transport simulations to later discuss the heat and mass transfer processes.
5.1.
Velocity, temperature and concentration profiles
The circulation process in the solar reactor is similar to a heat exchanger system. In such process, the fluid phase moves downward inside the inner pipe (Region 1) and upward through the annulus between the inner and outer pipes (Region 3). From the velocity profiles in Fig. 3, it is evident that the largest velocity values are located at the center of Region 1, i.e., at r ¼ r0. Furthermore, in the reaction cavity (Region 5) located at the bottom of the system, the flow changes direction drastically as shown in Fig. 3. Obviously, the amplitude of the velocity oscillations near the bottom of the reaction cavity increases with the imposed pressure gradient and this, in turn determine the methane residence time in the system. From the previous section, we notice that, aside from the pressure gradient, the only remaining degree of freedom in the model is the heat flux, Q0, that is applied at the external surface of the reactor contained in the chamber (AIT). In Fig. 4, we show temperature distributions in the reactor corresponding to three values of Q0. We notice that the temperature distribution at the external graphite walls is highly sensitive to the variations in Q0. In this way, for Q0 ¼ 50 kW/m2, the outer walls of the reactor can reach a temperature of about 1300 K (Fig. 4a). This temperature can be increased to 2000 K for Q0 ¼ 160 kW/m2 as shown in Fig. 4c. In all cases, the most significant variations of the temperature occur in the annulus and its walls (Regions 3 and 4, respectively). In fact, according to the results shown in Fig. 4, the temperature of the gas mix in the inner pipe (Region 1) is about 1000 K for the three cases here analyzed. This means that the reaction cavity (Region 5) experiences drastic changes of temperatures from the outside
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Fig. 3 e Example of velocity fields at the top and bottom of the reactor for an inlet and outlet pressure values of 1095.3 and 958 Pa, respectively.
to the center of the reactor. This has a direct impact in the methane consumption rate as is explained below. In Fig. 5 we present the methane yield profiles near the reaction cavity for the same heat fluxes considered in Fig. 4. In this work, we define the methane yield in the same way as Rodat et al. (see Eq. (2) in ref. [5]). This figure clearly shows that if the external heat flux, Q0, is not sufficiently high, the conversion of methane to hydrogen and carbon can be severely hindered. In the simulations we fixed the input methane concentration to be 40 mol/m3; notice that the conversion is quite poor through almost all the inner pipe, until approaching the reaction zone. Since the largest temperatures of this region are concentrated in its corners, it is not surprising that they become sinks for the methane transport and reaction process. Despite of this, we observe that for Q0 ¼ 100 kW/m2, the annulus pipes carry a stream with a conversion of about 60%. This value is highly sensitive to variations of the external heat flux and the residence time; in fact, from Fig. 5b, we notice that it decreases to about 20% for Q0 ¼ 50 kW/m2. Finally, for Q0 ¼ 160 kW/m2, complete methane conversion is achieved since there is no methane in the reactor output.
5.2. Average temperature and methane concentration in the annulus While the above results provide a first appreciation about the heat and mass transfer processes taking place near the reaction zone, a more thorough analysis is in order. With this aim, we computed the cross-sectional concentration, methane yield and temperature, T, profiles in the annulus and plotted them for several values of Q0 in Fig. 6. We observe the following: The temperature decreases in a stepwise manner along the reactor. There are two constant-temperature sections: the first one corresponds to the graphite wall that separates Region 5 from the collector chamber (i.e., z ˛ [0,103] m); the second section corresponds to a portion of the annulus that is located outside of the collector chamber and it goes from z ¼ 102 m to z ¼ 101 m. Notice that both temperature decrements have approximately the same magnitude, but they take place over different lengths. Interestingly, the imposition of different values of heat fluxes only affects the first temperature section, while for the second section all
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Fig. 4 e Temperature profiles in the reactor taking a) Q0 [ 50 kW/m2, b) Q0 [ 100 kW/m2 and c) Q0 [ 160 kW/m2.
temperature profiles collapse in a single curve only to be separated again near the reactor output. This means that heat transfer along the annulus is driven mostly by the endothermic chemical reaction taking place. In fact, we observed that if one neglects the sink term in the heat balance equation, the temperature profiles no longer collapse into a single curve. If the incident heat flux is not sufficiently high, the annulus temperature is smaller than 1500 K, thus preventing methane to dissociate in hydrogen and carbon and leading to an almost flat methane conversion profile. As the heat flux is increased, methane cracking is enhanced mainly in the reaction cavity (i.e., for z ˛ [2 103,102] m). This is in agreement with the observations made in Fig. 5. Away from Region 5, there is a competition between mass transfer and reaction that results in a valley in the methane yield profiles at about z ¼ 102 m. This sudden increase in the methane concentration can be attributed to the sudden changes of
Fig. 5 e Methane yield in the reactor taking a) Q0 [ 50 kW/ m2, b) Q0 [ 100 kW/m2 and c) Q0 [ 160 kW/m2.
the velocity (see Fig. 3) that may, in some cases, promote convective mass transfer despite the system high temperatures. Once this transition zone is passed, the methane concentration decreases drastically if the annulus temperature is sufficiently high (i.e, T 1500 K). If this is not the case, methane conversion is reduced and this species may be present in the output despite the high temperatures in the reaction cavity. In this way, the presence of a valley in the yield profiles is attributed to the competition between the transport and reaction processes taking place in the outflow tubes of the reactor. At the bottom of the system we have the reaction zone, where high conversions are achieved, however further
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a
Table 2 of the work by Rodat et al [5]; a detailed explanation of the experimental setup is available in Section 4.2 of the same reference. As explained by these authors, they assumed that the wall temperature of the reactor was practically constant and for this reason they only report one temperature value, which was obtained by a pyrometer. In our formulation we assumed that the heat flux is constant at the external walls of the reactor. For this reason we conveniently modified the value of Q0 in our computer code in order to match the experimental conditions reported by Rodat et al. [5]. In addition, the pressure gradient was modified in each experiment in order to match the reported residence time. The comparison between our theoretical predictions and the experimental data is shown in Fig. 7. Overall, we found good agreement with the experimental results, in fact the largest mean absolute error was found to be smaller than 5%. Nevertheless, a more exigent validation in which the experimental and theoretical temperature and concentration profiles within the system are compared should be performed. The above follows from the observations drawn from Fig. 6b, where it shown that high output conversions can certainly be achieved, but this does not necessarily means that the system is working efficiently. In fact, in order to enhance methane cracking in the reaction zone, in the following paragraphs we present the results that our simulations provide when modifying the length of this part of the system.
b
5.4. Influence of the reaction cavity length over the methane concentration
Fig. 6 e Cross-sectional averaged a) temperature and b) methane yield profiles in the solar reactor annulus as functions of Q0.
on the tubes, convection and diffusion mechanisms compete with the reaction rate. In fact, if the residence time is not sufficient, the transport mechanisms should be expected to overcome the reaction sink. Later on the system, the reaction is still taking place due to the high temperatures reached, thus producing a sigmoidal-like curve after the reaction zone. To the best of our knowledge, the observation of this phenomenon has not been addressed in the literature, since the concentration measurements are typically made at the exit of the system where it is only observed that larger conversions are achieved by providing more heat at the reactor walls, which is also predicted from our simulations. For this reason, the results from Fig. 5b should encourage more detailed experimental measurements that can shed some new light to better understand the transport processes taking place in the system.
5.3.
From the above paragraphs we learned that the reaction cavity is the place where the most drastic changes in momentum, heat and mass transfer occur. We observed that it is necessary to apply relatively large heat fluxes at the external walls of the reactor in order to achieve complete methane conversion. However, it is not hard to reason that there may be applications in which this is not a feasible option. This motivates exploring alternatives that lead to high methane conversions without employing such high heat fluxes. In this work, we propose increasing the length of the
Comparison with experiments
In order to validate our modeling effort, we include in our analysis a comparison with the experimental data reported in
Fig. 7 e Comparison of experimental and theoretical predictions of methane yield.
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Fig. 8 e Decrement of the average methane concentration with the length of the reaction cavity for Q0 [ 100 kW/m2.
reaction zone (L) to achieve such high conversions. With this aim, let us define the average methane concentration in the reaction cavity as
cAg
rc
¼
1 Vrc
Z cAg dV
(4)
Vrc
where Vrc is the volume of the reaction cavity. In Fig. 8, we consider the case in which the reactor walls are exposed to heat flux Q0 ¼ 100 kW/m2. For comparison purposes, we introduce the following dimensionless concentration and reaction zone length, cAg rc L ; z¼ U¼ L0 cAg rc;0
(5)
here we have used the subscript 0 to refer to the design conditions employed by Rodat et al. [5]. In Fig. 8 we present the average methane yield at the reaction zone and at the reactor output for several values of z. While the latter is not significantly affected by the variations of the reaction zone length, the first one is certainly dependent of this length. We observe that triplicating the length of the reaction zone considerably increases the average methane conversion and can be regarded as an optimum value since further modifications did not result in drastic variations. These observations were verified under different operating conditions. This suggests that increasing the bottom conversion can result in a reduction of dead zones in the system and thus an overall performance increment.
6.
Conclusions
In this work we carried out numerical simulations of the momentum, heat and mass transfer phenomena for methane cracking in a solar reactor. Despite the assumptions involved in the mathematical model, the results from this work may serve as guide for future design and optimization efforts. Our simulations evidence the existence of a high reaction zone located at the bottom of the system. In this region, rapid
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variations of the velocity, concentration and temperature take place. For the configuration and operation conditions used by Rodat et al.[5], we notice that the methane concentration is considerably reduced in the reaction cavity when its temperature surpasses 1500 K. However, a high temperature in the reaction cavity does not necessarily guarantee complete methane conversion. We found that for values of the heat flux applied to the reactor walls larger than 100 kW/m2, the (crosssection) average concentration profiles in the annulus increase near the end of the reaction cavity and they decrease along the annulus channel. This behavior is attributed to the competition between the mass transfer and reaction mechanisms that govern the methane concentration values. Interestingly, the sinks of the methane yields profiles occur at the place where the two steps in the temperature profiles join (see Fig. 6a and b). To validate our modeling effort we have compared our predictions with the experimental data from Rodat et al. [5] obtaining good agreement. However, this comparison is constrained at the reactor output, and more rigorous verification is certainly in order. Motivated by the above observations, we studied the influence of increasing the length of the reaction cavity over methane conversion. Our simulations show that significant energy savings can be achieved by simply triplicating the size of this portion of the reactor. This should reduce the formation of dead zones in the system and thus increase the residence time and the overall system performance. Finally, it is worth pointing out that the analysis has been focused to the reactor assuming that its external walls are exposed to a constant heat flux, Q0. This approach departs from previous studies where the temperature is assumed constant at the reactor walls. In addition, it is desirable to relax some of the (physical and geometrical) assumptions involved in the model. For instance, all the results presented here are constrained to steady-state conditions; consequently, relevant transport mechanisms, such as carbon deposition have been disregarded. Obviously, more sophisticated computations result in more expensive and timeconsuming simulations. We are currently working on this type of simulations and a comparison with experimental data will be presented in a future work.
Nomenclature
Ai AIT Ao AOT Aw cAg hcAg i hcAg irc cpg EA g DAg
cross-section area of the inner pipe, m2 area of the reactor inside the collector chamber, m2 cross-section area of the annulus pipe, m2 area of the reactor outside the collector chamber, m2 area of the pipe and annulus walls, m2 molar concentration of methane, mol/m3 cross-sectional averaged molar concentration of methane, mol/m3 averaged molar concentration of methane in the reaction cavity, mol/m3 specific heat of the fluid phase, J/kg K activation energy, J/mol gravity vector, m2/s methane molecular diffusion coefficient, m2/s
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kj k0 pg Q0 RAg Rg r r0 r1 r2 r3 r4 Tj T U Vrc Vrc vg
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 3 3 5 4 e3 3 6 3
thermal conductivity of the j -phase ( j ¼ g, k), W/mK pre-exponential factor, s1 pressure of the fluid, Pa heat flux irradiated to the reactor walls, W/m2 methane consumption reaction rate, mol/m3s ideal gases constant, J/mol K radial direction, m center of the reactor, m radius of the inner pipe, m radius of the pipe wall, m radius of the annulus, m radius of the annulus wall, m temperature of the j -phase ( j ¼ g, k), K cross-sectional averaged temperature, K dimensionless average methane concentration domain occupied by the reaction cavity volume of the reaction cavity, m3 fluid velocity, m/s
Greek symbols fluid density, kg/m3 rg mg fluid viscosity, kg/ms z dimensionless length of the reaction cavity
references
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