1. Introduction
Recent stringent emission regulations and depletion of energy sources have imposed special requirements on combustion technologies for the new millennium. By now it is well known that hydrocarbon sources, the bedrock of economic wealth and combustion science, are being depleted 100 000 times faster than they are being replenished. These factors will no doubt demand the development of novel combustion techniques. Among other concepts, combustion in a porous media offers a possible technological breakthrough and solutions for the near and long term. It can provide the basis for development for new combustion systems. The study of porous media phenomena itself can be a multidisciplinary field ranging from mechanical and chemical to geological and petroleum applications [1].
Porous media combustion, also known as filtration combustion, is defined as the process in which a self-sustaining exothermal reactive wave propagates over a porous reagent by means of gaseous oxidizer filtration through an inert solid matrix towards the reaction zone. As an internally self-organized process of heat recuperation, filtration combustion of gaseous mixtures in porous media differs significantly from the homogeneous flames. This difference is attributed to the following main factors: the highly developed inner surface of the porous medium results in efficient heat transfer between gas and solid; dispersion of the gas flowing through a porous media increases effective diffusion and heat transfer in the gas phase. To further elaborate, once a gas mixture is ignited inside the media, the heat release from the intense reaction zone is transferred to the solid matrix that subsequently feeds a fraction of the energy to the solid layers immediately above and below. This process facilitates a combustion process that ensures stability in a wide range of gas filtration velocities, equivalence ratios, and power loads.
Stationary and transient systems are the two major design approaches commonly employed in porous combustion [2-8]. The first approach is widely used in radiant burners and surface combustor-heaters where the combustion zone is stabilized within the finite element of the porous matrix. The second (transient) approach involves a traveling wave representing an unsteady combustion zone freely propagating in either downstream or upstream direction in the inert porous media (IPM). Strong interstitial heat transfer results in a low degree of thermal non-equilibrium between gas and solid. These conditions correspond to the low-velocity regime of filtration gas combustion, according to classification given by Babkin [9]. The relative displacement of the combustion zone results in positive or negative enthalpy fluxes between the reacting gas and the solid matrix. As a result, observed combustion temperatures can be significantly different from the adiabatic predictions and are controlled mainly by the reaction chemistry and heat transfer mechanism. The upstream wave propagation, countercurrent to filtration velocity, results in under-adiabatic combustion temperatures, while the downstream propagation of the wave leads to the combustion in a super-adiabatic regime with temperatures much in excess of the adiabatic one. Super-adiabatic combustion significantly extends conventional flammability limits to the region of ultra-low heat content mixtures.
Superadiabatic filtration combustion of rich and ultra-rich mixtures creates a situation in which partial oxidation and/or thermal cracking of hydrocarbons take place. This technology for hydrogen or synthesis gas (or syngas, a gas mixture that contains varying amounts of carbon monoxide and hydrogen) production uses an IPM [10-13]. The fuels used in porous combustion systems are basically of gaseous form due to fluidity, volumetric capacity, and shorter mixing length scale [14-21]. Liquid fuel reactors have been developed and used to a smaller extent [22-30].
According with the theory and technology of filtration combustion and the required new combustion systems, a new hybrid porous reactor can be developed changing an inert solid volume fraction by solid fuels. Now the porous medium is composed of uniformly mixed aleatory solid fuel and inert particles [31]. This change produces
As a result of composed porous medium, observed combustion temperatures can be lower than the IPM values and are controlled mainly by the heterogeneous reaction chemistry and heat transfer mechanism. Upstream and downstream wave propagations are present in the hybrid porous reactor. The upstream wave propagation in the composite bed is similar to the inert bed but the downstream wave propagation show a flat temperature profile with practically constant temperature along the reactor.
The combustion temperature in composite bed decreases from rich to ultra-rich gas fuel-air mixtures, and also with the increase of solid fuel volume fraction in porous medium. That suggests a change of dominant kinetic mechanism and a shift from homogeneous to heterogeneous chemistry. At high downstream propagation velocities near the stoichiometric conditions the role of gas phase kinetics is dominant. In these conditions, the upstream wave propagation suppresses the heterogeneous oxidation processes by the complete consumption of oxidizer. At higher equivalence ratios, the wave propagation is slower. This increases the role of heterogeneous kinetics. As a result, the ignition and combustion temperatures drop. In turn, this affects the wave velocity. The mechanism of heterogeneous combustion becomes dominant for downstream wave propagation. The slowly reacting solid fuel is directly exposed to oxidizer. The ignition initiated over the solid phase is further transferred to the gas phase. It is possible to suggest that the structure of the wave in this case involves a heterogeneous reaction front followed by the gas phase reaction front. These fronts are followed by a slow endothermic reaction between the formed steam and solid/gaseous fuels.
The propagation of downstream hybrid combustion waves in the fuel loaded medium has resulted in wide combustion fronts with superadiabatic combustion temperatures. Due to the wide flat temperature profiles it has been found impossible to determine the wave velocity with sufficient accuracy. The flat temperature profile also suggests that the fuel particles are burning upstream of the front.
The use of rich and ultra-rich mixtures of gas fuel with air hybrid filtration combustion for hydrogen and syngas production has big potential. Hydrogen and syngas concentration increases with an increase of equivalence ratio for gas fuel/air mixtures in the inert porous medium and composite bed. In comparison, more high concentration of hydrogen and syngas is obtained in the composite porous media. Hydrogen conversion for gas fuel/air mixtures for hybrid filtration combustion waves is 50% for higher equivalence ratio.
2. Physical and mathematical description of the hybrid process
Lean combustion results in complete burnout of the hydrocarbon fuel, with the formation of carbon dioxide and water. Thus, both the composition of the final products and the heat release are well defined. In contrast to the lean case, the partial oxidation products of rich and ultra-rich waves are not clearly defined. In such a case, fuel is only partially oxidized in the wave, and the total heat release could be kinetically controlled by the degree of partial oxidation. As a result, chemical kinetics, heat release, and heat transfer are strongly coupled in the rich and ultra-rich waves, rendering it a more complicated and challenging phenomenon than the lean wave.
In the following we describe the governing equations, derived from fundamental principles, as well as some suitable models and assumptions that allow the formulation of a mathematical model. Such a model can be tractable by numerical simulation. We consider the bulk volume
where
2.1. Conservation of mass for gaseous species
For an arbitrary volume
The first term on the left-hand side (LHS) is of course the local rate of variation of the molar quantity of species
Although the diffusion velocities
where
Among other parameters, the filtration velocity
By their definition, the mole fractions must satisfy
so that, one of the
The gas volume
2.1.1. Homogeneous reaction
The homogenous reaction of the
where M
respectively. Here,
The forward and backward reaction rates can be obtained from the law of mass action. Considering the mechanism (6) as composed of elementary reactions, the order of the reactions corresponds to the stoichiometric coefficients, and therefore
In these expressions,
where the constants
where
for the enthalpy, and as
for the entropy (as, for example, NASA polynomials).
2.1.2. Volatiles release
The process of volatiles release from the solid fuel, by thermal decomposition and pyrolysis, can be modelled as one or several irreversible reactions, which we can represent symbolically as
to indicate the conversion of the solid fuel into volatiles {V1, V2, ,V
as a function of the solid particles temperature
The model requires the activation temperatures
due to the volatilization process.
2.1.3. Heterogeneous reaction
The solid substances S
For some other fuels, whose fixed carbon fraction is mostly C, such as wood pellets, the treatment of S
where
The mass rate of consumption, per unit of bulk volume, through the γ-th reaction of the fuel that has remained solid (in the S form), can be formulated as
where
for which the activation energy
The factor (1-
Taking into account the production and consumption of gaseous species by the reactions (19), the net production of species
where
In summary, the species mass conservation equations can be written more explicitly as
where the net sources of species
2.2. Conservation of mass for solid fuel
To derive an equation expressing the mass conservation of solid fuel we consider first a region of volume
where
whence the governing equation for the partial density of fuel in the solid phase becomes
The loss of mass of fuel by volatilization is given by the summation of the
The evaluation of the rates
where
so that the value of
2.3. Conservation of energy of the gas phase
For the analysis of energy conservation in the gas, we consider the thermal and the chemical energies of the gaseous species, and neglect the kinetic energy of the flow. The energy per mole of gas is then
The enthalpies of the different species (
where
The fluxes in
Generally, it is preferred to use the enthalpy as the primitive variable for the gas energy equation. In that case Eq. (34) reads as
The pressure terms appearing in (35) are also associated with mechanical energy of the flow. They contribute in part to the energy of deformation due to gas expansion (which is stored in the gas as thermal energy), and also to the flow acceleration due to pressure gradients (which changes the kinetic energy). As stated above, we consider these mechanical energy contributions negligible, in comparison with the thermal energy in a reactor. Consequently, the first two terms on the RHS of Eq. (35) are discarded.
The energy flux vector
In this equation we have introduced again Fick’s law for the diffusion velocities, while
According to the processes described previously, the energy source term
With regards to the enthalpy flow contributed by the volatiles, it can be calculated as
where the total molar flow of species
The heterogeneous reactions involve the adsorption of gaseous species into the fuel particles, and the desorption of the reaction products back to the gaseous phase. Using the heterogeneous reaction model described in sub-section 2.1.3, we have that for the γ-th of such reactions, the enthalpy transport associated with those adsorbed and desorbed flows could be in principle estimated as
In the first expression the enthalpies of the incoming species can be evaluated at the temperature
with
(By definition,
We look now to the third component of
where ζ is the heat transfer coefficient, which can be estimated from empirical relations for porous media, as for example [33]
In this expression the characteristic length for the Reynolds and Nusselt numbers is taken as two times the particles size
Upon substituting Eq. (36) into (35), the equation for energy conservation in the gas phase becomes
Recall that we are using total enthalpies
This equation of energy, coupled with the equations for mass conservation of species, and the equations for the solid phase, give rise to a system of simultaneous partial differential equations that must be solved by a numerical iterative scheme. In that case Eq. (44) can be solved for
in each iteration. This equation for
2.4. Conservation of energy of the solid phase
The conservation of energy for the solid phase can be analyzed in the same volume
or equivalently
where
The source
The influx
Upon substituting these expression into Eq. (47), and converting the surface integral into volume integral, the equation for energy conservation of the solid phase becomes
2.5. Summary
In this section, we have presented the formulation of a mathematical model for hybrid filtration combustion, along with some model assumptions that would allow a computational approach. Such treatment will depend of course on the boundary and initial conditions for particular reactor designs. As we have shown, a crucial factor for the modelling of these complex phenomena is the availability of model parameters such as ε, the composition of the volatiles
3. Hydrogen production by hybrid filtration combustion
In this section, we show experimental results for wave velocities, combustion temperature, and H2 and CO concentrations for hybrid combustion of gas and solid fuels in porous media.
3.1. Natural gas and coal particles
The porous medium is composed of uniformly mixed aleatory coal and alumina spheres with varying volume fractions. This section provide the data on natural gas-air flames stabilized inside hybrid porous media with a volumetric coal content from 0 to 75% for an equivalence ratio φ = 2.3 and a filtration velocity of 15 cm/s.
The solid temperatures recorded for hybrid filtration combustion in coal-alumina beds, decreased from 1537 K at 15 % of coal in porous media to 1217 K at 75 % (Fig. 1a). The wave velocity is reduced with increase of coal volume fraction. At high coal contents the wave velocity is limited by the oxygen availability and the bed displacement resulting from the coal consumption. The latter factor suggests that the wave velocity in the packed bed with 100% coal content will be close to zero.
The hydrogen concentration increased with an increase of coal content with the maximum of 22% at a coal content of 75%. The result shows that high combustion temperatures facilitate hydrogen production in hybrid filtration combustion. The carbon monoxide also increased with an increase of coal content.
The maximum hydrogen conversion reached 55% at a coal content of 75% compare to 35.1% for natural gas flames propagating in the inert porous bed (Fig. 1b).
3.2. Butane and wood pellets
The porous media was composed of uniformly mixed aleatory wood pellets and alumina spheres. The equal volumes of 5.6 mm solid alumina balls and wood pellets were mixed resulting in the packet bed with a porosity of ~40%. Experimental data were collected for a slightly increasing filtration velocity in a range of equivalence ratios from stoichiometry (φ = 1.0) to φ = 2.6.
The solid temperature of butane/air mixtures in the inert porous medium increases from 1510 K at φ = 1.45 to 1610 K at φ = 2.6 (Fig. 2a). The solid temperatures recorded for hybrid filtration combustion in wood pellets-alumina spheres porous media, decrease from 1477 K at φ = 1.45 to 1216 K at φ = 2.6. For butane/air mixtures in the inert and composite porous media the maximum absolute velocity value of ~0.012 cm/s is observed for φ = 1.45 (Fig. 2b).
Hydrogen concentration increases with an increase of equivalence ratio for butane/air mixtures in the inert porous medium. In comparison, more than four times higher concentration of hydrogen is measured for butane/air mixtures in the composite porous media made of alumina and wood pellets. For butane/air mixtures in the inert porous medium the concentration of carbon monoxide increased with equivalence ratio and for an-inert porous media the concentration of CO remains almost constant with the equivalence ratio.
The hydrogen yield is calculated using the initial hydrogen content in butane for the case of inert bed and the initial hydrogen content in butane and wood pellets for the case of the composite bed. The maximum yield recorded for the inert porous medium is close to 10% at φ = 2.6 (Fig. 2c). The maximum yield recorded for the composite pellets is ~48% at φ = 2.4.
3.3. Propane and polyethylene pellets
The reactor is filled with a uniformly mixed aleatory polyethylene pellets and alumina spheres whose diameter is 5.6 mm. The geometry of polyethylene pellets are 2.4x5.0x4.4 mm. Experimental data were collected at a range of equivalence ratios (φ) from φ =1.0 to φ =1.7. The air/propane flow rate was maintained constant at 5.7 L/min yielding a filtration velocity of 11.3 cm/s.
The solid temperature of propane/air mixtures in the inert porous medium decreases from 1159 K at φ = 1.0 to 987 K at φ = 1.2 (Fig. 3a). Then the temperature increase to 1346 K at φ = 1.7. The solid temperatures recorded for hybrid filtration combustion in polyethylene pellets-alumina spheres porous media, shows similar behaviour and decrease from 1215 K at φ = 1.0 to 1070 K at φ = 1.4. Then the temperature increase to 1279 K at φ = 1.7. The experimental results for propane/air mixtures in the inert and composite porous media upstream wave were recorded in all the range of equivalence ratios studied (Fig. 3b).
Hydrogen concentration increases with an increase of equivalence ratio for propane/air mixtures in the inert porous medium and composite porous media made of alumina and polyethylene pellets. The maximum generated mole fraction of hydrogen is 6.7% for hybrid propane. Carbon monoxide is also generated in both porous media reactor.
4. Conclusion
In this chapter we have defined the hybrid filtration combustion process. The physical phenomena involved as well as their mathematical description by the governing equations enforcing mass and energy conservation for both the gas and solid phases are discussed.
We presented experimental evidence that such a process of hybrid filtration combustion can actually be achieved in practice. In particular we showed applications for reformation of gaseous and solid fuels into hydrogen and syngas. This was shown for several combinations of gaseous and solid fuels.
AcknowledgementThe authors wish to acknowledge the support by the CONICYT-Chile (FONDECYT 1121188 and BASAL FB0821 - FB/05MT/11).
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