High-Temperature Reaction in the Freeboard Region above a

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Ind. Eng. Chem. Res. 2010, 49, 2672–2680

High-Temperature Reaction in the Freeboard Region above a Bubbling Fluidized Bed Miloslav Hartman,* Otakar Trnka, Michael Pohorˇely´, and Karel Svoboda Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, 165 02 Prague 6-Suchdol, Czech Republic

A plug flow model is presented for the oxidation of hazardous carbon monoxide into inert carbon dioxide taking place in the freeboard region above a freely bubbling fluidized reactor. The extent of the reaction in oxygen- and water vapor-bearing flue gas is described as a function of the fraction of solids ejected into the freeboard from the bed surface, the relative throughput, the gas density, and the global rate of reaction. Experimental measurements were conducted to determine the axial concentration profiles of carbon monoxide and other species throughout the freeboard. Steady-state measurements were carried out in an electrically heated reactor with an inner diameter of 9.36 cm above a gently fluidized bed of heat-resistant ceramsite particles in which a precursive liguid fuel (isopropanol) was burned. The global burnout reaction is assumed to be first order in carbon monoxide and one-half order with respect to oxygen and water vapor. The rate parameters for CO and O2 reacting in the freeboard were determined from the measured concentration profiles. The numeric solutions of the model equations outline the possibilities and limitations for the performance of an afterburner chamber. Introduction The performance of a fluidized-bed reactor, operated under a given temperature and pressure, generally depends upon a combination of chemical factors such as thermodynamics, stoichiometry, and kinetics and a number of hydrodynamic factors such as residence time, bubble size, and gas distribution. The manner in which this combination is described, usually with different simplifying assumptions, constitutes different reactor models. There is widespread agreement that detailed modeling of fluidized-bed reactors should also take into account the reaction in the entry and exit regions of the bubbling bed1-3 as outlined in Figure 1. The ill-defined, embryonic stage of bubble development in the close vicinity of the gas distributor (grid) suggests the most intensive gas-solid contact in this section. Similarly, the temperature increases in the freeboard space above the bed in cases of exothermic gas-solid reactions indicate an additional conversion of reactant in this region. Thus, in general, it seems very realistic to model fluidized-bed reactors with three subsequent sections in mind: The narrow distributor (grid) zone,4,5 the bubbling bed itself,6-8 and the freeboard (space, region) above it. Our effort in this study was concentrated on exploring the performance of the freeboard, (i.e., the voluminous region above a dense bubbling bed). In a recent work of ours,9 we investigated the combustion of dried sewage sludge in a fluidized-bed reactor. The operating conditions employed ensured that no visible overbed burning of the sewage particles or the volatiles released occurred in any experimental run. Nevertheless, the influence of the freeboard on the overall combustor performance was significant. Experimental evidence indicated that the hot freeboard, with its low solid content, acted as an efficient afterburner chamber.10,11 Most useful models of freely bubbling fluidized beds are based on a two-phase theory of fluidization. The general assumption is that at gas velocities above the point of minimum fluidization, gas entering the bed is divided between the dense * To whom correspondence should be addressed. Tel.: +420 220 390 254. Fax: +420 220 661. E-mail: [email protected].

or interstitial (emulsion, continuous) phase and the bubble phase (bubbles, gas pockets). The type and design of the distributor determine the form of these heterogeneities, which are essentially empty of particles. In the bubbling bed, bubbles grow by coalescence and rise to the bed surface, where they burst.12,13 As the bubbles burst, solids are ejected from the wake of the gas bubbles above the bed surface. This region above the bed surface, where some particles are carried above the bubbling bed while others fall back to the bed, is considered the freeboard region.14-17 The entrainment rate of particles decreases considerably along the freeboard height. Therefore, the freeboard does not provide thermal stability as the dense fluidized bed does with its thermal ballast. On the other hand, it does not suffer from usually unwanted gas bypassing, which is commonplace with bubbling beds.

Figure 1. Schematic diagram of a fluidized-bed reactor with a dense, freely bubbling bed and freeboard region.

10.1021/ie901760f  2010 American Chemical Society Published on Web 02/11/2010

Ind. Eng. Chem. Res., Vol. 49, No. 6, 2010

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In this work, we wish to determine and describe the performance of the freeboard region above a dense bubbling fluidized bed under well-defined operating conditions. It is believed that our approach can be extended to other lean phase contacting units, such as fast or circulating fluidized beds. Oxidation Reaction. Important criteria for the performance evaluation of combustion or organic waste incineration processes usually include the concentration of carbon monoxide in the exit gas, CCO. For example, the combustion efficiency, CE, defined as CE ) CCO2 /(CCO2 + CCO)

(1)

indicates the effectiveness of a process to completely oxidize carbonaceous fuel or organic waste. Experimental evidence shows that concentrations of carbon monoxide in combustion products augment significantly before organics levels.18,19 Therefore, carbon monoxide concentrations in flue gas can generally be viewed as a conservative indicator of the combustion (oxidation) performance of any reaction unit. Although the overall reaction CO(g) + 0.5O2(g))CO2(g)

(2)

∆Ho(298.15 K) ) -282.96 kJ looks very simple, its detailed mechanism is still not understood well due to its complexity.20,21 The characteristics of reaction 2 include such striking features as sensitivity to quantities of water vapor and self-inhibition by higher amounts of carbon dioxide. A high surface area of particles in gas-solid suspensions can lead to the unwanted effective quenching of excited species and radicals recombining. Moreover, it appears that the extent of such reaction inhibition is affected by the temperature. It is also worth noting that reaction 2 is accompanied by a decrease in the mole number, i.e., ∆n ) -0.5 mol/mol of CO. Equilibrium Conditions. With the use of a standard thermochemical approach22-24 and newer thermodynamic data of Barin,25 the equilibrium constant of reaction 2 can be expressed algebraically as a function of temperature log Kp ) 14 685.04/T - 1.0704 log T+ (4.85775 × 10-4)T - (5.22338 × 10-8)T2 - 1.691676 (3) Similarly, the standard heat of reaction 2 can be described by a polynomial ∆Ho ) -281.14 - 0.0089T + (9.3 × 10-6)T2 (2 × 10-9)T3

(4)

Both eqs 3 and 4 were deduced from the tabulated thermochemical data in the range from 298 to 1900 K. As evident, aside from the equilibrium constant and the level of carbon monoxide and/or carbon dioxide, the equilibrium state of reaction 2 is also inherently affected by the partial pressure of oxygen as predicted by yCO ) yCO2 /[Kp(pyO2) ] 0.5

(5)

provided that the implicit assumption of ideal behavior of this reaction system remains plausible. Relationships 3 and 5 are presented in graphic form in Figure 2 for typical flue gas with yCO2 ) 0.15 and yO2 ) 0.06. As can be seen, thermodynamic constraints may become significant at temperatures higher than approximately 1050 °C, when the

Figure 2. Computed equilibrium concentration of carbon monoxide (yCO) as a function of thermodynamic temperature (T) at standard pressure. Predictions of eqs 3 and 5 for yCO2 ) 0.15, yO2 ) 0.06, and p ) 1.013 bar.

equilibrium concentration of carbon monoxide attains a value of 0.1 ppm by volume. Model for Carbon Monoxide Oxidation in a Vertical Freeboard. The system of gas flowing upward through the vertical freeboard region with uniformly dispersed inert solid particles thrown into it from the surface of the dense fluidized bed, as shown in Figure 1, is treated here under the following mostly simplifying assumptions: (1) Uniform conditions in the radial direction perpendicular to the axial flow. (2) The gas phase is in upward ideal plug flow. (3) The chemical reaction takes place in the empty space between particles. (4) The particle holdup in the vertical freeboard decreases with the distance from the bed surface. (5) The total molar flow rate through the freeboard is affected by the net consumption of molecules (moles) via oxidation reaction 2. (6) The freeboard is isothermal and in a steady-state mode of operation. A schematic flow diagram in Figure 1 depicts the freeboard and freely bubbling fluid bed with a perforated plate distributor; certain important flows, concentrations, solid hold-ups, and boundary conditions are also shown. Mass balance equations for the total molar flow rate and respective species over a differential element of the freeboard yield a set of six simple, coupled, presumably nonlinear, ordinary differential equations as follows du N )dw 2

(6)

where N is the dimensionless reaction term N) dyCO2 dw dyCO dw dyO2 dw dyH2O dw dyN2 dw

)

εrτ¯ g Fg

(7)

N (1 + 0.5yCO2) u

(8)

N ) - (1 - 0.5yCO) u )-

N (1 - yO2) 2u

(9) (10)

)

N y 2u H2O

(11)

)

N y 2u N2

(12)

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Table 1. Major Components of Ceramsite constituent

amount (wt %)

Al2O3 CaO Fe2O3 K2O MgO Mn3O4 Na2O P2O5 SiO2 TiO2

28.03 2.42 12.78 3.18 2.52 0.12 1.37 0.70 45.48 3.39

The boundary conditions are obvious; for the bottom of the freeboard (i.e., at the surface of the bubbling bed) we can write (u,yi,ε) ) (1,yi,ε)in (at w ) 0)

(13)

as indicated in Figure 1. The system of the equations above describes the concentration profiles of the respective species and the total flow rate profile in the freeboard. The freeboard performance depends on the rate of reaction, gas residence time, void fraction, and density of the gas. The fraction of carbon monoxide eliminated from the gas, i.e., its relative amount converted into carbon dioxide, in the freeboard can be expressed in terms of its concentrations and the molar flow rates at the inlet and outlet of the freeboard. X)

(yCO)in-(uyCO)out (yCO)in

(14)

Equations 6-12 form a set of simultaneous, nonlinear, ordinary differential equations of the first order with the given boundary conditions 13. In addition to several constants, the system also includes algebraic equations for the void fraction. The set of model equations above was conveniently solved using an explicit difference scheme with 100 increments (∆w ) 0.01). The basic physical condition

[∑ ] 5

(yi)calcd ) 1 ( 0.5 × 10-7

(14b)

i)1

was met at each value of w. Experimental Section Two different types of experiments were conducted to explore the freeboard performance: (1) The basic hydrodynamic characteristics were determined of a heat-resistant, particulate material (the minimum fluidizing velocity and the expansion and entrainment velocity for a bed of such material). (2) Steadystate gas concentration measurements of carbon monoxide, oxygen, and carbon dioxide were performed in the centerline of the freeboard above a hot, bubbling fluidized bed into which a precursory fuel (isopropanol) was introduced and burned. Materials Employed. Ceramsite was used as the heatresistant, smoothly fluidizable bed material. This term denotes an inexpensive, inert, and stable material which is manufactured via the high-temperature calcination of carbonaceous claystone rock at 1000 °C in an oxidizing environment.26 The chemical specifications of the calcined material are listed in Table 1. As can be seen, the main components of ceramsite are silicon dioxide (45 wt %), aluminum oxide (28 wt %), and iron oxide (13 wt %). Significant amounts of titanium oxide, alkali-earth metals, and alkali metals are also present. The main minerals found in ceramsite, with the use of X-ray diffraction analysis,

were mullit (Al6Si2O13, ∼58 wt %), quartz (SiO2, ∼20 wt %), hematite (Fe2O3, ∼20 wt %), kaolinite (Al2(OH)4Si2O5), and/ or cristobalite (SiO2). The physical properties of the ceramsite particles are as follows: The particle density (determined by mercury displacement), Fp ) 1470 kg/m3; the true solid density (determined by helium displacement), FHe ) 2,248 kg/m3; the fractional particle porosity, εp ) 0.3461. Commercial pellets of ceramsite were crushed, sieved, and calcined again for 2 h at 1000 °C in an electric muffle furnace. To smooth the sharp edges of the recalcined particles, they were vigorously fluidized for 4 h at ambient temperature. Then the smoothed and dedusted particles were carefully sieved by hand. The narrow fraction employed in this work was comprised of particles in the range of 0.25-0.40 mm with a mean (sieve) particle size of djp ) 0.325 mm. These particles belong to group B powders7,27 (sand-like solids) where interparticle forces are negligible and bubbles commence forming at or only slightly above the minimum fluidization velocity. The determined porosity of the just fluidized/just defluidized beds of these the particles amounted to εmf ) 0.52.28 To approximate a realistic nature of the oxidation process and ensure the homogeneity of the gas phase (very lean in carbon monoxide), isopropyl alcohol [(CH3)2CHOH, isopropanol] was employed in this work as a precursory carbonaceous fuel. Physical properties29 include a liquid density of 786 kg/ m3, a normal boiling point of 83 °C, an ignition point of 399 °C, and a net heating value of 30.620 kJ/kg. Filtered air with a relative humidity of φ ) 0.75, containing 2.1 vol. % of water vapor, was employed as a source of oxygen and a fluidizing gas. Dry air was considered here as a mixture of 20.95 vol % of oxygen and 79.05 vol % of nitrogen, i.e., their molar ratio amounts to k ) 3.7733 mol of N2/mol of O2. An effective method of routine stoichiometric and process calculations is outlined in the Appendix. Experimental Setup. Minimum fluidization velocities28 and entrainment (terminal) velocities30-32 of ceramsite particles at ambient and superambient temperatures were measured in the high-temperature reactor [9.36 cm inner diameter (i.d.)] that we used and described in our recent incineration studies.9,33 All combustion experiments were also conducted with this benchscale facility that was further modified for the needs of this work. The length of the electrically heated reactor tube above the perforated plate distributor was 98 cm. The whole reactor was thoroughly insulated to minimize heat loss. There was also a provision for independent preheating of the air entering the reactor, the flow rate of which was controlled by mass flow controllers. The temperature was measured at different spots along the height of the reactor by means of thermocouples placed in shielding tubes. The preheater and reactor tubes were heated by three independent electrical external coils. This makes it possible to control the respective temperatures of the inlet air, the dense fluid bed, and the freeboard region independently. Pressure taps were provided at appropriate points to measure the pressure drops. Carefully replicated measurements of the points of minimum fluidization and entrainment showed good reproducibility in the range of 2-6%. The precursive liquid fuel (isopropanol) was fed into the bottom of the fluidized bed. A linear dose pump was employed for accurate adjustment of the flow rate of the liquid fuel. It was introduced to the very bottom of the bed in a cooled tube. The level of the fuel inlet nozzle was about 10 mm above the gas distributor plate.


The reactor was fully instrumented to determine the required oxygen, CO, CO2, and water vapor concentrations in the gas phase. Continuous gas samples were withdrawn from the freeboard through a quartz sampling probe. This sampling tube was movable vertically, up or down in the centerline of the cylindrical freeboard. The end of the tube was packed with fine quartz wool to prevent particles and dust from blocking the analysis lines. Water vapor was removed from the gas stream to be analyzed in a condenser in the ice-water bath. The deeper removal of water vapor was achieved in a flask filled with calcium chloride. After the sampled gas was cleaned by special Teflon filters, the gas stream was analyzed. An infrared, crossinterference-compensating, Hartmann & Braun analyzer (UrasAdvance Optima System) was employed to determine the carbon monoxide concentration in the sampled product gas. The oxygen concentration in the gas was measured by a paramagnetic analyzer (Siemens Oxymat 5M). This employed experimental layout with the movable withdraw probe made it possible to measure concentration profiles throughout the freeboard. In order to specify the actual length of the freeboard as shown in Figure 1, we also explored the expansion of the bubbling bed of the ceramsite particles used in combustion experiments. The measurements of the bed expansion were conducted in a transparent glass fluidization column. The fluidization vessel was constructed of a hard glass tube, 400 cm high and 8 cm inner diameter (i.d.). The fluidization air was filtered and passed upward through the bed via a finely perforated plate distributor.8,12,13 The bed height was determined by direct visual observations as a mean level of the fluctuating surface of the more or less gently bubbling bed.

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Figure 3. Measured minimum fluidization velocity (Umf) of ceramsite at different temperatures (t). The symbols represent experimental values obtained under the following conditions: Mean (sieve) particle size, 0.325 mm; Archimedes number (Ar) ) 1816 - 67.5; and Reynolds number under minimum fluidization (Remf) ) 1.1 - 0.044.

Results and Discussion Incipient and Well-Fluidized State. As well established, quantities such as the minimum (incipient) fluidizing velocity, Umf, and the excess gas flow, U - Umf, most markedly affect the hydrodynamic behavior and performance of a fluidized bed, including bubble size, bed expansion, entrainment, and mixing of particles. The minimum fluidization velocity of dry ceramsite particles was appointed from the plot of the pressure drop of the bed versus the air velocity, when the flow rate of the air was gradually reduced from a well-fluidized state to the static bed.28 The points of incipient fluidization of the 0.325 mm particles (the mean, sieve size) were determined by experiments at temperatures in the range of 20-950 °C. The measured results are presented in Figure 3. As can be seen, the values of Umf decrease from 5.1 to 2.1 cm/s when the operating temperature is increased from 20 to 950 °C. This trend indicates that the point of minimum fluidization occurred on each occasion in the flow regime where the viscous energy losses outweighed the kinetic (inertia) energy losses34 at Remf ) 1.1 - 0.044. The entrainment velocity was determined from the plot of the pressure drop across the fluidized bed versus the air velocity. Details on this procedure can be found in recent studies by us.26,34 The values measured at elevated temperatures (up to 950 °C) decreased from 173 to 134 cm/s. The results are plotted in Figure 4. The slightly sigmoid shape of the experimental curve in this figure suggests that kinetic energy losses also tend to apply at lower temperatures (at higher entrainment velocities).30 It should be noted that the Reynolds number (Reem) varies from 37.3 at 20 °C to 2.74 at 950 °C. Knowledge of the fluid-bed expansion and its porosity (void fraction), which form part of the boundary conditions, is a prerequisite for the modeling or description of the freeboard region. The bed expansion is closely related to the bubbling

Figure 4. Measured mean entrainment (terminal) velocities (Uem) of ceramsite at different temperatures (t). The symbols represent experimental data obtained under the following conditions: Mean (sieve) particle size, 0.325 mm; Archimedes number (Ar) ) 1816-67.5; and Reynolds number at the mean entrainment velocity (Reem) ) 37.3-2.74.

phenomena35,36 in aggregative fluidized beds like ours. Due to their complexity, the bubbling phenomena are still far from being fully understood. The accurate height of a fluidized bed is not entirely easy to determine because the bed surface is subject to fluctuations, particularly at high gas velocities. As the two-phase theory suggests and our experience supports, the expansion of a given bed is mainly affected by the bubble flow through the bed, i.e., by the excess gas flow/velocity, (U - Umf). The average values of measured relative bed heights are plotted in Figure 5 against the superficial gas excess velocity. Over the explored range of the gas velocities (U - Umf ) 0-30 cm/s), the bed bubbled more or less gently, with a moderately undulating surface. Our experimental data on the bed expansion were fitted by means of the simple formula H/Hmf ) 1 + 0.032(U-Umf)0.702

(15)

with a degree of accuracy better than (9%. As shown in Figure 5, the fit of this equation to the measured results is fairly good. Correlation 15 provides a convenient means of interpolating the fluid-bed height within the range of variables involved in this experimentation, and a modest amount of extrapolation is also warranted.

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The material balance for the bed particles yields a relationship between the bubbling bed expansion ratio, H/Hmf, and the mean void fraction of the whole bed, jεb ε¯ b ) 1-(1-εmf)/(H/Hmf)

(16)

where the symbol εmf is the voidage of the (quiescent) bed under minimum fluidization conditions. Implicit in eq 16 is the assumption of single (mean) bubble size within the bed. Although it is a certain simplification, we believe that it reasonably reflects the essential behavior of bubbling fluidized beds. It should be remembered that the conditions at the top of the dense bubbling bed represent concurrently the boundary (inlet) conditions at the bottom of the freeboard as shown in Figure 1. A reduction in particle concentration (i.e., an increase in void fraction) with increasing freeboard height was also accounted for in the model. An exponential dependence was assumed ε ) 1-(1-ε¯ b)exp(-Chfw)

(17)

Figure 6. Dependence of void fraction in the freeboard (ε) on distance (h) above the surface of a dense bubbling fluidized bed: U - Umf ) 32.6 cm/s, Hmf ) 11.5 cm. The solid line shows the values predicted by eqs 15-18. (O) Experimental data points measured by means of a capacitance probe with 0.192 mm glass beads in a 9 cm metal column37 at room temperature.

in which the decay constant, C, is a linear function of the superficial excess gas velocity C ) 0.773-0.00902(U-Umf)

(18)

Relationships 17 and 18 were developed on the basis of extensive experimental data reported by Bakker and Heertjes.37 The authors measured the porosity distribution in the axis of a 9 cm i.d. bed of glass beads fluidized with air at ambient temperature and pressure. They employed a capacitance probe responding to a change in the local solid concentration.38,39 It is evident that the porosity in a certain fixed point in the freeboard is never strictly constant, and its fluctuations are not simple. Therefore, average values are taken by integration over time. Predictions of the proposed eqs 15-18 were subjected to testing with the use of the experimental data measured with 0.192 mm glass beads. Figure 6 illustrates a reasonably good agreement between the predicted porosity and the values measured at room temperature. The differences do not exceed approximately (9%. CO Oxidation Rate in the Freeboard. Quartz probe measurements of carbon monoxide concentrations were per-

Figure 7. Concentration profiles of carbon monoxide [yCO(w)] in the freeboard at different temperatures (t): Inlet superficial gas velocity, Uin ) 23.6 cm/s; total length of freeboard, hf ) 14.7 cm; mean gas residence time in the freeboard, jτg ) 0.625 s; inlet freeboard voidage, εin ) 0.624; mole fraction of oxygen, yO2 ) 0.059 - 0.058; mole fraction of water vapor, yH2O ) 0.136; mole fraction of carbon dioxide, yCO2 ) 0.087. (b) Experimental data points. The solid lines show the values predicted by the model.

formed in the central line of the cylindrical freeboard at temperatures in the range of 824-927 °C, and their results are plotted in Figure 7. The experimental data show a very important influence of temperature on the course of the oxidation reaction. As can be seen, the exit CO concentrations decrease from 102 ppm CO at the lowest temperatures to 101-100 ppm CO at the highest temperatures which were explored. In an attempt to describe quantitatively the oxidation performance of the freeboard, we assumed that the global rate of oxidation, r, occurring in eq 7, can be expressed as40 r ) A.f(T).yCO.yO20.5.yH2O0.5

(19)

where Figure 5. Measured relative bed expansion (H/Hmf) at different superficial excess gas velocities (U - Umf). The symbols represent experimental data obtained under the following conditions: Mean particle size of ceramsite, 0.325 mm; height of bed at the point of incipient fluidization (Hmf), 10.5 cm. The solid line shows the predictions of eq 15 (maximum relative deviation, 13%).

f(T) )

1 B exp 2 T T

( )

(20)

Symbols A and B represent by this time the unknown parameters. The available measured data are shown in Figure 7 as


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Table 2. Effective Kinetic Parameters for Oxidation of Carbon Monoxide (eqs 19 and 20) effective parameter

A [mol K2/(cm3 s)]

B (K)

value 95% confidence intervala variance

4.80 × 10 (5.280 × 106 2.218 × 106

14 770 (78.28 31.31

a

8

Upon the basis of the Student/Gosselt/Fisher distribution.

the sets of values yCO(w) for the whole length of the freeboard at five temperature levels between 824 and 927 °C. The parameters needed for eqs 19 and 20 were sought to minimize the standard deviation between the experimental concentration and the concentration estimated from the set of model eqs 6-13. Simplified simplex minimization, which had proved successful in our previous work,23,41 was employed as the optimization method. It should be noted that the fitted function, yCO(w,T), is not given by an analytical solution but is a numeric solution of a set of differential equations. The statistical evaluations are based on the Student t analysis, and the computational results of the nonlinear regression fitting are given in Table 2. The computed parameter B leads to a value of the apparent global activation energy as high as 122.8 kJ/mol. This is between the values of 62.8 and 134. kJ/mol reported in the literature.40 Figure 7 shows a good agreement between the computed profiles of carbon monoxide in the freeboard and the measured profiles. Of course, the freeboard model as well as the global reaction rate correlation developed here have the usual limitations and should be applied with caution outside the experimental conditions for which they were deduced. Computational Results. Reaction 2 is inherently accompanied by a decrease in the number of moles of the reaction mixture, which has been accounted for in our model of the freeboard. An example of such a decline is shown in Figure 8 for our operation range of low carbon monoxide concentrations. Although the decline in the overall gas flow rate is not great in this case, it cannot be neglected in general. For example, its knowledge is needed for the correct evaluation of the conversion of toxic carbon monoxide based upon the balance and embodied in eq 14. The relative amount of hazardous carbon monoxide converted into inert carbon dioxide in the freeboard (conversion, X) can serve as an important measure of the freeboard performance or its efficiency. This quantity is given by the solutions to a system

Figure 8. Decline of the relative superficial gas velocity (u) caused by the continuous oxidation of small amounts of carbon monoxide in the freeboard: Temperature, 850 °C; inlet concentration of CO, (yCO)in ) 0.004; outlet concentration of CO, (yCO)out ) 102 ppm; mean gas residence time, jτg ) 0.625 s; mole fractions of oxygen and water vapor, 0.059 - 0.057 and 0.136, respectively.

Figure 9. Dependence of the fraction of carbon monoxide (X) oxidized in the freeboard on the operating temperature (t) for a different mean gas residence time (τjg): Mole fractions of oxygen and water vapor, 0.059-0.057 and 0.136, respectively.

of differential eqs 6-12, with their boundary conditions 13, and by a set of algebraic relationships 15-20. Aside from the boundary conditions, these solutions depend upon a number of parameters and quantities occurring in the model equations. In essence, the mechanism of carbon monoxide conversion is dependent on the global rate of the oxidation reaction, the gas residence time, the void (solid) fraction in the freeboard, and the density of the gas phase. As is well established, the rate of carbon monoxide oxidation is a strong function of temperature. There is also general agreement that the burnout reaction is first order in carbon monoxide and approximately one-half order with respect to oxygen and water vapor. The work below is confined to the exploration of the influence of the operating temperature and mean gas residence time on the freeboard performance. The latter quantity is one of the fundamental practical parameters in the design of any chemical reactor as it relates its volume (size) to the throughput and the freeboard voidage. We did a systematic computation of the concentration and flow rate profiles by integrating the model equations. The attained (computed) conversion of carbon monoxide was evaluated from the concentrations and gas flow rates at the inlet and outlet of the freeboard as a practical measure (criterion) of its performance. Some results are plotted in Figure 9, where it is evident that the extent of CO oxidation in the freeboard increases remarkably with increasing temperature and gas residence time. For example, the presented results suggest that the four-nine conversion (i.e., X ) 0.9999; practically complete oxidation) can be reached at temperature of 938 °C and a mean gas residence time of 0.625 s or at 864 °C and jτg ) 1.31 s when excess oxygen (yO2 ) 0.059-0.057) and ample water vapor are available in the flue gas (yH2O ) 0.136). Some 15 years ago, we measured the axial temperature and concentration profiles in a pilot-plant (0.3 m × 0.3 m × 2 m) afterburner chamber equipped with a natural gas burner.11 At that time, our replicate experimental runs indicated safely that the complete combustion of carbon monoxide requires a gasphase residence time of at least 1.3 s under practical conditions of combustion (t > 800 °C, yO2 > 0.03). These previous findings on a much larger apparatus clearly support our present results, amassed with the use of an entirely different facility and a more rigorous approach to the problem. The results of our systematic computations provided a suitable basis for marking the boundaries for practically complete

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Figure 10. Relationship between the Celsius temperature (t) and the mean gas residence time (τjg) needed to attain virtually complete oxidation of carbon monoxide in the freeboard (X ) 0.9999): Mole fractions of oxygen and water vapor, 0.059-0.057 and 0.136, respectively.

the specific operation conditions for the efficient elimination of residual carbon monoxide from dilute flue gas. Other aspects of an afterburner reactor, such as a departure from the plug flow pattern and the possible occurrence of nonuniform temperature fields within the vessel, would also have to be taken into account in any realistic situation. Postlude. Low concentrations of carbon monoxide in the experiments may incite researchers to presume that the total molar flow rate through the freeboard is not affected by the net consumption of moles (molecules) by reaction 2. However, our experience indicates that this assumption is hardly plausible, at least from the standpoint of correct mass balance and computing. As demonstrated in Figure 11, the performance criterion CE (combustion efficiency), defined by eq 1, can bias or lose some of its informative value at lower conversions of carbon monoxide. While the combustion efficiency, as high as approximately 0.995, looks very optimistic, the corresponding conversion of carbon monoxide into carbon dioxide amounts to merely 0.85. Therefore, the conversion, introduced by eq 14, is employed as the performance criterion for the freeboard throughout the work. Conclusions

Figure 11. Relationship between the combustion efficiency (CE) and the conversion of carbon monoxide into carbon dioxide (X): Mole fractions of carbon dioxide and carbon monoxide, 0.0875-0.0905 and 3.58 × 10-4-0, respectively.

oxidation of carbon monoxide in the freeboard or in similar afterburner units. The term practically complete oxidation of CO is considered here as the state when the four-nine conversion of CO (i.e., X ) 0.9999) is attained. Instead of drawing numerous graphs of the model solutions, we developed a simple empirical relationship t ) 382 +

510.5 (for X ) 0.9999) τ¯ 0.2 g

(21)

The residual variance from this correlation indicates that t can be predicted within (0.6% (95% confidence interval over the range of the data). In its linearized form, eq 21 is shown in Figure 10. Equation 21 embodies the relationship between the Celsius temperature, t, and the mean gas residence time, jτg (in s), needed for the virtually complete elimination of carbon monoxide from flue gas (X ) 0.9999) provided that excess oxygen (yO2 ≈ 0.06) and ample water vapor (yH2O ≈ 0.14) are present in the reaction milieu. The computed results presented in this article are rather illustrative and not viewed as an actual, final design. Nevertheless, the findings rest on a solid engineering basis. They outline

This study indicates that a very significant amount of the oxidation of residual carbon monoxide can take place in the freeboard region above a dense bubbling bed. Most carbon monoxide present in wet, fuel-lean gas can be converted into carbon dioxide in the freeboard under adequate process conditions in terms of temperature and gas residence time. The simplified process model successfully describes measured gaseous species concentration profiles from an experimental, benchscale facility. The numeric solutions of the model equations, developed for the ideal plug flow behavior of the gas, suggest the operating conditions needed for the efficient oxidation of carbon monoxide in the freeboard. Experimental findings as well as model predictions indicate that the mean residence time of gas of 0.3-3 s and temperature of 1050-800 °C can be adequate for practically complete oxidation of residual carbon monoxide present in gas with excess oxygen and ample water vapor. Nomenclature AbbreViation ppm ) parts per million by volume Symbols A ) fitted reaction rate parameter, mol K2/(cm3 s) B ) fitted reaction rate parameter, K C ) fitted decay constant given by eq 18, 1/cm CE ) combustion efficiency defined by eq 1 Ci ) concentration of species “i” in the gas phase in eq 1 c ) number of atoms of carbon in the fuel formula djp ) mean particle size determined by sieving, mm, m Fr ) cross-sectional area of the reactor vessel; Fr ) 68.81 cm2 g ) acceleration due to gravity; g ) 9.807 m/s2 H ) average height of the expanded bubbling fluid bed given by eq 15, cm Hmf ) height of bed at the point of incipient fluidization, cm ∆H° ) standard heat of reaction 2, kJ/mol of CO h′ ) number of atoms of hydrogen in the fuel formula used in the definition of R h ) height above the fluid bed surface, cm hf ) Zr - H ) total height of freeboard; distance from the fluid bed surface to the exit of the gas stream, cm

Ind. Eng. Chem. Res., Vol. 49, No. 6, 2010 Kp ) pCO2*/[pCO* (pO2*) ] ) equilibrium constant for reaction 2, 1/bar0.5 k ) 0.7905/0.2095 ) 3.7733 ) mole ratio of nitrogen to oxygen in dry air ln PH2O* ) 18.1304 - 5041.68/T ) equilibrium pressure of water vapor given as a function of the thermodynamic temperature, kPa N ) ε rτjg/Fg ) dimensionless reaction term nf ) feed rate of fuel given by eq A3, mol of fuel/s ninw ) λR(1 + k + wa) ) amount of wet air used for combustion, mol of air/mol of fuel noutw ) λR(1 + k + wa) + ∆nw ) amount of wet exiting flue gas, mol/mol of fuel o ) number of atoms of oxygen in the fuel formula PH2O ) partial pressure of water vapor at a temperature of interest, k Pa p ) pressure, bar r ) global rate at which carbon monoxide is converted (oxidized) into carbon dioxide, mol/(cm3 s) T ) t + 273.15 ) thermodynamic temperature, K t ) Celsius temperature, °C U ) superficial gas velocity, cm/s, m/s U - Umf ) excess gas velocity/flow, cm/s Ueb ) superficial gas velocity at which entrainment begins, cm/s, m/s Uef ) superficial gas velocity at which virtually all particles are entrained, cm/s, m/s Uem ) (Ueb + Uef)/2 ) mean entrainment superficial gas velocity, cm/s, m/s Uin ) superficial gas velocity at the bottom of the freeboard (at w ) 0), cm/s, m/s Umf ) minimum fluidization velocity, cm/s u ) U/Uin ) relative superficial gas velocity w ) h/hf ) relative flow path length of gas in freeboard wa ) (1 + k)yH2Oa/(1 - yH2Oa) ) moisture in combustion air, mol of H2O/mol of O2 X ) fractional conversion of carbon monoxide into carbon dioxide defined by eq 14 yH2Oa ) φ PH2O*/101.325 ) mole fraction of water vapor in air yi ) mole (volume) fraction of species “i” in gas Zr ) H + hf ) distance from the distributor to the exit of the gas stream, cm 0.5

Fg ) 0.012187/T ) molar density of gas under standard (ambient) pressure, mol/cm3 FHe ) true (helium) solid density, kg/m3 Fp ) apparent (particle) density, kg/m3 jτg ) hf/Uin ) mean residence time parameter for gas in the freeboard, s φ ) PH2O/PH2O* ) relative humidity of air Other Symbols ln ) base e or natural logarithm log ) base 10 or Briggsian logarithm * ) equilibrium state or value Superscripts a ) air d ) dry basis m ) molar basis w ) wet basis Subscripts a ) air f ) fuel g ) gas in ) inlet (at the surface of the fluid bed) l ) liquid out ) outlet (at the exit from the freeboard)

Appendix. Combustion of Propanol in Wet Air The overall stoichiometry may be written as C3H8O(l) + λR(O2 + kN2 + waH2O)(g))3CO2(g) + (4 + λRwa)H2O(g) + λRkN2(g) + (λ-1)RO2(g) (A1) where R ) 4.5 mol of O2/mol of C3H8O, k ) 3.7733 mol of N2/mol of O2, and wa ) 0.098926 mol of H2O/mol of O2. The corresponding change in the total mole number in the gaseous phase caused by reaction A1 amounts to ∆nw ) 2.5 mol/mol of C3H8O. Two very useful tools for routine calculations were the following formulae relating the mole fraction of oxygen in the wet product gas, yO2w, to the coefficient of excess air, λ

Dimensionless Groups Ar ) Archimedes number; Ar ) djp3gFf(Fp - Ff)/µf2 Reem ) Reynolds number at the mean entrainment velocity; Reem ) UemdjpFf/µf Remf ) Reynolds number at the onset of fluidization; Remf ) UmfdjpFf/µf

λ)

1 + (∆nw /R)yO2w 1-(1 + k + wa)yO2w

(A2)

and the feed rate of propanol introduced into the reactor, nf, to the gas superficial velocity at the exit of the reactor, Uout, under the desired conditions of operation

Greek Letters R ) c + h′/4 - o/2 ) stoichiometric (theoretical, minimum) amount of oxygen needed for complete combustion, mol of O2/mol of C3H8O (fuel) ∆nw ) noutw - ninw ) h′/4 + o/2 ) change in the mole number in stoichiometric combustion on a wet basis, mol/mol of C3H8 (fuel) ε ) void fraction (porosity) in freeboard jεb ) mean void fraction (fractional porosity) of a fluidized bed given by eq 16 εmf ) bed voidage at the point of minimum fluidization λ ) excess air coefficient given by eq A2; ratio of actual air molar flow rate to stoichiometric air molar flow rate µf ) fluid viscosity; µair ) (4.261 × 10-7)T0.66, kg/(m s), Pa s Ff ) fluid (gas) density at the ambient pressure (101.325 k Pa); Fair ) 325.8/T, kg/m3

2679

nf )

FrUout Fg λR(1 + k + wa) + ∆nw

(A3)

It should be noted that the whole denominator in eq A3 gives the amount of wet gas product per mole of C3H8O, noutw, while its first term, λR(1 + k + wa), predicts the amount of wet air, naw, needed for the desired oxidation environment per mole of fuel. The concentration of carbon dioxide in the product gas was also checked by the measured oxygen concentration with the aid of eq A4 d yCO2 )

for λ > 1.

3 yd (λ - 1)R O2

(A4)

2680


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ReceiVed for reView November 6, 2009 ReVised manuscript receiVed January 21, 2010 Accepted January 28, 2010 IE901760F

High-Temperature Reaction in the Freeboard Region above a

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