Time-Dependent Combustion of Solid Fuels in a Fixed-Bed

Article pubs.acs.org/EF

Time-Dependent Combustion of Solid Fuels in a Fixed-Bed: Measurements and Mathematical Modeling Rafał Buczyński,† Roman Weber,*,† Andrzej Szlek,‡ and Radovan Nosek§ †

Clausthal University of Technology, Institute of Energy Process Engineering and Fuel Technology, Agricolastrasse 4, 38678 Clausthal-Zellerfeld, Germany ‡ Silesian University of Technology, Institute of Thermal Technology, Konarskiego 22, 44-101 Gliwice, Poland § University of Zilina, Univerzitna 8215/1 01026 Zilina, Slovakia ABSTRACT: This work is concerned with domestic boilers burning solid fuels. Time-dependent coal combustion in the counter-current fixed-bed has been investigated using both measurements and mathematical modeling. Three-dimensional, timedependent model of the fixed-bed has been developed as a submodel to a computational fluid dynamics (CFD)-based model of the whole boiler. The overall 0.0177 kg/(m2 s) and 0.0266 kg/(m2 s) coal combustion rates have been observed for air velocities of 0.17 m/s and 0.26 m/s, respectively. Two temperature peaks have been observed: one propagating downward the bed and the other one moving upward from the bed bottom. The developed three-dimensional model has demonstrated good agreement with the measured data. The char oxidation rate is paramount in predicting the temperature−time history of the bed. A 20% increase in its rate has resulted in a 20% increase in the overall combustion rate. A 20% increase in the fuel density has slowed down the combustion rate by around 5%. A 20% increase in the effective thermal conductivity of the fixed-bed has resulted in minor changes.

1. INTRODUCTION AND OBJECTIVES Fixed-bed combustion and gasification of solid fuels have been regarded for long as “old fashioned” technologies whose renaissance took place in the 1950's and 60's. Nowadays, however, due to the current energy problems associated with climate changes, both technologies have experienced a revival, which originates from the need of electricity production from biomass and low-grade fuels. The viable technological option of processing mixtures of coal and biomass, without pulverizing the fuels, makes both technologies economically attractive. The Koizumi’s1 paper is perhaps one of the first publications concerning fixed-bed combustion of chars. The Essenhigh’s group produced a substantial body of measured data on gasification of an anthracite in air/steam mixtures, as exemplified by ref 2. What followed was the work of Purnomo et al.3 on downdraft pressurized combustion of wood chips. More recently, due to the increased importance of biomass, a proliferation of papers on fixed-bed experiments and modeling can be observed, as exemplified by refs 4−9. The objective of our research is the development of a threedimensional (3D) mathematical model for predicting timedependent processes occurring in fixed-beds of coal and/or coal-biomass mixtures. The aim is to develop a mathematical tool for calculating not only the rate with which the combustion front moves along the bed but also to predict the timedependent composition of gases leaving the bed. The fixed-bed model forms the heart of an overall 3D computational fluid dynamics (CFD)-based model10 for predicting the performance of a small scale domestic retort boiler, shown in Figure 1. The boiler consists of three parts: a fuel container with a screwfeeder, a radiative section with a retort-burner, and a convective section. The retort-burner is an essential element of the boiler into which combustion air is supplied through a set of holes © 2012 American Chemical Society

Figure 1. Retort boiler for domestic applications (15 kW thermal input).

located at the bottom and on the retort side walls. Combustion takes place both in the retort-burner and in the space above it. The boiler is furnished with a deflector (suspended above the retort) whose role is to prolong presence of combustion products in the high temperature zone. To initiate the combustion, a small amount of volatile liquid fuel is spread on the top layer of the solid fuel and ignited using a torch. The 3D CFD-based mathematical model has been developed and used for optimization of the boiler performance.10 In this paper, we focus exclusively on the fixed-bed (retort-burner) submodel, which constitutes the heart of the 3D boiler model. Since the retort burner (not described in this paper) possesses 3D geometry, the fixed-bed model is also 3D. Reviewing the lengthy literature on both experiments and mathematical modeling of fixed bed processes is certainly beyond the scope of this paper and can be found, for example, Received: April 21, 2012 Revised: June 20, 2012 Published: June 25, 2012 4767

dx.doi.org/10.1021/ef300676r | Energy Fuels 2012, 26, 4767−4774

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in the publication of Saastamoinen and Taipale.8 However, the work of Horttanaien et. al9 contains a mathematical model whose essence is similar to our formulation. More precisely, Horttanaien et al.9 presented a one-dimensional (1D) model for calculating the quasi-steady-state speed of propagation of the combustion front in a fixed bed of different woods. Our time-dependent, 3D formulation does not require any quasisteady-state assumption and is therefore more comprehensive. To our best knowledge, there are no fixed-bed mathematical models of such a complexity with such a comprehensive coupling between the solid and the gas phases. In the following, we provide a detailed description of the equation used.

dp 2 = 1589.2w∞ − 50.22w∞ dh

(1)

where dp/dh stands for the pressure drop in Pa/m while w∞ is the superficial air velocity in m/s. This relationship provides pressure drops around 30% larger than those calculated using the Ergun equation.

3. MATHEMATICAL MODELING A two-temperature model has been developed so that at every point in the bed there are two temperatures Ts for the solid and Tg for the gas. Heat and mass transfer within the solid-bed is accounted for in such a way that the solid bed is considered to be a unit and no individual coal/char particles are considered. In the following, the conservation equations for momentum, energy, and mass are given together with a detailed description of the sinks/sources. 3.1. Conservation Equations for the Gas Phase. The momentum balance equation for the gas phase takes the form

2. EXPERIMENTAL SECTION A reactor of 0.28 m height and 0.045 m inner diameter filled with particles of EKORET solid fuel (almost monosize particles of demineralized coal) has been used, as shown in Figure 2. The 0.20

∂ (eρ wg) + ∇(eρg wgwg) = −e∇p + ∇(eT ) + eρg g + Ssolid ∂t g (2)

where ρg stands for gas density, wg is the gas velocity, e is the fixed-bed porosity, p stands for the static pressure, and g is gravity; T represents a Newtonian fluid tensor for a laminar flow, while Ssolid is the pressure drop across the fixed-bed (see eq 30). Although eq 2 is solved in this form, the first three terms appearing on the right-hand side are negligible if compared with the source term Ssolid. The Eq 2 is accompanied by the continuity equation for the gas phase: ∂ (eρ ) + ∇(eρg wg) = Gchar + Gvap + Gdev ∂t g

(3)

with the sources Gchar, Gvap, and Gdev calculated in kilogram per fixed-bed volume per second, and they are described in paragraph 3.3. Five gaseous species (water vapor, volatiles, carbon monoxide, carbon dioxide, and oxygen) are calculated using the following conservation equations:

Figure 2. Fixed-bed reactor.

∂ (eρ y ) + ∇(eρg wgyi ) = ∇(eρg Di ,eff ∇yi ) + Gig ∂t g i

m high fuel-bed of 0.35 initial porosity rests on a grate located at the bottom of the reactor. The fuel is ignited at the reactor top, nearby the exhaust port of the flue gas. Four thermocouples, equally spaced (5 cm spacing) along the reactor length (see Figure 2), determine the rate with which the combustion zone moves. The sheathed thermocouples are positioned at the reactor centerline, and they measure, with an accuracy of around 10−20 °C, temperatures that lie somewhere between the gas and the solid temperatures (see paragraph 4.1). The measured temperatures are not larger than 1200−1300 °C. The flue gas has been sampled and analyzed for three gaseous components: CO, O2, and CO2. Both the gas composition and the bed temperatures have been logged into a recorder that stored data within 30 s intervals. The ambient temperature air is supplied at the reactor bottom. Two cases are considered, which correspond to 1.0 m3/h (Case 1) and 1.5 m3/h (Case 2) air flow rate (0.17 m/s and 0.26 m/s superficial air velocities at 298 K, respectively). Composition (as delivered) of EKORET coal is as follows: proximate analysismoisture 7%, ash 5.3%, combustible matter 87.8%, ASTM volatile matter 31.5%, LCV28.24 MJ/kg; ultimate analysiscarbon 73.6%, hydrogen 4.37%, oxygen 7.94%, nitrogen 1.39%, sulfur 0.43%; 967 kg/m3 coal density; stoichiometric air requirement of 9.796 kg of dry air per kg of fuel. The fuel can be characterized by a uniform particle size distribution in the 3−4 mm range. The pressure drop across the fixed-bed has been measured in a separate experiment under ambient air conditions. The least-squares fit (0.99 correlation coefficient) to the measured data provides the following relationship

(4)

where yi is the mass fraction of the ith component and Di,eff stands for the effective diffusion coefficient; Ggi represents GHg 2O, Ggvolatiles, GgCO, GgCO2, GgO2 source terms, which are given in Table 1. The energy balance equation for the gas phase takes the form ∂ (eρ hg ) + ∇(eρg wghg ) ∂t g = ∇(ekg∇Tg) − Sconv + Sfg + Sco + Svol

(5)

where hg is the physical enthalpy of gas, kg is the thermal conductivity, and Sfg represents the source term due to the phase change between the solid and the gas phase (see eq 29); Sco and Svol are the sources representing CO and volatiles combustion, respectively (see reactions 23 and 24). 3.2. Conservation Equations for the Solid Phase. The following mass conservation equation ∂ [(1 − e)ρs gi] + ∇[(1 − e)ρs wg s i ] = − Gi ∂t 4768

(6)


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where Bdev = 107 kgs/(kgvol s). The char is oxidized to both CO and CO2 according to the following overall reactions

Table 1. Sources in the Gas-Phase Mass Balance Eq 4 species

source term

water vapor

G Hg 2O = Gvap(eq 10) + 1.278Gvol(eq 25)

volatilesa

g Gvolatiles = Gdev (eq 11) − Gvol(eq 25)

CO

g ′ (eq 27) GCO = GCO(eq 19) + 0.989Gvol(eq 25) − GCO

CO2

g ′ (eq 27) GCO = GCO2(eq 18) + 1.571GCO 2

O2

GOg 2

C+

⎛ ⎛2 ⎞ 1 1⎞ O2 → 2⎜1 − ⎟CO + ⎜ − 1⎟CO2 ⎝ ⎠ ⎝ ⎠ Θ Θ Θ

C + CO2 → 2CO with the CO/CO2 ratio determined by

a

= − 1.303Gvol(eq 25) − 0.571GCO(eq 27) − G (eq 16)

s=

a

Volatiles = C1.05H4.22O0.74N0.0751; Mvolatiles = 29.71 kg/kmol. The coefficients appearing in the source terms are calculated as follows: 1.278 = 2.11×18/29.71 kg water vapor/kg of volatiles (see eq 23); 0.989 = 1.05×28/29.71 kg of CO/kg of volatiles (see eq 23); 1.571 = 44/28 kg of CO2/kg of CO (see eq 24); 1.303 = 1.21×32/29.71 kg of O2/kg of volatiles (see eq 23); 0.571 = 0.5×32/29.71 kg of O2/kg of CO (see eq 24).

(12) (13)

13,14

⎛ 6240 K ⎞ CO = 2500 exp⎜ − ⎟ CO2 Ts ⎠ ⎝

(14)

so that the stoichiometric coefficient appearing in eq 12 is calculable as θ=

(1 + 1/s) (0.5 + 1/s)

(15)

The oxygen consumption rate in reaction 12 is calculated as11 ⎛ 96.4 kJ/mol ⎞ Ga = eMO2A sBcombCO2 exp⎜ − ⎟ RTs ⎠ ⎝

has been solved, where gi stands for mass fraction of moisture, volatiles, and char, while ρs stands for the solid phase density and Gi is the appropriate source/sink term (Gvap, Gvol, Gchar). These equations are accompanied by the continuity equation for the solid phase, which reads

where MO2 and CO2 are the oxygen molecular mass and oxygen concentration (in kmol/m3) in the gas phase, respectively; Bcomb = 4000 m/s, while Ga is in kilograms of O2 per fixed-bed volume per second; As represents the reaction surface area in m2 per volume of fixed-bed (see eq 35). The rate of CO2 consumption in reaction 13 is calculated as13

∂ [(1 − e)ρs ] + ∇[(1 − e)ρs ws] = −Gchar − Gvap − Gdev ∂t (7)

Ash is regarded as inert, and its mass fraction is calculated as gash = 1 − gchar − g vol − g w

⎛ 185.4kJ/mol ⎞ Gb = eMCO2Bgasification A sCCO2 exp⎜ − ⎟ RTs ⎠ ⎝

(8)

The energy balance equation for the solid phase is as follows:

(17)

and, therefore, the net rate of CO2 production, which is generated in reaction 12 and consumed in reaction 13, is

∂ [(1 − e)ρs hs] + ∇[(1 − e)ρs wh s s] ∂t = ∇(keff ∇Ts) + Sconv + Schar − Svap − Sdev + Sfs

(16)

GCO2 = θ

(9)

MCO2 ⎛ 2 ⎞ ⎜ − 1⎟Ga − Gb ⎠ MO ⎝ θ 2

where Sconv and Schar represent the convective heat transfer between the gas and solid phase and the enthalpy change due to the char exothermic and endothermic reactions, respectively; Sfs is the source term associated with the phase change (see eq 22) while Svap and Sdev represent the sinks due to evaporation and devolatilization, respectively. It is important to realize that radiative heat transfer within the solid bed is accounted for through the effective thermal conductivity, following the work of Atkinson and Merrick.19 3.3. Sources and Sinks in the Conservation Equations. Solid Phase. Due to the low moisture content of the fuel, the assumption is made that water encapsulated in the coal is given off into the gas phase in accordance with the relationship11

(18)

while the overall rate of CO formation is GCO = 2θ

MCO ⎛ M 1 ⎞⎟ a ⎜1 − G + 2 CO Gb θ⎠ MO2 ⎝ MCO2

(19)

The source/sink term that appears in eq 3 and eq 7 is calculated then as Gchar = θ

MC a MC b G + G MO2 MCO2

(20)

where MC is the molecular mass of carbon (the reader will notice that reactions 12 and 13 are marked in the equations using superscripts “a” and “b”, respectively). Sources and sinks (Schar and Sfs) occurring in energy eq 9 are calculated as follows:

⎛ 14.4 kJ/mol ⎞ Gvap = (1 − e)rvap = 4.01 exp⎜ − ⎟(1 − e)ρs g w RTs ⎝ ⎠

⎞M 2 1 ⎞⎟ MC a ⎛ a ⎛ ⎜ ⎜1 − Schar = θ ΔHCO − 1⎟ C Ga + 2θ ΔHCO 2⎝ ⎠ ⎝ θ MO2 θ ⎠ MO2

(10)

where R is the gas constant (8.3147 J/(mol K)) and the Gvap source term is calculated in kilogrammoisture per cubic meter of the fixed-bed per second. The rate of devolatilization is described using the relationship12

Ga + ΔH b

⎛ 158 kJ/mol ⎞ 2 Gdev = rdev(1 − e) = Bdev ρs g vol exp⎜ − ⎟(1 − e) RTs ⎝ ⎠

MC b G MCO2

(21)

a Sfs = Gac p,O2(Tg − T0) − GCO c (Ts − T0) 2 p,CO2 b + GCO c (Tg − T0) − GCOc p,CO(Ts − T0) 2 p,CO2

(11) 4769

(22)


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using the following reaction enthalpies: ΔHaCO2 = 32791.67 kJ/ kg, ΔHaCO = 9208.33 kJ/kg, ΔHb = −14375.00 kJ/kg; cp,i are specific heats of the gaseous components, and T0 is the reference temperature of 298 K (cartoon graphs showing all the mass and energy sources/sinks can be found in ref 10). Gas Phase. The model assumes that the two following homogeneous reactions take place in the gas phase:

Sinternal = Sinitial,0(1 − Xc) 1 − ψ ln(1 − Xc) = A 0mp(1 − Xc) 1 − ψ ln(1 − Xc)

where Sinitial,0 is the initial internal surface area determined on the basis of the specific surface area of the coal, mp is the mass of a particle, and A0 is the measured specific surface area of the fuel (in m2/kg). The ψ parameter is determined for noncombusted fuel samples on the basis of the particle initial porosity (ep,0) as

C1.05H4.22O0.74 N0.0761 + 1.21O2 → 1.05CO + 2.11H 2O + 0.038N2

(23)

ψ=

CO + 0.5O2 ⇔ CO2

(24)

where the formula C1.05H4.22O0.74N0.0761 has been calculated using the ultimate and proximate fuel analysis. The mass source term associated with reaction 23 is then15 Gvol = eM volk volatiles = 4.4 × 1011eM vol[volatiles]0.5 ⎛ 15098 ⎞ ⎟ [O2 ]1.25 exp⎜⎜ − Tg ⎟⎠ ⎝

1 −ln(1 − ep,0)

(25)

Sexternal =

(26)

The mass sink term for reaction 24 is calculated as16 8

As =

(27)

and the energy source is ′ ΔHCO SCO = −GCO

Sfg = −Sfs + Gvapc p,H2O(Ts − T0) + Gdev c p,vol(Ts − T0) (29)

Finally, the Ssolid source term representing the pressure drop across the bed, which appears in eq 2, is calculated as (30)

Stotalρs (1 − e) Stotal(1 − e) = mp /ρs mp,0(1 − Xc)

Sconv =

and, using the measured pressure drop (eq 1), the resistance coefficients take the following values: C = 2605.24 m−2 and 1/z = −2 806 527.33 m−1. 3.4. Fixed-Bed Structure. The total contact (reaction) surface area consists of an external surface area and an internal area (pores) Stotal = Sinternal + Sexternal

⎛ 6m (1 − X ) ⎞2/3 c = π ⎜⎜ 0 ⎟⎟ πρs ⎝ ⎠

(34)

(35)

3.5. Thermal Properties, Heat and Mass Transfer Coefficients. Kirov’s18 formulas for equivalent specific heats of volatiles, char, and ash have been used. Thermal conductivity of the fixed-bed is calculated following the work of Atkinson and Merrick,19 where the heat conduction within the bed is represented by three parallel processes: heat conduction due to moisture presence, conduction through the solid matter, and through the gas filling up interparticle space. The latter is enhanced by interparticle radiation. The appropriate expressions can be found in either the original sources18,19 or in refs 10, 14, and 20. The heat transfer rate between the gas phase and the solids is accounted for by the source term appearing in energy equations (eq 9)

(28)

where ΔHvol = 32666.67 kJ/kg and ΔHCO = 10106.88 kJ/kg. The source term Sfg associated with the physical enthalpy of reactants and products of reactions 12 and 13, moisture and volatiles, which appear in the energy balance equation of the gas phase, is calculated as

⎛μ C 2⎞ ⎟ Ssolid = −⎜ w∞ + ρair w∞ ⎝z ⎠ 2

πd p2

The reaction surface area enters eq 16 and eq 17 through the specific surface area parameter As, which is calculated per fixedbed volume, so that the resulting equation is

0.3

G′CO = eMCOk CO = −2.5 × 10 eMCO[CO][O2 ] ⎛ 8052 ⎞ ⎟⎟ [H 2O]0.5 exp⎜⎜ − ⎝ Tg ⎠

(33)

Relationship 32, which governs the internal surface area development, shows that for the considered fuel the internal surface area increases with the burnout and reaches a maximum of around 2.5Sinitial,0 at approximately 40% burnout; then, it decreases to zero. The external surface area is calculated under the assumption that the true density of solids remains constant while the bulk particle density decreases, so that

while the energy source reads Svol = Gvol ΔH vol

(32)

Sexternal αeff (Tg − Ts) V

(36)

where V represents the fixed-bed volume. The effective heat transfer coefficient consists of the convective and radiative parts αeff = αconv + αrad

(37)

where the convective part is calculated using the following correlation e Nu = 2 + 1.12 Re Pr 0.33 + 0.0056RePr 0.33 (38) 1−e

(31)

and both vary during the combustion process. The area of internal pores is calculated using the random pore model.17 Variations of the pore surface are related to the degree of char conversion Xc, which is defined as the ratio of the reacted char to its initial amount. The internal surface area development as a function of the particle burnout is calculated as

where Re = ((wds)/ν)(1/(1 − e)) and Pr = ((cpμ)/kg) so that αconv = 4770

Nu × kg 1 − e ds e

(39)


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peak is computed with a lower accuracy. Figure 4 shows the oxygen, carbon monoxide, and carbon dioxide mole fractions at

Absorption of radiation in the gas phase, although typically smaller than 10% of the convective part, has also been accounted for (see ref 10) by adding αrad, as shown in eq 37.

4. NUMERICAL CALCULATIONS The SIMPLE algorithm is used to solve the coupled continuity and momentum equations in the fixed-bed. As initial conditions, ambient air temperature is prescribed throughout the computational domain for both the gas and the solid phases, with exception of the top fuel layer, which is given as 2000 K to initiate the combustion. The heat losses from the reactor are calculated using the conjugated heat transfer (heat conduction through the reactor wall and natural convection outside) with the free convection coefficient of 5 W/(m2 K). Three-dimensional calculations are performed for a 45° sector of the fixed-bed using a structured grid consisting of 100 000 numerical cells. Doubling the grid provides minor changes to the predictions. A 0.5 ms time step is used for the time integration; the fixed-bed properties have been updated at each time step. Detailed validation of the developed mathematical model has been carried out10 for two measured cases corresponding to the superficial air velocities of 0.17 m/s and 0.261 m/s. The corresponding Reynolds numbers for the inlet air flows are 443 and 666, respectively. 4.1. Comparison with the Measured Data. In Figure 3 (Case 1; 0.17 m/s air velocity), four curves are displayed, which

Figure 4. Oxygen, carbon monoxide, and carbon dioxide at the exit of the fixed-bed reactor as a function of time; Case 1 (0.17 m/s superficial air velocity).

the exit of the reactor indicating that the combustion process lasts around 83 min. The calculated CO2 mole fraction in the exit gases agrees well with the measured values; however, the model predicts too much carbon monoxide; around 1 vol % CO has been measured, while the model predicts up to 5% CO. This discrepancy is also shown in the oxygen concentrations, which are measured to be around 3%, while the predictions show 1% since the oxygen is in the overpredicted CO levels. Thus, eq 14 for computing of CO/CO2 ratio may not be fully applicable for the case considered (identical model imperfections have been observed for Case 2), or the rate of CO oxidation (see eq 27) is overestimated. The overshoot in CO predictions (see Figure 4) in the initial part of the process is associated with the initiation of the numerical simulations, more precisely with the ignition method of the fixed-bed. The simulations have been initiated by prescribing a temperature to a top layer of the fuel. If the rate of reaction 12 calculated for this ignition temperature is large enough to compensate for the heat removal rate, the combustion begins (see paragraph 4.2), otherwise the bed is extinguished. For the results presented in Figure 4, the initial temperature of 2000 K (arbitrarily chosen value) has been used, which may be too high. Only in the initial period of around 25 min are the predictions sensitive to the prescribed initial temperature; later on, the sensitivity disappears. Despite many simplifications, the model has shown to accurately calculate the overall combustion rates, as indicated in Figures 3 and 4. It has been measured that the first temperature peak moves downward with a 22−34.6 cm/h velocity (27.9 cm/h average value), while the predicted propagation velocity is in the 15−36 cm/h range. The first temperature peak results from combustion of volatiles and carbon monoxide in the gas phase (reactions 23 and 24), which proceed in parallel with solid-state carbon oxidation (reaction 12). Such a front of around 2−4 cm thickness is shown in Figure 5 at the 30 min instance. When this front passes through the fixed-bed, the volatiles are burned and the combustion air stream, entering the bed at the bottom, initiates propagation of the high temperature region upward from the bottom. Thus, the occurrence of the second temperature peak that travels upward

Figure 3. Variation of the fixed bed temperature with time; Case 1 (0.17 m/s superficial air velocity). For thermocouple locations, see Figure 1.

show the temperature−time history at four locations in the coal-bed. Each temperature curve possesses two maxima; one at the beginning of the combustion process (within the first 40 min) and the second one occurring later, in the 70−100 min interval. The first thermo-element records the first temperature peak after around 10 min, while the fourth thermo-element records the first peak after around 50 min so the first temperature peak propagates downward. The fourth thermocouple is the first one that records the second temperature peak, indicating its propagation in the opposite direction, upward the bed. In Figure 3 the thermocouple readings are compared with the computed solid-phase temperatures (differences of around 100 °C have been observed between the computed solid-phase and gas-phase temperatures). The numerical simulations accurately predict both the value and occurrence of the first temperature peak however the second 4771


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conductivity (λ) are also examined. The assessment of the sensitivity of the calculated fixed-bed temperatures to the listed parameters is carried out by calculating the logarithmic sensitivity factor LSF:

LSF =

∂ln y ∂y p = ∂ln p ∂p y

(39)

which is then averaged over a time interval of the experiments, to produce an ALSF indicator, calculated as k−1

ALSF =

∑i = 1 |LSF(ti)(ti + 1 − ti)| tk − t1

(40)

Variations in both the pre-exponential factor and the activation energy (see Table 2) for the reaction of char Table 2. Average Logarithmic Sensitivity Factors for the Fixed-Bed Modela

Figure 5. Model predictions along the center-line of the bed at 30 min after ignition; Case 1 (0.17 m/s superficial air velocity): (A) fuel temperature, min 0, max 1100 °C; (B) gas temperature, min 0, max 1100 °C; (C) fixed-bed porosity, min 0, max 1; (D) equivalent specific heat, min 0, max 2400 J/(kg K); (E) oxygen mole fraction, min 0, max 0.20.

is associated with heterogeneous oxidation of the remaining char. The overall combustion rate for the period of up to 83 min is around 0.0177 kg/(m2 s), and the combustion proceeds at 1.17 excess air ratio. After 83 min, around 75% of combustibles are burned, and then, the remaining char is oxidized over a period of around 40 min with a continuously increasing oxygen content in the flue gas, as shown in Figure 4. Only ash remains at the end of the process, so almost 100% burnout is achieved. Both the experiments and the predictions concerning Case 2 (0.26 m/s superficial air velocity) show qualitatively similar curves to those shown in Figures 3 and 4. The main difference is in the increased combustion rate of 0.0266 kg/(m2 s) so 75% burnout has been observed after 60 min. In this case, the combustion proceeds also at 1.17 excess air ratio. As with any fundamentally based computer simulations, once a solution is determined, a large number of parameters of both the gas and the solid phases are accessible. Figure 5 shows the calculated porosity and specific heat along the bed height together with sharp changes in the solid-bed temperature and gas-phase oxygen concentration. As mentioned before, the differences between the gas-phase and the solid-phase temperatures are not larger than 100 °C. The observed 0.0177 kg/(m2 s) (Case 1) and 0.0266 kg/(m2 s) (Case 2) combustion rates are substantially lower than the 0.08 kg/(m2 s) rate measured by Thunman and Leckner4 and the 0.04−0.08 kg/(m2 s) rate measured by Horttanaien et al.9 for combustion of wood particles of similar size. Porteiro et al.21 measured the combustion rates of 4−7 mm biomass particles at 1.2 excess air to be in 0.065−0.08 kg/(m2 s) range where the lower figures correspond to refuse derived pellets and almond shell while the larger values are applicable to wood particles. Porteiro et al.20 observed, however, an opposite effect; for overstoichiometric combustion, the combustion rate decreased with the air velocity. 4.2. Sensitivity Analysis. The developed model requires a number of input parameters. This paragraph is to examine how variations in activation energy (Ea) and pre-exponential factor (kcomb) of reaction 12 alter the predictions. Coal density (ρs), effective heat transfer coefficient (α), and fixed-bed thermal

param

T1

T2

T3

T4

Ea Bcomb ρs α λ

2.517 0.401 0.458 0.205 0.020

2.247 0.566 0.566 0.317 0.022

1.938 0.721 0.664 0.383 0.033

1.591 0.837 0.782 0.462 0.066

T1÷T4 temperature readings, see Figure 2, Ea, kcomb = activation energy and pre-exponential factor of reaction 12, ρs = fuel density, αeffective heat transfer coefficient between the gas phase and the solid phase, λ = effective thermal conductivity of the fixed-bed. a

combustion have the largest impact on the model results. Much lesser sensitivity is observed for the heat transfer coefficient, while variations in the thermal conductivity remain nearly negligible for the model predictions. When the pre-exponential factor (kcomb) of char combustion reaction (reaction 12) is increased by 20%, the overall combustion rate increases from 0.0177 to 0.021 kg/(m2 s). When the activation energy (Ea) is increased by 20%, the combustion process is terminated. Larger values (increased by 20%) of the coal density and the intensification of heat transfer between the solid and the gas phases result in a slowdown of the process. The 20% increase of the thermal conductivity coefficient insignificantly affects the rate of the process inside the reactor.

5. CONCLUSIONS In this work, we have investigated time-dependent coal combustion in the counter-current fixed-bed using both measurements and mathematical modeling. The superficial air velocity has been the main rate controlling parameter; the coal combustion rates of 0.017 kg/(m2 s) and 0.024 kg/(m2 s) have been observed for the air velocities of 0.17 m/s and 0.26 m/s, respectively. In both cases the combustion proceeds at 1.17 excess air. Two temperature peaks have been observed: one, corresponding to volatile matter combustion, propagating downward the bed, and the other one, corresponding to the char combustion, moving upward from the bed bottom. The observed combustion rates are 3−4 times lower than biomass conversion rates under similar combustion conditions. The developed three-dimensional model for time-dependent combustion has demonstrated good agreement with the measured data. The predictions of fixed-bed temperatures and carbon dioxide concentrations can be regarded as good, whereas the CO and O2 predictions require improvements. 4772


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Article

ρ = density, kg m−3 θ = stoichiometric coefficient in eq 12 Ψ = parameter in eq 32 and eq 33 ν = kinematic viscosity, m2 s−1

The model accurately calculates the overall combustion rates and shows the two temperature peaks, which travel in opposite directions. Both the measurements and the model calculations have demonstrated an increased rate of coal combustion when the air velocity is increased. The effect of several model parameters on the temperature predictions has been examined. The rate of char oxidation reaction is paramount; a 20% increase in its rate has resulted in a 20% increase in the overall combustion rate. On the contrary, a 20% increase in the fuel density has slowed down both the combustion rate and the front velocity by around 5%. Similar effects have been observed when the effective heat transfer coefficient between the gas phase and the solid phase is increased by 20%. A 20% increase in the effective thermal conductivity of the fixed-bed has resulted in minor changes.

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Subscripts

char = char comb = combustion conv = convection dev = devolatilization eff = effective fs = phase change g = gas phase rad = radiation s = solid phase solid = solid phase vap = evaporation

AUTHOR INFORMATION

Superscripts

Corresponding Author

a = O2 consumption rate in reaction 12, see eq 16 b = CO2 consumption rate in reaction 13, see eq 17 g = source terms in gas phase eq 4 ′ = sink term for reaction 24, see eq 27

*Fax: 49-5323-724863. Email: [email protected]. de, [email protected]. Notes

The authors declare no competing financial interest.

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Abbreviations

NOMENCLATURE A = reaction surface area, m2 m−3 A0 = specific area of solids, m2 kg As = specific surface area, m2 kg B = pre-exponential factor, m s−1 c = specific heat, J kg−1 K−1 d = diameter, m D = diffusion coefficient, m2 s−1 e = fixed-bed porosity Ea = activation energy, J mol−1 g = gravity, m s−2 g = mass fraction of a solid phase component (eq 3) G = source terms in eq 3, kg m−3 h = fixed bed height, m h = enthalpy, J kg−1 k = thermal conductivity, W m−1 K−1 k = pre-exponential factor m s−1 m0 = initial particle mass, kg M = molecular mass, kg kmol−1 Nu = Nusselt number Ssolid = source term in eq 2, N m−3 t = time, s T = temperature, K T = Newtonian fluid tensor for a laminar flow p = static pressure, N m−2 R = gas constant, J mol−1 K−1 Re = Reynolds number Pr = Prandtl number s = CO/CO2 ratio in eq 14 S = reaction surface area, m2 V = fixed bed volume, m3 w = velocity, m s−1 w∞ = superficial air velocity, m s−1 Xc = char conversion degree y = mass fraction for a gaseous component z = vertical coordinate, m ΔH = reaction enthalpies, J kg−1

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LSF = logarithmic sensitivity factor ALSF = average logarithmic sensitivity factor

REFERENCES

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Greek Letters

α = convective heat transfer coefficient, W m−2 4773


Energy & Fuels

Article

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Time-Dependent Combustion of Solid Fuels in a Fixed-Bed

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