ARTICLE pubs.acs.org/EF
Experimental and Numerical Investigation of Lignite Particle Drying in a Fixed Bed Kai Zhang and Changfu You* Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, People’s Republic of China ABSTRACT: A multi-scale approach was used in a numerical investigation of lignite particle drying in a fixed bed. The multi-scale model simultaneously analyzed a macroscopic thin bed layer and a microscopic thin particle layer. The macroscopic heat and mass transfer between the drying gas and the lignite particle surfaces was calculated in conjunction with the microscopic intraparticle heat and mass transfer using transient boundary conditions. The microscopic intraparticle heat transfer was described assuming local thermodynamic equilibrium in the porous lignite particle with the mass transfer including convection of the free water, diffusion of the bound water, and convection and diffusion of the gas mixture in the lignite particle. The multi-scale model was verified by a series of experiments with varying gas velocities and temperatures at atmospheric pressure using two kinds of lignite particles. The simulations agree well with the experimental data for the average weight loss rate and the gas temperatures. The results show that the effects of the drying conditions, such as the lignite particle stack height and the temperature and velocity of the drying gas, on the fixed-bed drying process can be evaluated using this multi-scale drying model and that the intraparticle drying behavior at different bed heights in the fixed bed can also be described.
1. INTRODUCTION Fixed-bed dryers are one of the most common types of industrial dryers that are widely used in agricultural and chemical engineering systems.13 In recent years, numerical investigations have been used to analyze the physical phenomena associated with the complicated heat- and mass-transport process during drying. The ultimate goal of the numerical simulations is to optimize and develop equipment and processing strategies for the drying industry to replace expensive and time-consuming experiments.47 Most drying models for modeling fixed-bed drying are based on correlating measurements for the drying rate as a function of the moisture, possibly including the effect of the surroundings (temperature and relative humidity).816 However, these models do not consider the internal resistance to heat and mass transfer in the particles or give detailed information about the temperature and moisture distributions in the particles. In fact, such lumped models are only valid for very slow drying processes. The internal transport process has been considered in some studies of fixed-bed drying. Sitompul et al.1719 incorporated the moisture diffusion theory for single particles into a model of fixed-bed drying of grains, but the simulation results did not reflect detailed drying information inside the particles. Additionally, Saastamoinen et al.2023 analyzed the fixed-bed drying of wood chips with a modified shrinking core model based on various assumptions. Their solution depended upon the simplified equations describing the transport mechanisms; therefore, the simulation results did not adequately describe the real drying behavior inside the particles. The transport phenomena are generally far more complicated than assumed in previous analyses.2435 Criticisms of the receding core model and the diffusion model have recently been presented.3638 Therefore, a complete model of the heat and mass transfer in a single particle should be used to describe the r 2011 American Chemical Society
general transport processes to properly analyze all of the mechanisms for fixed-bed drying. This study gives a multi-scale numerical approach for lignite particle drying in a fixed bed. The lignite particles were chosen as the drying material, but the multi-scale model can also be applied to other materials. The multi-scale model simultaneously analyzed a macroscopic thin bed layer and a microscopic thin particle layer. The macroscopic heat and mass transfer between the drying gas and the lignite particle surfaces is calculated together with the microscopic intraparticle heat and mass transfer using transient boundary conditions. The microscopic intraparticle scale heat transfer was described assuming local thermodynamic equilibrium inside the porous particle, with the mass transfer including the convection of the free water, diffusion of the bound water, and convection and diffusion of the gas mixture in the lignite particle. The multi-scale model was verified by experiments with various gas velocities and temperatures at atmospheric pressure using two kinds of lignite particles. The multi-scale model results are compared to experimental results for fixed-bed drying of lignite particles. The intraparticle drying behavior in the fixed bed is then evaluated using the validated multi-scale model.
2. EXPERIMENTAL SECTION 2.1. Introduction. The two kinds of Chinese lignite used in the experiments were Huolinhe lignite and Hailaer lignite. The ultimate and proximate analyses of the raw lignite are listed in Table 1. Experiments investigating the drying of both a single particle and a fixed bed of lignite were set up to validate the multi-scale approach based on a particle level Received: May 22, 2011 Revised: July 29, 2011 Published: August 12, 2011 4014
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Table 1. Ultimate and Proximate Analyses of the Raw Lignite ultimate analysis (%) samples
Cd
Hd
Od
Nd
Sd
proximate analysis (%) Vd
FCd
Mar
Ad
Huolinhe lignite 55.45 3.83 15.25 0.93 0.57 38.46 37.57 31.93 23.97 Hailaer lignite
50.97 2.98 13.88 0.82 0.62 35.72 33.55 28.87 30.73
Figure 2. Lignite microstructure.
Figure 1. Schematic diagram of the experimental fixed-bed dryer system. model for a fixed bed. The drying kinetics of single lignite particles in hot air were investigated using the experimental platform of a single particle; the experimental details have been given elsewhere.39 The drying of the lignite particles is investigated in a fixed-bed test platform. 2.2. Fixed-Bed Test Platform. A schematic diagram of the fixed-bed dryer is shown in Figure 1. The air was blown by a fan into an electrical heater before entering the dryer, with the air velocity measured by a rotameter. The dryer was 900 mm in height and 120 mm in diameter and was insulated with 30 mm of mineral wool to ensure there were no radial temperature gradients inside the dyer. The hot air temperature at the dryer inlet was maintained at the desired value by the temperature control subsystem and measured by a K-type thermocouple. The relative humidity of the outlet air was measured with a digital humidity recorder. The thermocouple accuracy was (0.75%, and the humidity recorder accuracy was (0.1%. Three K-type thermocouples were positioned in the center of the fixed bed along its height to measure the temperature distribution during drying. Two of the thermocouples were set in the fixed bed at 100 and 300 mm above the gas distributor, with the third one set just above the top surface of the lignite particle stack to record the outlet gas temperature. This type of thermocouple provides an accuracy of (0.75% of the measured value. The electronic balance placed below the dryer to monitor the particle mass had an accuracy of (5 g. All experiments were performed at atmospheric pressure with the weights and temperatures recorded every 10 s. These measurements were all logged continuously by a data acquisition unit.
3. MULTI-SCALE LIGNITE PARTICLE DRYING MODEL FOR A FIXED BED The multi-scale drying model consists of a microscopic thin particle layer and a macroscopic thin bed layer to be solved together. 3.1. Heat and Mass Transfer in a Particle. The following simplifications were used to model the intraparticle drying
process: (1) The conditions within the lignite particles are independent of angle; therefore, a one-dimensional mathematical model can be used to describe the heat- and mass-transfer processes. (2) The lignite microstructure is shown in Figure 2. The moist porous lignite can be divided into solid (s), liquid free water (l), bound water (b), and gaseous (g) phases. The gaseous phase (gas mixture) consists of dry air and water vapor. (3) The transport processes include convection of the free water, diffusion of the bound water, and convection and diffusion of the gas mixture. (4) The gaseous phase can be treated as all ideal gas. (5) The liquid free water, bound water, and solid densities are all constant. (6) The particle size is constant, with the particle shrinkage neglected. (7) The lignite particles are in local thermodynamic equilibrium. (8) The convection and conduction heat transport are considered, while radiation heat transport is neglected. The averaged quantities are defined as Z 1 jdΛ for the spatial average ð1Þ Æjæ ¼ Λ Λi and Æjæi ¼
Z 1 jdΛ for the intrinsic phase average Λ i Λi
ð2Þ
The sum of the volume fractions of the four phases is equal to 1. εs þ εl þ εg þ εb ¼ 1 εs ¼
ÆFs æ ÆFl æ ÆF æ εb ¼ b b s εl ¼ l ÆFs æ ÆFl æ ÆFb æ
ð3Þ ð4Þ
The continuity equations obtained with the method of volume averaging are presented below for each of the four fluid phases (liquid free water, bound water, water vapor, and dry air). For the liquid free water phase ∂ÆFl æ 1 ∂ þ 2 ðr 2 ÆFl æl ÆVl æÞ ¼ ωl ∂t r ∂r
ð5Þ
where ωl is the phase change term representing the mass of evaporated liquid free water per unit volume of lignite particle and per unit time. 4015
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For the bound water phase
Darcy’s law for the superficial liquid free water velocity is
∂ÆFb æ 1 ∂ þ 2 ðr 2 ÆFb æb ÆVb æÞ ¼ ωb ∂t r ∂r
where ωb represents the phase change from bound water to water vapor per unit volume of lignite particle and per unit time. For the water vapor in the gaseous phase ∂ÆFv æ 1 ∂ þ 2 ðr 2 ÆFv æg ÆVv æÞ ¼ ðωl þ ωb Þ ∂t r ∂r For the dry air in the gaseous phase ∂ÆFa æ 1 ∂ þ 2 ðr 2 ÆFa æg ÆVa æÞ ¼ 0 ∂t r ∂r
ð7Þ
∂t
þ
ð8Þ
1 ∂ 2 ðr ÆFg æg ÆVg æÞ ¼ ðωl þ ωb Þ r 2 ∂r
ð9Þ
Combining the eqs 57, the moisture conservation equation for the free water, the bound water, and the vapor is ∂ÆFl æ ∂ÆFb æ ∂ÆFv æ 1 ∂ þ þ þ 2 ðr 2 ðÆFl æl ÆVl æ ∂t ∂t ∂t r ∂r þ ÆFb æb ÆVb æ þ ÆFv æg ÆVv æÞÞ ¼ 0
where ÆPl æl ¼ ÆPg æg Pc
ð10Þ
sv RT ∇T þ ∇ÆPv æg ÆPv æg Mv Mv
∑
T R ÆPv æ ln 0 T 0 Mv P
ÆFg æg ¼ ÆFa æg þ ÆFv æg
ðaÞ
ðcÞ
½Cpl ÆFl Vl æ þ Cpb ÆFb Vb æ þ Cpg ÆFg Vg æ ðdÞ
The meaning of the four terms in eq 22 are (a) heat storage/ accumulation, (b) heat absorption during vaporization of free liquid water and bound water, (c) heat conduction, and (d) thermal-driven internal convection, where FCp ¼ Cps ÆFs æ þ Cpl ÆFl æ þ Cpl ÆFb æ þ Cpg εg ÆFg æg Cpg ¼
ð13Þ
ð14Þ
Combining the eqs 5, 6, and 9, the fluid conservation equation including the free water, the gas mixture, and the bound water is ∂ÆFg æ ∂ÆFl æ ∂ÆFb æ 1 ∂ þ þ þ 2 ðr 2 ðÆFl æl ÆVl æ ∂t ∂t r ∂r ∂t þ ÆFb æb ÆVb æ þ ÆFg æg ÆVg æÞÞ ¼ 0
∂ÆTæ ∂r ð22Þ
g
ÆVv æ ¼ ÆVg æ ÆFg æg Deff ∇ðÆFv æg =ÆFg æg Þ=ÆFv æg
ð21Þ
The energy equation for the porous particle with all phases assumed to have the same temperature is ∂ÆTæ 1 ∂ ∂ÆTæ keff r 2 FCp Δhðωl þ ωb Þ ¼ 2 ∂t r ∂r ∂r ðbÞ
ð12Þ
The vapor velocities are due to molecular diffusion as given by Fick’s law.
ð20Þ
The sum of the partial densities is equal to the total density
where sv is the entropy, which is a state function of the temperature and the vapor pressure. sv ¼ sv 0 þ Cpv ln
ð19Þ
where the molecular weight of the gas mixture is !1 n ÆFi æg i ¼ a, v Mg ¼ g i ¼ 1 ÆFg æ Mi
ð11Þ
With the local thermodynamic equilibrium assumption, the chemical potential of the bound water must be equal to the chemical potential of the vapor present in the pores. The chemical potential of the vapor can be written in terms of the gradients of the vapor pressure and the temperature40 ∇ψb ¼ ∇ψv ¼
ð18Þ
Pc is the capillary pressure. For an ideal gas, this equation can be written as
The bound water migration is driven by the chemical potential of the bound water; therefore, the bound water flux can be expressed as ÆFb æb ÆVb æ ¼ Db εs ∇ψb
ð17Þ
ÆPg æg ¼ ÆFg æg R0 ÆTæ=Mg
Note that a single mass conversation equation can be written for the gas phase by combining eqs 7 and 8. ∂ÆFg æ
Kl Krl ð∇ÆPl æl ÆFl æl gÞ ÆVl æ ¼ μl
ð6Þ
n
∑
i¼1
Cpi
ÆFi æg ÆFg æg
i ¼ a, v
keff ¼ εg kg þ ðεl þ εb Þkl þ εs ks
ð23Þ ð24Þ ð25Þ
The evaporation rate of the free water and the bound water is equal to the vapor production rate. ∂ÆFv æ 1 ∂ þ 2 ðr 2 ÆFv æg ÆVv æÞ ¼ ðωl þ ωb Þ ∂t r ∂t
ð26Þ
The drying process is assumed to occur inside a one-dimensional particle. The moisture mass flux, heat flux, and pressure are continuous at the external drying surface.
ð15Þ
ðkeff ∇ÆTæ þ ÆFl æl ÆVl æΔh þ ÆFb æb ÆVb æΔhÞnjs ¼ hT ðÆTæsur Tf Þ
Darcy’s law is used for the velocities instead of solving the complete momentum equation to predict the gas mixture velocity and the liquid free water velocity in the porous particle. Darcy’s law for the superficial gaseous phase velocity is
ð27Þ
Kg Krg ð∇ÆPg æg ÆFg æg gÞ ÆVg æ ¼ μg
ðÆFl æl ÆVl æ þ ÆFv æg ÆVv æ þ ÆFb æb ÆVb æÞnjs ¼ hm ðÆFv æsur g Fv f Þ
ð28Þ
ð16Þ
ÆPg æg ¼ Patm 4016
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Table 2. Parameters Used in the Simulations parameter
correlation/value
ÆFsæhuos ÆFsæhais ÆFlæl
1435 kg m
3
reference
parameter
correlation/value 5
reference
this study
Dv
2.17 10 (101325/P)(T/27.3.16)
this study
Deff
Dv/20
1000 kg m3
Db
1.8 1014
εb
0.4
Dv-eff
1.165 105 m2 s1
εhuo
0.42
this study
Patm, P0
101325 Pa
εhai
0.38
this study
Pc
(ε/K)1/2σ(T)J(S)
36
Cpf Cps
1000 kg K 1000 J kg1 K1
40
Pv Pvsat
Pvsat{1 exp[2.53(T 273)0.47X1.58]} Patm exp(17.58 5769/T 0.005686T)
40 33
Cpl
4200 J kg1 K1
S
(ÆFbæ + ÆFlæ)/ÆFlæl/(1 εs)
1370 kg m3
1
1
1.88
35 45
Cpv
2000 J kg
33
X
(ÆFbæ + ÆFlæ)/ÆFsæ
Cpa
1000 J kg1 K1
33
krl
S2
ks
0.19 W m1 K1
41
krg
(1 S)2
42
ka-eff
0.0279 W m1 K1
σ(T)
0.1212 0.000167T
43
kl
0.658 W m1 K1
33
J(S)
0.364{1 exp[40(1 S)]} + 0.22(1 S) + 0.005/S
29
kg Kl
0.02577 W m1 K1 2 1016 m2
44 33
Δh Sv0
3174.9 2.46T 10377.4 J kg1 K1
33 45
Kg
2 1012 m2
33
T0
298.15 K
45
33
Mv
0.018 kg mol1
33
Ma
0.029 kg mol1
4
K
1 1
μl
5 10
μg
3 105 kg m1 s1
kg m
s
42
At the center, which is an adiabatic, impermeable surface, the air and moisture mass fluxes and the heat flux are all 0 ðkeff ∇ÆTæ þ ÆFl æl ÆVl æΔh þ ÆFb æb ÆVb æΔhÞnjcenter ¼ 0
ð30Þ
ðÆFl æl ÆVl æ þ ÆFv æg ÆVv æ þ ÆFb æb ÆVb æÞnjcenter ¼ 0
ð31Þ
ðÆFa æg ÆVa æÞnjcenter ¼ 0
ð32Þ Figure 3. Numerical solution procedure.
where ÆVa æ ¼ ÆVg æ ÆFg æg Deff ∇ðÆFa æg =ÆFg æg Þ=ÆFa æg
ð33Þ
3.2. Heat and Mass Transfer in the Fixed Bed. In the present paper, the contact heat and moisture transfer between particles is negligible. The drying air moisture and energy balance can then be written as ! ∂ðFv f Þ ∂ ∂ðFv f Þ 1 ∂ðV ðFv f ÞÞ ¼ Dv-eff ∂t ∂z ∂z εb ∂z ! 6ð1 εb Þ 1 þ ð34Þ hm ðÆFv æsur g Fv f Þ Dp εb
where Fvf and Dv-eff are the water vapor density of drying gas and its effective diffusion coefficient, respectively. The source term (6(1εb)/Dp)(1/εb)hm(ÆFvæsurg Fvf) takes into account mass transfer from particles into the drying gas, where hm, ÆFvæsurg, and Fvf stand for the mass-transfer coefficient, the water vapor density at a particle surface, and the water vapor density of drying gas, respectively. ∂ðFf Cpf Tf Þ ∂ ∂ðTf Þ 1 ∂ðFf Cpf Tf V Þ ka-eff ¼ ∂z ∂z εb ∂t ∂z ! 6ð1 εb Þ 1 þ hT ðÆTæsur Tf Þ ð35Þ Dp εb
Here, ka-eff and (6(1εb)/Dp)(1/εb)hT(ÆTæsur Tf) are the effective thermal conductivity of the drying gas and the heat transfer between a particle and the drying gas, respectively, where hT, ÆTæsur, and Tf are the heat-transfer coefficient, the surface temperature of a particle, and the surrounding drying gas temperature. The boundary conditions at the fixed-bed inlet are Tf jh ¼ 0 ¼ ðTf Þin
ð36Þ
Fv f jh ¼ 0 ¼ ðFv f Þin
ð37Þ
The parameters used in the simulations are listed in Table 2. 3.3. Numerical Solution Procedure. Such concurrent models require significant computational resources, because the variables in the microscopic particles have to be updated in time for each point of the macroscopic grid. The numerical solution procedure is shown in Figure 3, with the coupling between the two scales as a two-way process: (1) The source terms (heat, vapor, and liquid) crossing each particle surface at time t allow for the coupled macroscopic equations to be advanced in time by a macroscopic time increment dt. (2) New boundary conditions are then used at each microscopic particle surface to advance the solution in time to t + dt by a microscopic time interval dt. Consequently, the multi-scale model significantly increases the complexity of coupled heat- and mass-transfer analysis. Not only does coupling exist within each single microscopic particle because of the strongly coupled heat and mass transfer but also 4017
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Figure 4. Predicted and measured results for the average moisture content and temperature. Dp = 30 mm; Tf = 140 C; Vf = 1.5 m/s; AH = 0.012 kg/kg.
Figure 5. Predicted moisture content variations in a Huolinhe lignite particle. Dp = 30 mm; Tf = 140 C; Vf = 1.5 m/s; AH = 0.012 kg/kg.
between the gas and the particle through the two-way interaction between the macroscopic variables and the particle variables. In the fixed-bed drying of lignite particles, each single particle is simulated using the above-mentioned comprehensive computational model of the heat and mass transfer in the porous particle. In turn, the temperature and vapor density variations in the gas are determined from the balance equations involving the heat and mass fluxes computed for each particle. Because this model is computationally demanding, a 1D model was used at the microscopic level with a 1D model also used at the macroscopic level for the fixed bed to reduce the computational time because of the strong coupling between scales.
4. RESULTS AND DISCUSSION 4.1. Drying of Single Particles. The single particle model incorporated into the fixed-bed drying model was evaluated by comparing experimental and numerical results for the convective drying of a single particle. The drying kinetics of single lignite particles in hot air were investigated using an experimental platform to monitor the convective drying of a single particle. Then, the validated particle model was used to predict the moisture content, liquid water velocity, gas velocity, and other parameters that describe physical processes. Figure 4 compares the predicted and measured temperature and average moisture content profiles for 30 mm diameter Huolinhe lignite and Hailaer lignite particles heated at 140 C. The predicted moisture content at each node was used to calculate the average moisture content for the particle for comparison to the experimental moisture levels. The results in
Figure 6. Predicted moisture content variations in a Hailaer lignite particle. Dp = 30 mm; Tf = 140 C; Vf = 1.5 m/s; AH = 0.012 kg/kg.
Figure 4 show that the predicted average moisture contents agree reasonably well with the experimental data. The predicted temperatures at the half radius and the center for both types of lignite particles show some small differences at 4000 s. The moisture content variations in the particles are more interesting and not well-reported in the literature. Figures 5 and 6 show the moisture content distributions in the two kinds of lignite particles. As expected, the external layers dry more rapidly than the internal layers. The moisture content at the particle surface decreases rapidly and quickly approaches the equilibrium value. A large moisture content gradient appears in the particle during drying. Thus, the internal masstransfer resistance significantly affects the particle drying process, and the lumped moisture model cannot correctly describe the heat and mass transfer during drying. The moisture content variations in the lignite particle are similar to those obtained by other authors46,47 for the drying of cocoa beans and pears. The transport of the free water and the gas mixture through the particle at various times during the convective drying process is described in Figures 7 and 8. Negative values are toward the exposed external surface. In Figure 7, the free water predominately moves toward the external surface because of capillary effects, with similar trends obtained for the transport of the gas mixture because of the mixture pressure in Figure 8. The flow of the free water toward the surface compliments the capillary flow induced by the moisture content gradient. After approximately 10 000 s, all of the free water has been removed from the particle and the velocities of the free water and the gas mixture decrease to 0. The variations of the vapor density and the vapor production rate with time are shown in Figures 9 and 10 at different radial 4018
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Figure 7. Predicted spatial variations of the superficial liquid free water velocity during drying of Huolinhe lignite. Dp = 30 mm; Tf = 140 C; Vf = 1.5 m/s; AH = 0.012 kg/kg.
Figure 8. Predicted spatial variations of the superficial gas velocity during drying of Huolinhe lignite. Dp = 30 mm; Tf = 140 C; Vf = 1.5 m/s; AH = 0.012 kg/kg.
Figure 9. Predicted vapor density at different radial positions for Huolinhe lignite. Dp, 30 mm; Tf, 140 C; Vf, 1.5 m/s; AH, 0.012 kg/kg.
positions in the lignite particles. Figure 9 shows that the vapor density first increases and then decreases to the ambient vapor density. Figure 10 shows that vapor is generated first near the outside of the particle and then more near the inside. During the drying, the outside temperature is higher than the inside temperature; therefore, evaporation is initially higher near the outside, while the mass-transfer resistance to the generated vapor
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Figure 10. Predicted vapor production rate at different radial positions for Huolinhe lignite. Dp = 30 mm; Tf = 140 C; Vf = 1.5 m/s; AH = 0.012 kg/kg.
flow leads to the increased vapor density. This finding is in agreement with the drying behavior of wood.33 These numerical results agree well with the experimental data for various drying conditions, and a detailed comparison has been given elsewhere.39 4.2. Drying in the Fixed Bed. 4.2.1. Gas Temperature Profiles. The multi-scale model was then applied to predict the gas temperature profiles at different bed heights above the gas distributor. The variations of the gas temperature with time are shown in Figure 11 at 100 and 300 mm above the gas distributor and at the outlet. The inlet gas velocity is 1.7 m/s with a temperature of 155 C, and the lignite particle stack height is 500 mm. Figure 11 shows that the gas temperature gradually increases until eventually reaching the inlet gas temperature. The predicted gas temperatures agree well with the measurements in Figure 11. The gas temperature in the lower layer is higher than in the upper layer, which shows that the gas temperature varies significantly with heights, and this temperature delay lead to the drying difference of particles. 4.2.2. Average Weight Loss Rate of Particles in the Fixed Bed. The variations of the average weight loss rate with time are shown in Figure 12 for the lignite particles for various drying conditions. The drying behavior is similar in all of the tests, although the duration of each drying process differs depending upon the particle stack height, inlet air temperature, and velocity. For the range of operating conditions investigated in this study, the drying time was reduced by increasing the inlet gas temperature and velocity and decreasing the particle stack height for both types of lignite. The predicted average weight loss rate variations over time agree well with the experimental results. The slight differences in drying times for the two kinds of lignite result from differences of the thermophysical properties and the intraparticle porosity of the lignite. Figure 12 shows that an increasing gas temperature reduces the drying time because a higher gas temperature improves the convection of the free water and the diffusion of the bound water. An increasing air velocity reduces the time required to achieve a desired level of average moisture content. The drying air velocity is also an important factor affecting the drying process, because it determines the heat- and mass-transfer coefficients on the external surface with higher air velocities, giving greater heatand mass-transfer coefficients. The strong influence of the particle stack height is readily observed with a more rapid decline in the average weight loss rate with time for the 125 mm particle 4019
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Figure 11. Predicted and measured gas temperatures. H = 500 mm; Tf = 155 C; Vf = 1.5 m/s.
Figure 12. Predicted and measured drying curves for different drying conditions.
stack height compared to the 250 and 500 mm particle stack heights because a lower particle stack height has a higher average gas temperature and a lower average relative humidity. 4.3. Intraparticle Drying Characteristics in a Fixed Bed. Numerical simulations can provide detailed information inside the particle, which is difficult to measure but very important. The numerical results have been shown to agree well with the experimental data, verifying that the mathematical model can properly evaluate the detailed moisture and temperature information inside the particle. 4.3.1. Intraparticle Moisture Variations at Different Bed Heights. Predicted intraparticle moisture variations with time are shown in Figure 13 for the lignite particles at different bed heights for fixed-bed drying. The inlet gas velocity is 0.6 m/s with a temperature of 155 C, and the lignite particle stack height is 500 mm. As expected, the lower layers dry more rapidly than the upper layers. At the inlet to the first layer, the drying conditions are
close to the inlet gas parameters. The drying medium can be considered to be infinite; thus, its conditions do not change during the drying process. Therefore, the drying process in the first layer is very similar to conventional convection drying at operating parameters equal to the inlet temperature and relative humidity. Figure 13 shows that the moisture content at the particle surface quickly decreases in the initial period. A large saturation difference appears in the particle for most of the drying process. In this case, the internal heat- and mass-transfer resistances significantly affect the drying process of this layer. Apparently, the lumped moisture model gives an incorrect description of the heat and mass transfer during drying. The outlet temperature and humidity of each layer then significantly affect the drying patterns of the following layers. Lower gas temperatures and higher gas relative humidities outside the particle will affect the moisture distribution in the particle. 4020
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Figure 13. Predicted intraparticle moisture variations at different bed heights.
Figure 14. Predicted intraparticle temperature variations at different bed heights.
4.3.2. Intraparticle Temperature Variations at Different Bed Heights. Predicted intraparticle temperature variations with time are shown in Figure 14 for the lignite particles at different bed heights for fixed-bed drying. The inlet gas velocity is 0.6 m/s with a temperature of 155 C, and the lignite particle stack height is 500 mm. The temperature distribution is quite different inside particles at different heights, with large temperature gradients inside each particle during drying. The temperature profiles reach a quasi-steady state, in which the temperature rises to an asymptotic value well below the inlet air temperature and remains there for a short period. The temperature then continues to rise to the external air temperature. The drying rate is relatively slow initially; therefore, the temperature increases because of heat absorption from the hot air without much evaporation. The temperatures then become quasi-steady as the heat transfer from the ambient is balanced by the heat absorbed by the evaporation. As the drying rate then slows, the heat transfer from the hot air results in temperature increases until all of the water is evaporated.
5. CONCLUSION A multi-scale approach was used for numerical investigations of lignite particles drying in a fixed bed. The multi-scale model simultaneously analyzed a macroscopic thin bed layer and a microscopic thin particle layer. The macroscopic heat and mass transfer between the drying gas and the lignite particle surfaces was calculated in conjunction with the microscopic intraparticle heat and mass transfer using transient boundary conditions. The microscopic intraparticle heat transfer was described assuming local thermodynamic equilibrium in the porous lignite particle with the mass transfer including convection of the free water, diffusion of the bound water, and convection and diffusion of the gas mixture in the lignite particle. The multi-scale model was
verified by comparison to a series of experiments with various gas velocities and temperatures at atmospheric pressure using two kinds of lignite particles. The simulations agree well with the experimental data for the average weight loss rate and the gas temperatures. The multi-scale simulations show that the effects of the drying conditions, such as the lignite particle stack height and the temperature and velocity of the drying gas, on the fixedbed drying process can be evaluated by this multi-scale drying model and that the intraparticle drying behavior at different bed heights in the fixed bed can also be described. This multi-scale model is applied to fixed-bed drying that allows the reader to realize the potential of such a model, namely, when applied to practical applications. In the future, this model will be extended to unstructured 2D modeling at the macroscopic level, with a wider range of possibilities: through drying and continuous drying. Then, this model will be extended to unstructured 2D modeling at the microscopic level considering the shape of particles. This would allow for a much broader set of problems to be solved: conveyor dryers, air-through drying, moving-bed drying, etc., with particles that can be different in size and shape.
’ AUTHOR INFORMATION Corresponding Author
*Telephone: +86-10-62785669. Fax: +86-10-62770209. E-mail:
[email protected].
’ ACKNOWLEDGMENT This research was supported by the National Natural Science Foundation of China (51076083) and the Special Funds for Major State Basic Research Projects National 973 Project (2006CB200305). 4021
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’ NOMENCLATURE AH = absolute humidity (kg kg1) C = specific heat (J kg1 K1) D = diffusivity (m2 s1) Dp = particle diameter (mm) g = acceleration of gravity vector (m s2) h = distance from the gas distributor (mm) hm = mass-transfer coefficient (m s1) hT = heat-transfer coefficient (W m2 K1) H = particle stack height (mm) J = Leverett function k = thermal conductivity (W m1 K1) K = intrinsic permeability (m2) Kr = relative permeability M = molecular weight (kg mol1) n = unit normal vector with direction out of surface P = pressure (N m2) r = distance from the particle center (m) R = universal gas constant (J K1 mol1) s = entropy (J K1 mol1) S = saturation t = time (s) T and ÆTæ = temperature (K) V = velocity (m s1) X = dry-basis moisture content (kg kg1) Δh = latent heat of vaporization (J kg1) Greek Letters
ε = porosity Λ = volume (m3) Λi = volume occupied in Λ by phase i μ = dynamic viscosity (kg m1 s1) F = density (kg m3) j = general variable ψ = chemical potential (J kg1) ω = production rate (kg m3 s1) Subscripts and Superscripts
0 = standard state a = air b = bound water c = capillary force eff = effective f = drying gas g = gas mixture hai = Hailaer lignite huo = Huolinhe lignite i = phase i in = inlet l = liquid free water p = constant pressure s = solid sat = saturated state v = water vapor center = center of particles sur = surface of particles
’ REFERENCES (1) Miknia, F. P.; Netzel, D. A.; Turner, T. F.; Wallace, J. C.; Butcher, C. H. Energy Fuels 1996, 10 (3), 631–640. (2) Hassan, K.; Rajender, G. Energy Fuels 2009, 23, 3392–3405.
ARTICLE
(3) Nagle, M.; Gonzalez-Azcarraga, J. C.; Phupaichitkun, S. Int. J. Food Sci. Technol. 2008, 43 (11), 1979–1987. (4) Nagle, M.; Azcarraga, J. C. G.; Mahayothee, B. J. Food Eng. 2010, 99 (3), 392–399. (5) Nganhou, J. Heat Mass Transfer 2004, 40, 727–735. (6) García-Perez, J. V.; Carcel, J. A.; García-Alvarado, M. A.; Mulet, A. J. Food Eng. 2009, 90, 308–314. (7) Srivastava, V. K.; John, J. Energy Convers. Manage. 2002, 43, 1689–1708. (8) Abhari, R.; Isaacs, L. L. Energy Fuels 1990, 4, 448–452. (9) Androutsopoulos, G. P. Chem. Eng. Sci. 1986, 41, 2053–2059. (10) Vorres, K. S. Energy Fuels 1994, 8, 320–323. (11) Wang, H. H. Energy Fuels 2007, 21, 3070–3075. (12) Miura, K.; Mae, K.; Li, W.; Kusakawa, T.; Morozumi, F.; Kumano, A. Energy Fuels 2001, 15, 599–610. (13) Hemisa, M.; Bettaharb, A.; Singhc, C. B.; Bruneaud, D.; Jayas, D. S. Drying Technol. 2009, 27, 1142–1151. (14) Naghavi, Z.; Moheb, A.; Ziaei-rad, S. Energy Convers. Manage. 2009, 518 (3), 936–942. (15) Salah, B. M.; Besma, K.; Mohamed, S. Appl. Therm. Eng. 2006, 26, 2110–2118. (16) Aregba, A. W.; Sebastian, P.; Nadeau, J. P. J. Food Eng. 2006, 77, 27–40. (17) Sitompul, J. P.; Istadi, I.; Sumardiono, S. Drying Technol. 2003, 21 (2), 217–229. (18) Sitompul, J. P.; Istadi, I.; Widiasa, I. N. Drying Technol. 2001, 19 (2), 269–280. (19) Istadi, I.; Sitompul, J. P. Drying Technol. 2002, 20 (6), 1123–1142. (20) Saastamoinen, J. J. Drying Technol. 2005, 23 (5), 1003–1025. (21) Yrjola, J.; Saastamoinen, J. J. Drying Technol. 2002, 20 (6), 1077–1099. (22) Saastamoinen, J. J.; Impola, R. Drying Technol. 1997, 15 (68), 1919–1929. (23) Saastamoinen, J. J.; Impola, R. Drying Technol. 1995, 13 (57), 1305–1315. (24) Luikov, A. V. Int. J. Heat Mass Transfer 1975, 18, 1–14. (25) Whitaker, S. Adv. Heat Transfer 1977, 13, 119–203. (26) Plumb, O. A.; Spolek, G. A.; Olmstead, B. A. Int. J. Heat Mass Transfer 1985, 28, 1669–1678. (27) Ilic, M.; Turner, I. W. Appl. Math. Model. 1986, 10, 16–24. (28) Ilic, M.; Turner, I. W. Int. J. Heat Mass Transfer 1989, 32, 2351–2362. (29) Nasrallah, S. B.; Perre, P. Int. J. Heat Mass Transfer 1988, 31, 957–967. (30) Quintard, M.; Whitaker, S. Adv. Heat Transfer 1993, 23, 3 69–464. (31) Rogers, J. A.; Kaviany, M. Int. Commun. Heat Mass Transfer 1992, 35, 469–480. (32) Perre, P.; Turner, I. W. Int. J. Heat Mass Transfer 1999, 42, 4501–4521. (33) Melaaen, M. C. Numer. Heat Transfer, Part A 1996, 29 (4), 331–355. (34) Nijdam, J. J.; Langrish, T. A. G.; Keey, R. B. Chem. Eng. Sci. 2000, 55, 3585–3598. (35) Lu, T.; Jiang, P. X.; Shen, S. Q. Heat Mass Transfer 2005, 41, 1103–1111. (36) Wang, Z. H.; Chen, G. H. Chem. Eng. Sci. 1999, 54 (17), 3899–3908. (37) Schlunder, E. U. Drying Technol. 2004, 22 (6), 1517–1532. (38) Tsotsas, E. Measurement and modelling of intraparticle drying kinetics: A review Proceedings of the 8th International Drying Symposium; Amsterdam, The Netherlands, 1992; Part A, pp 1741. (39) Zhang, K.; You, C. F. Energy Fuels 2010, 24, 6428–6436. (40) Chen, Z.; Wu, W.; Agarwal, P. K. Fuel 2000, 79, 961–973. (41) Agroskin, A. A. Thermal and Electrical Properties of Coals; Science and Technology Press: Moscow, Russia, 1959. 4022
dx.doi.org/10.1021/ef200759t |Energy Fuels 2011, 25, 4014–4023
Energy & Fuels
ARTICLE
(42) Couture, F.; Fabrie, P.; Puiggali, J. R. Drying behavior as influenced by the relative permeability relations Proceedings of the 9th International Drying Symposium; Brisbane, Queensland, Australia, 1994; Vol. 2, pp 263276. (43) Huang, C. L. D.; Siang, H. H.; Best, C. H. Int. J. Heat Mass Transfer 1979, 22 (2), 257–266. (44) Kansa, E. J.; Perlee, H. E. Combust. Flame 1977, 29, 311–324. (45) Stanish, M. A. Wood Sci. Technol. 1986, 20, 53–57. (46) Wang, Z. H.; Chen, G. H. Chem. Eng. Sci. 1999, 54, 4233–4243. (47) Guine, R. P. F.; Rodrigues, A. E.; Figueiredo, M. M. Appl. Math. Comput. 2007, 192, 69–77.
4023
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