Fluid dynamic modeling of a large bubbling fluidized bed for biomass combustion: Mass transfer in bubbles

Chemical Engineering Science xxx (xxxx) xxx

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Fluid dynamic modeling of a large bubbling fluidized bed for biomass combustion: Mass transfer in bubbles Juan Grimaldo Villanueva-Chávez, Waldir Antonio Bizzo ⇑ School of Mechanical Engineering, University of Campinas – UNICAMP, Cidade Universitária Zeferino Vaz, 13083-860 Campinas, SP, Brazil

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


Model includes the throughflow and

bypass flow in the bubble phase.
Emulsion phase not to remain under

minimum fluidization conditions.
Influence of downward particles in

emulsion phase was considered.
Correction factor for mass transfer

coefficient takes into account the bypass flow.

a r t i c l e

i n f o

Article history: Received 20 July 2018 Received in revised form 12 October 2018 Accepted 9 November 2018 Available online xxxx Keywords: Mathematical model Fluid dynamics Bubbling fluidized bed Combustion Biomass

a b s t r a c t A one-dimensional mathematical model of the fluid dynamics and combustion process in a bubbling fluidized bed was developed. In the bubble phase, the model includes the throughflow and bypass flow, which crosses the bed without taking part in combustion because of the preferential bubble paths expected in large fluidized-bed systems. Unlike in the classic approach, the emulsion phase was considered not to remain under minimum fluidization conditions, and the influence of downward particles was considered. A correction factor for the equation of the mass transfer coefficient previously described by other authors was therefore proposed to take into account the bypass flow expected in large systems. The main results provided by the model are the velocities and volumetric flows of the gases in the bed (emulsion, visible bubble and throughflow gases), the mass transfer between bed phases and the oxygen profile in the bed. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Biomass-based energy generation is of global interest because it allows fossil fuels to be replaced by fuels from renewable sources. Combustion of biomass and industrial waste using fluidized-bed technology is gaining importance because of its fuel flexibility and low pollutant emissions (without the need for large gascleaning systems). As a result, the number of scientific publications about biomass combustion and gasification in fluidized beds has ⇑ Corresponding author. E-mail address: [email protected] (W.A. Bizzo).

increased steadily over the last decade. In addition, large bubbling fluidized-bed boilers have been built to generate thermal and electrical energy from biomass in countries such as Brazil and the United States in recent years, showing that bubbling fluidized-bed technology can be the best solution even for largescale energy production from biomass. The popularity of fluidized-bed combustion is due mainly to the technology’s fuel flexibility and its ability to meet low-emissions requirements without expensive flue-gas treatment. Because of their high fuel flexibility, fluidized-bed boilers can efficiently burn a wide range of fuels, from high-calorific-value fuels such as coal to medium- and low-calorific-value ones such as peat, biomass and a

https://doi.org/10.1016/j.ces.2018.11.023 0009-2509/Ó 2018 Elsevier Ltd. All rights reserved.

Please cite this article as: J. G. Villanueva-Chávez and W. A. Bizzo, Fluid dynamic modeling of a large bubbling fluidized bed for biomass combustion: Mass transfer in bubbles, Chemical Engineering Science, https://doi.org/10.1016/j.ces.2018.11.023

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J.G. Villanueva-Chávez, W.A. Bizzo / Chemical Engineering Science xxx (xxxx) xxx

Nomenclature

aw db

c w

lg qC qg ee emf ee n A0 A a CC C O2;b C O2;e dB dC d
C

DG DO2 Dg;e Ds;e f g Hmf H K be

bubble wake fraction bubble phase fraction correction factor parameter gas viscosity (kg s1 m1) carbon particle density (kg m3) gas density (kg m3) emulsion phase porosity bed porosity at minimum fluidization velocity emulsion phase porosity number of moles of carbon burned for mole of oxygen cross-sectional area of the bed divided by the total number of orifices (m2) cross-sectional area of the bed (m2) throughflow parameter concentration of carbon particles, C C (kmol m3) oxygen concentration in the bubble phase (kmol m3) oxygen concentration in the emulsion phase (kmol m3) bubble diameter (m) fixed-carbon-particle diameter (m) mean carbon-particle diameter (m) molecular diffusivity of the gases (m2 s1) oxygen diffusivity (m2 s1) gas dispersion coefficient in the emulsion phase (m2 s1) axial solids dispersion coefficient in the emulsion phase (m2 s1) stoichiometric coefficient gravitational acceleration (m s2) bed height at minimum fluidization velocity (m) expanded bed height (m) mass transfer coefficient between bubble and emulsion (s1)

variety of different types of municipal and industrial organic waste (Jakobsen, 2008). A one-dimensional mathematical model of the fluid dynamics and combustion process in a bubbling fluidized bed was developed. In the bubble phase, the model includes the throughflow and bypass flow, which crosses the bed without taking part in combustion because of the preferential bubble paths expected in large fluidized-bed systems. Unlike in the classic approach, the emulsion phase was considered not to remain under minimum fluidization conditions, and the influence of downward particles was considered. A correction factor, c, for the equation for calculating the mass transfer coefficient described by Sit and Grace (1981) was therefore proposed to take into account the bypass flow expected in large systems. The main results provided by the model are the velocities and volumetric flows of the gases in the bed (emulsion, visible bubble and throughflow gases), the mass transfer between bed phases and the oxygen profile in the bed.

kc keff kg Mc _ ar;p m NC NC;tot Q B;v is Qe Q tf Q total RC;s RC;v R Sh uB;1 uB ub U e;o ue Ue U mf Uo utf U

vs

yc z

kinetic reaction rate coefficient (m s1) effective reaction rate coefficient (m s1) mass transfer coefficient of gas in the boundary layer of the carbon particle (m s1) molecular weight of carbon (12 kmol kg1) primary air flow (kg s1) number of carbon particles per volume (m3) number of carbon particles in the bed visible bubble flow (m3 s1) flow in the emulsion phase (m3 s1) throughflow (m3 s1) total volumetric flow (m3 s1) superficial combustion rate (kmol m2 s1) volumetric combustion rate (kmol m3 s1) universal gas constant Sherwood number isolated bubble rise velocity (m s1) bubble rise velocity (m s1) bubble phase velocity (m s1) air superficial velocity in the emulsion phase at bed inlet (m s1) intersticial gas velocity in the emulsion phase (m s1) gas superficial velocity in the emulsion phase (m s1) minimum fluidization velocity (m s1) fluidization velocity at the bed inlet (m s1) throughflow velocity (m s1) superficial fluidization velocity (m s1) vertical solids velocity in the emulsion phase (m s1) carbon-particle volumetric fraction in the bed vertical position above distributor (m)

1.1.1. Gas throughflow The model proposed by Davidson and Harrison (1985) shows the differences between gas throughflow generated in smallparticle systems (Geldart type A) and medium- and large-particle ones (Geldart types B and D). In the first case, bubbles rise through the bed faster than the emulsion-phase gas and a cloud is generated around the bubbles (Fig. 1a). In large-particle systems, bubbles rise slower than the emulsion-phase gas and two types of gas flow pass through the bubble (Fig. 1b): the first passes through the bubble and continues on its way in the emulsion phase (direct

1.1. The influence of mass transfer of gases on bubbling fluidized-bed combustion An important factor that affects the combustion process is the mass transfer of gases in the bed. Mass transfer phenomena have a major influence on fixed-carbon combustion rates and determine the oxygen-concentration distribution in the bed. Two important fluid dynamic phenomena must be considered in any fluidizedbed combustion model: gas throughflow and the effect of preferential bubble paths.

Fig. 1. Throughflow for (a) fast bubbles and (b) slow bubbles (Hilligardt and Werther, 1987).

Please cite this article as: J. G. Villanueva-Chávez and W. A. Bizzo, Fluid dynamic modeling of a large bubbling fluidized bed for biomass combustion: Mass transfer in bubbles, Chemical Engineering Science, https://doi.org/10.1016/j.ces.2018.11.023

J.G. Villanueva-Chávez, W.A. Bizzo / Chemical Engineering Science xxx (xxxx) xxx

throughflow), and the second is an annular flow which, like the cloud, recirculates around the bubble. The amount of recirculation flow depends on the pressure field around the bubble and increases with bubble velocity. Chavarie and Grace (1976) and Sit and Grace (1981) found that mass transfer between bed phases is significantly higher during bubble interaction. Gera and Gautam (1995) observed that the volume of a bubble produced by coalescence of two bubbles is greater than the sum of the volumes of the original bubbles, showing that part of the emulsion-phase gas is transferred to the new bubble during coalescence. Therefore, throughflow in freely bubbling beds is higher because of bubble coalescence. Hilligardt and Werther (1987) calculated the throughflow in slow bubbles in freely bubbling beds and found that the velocity through the maximum cross-sectional area of the bubbles is utf ¼ 2:7 U mf , being U mf the minimum fluidization velocity. According to Clift and Grace (1985), if we consider that the velocity of the emulsion gas (U e ) does not remain equal to the minimum fluidization velocity, i.e., U e > U mf , then the parameter U mf in the throughflow velocity correlations can be replaced by U e . Therefore, in general, we can write:

3

2. Mathematical model A gas flow can pass across a horizontal cross section of a bed by the following mechanisms: (1) interstitial flow in the emulsion phase, Q e , (2) visible bubble flow, Q B;v is , and (3) throughflow, Q tf . Thus, we can write the mass balance of gases as follows:

Q total ¼ Q e þ Q B;v is þ Q tf

ð2Þ

where Q total is the total volumetric flow of gases crossing a horizontal cross section of the bed. Writing the flows in the above equation in terms of the corresponding velocities, we obtain:

U ¼ ue ee ð1  db Þ þ uB db þ utf db

ð3Þ

where a is the throughflow parameter. Valenzuela and Glicksman (1985) found theoretically that utf ¼ 3 U e for low bubble fractions, which is very close to the experimental value reported by Hilligardt and Werther (1987), and showed that bubble shape can have a significant influence on the throughflow parameter a. For elongated bubbles this parameter increases, while the opposite effect occurs when the bubbles are flat. They also showed that throughflow can increase significantly in systems with preferential bubble paths.

where ue is the intersticial gas velocity, ee is the emulsion phase porosity, db is the bubble phase fraction in the bed, and uB is the bubble velocity Operating conditions typically found in industrial bubbling fluidized-bed boilers using biomass as fuel were adopted here, i.e., fuel fed from above the bed and substoichiometric combustion in the bed. Because volatiles are burned mainly in the splash zone and freeboard and because of the relatively low fixed-carbon content in biomass as well as its high intrinsic reactivity, substoichiometric combustion is appropriate for modeling fluidized beds. Under these conditions the biomass can be considered to have dried when it reaches the surface of the bed, and combustion of the volatiles can be considered to occur mainly in the splash zone and freeboard. Even if it is accepted that devolatilization also occurs in the bed, most of the volatiles released in the bed will pass through it unburned (Scala and Salatino, 2002). The main assumptions made to develop the model were as follows:

1.1.2. Bubble distribution and preferential bubble paths According to Croxford and Gilbertson (2011), bubble distribution in a bubbling is very important because it determines the pressure field and gas flows in the bed. Close to the bed walls, bubbles can move only vertically, while far from the walls they can move vertically and horizontally. As a result, most bubbles are concentrated far from the walls. In large-particle systems, such as those typically used in combustion applications, the existence of preferential bubble paths depends on the operating conditions. For example, Glicksman and McAndrews (1985) did not find preferential bubble paths in a 1.2 m  1.2 m system with 1 mm particle diameter operating with a velocity ratio U=U mf ¼ 1:8. On the other hand, Pallarès et al. (2007) found preferential bubble paths in a 1.2 m-wide bidimensional system with a mean particle diameter of 330 lm. Industrial bubbling fluidized-bed boilers operate with fluidization velocities in the range U ¼ 1:5—2 m s1 (much greater than the minimum fluidization velocity) and a relatively low pressure drop in the distributor, causing large, eruptive bubbles. Olsson et al. (2010), using the same system conditions as Pallarès et al. (2007), proved experimentally that a reduction in distributor pressure drop affects the homogeneous distribution of bubbles in the bed, leading to the formation of bubble paths. Bubble caps, which are commonly used in industrial boilers, also favor the formation of preferential bubble paths. According to Fitzgerald et al. (1984) and Oka (2004), systems with preferential bubble paths increase system bypass flow significantly. Bypass flow is the flow that passes through the bed without mixing with the gas in the emulsion phase and therefore does not participate in the combustion process. This article describes a mathematical model of fixed-carbon combustion in bubbling fluidized beds. Emphasis is placed on the mass transport phenomena that control the oxygen distribution in the bed. Application of the model to a large-scale bubbling fluidized-bed boiler burning biomass is also described.

1. The fluidized bed is divided into two phases: a bubble phase and an emulsion phase. The bubble wake is considered part of the emulsion phase. 2. Bubbles are particle free, and fuel combustion can occur only in the emulsion phase. In addition, since solid transfer between the emulsion and bubble wake is not considered, the wake is assumed to be free of fuel particles. 3. The model is one dimensional; thus, properties only vary along the vertical axis, z. 4. The system is operating in the steady-state regime. 5. The system is isothermal. 6. The gas and solid dispersion coefficients, Dg;e and Ds;e , are assumed not to vary with height, i.e., mean values for these coefficients were used. 7. Inert particles are a constant size and uniformly distributed in the bed; therefore, the formation of fines due to friction or combustion was ignored. 8. There is no solid entrainment from bed to freeboard. 9. When fuel particles reach the surface of the bed their moisture content is zero, and volatiles are burned in the splash zone and freeboard. 10. The fixed carbon consists only of pure carbon. 11. The effects of ash on the fluid dynamics of the bed, whether due to agglomeration or interparticle forces, can be neglected. 12. Particle density is constant, and particle diameter varies during combustion as the shrinking-core combustion model was used. 13. All fuel particles reach the surface of the bed with an initial diameter dC;o , and the number of active particles does not vary with height in the bed (constant number density of carbon particles, N c ). 14. Ash layers formed during combustion can be neglected. In other words, these are assumed to be moved by the abrasive action of the bed.

utf ¼ a U e

ð1Þ

Please cite this article as: J. G. Villanueva-Chávez and W. A. Bizzo, Fluid dynamic modeling of a large bubbling fluidized bed for biomass combustion: Mass transfer in bubbles, Chemical Engineering Science, https://doi.org/10.1016/j.ces.2018.11.023

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15. The superficial combustion rate, RC;s , is proportional to the oxygen concentration in the emulsion phase, i.e., a firstorder reaction was considered. The main fluid dynamic and combustion parameters considered in the mathematical model were as follows: – Fluidization velocity, U: This is the fluidization velocity of two combined flows - primary air entering through the distributor and the gas flow generated during the combustion process. Hence, we have:

U¼

_ ar;p M c m þ qg A qg A

Z

z

0

ð4Þ

RC;v dz

where RC;v is the combustion rate expressed per unit volume of _ ar;p is the primary air flow emulsion gas (kmol s1 m3). Also, m (kg s1), M c is the molecular weight of carbon (12 kmol kg1), A is the cross-sectional area of the bed, qg is the gas density and z is the vertical position above distributor. – Bubble fraction, db : This was estimated by performing a mass balance in the bed. From Eq. (3) we obtain:

db ¼

U  ue ee uB þ utf  ue ee

ð5Þ

– Superficial velocity in the emulsion phase, U e : This varies exponentially with height above the distributor, as proposed by Sane et al. (1996). If we assume that U e ðz ¼ 0Þ ¼ U e;o and U e ðz ¼ HÞ  1:2 U mf ; H being the expanded bed height, we have:

    U e ðzÞ ¼ 1:2 U mf þ U e;0  1:2 U mf e5z þ Z  0

Mc

qg ð1  db ÞA

z

ð6Þ

RC;v dz

U e;o was calculated using the equation proposed by Hilligardt and Werther (1987). This gives the initial superficial velocity in the emulsion phase as a function of initial fluidization velocity:

U e;o ¼ U mf þ

 1 U o  U mf 3

ð7Þ

– Emulsion phase porosity, ee : This was calculated using the equation proposed by Delvosalle and Vanderschuren (1985), emf is the bed porosity at minimum fluidization velocity:



ee ¼ emf

Ue U mf

1=6:7 ð8Þ

– Bubble diameter, dB : Darton’s equation was used with U mf for ambient conditions (Darton, 1979). For high-temperature conditions the graph proposed by Hilligardt and Werther (1987) was used. This gives a correction factor of 0.91 for U  U mf  1. Darton’s equation can therefore be written as

 dB ¼ 0:91  0:54 U o  U mf T

0:4 amb

pffiffiffiffiffi 0:8 z þ 4 A0 g 0:2

ð9Þ

where A0 is the total cross-sectional area of the bed divided by the total number of orifices. A value of A0 ¼ 0:000375 m2 was used. g is the gravitational acceleration. – Rising velocity of bubbles, uB : The equation proposed by Werther (1977) was used. This expresses bubble velocity as a function of the parameter w, which is the ratio between visible   bubble flow (uB;1 ) and excess gas flow, A U  U mf :

  uB ¼ w U  U mf þ uB;1

ð10Þ

– Throughflow parameter, a: This parameter cannot be determined very accurately because it depends on several factors.

It was therefore decided to investigate its influence on other system parameters. Table 1 shows the values of various fluid dynamic parameters for values of a from 3 to 7. H is the height of the expanded bed and Hmf is the bed height at minimum fluidization velocity. Values of a ¼ 4 and a ¼ 5 provide results that more closely reflect experimental evidence. Higher values of a yield lower bed-height expansion than expected and bubble velocities much higher than for the emulsion gas, contradicting experimental evidence, which shows slow bubbles in large-particle systems. Hence, for the purposes of simulation, a mean value of a ¼ 4:5 was assumed. – Mass transfer coefficient between bubble and emulsion, K be : In systems with preferential bubble paths, a fraction of the throughflow passes through the bed without mixing with the emulsion phase, reducing mass transfer by convection between bed phases. Therefore, a correction factor, c, was used in the convection term of the equation proposed by Sit and Grace (1981). Thus, we obtain:

 
tf emf DG uB 0:5 u K be ¼ 1:5 c
þ 6:77 dB d
B 3

ð11Þ

where c is an effectivity factor such that when c ¼ 1 no gas bypass is expected in the bed and all the throughflow passes through the emulsion phase (after leaving the bubble), while a value of c lower than 1 ð0 < c < 1Þ means that part of the gas throughflow, even though it crosses the bubble boundaries, remains in a bubble path and does not mix with the emulsion phase. The bubble diameter is dB , and DG is the molecular diffusivity of the gases. Table 2 shows the results for different values of c. There is little data in the literature about mass transfer coefficients in large-scale boilers for conditions like those considered here. Vepsäläinen et al. (2014) found values of around 5 s1 for similar operating conditions (dp ¼ 1 mm; U ¼ 2 m s1) but used a value of a ¼ 3, which reduces the interphase mass transfer coefficient significantly. As values of K be for c ¼ 0:7 seem to be very high compared with those reported by Vepsäläinen et al. (2014) and as bypass flow is expected to increase with height because of bubble coalescence, c was chosen to be 0.6 (40% bypass) at the base of the bed, decreasing to 0.4 (60% bypass) at the surface of the bed. Although this choice is somewhat intuitive, it should be remembered that preferential paths and gas bypasses depend on bubble distribution, which in turn depends on many factors, such as distributor pressure drop, bed geometry and operating conditions; therefore, c would appear to be very system dependent. – Substoichiometric combustion:

ð1 þ f Þ C þ O2 ! 2f CO þ ð1  f ÞCO2

ð12Þ

Thus, the number of moles of carbon burned for each mole of oxygen is

n¼1þf

ð13Þ 1

– Mass transfer in the boundary layer, kg (m s ): This was estimated from the Sherwood number, Sh, oxygen diffusivity, DO2 , and fixed-carbon-particle diameter, dC :

Table 1 Fluid dynamic parameters for different values of a. a

3

4

5

6

7

H (m) ðH  Hmf Þ=Hmf db w

0.79 0.58 0.31 0.32

0.73 0.46 0.25 0.24

0.69 0.39 0.21 0.19

0.67 0.34 0.18 0.16

0.65 0.30 0.16 0.13

Please cite this article as: J. G. Villanueva-Chávez and W. A. Bizzo, Fluid dynamic modeling of a large bubbling fluidized bed for biomass combustion: Mass transfer in bubbles, Chemical Engineering Science, https://doi.org/10.1016/j.ces.2018.11.023

J.G. Villanueva-Chávez, W.A. Bizzo / Chemical Engineering Science xxx (xxxx) xxx Table 2 Variation in the mass transfer coefficient with parameter c.

c K be (s

1

)

0.3

0.5

0.7

9.0

14.5

20.1

Sh DO2 kg ¼ dC

ð14Þ

The molecular diffusivity of oxygen in the boundary layer was assumed to be DO2 ¼ 0:000132 m2 s1, as used by Vepsäläinen et al. (2014). – Kinetic reaction rate coefficient, kc (m s1): The formula described by Canò et al. (2007) was used with parameters for combustion of sub-bituminous coal:

kc ¼ 16 exp

  30350 R Tc

ð15Þ

where R is the universal gas constant and T c is the absolute temperature of carbon particle. – Effective reaction rate coefficient, keff (m s1): Assuming a firstorder reaction rate and shrinking-core combustion model, the effective reaction rate coefficient is given by

keff ¼

n kc kg kc þ n kg

ð16Þ

where kg is the mass transfer coefficient of gas in the boundary layer of the carbon particle. – Superficial combustion rate, RC;s : For a first-order reaction this is given by

RC;s ¼ keff C O2;e

ð17Þ

being C O2;e the oxygen concentration in the emulsion phase (kmol m3). – Volumetric combustion rate, RC;v : This can be written as a function of the concentration of carbon particles, C C (kmol m3), and their number density, N C , the number of carbon particles per volume (m3):



 2  RC;v ¼ aC RC;s ¼ NC p dC keff C O2;e  2=3 6 MC p0:5 1=3 2=3 NC C C keff C O2;e ¼

qC

where qC is the fixed-carbon particle density (kg m3). Mass balance equations Oxygen concentration in the bubble phase C O2;b : The bubble phase is modelled without a gas diffusion coefficient:

    d ub db C O2;b ¼ db K be C O2;b  C O2;e dz

ð19Þ

Oxygen concentration in the emulsion phase C O2;e : The oxygen balance in the emulsion phase includes a gas diffusion coefficient and a combustion rate term which represents oxygen consumption in the emulsion phase due to particle combustion:



d d d ½ð1  db Þee C O2;e  Dg;e ½ue ð1  db Þee C O2;e  ¼ dz dz dz   þ db K be C O2;b  C O2;e  ð1  db Þ ee

A1 N1=3 C C2=3 keff C O2;e n

Carbon-particle concentration in the emulsion phase C C : The mass balance for carbon particles in the emulsion phase is given by:



d½v s ð1  db Þ ee C C  d d½ð1  db Þ ee C C  ¼ Ds;e dz dz dz 2=3  ð1  db Þ ee A1 N1=3 C C C keff C O2;e

ð20Þ

 2=3 The constant A1 ¼ 6 MC p0:5 =qC was defined to simplify the differential equation.

ð21Þ

where v s is the mean vertical solids velocity in the emulsion phase and Ds;e is the axial solids dispersion coefficient in the emulsion phase. Boundary Conditions Oxygen concentration in the bubble phase: As air is fed into the bed through the distributor, the oxygen concentration at the bed inlet is equal to the oxygen concentration in the air:

C O2;b ðz ¼ 0Þ ¼ C O2;in

ð22Þ

Oxygen concentration in the emulsion phase: As in the bubble phase, the oxygen concentration at the bed inlet is equal to the oxygen concentration in the air. For the second boundary condition, the concentration gradient at the surface of the bed is assumed to be zero.

C O2;e ðz ¼ 0Þ ¼ C O2;in

ð23Þ

 dC O2;e  ¼0 dz z¼H

ð24Þ

Carbon concentration in the emulsion phase: As all the carbon is burned in the bed, the carbon concentration (kmol m3) at the base of the bed is assumed to be zero, as in Eq. (25). For the second boundary condition, since the biomass is fed from above the surface of the bed, the concentration at the surface is equal to the concentration of carbon entering the bed, given by Eq. (26) below.

C C ðz ¼ 0 Þ ¼ 0

ð25Þ

C C ðz ¼ HÞ ¼ C C;in

ð26Þ

where the carbon concentration at the surface of the bed is given by

C C;in ¼ ð18Þ

5

3 qC NC p dC;o

MC

6

ð27Þ

The particle number density, N c , does not vary with height above the distributor and can be calculated as a function of the carbon-particle volumetric fraction in the bed, yc , and mean carbon-particle diameter, d
C .

NC ¼

6 yC ð1  ee Þ

p d
C 3

ee

ð28Þ

The differential equations in the model were solved using the control volume method (Patankar, 1980) and upwind discretization scheme for the bubble phase and the hybrid scheme for the emulsion phase. 3. Results and discussion To analyze the fluid dynamic behavior of the bed, the model was tested using real operating conditions for a large-scale fluidized-bed boiler. The boiler operating conditions are shown in Table 3. The bed operating conditions are show in Table 4. Table 5 shows the chemical composition and results of proximate analysis of the biomass and the main properties of the fixed carbon. The values of the main fluid dynamic parameters predicted by the model are shown in Table 6. Table 7 shows the values of the

Please cite this article as: J. G. Villanueva-Chávez and W. A. Bizzo, Fluid dynamic modeling of a large bubbling fluidized bed for biomass combustion: Mass transfer in bubbles, Chemical Engineering Science, https://doi.org/10.1016/j.ces.2018.11.023

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J.G. Villanueva-Chávez, W.A. Bizzo / Chemical Engineering Science xxx (xxxx) xxx

Table 3 Boiler operation conditions. Steam production Steam pressure Steam temperature Boiler feedwater temperature Boiler thermal efficiency, gt

Table 6 Values of the main fluid dynamic parameters. 69.45 kg s1 10 000 kPa 540  C 140  C 90%

(250 000 kg h1) (100 bar)

Table 4 Bed operating conditions. Bed operating conditions Bed temperature Bed height at minimum fluidization, Hmf Bed porosity at minimum fluidization, emf Excess air Primary air (fluidization air) Bed area, A Air fluidization velocity, U 0 Bed material: silica sand Mean diameter Inert-particle density, qp Sphericity, /s Combustion gas properties Density, qg Viscosity,

lg

800  C 0.5 m 0.43 25% 38 kg s1 72 m2 1.48 m s1 0.92 mm 2500 kg m3 0.85 0.367 kg m3 4.19  105 Pa s

Table 5 Biomass properties. Elemental analysis Carbon Hydrogen Oxygen Nitrogen Sulfur Moisture Ash

% weight (w.b.) 23.48 3.17 21.85 0.0 0.0 50.0 1.5

LHV (MJ kg1, wb)

7.66

Proximate analysis

% weight (w.b.)

Moisture Volatiles Fixed carbon Ash

50.0 36.5 12.0 1.5

Fixed-carbon properties Initial diameter, dC;o Density, qc Molar mass, M C

_ cf ) Calculated carbon feed, n_ cf (M

1 mm 180 kg m3 12 kg kmol1 292 mol s1 (3.5 kg s1)

wb = wet basis; LHV = lower heating value.

fluid dynamic parameters predicted by the model for the bubble and emulsion phases. The downward particle velocity, v s , in Table 7 is very low because of the small bubble wake fraction, aw ¼ 0:2, found in large-particle systems and thus does not have a significant influence on the interstitial velocity. The value of the Werther constant is in line with experimental values found by Werther (1977) (w ¼ 0:26) for 0.5 mm-diameter particles and by Glicksman et al. (1987) (w ¼ 0:1—0:2) for 1 mm-diameter particles. The mean bubble velocity, uB ¼ 1:1 m s1, is less than the gas velocity in the emulsion phase, ue ¼ 1:4 m s1, as expected for a system with Geldart group D particles. While bubble velocity increases with height above the distributor, the velocity of gases in the emulsion phase decreases, as shown in Fig. 2, which also shows how the throughflow velocity, utf and relative velocity, ue , vary with height.

Parameter Expanded bed height, H Voidage, e Terminal velocity, ut Relative velocity, ue:s Mass transfer coefficient, K be

0.71 m 0.60 3.72 m s1 1.47 m s1 13.8 s1

Conditions at minimum fluidization Bed height, Hmf Voidage, emf Minimum fluidization velocity, U mf

0.50 m 0.43 0.36 m s1

Table 7 Mean values of the fluid dynamic parameters for the bed phase. Bubble phase Mean bubble diameter, dB Werther constant, w Bubble fraction, db Bubble velocity, uB Throughflow parameter, a Throughflow velocity, utf (=a U e ) Bubble-phase velocity, ub

150 mm 0.22 0.24 1.1 m s1 4.5 3.2 m s1 4.3 m s1

Emulsion phase Gas volume, V g;e Superficial velocity, U e (>U mf ) Voidage, ee (>emf ) Solid-particle velocity, v s Interstitial velocity, ue Gas dispersion coefficient, Dg;e Solid dispersion coefficient, Ds;e

19.2 m3 0.72 m s1 0.48 0.04 m s1 1.4 m s1 0.03 m2 s1 0.02 m2 s1

The bubble velocity is slightly higher than the emulsion-gas velocity in regions close to the surface of the bed. This is an undesired effect because it creates gas recirculation around the bubbles and reduces convective interphase mass transfer. Fig. 3 shows the variation in gas flow with height above the distributor. Gas throughflow is about half of the total volumetric gas flow. As mentioned before, part of this flow passes through the bed inside the preferential bubble paths as bypass gases. Fig. 4 shows the variation in mass transfer coefficient with height above the distributor calculated using the equation proposed by Sit and Grace (1981) with the correction factor, c. K be decreases with height, which can be explained by the increase in bubble diameter with height. As expected from Eq. (11), both the convection and diffusion terms decrease with bubble size. Fig. 4 also shows that the convection term is far more important than the diffusion term. It can therefore be deduced that the former predominates in systems with high throughflow even under high-temperature conditions. This corroborates the approach adopted by Hernández-Jiménez et al. (2013), who disregard the diffusion term in their model. Combustion and oxygen profile Table 8 shows the main combustion parameters predicted by the model. The carbon-particle fraction found was yc ¼ 6:2%, which agrees with values reported in the literature. This value is directly related to the carbon concentration, C C , which is calculated by the model so as to ensure that the rate at which combustion of carbon particles takes place is equal to the fixed-carbon feed rate, n_ cf (291 mol s1). Fig. 5 shows the oxygen concentration profile in the emulsion and bubble phases. In the emulsion phase, O2 is consumed quickly in the lower region of the bed (0 < z < 0:2) because of the higher concentration of O2 in this region and, thus, the higher specific combustion rate, Rc;s ¼ keff C O2;e . Since there is more oxygen in the feed air than required in the substoichiometric

Please cite this article as: J. G. Villanueva-Chávez and W. A. Bizzo, Fluid dynamic modeling of a large bubbling fluidized bed for biomass combustion: Mass transfer in bubbles, Chemical Engineering Science, https://doi.org/10.1016/j.ces.2018.11.023

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Fig. 2. Gas flow velocities vs. height above distributor.

Fig. 4. Variation in mass transfer coefficient with height above the distributor.

Table 8 Values of the main combustion parameters predicted by the model. Mean carbon-particle diameter Carbon-particle volume fraction, yc Specific surface area, ac Sherwood number, Sh Mean combustion rate, Rc;v Mean carbon-particle concentration Carbon-particle residence time, s Fixed-carbon consumption in the bed Oxygen consumption in the bed

0.74 mm 6.2% 272 m2 m3 2.57 15.2 mol m3 s1 588 mol m3 39 s 291 mol s1 245 mol s1

4. Validation of the model

Fig. 3. Variation in gas flow with height above the distributor.

reaction assumed in the model, oxygen is left in the bed even in the emulsion phase because of mass transfer from the bubble phase. Fig. 6 shows a comparison of the diffusion coefficient in the boundary layer, kg , and the kinetic chemical reaction coefficient, kc . Since the diameters of the carbon particles decrease as the particles travel from the surface of the bed to the bottom, there is a significant increase in kg and, thus, an increase in keff in the lower region of the bed, as shown in Fig. 6. In Fig. 6.a the kinetic coefficient is higher than the diffusion coefficient at most heights in the bed. It can therefore be deduced that in this study the combustion process is controlled mainly by diffusion of oxygen between the bed and the boundary layers of active particles. Only in the lowest region of the bed, where carbon-particle diameter is expected to be very low, is the combustion process controlled by the kinetics of the reaction.

The results for the fluid dynamic parameters were validated by comparing them with the experimental results reported by Shen et al. (2004), and the oxygen profile and results for the combustion model were compared with those reported by Vepsäläinen et al. (2014), who developed a model for biomass combustion under similar conditions to those considered here. Using digital image analysis, Shen et al. (2004) estimated some fluid dynamic properties for an experimental bed 0.68 m wide and 0.07 m deep. The operating conditions they used are given in Table 9. Fig. 7 shows the variation in bubble diameter with height for the model described here and the experimental results obtained by Shen et al. (2004). Like the model developed by Shen et al. (2004), the present model does not predict the reduction in the rate of increase of the bubble diameter observed experimentally, where the bubble diameter appears to approach a maximum value close to the bed surface. Fig. 8 shows the variation in bubble velocity with height above the distributor for the model described here and the experimental values reported by Shen et al. (2004). The results are very similar for values of U up to approximately U ¼ 2:5 U mf . Above this, however, the bubble velocity predicted by the present model is slightly higher. The greatest difference is when U ¼ 4 U mf , at which point the bubble velocity predicted by the present model is about 10% higher than the experimental value at half the bed height (z ¼ 260 mm) and about 25% higher at the surface of the bed.

Please cite this article as: J. G. Villanueva-Chávez and W. A. Bizzo, Fluid dynamic modeling of a large bubbling fluidized bed for biomass combustion: Mass transfer in bubbles, Chemical Engineering Science, https://doi.org/10.1016/j.ces.2018.11.023

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Fig. 5. Variation in oxygen concentration with height above the distributor.

Fig. 6. (a) Variation in diffusion coefficient, kg , and kinetic coefficient, kc with height above the distributor. (b) Variation in effective reaction rate with height above the distributor.

Table 9 Operating conditions used in Shen et al. (2004). Bed material Inert-particle density, qp Mean inert-particle diameter, dp Minimum fluidization height, Hmf Distributor area divided by number of orifices, Ao Bed temperature, T Fluidization velocity, U

Silica sand 2600 kg m3 0.79 mm 0.41 m 8:56  105 m2 25  C ð1:5—4:0ÞU mf m s1

Fig. 9 shows the variation in bubble fraction with fluidization velocity predicted by the present model and the experimental values reported by Shen et al. (2004). The experimental value increases very slowly with height, particularly for velocities above

Fig. 7. Bubble diameter vs. height above distributor. Solid lines: this work; symbols: Shen et al. (2004).

Fig. 8. Bubble velocity vs. height above distributor. Solid lines: this work; symbols: Shen et al. (2004).

U ¼ 2:5 U mf , at which point the bubble fraction estimated by the present model is about 20% higher. At higher fluidization velocities, however, the difference is much greater, and at maximum velocity, U ¼ 4 U mf , the bubble fraction is about twice the experimental value. While Shen et al. (2004) measured bubble velocity and bubble diameter experimentally using sensors to determine the position of the bubble, they did not measure bubble fraction directly. The resulting experimental errors may therefore have contributed to the differences discussed above. Shen et al. (2004) used a bidimensional bed 70 mm thick and measured bubble volume by taking photographs of the bed walls. Consequently, bubbles with a diameter of less than 70 mm could not be detected because the camera

Please cite this article as: J. G. Villanueva-Chávez and W. A. Bizzo, Fluid dynamic modeling of a large bubbling fluidized bed for biomass combustion: Mass transfer in bubbles, Chemical Engineering Science, https://doi.org/10.1016/j.ces.2018.11.023

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J.G. Villanueva-Chávez, W.A. Bizzo / Chemical Engineering Science xxx (xxxx) xxx Table 10 Operating conditions in the model proposed by Vepsäläinen et al. (2014). Fixed-carbon combustion parameters Bed temperature, T Minimum fluidization height, Hmf Inert-particle diameter, dp Fluidization velocity, U Solid-particle density, qp Solid-particle sphericity, /s Gas density, qg Gas viscosity,

800  C 0.5 m 0.5 mm 1 m s1 2500 kg m3 0.85 0.31

lg

Gas dispersion coefficient in the emulsion phase, Dg;e Kinetic reaction rate coefficient, kc

45  106 kg s1 m1 0.0 (m2 s1) 0.1 m s1

Table 11 Comparison of results.

dp (mm) U (m s1)

emf

Fig. 9. Bubble fraction vs. fluidization velocity ratio: (a) This work, (b) Shen et al. (2004).

U mf (m s1) K be (s1) db (–) dB (mm) ub (m s1) ue:s (m s1) ue (m s1)

Vepsäläinen et al. (2014)

This work

0.5 1.0 0.43 0.12 2.9 0.37 67 2.3 0.53 (as U e =emf ) –

0.5 1.0 0.47 0.10 7.7 0.30 159 2.8 0.62 0.56

only captured bubbles when they occupied the space between the bed walls. In addition, the software used to generate the binary images based on the photographs determined the total bubble fraction and emulsion fraction of the bed using an image contrast criterion according to which a value above a certain critical voidage indicated the presence of a bubble. This subjective criterion could be another source of error in the calculation of the bubble fraction. Vepsäläinen et al. (2014) developed a Eulerian CFD model of a bubbling fluidized-bed system. Using the parameter results from CFD model, the authors used a 1-D steady-state model which includes mass balance equations similar to that used here, but does not include a diffusion term for the emulsion phase (Dg;e ¼ 0). Both phases are modelled in plug flow, and inert particles with a diameter of 0.5 mm and density of 2500 kg m3 are assumed. The fluidization velocity is U ¼ 1 m s1. The other operating conditions used in the model are shown in Table 10. As Vepsäläinen et al. (2014) assumed complete combustion in the bed, the same condition was assumed in the present model to allow it to be properly validated. The stoichiometric equation assuming complete carbon combustion in the emulsion phase is:

C þ O2 þ 3:76 N2 ! CO2 þ 3:76 N2

ð29Þ

Stoichiometric ratio between total fluidization air entering into the bed and fuel considered in this comparison was 1.1. Table 11 shows the results obtained using the present model and the model described by Vepsäläinen et al. (2014) for the same operating conditions. Finally, Fig. 10 shows the oxygen concentration profiles predicted by each model. In the model proposed by Vepsäläinen et al. (2014), almost all the oxygen is consumed within several centimeters of the bottom of the bed. The profile predicted by the present model, in Fig. 10, is very similar, although the decrease in the oxygen concentration near the bottom of the bed is not quite as fast. This difference is due to the greater mass transfer coefficient used here (K be ¼ 7:8 s1), which means that the bubble phase can provide more oxygen to the emulsion phase. Although the mass transfer coefficients in the models are different, the oxygen concentration profiles, expanded bed height (H  0:9 m) and average

Fig. 10. Oxygen concentration profile: this work, and Vepsäläinen et al. (2014).

oxygen concentration at bed inlet (z ¼ 0) and bed outlet (z ¼ H) are similar. Fig. 10 shows that the oxygen concentration in the emulsion phase increases close to the surface of the bed, indicating the start of the splash zone, where there is no longer a clear separation between bubble and emulsion phases.

5. Sensitivity study In this section the sensitivity of the inert-particle diameter is discussed. The variation in mass transfer coefficient, K be , with mean bed-particle diameter is shown in Fig. 11. The increase in

Please cite this article as: J. G. Villanueva-Chávez and W. A. Bizzo, Fluid dynamic modeling of a large bubbling fluidized bed for biomass combustion: Mass transfer in bubbles, Chemical Engineering Science, https://doi.org/10.1016/j.ces.2018.11.023

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Fig. 11. Variation in mass transfer coefficient with mean inert-particle diameter.

Fig. 12. Variation in the coefficients kg ; kc and keff with mean inert-particle diameter.

the coefficient with particle diameter is due to the smaller bubble diameter in large-particle systems (for the same fluidization velocity). In their work, Vepsäläinen et al. (2014) obtained a similar result. Fig. 12 shows the variation in the effective combustion rate coefficient, keff with mean inert-particle diameter. The increase in the coefficient as the inert-particle diameter increases is due to the significant increase in the diffusion coefficient, kg . Fig. 12 also shows that the diffusion process in the particle boundary layer is more intense in large-particle systems, increasing the effective combustion rate coefficient and producing more oxygen for the combustion process. Fig. 13 shows the variation in oxygen concentration with height above the distributor for inert particles with diameters dp ¼ 0:75 mm and dp ¼ 1:25 mm. The oxygen concentration in the emulsion phase is lower in large-particle systems.

Interestingly, despite the increase in the interphase oxygen transfer coefficient, K be , and the gas flow in the emulsion phase, Q e , with mean inert-particle size, the oxygen concentration in the emulsion phase decreases. This is because the gas flow transferred from bubbles to emulsion phase, besides mass transfer coefficient, also depends proportionally on bubble fraction, which is lower in large particles bed. In addition, air flow entering in emulsion phase is higher in large particle systems, but this increases combustion rate in emulsion phase (high superficial reaction rate, Rc;s , at the bed inlet), rather than in smaller particle beds, as can be seen in Fig. 13. Because of the lower oxygen transfer rate, the number of carbon particles in the bed, N C;tot , increases in large particle beds. That discussion above is valid only for large particle beds. In fine particle beds, recirculation flow (or annular flow) around bubbles occurs, which has an important negative effect on mass transfer between phases.

Fig. 13. Variation in concentration of O2 with height above the distributor: (a) dp ¼ 0:75 mm, (b) dp ¼ 1:25 mm.

Please cite this article as: J. G. Villanueva-Chávez and W. A. Bizzo, Fluid dynamic modeling of a large bubbling fluidized bed for biomass combustion: Mass transfer in bubbles, Chemical Engineering Science, https://doi.org/10.1016/j.ces.2018.11.023

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6. Conclusions A mathematical model of biomass combustion in a bubbling fluidized-bed boiler was described with an emphasis on mass transport of gases. The results of simulation showed that slow bubbles generated in large-particle systems lead to a high mass transport coefficient because of the significant direct throughflow. It was also found that bubble throughflow, which is usually neglected in the mass balance of fine-particle systems, is of supreme importance in gas flow distribution in large-particle systems: almost half of the total gas flow passes across the bed as throughflow. The validation of the model shows good agreement in bubble diameter and bubble velocity results when compared with the work of Shen et al. (2004). Oxygen concentration profile is also in good agreement with Vepsäläinen et al. (2014), but the oxygen consumption in Vepsäläinen et al. (2014) was faster than in the present work. Furthermore, bubble diameter and bubble velocity results are higher in this work. The present model was developed for large particles bed, and, thus, it was possible to assume that maximal bubble diameter and recirculation around the bubbles dont occur. Therefore, the model has some limitations when validated with a particle diameter system with dp ¼ 0:5 mm where both maximum bubble diameter and gas recirculation around bubbles might take place. The sensitivity study showed that an increase in mean inertparticle size reduces bubble size, increases direct throughflow and reduces the possibility of preferential bubble paths forming. If the kinetic reaction rate coefficient, kc , is constant, the effective reaction rate coefficient, keff , increases with inert-particle size. However, the present study should be complemented with a heat-transfer analysis and a more complete combustion model to determine the effect of inert-particle diameter on the variation in the kinetic reaction rate coefficient, kc , which determines the temperature of the active particles and the combustion efficiency of the system. Results showed that, although the mass transfer coefficient and the effective reaction rate coefficient increase, the overall reaction rate, RC;s , and oxygen concentration in the emulsion phase decrease. Carbon concentration increases with the increase in the size of the inert particles in the bed because of the lower oxygen mass transfer. References Canò, G., Salatino, P., Scala, F., 2007. A single particle model of the fluidized bed combustion of a char particle with a coherent ash skeleton: application to granulated sewage sludge. Fuel Process. Technol. 88 (6), 577–584 . Chavarie, C., Grace, J.R., 1976. Interphase mass transfer in a gas fluidized bed. Chem. Eng. Sci. 31 (9), 741–749 . Clift, R., Grace, J.R., 1985. Continuous bubbling and slugging. In: Fluidization, pp. 73–132. .

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Please cite this article as: J. G. Villanueva-Chávez and W. A. Bizzo, Fluid dynamic modeling of a large bubbling fluidized bed for biomass combustion: Mass transfer in bubbles, Chemical Engineering Science, https://doi.org/10.1016/j.ces.2018.11.023