MODELING OF REACTIVE BOUNDARY LAYERS IN
KRAFT CHAR BED BURNING
MARKUS ENGBLOM*, ANDERS BRINK, CHRISTIAN MUELLER, and MIKKO HUPA
Åbo Akademi University, Process Chemistry Centre, Combustion and Materials Chemistry, Finland
* Corresponding author: e-mail: markus.engblom@abo.fi, tel: +358-2-2154421
ABSTRACT
A model is presented for simulating the reactive boundary layer in black liquor char
bed burning. The model describes a turbulent reactive flow over a reactive carbon
surface. Mass transfer from the turbulent free stream to the laminar region at the
char bed surface is calculated by resolving the boundary layer. Gas phase reactions
are included, and a model is developed for describing turbulence-chemistry
interaction in the region inside the boundary layer where transition from turbulent
to laminar flow takes place. Char carbon conversion by direct oxidation and
gasification is considered, and a model for calculating the conversion is developed.
The model is validated in simulation of laboratory char bed burning experiments.
KEYWORDS
Modeling; reactive boundary layer; black liquor; char bed.
INTRODUCTION
Black liquor is by quantity one of the most important industrial bio fuels in the
world (Raiko et al., 2002). Black liquor is the by-product of chemical pulping,
consisting of spent pulping chemicals, dissolved organic matter and water. It is
burned to recover chemicals and the energy content of the organic matter. Typical
dimensions of a modern black liquor recovery boiler are 13x13 m cross section and
60 m height. Thermal input is about 500 MW. Black liquor is introduced as a
relatively coarse spray into the furnace where burning takes place both in-flight and
on a char bed which is formed on the floor of the boiler.
Black liquor char is very reactive. Reactions with oxygen, carbon dioxide, and
water vapor are considered the most relevant gas-solid reactions (Adams et al.,
1997). While gasification reactions with carbon dioxide and water vapor take place
in conversion of many carbonaceous materials, for black liquor, the reactivity is as
much as 4 orders of magnitude higher as compared to coal char (Li and van
Heiningen, 1991).
Mathematical modeling of kraft black liquor char beds has been on-going for nearly two
decades (Frederick & Hupa, 1991; Wessel et al., 1997; Sutinen et al., 2002; Ohran et al.,
2004; Bergroth et al., 2004). Char bed burning involves transport of gas phase reactants
from the free stream through the boundary layer. At sufficiently high temperatures, gas
phase reactions inside the boundary layer can influence the transfer of reactants through
the layer. Such an effect has been observed in laboratory studies (Brown et al., 1989).
However, this effect is not included in the current char bed models.
While empirical data was obtained on reactive boundary layers in the Brown
experiments, the conditions were limited as compared to those found in industrial
combustion. Therefore, deeper knowledge of reactive boundary layers is needed for
assessment of the importance and implications of the phenomenon for industrial char
bed burning, as well as for modeling.
In this paper, a mathematical model is presented for studying reactive boundary
layers in char bed burning.
MATHEMATICAL MODELING
A commercial computational fluid dynamics (CFD) software is used for solving the
velocity, species and temperature fields above the char surface. The main features
of these models are shortly presented. Sub-models are developed for describing
turbulence-chemistry interaction in the boundary layer, as well as for char bed
conversion. With the char bed represented by a boundary wall, the influence of char
bed chemistry on the boundary layer is included through mass and energy source
terms.
Standard models. The RNG k-ε turbulence model is used for calculating the gas
flow. A near wall turbulence modeling approach (Fluent, 2005) is used in which the
velocity profile of the boundary layer is resolved using the empirical correlation
known as “the law of the wall” and which accounts for the influence of the char
surface on turbulent fluctuations in the boundary layer. This approach results in a
velocity profile with a smooth transition from the turbulent free stream to the
laminar flow close to the char surface. The influence of turbulent fluctuations on
momentum transfer is characterized by a turbulent viscosity. Molecular viscosity is
calculated based on kinetic theory.
The influence of turbulent fluctuations on transport of energy and species is calculated
based on the concept of Reynolds’ analogy. Location specific turbulent Prandtl numbers
are calculated in the boundary layer as well as molecular thermal diffusivities based on
kinetic theory. The effective Prandtl number ranges from 0.7 at the char surface to 0.85
in the free stream. Turbulent mass transfer is calculated assuming turbulent Schmidt
numbers equal to turbulent Prandtl numbers. Molecular mass transfer is calculated
based on multicomponent equations; with molecular diffusion coefficients based on
kinetic theory. Source terms from chemical reactions are included in calculation of
energy and species transport. A two step reaction mechanism describes gas phase
chemical kinetics.
H 2 + 12 O2 → H 2 O
(R1)
CO + H 2 O ↔ CO2 + H 2
(R2)
k = A ⋅ T b ⋅ exp(− E /( R ⋅ T ))
(R3)
k1:
A = 2.5·1016, b = -1, E = 1.68·105 (J/mol)
k2+:
A = 2.75·109, b = 0, E = 8.3·104 (J/mol)
k2-:
A = 6.853·109, b = 0, E = 1.138·105 (J/mol)
The reactions considered are based on the Jones-Lindstedt methane conversion
mechanism (Jones and Lindstedt, 1988). Reaction 1 is assumed irreversible due to the
relatively low temperatures of the modeled system.
Turbulence-chemistry interaction. The standard “eddy dissipation/finite rate”
turbulence-chemistry model calculates the effective rate of reaction based on which
is lower: the rate of mixing of reactants due to turbulent dissipation (turbulent
reaction rate) or the finite kinetic rate of reaction (laminar reaction rate). The
standard model predicts effective reaction rates equal to the limiting turbulent rate
in the region close to the char surface. A modification of the standard model is used
to calculate the effective rate of reaction (Eq1). Turbulent (νturb) and laminar
viscosity (νlam) are used in determining to which degree the flow, and consequently
the chemistry, is turbulent or laminar in the boundary layer. The effective reaction
rate (reff) is calculated as a weighted sum of the turbulent (rturb) and laminar rate
(rlam), and approaches smoothly the laminar rate towards the wall.
reff =
ν turb ⋅ rturb + ν lam ⋅ rlam
ν turb + ν lam
(1)
Char bed chemistry. The char bed is represented by a smooth surface. Reactions
with oxygen, carbon dioxide, and water vapor are considered; with reaction rates
(mol/s/m2) calculated in each position along the bed. The char bed reactions
considered are:
C ( s) + O2 ( g ) → 2CO( g )
(2)
C ( s) + CO2 ( g ) → 2CO( g )
(3)
C ( s) + H 2 O( g ) → CO( g ) + H 2 ( g )
(4)
The reaction with oxygen is assumed fast and always considered mass transfer
limited. The reactions with carbon dioxide and water vapor can be calculated in two
alternative ways: either having a finite rate or assuming mass transfer limited
reaction. Equations for multicomponent mass transfer are used to calculate
diffusion over the gas-char bed interface (Eq5) (Wesselingh and Krishna, 2000).
Depending on the number of mass transfer limited reactions, the equation system
consists of one or three equations, i.e., one for each reactant species. In Eq5, the
index (i) refers to the reactant in question and the index (j) to respective other
species in the mixture. The fluxes (N) of reactants are solved with the fluxes of
products given by stoichiometry. The mole fraction gradient (left side of Eq5) is
calculated assuming zero mole fraction at the bed surface. The values for mole
fractions (y) and gas concentration (Cgas) are from the cell next to the bed, assuming
changes due to gradients from the cell to the char surface to be negligible. The
binary diffusion coefficients (Di,j) are for each pair of species in the mixture.
y j ⋅ N i − yi ⋅ N j
Δy i
=∑
Δx i ≠ j
Di , j ⋅ C gas
(5)
Li and van Heiningen determined the reactivity of black liquor char with carbon
dioxide (Li and van Heiningen, 1990) and water vapor (Li and van Heiningen,
1991). Rates were found to be proportional to the reactant concentration and
inversely proportional to product concentration, and described by LangmuirHinshelwood type kinetic expressions. Järvinen (2002) used the results of Li and
van Heiningen in a model for black liquor droplets/particles. The rate equations
according to Järvinen are used, and are given by:
rC / CO2 = 3.94 ⋅ 10 ⋅ As ⋅ C c ⋅ e
8
rC / H 2O = 1.60 ⋅ 10 ⋅ As ⋅ C c ⋅ e
7
−250000
R ⋅T
−210000
R⋅T
⋅
⋅
C CO2
(C CO2 + 3.4 ⋅ C CO )
C H 2O
(C H 2O + 1.42 ⋅ C H 2 )
(6)
(7)
With specific surface area (As=160 m2/g) according to Li and van Heiningen (1990),
and carbon concentration (Cc=294 mol/m3) calculated based on reported bulk
density and carbon mass fraction of the char bed (Brown, 1989).
Calculation of the gasification reaction rate is based on the procedure for catalytic
reactions by Levenspiel (1972) with char carbon conversion estimated as a first
order reaction (rC/X=k·CX) and pore diffusion. A sufficiently long pore length (L=3
cm) was chosen, so that reactant concentrations reached a value of zero inside the
bed. The bed temperature is given as a parameter and assumed constant throughout
the bed. The rate coefficient (k) (Eq8) is calculated at the bed surface using gas
concentrations from the cell next to the bed and assumed constant with distance into
the bed. The reactant concentration decreases from the surface value with distance
into the bed. An effectiveness factor (α) describes the influence of decreasing
reactant concentration on the reaction rate (Eq9). The effectiveness factor is
calculated based on a Thiele modulus (m·L), characterizing the influence of pore
diffusion resistance on the rate of reaction (Eq10). Pore diffusion is described by an
effective diffusion coefficient (D,eff), calculated according to Epstein (1989) (Eq11),
with the diffusion coefficients in the gas (D) for carbon dioxide and water vapor
calculated as mole fraction weighted sum of binary diffusion coefficients. The
effects of porosity and tortuosity factor are estimated as a lumped parameter with
values (p=1) and (τ2=2), respectively. The tortuosity factor corresponds to a
tortuosity (τ=1.414) of a pore at 45° angles to the nominal direction as used by
Järvinen (2002). The rate of reaction per surface area (rC/X/A) (Eq12) is calculated
using the reactant concentration in the next-to-bed cell with the decrease in
concentration due to the concentration gradient from the cell to the bed surface
assumed negligible.
k=
rC / X bed
| surface
CX
(8)
α=
tanh( m ⋅ L)
m⋅L
(9)
m=
k
Deff
(10)
Deff =
D⋅ p
τ2
rC / X / A = α ⋅ k ⋅ L ⋅ C X |bed
surface
(11)
(12)
SIMULATION CASES
The geometry of the Brown (1989) experiments is relevant for char bed burning,
where combustion air jets are directed towards and over the bed. The char bed was
a collection of pyrolysed black liquor droplets. A slot jet of width 20 cm and height
7.6 mm was directed over the surface of a char bed of width 20 cm and length 10
cm. The temperature of the gas jet was 500 °C, and gas velocity at the nozzle 5.7
m/s. Mixtures consisting of oxygen, carbon dioxide, and water vapor in nitrogen
were used as reactant gases. The char bed, of which the leading edge was located 15
cm from the slot nozzle, was placed on a tray and driven up to replace converted
char and to maintain the burning geometry. Electrically heated walls were used to
elevate the bed temperature to around 800 °C, with the bed surface temperature
increased additionally by combustion. Temperature was monitored by
thermocouples inside the bed. Char carbon conversion was determined from the
carbon monoxide and carbon dioxide leaving the reactor. Table 1 summarizes the
main variables of the experiments.
Table 1. Composition of the gas jet, bed surface temperature, and carbon conversion in
experimental char burning by Brown (1989).
If the individual char carbon reactions had proceeded in parallel, then the
experimental carbon conversion could be expected to have shown a trend which
increases with increasing oxygen available in the gas feed. Instead, a maximum was
observed in the case of oxygen and carbon dioxide as reactants. Gas phase reactions
which occurred inside the boundary layer and affected the net mass transfer of
reactants to the bed surface were given as the explanation to the observation.
The experimental configuration can be idealized as turbulent flow along a plate
(Figure 1). While the exact shape is not reported, the char bed shape deviates from
the ideal plate. In a schematic by Brown, the bed has a somewhat round shape, with
the highest point located between the center and the trailing edge of the bed. Such a
shape would result in impingement of the jet on the leading part of the bed, and
separation could occur towards the trailing edge of the bed. The actual shape of the
char bed is not included in the modeling. Instead, smooth flat plate geometry is
used. The assumed bed geometry is a source of uncertainty since the flow
conditions above a real bed can be considerably different.
Figure 1. Schematic of the experimental char burning configuration.
The model was tested by simulating the experiments of Brown. A series of cases
was calculated where the gas jet compositions and bed surface temperatures were
set as given in Table 1. To study the influence of the gas phase reactions on char
carbon conversion, both reactive and non-reactive cases were calculated. Based on
the reported char analysis (Brown et al., 1989), hydrogen was assumed to be
released in proportion to converted char carbon. A release ratio (H2/C) of 0.18 mol
hydrogen per mol organic carbon was used. The gasification reactions were
calculated with finite rates using equations 6 and 7.
The char burning configuration was assumed symmetrical along the width of the
bed, reducing the calculation domain to 2D. The gas jet was assumed fully turbulent
at the nozzle.
RESULTS AND DISCUSSION
Typical simulated velocity and mole fraction contours are shown in Figures 2 and
3, respectively. The oxygen boundary layer grows in thickness when moving from
the leading edge towards the trailing edge of the char bed.
Figure 2. Simulated velocity (m/s).
Figure 3. Simulated oxygen mole fraction.
The gas phase reactions affected species concentration profiles inside the boundary
layer (Figure 4). This affected char carbon conversion (Table 2). The contribution
of respective carbon conversion reaction changed. In general, the oxygen flux to the
bed surface decreased and the fluxes of carbon dioxide and water vapor increased.
In Cases 1-3, the gas phase reactions resulted in carbon conversion taking place via
all three conversion routes, although the reactants for these routes are not originally
present in the gas feed. The increase in conversion by carbon dioxide and water
vapor only partly compensates for the decrease in conversion by oxygen. As result,
the overall carbon conversion was decreased by 11-15% (Figure 5).
Figure 4. Mole fraction profiles in a non-reactive (upper) and reactive (lower) boundary layer.
0.01 mol/(s-m2)
40
30
Exp
20
N-R
R
10
0
Case 1
Case 2
Case 3
Case 4
Figure 5. Experimental (Exp) and simulated carbon conversions. Simulated conversions are for
non-reactive (N-R) and reactive (R) gas phase. Cases 1-4 are described in Table 2.
Table 2. Carbon conversions (0.01 mol/(s-m2)) for non-reactive and reactive gas phase in
simulation of the Brown (1989) experiments.
As seen in Figure 5, the simulation results differ from the experimental ones in two
ways: i) the simulated overall carbon conversion is lower as compare to the
experimental; the discrepancy being smaller for cases 3 and 4 as compared to cases
1 and 2, and ii) the simulated overall conversion increases with increasing oxygen
available in the gas feed. A likely reason for the lower simulated conversion is the
assumptions of the char surface geometry, and the associated differences in
experimental and simulated flow conditions above the bed.
CONCLUSIONS
Gas phase reactions influence the concentration profiles of species inside the
boundary layer. This consequently affects char carbon conversion. Oxygen is
consumed resulting in a decrease in conversion by the oxygen-carbon reaction.
Carbon conversion by carbon dioxide and water vapor is increased. The overall
conversion is decreased as the gasification reactions only partly compensate for the
decrease in direct oxidation.
ACKNOWLEDGEMENTS
This work has been carried out within the project ChemCom 2.0 as part of the activities
of the Åbo Akademi Process Chemistry Centre. Funding by the Academy of Finland in
their Centres of Excellence Program, National Technology Agency of Finland and
industrial partners Andritz Oy, Metso Power Oy, Oy Metsä-Botnia Ab, Foster
Wheeler Energia Oy, UPM-Kymmene Oyj, Clyde Bergemann GmbH, International
Paper Inc is gratefully acknowledged.
Jan Eriksson, Vattenfall Research and Development AB Sweden, is gratefully
acknowledged for the discussions around boundary layer theory.
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