Energy and Power E ngineering, 2013, 5, 1-5
doi:10.4236/epe.2013.54B001 Published Online July 2013 (http://www.scirp .o rg/journal/epe)
A Mathematical Model of Biomass Briquette Fuel
Combustion
Jingxia Sui1, Xiang Xu1,2, Bo Zhang1*, Changjiang Huang2, Jinsheng Lv1
1School of Energy and Power, Dalian university of technology, Dalian, China
2Wen Zhou Speci al Equipment Inspection Center, Wenzhou, China
Received March, 2013
ABSTRACT
The numerical simulation model is proposed according to the characteristics of the biomass briquette fuels, which in-
volves two main areas o f i nterest: t he solid combustion mod e l in the bed and the out-of-bed gas c o mb ust ion mod el . The
contents and characteristics of 3 kinds of biomass and coals were experimentally tested. The biomass fuels compared
with the coal fuel have the following characteristics: 1) Higher volatile content, lower fixe d c ar bo n co nte nt and calorific
value; 2) Lower carbon content, higher oxygen content; 3) Lower ignition temperature, faster burning velocity. The
discredited equations were established by the finite element analysis method, which analyzed the fuel endothermic
process on the grate, while the out-of-bed gas combustion process was simulated by CFD. These two processes are
strongly coupled . The results of the numerical simula tion contain the stead y state temper ature distribution, oxyge n dis-
tribution, carb on dioxide distr ibution and so on, which are used to judge bur ning e ffec t and p rovide the correct furnace
transformat i on me th o d.
Keywords: Biomass; CFD; Simulation; Boiler; Combustion
1. Introduction
At present, the outbreak of the global energy crisis is
making energy situation more serious in the world. M.
Fatih Demirbas [1] pointed out that the biomass fuel is a
renewable energy source and its importance would in-
crease along with the national energy policy, focusing
more on renewable sources. China is rich in bio mass but
its utilization is still lacking, causing a large amount of
energy wasted. If these fuels could be effectively and
efficientl y used, China and even the world will benefit on
the energy supplyin g and environmental prote c tio n.
Using the coal-fired boilers to burn the biomass fuels
is an ineffective method of utilization, according to pre-
viou s studie s, whic h invol ved the follo wing phe no menon,
such as the combustion instability, heat congregation
before furnace, the flame into fuel damper to ignite the
fuels in the hopper, black smoke causing from bad air
distribution, low thermal efficiency and poor environ-
mental benefits. Therefore, careful study on biomass
furnace design based upon the coal-fired’s becomes im-
portant. The topic is to improve the biomass fuels com-
bustion efficiency. Guo Y [2] pointed out that the coal-
fired boilers have to be improved to adapt to biomass
fuel, because so many differences exist between the bio-
mass and the coal such as the fuel properties, the com-
bustion phenomenon, the coking properties and the most
suitable furnace structure.
Currently, many domestic and oversea experts are
working on improving the biomass briquette combustion
efficiency. Liang YD [3] pointed out that reducing the
grate length, changing the front arch and the rear arch
structures and setting the dust barrier wall are necessary
way s t o transform the existing coal-fired bo iler . Li n P [4]
studied the combustion characteristics of different bio-
mass fuels, analyzed the main influence factors on com-
bustion (fuel characteristics, shapes and sizes, and air
distribution, etc.). Wan g L [5] inve sti gated o n the coking
problem in bio mass c ombustio n process, and discussed a
variety of measures to reduce the ash. The main research
methods on biomass combustion are experiments and
simulations. Experimental studies can accurately and
directly determine the burning effect, but the investment
is large. Simulations have the advantages of s imple, effi-
cient and s mall inves tment, b ut it is idealized, so there is
a big gap compared to the actual res ults. Therefore, more
accurate numerical simulation methods become particu-
larly importan t.
In this paper, the discrete equations were established
by t he fi nite e le ment ana l ysis metho d whic h anal yzed the
fuel endothermic process on the grate, and the results as
*Corresponding author.

J. X. SUI ET AL.
2
the boundary condition of the out-of-bed gas combustion
models, and finally the results of the gas combustion are
displayed by CFD.
2. Experiments
2.1. Analysis Experiments
One kind of coal fuel and two kinds of woody biomass
fuels are selected in this paper, and their physical proper-
ties were shown through industry analysis, elemental
analysis and heat measurements. S1 is the coal fuel, S2
and S3 are the biomass fuels, and results are shown in
Table 1 and Table 2.
The volatile content in the table refers to the dry ash-
free basis volatile content. Fixed carbon content, mois-
ture content and ash content refer to the content in the air
dried basis. Comparing the biomass fuel with the coal
fuel, it can be seen that:
• The biomass fuels contains a large proportion of
volatile, a small amount of fixed carbon, so the combus-
tion is more close to the gas combustion, which is clea rl y
different from the fixed-carbon coal combustion.
• The b iomass fuel s co ntai n mo re oxyge n co ntent and
less carbon, so they need less theoretical air quantity.
• The b iomass fue ls have l ow calorie values, so when
the same heat load required, the biomass fuel consump-
tion i s highe r tha n the coal.
2.2. The TGA Experimental
Wu HX [7] made research on the pyrolysis performance,
as well as their mixture, pointing out the different bio-
mass at initial volatile releasing temperature and the first
maximum peak temperature of co-pyrolysis increasing
with more lignite in blend by t he r mo gr avi me tr ic analysis.
It can be found that the differences between the biomass
and the coal in thermal decomposition and combustion
Table 1. Industrial analysi s.
Fuel
name
The fuel main components
Volat ile
(%) Fixed carbon (%) Moisture (%) Ash (%)
S1 6.89 83.14 7.75 3.21
S2 80.13 17.67 9.87 1.32
S3 83.61 14.64 10.14 0.58
Table 2. Element analysis and the calorie value.
Fuel
name C (%) H (%) O (%) N (%) S (%) LCV MJ/kg
S1 84.81 1.97 8.93 0.94 0.13 30.49
S2 48.56 0.47 49.28 0.24 0.12 18.5
S3 48.78 1.15 49.3 0.09 0.11 18.47
by ma king t he T GA exp er ime nts i n thi s pap er . The expe-
rimental conditio ns wer e that the temperature rise rate of
20 degrees per minute in an air atmosphere. The experi-
mental results are shown in Figure 1.
On the basis of the TGA experimental results, it co uld
be seen that:
• Comparing to the coal fuel, the extrapola ted onset
and decomposition temperatures are 200℃ lower, and
the termination temperature is only a half, which means
that the biomass fuel is easier to be decomposed and its
ignition temper a ture is lower.
• All the fuels contain higher moisture, so at the be-
ginning of the experiment, there is precipitation of the
moisture and the fuel quality reduced, and then their
mass close to the same stage in a period of time.
• As far as bio mass fuels, the extrapolated onset tem-
perature is around 250℃, the dec omposition temper ature
is of 50%, around 350℃ and ep ita xial ter minate temper-
ature around 500℃.
3. The Numerical Simulation of the Biomass
Particles
Many numerical researches related to the combustion
simulations have been carried out. For example, Chaouki
Ghenai [6] directly simulated pulverized biomass mixed
with pulverized coal combustion, providing select ions of
models and drawing the conclusion that increasing the
residence time and enhancing vortex could improve the
combustion efficiency. The shape of the fuel has an im-
portant effect on the combustion, so the simulation met ho d
of the pulverized fuels combustion is not suitable for the
biomass briquette fuels. T here are three ways to solve the
above problem.
Firstly, a simple approach is to use inlet conditions for
the top of the fuel bed based on the experimental mea-
surements [8].The inlet conditions contain the gas tem-
perature, speed and species. Secondly, a more complex
method is to develop a separate sub-mode l that ca lcula tes
the temperature, velocity and species at the top of the
Figure 1. Three fuel TGA experiments.

J. X. SUI ET AL.
3
fuel bed. The CFD code can then be coupled with the bed
sub-model, and the radioactive flux emi tted by the flame
and furnace walls to the top fuel layer, fed back for the
next interaction of the bed model [9].The third type of
approach, which is not so commonly adopted, is to define
a user defined sub-ro utine s (U DF) withi n the F luent cod e.
This code contains the essential details to characterize
the solid and gas phase interactions [10, 15].
In this paper, the second app roach is combined with
the third. The mathematical model consists of two sub-
models: one model for the burning bed of biomass bri-
quette, and the other model for the gas co mbustion in the
furnace above the bed. The fue l is continuously lost mass
during moving in the bed ( moisture evaporation, devola-
tilization and char combustion). The conditions for the
top of the bed are calculated from overall heat and mass
balances of the fuel components and the primary air ve-
locity. To simulate the gas ph ase reactio ns within the full
geometry of a biomass furnace in CFD, a model for tur-
bulence flow and radiation transfer is need. The inlet
boundary condition based on the conditions for the top of
the bed, is achieved by a user defined sub-routines (UD F)
within the CFD code. The modeling schematic view of
the model is shown in Figure 2:
3.1. The Combustion Model on the Grate
In order to model the heat and mass transfer process in
the bed, the fuel in the bed along with the grate move-
ment is discredited, and the mass conservation equations
for each element are based on moisture evaporation, vo-
latile release and char combustion. Heat conservation
equations for each element are based on radioactive heat
transfer, convective heat transfer and combustion heat
production. The interaction between the gas and solid
phase occurs through the relevant source terms in the
conservation equation. The mass and energy conversion
relationship for an element is shown in Figure 3.
CFD
Inlet boundary
Grate
Primary air
Bed model
Bed-gas interface
Radiative transfer
Height
Out boundary
(Gas combustion model)
Figure 2. Numerical simulation model.
Inlet Outlet
dy
dx
Radiactive heat transfer
Convective heat transfer
Combustion heat production
Primary air
Mixture gas
Figure 3. The computing element.
It is assumed that the fuels in the bed are continuous
porous medium, the bulk density of the fuel and the bed
voidage remain unchanged; the heat transfer in the fuel
height direction is i gnored and the volatiles in t he release
process have no combustion reaction. The primary air is
evenly distributed. According to the formulas about
moisture evaporation rate and volatile release rate [11,
12], and combi ned wit h the combustion characteristics in
this paper, the followin g d iscrete equations can b e got.
1) Char without oxidatio n:
a) Mass conservation,
V
ρudy / (ydx)=RevpR−−
(1)
b) Energy conservatio n,
'
ρu2dT / (dx)=Sh(TT) /1000
a1 sg
44
Sεσ(T T
a) 2/10 0 l0
−−
+−
(2)
2) Char oxidatio n:
a) Mass conservation,
V C(s)
ρudy / (ydx)=RevpRR− −−
(3)
b) Energy conservatio n,
'
ρu2dT / (dx)=Sh(TT) /1000
a1 sg
44
Sεσ() /10T0TW
a2 lchar
0
−−
++−
(4)
3) The rate of moisture evaporation can be express as:
a) when T<100 ℃,
w,s w,g
Revp Sahs CC= −（）
(5)
b) when T ≥100℃,
cr evp
RevpQ/H=
(6)
( )
' 44
cra1 sga2l
QSh TTSεσ(TT )= −+ −
(7)
4) The rate of volatile devolati satio n can be express as,
VV v
RρY Avexp/(E )(RT )= −
(8)

J. X. SUI ET AL.
4
5) The rate of char oxidation can be express as,
C(s) o2rd
RC/(1/k1/k)= +
(9)
The moisture cont ent and volatile content,
w,s w,sw,s
CCSahsC dt= −
(10)
V VVVV
YYρY Aexp/(( ERT))dt
=−−
(11)
where ρ is the bulk density of the fuel, u is the speed of
the grate, Sa is the particle surface area, hs is the co nnec-
tive mass transfer coefficient bet ween solid and gas, C(w,s)
is the moisture concentration at solid surface, C(w,g) is the
moisture concentration in the gas phase, YV is the mass
fraction of volati le matter remaining in biomass briquette,
Av is the pre-exponential factor, Ev is the activation
energy, R is the gas constant, Sa1 is the particle convec-
tive heat transfer surface area, Sa2 is the particle radioac-
tive heat transfer surface area, Tg is the primary air tem-
perature T1 is the furnace temperature, T is the fuel tem-
perature.
Several results can be got according to the above cal-
culat io n, such as the f ue l hei g ht, the moi s tur e a nd volat il e
content, the fuel temperature, the mass fraction in the
mixture, the temperature and the velocity about the mix-
ture, the mixed gas temperature and velocity. All the re-
sults as the inlet boundary conditions to the Fluent to
simulate the gas phas e.
3.2. Out of Bed Gas Combustion Model
Volatile combustion occurs in the gas phase, and Fluent
was selected to simulate the gas combustion. To simulate
the gas phase reactions within the full geometry of a
biomass furnace, models for turbulence and radiation
need to be selected. To model the turbulent interactions
within the boiler, the standard Realizable k-epsilon Mod-
el was adopted. Radiation heat transfer in biomass fur-
nace was modeled with the P1 radiation model [12].
The kinetics of gas phase reaction and the mixing rate
of oxidizer and fuel are the dominant factors to influence
the gas combustion rate. The gas phase reactions are ki-
netically fast above the fuel bed, where the temperature
is high and the reactions quickly, leading to the combus-
tion is only controlled by the mixing rate The rate of a
reaction in particular cell is determined by the minimum
limiting value between the kinetics and the mixing
rate[13,14].
4. Results Analysis
The simulation model is used to calculate the biomass
briquette combustion in the grate. Several results can be
got according to the calculation on the solid combustion
in the bed, which are shown in Figure 4.
The figure shows t he mixture fraction distributio n and
temperature distribution above the grate. These results
wo u ld be as the boundary condition for the furnace si-
mulation.
The simulation on biomass combustion in the two dif-
ferent furnaces under the condition that keep the fuel
characteristic, the grate speed, the air temperature, flow
rate and velocity constant. The simulation results about
the bi omass b urning in the coal -fired b oiler are shown in
Figure 5, contain the temperature distribution and the
mass fraction of O2.
Figure 4. The solid combus ti o n re sul ts.
Figure 5. The combus t ion results of coal-fired boiler.

J. X. SUI ET AL.
5
Figure 6. The combus t ion results of transformation boi ler.
The simulatio n resul ts sho ws t hat the b iomass b urnin g
in the coal-fired boiler have some problems such as the
high temperature.
The simulation results about the transformation boiler
are shown in Figure 6, contain the temperature distribu-
tion and the mass fraction of O2. Compared with the
coal-fired boiler, the arch angle increase and the front
arch covered area decrease.
Through the simulation results, the conclusion can be
drawn:
1) The o xyge n i s l i kely lack t o b ur n t he vo la ti le s in th e
middle of furnace.
2) The combustion of the biomass is closer to the gas
combustion because the fuel is about around 80% vola-
tile, which is have a huge different from the coal.
3) The flame positio n in the furnace clearly down after
the transformation, which improved the convective heat
transfer of the flue gas and the efficienc y of the boil er.
4) A large space to ensure the stable and complete
combustion of volatile gases after the transform the fur-
nace structures are needed, but the transformation wea-
kens t he disturbance of the mixture.
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