http://ago.helion.pl ISSN 1733-4381, Vol. 4 (2006), p-93-106
Mathematical modelling of biomass combustion process on mechanical stoker
Nadziakiewicz J., Czekalski R.
Silesian University of Technology, Department of Technology and Installations for Waste Management, Konarskiego 18, 44-100 Gliwice, POLAND
ph.: +48 32 237 2104, fax: +48 32 237 1116 e-mail: rafal.czekalski@polsl.pl
Streszczenie
Modelowanie matematyczne procesów spalania biomasy na ruszcie mechanicznym Artykuł prezentuje model procesu spalania warstwy biomasy na ruszcie mechanicznym. Ustalony proces dwuwymiarowy spalania warstwy na ruchomym ruszcie (będący uproszczeniem rzeczywistego procesu) został zastąpiony jednowymiarowym nieustalonym procesem spalania fragmentu warstwy. W modelowaniu uwzględniono suszenie, odgazowanie i spalanie ziaren a także reakcje w fazie gazowej. Rezultatem obliczeń modelu są zmiany temperatur fazy stałej i gazowej oraz składu gazu w czasie, co odpowiada kolejnym położeniu badanego fragmentu na ruszcie rzeczywistym. Planowanym dalszym etapem badań jest przeprowadzenie pomiarów w skali laboratoryjnej.
Abstract
The paper presents model of biomass combustion process on a mechanical stoker. Continuous two-dimensional process (which is simplification of real, three-dimensional one) was substituted with one-dimensional unsteady process of combustion of separated bed segment. The model considers drying, devolatilization, combustion of particles and reactions in gaseous phase. Results of the computation process are changes of temperatures of solid and gaseous phase, as well as gas composition in time, which corresponds to the values of those parameters in different places on mechanical stoker. The further part of investigation are laboratory measurements of the process.
1. Introduction
In recent years the meaning of biomass in power engineering has increased. Biomass (straw, wood scraps) becomes an important source of energy. Boilers fed with coal are liquidated and substituted with the ones fed with gas, oil and biomass. In Poland, in years 2001-2004, over 900 coal boilers, of thermal power over 500 MW, were liquidated, while in the same period over 130 boilers for biomass, of thermal power over 155 MW, were started. Tab. 1.1 presents production of renewable energy in the form of biomass in Poland.
Table 1.1. Production of renewable energy (biomass only) in Poland in thousands of tons of oil equivalent (1 toe = 41,868 GJ) [1].
year 1999 2000 2001 2002 2003 2004
production 3541 3578 3830 3901 3929 4062
Similar tendency is noticeable in countries of European Union. Tab. 1.2 presents production of renewable energy from biomass and waste combustion in last years. This production becomes more and more important in power engineering.
Table 1.2. Production of renewable energy from biomass and waste combustion in EU in thousands of tons of oil equivalent (1 toe = 41,868 GJ) [1].
year 1990 2000 2003
EU 25 49002 58312 68463
EU 15 42766 50841 57749
Poland 3821 3626 4918
This growth of use of biomass requires theoretical and practical investigation of combustion process, the more that models of coal combustion would be not suitable in case of biomass, because of differences of chemical and physical properties. This paper presents model of biomass combustion process on mechanical stoker. The model considers drying, devolatilization, char combustion and reaction in gaseous phase.
2. Application of one dimensional model in simulation of real process
Fig. 2.1 presents general idea of application of one dimensional model in simulation of biomass combustion on mechanical stoker. The left side presents biomass moving on stoker in two dimensional system (which is simplification of real, three-dimensional process). Observation of one separated segment of moving bed leads to one conclusion: the part of drying, devolatilization and char combustion processes in succeeding places is changing. Similar process is presented on the right side of Fig. 2.1. There, only this small segment of bed is considered, and actual state of proceedings processes corresponds to succeeding places on the stoker. One-dimensional unsteady process, where changes in bed are determined along height only in time, simulates two-dimensional continuous process of biomass bed combustion on mechanical stoker.
Fig. 2.1. Application of one-dimensional model in simulation of biomass combustion process on mechanical stoker.
However, this analogy requires one assumption: heat conduction in horizontal way in bed is much smaller than heat convection in vertical way caused by gas flow. Criterion of similarity in this case is Peclet number (Eq.2.1), which represents ratio of heat transported by convection to heat transported by conduction [2], thus assumption is fulfil, when Pe >> 1. For example, for layer of wooden scraps (thermal heat conduction λ = 0.093 W/m⋅K, heat capacity c = 2510 J/kg⋅K and density ρ = 250 kg/m3), and bed of length l = 5 m, travelling speed w = 0.002 m/s, Pe = 67473.
a
l
w
Pe
=
⋅
(2.1)where: w – travelling speed, m/s
l – length of bed, m
a – temperatures compensation coefficient (Eq. 2.2), m2/s
ρ
ρ
ρ
ρ
λ
λ
λ
λ
⋅⋅⋅⋅
=
=
=
=
pc
a
(2.2)where: λ – thermal conductivity, W/m⋅K,
cp – heat capacity, J/kg⋅K
ρ – density, kg/m3
Despite some simplification in this example (λ is taken as a constant in ambient temperature, and for solid phase, not for bed) Peclet number is relatively high, so the assumption is right. This observation leads to important conclusion for practical research: investigated segment bed should by thermally insulated to simulate combustion within burning layer.
3. Mathematical model
In order to investigate combustion process of biomass on mechanical stoker, a mathematical model was created, which is described in this section.
3.1. Aims, assumptions and considered processes
Mathematical model, which is presented here, has main three aims:
1) Calculation of temperature of solid and gas phase along bed height in time, 2) Calculation of gas composition in bed,
3) Calculation of mass loss of bed in time.
First point is important from thermodynamic point of view, and gives some information about expected temperatures, which may occur in bed. The second one gives information about gaseous substances, which may be generated during the process. The last one may be interesting in case of determination how moisture and volatile matter and kinetic of drying, devolatilization and char combustion influence on change of bed mass in time.
In model, the following assumptions were made:
1) Solid fraction consists of fixed carbon, volatile matter, moisture and ash,
2) Solid particles has a spherical shape, and its diameter decrease only in case of their combustion, however other shapes can be investigated by correction of surface to volume ratio,
3) Gas fed to the process consist of N2, O2, H2O,
4) Composition of gas from devolatilization process depends on heat rate of particles and their temperature,
5) In gaseous phase a chosen group of gases and their reactions are considered: CO2,
O2, N2, CO, CH4, H2, CxHy, tar and H2O,
6) Pressure in bed is constant and equals the ambient pressure. In model, the following processes were taken into consideration:
1) Heat conduction in solid phase, 2) Heat convection in gaseous phase,
3) Conversion and transfer of mass (drying, devolatilization and char combustion) 4) Heterogeneous reaction of particle combustion,
5) Homogenous reactions in gas phase. 3.2. General equation used in model
In order to consider mentioned processes in section 3.1, and calculate parameters, equations of energy balance and mass balance were used. Those equations, in general form are similar from the mathematical point of view (Eq. 3.1).
S
x
x
x
w
t
+
∂
Φ
∂
⋅
Γ
∂
∂
=
∂
Φ
⋅
⋅
∂
+
∂
Φ
⋅
∂
(
ρ
)
(
ρ
)
(3.1) where: ρ – density, kg/m3 t – time, s w – velocity, m/s x – geometric variable, mΦ – dependent variable (parameter to calculate), Γ – diffusion coefficient,
S – source.
The equation consists of four terms: unsteady term, convection term, conduction term and source term, however not all of them occur in each equation. Table 3.1 presents individual equations and meaning of Φ, Γ and S. All equations create the set of equations, which consist of two energy balances (for solid and gas phase), equations of conservation of chemical species (the number of those equations depends of number of considered gas substances) and gas continuity equation for determining gas stream. Equations are solved using numerical method described in [3].Table 3.2. Equations applied in model.
Equation Dependent
variable Φ Diffusion coefficient Γ Source S
Energy balance for solid phase (lack of convection term) Enthalpy of solid phase: is, J/kg Ratio of thermal conductivity [4] to heat capacity of bed, kg/(m·s) s p c λ λ λ λ Heat source, W/m3
((((
))))
char O H s gQ
Q
T
T
A
+
+
+
+
+
+
+
+
+
+
+
+
−
−
−
−
⋅⋅⋅⋅
⋅⋅⋅⋅
2α
α
α
α
Energy balance for gas phase Enthalpy of gas phase: ig, J/kg Ratio of thermal conductivity [4] to heat capacity of gas [5], kg/(m·s) g p c λ λ λ λ Heat source, W/m3((((
))))
g g sQ
T
T
A
+
+
+
+
+
+
+
+
−
−
−
−
⋅⋅⋅⋅
⋅⋅⋅⋅
α
α
α
α
Conservation of chemical species Mass part of i species: gi Dynamic diffusion coefficient of i specie through gas; δi-gas,kg/(m·s)
Mass source of i specie
ri, kg/(m3·s):
Gas continuity Gas velocity component: wg,y
(lack of diffusion term) Gas source rgas,
kg/(m3·s): where:
α – heat transfer coefficient, W/m2⋅K
A – volumetric surface area, m2/m3
Q – volumetric heat generation in combustion process (char and gas), and consumption (drying), W/m3
3.3. Discretization of space and time, boundary and initial conditions
Considered segment of bed of height H and surface F is divided into n elements of ∆x
height (Fig. 3.1). Grid is regular with distance between nodes δxn = δxs = ∆x. Calculation
time is divided into regular steps ∆t. Initial condition are solid and gas temperatures Ts0 and
Tg0. Boundary conditions are: gas stream mg of temperature Tg0, temperature over the bed T
and heat transfer coefficient α2 (third boundary condition, which initiate the whole process,
however the other ones may be used as well).
Fig. 3.1. Discretization of considered segment of bed. 3.4. Mass sources and sub-models of considered processes
Mass source ri of H2O and products of devolatilization process are determined from Eq.
3.2.
t
c
c
r
i∆
∆
∆
∆
−
−
−
−
=
=
=
=
0 (3.2) where: c0 – amount of substance (in element) at the beginning of time step, kg/m3∆t – time step, s
ri – mass source, kg/m3⋅s
Drying and devolatilization are considered as first step reactions, thus amount of substance at the end of time step is determined from Eq. 3.3:
((((
k
t
))))
c
c
=
=
=
=
0⋅⋅⋅⋅
exp
−
−
−
−
⋅⋅⋅⋅
∆
∆
∆
∆
(3.3)where: k – kinetic constant, 1/s
T
R
E
A
k
a⋅⋅⋅⋅
−
−
−
−
⋅⋅⋅⋅
=
=
=
=
exp
(3.4)where: A – Arrhenius constant, 1/s Ea – activation energy, kJ/mol
R – universal gas constant, kJ/mol⋅K T – temperature, K
3.4.1. Drying process model
Drying process is modelled according to reaction (3.5). Kinetic parameters and heat consumption are taken from [6]. In this process amount of moisture decreases from initial value defined in solid phase to zero.
vapour
moisture
→
→
→
→
(3.5)3.4.2. Devolatilization process model
The main aim of this model is to determine amount of devolatilization products and its composition. Devolatilization products consists of tar and gas phase. Parts of those two phases depends on heating rate. Composition of gas phase depends on particle temperature. This process is modelled by functions, which returns suitable values based on functions that are valid for some range of heating rate and temperatures. Some research of devolatilization process investigate only mass loss of heating substance[7, 8], the other ones determine composition of devolatlization products as a function of heating rate [7, 9], or some temperatures [9, 10, 11]. The function are created by linear dependences between points taken from those research in suitable range. All those research should be carried out for the same (or at least similar) solid substance and physical conditions. Fig. 3.2 presents dependence of gas part in devolatilization process products as a function of heating rate. Fig. 3.3 presents part of CO2 in gas from devolatilization process as a function of
temperature. Similar function may be obtained for other substances, like CO, CH4, CxHy,
Fig. 3.2. Mass part of gas as a function of heating rate for wood [7,9]
Fig. 3.3. Mass part of CO2 in gas from devolatilization process of wood [9,10,11]
3.4.3. Particle combustion model
Combustion process of fixed carbon is modelled according to reaction (3.6). Parameter x is a function of temperature [12].
2
2
2
(
1
x
)
CO
(
2
x
1
)
CO
xO
C
+
+
+
+
→
→
→
→
⋅⋅⋅⋅
−
−
−
−
+
+
+
+
⋅⋅⋅⋅
−
−
−
−
(3.6) Combustion of particles is a surface process, which is determined by rate of chemical reaction and diffusion of oxygen to particle’s surface, thus constant rate of particle’s combustion is calculated from Eq. 3.7:β
β
β
β
1
1
1
+
+
+
+
=
=
=
=
chem ck
k
(3.7)where: kc – kinetic constant of particle combustion, m/s
kchem – kinetic constant of chemical reaction [12], m/s
β – oxygen diffusion coefficient [10,13], m/s
Loss of fixed carbon rchar in element is a function of particles’ surface area and oxygen
concentration: 2 O c c
k
F
C
r
=
=
=
=
⋅⋅⋅⋅
⋅⋅⋅⋅
(3.8)where: F – particles’ surface area, m2 CO2–concentration of oxygen, kg/m3
Total mass source rg (conversion of solid phase to the gaseous one) is a sum of mass
sources of drying, devolatilization and fixed carbon combustion processes:
comb vol O H g
S
S
S
r
=
=
=
=
+
+
+
+
+
+
+
+
2 (3.9)where: SH2O – moisture source, kg/m3⋅s
Svol – volatile matter source, kg/m3⋅s
Scomb – source of gaseous products of fixed carbon combustion, kg/m3⋅s
Heat (energy) sources Qi are expressed as follows: i
i i
r
D
Q
=
=
=
=
⋅⋅⋅⋅
(3.10)where: ri – mass source of i component, kg/m3⋅s
Di – heat of reaction (of heat of combustion) of i component, J/kg
3.4.4. Models of chemical reaction in gaseous phase on example of CO combustion
Functions that model chemical reaction in gaseous phase, calculate mass sources of all substrates (negative sources) and products (positive sources). The basis of calculation is chemical reaction: 2 2 2 1O
CO
CO
+
→
(3.11)On the basis of chemical parameters and reaction rate [14, 15], all sources that are used in suitable equations, are determined. The number of reactions may not be only limited to the substances from devolatilization process. Any reaction may be added if it is somehow connected with present substances, it is a matter of another function and equation of conservation.
3.5. Solution
Simplified algorithm of solution of the equations’ set is presented on Fig. 3.4. Initial conditions (gas and solid properties and temperatures) are data for first step. At the
beginning of each step all values Φiare assumed in order to calculate all coefficients that
are necessary to solve equations. Then all equations are solved, and new improved values of Φi’ are obtained. If criterion of convergence is not fulfilled, then all Φi = Φi’ and
calculation process returns to point of calculation of indirect coefficients (iterative loop). If criterion of convergence is fulfilled, then final values Φi are start values Φ0 and calculation
process returns to the beginning (time step loop). In case when calculation process reach assumed end time of calculation tend, then it is complete.
Fig. 3.4. Simplified algorithm of solution. 3.6. Example results
Computation process presented in Fig. 3.4 is realized by program written in C++ language. At this stage of research, the program still is being developed, nevertheless its form is advanced. In this section some results are presented for wooden scraps composed of (mass parts): volatile matter 55%, fixed carbon 14%, ash 1% and moisture 30%. Computation domain is cylinder of height H = 0.6 m and diameter d = 0.15 m. Particle diameter is dp =
0.01 m and bed porosity ε = 0.4. Boundary conditions over the bed, which initiate the process, are the one of third kind – temperature T = 1600 K and heat transfer coefficient α2
= 40 W/m2⋅K. Air stream is mg = 0.14 kg/m 2⋅s
, its temperature Tg0 = 293 K and humidity
Fig. 3.5 presents mass loss in time. This process accelerates to some constant value through first 180 s, which is connected with drying of the bed. From t = 536 s mass loss process decelerates this is the point, when all volatile matter released to gas and only in solid phase only char left.
Fig. 3.5. Mass loss in time.
Fig. 3.6 presents temperatures of gas and solid phases in different times of the process. As it is seen, the height of bed, where essential process occurred is about 0.1 m. Relatively high temperatures of solid phase may be caused by omission of heat loss in energy balance. Fig. 3.7 presents mass parts of CO2 and O2. Two processes influence the parts of those
gasses: devolatilization and char combustion. This influence is seen as two changes of lines (from the bottom): a sudden one connected with char combustion and slower one connected with devolatilization process. Above this changes gas composition changes as well – this is connected with reaction in gas phase that still proceeds. Very small part of CO2 after t = 600 s is caused by lack of volatile matter in solid phase (see Fig. 3.5), and major product of char combustion is CO (according to the reaction Eq. 3.6) because of high temperature.
Fig. 3.6. Temperatures of solid and gas phases.
As an example of hazardous substance in gas, Fig. 3.8 presents CO part in gas phase. Three processes have influence on changes of CO in gas (from the bottom):
- abrupt increase caused by char combustion, according to Eq. 3.6,
- slower increase caused by devolatilization process – devolatilization zone is above combustion zone,
- decrease of CO above bed according to Eq. 3.11 that proceeds in gas phase. This reaction is considered in whole computation domain (also in combustion and devolatilization zones) but its influence is particularly seen above solid phase.
Fig. 3.8. Mass part of CO.
4. Conclusion and further work
Biomass becomes an important source of energy, thus the necessity of investigation of biomass combustion process occurs. In presented case a mathematical model of biomass combustion on a mechanical stoker was created. The model considers drying, devolatilization and char combustion of solid phase, as well as reaction in gaseous phase. Owing to the relatively small heat conduction in horizontal way in bed to heat convection in vertical way caused by gas flow, two-dimensional steady and continuous process of biomass combustion on mechanical stoker may be substituted with one-dimensional unsteady process of combustion of separated bed segment. The model determines gas and solid phases’ temperatures and gas composition along height of separated segment in time, which corresponds to the values of those parameters in different places on mechanical stoker.
- development of the model and addition of another reaction in gas phase,
- design of laboratory installation and carry out practical experiment of biomass combustion process,
- comparison of theoretical investigation with practical one and model’s verification. This model may be also used as a part of another one, which models not only processes that occur on the grate, but also in the whole boiler (reactions above grate in combustion chamber).
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