Mathematical model of gasification and combustion of biomass

Monika Žecová, Ján Terpák, Ľubomír Dorčák Institute of Control and Informatization of Production Processes

Faculty of BERG, Technical University of Košice Košice, Slovakia

monika.zecova@tuke.sk, jan.terpak@tuke.sk, lubomir.dorcak@tuke.sk

Abstract—This contribution deals with the creation of mathematical model of biomass gasification and combustion. In the introduction of contribution an analysis is given of biomass in terms of its occurrence, composition, and caloric value and also in terms of processes taking place with the biomass gasification and combustion. The idea for a complex model for the gasification and combustion of biomass is derived from the initial process analysis, which was suggested as a synthesis of elementary process models. In the case of elementary models the heating model, drying model, thermal decomposition model, oxidation of the solid component model, and oxidation of the volatile component model are considered. The heating model is based on the processes of heat accumulation and the transfer of heat by convection. The basis of the evaporation model is a process of the transformation of liquid water into water vapour. The remaining three models include the thermal decomposition of biomass, release of the volatile components and the burning of the solid components from it. Elementary process models were independently implemented and verified in a MATLAB environment as individual m-functions. The results from the simulations are also stated in this contribution, which are analyzed, and further use and method of model gasification and combustion is suggested.

Keywords-biomass; gasification; combustion; mathematical modelling

I. INTRODUCTION Energy consumption has increased due to the growth of the

Earth’s population, and so the need to look for new energy resources. Biomass is a renewable resource produced by the Sun. It can be divided into plant mass (wood biomass and phytomass) and animal mass (zoomass). This includes for example wood, straw, organic farm waste, parts of communal waste as well as artificially grown energetic plants [1, 2].

In biomass elements such as nitrogen, phosphor, sulphur, potassium, sodium, chlorine, calcium, magnesium, iron, copper, arsenic, lead and other elements which make their way into the biomass during its growth as it absorbs nutrients from the soil and air. It also contains free water and bound water. The heating capacity of wood biomass by combustion depends mainly on the amount of moisture, the more moist the less the heating power [1, 2, 3].

II. GASIFICATION PROCESS OF BIOMASS Gasification is a process in which flammable gasses like

hydrogen, carbon monoxide, methane and some inflammable products are produced. The whole process takes place with the incomplete combustion and heating of biomass with the heat produced during combustion. The resulting mixture of gasses has a high energy value.

Gasification of biomass is a process during which the chemical energy of a solid fuel transforms the biomass into a chemical and heat energy gas fuel. The gasification of biomass is an automatic process during which heat for endothermic gas reactions is obtained from the combustion of some of the biomass with a deficiency of combustible air at a certain temperature. Oxygen, water vapour or carbon dioxide can also be used as a medium. Any type of biomass that does not have very high moisture content can be used in the gasification process. This means that the amount of heat to evaporate the moisture in 1kg of biomass is less than the heating power of 1kg of fuel. The main product from the gasification of biomass is synthesis gas – wood gas, made up mainly of carbon monoxide and dioxide, hydrogen, methane, water vapour, nitrogen and contaminants [2, 3].

III. COMBUSTION PROCESS OF BIOMASS Combustion is an oxidation process in which flammable

components of fuel are oxidized by oxygen whereby the energy content of the fuel is changed into heat. Biomass combustion products are ash, tar, and burnt gases (Fig. 1).

The technology of direct combustion of biomass is the most common way its energy is used. It is a verified method and commercially available on a high level. The heat generated is used as a resource in technological processes (process heat) or for the production of electrical energy. For effective combustion a sufficiently high temperature must be present, enough air and enough time for complete combustion of the biomass [2, 3].

IV. MATHEMATICAL MODEL During the initial creation of a mathematical model

an analysis of individual partial models and the processes occurring in them was performed (Fig. 1). Each of the models

978-1-4577-1868-7/12/$26.00 ©2012 IEEE 780

were assigned input and output parameters. A mathematical model consists of the following five elementary models:

1. heating model,

2. water evaporation model,

3. thermal decomposition model,

4. combustion model of solid component,

5. combustion model of volatile component.

Figure 1. Processes occurring during the gasification and combustion of biomass [2]

A. Heating model An input and output for the model of heating wood biomass

is the wood biomass itself and the burnt gases resulting from the combustion used for heating wood biomass. The heating model is based on processes of heat transfer by convection and accumulation of heat.

The following equation is a valid example for the process of heat transfer by convection [2, 4, 5, 6]

( )bgwbSQ TTSkI −= .. (W) (1)

where QI is heat flux (W), Sk is the convection heat transfer

coefficient (W.m-2.K-1), S is surface transfer (m2), wbT is the

wood biomass temperature (K) and bgT is burnt gases temperature (K).

In the case of the process of heat accumulation the amount of accumulated heat is proportional to the temperature change according to this equation [5, 6]

ττ d

dTcmddQ ..= (W) (2)

where Q is the volume of thermal energy (J), m is the weight (kg), c is the specific heat capacity (J.kg-1.K-1), T is the temperature (K) and τ is a time (s).

The description of heat exchange, i.e. the heating model arises from an energy balance, which generally reflects the relation [2, 7]

Accumulation = Input – Output + Source – Consumption (3)

B. Water evaporation model The water evaporation model follows immediately after the

model of wood biomass heating because the evaporation can take place or intensively take place only after prior heating.

The basis for the water evaporation model is the process of transforming liquid water into water vapour according to the equation [2]

( ) ( )gl OHOH 22 → (4)

The evaporation velocity kH2O (kg.m-2.s-1) can be determined using several methods [4, 8], for example the approximate method based on the ratio ks/cg, thus the ratio of convection heat transfer coefficient and specific heat capacity of the gas component. If the available experimental data obtained for example from Thermo-gravimetric analysis [9], then the evaporation rate can be obtained by approximating of experimental data (Fig. 2).

Figure 2. Experimental evaporation rate of water

The following relation gives the course of the rate of evaporation shown in Fig. 2

∑=

=3

02

i

ideniOH Tak ( )12.. −− smkg (5)

where Tden is the wood biomass temperature (K) from the interval <35, 105> and ai (1,0117.10-4;-1,1841.10-5;3,3994.10-4; -2,1895.10-9) are the polynomial coefficients.

C. Thermal decomposition model The thermal decomposition model of wood biomass

follows on the heating model and water evaporation model. Thermal decomposition occurs after the evaporation of water and subsequent increase of temperature above 300 °C.

7812012 13th International Carpathian Control Conference (ICCC)

The velocity of thermal decomposition kvol is similarly determined as evaporation rate, i.e. experimental on the base of data of Thermo-gravimetric analysis [9] (Fig. 3).

Experimentally measured values of thermal decomposition rate shown in Fig. 3 were approximated by the following formula

∑=

=3

0i

idenivol Tak ( )12.. −− smkg (6)

where Tden is the wood biomass temperature (K) from the interval <250, 350> a ai (3,5888.10-1; -3,8904.10-3; 1,3917.10-5; -1,6374.10-8) are the polynomial coefficients.

Figure 3. Experimental velocity of thermal decomposition

D. Combustion model of volatile and of solid component Combustion model of volatile component derives from

a model of combustion of gaseous fuels in the field of imperfect and perfect combustion. The volatile component contains flammable components similarly gaseous fuels (carbon monoxide, hydrogen, methane and so on), which react with oxygen from the air to produce waste gases. The basis of combustion model is the material balance from which the results are the quantity and composition of waste gases. For the total model is the heating power of volatile component an important parameter, which is determined on the base of composition of volatile component. Model of combustion is more detailed described in literature [10, 11, 12] and this model is implemented in MATLAB, available as Combustion toolbox [13].

E. The total model Based on a detailed analysis of individual models energy

balance equations were created, the resultant shape of which represents a system of two first order differential equations, namely for the gaseous component (7) and wood biomass (8)

( )

111111

20

111

20

2010111

101

101

1

110

...

....

..

..

... 22

VcHI

VccTm

Vc

cTmTT

VcSk

TVI

TVI

dtdT

p

plV

p

vpprch

p

OHpOH

p

SVV

ρρ

ρρ

++

++−−−= (7)

( )

222222222

20

222

222

20

2010222

202

202

2

220

...

...

....

...

..

..

...

22

22

VcHm

VcHm

VccTm

VcHm

Vc

cTmTT

VcSk

TVI

TVI

dtdT

p

Tsc

p

volvol

p

volpvol

p

evOHOH

p

OHpOH

p

SVV

ρρρρ

ρρ

+−−−

−−−+−= (8)

where 1T / 2T is an incoming gas/wood biomass temperature

(K), 10T / 20T is an outgoing gas/wood biomass temperature

(K), 1VI / 2VI is an incoming flow volume of gas/wood

biomass (m3.s-1), 10VI / 20VI is an outgoing flow volume of

gas/wood biomass (m3.s-1), plVI is a flow volume of volatile

combustible component (m3.s-1), 1V / 2V is a volume of

gas/wood biomass (m3), 1ρ / 2ρ is the gas/wood biomass

density (kg.m-3), OHm2

is the mass flow of evaporated water

(kg.s-1), volm is the mass flow of volatile components (kg.s-1),

scm is the mass flow of a combustible solid component (kg.

s-1), 1pc / 2pc is the specific heat capacity of gas/wood biomass

(J.kg-1.K-1), volpc is the specific heat capacity of volatile

components (J.kg-1.K-1), OHpc

2is the specific heat capacity of

water (J.kg-1.K-1), H is the heating value of volatile

combustible component (J.kg-1), evOHH

2is the evaporation

heat of water (J.kg-1), volH is the decomposition heat of

volatile components (J.kg-1), TH is the heating value of solid component (J.kg-1).

V. IMPLEMENTATION Individual models of elementary processes of the

gasification and combustion of biomass have been implemented in the programming environment MATLAB [14, 15, 16]. Implementation was primarily carried out for the heating model, water evaporation model and thermal decomposition model.

A. Heating model The heating model is represented by the function of

heating which can be declared, with the corresponding inputs and outputs, as follows

function [tau,out] = heating(in,T1p,T2p,ks,S,time)

782 2012 13th International Carpathian Control Conference (ICCC)

where in is a data structure of an array type containing two items (1 – air, 2 – wood biomass), each item of array is the type of record containing the following items: ro – density, cp – specific heat capacity, V – volume, Iv – flow volume, T – temperature; T1p, T2p are the initial temperatures of gas and wood biomass; ks is the convection heat transfer coefficient; S is the heat transfer surface; time is the length of simulation; out is the data structure of an array type containing two items, each item of array is a vector of temperatures (1) of gaseous component and (2) wood biomass.

B. Water evaporation model The evaporation model was realized by the function

heating_drying which is based on the function heating, completed with the evaporation of water from the wood biomass, which requires the addition of input variables on the rate of evaporation kH2O. Function declaration with its inputs and outputs has the form

function [tau,out]=heating_drying(in,T1p,T2p,ks,kH2O, S,time)

C. Thermal decomposition model Thermal decomposition model was implemented by the

function heating_drying_thermal which is based on the function heating_drying expanded by the velocity of thermal decomposition kvol. The header of this function has the following form

function [tau,out]=heating_drying_thermal(in,T1p,T2p, ks,kH2O,kvol,S,time)

VI. SIMULATIONS The main objective of simulations, which were realized

with individual implemented models, is the qualitative of verification and the sensitivity analysis of models.

The basic simulation of the heating model was specifically implemented for wood biomass of spruce, which was heated by a gaseous component formed by flowing air. Input parameters for wood biomass: density 470 kg.m-3, specific heat capacity 1800 J.kg-1.K-1, volume 1,06 m3, initial temperature 20°C, surface 1,34 m2 and air with parameters: density 1,2 kg.m-3, specific heat capacity 1012 J.kg-1.K-1, flow volume 0,375 m3.s-1, initial temperature 120°C, volume of space above wood biomass 1,06 m3 and convection heat transfer coefficient 300 W.m-2.K-1. Then simulations were carried out to the basic simulation, in which the input air temperature (60 and 180 °C), the volume above wood biomass (0,53 and 1,59 m3) and convection heat transfer coefficient (150 and 450 W.m-2. K-1) were altered.

Figure 4. The course of the simulation heating (ks = 300 W.m-2.K-1)

Figure 5. The course of the simulation heating (ks = 450 W.m-2.K-1)

In the case of setting parameters of the basic simulation it leads to stabilization of temperatures of wood biomass and air in a time of 2370 s (Fig. 4). If we increase the heat intensity, i.e. increasing the convection heat transfer coefficient for example by 50% the value 450 W.m-2.K-1, leads to stabilization of wood biomass temperatures and air in a time of 1950 s (Fig. 5), which is about 20,73% earlier than in the case of baseline simulation. For comparison, in the case of reduction of area above wood biomass from 1,06 to 0,53 m3, leads to stabilization of temperatures in a time of 2370 s, which is only 3,66% earlier than in the case of baseline simulation.

From the above, but also from further results of simulations we conclude that the heating model responds most sensitively to a change of the heat transfer coefficient by convection. Furthermore, we can also state that in qualitative terms the heating model responds to changes of inputs and parameters by the corresponding change of dynamics, i.e. corresponding the course of temperatures in a time.

7832012 13th International Carpathian Control Conference (ICCC)

Figure 6. Simulation process without evaporation of water

Figure 7. Simulation process with evaporation of water

Simulations of water evaporation model from biomass follow from the same parameters and inputs, as in the case of the heating model only a higher value was used for air temperature at the input. An initial simulation with zero velocity of evaporation was made to compare the curves of model simulations of this evaporation shown in Fig. 6. Subsequently, simulations were performed with various multiples of the rates of evaporation. In the case of velocity according to equation (5) the course of the simulation (Fig. 7) is seen to reflect the evaporation of water when compared with the course in Fig. 6. In the section from 60 °C to 110 °C the increase of biomass temperature slowed down, due to the evaporation of water from it.

Similarly as in the case of the water evaporation model, simulations were performed with the model of thermal decomposition, i.e. simulations without thermal decomposition (Fig. 8) and with thermal decomposition (Fig. 9).

Figure 8. Simulation process without thermal decomposition

Figure 9. Simulation process with thermal decomposition

From the curves in Fig. 8 and Fig. 9 it can be seen that under thermal decomposition the increase in the temperature of the biomass and gas is slowed, this is caused by the consumption of heat for thermal decomposition in the interval of temperatures 250 to 350 °C, i.e. not all the heat that is transferred from the gas component by convection is used for wood biomass heating.

Finally simulations were carried out that resulted from the simulation model comprising the three partial models, i.e. the heating model, the water evaporation model and the thermal decomposition model. In Fig. 10 a process simulation with a zero velocity of evaporation and with a zero velocity of thermal decomposition as a comparative process is mentioned, thus a process without evaporation and thermal decomposition. Taking into account the experimental velocity of evaporation and thermal decomposition, in Fig. 11 the corresponding simulation is shown. From the course of temperatures it is evident at what temperatures and at what time evaporation and thermal decomposition occur. From the results we see that the temperature increase being slowed down leads to increase in the time it takes to achieve their stabilization.

784 2012 13th International Carpathian Control Conference (ICCC)

Figure 10. Simulation process without evaporation and thermal decomposition

Figure 11. Simulation process with evaporation and thermal decomposition

VII. CONCLUSION The importance of biomass energy use can only be

evaluated positively. The result of the use is not only obtaining its own energy, but biomass also has other aspects that predispose it to more intensive use, for example biomass is a certain alternative to fossil fuel resources.

The purpose of this work, which is initiated in this contribution, has been to create a mathematical model of the combustion and gasification of biomass, to carry out a qualitative verification and to find out the sensitivity of inputs and parameters on the course of processes. The results of simulations from three partial models, namely from the heating model, evaporation model and thermal decomposition model, and simulations model made by the synthesis of partial models, are listed in this work.

Created partial models can be used for process simulations of heating, evaporation and thermal decomposition in terms of

analysis of the processes and the study of the impact various parameters have on the partial processes. Further use of the model is in terms of design of device parameters for the gasification and combustion of biomass. The model can even be used in the design and implementation of management processes of combustion and gasification of biomass.

ACKNOWLEDGMENT This contribution was supported by projects VEGA

1/0746/11, 1/0479/11 and 1/0729/12.

REFERENCES [1] Z. Pastorek, J. Kára, P. Jevič, Biomasa obnoviteľný zdroj energie

(Biomass renewable energy resource), FCC PUBLIC, 2004. p. 288, ISBN 80-86534-06-5

[2] A. Klenovčanová, I. Imriš, Zdroje a premeny energie (Sources and energy conversion), Edícia vedeckej a odbornej literatúry – Strojnícka fakulta TU v Košiciach, 2006. p. 492, ISBN 80-89040-29-2

[3] P. Basu, Biomass Gasification and Pyrolysis: Practical Design and Theory, Academic Press, 2010, p. 376, ISBN 978-0123749888

[4] W. M. Kays, M. E. Crawford, Convective Heat and Mass Transfer, McGraw-Hill, Inc., New York, Third Edition, 1993, p. 602, ISBN 0-07-033721-1

[5] M. Žecová, Matematické modelovanie splyňovania a spaľovania biomasy (Mathematical modelling of gasification and combustion of biomass), Diploma theses, Košice : Technická univerzita v Košiciach, Fakulta BERG, 2009, p. 115.

[6] J. Terpák, Ľ. Dorčák, Procesy prenosu (Transfer processes), Košice: Technická univerzita v Košiciach, 2001, p. 212.

[7] R. K. Sinnott, Coulson&Richardson‘s Chemical Engineering: Chemical Engineering Design, Volume 6, Elsevier Butterworth-Heinemann, Amsterdam, 1999, p. 1056, ISBN 978-0750665384

[8] J. R. Backhurst, J. H. HARKER, J. M. COULSON, J. F. RICHARDSON, Coulson&Richardson‘s Chemical Engineering: Fluid Flow, Heat Transfer and Mass Transfer, Volume 1, Elsevier Butterworth-Heinemann, Amsterdam, 1999, p. 928, ISBN 978-0750644440

[9] M. Vladárová, Sledovanie termickej degradácie vzoriek buka v kontinuálnej a prašnej forme metódami termickej analýzy (Monitoring the thermal degradation of samples of beech in a continuous and suspended form by thermal analysis methods), Technická univerzita vo Zvolene, Drevárska fakulta: [cit 2009-03-15]. Available from: https://is.tuzvo.sk/lide/clovek.pl?id=905;zalozka=7;lang=sk

[10] R. Aris, Mathematical Modelling Techniques, Ritman Advaced Publishing Program, San Francisco, 1979, p. 192, ISBN 0-273-08413-5

[11] R. Aris, Mathematical Modeling: A Chemical Engineer’s Perspective, Academic press, San Diego, 1999, p. 480, ISBN 0-12-604585-2

[12] R. Aris, Elementary Chemical Reactor Analysis, DOVER PUBLICATIONS, INC. Mineola, New York, 1989, p. 352, ISBN 0-486-40928-7

[13] Combustion toolbox - File Exchange - MATLAB Central, Update 04-10-2011 [cit 2011-10-05]. Available from: <http://www.mathworks.com/matlabcentral/fileexchange/26492-combustion-toolbox>

[14] P. Karban, Výpočty a simulace v programech Matlab a Simulink (Calculations and simulation programs in Matlab and Simulink), Brno: Computer Press, a.s, 2006, p. 220, ISBN 80-251-1301-9

[15] B. Doňar, K. Zaplatílek, Matlab - tvorba uživatelských aplikací 2. díl (Matlab – creation of user applications 2nd part ), Ben, 2004, p. 216, ISBN 80-7300-133-0

[16] R. Bartko, M. Miller, MATLAB I.: algoritmizácia a riešenie úloh 2. vydanie (MATLAB I.: algorithms and tasks solving 2nd edition), Trenčín: DIGITAL GRAPHIC, 2005, p. 290, ISBN 80-969310-0-8

7852012 13th International Carpathian Control Conference (ICCC)