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Computers and Chemical Engineering 35 (2011) 25–40

Contents lists available at ScienceDirect

Computers and Chemical Engineering

journa l homepage: www.e lsev ier .com/ locate /compchemeng

odeling and simulation of an oxy-fuel combustion boilerystem with flue gas recirculation

de Haryantoa,1, Keum-Shik Hongb,∗

School of Mechanical Engineering, Pusan National University, 30 Jangjeon-dong, Gumjeong-gu, Busan 609-735, Republic of KoreaDepartment of Cogno-Mechatronics Engineering (W.C.U. program), Pusan National University, 30 Jangjeon-dong Gumjeong-gu, Busan 609-735, Republic of Korea

r t i c l e i n f o

rticle history:eceived 6 April 2009eceived in revised form 27 February 2010ccepted 1 May 2010vailable online 12 May 2010

a b s t r a c t

In this paper, a mathematical model of an oxy-fuel combustion boiler system with flue gas recirculationis investigated. The reduction of CO2 emission from coal-fired power plants is an important researchissue in alleviating the global warming. The entire dynamics are decomposed in two main parts; fire-side dynamics and water-side dynamics. The fire-side dynamics consist of the mass and energy balanceequations in the furnace (combustion process) and the flue gas dynamics represented by the mass balance

eywords:xy-fuel combustion boileroal power plantodeling

imulation

equations of five gases (O2, CO2, SO2, H2O and NO2). The water-side dynamics include a drum pressureequation and a steam temperature equation. To validate the developed models, the real experimentaldata in Karakas, Koumanakos, et al. (2007) are used. To investigate the local behavior near an operatingpoint, a linearization method at its steady-state condition is pursued. The time responses of the entiredynamics using step inputs (the oxygen mass flow rate, the coal mass flow rate, the primary air mass

scuss

ass and energy balanceodel validation

flow rate, etc.) are also di

. Introduction

Global warming is currently one of the most serious environ-ental challenges in the world. The increase of carbon dioxide

CO2) in the atmosphere is a dominating factor to global warming.arbon dioxide is emitted to the atmosphere through combustionf fossil fuels in power plants, automotive engines, industrial pro-esses, and other heating processes. Most power plants still dependn the use of fossil fuels and will continue to do so for a longime, due to the lack of effective alternative energy sources. Lately,oncerns over the role of greenhouse gases in increasing globalarming have led to international agreements like the Kyoto Proto-

ol, which sets targets for controlling CO2 emission. The measuresn these agreements force power plants to operate their steam gen-ration systems more efficiently and closer to the admissible level

f the operating region to minimize operation cost as well as toupply more electricity with less CO2 emission.

This paper focuses on the oxy-fuel combustion of pulver-zed coal power plants. In conventional coal-fired combustion,

Abbreviations: ESP, electrostatic precipitator; RFG, recycled flue gas; FG, flueas; ASU, air separation unit; RC, raw coal.∗ Corresponding author. Tel.: +82 51 510 2454; fax: +82 51 514 0685.

E-mail addresses: a.haryanto@pusan.ac.kr (A. Haryanto),shong@pusan.ac.kr (K.-S. Hong).1 Tel.: +82 51 510 7326; fax: +82 51 514 0685.

098-1354/$ – see front matter © 2010 Elsevier Ltd. All rights reserved.oi:10.1016/j.compchemeng.2010.05.001

ed.© 2010 Elsevier Ltd. All rights reserved.

ambient air is used for burning fuel (coal). Recently, studies onCO2 capturing technologies (Buhre, Elliot, Sheng, Gupta, & Wall,2005; Karakas, Doukelis, Giannakopoulos, & Koumanakos, 2007;Zanganeh & Shafeen, 2007) indicated that oxy-fuel combustionmight be a favorable option for retrofitting the conventional coal-fired power plant. In this type of combustion, coal is burned withnearly pure oxygen to produce a flue gas that is mostly CO2.Practically, coal combustion in pure oxygen generates very hightemperatures in the furnace (Katsuki et al., 2009). To regulate thehigh temperature and to compensate the volume fraction of miss-ing N2 that ensures sufficient gas to carry heat through the boiler,part of the flue gas (mostly consisting of CO2, H2O, and some excessoxygen) is recycled back to the burner.

To maintain a high performance in oxy-fuel combustion boilers,an effective control system is needed. The design and implementa-tion of such a control system for an oxy-fuel combustion boilerrequires mathematical models that can adequately capture thebehaviors and dynamics of the combustion and boiler. The develop-ment of dynamic models of oxy-fuel combustion for control systemdesign purposes has not been sufficiently studied; in fact, no liter-ature exists about the modeling of oxy-fuel combustion for controldesign purposes. Most literatures (Chui, Douglas, & Tan, 2003; Chui,

Majeski, Douglas, Tan, & Thambimutu, 2004; Li, Wei, & Jin, 2003)discuss modeling issues of the conventional (and/or oxy-fuel) com-bustion for the purpose of computational fluid dynamics analysis,not for the purpose of control. These models are relatively complexand not adequate for control system design.

26 A. Haryanto, K.-S. Hong / Computers and Chemical Engineering 35 (2011) 25–40

bustio

(pmtstcmit

Fig. 1. Schematic of a typical oxy-fuel com

In this paper, dynamic/mathematical models of the fire-sideincluding the recycling part) and water-side of an oxy-fuel powerlant are investigated. The models are obtained by applying theass and energy conservation laws and chemical reaction equa-

ions. The fire-side models include the dynamics (char, sulfur, andolid/gas temperatures) in the furnace and the flue gas emissions at

he boiler exit (O2, CO2, SO2, H2O and NO2). The water-side modelsonsist of the drum pressure dynamics, the mass flow rate of theain steam and the temperature equation of the steam product. To

nvestigate disturbance effects as well as the plant normal behavior,he paper also considers additional stochastic disturbances in the

n boiler system with flue gas recirculation.

forms of coal quality changes, recycled flue gas (RFG) fluctuations,and oxygen production fluctuations from the air separation unit(ASU). The disturbances become crucial if their appearance affectsthe stability and thermal efficiency of the boiler system.

The contributions of this paper are the following. This is the firstwork on the development of mathematical models of an oxy-fuel

combustion boiler system. Using the data in Karakas, Koumanakos,Doukelis, Giannakopoulos and Vorrias (2007), an operating pointof the developed model (which corresponds to the steady-statecondition of Greenfield power plant) is established. To investigateinput–output characteristics at the steady-state operation, the non-

A. Haryanto, K.-S. Hong / Computers and Chemical Engineering 35 (2011) 25–40 27

n proc

lemfltittglirttdttisfco

pfwsIec

2

2

wpKgmfsvthaiT1

Fig. 2. Oxy-fuel combustio

inear furnace dynamics are linearized at its operating point. A statequation that relates four inputs (coal mass flow rate, primary airass flow rate, secondary air mass flow rate, and oxygen mass

ow rate) to four outputs (char mass, sulphur mass, solid particleemperature in the furnace, and gas temperature in the furnace)s derived. Since the plant will operate mostly at its steady state,his linear analysis will give a good intuition on what parametero change to improve the steady-state performance. To verify thelobal behavior of the plant, the time responses of the entire non-inear equations are also investigated: In this case, the used twonputs are the coal mass flow rate and the primary air mass flowate, whereas the obtained four outputs are the gas temperature,he char mass, the steam temperature, and the drum pressure. Also,he consistency of the obtained results with the real experimentalata in Karakas, Koumanakos, et al. (2007) is confirmed. The inves-igation on the concentration changes of O2, CO2, H2O and NO2 inhe flue gas upon the step change of the mass flow rate of the RFGs another meaningful work. The disturbance effects in obtaining atable gas temperature that are caused by O2 concentration changesrom the ASU, CO2 concentration changes in the primary air, andoal quality changes are addressed as well. Most of all, the devel-ped model can be used for a model-based control system design.

The paper is structured as follows. In Section 2, the basicrinciples and nonlinear characteristics of the fire-side in oxy-uel combustion are described. In Section 3, the dynamics of theater-side are discussed. In Section 4, a linear analysis and the

teady-state behavior analysis of an oxy-fuel furnace are presented.n Section 5, simulations of the full dynamics including disturbanceffects are conducted and discussions are drawn. In Section 6, con-lusions are made.

. Fire-side dynamics: combustion and flue gas

.1. Oxy-fuel combustion boiler

Fig. 1(a) shows the typical oxy-fuel combustion boiler systemith flue gas recirculation (with some simplifications for modelingurposes) considered in this study. Fig. 1(b) adopted from Karakas,oumanakos, et al. (2007) depicts a process flow diagram. The oxy-en (O2) is separated from the air in the cryogenic ASU and thenixed with a recycled stream of the flue gas (�RFG), which comes

rom the boiler exit. The mixture of RFG plus O2 is referred to asynthetic air. The primary synthetic air (�pri) transports the pul-erized coal into the furnace at the mass flow rate �coal,in, whilehe secondary synthetic air (�scn) enters the furnace to provide the

igher mass and volumetric flow. To improve the flame stabilitynd to decrease the unburnt carbon content of the ash, pure O2 isnjected (�oxy) at the centre of the burner (Kimura, Omata, Kiga,akano, & Shikisima, 1995; Nozaki, Takano, Kiga, Omata, & Kimura,997).

ess with CO2 recirculation.

As shown in Fig. 2, the constituents of the flue gas (O2, CO2, H2O,SO2 and N2) emitted from combustion process can be monitored byusing a flue gas analyzer. In the oxy-fuel combustion, about 70–80%of the total CO2 emission is recycled into the burner, and the non-condensable CO2 is stored in the carbon capture and storage (CCS)system.

2.2. Mass and energy balance in the furnace

Coal combustion is usually modeled based on the assumptionthat coal is converted in three steps: pyrolysis of raw coal, com-bustion of volatiles, and char (carbon reach solid residue) burnout(Chomiak, 1990). When coal is heated in the temperature range of200–1200 K, it decomposes into hydrogen rich fraction, volatiles,and char. This process is called pyrolysis, which produces threemain products of coal combustion: char, tar (CxHyOz with an H/Cmolar ratio of 1.1 and an O/C molar ratio equal to the parent coal)and gas (Solomon, Serio, & Suuberg, 1992). In this paper, a numberof mathematical models are derived by assuming that the incomingsolid components into the furnace consist of char and sulphur. Thereactivity and structure of chars depend on the type of coal, tem-perature of pyrolysis, heating rate, particle size, and the residencetime of the coal particle in the reactor (Yu, Lucas, & Wall, 2007).

Dynamics models of the combustion in the furnace and of theflue gases at the boiler exit are based on the mass and energy bal-ance and the chemical reactions of coal combustion. Under theassumption that the furnace is a stirred reactor in which het-erogeneous (solid–gas) reactions take place, the mass and energybalances for the solid components in the furnace are given by

dmchar

dt= �wt

char�coal,in − �char,react − �char,out, (1)

dmsulp

dt= �wt

sulp�coal,in − �sulp,react − �sulp,out, (2)

d

dt(mcharCp,char(Ts − T0) + msulpCp,sulp(Ts − T0))

= �wtchar�coal,inCp,char(Tcoal − T0) + �wt

sulp�coal,in × Cp,sulp(Tcoal − T0)

− �char,outCp,char(Ts − T0) − �sulp,outCp,sulp(Ts − T0)

− �char,reactCp,char × (Ts − T0) − �sulp,reactCp,sulp(Ts − T0)

− �priCp,FG(Ts − Tpri) + �char,react�LHV �HLHV + �sulp,react�Hsulp

+ qrad, (3)

where mchar and msulp are the total masses of the char and sulphurparticles in the furnace (kg), respectively; �coal,in is the mass flowrate of the inlet coal (kg/s); �char,out and �sulp,out are the mass flowrates of the unconverted char and generated sulphur that leave thefurnace through the ash (kg/s), respectively; �char,react and �sulp,react

2 nd Ch

arstfltatewho

gH

q

w

A

a(itc(

˛

wcc1ttcacia

asr

(

&mtAcd

k

ws

8 A. Haryanto, K.-S. Hong / Computers a

re the mass reaction rates of the char and sulphur particles (kg/s),espectively; �wt

charand �wt

sulpare the mass fractions of the char and

ulphur in the coal (wt%), respectively; Cp,char , Cp,sulp and Cp,FG arehe specific heat capacities of the char, sulphur particle and theue gas (kJ/kG K), respectively; T0 is the environment (reference)emperature (298 K), and Ts and Tg are the temperatures of the solidnd the gas phases of the coal in the furnace (K), respectively. Theerms �char,react�LHV �HLHV and �sulp,react�Hsulp in (3) describe thenergy released from the char and sulphur reactions, respectively,here �LHV is the energy distribution factor, �HLHV is the lowereating value of the coal (kJ/kG) and �Hsulp is the specific enthalpyf the sulphur reaction (kJ/kg).

The term qrad in (3) indicates the radiative heat flux from theas to the char particles, and the linearized form of qrad is given byottel and Sarofim (1967)

rad = A˛(εgTg − ˇgTchar), (4)

here

= AT

(1/εg) + (1/Csεchar) − 1(5)

nd A is the burning area (m2); AT the total furnace envelope aream2); ˇg is the absorptivity of the gas; εg and εchar are the emissiv-ties of the gas and char, respectively; Cs is the sink fraction of theotal furnace envelope area, and ˛ is the convective heat transferoefficient (W/m K). ˛ can be obtained from the Nusselt numberNu) equation as follows:

= Nukf

L, (6)

here kf is the thermal conductivity of the gas (W/m K) and L is theharacteristics length (m) of the furnace. In this paper, to reduceomputation, a fixed Nusselt number (0.036, Karlekar & Desmond,977) is used throughout the combustion process by assuming thathe temperature difference between the bulk fluid and the heatransfer surface is minimal (i.e., �/�s ≈ 1, where � is the fluid vis-osity at the bulk fluid temperature and �s is the fluid viscosityt the heat transfer boundary surface temperature). For detailedombustion modeling (for instance, in computational fluid dynam-cs), varying Nusselt numbers can be incorporated by taking intoccount of the viscosity changes (� and �s).

Under the assumption that the amounts of the unconverted charnd generated sulphur leaving the furnace through the ash are verymall (�char,out, �sulp,out ≈ 0), the substitution of (1) and (2) into (3)esults in the following equation of the energy balance:

Cp,charmchar + Cp,sulpmsulp)dTs

dt

= (�wtcharCp,char + �wt

sulpCp,sulp)�coal,in(Tcoal − Ts) − �priCp,FG

× (Ts − Tpri) + �char,react�LHV �HLHV + �sulp,react�Hsulp + qrad. (7)

According to the principle of pulverized coal combustion (SmootSmith, 1985), the total reaction rate of the char particle is deter-ined not only by the rate of chemical reactions, but also by

he intensity of the oxygen mass supplied to the reaction zone.ssuming that char is pure carbon (C), the total reaction rate coeffi-ient of the char particle (kchar,react) can be calculated based on theiffusive-kinetic theory of combustion below.

char,react = YO2

1/kr,char + 1/kd(8)

here YO2 is the molar concentration of O2 near the char particleurface (kmol/m3), kd is the diffusion parameter of mass transfer

emical Engineering 35 (2011) 25–40

(m/s), and kr,char is the reaction rate parameter of the char particlein kinetic regime (m/s) given by Arrhenius expression. That is,

kr,char = k0,char exp

(−EA,char

RuTg

), (9)

where k0,char is the pre-exponential factor of char particle reaction(m/s), Ru is the universal gas constant (J/kmol K), and EA,char is theactivation energy of char particle reaction (J kmol). Therefore, thechar particle reaction rate (�char,react) in (1) can be calculated as

�char,react = kchar,reactacharmchar

= YO2

1/kr,char + 1/kdacharmchar

, (10)

where achar is the interfacial surface area of the char particle(m2/kg).

In combustion systems, radiation is a major heat transfermechanism among the solid particles in combustion. For detailedcombustion modeling, the radiation fluxes may have to be com-puted using both diffusivity and scattering coefficients. However,in this paper, as done in Yang, Ryu, Khor, Sharifi, and Swithenbank(2005), we assume that the scattering coefficient is very small (i.e.,close to zero). Therefore, the radiation flux is given as a function ofonly the diffusivity coefficient. The parameter kd in (8) is given as afunction of the non-dimensional Sherwood number Sh as follows:

kd = ShD

dp, (11)

where dp is the diameter of the char particle (m) and D is thediffusion coefficient of O2 in air, which is given as an empiri-cal expression for high temperature combustion products (K−1)(Smoot & Smith, 1985):

D = 9.8 · 10−10T1.75g . (12)

Based on the investigation of Várheyi & Till (1999), the kinet-ics of a solid particle with O2 reaction is not influenced by thepresence of high amounts of CO2 both in atmospheric thermo-gravimetry and in pressurized thermogravimetry. This means therate of char particle combustion (�char,react) of (8) can be used fordescribing oxygen-mixed CO2 combustion (oxy-fuel combustionwith CO2 recirculation).

The total mass balance of the gas phase is straightforward andcan be integrated in the energy balance of the gas phase as follows:

�gVgCp,gdTg

dt= �oxyCp,FG(Toxy − Tg) + �priCp,FG(Ts − Tg)

+ �scnCp,FG(Tscn − Tg) + �char,reactCp,FG(Ts − Tg)

+ �char,react(1 − �LHV )�HLHV − qrad, (13)

where �g is the gas density (kg/m3), Vg is the gas volume m3, Cp,g

is the specific heat capacity of the gas (J/kg K), Toxy and Tscn are theO2 injection and synthetic secondary air temperatures (K), respec-tively. The first to the fourth terms of the right-hand side of (13)describe the contributions of the convective heat from the oxygeninjection and from the primary and secondary synthetic airs, andfrom the amount of solid material converted into gas, respectively.The last term �char,react(1 − �LHV )�HLHV describes the released heatby gas reaction.

2.3. Dynamics of the flue gases

This subsection describes the dynamics of the flue gases (O2,

CO2, SO2, H2O and N2). During the change of constituents of the fluegas, a complex connection of gases will occur due to the chemicalreactions between O2 and the other components of the flue gas. Thecombustion of the coal in its simplest form is a high temperatureoxidation of carbon into CO2 at the particle surface, as expressed by

A. Haryanto, K.-S. Hong / Computers and Chemical Engineering 35 (2011) 25–40 29

n pro

CraodTcpHS

ys(bct&tcp

dr

TC

Fig. 3. Carbon reactio

+ O2 → CO2 (exothermic reaction). However, the actual chemicaleaction even on a non-porous char particle may not be as simples the above reaction. Other possible stages may exist: pyrolysisf raw coal, combustion of volatiles, and char burnout. A detailedescription of these stages can be found in Smoot and Smith (1985).he reaction models of carbon particles in oxy-fuel combustionan be described as shown in Fig. 3: The rate equations and thearameters of the reactions are summarized in Table 1 (Badzioch &awksley, 1970; Förtsch, Kluger, Schnell, Splietheff, & Hein, 1998;erio, Peters, & Howard, 1987; Zimonth & Trushin, 1967).

The pyrolysis process consists of the primary reaction {C1}ielding three main products, namely, char, tar, and gas, followed byecondary reactions {C2}, {C3} and {C4} yielding soot (C), hydrogenH2), light hydrocarbons, and carbon monoxide (CO). The com-ustible gaseous products of the pyrolysis (H2, CmHn, and CO) areonverted via {C5}, {C6}, {C7} and {C8} reactions. Soot particle reac-ion {C9} is treated as a gaseous reaction in combustion (Magnussen

Hjertager, 1976). All the homogenous reactions {C1}–{C9} arereated as irreversible reactions, and the heterogenous reaction of

har burnout {C10} is assumed to be a surface reaction of the Carticle.

Since the gas emissions in combustion are of our interest, theynamics of the flue gases are derived based on their combustioneactions and mass balance principles as follows. According to the

able 1arbon reaction equations and parameter values.

Rate equations

{C1} dmcoaldt

= k0,c1 · exp(−EC1 /RT) · mcoal

{C2} dYtardt

= k0,c2 · exp(−EC2 /RT) · Ytar

{C3} dYtardt

= k0,c3 · exp(−EC3 /RT) · Ytar

{C4} dYtardt

= k0,c4 · exp(−EC4 /RT) · Ytar · YO2

{C5} dYCmHndt

= k0,c5 · T0.5 exp(−EC5 /RT) · YCmHn · YO2

{C6} dYCOdt

= k0,c6 · exp(−EC6 /RT) · YCO · YO20.5 · YH2O

0.5

{C7}dYH2

dt= k0,c7 · YH2 · YO2

{C8} dYCmHndt

= k0,c8 · exp(−EC8 /RT) · YCmHn · YH2O

{C9} dmsootdt

= k1 ·exp(−E1/RT)·p2

1+k2 ·exp(−E2/RT)·p2 Asoot

{C10} Eq. (9)

cesses in the furnace.

reactions in Fig. 3, the balance equation of O2 can be written as

dMO2

dt= FO2,in − FO2,cons − FO2,FG. (14)

Eq. (14) means that the change of the total molar number of O2MO2 , kmol is equal to the sum of the total molar flow rate of O2 atthe furnace inlet (FO2,in), the molar consumption rate of O2 in thefurnace (−FO2,cons), and the outgoing molar flow rate of O2 from thefurnace (−FO2,FG).

Based upon the evaluation of the residence time obtained from(7) and (13), the accumulation of O2 in the furnace can be neglected.The residence time of the char particle (char) in the furnace is muchlonger than that of the gas particle (g), that is,

char = Cp,charmchar

�coal,inCp,char − �priCp,FG + A˛ˇg� g

= �gCp,fgVg

(�pri + �scn + �oxy)Cp,FG − A˛εg. (15)

For this reason, the O2 balance is straightforward as follows:

FO2,in − FO2,cons = FO2,FG, (16)

Parameter values

k0,C1 = 1.5 × 105 s−1

EC1 /R = 8.9 × 103 Kk0,C2 = 5.02 × 108 s−1

EC2 /R = 2.39 × 104 Kk0,C3 = 5.42 × 104 s−1

EC3 /R = 1.21 × 104 Kk0,C4 = 3.8 × 107 m3/(kmol s)EC4 /R = 6.67 × 103 K

k0,C5 = 3.8 × 107 m3/(kmol s)EC5 /R = 6.67 × 103 Kk0,C6 = 1.3 × 1011 m3/(kmol s)EC6 /R = 1.51 × 104 K

k0,C7 = ∞k0,C8 = 4.4 × 1011 m3/(kmol s)EC8 /R = 1.51 × 104 K

k1 = 3.05 × 10−3

k2 = 3.1 Pa−2

E1/R = 2.9 × 104 KE2/R = 2.93 × 104 K

30 A. Haryanto, K.-S. Hong / Computers and Chemical Engineering 35 (2011) 25–40

on pro

wf

F

a

F

c

Y

wtmf

Hm

�

TN

Fig. 4. Nitrogen reacti

here the O2 consumption (FO2,cons) follows directly from (9) asollows:

FO2,cons = YO2 kr,characharmchar

= YO2 acharmchar

1/kd + k0 exp(−EA,char/(RuTg)

) . (17)

The molar flow rate of the incoming O2 is given by

O2,in = (�pri + �scn)YO2,in + �oxyYO2,ASU

�air, (18)

nd the molar flow rate of O2 of the flue gas is calculated as

O2,FG = �FG

�FGYO2,FG. (19)

Hence, the molar concentration of O2 of the flue gas can beomputed as follows:

O2,FG =(

(�pri + �scn)YO2,syn + �oxyYO2,ASU/�air

�FG�FG

+ achar mchar1/kd+k0 exp(−EA,char /Rg Ts)

), (20)

here YO2,syn and YO2,ASU are the molar concentration of O2 fromhe synthetic air and from the ASU (kmol/m3), respectively. The

ass balance of the gas phase in the furnace holds in general asollows:

dmg = �pri + �scn + �oxy + �char,react − �FG. (21)

dt

owever, considering the fact that s � g (i.e., dmg/dt ≈ 0), theass flow rate of the flue gas (�FG) can be assumed as

FG = �pri + �scn + �oxy + �char,react . (22)

able 2itrogen reaction equations and parameter values.

Rate equations

{N1} dXHCNdt

= k0,N1 · exp(−EN1 /RT) · XHCN · XO2

{N2}dXNH3dXNH3

=k0,N2

·XOb

2k0,N3

·XNO· exp(EN3 /RT − EN2 /RT)

{N3}

{N4} dXNOdt

= −k0,N4 · exp(−EN4 /RT) · XNO · XCmHn

{N5s} dMNOdt

= −k0,5s · exp(−EN5s/RT) · pNO · Asoot

{N5c} dMNOdt

= −k0,5c · exp(−EN5c /RT) · pNO · Apar

{N6} dXNOdt

= k0,N6 · exp(−EC6 /RT) · XN2 · (XO2 · �g )0.5

cesses in the furnace.

Also, the CO2 concentration of the flue gas can be simply con-sidered as the accumulation of CO2 (

∑CO2) that comes from the

gas phase reactions (in Fig. 3) and some CO2 contributions from theRFG. A similar mechanism also applies to the H2O concentration ofthe flue gas.

After O2 and CO2 dynamics are obtained, the production ofother combustion gases is considered. In the combustion process,nitrogen dioxide (NO2) can be formed by the fixation of molecularnitrogen in the combustion air or by the nitrogen chemically boundin the coal. The reaction models of coal-nitrogen in the oxy-fuelcombustion furnace can be presented as shown in Fig. 4: The rateequations and the parameters are summarized in Table 2 (Chen,Smoot, Hill, & Fletcher, 1996; Cheng, Kirsch, & Lester, 1989; Miller& Bowman, 2003; Mitchel & Tarbell, 1982). The coal-nitrogen reac-tions consist of the decay of the CN subsystem initiated by attackingoxygen-containing species {N1}, oxidation of NHi {N2}, reductionof NO {N3}, reburning of nitric oxide {N4}, further destruction ofNO by soot {N5s} and char {N5c} and nitrogen thermal mechanism{N6}.

Finally, sulphur compounds are formed through a series ofreactions involving the organically bound sulphur and the sulphur-bearing inorganic compounds in the mineral matter (e.g., pyrites)of coal particles. The predominant combustion product is sulphurdioxide (SO2) with small amounts of sulphur trioxide (SO3). A con-siderable amount of sulphur (approximately about 15%) is retainedin the residual coal ash. The formation of sulphuric pollutantsduring combustion is depicted in Fig. 5. The reactions of sulphur

involving O2 yield the major sulphuric product, SO2, during com-bustion via {S1} and {S5}, and a small amount of retained sulphuris formed by reaction {S7}. The rate equations and the parametersof the sulphur reactions in the furnace are summarized in Table 3(Dowling & Clark, 1999; Dowling, Hyne, & Brown, 1990; Gómez,

Parameter values

k0,N1 = 1.94 × 1015 s−1

EN1 /R = 3.95 × 104 K

k0,N2 = 2.8 × 1010 s−1

k0,N3 = 3.0 × 1012 s−1

EN2 /R = 3.37 × 104 KEN3 /R = 3.02 × 104 Kk0,N4 = 9.2 × 104 s−1

EN4 /R = 9.46 × 103 Kk0,N5s = 4.47 × 10−7 m3/(kmol s)EN5s /R = 9.65 × 103 Kk0,N5c = 4.18 × 10−4 m3/(kmol s)EN5s /R = 1.75 × 104 Kk0,N6 = 1.0 × 1013 m1.5/(kg0.5 s)EN6 /R = 6.81 × 104 K

A. Haryanto, K.-S. Hong / Computers and Chemical Engineering 35 (2011) 25–40 31

n pro

F1

nuef

w((fisrfl

3

3

cTeAdtw

TS

Fig. 5. Sulphur reactio

ueyo, & Tomás, 2007; Karan, Mehrotra, & Behie, 1998; Westley,980).

According to the reactions described in Figs. 3–5 for carbon,itrogen and sulphur, respectively, we derive the mass and vol-me balances for flue gases NO2, SO2, CO2, and H2O to obtain thequations of flue gas dynamics. The general gas balance equationor each gas constituent in the furnace can be written as

d

dt(MgXi) = Fi,in − Fi,FG + Fi,gen − Fi,cons + Fi,RFG, (23)

here Mg is the total molar number of the gas in the furnacekmol), Xi is the mole fraction of the ith gas species in the furnacekmol/kmol), Fi,in is the molar flow rate of gas species i in the aireed flow (kmol/s), Fi,FG is the molar flow rate of the flue gas speciesout of the furnace (kmol/s), Fi,gen is the molar generation rate of gaspecies i from reactions (kmol/s), Fi,cons is the molar consumptionate of gas species i by reactions (kmol/s), and Fi,RFG is the molarow rate of gas species i from the RFG (kmol/s).

. Water-side dynamics

.1. Drum pressure

In a power plant, the heat released from the combustion pro-ess is used to convert feedwater into steam in the boiler system.he steam is used by the turbine to generate electricity. Recent lit-

ratures have reported several models of water-tube boilers (e.g.ström & Bell, 2000; Leva & Maffezzoni, 1999). These models wereeveloped by utilizing the basic laws of mass, energy and momen-um balances as well as the thermodynamic properties of theater-steam mixture.

able 3ulphur reaction equations and parameter values.

Rate equations

{S1} dMSdt

= k0,S1 · exp

(−ES1

RT

)· MS

{S2} dYSdt

= k0,S2 · exp(−ES2 /RT) · YS · YCO2

{S3} dYSdt

= k0,S3 · exp(−ES3 /RT) · YS · YH2O

{S4}dYH2S

dt= k0,S4 · exp(−ES4 /RT) · YCO2 · YH2S

{S5}dYH2S

dt= k0,S5 · exp(−ES5 /RT) · YSO2 · YH2O

{S6}dYH2S

dt= k0,S6 · exp(−ES6 /RT) · YCO · YCOS

{S7} dYCOSdt

= k0,S7 · exp(−ES7 /RT) · YH2S · YCS2

{S8}dYCS2

dt= k0,S8 · exp(−ES8 /RT) · YCS2

cesses in the furnace.

For the drum pressure, the following differential equation wasderived by Aström and Bell (2000):

edp

dt= Q − �fw(hw − hfw) − �steamhc, (24)

where p is the pressure of the drum boiler (kPa), Q is the heat trans-ferred from the gas phase of the furnace to the boiler section (kJ),�steam is the steam mass flow rate (kg/s), hw and hfw are the spe-cific enthalpies of the water in the boiler section and the feedwater(kJ/kg), respectively, while hc represents the condensation enthalpy(kJ/kg). �fw(hw − hfw) represents the increase of the enthalpy ofthe feedwater entering the boiler section. The e term results fromthe relation between the internal energy of the feedwater and theenthalpy of the steam. A good approximation of e (Aström & Bell,2000) is

e ≈ �wVw∂hw

∂p+ mmetalCp,metal

dTsteam

dt, (25)

where Vw represents the total volume of the water in the system(m3), mmetal is the total mass of the metal of the drum boiler and theevaporators section (kg), and Cp,metal is the specific heat capacity ofthe metal of the drum and evaporators (J/kg K), and Tsteam is thesteam temperature (K). Eq. (25) shows that the dynamics of theevaporators-drum system is determined by the energy of the waterand the total mass of the metal in the system.

3.2. Steam product

Since the amount of the steam product is our interest, (24) hasto be connected with a hydrodynamic relationship for the steamflow. The amount of the required steam is determined by the user.To simplify the analysis, the steam turbine can be regarded as a

Parameter values

k0,S1 = 1.4 × 1012 s−1

ES1 /R = ±50 Kk0,S2 = 1.3 × 1012 m3/(kmol s)ES2 /R = 37, 600 Kk0,S3 = 1.3 × 10−1 m3/(kmol s)ES3 /R = 0 K

k0,S4 = 4.0 × 1012 m3/(kmol s) ES5 /R = 66, 530 K

k0,S5 = 6.3 × 1012 m3/(kmol s) ES5 /R = 200 ± 150 K

k0,S6 = 1.3 × 1012 m3/(kmol s) ES6 /R = 37, 600 Kk0,S7 = 1.7 × 1012 m3/(kmol s) ES7 /R = 2050 ± 230 K

k0,S8 = 3.9 × 1011 m3/(kmol s)ES8 /R = 0 K

32 A. Haryanto, K.-S. Hong / Computers and Chemical Engineering 35 (2011) 25–40

Table 4Coal (dried lignite) data used in simulation (Karakas,Koumanakos, et al., 2007).

Components Values

C 36.5 wt%H 2.9 wt%S 0.8 wt%O 17.2 wt%N 1.1 wt%

tiiiMt(

�

wbiss

t

�

w1f

4. Linear analysis of furnace dynamics

Ash 29.5 wt%H2O 12.0 wt%LHV 13,025 kJ/kg

hrottle valve. Inside the valve, the amount of the produced steams dependent on the drum pressure and the extent of superheat-ng. When the steam is saturated, it behaves like water, and whent is superheated extensively, it behaves like an ideal gas (Leva &

affezzoni, 1999). The Instrument Society of America introducedhe following relationship for moderate superheating of steamLeva & Maffezzoni, 1999).

steam = kvalvep(1−ı)�ısteam, (26)

here kvalve is the system dependent constant (valve area, adia-atic index amongst others), �steam is the steam density at the valve

nlet (kg/m3), p is the steam drum pressure (kPa), and ı is a con-tant between 0 and 0.5 (ı = 0 for saturated steam and ı = 0.5 foruperheated steam).

The linearization of (26) around an equilibrium value results inhe following equation:

steam = kvalve(1 − ı)p0−ı�ı

steam(p − p0), (27)

hich is allowed for most practical situations (Leva & Maffezzoni,999). Rearranging (27) and substituting it into (25) results in theollowing first order differential equation for calculating the mass

Fig. 6. Simulink block diagram for sim

Fig. 7. The conversion rates of char and sulphur used in simulation: The curves areobtained by solving (30) and (31) under the steady-state operation assumption.

flow rate of the steam.

e1

kvalve

(p0

�steam

)ı d�steam

dt= Q − �fw(hw − hfw) − �steamhc. (28)

The amount of heat transferred from the gas phase in the com-bustion process to the boiler (Q) can be related to the gas phasetemperature by the convective heat transfer equation as follows:

Q = ��FGCp,FG(Tg − Tsteam), (29)

where � is the efficiency factor regarding the heat losses in theboiler (%).

For dynamical analyses, the equations developed in Sections 2and 3 for the considered oxy-fuel combustion boiler system withflue gas recirculation are re-arranged as follows:

ulating the developed models.

A. Haryanto, K.-S. Hong / Computers and Chemical Engineering 35 (2011) 25–40 33

Table 5Heat and mass balance data used in simulation (Karakas, Koumanakos, et al., 2007).

Plant unit Symbol in Fig. 1(a) p(bar) T (◦C) � (kg/s) h (kJ/kg)

Air A1 1.01 15.0 319.8 15.2Oxygen from ASU A8 1.03 350.0 76.4 337.1Dried coal for combustion F3 1.02 106.0 69.1 174.3Flue gas (FG) G1 1.02 1701.5 390.0 2424.4

1.01.0

232.1227.7

Fd

the real mass and energy balance data of an oxy-fuel combustionprocess. The process flow diagram of the Greenfield plant is shownin Fig. 1(b). The main difference between the conventional andoxy-fuel combustion systems is the existence of some additionaloperation units (i.e., an ASU, a RFG system and some operation units

Recycled flue gas (RFG) G8Un-recycled flue gas G9Feedwater S3Steam from drum S4

Furnace

dmchar

dt= �wt

char�coal,in − �char,react, (1)

dmsulp

dt= �wt

sulp�coal,in − �sulp,react, (2)

(Cp,charmchar + Cp,sulpmsulp)dTs

dt

= (�wtcharCp,char + �wt

sulpCp,sulp)�coal,in(Tcoal − Ts) − �priCp,FG

× (Ts − Tpri)+�char,react�LHV �HLHV + �sulp,react�Hsulp + qrad, (7)

�gVgCp,gdTg

dt= �oxyCp,FG(Toxy − Tg) + �priCp,FG(Ts − Tg)

+ �scnCp,FG(Tscn − Tg) + �char,reactCp,FG(Ts − Tg)

+ � (1 − �LHV )�HLHV − q , (13)

char,react rad

Flue gas

Fi,in = Fi,FG + Fi,gen − Fi,cons + Fi,RFG, (14)

ig. 8. Nyquist plots of the transfer function (32) from �oxy to Tg : Comparison of twoifferent char conversion rates.

3 369.2 265.0 430.13 260.8 132.8 295.2

320.8 257.5 1445.5404.9 257.5 2736.8

Water steam

edp

dt= Q − �fw(hw − hfw) − �steamhc, (24)

e1

kvalve

(p0

�steam

)ı d�steam

dt= Q − �fw(hw − hfw) − �steamhc. (28)

To verify the applicability of the developed models above,the Greenfield (oxy-fuel combustion) pulverized power plant inKarakas, Koumanakos, et al. (2007) is adopted, because it exhibits

Fig. 9. Time responses of Tg when a step change of �oxy occurs at time 5 min.

34 A. Haryanto, K.-S. Hong / Computers and Chemical Engineering 35 (2011) 25–40

F eam td

fca

vabomon

4

v

ig. 10. Fire-side (gas temperature, char mass) and water-side (drum pressure, stecrease) at time 10 min.

or carbon capture and storage). The Greenfield plant uses a typi-al low grade coal (Lignite) as fuel, whose dried lignite ultimatenalysis is provided in Table 4.

The developed models were implemented in Matlab/Simulink,ersion R2008b: Fig. 6 shows the overall scheme of simulation. Theims of this simulation are to investigate an open-loop dynamicehavior of the oxy-fuel combustion system with the change(s)f parameter(s) of the plant (for instance, conversion rate, oxygenass flow rate, coal mass flow rate, etc.) and to develop a control-

riented model for a model-based control (but the control issue isot addressed in this paper yet).

.1. Steady-state characteristics

In this paper, as user-defined optimal conversion rates, 95% con-ersion rate of char and 80% conversion rate of sulphur are chosen

emperature) dynamics when �coal,in changes 10% suddenly (step increase or step

(which is based upon the data from Karakas, Koumanakos, et al.(2007)). The steady-state conditions (material balances) for charand sulphur in the furnace are obtained as follows (by putting theright-hand sides of (1) and (2) equal to zero).

0 =mchar,in − mchar

YO2 achar kd

kd + k0,char exp(−EA,char /RuTg )k0,char exp

(−EA,char /RuTg

)= mchar,in(1 − �char )fchar (Tg )

, (30)

0 = msulp,in − msulpk0,sulp exp(−EA,sulp/RuTg)= msulp,in(1 − �sulp)fsulp(Tg)

, (31)

where �char = 1 − mchar/mchar,in (char conversion rate) and �sulp =

1 − msulp/msulp,in (sulphur conversion rate). Fig. 7 summarizes theconversion rate vs. the gas temperature (by solving (30) and (31))as a chart for simulation. It can be seen that the optimal 95% charconversion rate and 80% sulphur conversion rate are obtainable atabout 1700 ◦C (in relation to the steady-state design of Greenfield

A. Haryanto, K.-S. Hong / Computers and Chemical Engineering 35 (2011) 25–40 35

when

pha

4

cp(

Fig. 11. Fire-side and water-side dynamics

ower plant), and for any other conversion rate that is lower origher than these values, two solutions (temperatures) are avail-ble.

.2. Linearization of the furnace dynamics

Considerable insight into the dynamic behavior of the oxy-fuelombustion system can be gained by exploring the effects of variousarameters on a linearized version of the system equations: (1),2), (7) and (13). Dynamic features such as the speed of response

�pri changes 10% suddenly at time 10 min.

and the (local) stability can be clearly revealed using this linearmodel. The nonlinearities occur in the solid and gas temperatureequations in the furnace and in the exponential temperature termof reactions. Expanding these nonlinear terms in a Taylor seriesand truncating the higher order terms after the first term gives

the state space equation (A9) in Appendix A. The correspondingsteady-state conditions of the Greenfield power plant (for instance,Tg = 1700 ◦C, �oxy = 77.4 kg/s, and see Table 5 for others) are chosenas an operating point in the linearization of the nonlinear equations,(1), (2), (7), and (13).

36 A. Haryanto, K.-S. Hong / Computers and Chemical Engineering 35 (2011) 25–40

F5

(aU

Table 6Flue gas composition data used in simulation (Karakas,Koumanakos, et al., 2007).

Components Values (wt%)

N + Ar 8.29CO2 65.96

mass flow rate of primary air �pri changes 10% suddenly at time10 min. In this simulation, we assume that the throttle valve open-

ig. 12. O2, CO2, NO2, and H2O concentration changes (vs. Tg ) when �RFG increases%.

Now, we want to know the influence of design parameters

for instance, char conversion rate, coal mass flow rate, primaryir mass flow rate, etc.) to the open-loop behavior of the plant.sing (A9), the transfer functions from �oxy to Tg is obtained as

H2O 18.80SO2 0.80O2 1.28Ash 4.87

follows:Tg (s)

�oxy (s)= m3s3 + m2s2 + m1s + m0

s4 + n3s3 + n2s2 + n1s + n0

=

⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩

0.0002146s3 + 4.33e − 8s2 + 0.034s + 0.13s4 + 1.305s3 + 0.0352s2 + 0.002983s + 5.942e − 7

,

for �char = 95%

0.000614s3+1.471e − 7s2+0.00231s+0.025s4+0.004401s3+1.507e − 7s2+4.005e − 9s+0.014

,

for �char = 80%

(32)

where

m3 = b44, m2 = −(a11 + a22 + a33)b44,

m1 = (−a11 − a22 + a11a22)b44, m0 = −a11a22a33b44,n3 = −(a11 + a22 + a33 + a44),

n2 = ((a11 + a22)(a34 + a44) + a33a44 + a11a33 − a24a42),

n1 = (−a33a44(a11 + a22)

− a11a33(a33 + a44) − a24a42(a11 + a33) − a24a32a43),n0 = −a11a24a33a42 − a11a24a32a43 + a11a2

33a44 − a11

and aij are defined in (A9). Fig. 8 depicts the Nyquist plots of thetransfer function from �oxy to Tg for two cases: 95% and 80% charconversion rates. Fig. 8(a) shows a stable Nyquist plot when thechar conversion rate is 95%, whereas Fig. 8(b) depicts an unsta-ble Nyquist plot when the char conversion rate is set to 80%. Fig. 9compares the time responses of the gas temperature Tg when a stepchange of the oxygen mass flow rate �oxy occurred at time 5 min.Fig. 9(a) depicts the case of 10% increase of �oxy, whereas Fig. 9(b)shows the case of 10% decrease. An unstable behavior of 80% charconversion rate is shown in both cases. Now, with the above linearanalyses, the usability of the developed models is clearly demon-strated.

5. Simulations and discussions

5.1. Step responses

The main purpose of this section is to validate the developedmodels in Sections 2 and 3. As starting values (initial conditions),the mass and energy balance data (steady-state conditions) of theselected units from the Greenfield plant given in Table 5 are used.Fig. 10 compares the fire-side dynamics (the gas temperature in thefurnace, the char mass of char) and the water-side dynamics (thedrum pressure, the steam temperature) when the coal mass flowrate �coal,in changes 10% suddenly (step increase or step decrease)at time 10 min. Similarly, Fig. 11 repeats those of Fig. 10 when the

ing of the turbine is constant, and the mass flow rate of feed waterand that of recycled flue gas are assumed constant as well. Theobservation in Figs. 10 and 11 concludes that when the coal feed

A. Haryanto, K.-S. Hong / Computers and Chemical Engineering 35 (2011) 25–40 37

2 con

risWaaptsatrbc

ifi9coF

Fig. 13. The time responses of Tg in the presence of disturbances (O

ate increases suddenly, more heat is produced in the furnace ands absorbed by the waterwall. As a result, the gas pressure in theteam drum and the steam temperature increase correspondingly.

hen the coal feed rate decreases, the pressure in the steam drumnd the steam temperature decrease. Also, the main steam temper-ture and the drum pressure increase when the mass flow rate ofrimary air decreases. This is related to the heat transfer process inhe furnace, as discussed in Kimura et al. (1995), in which it washown that the CO2 recycled stream (CO2 contained in primaryir) absorbs the heat from combustion. When the CO2 volume inhe furnace decreases, the combustion temperature increases as aesult of coal combustion using pure oxygen. More heat is absorbedy the steam, and consequently, the steam temperature increasesorrespondingly.

As discussed in Section 4, the setting of a char conversion rates an important factor in designing a stable furnace. The Green-

eld power plant revealed a (optimal) conversion rate, which is5%. All process variables revealed a stability behavior when thehar conversion rate was 95%. A degradation of furnace stabilityccurred when the char conversion rate was set to below 95%.rom this context, it may be concluded that 95% char conver-

centration, primary air feed, CO2 concentration, and coal quality).

sion rate is set as a control objective in the future control systemdesign.

Fig. 12 shows the flue gas dynamics (O2, CO2, NO2, H2O con-centration changes in comparison with the change of Tg) when themass flow rate of the recycled flue gas increases 5%. Overall, the CO2contained in the recycled flue gas has an important role in reducingthe furnace gas temperature and in monitoring the flue gas concen-tration at the furnace exit. Correspondingly, all the input variablesthat influence the gas temperature will affect the concentrations ofthe flue gases in the furnace exit.

5.2. Disturbances

The developed models in (1), (2), (7), (13), (14), (24), and (28)are deterministic equations that do not take into account of distur-bances (for instance, coal composition, coal humidity, char particle

size, oxygen concentration fluctuation from the ASU, CO2 concen-tration fluctuation in the RFG, etc.). In this subsection, the effectsfrom four disturbances (O2 purity from the ASU, primary air feed,CO2 fluctuation in the flue gas, and coal quality) to the nonlinearmodels are discussed. Fig. 13(a) show the time responses of Tg when

3 nd Ch

OtTutt

cetp

5

pprtKartflToCa

6

bmsofttsec

A

PLt

A

r

g 41 42 43 44 g⎡b11 b12 b13 b14

⎤⎡�coal,in

⎤

8 A. Haryanto, K.-S. Hong / Computers a

2 concentration from the ASU, primary air feed, and CO2 concen-ration in the RFG are disturbed by 15% (decrease) at time 20 min.he high purity of O2 concentration from the ASU and the high vol-metric O2 contained in primary air contribute to the increase ofhe temperature in the furnace. To avoid superheating, it is seenhat the CO2 from the FG should be recycled to the furnace.

Fig. 13(c) shows the time response of Tg upon the variation ofoal quality (coal humidity, coal particle size, calorific value of coal,tc.). The simulation result of ±2.5% coal quality variation revealshat the coal quality has to be controlled to keep the furnace tem-erature.

.3. Further discussion

With the developed models, it is possible not only to study therocess behavior and the emission characteristics of the powerlant but also to design the appropriate control system. The mainesults of the simulations well match with the provided data ofhe Greenfield power plant of (Karakas, Koumanakos, et al., 2007;arakas, Doukelis, et al., 2007). The significant results were partiallyttributed to the dynamics of the gas temperature, steam mass flowate, steam temperature and dynamics of the flue gas emissions athe boiler exit. The CO2 capture efficiency is strongly related to theue gas composition at the boiler exit, which is provided in Table 6.he higher content of condensable CO2 at the boiler exit is evidencef the effectiveness of the CO2 capture technology. The amount ofO2 increased in the flue gas is due to the 95 vol% purity of the O2t the exit of the ASU (Karakas, Koumanakos, et al., 2007).

. Conclusions

This paper developed a novel model for an oxy-fuel combustionoiler system. The mass and energy balance equations were used inodeling the combustion process, flue gas recirculation, and water-

ide dynamics. To simplify the developed nonlinear equations, anperating point (the steady-state operation condition) was chosenrom real data available in the literature and a linearized state equa-ion was developed. The time responses of the developed modelso various inputs and parameter values were also analyzed. Theimulation results of the proposed models are encouraging. The rel-vance to the application of a model-based control to real oxy-fuelombustion boiler systems in the industry was also demonstrated.

cknowledgments

This work was supported by the Regional Research Universitiesrogram (Research Center for Logistics Information Technology,IT) granted by the National Research Foundation of Korea underhe Ministry of Education, Science and Technology, Korea.

ppendix A. Linearization of the furnace dynamics

The nonlinear furnace dynamics of (1), (2), (7), and (13) areewritten as follows:

dmchar

dt= �wt

char�coal,in − f1(mchar, Tg), (A1)

dmsulp

dt= �wt

sulp�coal,in − f2(msulp, Tg), (A2)

dTs

dt= k1�coal,inTcoal,in − k1�coal,inTs − k2�priTs + k2�priTpri

+ k3f1(mchar, Tg) + k4f2(msulp, Tg) + k5(Tg − Ts), (A3)

dTg

dt= k1�oxyToxy − k6�oxyToxy + k7�priTg + k8�scnTscn − k8�scnTg

+ k8f1(mchar, Tg) − k5Ts + k5Tg, (A4)

emical Engineering 35 (2011) 25–40

wheref1(mchar, Tg) = YO2

achar mchar kd

kd+k0,char exp(−EA,char /RuTg ) k0,char

exp(−EA,char/RuTg), f2(msulp, Tg) = k0,S1 · exp(−ES1 /RTg) · msulp,

k1 =�wt

CCp,char+�wt

sulpCp,sulp

(Cp,char mchar+Csulpmsulp) , k2 = Cp,FG(Cp,char mchar+Csulpmsulp) ,

k3 = �LHV �HLHV(Cp,char mchar+Csulpmsulp) , k4 = �Hsulp

(Cp,char mchar+Csulpmsulp) ,

k5 = A˛(Cp,char mchar+Csulpmsulp) , k6 = Cp,FG

�g Vg Cp,g, k7 = (1−�LHV )�HLHV

�g Vg Cp,g, and

k8 = A˛�g Vg Cp,g

.

Using the Taylor series expansion and truncating the higherorder terms, the linearized dynamics of (A1)–(A4) around thesteady-state values (ms

char, ms

sulp, Ts

s , Tsg) are given as follows:

d(mchar − mschar

)

dt= −f1,mchar

(mschar, Ts

g)(mchar − mschar)

− f1,Tg (mschar, Ts

g)(Tg − Tsg)

+ �wtchar(�coal,in − �s

coal,in), (A5)

d(msulp − mssulp

)

dt= −f2,msulp

(mssulp, Ts

g)(msulp − mssulp)

− f2,Tg (mssulp, Ts

g)(Tg − Tsg)

+ �wtsulp(�coal,in − �s

coal,in), (A6)

d(Ts − Tss )

dt= k3 f1,mchar

(mschar, Tg)(mchar − ms

char)

+ k4 f2,msulp(ms

sulp, Tsg)(msulp − ms

sulp)

+ (−k1�scoal,in − k2�s

pri − k5)(Ts − Tss )

+ (k3 f1,Tg

(ms, Ts

)k4 f2,msulp

(ms

sulp, Tsg

)+ k5)

× (Tg − Tsg) + (k1Ts

coal − k1Tss (�coal,in − �s

coal,in)

+ k2Tss (�pri − �s

pri), (A7)

d(

Tg − Tsg

)dt

= k7 f1,mchar

(ms

char, Tg

)(mchar − ms

char

)+(

k6Tss − k5

)(Ts − Ts

s

)+ k6Ts

scn

(�scn − �s

scn

)+(

k6Tsoxy − k6Ts

g

)(�oxy − �s

oxy

)+(−k6�s

oxy−k6�spri+k6�s

scn + k7 f1,Tg

(ms, Ts

g

)+ k5

)×(

Tg − Tsg

)+(

k6Tss − k6�s

pri

)(�pri − �s

pri

), (A8)

where f2,Tg (msulp, Tg) = ∂�sulp,react

∂Tg

∣∣∣(msulp,Tg )=(ms

sulp,Ts

g ),

f2,msulp(msulp, Tg) = ∂�sulp,react

∂msulp

∣∣∣(msulp,Tg)=

(ms

sulp,Ts

g

).

Finally, the state space equation of (A5)–(A8) is obtained as fol-lows:

d

dt

⎡⎢⎣

mchar

msulp

Ts

T

⎤⎥⎦ =

⎡⎢⎣

a11 a12 a13 a14a21 a22 a23 a24a31 a32 a33 a34a a a a

⎤⎥⎦⎡⎢⎣

mchar

msulp

Ts

T

⎤⎥⎦

+ ⎢⎣ b21 b22 b23 b24b31 b32 b33 b34b41 b42 b43 b44

⎥⎦⎢⎣�pri

�scn

�oxy

⎥⎦ (A9)

nd Ch

wa

a

a

−

a

−b

b

A

aAACC

C

dDEF

F

F

Fh

��kkkk

kkLm

mM

M

NppqQRST

T

T

A. Haryanto, K.-S. Hong / Computers a

here a11 = f1,mchar

(ms

char, Ts

g

), a14 = f1,Tg

(ms

char, Ts

g

),

12 = a13 = a21 = a23 = b12 = b13 = b14 = b23 = b33 = a34 =41 = 0, a22 = f2,msulp

(ms

sulp, Ts

g

), a24 = f2,Tg

(ms

sulp, Ts

g

),

31 = k3 f1,mchar

(ms

char, Ts

g

), a32 = k4 f2,msulp

(ms

sulp, Ts

g

), a33 =

k1�scoal,in

(ms

sulp, Ts

g

)− k2�s

pri− k5, a34 = k3 f1,mchar

(ms

char, Ts

g

),

41 = k7 f1,mchar

(ms

char, Ts

g

), a43 =

(k7�s

pri− k5

), a44 =

k6�soxy − k6�s

pri+ k6�s

scn + k7 f1,Tg

(ms

char, Ts

g

)+ k5, b11 = �wt

char,in,

21 = �wtchar,in

, b31 = k1(

Tscoal

− Tss

), b32 = k2Ts

s , b42 = (k6Tss − k5) ,

43 = k6Tsscn, and b44 = k6

(Ts

oxy − Tsg

).

ppendix B. Nomenclature

char interfacial surface area of a char particle (m2/kg)burning area (m2)

T total furnace envelope area (m2)s sink fraction of the total furnace envelope areap,char , Cp,sulp, Cp,g specific heat capacities of the char, sulphur par-

ticles and gas in the furnace (J/kg K), respectivelyp,FG , Cp,metal specific heat capacities of the flue gas and the metal

of the drum and evaporators (J/kg K), respectivelyp diameter of a solid particle (m)

diffusion coefficient of oxygen (K−1)A,char activation energy of char particle (J/kmol)i,in, FO2,in total molar flow rates of the ith species and O2 at the

furnace inlet (kmol/s), respectivelyi,cons, FO2,cons total molar consumption rates of the ith species and

O2 in the furnace (kmol/s), respectivelyi,FG, FO2,FG outgoing molar flow rates of the ith species and O2

from the furnace (kmol/s), respectivelyi,rRFG molar flow rate of ith gas species from the RFG (kmol/s)w, hfw, hc water, feedwater and condensation specific enthalpies

(kJ/kg), respectivelyHLHV lower heating value of fuel (kJ/kg)Hsulp reaction enthalpy of sulphur (kJ/kg)

char,react total reaction rate parameter of char particle (m/s)d diffusion parameter of mass transfer (m/s)f thermal conductivity of gas (W/m K)r,char reaction rate parameter of char particle in kinetic regime

(m/s)0,i pre-exponential factor of i-species reaction (m/s)valve valve constant

characteristics length of heat transfer (m)char, msulp total mass of char and sulphur particles in the furnace

(kg), respectivelymetal total metal mass of the boiler and evaporators (kg)g, MO2 total molar numbers of gas and O2 (kmol), respectivelyvolO2

molar number of O2 near the solid particle (kmol/m3)u Nusselt number

drum pressure (kPa)0 equilibrium drum pressure (kPa)rad radiative heat flux from gas to solid particle (kJ/s)

combustion heat (kJ)u universal gas constant (J/kmol K)h Sherwood number0, Tcoal temperatures of the environment and coal (K), respec-

tivelyg , Ts temperatures of the gas phase and solid particles in the

furnace (K), respectivelypri, Tscn temperatures of the synthetic primary and secondary air

(K), respectively

emical Engineering 35 (2011) 25–40 39

Toxy, Tsteam temperatures of the O2 injection and steam (K), respec-tively

Vg volume of gas (m3)Y molar concentration (kmol/m3)

Greek letters˛ convective heat transfer coefficient (W/m K)ˇg gas absorptivity�LHV energy distribution factorı steam constant (between 0 and 0.5)εg, εchar emissivities of the gas and the char particles in the fur-

nace, respectively� efficiency of the boiler (%)�g, �steam gas and steam densities (kg/m3), respectively�coal,in coal mass inflow rate (kg/s)�oxy oxygen injection mass flow rate (kg/s)�pri, �scn mass flow rates of the primary and secondary synthetic

air (kg/s), respectively�FG , �RFG mass flow rates of the flue gas and recycled flue gas (kg/s),

respectively�char,out , �sulp,out mass flow rate of the unconverted char and gen-

erated sulphur that leave the furnace through ash (kg/s),respectively

�steam steam mass flow rate (kg/s)�fw feed water mass flow rate (kg/s)�char,react , �sulp,react mass reaction rates of the char and sulphur

particles of coal (kg/s), respectively�wt

char, �wt

sulpmass fractions of char and sulphur in coal (wt%),

respectively�wt

icomposition of the i-species (wt%)

char, g residence times of the char particle and gas in the fur-nace (s), respectively

� fluid viscosity at bulk fluid temperature (kg/(s m))�s fluid viscosity at heat transfer boundary surface temper-

ature (kg/(s m))

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