Mathematical Modeling of a Single-Stage, Downward-Firing,Entrained-Flow GasierJob S. Kasule,, Richard Turton,*,, Debangsu Bhattacharyya,, and Stephen E. Zitney

National Energy Technology Laboratory, U.S. Department of Energy, Morgantown, West Virginia 26507, United StatesDepartment of Chemical Engineering, West Virginia University, Morgantown, West Virginia 26506, United States

ABSTRACT: Gasiers are the centerpieces of coal-red integrated gasication combined cycle (IGCC) plants. Mathematicalmodels of gasiers have been developed in recent literature to describe the physical and chemical processes taking place insidethe reactor vessels. These models range from simple one-dimensional (1D) steady-state equilibrium models to higher-order,sophisticated, dynamic 2D and 3D computational uid dynamics (CFD) models that describe coupled gassolid hydrodynamics,heat and mass transfer, and reaction kinetics over the complex gasier geometry. In the current work, a 1D steady-state model ofa single-stage, downward-ring, oxygen-blown, slurry-fed, entrained-ow gasier has been developed for use in the context ofIGCC process simulation. In this mathematical model, mass, momentum, and energy balance equations for solid and gas phasesare considered. The model includes a number of heterogeneous and homogeneous chemical reactions along with devolatilizationand drying of the slurry feed. The solidgas heterogeneous reaction rates are calculated using the unreacted shrinking-coremodel. A detailed model of the radiative heat transfer has been developed considering interactions between the solids and allinternal gasier surfaces (side wall, top, and bottom surfaces), as well as interactions between the surfaces themselves. No a prioriwall temperature prole is assumed in this model. The heat loss from the gasier wall to the environment is also considered inthe energy balance equations. In slurry-fed gasiers, recirculation near the inlet of the gasier is promoted by rapid mixing of theslurry feed with a portion of the hot reaction products. This violent mixing results in a signicant rise in temperature that helps inevaporating the water and devolatilizing the coal. The recirculation is achieved by appropriately designing the feed burner andfeeding the oxygen through a swirling annular injector. In the current gasier model, a heuristic recirculation model has beendeveloped and the conservation equations have been appropriately modied. The equations describing the gasier are formulatedas a set of ordinary dierential equations (ODEs) in Aspen Custom Modeler (ACM). The ODEs are discretized using nitedierences, and the resulting highly nonlinear system of algebraic equations is solved using a Newton-type method. The gasiermodel is then validated using pilot plant and industrial data. This paper presents a number of parametric studies that have beenperformed using the 1D steady-state gasier model to provide insight into the gasier performance as the inlet and operatingconditions change. Results are presented as proles for species concentration and gas, solid, and wall temperatures. The eect ofcoal feed types on composition are also presented. In addition, a radiant syngas cooler (RSC) model has been developed inAspen Plus and coupled with the gasier model, thereby enabling the RSC exit stream composition to be compared to availableindustrial data.

1. INTRODUCTIONThe integrated gasication combined cycle (IGCC) process is apromising option for power generation because of its highereciency and environmental advantages over conventional coalutilization technologies.14 The gasier plays a key role in theIGCC process by converting solid carbonaceous fuels, such ascoal, petcoke, or biomass, into synthesis gas or syngas (amixture of mainly CO and H2). The hot raw syngas is cooled ina water quench or radiant syngas cooler (RSC) to recover heatfor producing steam in a steam turbine. The synthesis gas isthen cleaned and subsequently combusted in a gas turbine(GT) to generate electricity. It is critical that optimal operationof the gasier is understood for ecient operation of the IGCCplant. The extremely intense conditions and low residence timeinside the gasier cause rapid heating and reaction rates, givingrise to multiple time scales for the physical and chemicalprocesses. Numerical simulations can help in gaining insightand developing a deeper understanding of the optimaloperation of the gasiers.

Several mathematical models of entrained-ow gasiers havebeen developed, ranging from simple one-dimensional(1D)510 and equilibrium11 models to sophisticated dynamic3D computational uid dynamics (CFD) models1216 thatdescribe coupled gassolid hydrodynamics, heat and masstransfer, and reaction kinetics over the gasier geometry. Thehigher-order models generally include additional details such asturbulence but are too computationally expensive to be useddirectly in operability and controllability studies. Thus lower-dimensional models are required for these applications.Varying degrees of simplications have been made while

developing steady-state 1D gasier models. Some haveconsidered only mass and energy balances while neglectingmomentum balances.510,17 Most of these models have alsoassumed an arbitrary wall temperature prole.6,7 The

Received: September 16, 2011Revised: April 2, 2012Accepted: April 11, 2012Published: April 11, 2012

Article

pubs.acs.org/IECR

2012 American Chemical Society 6429 dx.doi.org/10.1021/ie202121h | Ind. Eng. Chem. Res. 2012, 51, 64296440

assumption of plug ow within the gasier with no mixing andrecirculation has been made in almost all the models exceptthose by Ubhayakar et al.5 and Monaghan et al.18 Most of thesestudies assume that the feed enters the gasier at temperaturesgreater than 550 K so that all the slurry makeup water hasalready evaporated and enters the gasier as steam. Therefore,the devolatilization is assumed to be instantaneous. However, inreality, the slurry feed has to travel a nite length inside thegasier before attaining the high temperature needed to initiatethe volatilization. In this length, mixing and recirculation play akey role. This length depends upon the feed inlet conditionsand can aect the overall residence time of the reactants insidethe gasier. Therefore, neglecting this phenomenon is notappropriate in models intended for studying the eect ofdisturbances in feed inlet conditions and for analyzing dynamicsand control.The major objective of the current study is the development

of a detailed model of a downward, entrained-ow, slurry-fed,oxygen-blown (GEE-Texaco type) gasier that will beeventually used for dynamic studies. The model includesdetailed energy balance equations for the reacting phases andthe gasier wall. Energy loss to the environment is alsoconsidered. No assumptions about the wall temperature proleare made. A heuristic mixing and recirculation model, simplerthan that of Smith and Smoot17 and similar to that ofMonaghan et al.,18 is included in the gasier model to capturethe initial energy transfer that promotes a stable ame zonewithin the initial section of the gasier. This gasier model isdeveloped with the aim of incorporating it into an existingplant-wide simulation of an IGCC plant.4

2. GASIFIER MODEL DESCRIPTION

The following assumptions are made in the gasier modeldevelopment:

The radial dispersions of mass, momentum, and energyare neglected.

The entrained-ow system is assumed to be very dilute inthe solid phase such that the interparticle interactionsmay be neglected. The ash layer formed due to thereaction of the coal particle is assumed to remain on theparticle surface, and consequently a shrinking-core modelis assumed.

The ideal gas law is assumed to hold for the gas phase. The temperature inside the solid particle is assumed to

be uniform. The ash is assumed to be inert, but its eect as a catalyst

has been considered in the relevant kinetic equations.

While carrying out the energy balances, potential andkinetic energies of the system are considered to benegligible in comparison to the thermal energy due tothe high temperature in the gasier.

No particle attrition is considered in the model.In the two-phase model, conservation equations for mass,

momentum, and energy for each phase are developed andsolved in conjunction with the required constitutive closureequations.These balance equations are written for a control volume

(CV) in the gasier as shown in Figure 1. A heuristicrecirculation model is incorporated in the gasier model duringthe initial processes of evaporation and devolatilization. Thisinvolves recirculation of a predetermined fraction () of the gasfrom the higher temperature combustion zone to the colderregion (mixing zone) just after the gasier entrance. Thefraction () is the ratio of the recirculated gas to the inlet gasstream ow rates. The eect of the recirculation is accountedfor on the mass and energy balances in the gas phase, while itseect on the momentum balance is neglected. Details of themodel equations for the recirculation zone are given in theAppendix.2.1. Continuity Equations. The continuity equations for

the solid and gas phases respectively, are obtained as

=

U

x

d( (1 ) )

d(1 )s s s g (1)

= +

U

xm m

d( )

d(1 )

g gs g rg mg (2)

where s and g are the densities of the solid and gas phases,respectively, is the void fraction in the gasier, and sg is thenet rate of consumption of the solid phase (coal) by theheterogeneous reactions. The last two terms on the right-handside of eq 2 account for the mass recirculated from the hottercombustion region to the colder inlet region as illustrated in theAppendix. The term mrg represents the mass that enters a CV,while the term mmg represents the mass that leaves a CV.Species conservation equations are written as

= +x

U y R m y md

d( )i i i ig g g g rg g mg g (3)

=x

Ux Rd

d((1 ) )j js s s s (4)

where eqs 3 and 4 are the species balances in the gas and solidphases, respectively, and gi is dened in the Appendix.

Figure 1. Schematic of a control volume (CV) in the gasier.

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The gas phase can be modeled as a compressible gas obeyingan ideal gas law such that its density is calculated from thefollowing equation:

= =RT

Py

1( /MW)

i

N

i ig

g

g 1 (5)

where yi and MWi are the mass fraction and molar weight of theith gaseous species, respectively, and N is the total number ofgaseous species.2.2. Chemical Reactions. The coal slurry mainly under-

goes two broad reaction stages: the initial stage reactions(processes) that occur when the fresh coal feed is rst heatedand the subsequent combustion and gasication reactions.In some studies,6,7,19 the reactor is divided into several

reaction zones, such as drying, devolatilization, combustion, andgasication zones, in which various sets of reactions areconsidered. No such restriction is made in the current model,thus eliminating the need to determine the interface betweenthese zones that would otherwise result in a multipointboundary value problem.20 Various reactions are considered totake place simultaneously within the gasier with their ratesdetermined solely by the conditions at each point in thereactor.

2.2.1. Initial Stage Processes. The initial stage reactions/processes occurring when coal is heated are complex in natureand lead to a wide variety of products whose compositiondepends not only on the type of coal but also on the processingconditions. The three initial stage reactions are postulated asdrying/water evaporation, devolatilization, and heterogeneouschargas reactions.

moisture steam (6)2.2.2. Drying/Water Evaporation. The moisture entering

the gasier is assumed to be the combination of the makeupwater in the coal slurry feed and the original moisture in thecoal, as specied in the proximate analysis of the coal. Thewater evaporation model adopted in this study assumes that thetwo types of water exist as a single water phase and a singleevaporation rate is used. The evaporation rate is based on thework of Rao et al.21

2.2.3. Devolatilization. During devolatilization, the dry coalis thermally decomposed to release the volatile matter (VM),leaving behind a high carbon residue generically known as char.This process is shown below:

+ + ++ + + ++

VM tar CO CO CH

H H O H S NH

higher hydrocarbons

d dCO

dCO

2 dCH

4

dH

2 dH O

2 dH S

2 dNH

3

2 4

2 2 2 3

(7)

where VM is obtained from the proximate analysis of the coal.The tar produced during the devolatilization reaction under-goes further cracking reactions:

+ + + ++ + ++

tar FC CO CO CH H

H O H S NH

higher hydrocarbons

c cCO

cCO

2 cCH

4 cH

2

cH O

2 cH S

2 cNH

3

2 4 2

2 2 3

(8)

where FC is the xed carbon.Various devolatilization models, with varying degrees of

complexity, exist in the literature.2224 In the current study, thedevolatilization model used is taken from the MGAS model of

Syamlal and Bisset.25 This simple phenomenological modelpredicts the yields of tar and some major gas components whilepreserving a strict elemental balance. This model is based ondata such as proximate and ultimate assays, tar composition,etc., obtained from certain lab-scale experiments that character-ize the coal. A number of assumptions are made in the model todetermine the stoichiometric coecients of the devolatilizationand cracking reactions. For example, all the sulfur in the coal isconverted to H2S while all the nitrogen is converted to NH3.The kinetic parameters of the above reactions/processes aregiven by Syamlal and Bisset.25

2.2.4. Heterogeneous CharGas Reactions. After coaldevolatilization, the residual char, represented as carbon (C),can undergo any of the following heterogeneous reactions: charcombustion, charsteam gasication, charcarbon dioxide, andcharhydrogen. These reactions are shown in Table 1.

In the char combustion reaction, is a mechanism factorthat gives the ratio of CO2 to CO in the reaction products. Thisfactor varies signicantly with the temperature of the reaction.26

For the high temperature environment prevailing in slagginggasiers, carbon monoxide is favored at higher temperatureswhile carbon dioxide is favored at lower temperatures.27

It has been generally accepted that, in the high temperatureenvironment within the entrained gasier (T > 1000 C), theheterogeneous, chargas reactions can be considered as surfacereactions. Due to the dilute nature of the entrained gasier,particleparticle collisions are less frequent and the ash layerformed may be assumed to remain on the reacting particle.Thus, it is reasonable to apply the shrinking-core model28

(SCM) to estimate the chargas reaction rates. In thisformulation, it is also assumed that the temperature is uniformthroughout the particle. According to the SCM model, theoverall reaction rate can then be written as

=+ +

*( )

P Prate1

1( )

k k Y k Y

i i1 1 1 1

diff ash s2 (9)

where Y = rc/Ro; rc is the radius of the unreacted core; Ro is theoriginal radius of the particle; and kdi, kash, and ks are the gaslm diusion coecient, ash diusion coecient, and thesurface reaction constants, respectively.6 The ash diusionconstant is obtained using the correlation given by Syamlal andBisset.25

=k k ( )ash diff ash2.5 (10)where ash is the voidage of the ash layer, Pi Pi* is theeective partial pressure of the ith component (O2, H2, H2O, orCO2) in the gas participating in the gasication reactions andtakes into account the reverse reaction eect, Pi is the partial

Table 1. Solid Phase Reactions

reaction stoichiometry reference

charcombustion

+ +

C

1O 2

2CO

21 CO2 2

Wen andChaung6

steamgasication

+ +C H O CO H2 2 Wen andChaung6CO2gasication

+ C CO 2CO2 Wen andChaung6H2gasication

+ C 2H CH2 4 Wen andChaung6

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pressure of component i, and Pi* is the equilibrium pressure6 of

reactant i.2.2.5. Homogeneous GasGas Reactions. A number of

homogeneous reactions are possible in the gasier, but thisstudy is limited to the reactions shown in Table 2.

The kinetic parameters for the above reactions were obtainedfrom the references in Table 2. The kinetics for the water gasshift reaction (WGS) were modeled as a combination of thecatalytic rate of Wen and Onozaki31 and a noncatalytic rate.The latter is a slightly modied form suggested by Karan et al.32

2.3. Momentum Balance. The momentum balanceequations for gassolid systems have been developedpreviously3537 and have been modied in the current workusing some simplications such as neglecting the shear stressand particleparticle interaction forces, to give the followingbalance equations:

= +

U

xPx

g fd( )

ddd

(1 )g g

2t

g s (11)

= +

+

U

xPx

g

f

d((1 ) )

d(1 )

dd

(1 )

(1 )

s s2

ts

s (12)

where fs is the drag force per unit volume of particles, Us and Ugare the solid- and gas-phase velocities, and Pt is the totalpressure in the system, taken to be the same as the gas-phasepressure.The drag force per unit volume, fs, is given by the correlation

of Arastroopour and Gidaspow38 as

=

| |f

C U U U U

d

3 (1 ) ( )

4sD g

2.65g s g s

p (13)

where the drag coecient, CD, is given by Rowe andHenwood39 as

=+