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Development and testing of an interconnected multiphase CFD-modelfor chemical looping combustionH. Kruggel-Emden a,b, n , S. Rickelt c , F. Stepanek a , A. Munjiza ba Department of Chemical Engineering, South Kensington Campus, Imperial College London, SW7 2AZ London, UK b Department of Engineering, Queen Mary, University of London, Mile End Road, E1 4NS London, UK c Department of Mechanical Engineering, Ruhr-University Bochum, Universitaetsstrasse 150, 44801 Bochum, Germany

a r t i c l e i n f o

Article history:Received 27 February 2010Received in revised form11 May 2010Accepted 14 May 2010Available online 24 May 2010

Keywords:Chemical looping combustionInterconnected modelDynamic simulationMultiphase owMultiphase reactionsFluidization

a b s t r a c t

An interconnected multi-phase CFD model is developed capable of describing the transient behavior of a coupled chemical looping combustion systems comprising of both air and fuel reactors. The air reactoris modeled as a high velocity riser, the fuel reactor as a bubbling uidized bed. The models of bothreactors are implemented as separate CFD simulations allowing for an exchange of solid mass throughtime-dependent inlet and outlet boundary conditions as well as mass, momentum, heat and speciessinks. The developed framework is applied to a chemical looping combustion system based on Mn 3 O4 ascarrier material in combination with CH 4 as fuel gas. Starting from a base case, different systemcongurations are investigated. The results indicate clearly that interconnected multi-phase CFDmodels are well suited for the design process of coupled chemical looping systems.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Many scientic studies come to the conclusion that a promptreduction of greenhouse gas emissions is important to limit theeffects of global warming ( IPCC Fourth Assessment Report, 2007 ).Different greenhouse gases can be identied whereas carbondioxide emissions from power generation and other industrialprocesses represent the most dominant sources.

Due to the fact that a change in energy production towardsfully carbon neutral sources is not likely in the near future,combustion of fossil fuels in combination with carbon capture andsequestration appears as a suitable interim solution ( Herzog et al.,2000; Lyngfelt and Lecker, 1999 ). Among possible technologieslike pre-combustion, oxy-fuel combustion or post-combustion,chemical looping combustion is a method which has a goodpotential to become an important capture technology. It has a lowenergy penalty due to the fact that the carbon dioxide from thecombustion process is inherently not diluted with nitrogen whichwould otherwise require energy intensive processing ( Rao andRubin, 2002; Naqvi et al., 2007 ).

The process of chemical looping combustionmay be utilizedwitheither solid or gaseous fuels involving static ( Noorman et al., 2007;

Noorman et al., 2009 ), moving ( Gnanapragasam et al., 2009; Fanet al., 2008 ) or uidized beds ( Lyngfelt et al., 2001; Son and Kim,2006 ) in which the oxygen necessary for the combustion is providedby a solid carrier. A basic outline of the process is shown in Fig. 1.

Two steps are required: an initial oxidation and a subsequentreduction step of the oxygen carrier. Currently implementedsystems are mostly based on the uidized bed technology due tothe fact that solid fuels are addressable, a good mixing of gas andsolid carrier is provided and the circulation and replacement of the carrier material become easy. The process is usually realizedthrough the combination of a bubbling uidized bed operated asthe fuel reactor in combination with a high velocity riser operated

as air reactor as originally proposed by Lyngfelt et al. (2001) .Intensive research has been performed over the past decade

involving chemical looping combustion ( Hossaina and de Lasa,2008 ), but it is still away from being a commercially availabletechnology. In the current state of development, laboratory scalesystems can be operated with different types of fuel up to140 kWth ( Abad et al., 2006; De Diego et al., 2007; Berquerandand Lyngfelt, 2008; Berguerand and Lyngfelt, 2008; Adanez et al.,2009; Kolbitsch et al., 2009 ) with the aim to realize systems of upto 1 MWth ( Epple and Stroehle, 2008 ) in the near future. In thiscontext robust and reliable simulation methods will becomeimportant for the detailed design and scale up.

Simulations of chemical looping combustion can be performedon different levels of accuracy with differing methodologies and

varying related computational costs ( Mahecha-Botero et al., 2009 ).

ARTICLE IN PRESS

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/ces

Chemical Engineering Science

0009-2509/$- see front matter & 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2010.05.022

n Corresponding author at: Department of Chemical Engineering, SouthKensington Campus, Imperial College London, SW7 2AZ London, UK

E-mail address: [email protected] (H. Kruggel-Emden).

Chemical Engineering Science 65 (2010) 47324745


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Author's personal copyARTICLE IN PRESS

The simulation approaches can be categorized as particle basedmethods, macroscopic balance models and multi-phase uiddynamics models. Particle based methods offer a high level of

detail but are computationally very demanding and limited in thenumber of particles they can address ( Zhu et al., 2007 ). In casethat realistic particle sizes are used ( De Diego et al., 2007 ) thesystem size that can be simulated is also restricted. On currentlyavailable computer systems a modeling of real size vessels evenon laboratory scale becomes impracticable. In contrast to the highlevel of detail resolvable through particle based methods,macroscopic balance models ( Noorman et al., 2007; Xu et al.,2007; Bolhar-Nordenkampf et al., 2009; Kolbitsch et al., 2009;Abad et al., 2010 ) allow for a coarse modeling at low computa-tional cost. However, the formation of internal structureswithin the domain like bubbles or the development of gradientswithin different regions of the model can often not be resolvedsatisfactorily.

Multi-phase uid dynamics modeling forms a suitable com-promise between coarse and detailed modeling possible throughthe previously discussed approaches with respect to bothcomputational cost and level of detail. Within multi-phase uiddynamics modeling the particles and uid phase are modeled inthe framework of the NavierStokes equations using averagedquantities. Closure equations for the solid phase pressure and thesolid phase viscosity have to be provided derived from the kinetictheory of granular ow ( Ding and Gidaspow, 1990 ). The kinetictheory of granular ow is an extension of the classical kinetic gastheory ( Patil et al., 2004; Patil et al., 2004 ). Although these modelshave been frequently used for bubbling uidized beds ( Enwaldand Almstedt, 1999 ), mixing ( Cooper and Coronella, 2005 ),downow reactors ( Vaishali et al., 2008 ) and spouted beds(Gryczka et al., 2009 ), Jung and Gamwo (2008) were the rst toapply multi-phase CFD modeling for chemical looping combus-tion processes followed by ( Deng et al., 2008; Deng et al., 2009 )and Jin et al. (2009) . They restricted their considerations to thefuel reactor operated as a bubbling bed in batch mode(Fig. 1grey line). This perspective leaves the air reactor andthe complex interaction between both vessels unconsidered.

In this study a coupled model of both air and fuel reactors isdeveloped using a multi-phase uid dynamics framework(Fig. 1black line). Methane is used as gaseous fuel and Mn 3 O4supported on MgZrO 2 (Zafar et al., 2007 ) is applied as oxygencarrier.

2. Multiphase uid dynamics modeling framework

The interconnected multi-phase framework was implementedas a two-phase Euler-model into the commercial computational

uid dynamics software FLUENT 12.1.4. Balance equations aresolved for each individual phase regarding the exchange of momentum, heat and mass transfer. The solid phase is modeledthrough the kinetic theory of granular ow. Air and fuel reactorare modeled in separate uid dynamics simulations allowing foran exchange of solid ow through time-dependent boundary

conditions and sinks. The chosen approach is computationallymuch less demanding than a full three dimensional transientmodel as suggested e.g. in the case of circulating uidized beds(Zhang et al., 2008 ). The lower computing time allows using theinterconnected framework for sensitivity studies for which manysimulation runs have to be performed. The effect of a cyclone andsiphons as necessary for a real chemical looping process is notrepresented in the interconnected framework proposed here. Allgoverning equations are given in the following subsections.Details on the interconnected model and the model setup arediscussed in the section thereafter.

2.1. Continuity and momentum equations

In the Eulerian two-phase model the volume fractions for bothgas e g and solid phase es sum up to one. The continuity equationsfor gas and solid phase are

@e g r g @t r U e g r g u! g S gs , 1

@esr s@t r U esr s u! sS sg , 2

with S gs S sg is the mass transfer between both phases due toheterogeneous reactions, u! the velocity and r the density. Themomentum equations for the gas phase and the solid phase canbe obtained as

@e g r g u! g @t r

U

e g r g u! g u! g

e g

r p

r U t g

e g r g g !

bu! g u! sS gs u! g , 3

@esr s u! s@t r U esr s u! s u! s esr pr U t s r P s e g r g g !

bu! g u! sS sg u! s , 4with the inter-phase momentum transfer coefcient b , gravity g ! ,the gas pressure p, the solid pressure P s and the stressstraintensor t i calculated for both gas and solid phase as

t i eimir u! i r u! i T eil i 2=3mir U u! i I , 5with the viscosity mi, the bulk viscosity l i which is assumed zerofor the gas phase and I the unit tensor.

2.2. Energy equations

The conservation of energy of the gas and solid phase isgoverned through the equations

@e g r g h g @t r U e g r g u! g h g r U l g r T g Q gs S g , 6

@esr shs@t r U esr s u! sh sr U l sr T sQ sg S s , 7

with h being the enthalpy, l the thermal conductivity, Q gs Q sg the inter-phase heat transfer and S g , S s the heat released due to

chemical reactions. The inter-phase heat transfer can be calcu-lated based on

Q sg a sg T s T g 8

Fig. 1. Outline of an interconnected uidized bed chemical looping combustionsystem.

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where asg is the heat transfer coefcient derivable from theNusselt-number which can be obtained from empirical correla-tions e.g. Gunn ( Gunn, 1978 )

a sg 6k g e g esNu s

d p2 , 9

Nus 7 10 e g 5e2 g 1 0:7Re0:2 p Pr

1=31 :33 2 :4e g 1 :2e2 g Re0:7 p Pr

1=3,

10with Pr the Prandtl-number, Re p the particle Reynolds-numberand d p the particle diameter.

2.3. Species transport equations

The conservation of species j is realized through the followingequation within an arbitrary phase i:

@eir iY i, j@t r U eir i u! i Y i, j r U ei J ! i , jRhe 11

where Y i,j is the mass fraction of species j in phase i, J ! i, j thediffusive mass ux and Rhe the heterogeneous reaction rate.

2.4. Inter-phase momentum transfer coefcient

The inter-phase momentum transfer coefcient b, can bederived from different empirical approaches. A widely used modelwas suggested by Gidaspow (1994) which is a combination of theequations of Wen and Yu (1966) and Ergun (1952) reading

b 34

C de g 1 e g

d pr g 9u! g u! s9e g 2 :65 for e g 4 0:8 , 12

C d 24Re p

1 0:15 Re p0:687h i, Re p r 1000

0:44 Re p 4 1000,8>

:13

b 150m g 1 e g

2

e g d p2 1 :75 1 e g

r g d p

9u! g u! s9 for e g r 0:8 : 14

2.5. Kinetic theory of granular ow

In order to solve the NavierStokes equations for the solidphase, equations for the granular pressure P s, the granular shearviscosity ms and the bulk viscosity l s have to be provided whichare linked to the rheology of the particle phase. Information onthe rheology of the particle phase can be derived by the theoryof kinetic granular ow. Thereby the particle phase velocities can

be separated into a local mean velocity u! s and a uctuatingvelocity u! 0s .u! s u! s u! 0s : 15

Through introduction of the granular temperature Y s 1=3u! 0s u! 0s a balance equation for the uctuation energy within theparticle phase can be derived ( Ding and Gidaspow, 1990 )

32

@esr sY s@t r U esr s u! sY s P sI t s

: r u! s r U kY sr Y s gY s f Y s : 16 Within this equation gY s is the dissipation of the uctuation

energy due to particle collisions given by Lun et al. (1984) as

gY s 12 1 e2e2s r s ffiffiffiffiffiffiffiffiffiY3

sp d2 ps , 17 where e is the coefcient of restitution.

The exchange of uctuation energy due to particle uidinteraction f Y s dened in Eq. (16) is given following an approachby Ding and Gidaspow (1990) with

f Y s 3bY s : 18The diffusion of uctuation energy kY s can be calculated

according to Lun et al. (1984) withkY s kdenseY s kthinY s , 19

kdenseY s 15 r sdses ffiffiffiffiffiffiffiffiffiffiY spp 441 33 Z 1

125 Z4Z 3

1615 p 41 33 Z Zes g 0 ,

20

kthinY s 25 r sds ffiffiffiffiffiffiffiffiffiffiY spp 16 g 0 Z41 33 Z 1

125 Z

24Z 3es g 0 , 21where

Z0:51 e: 22The solid pressure P s can be dened according to Lun et al.

(1984) as

P s 1 21 ees g 0 esr sY s: 23Most of the above equations rely on the radial distribution

function which is a measure of how close the particle distributionis to uniform. A suitable model was proposed by Ding andGidaspow (1990)

g 0 3=5 1 eses , max

1=3" #1

: 24The bulk viscosity l i for the solid phase can be calculated

according to Lun et al. (1984) from the kinetic theory of granularow as

l s 43 esr sd p g 01 e ffiffiffiffiffiffiY spr : 25The solids shear stress tensor is arising due to contributions from

particle collisions, particle motion ( Gidaspow et al., 1992 ) and due tofrictional effects ( Schaeffer, 1987 ). All contributions are added up as

ms ms , col ms , kin ms , fr 26with its single components being

ms , col 4=5esr s g 0 d p1 e ffiffiffiffiffiffiY spr , 27ms , kin

10 dsr s ffiffiffiffiffiffiffiffiffiffiY spp 96 es1

e

g 0 1 5=4es g 01 e

2, 28

ms , fr P s sin x2 ffiffiffiffiffiffiffiI 2Dp

, 29where x is the angle of internal friction and I 2 D the second invariantof the deviatoric stress tensor.

2.6. Modeling of the reaction kinetics

The oxygen carrier used in the investigation here is Mn 3 O4supported on MgZrO 2 (Zafar et al., 2007 ). Manganese has theadvantage to provide a medium oxygen carrier capacity combinedwith quick kinetics when used with methane as fuel gas ( Hossainaand de Lasa, 2008 ). It is chosen because it is expected to revealinsights into the dynamics of the interconnected uidized bedsystem on small time scales ( Kruggel-Emden et al., submitted forpublication ). Reduction and oxidation of the carrier are described by

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outlined in Section 3.1 followed by a detailed description of theconsidered base case and base case variations.

3.1. Model setup

The combined model setup is spatially 2D. A schematicdrawing of it is shown in Fig. 3. The fuel reactor is designed as abubbling bed uidized from the bottom through a velocity inletand equipped with a weir. At the lower sidewall an inow for thesolid phase is realized through a velocity inlet boundarycondition. The solid phase can exit the vessel at the left of thefuel reactor through a cell row in which mass, momentum, heatand species sinks are applied. Through the weir a constant llinglevel is enforced in the fuel reactor. The gas phase leaves the fuelreactor through the top, implemented as a pressure outlet. The airreactor is modeled as a high velocity riser. Solid and gas phaseenter the vessel at the bottom through a combined velocity inlet.At the top of the air reactor both phases leave the vessel through apressure outlet.

In order to ensure a sufcient lling level in the bubbling bed abuffer is introduced into the coupled system. Two differentdesigns are considered. The buffer can be placed upstream(Fig. 3a) or downstream ( Fig. 3b) from the bubbling bed. Thebuffer is not implemented as an entity in the CFD-frameworkthough, its purpose is to even out possible uctuations in the

solids owrate. A solid phase stream _m s , feed is fed into the buffer incase that the inow _m s , ox in Fig. 3a or _m s , red in Fig. 3b from theupstream situated vessel drops below the target solid phasecirculation rate _m s , buf between both vessels. The solid feed _m s , feedis compensating for any lacking ow. In case that _m s , ox or _m s , red isexceeding the desired inter-vessel solid circulation rate, mass is

stored in the buffer and discharged at a later point in time. Thebuffer is assumed as an ideal mixer. The degree of conversion X within the buffer and therewith in the leaving solid stream _m s , buf is calculated from the degrees of conversion X of the inlet streams_m s , feed and _m s , ox , _m s , red . All vessels are assumed to be adiabatic.

3.2. Base case model parameters

Within the CFD-software FLUENT version 12.1.4 the set of partial differential equations outlined in Section 2 is solvedthrough the nite volume method. The pressurevelocity cou-pling for both uid and solid phase is achieved through a phasecoupled SIMPLE algorithm. The second-order QUICK-scheme isemployed. A time step of Dt

0.0002 s is used for the temporal

discretization. A convergence criterion of 10 3 is chosen for allquantities. In each time step 20 iterations are performed.The bubbling bed fuel reactor is discretized through 2500quadrilateral cells and the air reactor designed as a riser through1500 quadrilateral cells. Grid renement was tested and has only

Table 1Kinetic parameters of the applied oxygen carrier material Mn 3 O4 supported on MgZrO 2 with a diameter distribution of d p

n

125180 mm ( Zafar et al., 2007 ).Spherical shrinking core model Reduction Oxidation

Apparent reaction order ( n) 0.9344 0.58052Reaction preexponential factor ( k) 1935.8 m 3 n 2 mol 1 n s 1 0.17291 m 3 n 2 mol 1 n s 1

Reaction activation energy ( E ) 124.88 kJ/mol 27.156 kJ/molLinear shrinking core model Reduction Oxidation

Apparent reaction order ( n) 0.85264 0.54212Reaction preexponential factor ( k) 873.95 m 3 mol n s 1 0.10526 m 3 mol n s 1

Reaction activation energy ( E ) 111.7 kJ/mol 17.184 kJ/molStoichiometric coefcient ( b) 4 6

Fig. 3. Outline of the combined modeling framework consisting of a bubbling uidized bed used as fuel reactor and an air reactor implemented as a riser. Outlines (a) and(b) vary in the position where the buffer is placed.



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minor effect on the ow behavior. Mass ow rates, temperaturesand compositions of both solid and gas phases are only minimallyaffected. The k e model is used for both uid and solid phasewith a standard wall function to model for turbulence. The massexchange between the vessels as well as the reaction model isachieved within FLUENT through user-dened functions. Mass,

temperature and composition of the solid phase are exchanged

between the vessels after each time step. An overview over thegeneral simulation parameters and the specications of the basecase is provided in Table 2 .

The base case is designed as outlined in Fig. 3a with the bufferplaced upstream from the bubbling bed. The inlet gas velocity forthe bubbling bed is following a ramp function reaching its

maximal velocity after 7 s. The mass inlet at maximal velocitycorresponds to 0.5 MW th . The solid circulation rate and the vesseldimensions were chosen to match design recommendations givenby Zafar et al. (2007) .

3.3. Base case variations

The base case conguration of the chemical looping system asoutlined in the previous section will be systematically modied.An overview of the applied changes can be found in Table 3 .Modications imply a change of the buffer position within thesystem. A partially oxidized feed stream is injected into the bufferand initially available in the fuel reactor. A different kinetic modelin the form of the linear shrinking core approach is used in bothair and fuel reactors. The circulating solid mass ow is varied from3.0 up to 5.0 kg/s. The riser length is altered from 4 m in the basecase to 5 m and later 6 m.

4. Computational results and discussion

In the following, results for the base case are discussed in detail.Results from the case alterations are discussed briey focusing ondifferences in the results with respect to the base case.

4.1. Results for the base case

The base case is simulated for a duration of t 62 s. A widevariety of properties is transiently available from the simulations.Contours plots of the instantaneous solid fraction, the solidtemperature, the state of oxidation and the mass fraction of CH 4and O 2 within the bubbling bed and riser domain are shown inFig. 4 at t 30.01 s. At the beginning of the simulation thebubbling bed is partially pre-loaded with solids and the system isslowly lled to the operating level through the buffer which isplaced upstream from the bubbling bed. After a while ( t 5 s)with increasing gas ow, bubbles form within the bottom regionof the fuel reactor. A uctuating mass ow is released from thebubbling bed due to the weir. This uctuating mass ow isdirectly entering the riser and moving through it in dilute plugs.These variations in the solid fraction can be identied in the riserat e.g. 2 m height in Fig. 4a for t

30.01 s. Through the uidization

of both vessels with cold gas at 300 K a temperature distributiondevelops which is not resolved in detail through the applied grid(Fig. 4b). The endothermic reaction in the bubbling bedadditionally consumes heat. In the riser the solid phase heats updue to the exothermic reaction as can be seen in Fig. 4b. Thedegree of reduction of the solid in the bubbling bed is lower at thebottom where regenerated solid phase is entered from the side. Inthe riser the degree of reduction decreases along the length of thevessel due to the exothermic reaction of the carrier with oxygen(Fig. 4c). The selected bed height in the fuel reactor is sufcient toensure a nearly complete reaction of the methane with theoxygen carrier. In the riser the contour plot of the mass fraction of O2 indicates temporal uctuations. Only at positions whereenough solid material is available, the oxygen concentrationdecreases signicantly ( Fig. 4d).

The mass ow from and to the buffer which is placed upstreamfrom the bubbling bed is outlined in Fig. 5. The mass ow _m s , ox

Table 2System properties and parameters for the simulations.

General parameters

Time step Dt (s) 0.0002Mean particle diameter d p (mm) 0.1525Angle of internal friction x (1 ) 30Maximal packing limit es , max ( ) 0.6Restitution coefcient e ( ) 0.9Kinetic model Spherical shrinking core

Buffer specicationsInitial mass (kg) 0Initial state of reduction X ox ( ) 0Initial temperature (K) 1223Mass ow _m s , buf (kg/s) 3.5275Feed temperature (K) 1223Feed state of oxidation X ox ( ) 0

Fuel reactor specicationsWidth of vessel (m) 0.25Height of vessel (m) 0.8Weir height (m) 0.4Initial bed height (m) 0.1475Initial solids packing ( ) 0.42Initial temperature (K) 1223Initial state of reduction X ox ( ) 0Grid number ( ) 2500Inlet gas temperature (K) 300Inlet gas velocity (m/s) Min(0.061; t 0.0102 1/ s+0.01)Inlet gas composition (kg/kg) CH 4 : 1

Air reactor specicationsWidth of vessel (m) 0.15Height of vessel (m) 4.0Grid number ( ) 1500Inlet gas temperature (K) 300Inlet gas velocity (m/s) 1.45Inlet gas composition (kg/kg) N 2 : 0.77; O 2 : 0.23

Table 3Applied base case alterations.

Variant Specications

1 Buffer is placed upstream from the air reactor2 Buffer is placed upstream from the air reactor Initial buffer feed state of reduction X ox 0.6 Initial fuel reactor state of reduction X ox 0.4

3 Specications as in variant 2 Linear shrinking core model applied4 Specications as in variant 2 Mass ow _m s , buf 3.0 kg/s5 Specications as in variant 2 Mass ow _m s , buf 4.0 kg/s6 Specications as in variant 2 Mass ow _m s , buf 4.5 kg/s7 Specications as in variant 2 Mass ow _m s , buf 5.0 kg/s8

Specications as in variant 2

Height of air reactor h 5 m9 Specications as in variant 2 Height of air reactor h 6 m



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from the riser is subject to strong variations due to the weir inthe bubbling bed. Temporarily the mass ow reaches values of up to 35 kg/s. The outlet stream from the buffer is xed at3.5275 kg/s. Up to t 7 s the mass ow from the buffer iscompletely sustained through the feed stream _m s , feed . Up to 15 sinto the simulation it is constantly necessary to add mass throughthe feed stream _m s , feed into the system to reach the desiredcirculation rate. At later points in time it is only occasionally

necessary to compensate for any deciencies in the mass owfrom the riser.

The evolution of the solid temperature over time of theinow and outow from the buffer and of the solid inside thebuffer itself is shown in Fig. 5b. Up to 7 s into the simulationthe solid from the buffer is fully originating from the feedstream _m s , feed being at 1223 K. Later the regenerated solidcarrier temperature is varying strongly being usually lower than

Fig. 4. (a) Contour plots of the solid fraction, (b) the solid temperature, (c) the degree of reduction and (d) the mass fraction of CH 4 in the fuel reactor and of O 2 in the airreactor for the chemical looping base case conguration at t 30.01 s.



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the temperature of the feed stream. Temperature minima inthe solid ow from the riser are balanced out through the solidmass which is stored in the buffer. With less feed stream neededat later points in time the solid temperature in the buffer agreeswell with the outlet stream leaving the buffer. From t 40 sonwards the degree of reduction increases sufciently positivelyaffecting the reactivity in the air reactor which results in atemperature increase of the solid stream released.

The degree of reduction within the inow and outow of thebuffer is plotted in Fig. 5c. In all ows the degree of reduction iscontinuously increasing. The rise in its conguration as used inthe base case does not provide for sufcient regeneration of thecarrier material. Peaks in the degree of reduction of the outletstream from the buffer result from the addition of fully oxidizedcarrier through the feed stream.

The degree of reduction and the temperature of the solidinow and outow from the air and the fuel reactor as well as thegas outow temperature of both air and fuel reactors are given in

Fig. 6. The degree of reduction of the solid entering and leavingthe air reactor is constantly inclining. The ability of the airreactor to regenerate the solid phase is evidently too small(Fig. 6a). The difference in the degree of reduction between theinow and outow of the air reactor is increasing. This is due tothe growing ability of the air reactor to regenerate the solid

oxygen carrier at larger degrees of reduction. The degree of reduction of the air reactor inow is subject to nearly nouctuations; the degree of reduction at the outow, however, isvery intermittent which is a result of the varying solid mass in theriser. The temperatures of the solid phase at the inow of the airreactor decline smoothly down to 1100 K at t 40 s. Later in thesimulation it increases again, due to the growing heat generationin the air reactor resulting out of the larger degree of reduction.The outow temperature of the solid reveals strong uctuations(Fig. 6b). In the beginning of the simulation, the temperatures arelower than the initial solid temperature of 1223 K; further intothe simulation temperatures reach peak values larger than1300 K. The gas outow temperature in the air reactor is equalto the solid outow temperature. The peaks in the evolution of the

degree of reduction and in the temperature entering the fuelreactor as displayed in Fig. 6c and d are a result of freshly addedsolid to the buffer which is at T 1223 K and X ox 0. The evolutionof the temperature and the evolution of the degree of reductionin the solid stream from the fuel reactor are smoother than thoseof the stream entering the fuel reactor from the buffer as plottedin Fig. 6c and d.

The evolution of the mass fraction of O 2 at the outow incontrast to that at the inow gives insight into the operation of the air reactor ( Fig. 7a). In the beginning of the simulation themass fraction of O 2 decreases only marginally. Later in thesimulation the decrease is more pronounced, which indicates astronger regeneration of the oxygen carrier passing through theair reactor. The evolution of the mass fraction of O 2 is very

unsmooth. The mass fraction of CH 4 at the gas outlet of the fuelreactor increases over time with decreasing reactivity of the oxygen carrier material in the bubbling bed. This is due tothe increasing degree of reduction in the system and droppingsolid temperatures. However, peak values remain below 3%. Themass distribution in the different vessels including air and fuelreactor as well as the virtual buffer over time is outlined in Fig. 7b.The mass in the fuel reactor is linearly inclining in the rst 7 sof the simulation. At this point in time the rst solid reachesthe air reactor. The mass in the buffer and the air reactor areboth uctuating strongly not reaching values larger than 10 kg.The mass in the bubbling bed reaches a saturation level of around 60 kg.

4.2. Results for the base case variations

In the following the base case alterations are discussed.Simulations are performed for a duration of at least t 50 s.

Case 1: Buffer placed upstream from the air reactor In order to prevent the strong variations in mass ow passing

through the air reactor which also result in uctuating solid andgas temperatures at the outow of the air reactor the buffer isplaced upstream from the air reactor in the alteration 1. Thisconguration leads to a constant mass ow entering the airreactor. The mass ow leaving the air reactor is subject to minoructuations as indicated in Fig. 8a. The overall variations as wellas the peak values in the mass ow rate from the fuel reactordecrease in contrast to the base case. The overall solidtemperature in the system is constantly decreasing over time.Especially in the beginning of the simulation up to 30 s thisdecrease is most signicant. Solid temperature drops below

Fig. 5. (a) Mass ow into and out of the buffer, (b) temperature and (c) degree of reduction of the different solid ows from and into the buffer and of the bufferitself for the base case.



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1000 K after 60 s of simulation time. This strong decrease intemperature is a result of the feed entered fully oxidized directlythrough the buffer into the air reactor. In contrast to the base caseno carrier material is reacting with oxygen in the early state of thesimulation within the air reactor because the carrier is fullyregenerated. With no reaction heat released, temperatures droprapidly. Solid temperatures at the outlet of the air reactor are evensmaller than the temperature of the solid from the bubbling bed

entering the air reactor as outlined in Fig. 8b. In contrast to thebase case the temperature evolution is much smoother. Peaksare occasionally originating from fresh feed material entering thebuffer. The degree of reduction of the solid streams both upstreamand downstream of the air reactor is continuously increasing.Similar to the development of the temperatures, the evolution of the degrees of reduction is smoother. With increasing simulationtime and increasing overall degree of reduction the slope of the

Fig. 6. (a) Degree of reduction and (b) solid temperature of the inow and outow from the air reactor as well as the gas outow temperature in the air reactor. (c) Degreeof reduction and (d) solid temperature of the inow and outow from the fuel reactor as well as the gas outow temperature from the fuel reactor. Results are obtained forthe base case.

Fig. 7. (a) Mass fraction of CH 4 and O 2 in the gas phase at the inow and outow of the air and fuel reactor and (b) mass in the buffer, air and fuel reactor for the base caseconguration.



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degree of reduction of the solid leaving the air reactor becomesatter than the slope of the degree of reduction of the solidleaving the fuel reactor. This indicates an increasing regenerationof the carrier material in the air reactor despite decliningtemperatures which is only stimulated by the increasing overalldegree of reduction ( Fig. 8c).

The mass fractions of CH 4 and O 2 at the inow and outow of the air and fuel reactor are plotted in Fig. 9a. Up to 10 s into thesimulation the oxygen mass fraction does not decline whichindicates that no reaction takes place in the air reactor. Furtherinto the simulation the consumption of oxygen increasescontinuously. The evolution of the mass fraction of CH 4 at theoutlet is zero up to 10 s into the simulation. Later it inclinescontinuously up to values of 16% at t 60 s ( Fig. 9b). Thecomparatively large loss in CH 4 results from the lowtemperatures in the fuel reactor which slows down the reactionof methane with the oxygen carrier signicantly. A larger bedmass would be needed at these temperatures. The evolution of the mass in the air and fuel reactor and the riser are outlined inFig. 9b. The solid mass in the riser reaches a constant level after it

is fully charged. Very well visible is the order in which air and fuelreactor are lled. The overall mass in the chemical looping systemis larger when the buffer is placed upstream from the air reactoras done here compared to the base case conguration. The buffermass uctuations are smaller than encountered for the base case.

Case 2 : Usage of partly reduced carrier materialThe modication in Case 1 where the buffer is placed upstream

from the air reactor can be identied as more feasible than thebase case setup due to the more constant properties in the airreactor. However it must be tried to compensate for the decline intemperature in the system. Therefore in a new simulation casepartly reduced material is placed in the fuel reactor with X OX 0.4and the feed stream enters the buffer with X OX 0.6. Mass owrates and masses in the different vessels of the system are not

affected by this variation and therefore not addressed in thefollowing.The development of the temperatures over time is outlined in

Fig. 10a. In the beginning of the simulation the solid leaving theair reactor which is initially partly reduced with X OX 0.6 atthe inlet reaches temperatures of up to T 1280 K. After a certaintime the system is lled and the solid material from the bubblingbed is recirculated into the air reactor. This material is lessreduced ( Fig. 6b). Therefore temperatures of the solid leaving theair reactor drop after some time. With increasing simulation timethe overall level of reduction increases. This automatically

Fig. 8. (a) Mass ow, (b) temperatures and (c) degree of reduction of the differentsolid ows and the mass in the buffer of the variant 1 where the buffer is placedupstream from the fuel reactor.

Fig. 9. (a) Mass fraction of CH 4 and O 2 in the gas phase at the inow and outow of the air and fuel reactor and (b) mass of the solid in the buffer, air and fuel reactor for thevariant 1 where the buffer is placed upstream from the fuel reactor.



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triggers increasing temperatures of the solid in the system. Thetemperatures in the air reactor increase faster than thetemperatures in the fuel reactor. Peaks in the temperature ordegree of reduction prole for the solid stream leaving the bufferare originating from solid feed occasionally entered into thesystem. Sometimes temperature peaks in the solid stream leavingthe fuel reactor can be detected which originate from larger massreleases over the spill way. The mass fraction of O 2 at the outletplotted in Fig. 10c indicates that with increasing temperature andreduction more oxygen is consumed. At t 60 s half of the oxygenprovided through the inlet air is consumed. Due to the largetemperature of the solid only minor fractions of methane arereleased uncombusted from the fuel reactor despite the largelevel of reduction in the system.

Case 3: Linear shrinking core model appliedIn order to investigate the effect of different kinetic models in

interconnected chemical looping systems, Case 2 studied in theprevious section relying on a spherical shrinking core model (32)

for the reaction kinetics is modeled through a linear shrinkingcore model (33). Kinetic parameters are used according to Table 1 .Results on the solid temperatures are shown in Fig. 11 a. Thegeneral temperature level within the system is declining.Temperatures of the solid leaving the air reactor are atT 1190 K at t 55 s and solid leaving the fuel reactor is atT 1150 K. This temperature trend is completely opposite to thatencountered for the case where the spherical shrinking coremodel was applied. The evolution of the degree of reduction overtime is plotted in Fig. 11 b. Larger overall levels of reduction areobtained in the system compared to Case 2 for the sphericalshrinking core model. In contrast to the previous investigation theevolution of the degree of reduction of the solid leaving andentering the air reactor is not developing apart. This is a directresult of the linear shrinking core model that is insensitive to theoverall degree of reduction. In Fig. 11c results for the massfraction of O 2 and CH 4 are shown. The consumption of O 2 isconstant and not affected signicantly by the decrease in

Fig. 10. (a) Temperatures, (b) degree of reduction of the solid and (c) mass fractionof CH4 and O 2 in the gas phase at the inow and outow of the air and fuel reactorfor variant 2 where the initial oxygen carrier is partly oxidized.

Fig. 11. (a) Temperature and (b) degree of reduction of the solid and (c) massfraction of CH 4 and O 2 in the gas phase at the inow and outow of the air and fuelreactor for case 3 where a linear shrinking core model is applied for the reactionkinetics.



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temperature in the system. Over time signicant amounts of CH 4are released. At t 55 s nearly 10% of CH 4 is leaving the fuelreactor unreacted. The results above clearly indicate that the useof a different reaction kinetic model can have signicant effects onthe simulation outcome, especially if the degree of reduction inthe chemical looping system is varying over time. An accurate

representation of the real reaction kinetics in a model is thereforeessential.

Cases 47: Modication of the solid circulation rateBased on the simulation Case 2 a variation of the solid

circulation rate is performed. The solid ow is considered withdm /dt {3, 4, 4.5, 5} kg/s. Investigated are the temperatures anddegrees of reduction of the solid ow entering and leaving the airreactor.

The temperature of the solid entering and leaving the airreactor is plotted in Fig. 12a. For a circulation rate of 3 kg/s thetemperature of the solid ow entering the air reactor is decreasingalthough the temperature of the ow leaving the air reactor isincreasing. With increasing mass ow the temperatures of bothsolid entering and leaving the air reactor are increasing. The

temperature difference at t 45 s for 3 kg/s and 5 kg/s solidcirculation rate is 200 K. Increased circulation rates also affect theoverall degree of reduction in the system. With an increased solidcirculation rate the increase in the degree of reduction for theconsidered system can be softened ( Fig. 12 b).

Cases 89: Altered air reactor lengthThe effect of an altered air reactor length is shown in Fig. 13. An

increased length of the air reactor leads to larger solid outlettemperatures at the top of the reactor. The overall temperaturelevel in the chemical looping system also increases. The relativetemperature gain resulting from an elongation of the air reactor from

4 to 5 m is larger than that for an elongation from 5 to 6 m. The levelof oxygen towards the top of the air reactor is decreasing. In a leaneroxygen atmosphere the reactivity gain becomes smaller. Therefore anextension of the vessel length as a constructive measure is limited inits effect when also not adjusting the inlet air ow. For the degree of conversion in the system, an increased reactor length dampens theoverall increase of the degree of reduction over time ( Fig. 13b).

5. Conclusions

An interconnected CFD-framework for chemical loopingcombustion was developed. The chemical looping system con-sidered consists of an air reactor operated as a high velocity riser

and a fuel reactor operated as a bubbling bed. Mass, temperatureand composition of the solid phase circulated between bothvessels is exchanged through time-dependent boundary condi-tions and mass, momentum, species and heat sinks placed in thebubbling bed equipped with a weir.

Fig. 12. (a) Temperature and (b) degree of reduction of the solid stream leaving and entering the air reactor. Solid ow is considered with dm /dt {3, 4, 4.5, 5} kg/s for theconguration of case 2.

Fig. 13. (a) Temperature and (b) degree of reduction of the solid stream leaving and entering the air reactor. The air reactor length is changed to 5 m and 6 m for theconguration of case 2.



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The developed framework is tested for chemical loopingoperated with methane as fuel gas and Mn 3 O4 as oxygen carrier.Simulations of up to 60 s were performed addressing the start-upperiod of the system. In theory simulations of up to severalminutes can be performed with reasonable effort on moderncomputer systems taking advantage of e.g. parallel computing.

Starting from a base case different system variations wereconsidered including alterations of the position of the buffer,the initial degree of reduction of the solid, the kinetic model, thesolid circulation rate and the air reactor length.

A wide variety of properties related to chemical loopingcombustion can be resolved transiently in the performed inter-connected CFD-simulations. Among them are volume fractions,masses and mass ow, velocities, temperatures and speciesdistributions of gas and solid phase just to mention a few. Acoupled CFD-framework accounts transiently for the intercon-nected nature of air and fuel reactor in chemical loopingcombustion. The interdependence of both reactors cannot beaddressed through CFD-batch simulations of individual vessels asperformed so far in literature. Furthermore, a coupled CFD-

framework resolves more details than macroscopic modeling(Mahecha-Botero et al., 2009 ) and therefore qualies to be used asa potent design tool for chemical looping systems. In contrast tofully three dimensional full-loop modeling in case of circulatinguidized beds ( Zhang et al., 2008 ) the proposed interconnectedframework offers much faster computation and qualies espe-cially for sensitivity studies in which many simulation runs haveto be performed. A disadvantage however is that siphons andcyclones which are of importance in the chemical looping processare not modeled. They could either be realized as entities in theCFD-framework or as virtual equipment similar to the bufferalready in use.

The different cases investigated in the study here ratherrepresent design examples than operational chemical looping

setups. They are not capable of regenerating sufcient oxygencarrier and do not release enough heat through the gas leaving theair reactor for a stable operation of the system. In an operationalsetup the air reactor needs to be broadened, extended in lengthand eventually equipped with additional cooling. A comparison of simulation results with experimental investigations is desirablefor the future. The use of a two buffer system is advisable toreduce mass ow uctuations. For a better comparison of thedifferent cases longer simulations have to be performed to reach asteady state in the systems. This and the elaboration of thestability of operation points, the test of appropriate controlstrategies and the analysis of the part-load behavior of chemicallooping systems are of interest for future investigations utilizingthe coupled CFD-framework developed here.

Acknowledgements

The authors gratefully acknowledge the nancial support bythe Humboldt Foundation. The opportunity to use additionalcomputing facilities at the Department of Energy Plant Technol-ogy, Ruhr-University Bochum is appreciated.

References

Abad, A., Ada nez, J., Garca-Labiano, F., de Diego, L.F., Gaya n, P., 2010. Modeling of the chemical-looping combustion of methane using a Cu-based oxygen-carrier. Combustion and Flame 157 (3), 602615.

Abad, A., Mattisson, T., Lyngfelt, A., Ryden, M., 2006. Chemical-looping combustionin a 300 W continuously operating reactor system using a manganese-based

oxygen carrier. Fuel 85 (9), 11741185.Adanez, J., Dueso, C., de Diego, L.F., Garcia-Labiano, F., Gayan, P., Abad, A., 2009.

Methane combustion in a 500 Wth chemical-looping combustion system usingan impregnated Ni-based oxygen carrier. Energy and Fuels 23 (1), 130142.

Berguerand, N., Lyngfelt, A., 2008. Design and operation of a 10 kW(th) chemical-looping combustor for solid fuels. Testing with South African Coal Fuel 87 (12),27132726.

Berquerand, N., Lyngfelt, A., 2008. The use of petroleum coke as fuel in a 10 kW(th)chemical-looping combustor. International Journal of Greenhouse Gas Control2 (2), 169179.

Bolhar-Nordenkampf, J., Proll, T., Kolbitsch, P., Hofbauer, H., 2009. Comprehensivemodeling tool for chemical looping based processes. Chemical Engineering andTechnology 32 (3), 410417.

Cooper, S., Coronella, C.J., 2005. CFD Simulation of particle mixing in a binaryuidized bed. Powder Technology 151, 2736.

De Diego, L.F., Garcia-Labiano, F., Gayan, P., Celaya, J., Palacios, J.M., Adanez, J.,2007. Operation of a 10 kWth chemical-looping combustor during 200 h witha CuOAl 2 O3 oxygen carrier. Fuel 86 (78), 10361045.

Deng, Z.Y., Xiao, R., Jin, B.S., Song, Q.L., 2009. Numerical simulation of chemicallooping combustion process with CaSO 4 oxygen carrier. International Journalof Greenhouse Gas Control 3 (4), 368375.

Deng, Z.Y., Xiao, R., Jin, B.S., Song, Q.L., Huang, H., 2008. Multiphase CFD modelingfor a chemical looping combustion process (fuel reactor). Chemical Engineer-ing and Technology 31 (12), 17541766.

Ding, J., Gidaspow, D., 1990. A bubbling uidization model using kinetic theory of granular ow. AIChE Journal 32 (1), 523538.

Enwald, H., Almstedt, A.E., 1999. Fluid dynamics of a pressurized uidized bed:comparison between numerical solutions from two-uid models and experi-mental results. Chemical Engineering Science 54, 329342.

Epple, B., Stroehle, J., 2008. CO 2 capture based on carbonate and chemical looping.

VGB Powertech 11, 8588.Ergun, S., 1952. Flow through packed columns. Chemical Engineering Progress 48(2), 89.

Fan, L., Li, F., Ramkumar, S., 2008. Utilization of chemical looping strategy in coalgasication processes. Particuology 6, 131142.

Gidaspow, D., 1994. Multiphase Flow and Fluidization. AcademicPress, SanDiego.Gidaspow D., Bezburuah R., Ding J., 1992. Hydrodynamics of circulating uidized

beds, kinetic theory approach. In: Proceedings of the Seventh EngineeringFoundation Conference on Fluidization, Fluidization, vol. 7, pp. 7582.

Gnanapragasam, N.V., Reddy, B.V., Rosen, M.A., 2009. Hydrogen production fromcoal using coal direct chemical looping and syngas chemical loopingcombustion systems: assessment of system operation and resource require-ments. International Journal of Hydrogen Energy 34, 26062615.

Gryczka, O., Heinrich, S., Deen, N.G., Annaland, M.V., Kuipers, J.A.M., Jacob, M., Moerl,L., 2009. Characterization and CFD-modeling of the hydrodynamicsof a prismaticspouted bed apparatus. Chemical Engineering Science 64, 33523375.

Gunn, D.J., 1978. Transfer of heat or mass to particles in xed and uidised beds.International Journal of Heat and Mass Transfer 21, 467476.

Herzog, H., Eliasson, B., Kaarstad, O., 2000. Capturing greenhouse gases. ScienticAmerican 282 (2), 7279.

Hossaina, M.M., de Lasa, H.I., 2008. Chemical-looping combustion (CLC) for inherentCO2 separations a review. Chemical Engineering Science 63 (18), 44334451.

IPCC Fourth Assessment Report, 2007. Paris, France. Jin, B.S., Xiao, R., Deng, Z.Y., Song, Q.L., 2009. Computational uid dynamics

modeling of chemical looping combustion process with calciumsulphate oxygen carrier. International Journal of Chemical Reactor Engineering7 Art no. A19.

Jung, J.W., Gamwo, I.K., 2008. Multiphase CFD-based models for chemical loopingcombustion process: fuel reactor modeling. Powder Technology 183 (3),401409.

Kolbitsch, P., Bolhar-Nordenkampf, J., Proll, T., Hofbauer, H., 2009. Comparison of two Ni-based oxygen carriers for chemical looping combustion of natural gasin 140 kW continuous looping operation. Industrial and Engineering Chem-istry Research 48 (11), 55425547.

Kolbitsch, P., Proll, T., Hofbauer, H., 2009. Modeling of a 120 kW chemical loopingcombustion reactor system using a Ni-based oxygen carrier. ChemicalEngineering Science 64 (1), 99108.

Kruggel-Emden, H., Stepanek, F., Munjiza, A., A comparative study of reactionmodels for chemical looping combustion. Computers and Chemical Engineer-ing, submitted for publication.

Kruggel-Emden, H., Stepanek, F., Munjiza, A., A study of the role of reaction modelingin multi-phase CFD-based simulations of chemical looping combustion. Inter-national Journal of Greenhouse Gas Control, submitted for publication.

Lun, C.K.K., Savage, S.B., Jeffrey, D.J., Chepurniy, N., 1984. Kinetic theories forgranular ow inelastic particles in Couette-ow and slightly inelasticparticles in a general oweld. Journal of Fluid Mechanics 140, 223256.

Lyngfelt A., Lecker B., Technologies for CO 2 separation, Proceedings of theMinisymposium on CO 2 Capture and Storage, G oteborg, Sweden (1999).

Lyngfelt, A., Leckner, B., Mattisson, T., 2001. A uidized-bed combustion processwith inherent CO 2 separation; application of chemical-looping combustion.Chemical Engineering Science 56 (10), 31013113.

Mahecha-Botero, A., Grace, J.R., Elnashaie, S.S.E.H., Lim, C.J., 2009. Advances inmodeling of uidized-bed catalytic reactors: a comprehensive review.Chemical Engineering Communications 196 (11), 13751405.

Naqvi, R., Wolf, J., Bolland, O., 2007. Part-load analysis of a chemical-looping combustion (CLC) combined cycle with CO 2 capture. Energy 32,

360370.Noorman, S., Annaland, M.V., Kuipers, H., 2007. Packed bed reactor technology for

chemical-looping combustion. Industrial and Engineering Chemistry Research46 (12), 42124220.



14/14


Noorman,S., Annaland, M.V., Kuipers,J.A.M., 2009. Experimental validation of packedbed chemical-looping combustion. Chemical Engineering Science in press.

Patil, D.J., Annaland, M.V., Kuipers, J.A.M., 2004. Critical comparison of hydro-dynamic models for gassolid uidized beds part II: freely bubbling gassolid uidized beds. Chemical Engineering Science 60 (1), 7384.

Patil, D.J., Annaland, M.V., Kuipers, J.A.M., 2004. Critical comparison of hydro-dynamic models for gassolid uidized beds part I: bubbling gassoliduidized beds operated with a jet. Chemical Engineering Science 60 (1), 5772.

Rao, A.B., Rubin, E.S., 2002. A technical economic and environmental assessment of amine-based CO 2 capture technology for power plant greenhouse gas control.Environmental Science and Technology 36, 44674475.

Schaeffer, R.W., 1987. Instability in the evolution equations describing incom-pressible granular ow. Journal of Differential Equations 66, 1950.

Son, S.R., Kim, S.D., 2006. Chemical-looping combustion with NiO and Fe 2 O3 in athermobalance and circulating uidized bed reactor with double loops.Industrial Engineering and Chemical Research 45 (8), 26892696.

Vaishali, S., Roy, S., Mills, P.L., 2008. Hydrodynamic simulation of gassolidsdownow reactors. Chemical Engineering Science 63, 51075119.

Wen, C.Y., Yu, Y.H., 1966. Mechanics of uidization. Chemical Engineering ProgressSymposium Series 62, 100111.

Xu, M., Ellis, N., Ryu, H.J., Lim, C.J., 2007. Modeling of an interconnected uidizedbed reactor for chemical looping combustion, in: Proceedings of the 12thInternational Conference on Fluidization, Vancouver, Canada.

Zafar, Q., Abad, A., Mattisson, T., Gevert, B., Strand, M., 2007. Reduction andoxidation kinetics of Mn 3 O4 /MgZrO 2 oxygen carrier particles for chemical-looping combustion. Chemical Engineering Science 62, 65566567.

Zhang, N., Lu, B., Wang, W., Li, J., 2008. Virtual experimentation through 3D full-loop simulation of a circulating uidized bed, Particuology. Simulation andModeling of Particulate Systems, 529539, doi:10.1016/j.partic.2008.07.013.

Zhu, H.P., Zhou, Z.Y., Yang, R.Y., Yu, A.B., 2007. Discrete particle simulation of particulate systems: theoretical developments. Chemical Engineering Science62 (13), 33783396.


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