For Presentation at 7th Fluidization Conference CONF-920502--I

f

May 3,, 1992 DE92 002879

HYDRODYNAMICS OF CIRCULATING FLUIDIZED BEDS"KINETIC THEORY APPROACH

byi[ Dimitri Gidaspow, Rukmini Bezburuah and J. Ding

Department of Chemical Engineeringj IU;nois Institute of Technology, Chicago, IL 60616

ABSTRACT

Rigorous methods of kinetic theory were used to derive particldar phaseviscosities and granular conductivities. This new kinetic theory predictedflow behavior and oscillations in _, complete loop of a CFB. The results werecompared to computations with in-posed gas phase turbulence in the riser.The computations were repeated for production of synthesis gas from char.

The hydrodynamics of solids processing plants, slmh as circldating fluidizedbed combustors that are being b,lilt to burn high sulfilr coals is not wellunderstood. As an aid for better design for such systems, a particulate mul-tiphase Navier-Stokes' equation solver w.-_sdeveloped. Partic, tlate viscositiesand solids pressures can be comp,lted by a subroutine that solves a fllmtu-ating kinetic energy equation for the particles.

Kinetic Theory Model=

Savage (1) and Jenkins and Savage (2) have shown how to obtain constitu-tive equations and conservation laws for granular flow. Ding and Gidaspow(3) extended their approach to gas-particle flow. Since Ding and Gidmspowused a Maxwelfian distribution their approach was restricted to dense flow.Recently Gidaspow extended this approach to cover dilute and dense particle-fluid flow. The mathematics is very similar to that described in detail in theclassical text on kinetic theory by Chapman and Cowling (4). A summaryof the techniq, ms and the results is pre_nted below.

Starting with the Boltzmann integral-differential equation for the freq_mncy| "__.. of particle velocity distrib,ttions, f, the dense phase transport theorem shown- _,... below was obtained by the authors cited above.

0 0,/,•,J 0--7 < ¢ >) + < > =< "f' 37v,.> (1)%.

where F, is the body and the drag force acting on the system, n = f f(tc::_ and < _/, >= l f Cfd£lrl

t

i _ lt frf ,c_ P¢ -- --_go,e,)d_ (¢, - ¢,)/, f2fc(£,2, fc)dkde, dg.2 (2)

-lgo(,,)d_ (¢, - ¢,)f,f2Vln(-f_)g(e,2.

i i Dimitri Gidaspow _ *_ _ _ _'

DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED

q

and

- / / f + ¢' - - - ¢' ' (3)

The particle conservation of mass and momentum eq, lations are obtained bysetting 7_= rn and _ me.-',respectively as done by Ding and Glda. pow andprevious authors. The new part of tlm theory was to note that for the first.perturbation upon the Maxwellian distribution the collision integral givenby Equation (2) consists of two integrals which became ms shown below.

Pc = Pcl + Pc't (4)

2(1+ < > +c- 5 g_pp_, I) (5)O.9

Pc2 = 2e.,t£,cV i)' + e,_,V • +7I (6)

o,where _' is the rate of shear tensor, [SI and p,c is the coefficient of viscos-ity, simply called viscosity by Ding and Gida.spow (3). For a Maxwelliandistribution the first integral does not contribute to the viscosity since thenon-diagonal terms of < CC > vanish. The expressions for the viscosityand the granular conductivity given here have been generalized to the firstperturbation for the frequency distribution. They are thus valid for dihlteand dense flow. Equation (T1.5C) gives this shear viscosity. The standarddilute phase viscosity is given by Equation (T1.5d). Note that the kinematicviscosity is simply a product of the mean free path times a random velocity.

A conservation equation for this random veiocity can be obtained by sub-stituting ¢ = 1_mc into Equation (1). The result is the fluctuating energyequation for the granular temperature 0 given by Equation (T1.6). The con-ductivity given by Equation (T1.6c) was obtained from Eq, mtion (2) andthe collisional dissipation "7 due to the non- elasticity of the particles wasobtained from Equation (3). The restitution coefficient "e" is the normalrestitution coefficient. There also exists a tangential restitution coefficientassociated with particle rotation that was not considered in the theory de-veloped so far.

CFB LOOP

The equations shown in Table 1 were solved for the loop shown in Fig 1. Fig2 shows that 8 sec. after start-up, there is the expected dense flow in thedowncomer, strong downflow at one wall of the riser, a reasonable vahie ofthe solids granular temperature and viscosity. Such reasonable viscosities andparticle oscillations were achieved by adjusting the value of the restitutioncoefficient until the viscosity matched Miller's (5) measurements, _.s shown inFigure 2. Miller has also observed the fluctuations of the particle velocities,as computed in Fig. 4. The discharge velocity from the standpipe to the riseris shown in Fig. 5. The 1 m/see velocity is of the order of discharge velocityfrom hoppers. The new kinetic theory model computations do not differgreatly from Ding's (6) earlier computations using the turbulent viscosityshown in Table 1 and dense kinetic theory (e.g. Fig. 5). Time averaged

Jl 2 Dimitri _,Idaspow

values of the mass fluxes, solids concentrations and velocities are given inFigs. 6 to 9. At 2 m/see there is a strong asymmetry caltsed by the inletgeometry. As expected, the bed is denser near the inlet. A color video showsthe turbulent structure of the particles as a function of time.

COAL REACTIONS

Ding's (6) turbulence model and dense kinetic theory were llsed to simulatethe reactions of char particles for the conditions given in Fig. 1. Char wasassumed to consist of 88% carbon. The CFB was initially filled with the N2a.t 1300°K. At the riser bottom a mixt_ire of 40% 0= and 60% H20 enteredat 700°K, at a pressure of 3.71 atm. Table 2 summarizes the energy and thespecies equations while Table 3 gives the principal reactions.

Figure 10 shows typical mole fractions profiles in the reactor 1.5 seconds afterstart-up. The oxygen was ali consumed near the inlet. Fig. 11 shows somehot spots. Fig. 12 shows that the exit compositions reach a near steady state10 seconds after start-up.

ACKNOWLEDGEMENT

Thi.q study w_,_._,pport, ed hy a U.S. Dc'part.ment of Energy grant, DE-FG-22-89PC89769.

NOTATIONc fluct,ating velocity of particle P press, re ten.qorC fluchtating minus bydrodynnmic velocity q flux vector of fluctlmt.intg energy

C,t drag cnemcient R,. Reynolds n,_mlmrdj, particle diameter r i reaction rateD diffusivit, y S deformation rate t_,nsore coefficient of restitution Tq,T,, temperature of gas and solidg gravity t:q,,,., gas and sr,lid vel,,t'ity vector

g,, radial di._trihution f, nction Y,, weight, fraction of gn.qof species nh, volumO.ric heat, trrmsfer coefficient t timeh enthalpy

AH ° standard heat.of reaction Greek Letters[¢',q eq,ilibri,m cnn.ct.anf,of reaction _ f.wophn.,_edrag coemcientKr,i rate consf.ant, of reaction i 7 colli._intml ent,rgy ,li._.qipnt.itm

k 9, k, thermal conductivities of the gas nrel solid 7,,, .qtoichiometric ec,emcient of .qpecies nM m.,lecular weight. _, _* ga.q anti solid vol,mo fracti,,,._

Nu gn._ particle Nusselt. numlmr _/ effect.ivene.qs factor for renctinn i_. _-mnductivit.y of granular temperaf.,lro

p presmre lt shear viscosity( bulk vi._co_ityp den.city0 gran, lar temperatltre = I < C 2 >

LITERATURE CITED

1. Savage, S.B. in "Theory of Dispersed Mulliph;t_eFlow,"cd. R.E. Meyer, Academic Press,

2. Jenkins,J.T. _nd Savage, S.B.J. FluidMech., 13___0,187 (198._).3. Ding, J. and D. Gid:tspcvs,,AIChE Journal,36. 523 (1990).4. Chapman,S. andT.O. Cowling."the MalhemalicalTheory of Non-UniformGase.,;."2ndEtl.,

Cambridge Univ. Press (1961).

5. Miller, Aubrey, Ph.D. Thesis, Illinois Institute of Technology, Chicago 1991.6. Gidaspow, D., J. Ding and U.K. Jaya._ral. in "NumeticMMethods for Multiphase Flows,"

FED-Vol. 91, American Society of MechanicMEngineering.p. 47 (1990).

lm 3 Dimitri Gidaspow

TABLE I:KINETIC TIIEORY MODEL FOR MUI,TIPIIASg FLOW

1. CONT|NUITY EQIJATION 2. I_[OMENTIJM EQIIATION FOP,.FOIl. PIIASE k(= g,_) PHASE k(-- g,_; I-- g,.q)

(w;.i)

3. C;ONSTITUTIVE EQ[JATIONFOR STRESS 4. Gna Phone Strpsa

_¢ = 2r,dl ,. _q (TI. !)

T, Irh.l,'nt Vi_ro_ily ([l_,'d ['or rnml,ari-_hore agn only)

J-v.I l,. = ,, + t,, = pj.,/_y(2,_,. },)_, ! p,

(7"1 ..'b0 (TI. t,,)with r, = 0.1 and A = x/_.¢.--_

•_. Solh] Phase Stress

glnr'tic "l'hr'ory Modr'l ((;i,la_po,x,', _. FI,UCTIIATING ENERGY (6) =19.ql exten_ion oi" Sav._g-,lg_3 and Dinll_ C_and Gid_qpow's. 19li0 r;xprt,ssions to di2 _ < >) EQUATIONI.te and dense, flow)

Sollrl_ Pha._ Pr_,._._,re _3 __,p,O) F V •(,,p,,,,O) = r, : V,,2

r, =/,,_,0[I +_(i _).qo,,] (7"l..s,_) -v._-7 cr!.n)

Solids Pha._e Ihflk Viscosity Collisional EnrrRy I)i._._ipation 7

_. = _,_p,d_.9,.(14 e)( O---)I_. (Tl.Sb) 7 = 3( i - e')'_.P..q.63 ( 4;( O )_ - V ' ".){7"1._.)

Soli,hPha-_- Shear ViscosityFl.x of Fl.ct.atinlg gn0re:y q

21,..,, [ 4 1' q=-.gT63 (7"!.6b)!'. - (! t- e).q,, 1 t- _(I I e).q,,_. ('ond,,ctivity of Fl,,ctua_in_ EnorRy

4 , O)| (7'i.5e) r. 2 II , n 1'+ g,.,,a,.¢.(l t-_}(; _ (__-,).q. _( ! ._,),.,. _,,Solid, Pha._e Dil,,to Viscosity q_

.t.2,:e,a, qo(__ _)(_)t (Wl.n,)•S__v_,a,ol (t'._a) t)i_,,,,,t,l,_,e ('_,,1,1y"ry,,,") C.,an,,iar

/'.ai, - 96 Cond.ctivityll.adiAi Di_trihntlon F.nction

_cail= 7_"_5_.v/_PrdrF3t (7"1.6d)

_. = g ! - (_)I (T_..s,-)

7. GAS - SOLID DRAG COEFFI-CIENTS

For r, < 0.8 (ha._e,I Mn Ergnn eq,oation) whr're

_, 24 ISR n I fnrRr_,< lO0,,50':"' 1.75e':'l - v'l C, = [I ;-O. ,n,'0,,

fl- I. ,d_ + (TI.7n) _ ' (7"1.7c)For r, > O.R (based on empirical corre-

lation) Ca = 0.44,for Re n > lO00 (7'1.7d)

3C ":,r'_l",- ",l-_sfl = _ -a _ (TI.7b) _P,l"_- ".l d,R% = (TI.7,)

He

_I 6 Dtmitri Cidaspo_

TABLE 2" CONSERVATION OF SPECIF.qAND ENERGY

CONSERVATION1. EQUATION(4R_°*__"," 2oo<n_<2ooo

OF GAS COMPONENT "n" N% -- 0.123 _ dp ] "l, , -# ,-_(,p,}.) + v.(,p,v.,,o) = m. _ v...,.

(2.1) N,% = 0.61ReonvS_,. He > 20002. ENERGY EQUATIONS

Gas Phase _ > 0.8

?Iuv = (2 + 0.16 Ren_z).qp, Re._<200• 0p(,a,h,)+ v. (,ash,us)= _(_-4-,-Vr,)

+c2__r,,AIIo+h,(T,_T,)+V.(kt(VT,) Nu, = 8.2Ren_Sp, 200 < Re _<lO00(2.2)

Solid PhnseNu, = 1.06fte°'4ssT.Fp, Re > I000

O (_,p,h,)+V.(,,pph,v,) +he(Ts-Ts ) where

+v-(t,_,VT,) (2.3) Re--dppsi"s- v,lGas - Pmrtlele Heat Trnnsfer h,, IlsFor _ < 0.8,

6

oel,= ¢,_; and N%, = h,dp/k eN% = (24-1.1Re°'_Pr})Sp, Re >_200

TABLE 3. KEY REACTIONS

_.(p,-p.)rl ----"di# di#_{i-a)/rf I4-

I=,o,,., 4- -'_-Afl".,l_.OSat=,,,_ _,.,c_, 40.3

1. COMBUSTION REACTION (b)C 4- ll,O ---* CO 4- II_

C+_/tO_ ---* 2(1- Tr)CO + (2"!!- 1)C02

-4.5ooo)where"ft lJ determined by K,_ = 930*'xp( R.--_ '

_ 16326.1CO 2(1 7t) 10_.4exp( ) Plt_Pco = exp(17.3 )CO_ 2-It - l - K._ = (l,;t,o)_ T,

s -27000 All°.41_98°k = 32.4K,,t -- 1.79x lO exp(R----ff_) 3. WATER SIIIFT REACTION

Co 4- ll=O _ CO_ 4- ll_

An°._1=9S%= (- 97.7)(2>,-t)4-2(-2S.7t4)-8421.3 )paS- _ (2coztt, o

( l - "ts) 4- 2.4 and p_, = 0.0 rs = 0.775exp( Ts2. GASIFICATION REACTIONS

=co, zm )( ! - ;V_)t,_t_,(a)C 4- CO_ ---* 2C0 K,,,t

7860)-45000 K,,e = 0.027exp(-_---K,, = 930exp(_) .ts

An°l,OS°t= -9.84

pc.--_ = t._ x t0' _p(-4°'_°°"moo, _.--_7-,_

5 Dlmltrl Gldaspow

IIq

pwelM MPe

........, Inlet (/n.rlillr,._fi L !

I .... "|_rmln_l vel.cil.y .f parLiclo._ ---- I.I m/_

(_q flow r_Le aL hnLt.nm .1".qLn.,ll,ipe ---. 2..5 rm/e(Mi.h..m II.irli_aLin. vr'lncil.y)

I I_"_'_"_"'/'_'__'e_li j.5_:_.__._ _ |q,_,_ll_l-|| Air inlel. (ri_er)w, lnciLy - 2,./q

Vw. - _lt - _l_ft,mle

FIOURR I. C1FRLeap lndudlnS InllUI andInlet II xe_x P x,e.q

.;_.;.:_:_ ......

..... I

FIOURI_.Z Prank'leCo,_entrmlan,Veladlle_,Or_ulerTemper_ture_(_nA_)_ _nd _Id Vl_mn_Itles_(Pol_e)

_ __ • = O.gggog "-e : 0.g¢19

.... e = O.O

! • -- 0.9 _._.

: I0 "' (Y|_ee)slty fr--. Miller'._ men_,,rement._ = 9.0_'I0"') n_ :_.

Z --

I:::"_ I0 "' ,-.,

".---- ..............

,'Infl

Rm_l,.I Ill_t_nee Irrnm the l_ff 111'tll ni' the Hifar (eta) I _-----J I .._j , ._, \1._1 .... o I o" _._ --'_ il ..... _/i--" l_..il --- ---li_l_°"-_n

Fig. 3. F,F.fect oi Restitution Coefficient ,,v.l..--_

on Solid_ Vl_eo_ty Figure &

6 Dlmitrl Cldaspow

II

Ii.,.il_I.|(- • I.IlllMw,i'e il,.l,,l(.lob l.tm.d*_ew| ll-,,,,II.4oI . • • Ill)

o_l_ 0ro,lm "_'__ nine-, I,.,4ol (.,.Ilk t.tk,_l,,,,,*-)

_n4iimlm

i.. ' tj\iI'- I .

t olen lwl

I .Imlll, r--.--L-llr_--11_r---,-11_l--"-- i1_3--'- 1!I/o _lnmll, '.itlr'l_l-'irlll 'iii 'pllli'l_li'I7 I'll_l'l_l'il_tli_ (,,m,I lanl #-,_1

F1('IIIRE S. l'_rlie from Sinndl'_pe lo ill_r

At Ill_lpr llpllht -- l0 in

Rtnor ifpliihl -- 111 m ni_il__ ll,.-, u,,,l,,i (,. = ni,ni (,o ,, 2 m/,) . .-- - I)lnl°I lilodel wttil l*llrilrlill.nee ('ii " _! m/li) __ Hew 14,J4.1 (., .-O.000) . .

_- -- lllnlI'll M_l_41,1wtlh Tilrkilll, nell (l i :ii ,1 mini i _ _ lllni'9 Mil,4,.I (itlh tillrhliii'n¢'-I

lA rt# % iii % I

.,<., .--___

i "II "_'""t-.,.,\ "" '.

-'_,I_---_- _--ilr'-i_ -'--'illl...._ o._I---'--_--'---illl---_-*-i_l_'--'-_ ....li, Iii. Bt_clrANIL-I_._ LIIII'T llllllJ. _ _ (i,m) - lll_llllL lltq'Tlltt:l_. IMintl iJ!ll'l' IAll _ _ I,'"i

I_IGUlllP_.6. _ AveniledIll(lbl Mllm Fliri I'l_,lflks l_ICtUli! "#."11n_ Avei_leclIllldllll Y,z_idllVolume Frllc"iloePiffle

Itlm, r Ib.lliht -- II1 inii _ N#", Id,_4,.I (* • O IOO}

__ lte. lie,4,.I (. -- ii.Ni)(n i .-li'n/ni -. { _ rll.l',l II.l,,,I (wOk tllrh.ll, fir,,)

_ _ Dtitl'O lod#l -tlh T,l,,lt,ll,,nee (% ..-lm/oi

Ilflit _l - __ I)#nii'l Hod-1 ,,llill Tllrk,.llt.n,"ll (,lie-.'lm/I

.-- ,",

/ \\\ #

-i_-_' _l L'-'l_l._lf--"-lqlii ' '_ 't J- "nn'..... I .......... _i_tf"--'---_'-lll_/J_AL PlY_ANt_IRI lltlP'lr vail. _ _ I--.I Ill--TR ill, lt:rtr (-ml .

FIGURE 8. Tlme AversBed R_Hal ,_olidlVelodty Profile FIOURE 9. Areil Averaged Axial _ Volume Frxcllon Profile

DISCLAIMER

Th.:s report was prepared as an account of work sponsored by an agency of the United StatesGovernment. Neither the UrAted States Government nor any agency thereof, nor any of their

employees, makes any warranty, express or implied, or assumes any legal liability or responsi-bility for the accuracy, completeness, or usefulness of any information, apparatus, product, orprocess disclosed, or represents that its use would not infringe privately owned rights. Refer-ence herein to any specific commercial product, process, or service by trade name, trademark,

manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom-mendation, or favoring by the United States Government or any agency thereof. The views

and opinions of authors expressed herein do not nexessarily state or reflect those of theUnit_,_l_S!.at_ Government or any agency thereof.

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['_00 t t,A_ T_I4PERATUREAT IIEl_lrr : 4.._(m) HF.AR 0.S__ c£1¢re:i_nv RISER ": _o= 0.4 OOTL__UZr_cxzo_o,

..... COt "1 .... _ WALLn_ ms_e .,, _ __co1450-] _ _ n,ClIT ealJ. or mse:e / : _o3 --

, . ' o

:' ' ', "0_-: .... -- ..:..: - ,-:. -

3 1400 ; ', : ', 0.t _'...--.........................

_d 1 , i . i

- , '"- s ,D

_,_/_.-. _,_ s lo ,s1350 _ -, 71 m (ssc1

..__// "" FIGURE 12. Outlet Gas Comlx_itions_- - _-,.---_"--- . .... ,

t300 .......... , ......... t ....... '.. • for the CFB Synthesis Gas Producer0 5 I0 15

_uv. (sr.c)

FIGURE II. Gas Temperature

8 Dimitr_ C,Id aspow

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