MODELLING OF DENSE GAS-PARTICLE FLOWS USING KINETIC THEORY OF GRANULAR FLOW J.A.M. KUIPERS TWENTE UNIVERSITY THE NETHERLANDS

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1 MODELLING OF DENSE GAS-PARTICLE FLOWS USING KINETIC THEORY OF GRANULAR FLOW J.A.M. KUIPERS TWENTE UNIVERSITY THE NETHERLANDS

2 DENSE GAS-SOLID FLOWS hiting and Tanzania

3 DENSE GAS-SOLID FLOWS cluter in co-current vertical ga-olid low

4 INTRODUCTION dene ga-particle low in luid bed amily o contactor 1: bubbling bed 2: turbulent bed 3: circulating bed 4: rier 5: downer 6: lateral taged bed 7: vertical taged bed 8: pouted bed 9: loating bed 10: twin bed

5 INTRODUCTION APPLICATIONS OF FLUIDIZED SYSTEMS + heat exchange and drying + coating and granulation + ga puriication via adorption + chemical ynthei acrylonitrile, maleic and phtalic anhydride + polymerization o lower oleine propylene + Ficher-Tropch ynthei + Fluid Coking and Flexi-Coking + combution and incineration + Fluid Catalytic Cracking FCC

6 INTRODUCTION Fluid Catalytic Cracking FCC unit

7 ELEMENTARY PROPERTIES OF GAS-FLUIDIZED BEDS dene bed

8 FLOW REGIMES + KEY PHENOMENA map o low regime in particle-laden low

9 MULTI LEVEL MODELLING MULTI LEVEL MODELLING OF DENSE GAS-SOLID FLOWS Van der Hoe et al., CES 2004

10 SIMULATION CONDITIONS DBM SIMULATION indutrial ize column Indutrial cale column: Dimenion: 4 m x 4 m x 8 m Ga velocity: 2.5U m =0.25 m/ Emulion phae propertie: Denity: 400 kg/m 3 Vicoity: 0.1 Pa. Bubble propertie: Initial bubble ize: 8 cm Maximum bubble ize: 80 cm Typically ~ 5000 bubble

11 DPM + KTGF SIMULATION bubble ormation: 15 cm bed W=0.15 m d p =1.5 mm ρ =2526 kg/m 3 U b =0.85 m/ U j =15.0 m/ N p =120000

12 DPM SIMULATION pouted bed

13 DPM SIMULATION pouted bed u / u = 16.0 u / u = 1.2 m b m particle coniguration particle velocity map

14 DPM SIMULATION pouted bed u / u = 16.0 u / u = 1.2 m b m experimental imulated

15 DNS IBM low through cubic array o 64 particle at Re p = Eulerian grid N=d p /h=20 Dimenionle drag F=10.9 computed F=10.2 analytical

16 DNS IBM low through random array o 1326 particle at Re p =120

17 DNS IBM low through random array o 1326 particle at Rep=120

18 DNS IBM luidization o 3600 dic

19 BASIC FEATURES KINETIC THEORY BASED MODELS + tatitical mechanical decription o particle-particle encounter ADVANTAGES + baed on more undamental decription o particle-particle interaction compared to claical two-luid model DISADVANTAGES + incorporation o dierent particle propertie polydiperity i quite diicult and lead to many additional equation CPU limitation

20 KINETIC THEORY BASED MODELS LIMITATIONS AND PRESENT DIFFICULTIES + nearly pherical particle + not uited or dene ga-particle low where quai-tatic particle zone prevail hopper, ixed bed and moving bed + incorporation o detailed particle-particle interaction model diicult + ytem with broad ditribution in phyical propertie ize, denity + ytem with rapid change in particle ize polymerization

21 CONTINUUM MODEL BASED ON KINETIC THEORY DEFINITION OF PARTICLE VELOCITIES + intantaneou particle velocity: c + enemble averaged particle velocity: v + luctuating particle velocity: C = c v DISTRIBUTION OF FLUCTUATING VELOCITIES KTG 2 m 3 / 2 mc = n exp Maxwell velocity ditribution 2πkT 2kT number denity Boltzmann contant

22 CONTINUUM MODEL BASED ON KINETIC THEORY TRANSPORT MECHANISMS FOR PARTICLE PROPERTY φ

23 CONTINUUM MODEL BASED ON KINETIC THEORY BOLTZMANN EQUATION IN TERMS OF BOLTZMANN EQUATION IN TERMS OF SUBSTANTIAL DERIVATIVE: t F c c F r c t e = : t F C r v C C r C C Dt Dv Dt D e = + + r v t Dt D + = c v c C =

24 CONTINUUM MODEL BASED ON KINETIC THEORY MAXWELL TRANSPORT EQUATION FOR PROPERTY φ D n < φ > Dt + r n < φc > + n < φ > r v n[ < Dφ Dt > + < C φ > + < r F φ C Dv > Dt < φ C > v r : < C φ C > ] = nδ < φ >= e φ t dc = φ = 1 ENSEMBLE AVERAGE OF PROPERTY φ φ = mc < φ >= φdc φ = 1 2 m C C = 1 2 mc 2

25 MICRO BALANCE EQUATIONS CONTINUITY EQUATIONS MOMENTUM EQUATIONS 0 = ρ ε + ρ ε u t 0 = ρ ε + ρ ε v t g v u p uu u t ρ + ε β τ ε ε = ρ ε + ρ ε g v u p p vv v t ρ + ε + β τ ε ε = ρ ε + ρ ε

26 MICRO BALANCE EQUATIONS GRANULAR TEMPERATURE EQUATION 3 [ 2 t ε ρ Θ + ε ρ Θv] = p I + ε τ : v + ε κ Θ + β[ c c 3Θ] γ ADDITIONAL EQUATIONS AND CLOSURES + phae denitie + phae tre tenor and phae vicoitie + peudo Fourier energy lux and olid peudo conductivity + olid preure + interphae momentum exchange coeicient + covariance between luid and olid luctuating velocitie or dene low thi term can aely be neglected

27 CLOSURE OF MICRO BALANCE EQUATIONS interphae momentum traner coeicient Ergun equation ε <0.8: 1 ε μ β = ε ε 2 d 2 p ρ d p u v Wen and Yu equation ε >0.8: β = ε ε Cd ρ u v ε 4 d p Drag coeicient: Re p = ε exponent depend on particle Reynold number Re p ρ u v d μ p C d = [ Re p ] C = Re d p Re p <1000 Re p >1000

28 DRAG CLOSURE Ergun equation

29 CONTINUUM MODEL BASED ON KINETIC THEORY SUMMARIZING THE KEY FEATURES OF KTGF + particle interact through binary nonideal colliion no riction + non-ideal particle-wall colliion are accounted or + departure rom Maxwellian velocity ditribution unction i mall + one additional equation granular temperature equation + cloure or olid vicoity, preure and peudo conductivity + random granular motion and no collective granular motion

30 NUMERICAL SOLUTION METHOD KEY FEATURES + explicit treatment o convection and diuion term + implicit treatment o poroity preure in momentum equation + taggered computational meh + high order cheme or convection or ma and momentum tability condition < 1 Δ Δ + Δ + Δ t z u y u x u z y x < 1 Δ Δ + Δ + Δ t z v y v x v z y x ] [ z y x t Δ + Δ + Δ < Δ ν ] [ z y x t Δ + Δ + Δ < Δ ν

31 NUMERICAL SOLUTION METHOD DEFINITION OF EULERIAN VARIABLES x z y calar variable x-velocity component y-velocity component z-velocity component

32 NUMERICAL SOLUTION METHOD OVERALL COMPUTATIONAL STRATEGY PER CYCLE compute convection and diuion term or g+ momentum equation etimate g+ velocity ditribution uing old poroity + preure ield olve poroity and preure Poion equation uing ICCG compute g+ velocity ditribution with new poroity + preure ield olve granular temperature equation

33 RESULTS OF KTGF MODEL bubble ormation at a jet uing 3D model

34 RESULTS OF KTGF MODEL: MONODISPERSE SYSTEMS bubble ormation: 30 cm bed W=0.30 m d p =2.5 mm ρ =2526 kg/m 3 U b =1.20 m/ U j =20.0 m/ N p =60000

35 RESULTS OF KTGF MODEL eect o retitution coeicient on bed dynamic

36 RESULTS OF KTGF MODEL eect o retitution coeicient on bed dynamic

37 RESULTS OF KTGF MODEL: BIDISPERSE SYSTEMS egregation rate in bidipere ytem

38 RESULTS OF KTGF MODEL: BIDISPERSE SYSTEMS egregation rate in bidipere ytem

39 RESULTS OF KTGF MODEL eect o lateral egregation on rier reactor perormance RISER FLOW + particle diameter FCC 40 μm + rier diameter 0.3 m + upericial ga velocity 6.3 m/ + olid ma lux 390 kg/m 2. FEATURES + two-luid model incorporating kinetic theory o granular low + turbulence model: Prandtl mixing length model + axi-ymmetrical low

40 RESULTS OF KTGF MODEL eect o lateral egregation on rier reactor perormance RISER FLOW RADIAL PROFILE OF SOLIDS VOLUME FRACTION ε 0.20 [ε] r/r [-]

41 RESULTS OF KTGF MODEL eect o lateral egregation on rier reactor perormance RISER FLOW RADIAL PROFILE OF AXIAL SOLIDS VELOCITY V z 17.0 v z [m. -1 ] r/r [-] 1.0

42 RESULTS OF KTGF MODEL eect o lateral egregation on rier reactor perormance REACTION SCHEME: k1 k2 A + [*] B + [*] C k3 [*] [ ] + [*] KINETICS: r = ε [*] ρ k x r =+ ε [*] ρ k x k x r r A 1 A B 1 A 2 B =+ ε [*] ρ k x C 2 B * = ε [*] ρ k 3 k k k = 25 = = 0.2 1

43 RESULTS OF KTGF MODEL eect o lateral egregation on rier reactor perormance AXIAL PROFILE OF FLOW-AVERAGED FRACTIONS IN RISER 1.0 X i [-] 0.5 A B [*] C IDEAL z/l [-] 1.0 X i [-] 0.5 A [*] B C NON-IDEAL z/l [-]

44 CONCLUSIONS BUBBLING BED + igniicant eect o e on bubble dynamic + diipation level to low riction i not included in KTGF CFB RISER + radial egregation in dene rier low can be predicted + igniicant eect o radial egregation on rier reactor perormance