Supporting information for: Modelling tar recirculation in biomass fluidised bed gasification Wolfram Heineken,, Daniel De La Cuesta,, and Nico Zobel Fraunhofer Institute for Factory Operation and Automation IFF, Magdeburg, Germany, and University of Vigo, Spain E-mail: wolfram.heineken@iff.fraunhofer.de Bed fluidisation The fluidised bed is assumed to contain sand particles of diameter d sand, fuel particles of diameter d fuel, and char particles of diameter d char. For sand, fuel (wet, boiling, dry), and char, particle densities are denoted by ρ sand, ρ fuel(wet), ρ fuel(boiling), ρ fuel(dry), and ρ char, respectively, and mass fractions in the bed are w sand,bed, w fuel(wet),bed, w fuel(boiling),bed, w fuel(dry),bed, and w char,bed, respectively. Fuel particle densities are estimated according to ρ fuel(wet) = ρ fuel(dry) /(1 w water,fuel ) and ρ fuel(boiling) = ρ fuel(dry) /(1 w water,fuel /2). An average particle diameter is defined by d P = w sand,bed d sand + (w fuel(wet),bed + w fuel(boiling),bed + w fuel(dry),bed ) d fuel + w char,bed d char To whom correspondence should be addressed Fraunhofer-Institut für Fabrikbetrieb und -automatisierung IFF, Sandtorstr. 22, 39106 Magdeburg, Germany Escola de Enxeñaría Industrial, Universidade de Vigo, Lagoas-Marcosende s/n, 36310 Vigo, Spain S1
and an average particle density by ρ P = w sand,bed ρ sand + w fuel(wet),bed ρ fuel(wet) + w fuel(boiling),bed ρ fuel(boiling) + w fuel(dry),bed ρ fuel(dry) + w char,bed ρ char. The properties and behaviour of fluidised beds have been subject to a large amount of research, see e.g. the textbooks of Kunii & Levenspiel S1 and Oka. S2 In our model, the expansion of the fluidised bed is calculated using a correlation given by Aerov & Todes, S3 see also Oka. S2 It will be described in the following. Let ɛ 0 be the voidage of the bed at rest. Common values for ɛ 0 obtained in measurements are in the range between 0.36 and 0.45. In our model, we set ɛ 0 = 0.39. The fluidised bed is characterised by the Archimedes number Ar = g d 3 P ( ρ P ρ G ) ν 2 G ρ G and the Reynolds number (based on the superficial velocity) Re sup = v sup,g dp /ν G, where g = 9.81 m/s 2 is gravitational acceleration, ρ G is the average gas density, ν G is the average kinematic viscosity of the gas, and v sup,g is the average superficial gas flow velocity in the fluidised bed. We define the expressions ɛ = ((18 Re sup + 0.36 Re 2 sup)/ar) 0.21 and Re max = Ar/(18 + 0.61 Ar 1/2 ). Depending on the flow velocity, one of the following cases occurs: ˆ If ɛ ɛ 0 holds, then the bed is at rest. ˆ If ɛ > ɛ 0 and Re sup < Re max holds, then a fluidised bed exists and has the voidage ɛ. ˆ If Re sup Re max holds, then the particles are carried with the flow and no fluidised S2
bed is formed. The minimum Reynolds number Re sup,mf needed to fluidise the bed is then, obviously, given by the relation ɛ 0 = ((18 Re sup,mf + 0.36 Re 2 sup,mf)/ar) 0.21, and the minimum superficial fluidisation velocity is v sup,g,mf = Re sup,mf ν G / d P. Particle heating In order to calculate the time needed for heating up the particles in the fluidised bed, we consider a small control volume V in the bed. The energy balance for this control volume reads Q GP = c p,g ṁ G (T G,in T G,out ) (1) = c p,p m P dt P dt, (2) where Q GP is the heat flux from the gas to the particles, c p,g and c p,p are the specific heat capacities of gas and particle, respectively, ṁ G is the mass flow of gas through the control volume, m P is the mass of particles in the control volume, T G,in and T G,out are the gas temperatures at inlow and outflow of the control volume, and T P is the particle temperature. On the other hand, the convective heat flux can be calculated by Q GP = h A T G,in T G,out ln(t G,in T P ) ln(t G,in T P ), (3) where h is the heat transfer coefficient and A is the total surface area of the particles in the control volume, see e.g. VDI heat atlas. S4 The heat transfer coefficient is related to the Nusselt number via h = k G Nu/d P, where k G is the heat conductivity of the gas and d P is the particle diameter. In the limit V 0, the gas temperatures T G,in and T G,out approach a common gas temperature T FB, called the temperature of the fluidised bed, and the time t heat (T 1, T 2 ) needed to heat up a spherical particle from temperature T 1 to temperature T 2 S3
can be calculated analytically from (1) (3), leading to t heat (T 1, T 2 ) = c p,p ρ G d 2 P 6 k G Nu ln T FB T 1 T FB T 2. The Nusselt number appearing in this formula is calculated using correlations given in VDI heat atlas: S4 Re = vg dp/νg, with advection velocity v G = v sup,g /ɛ of the gas, Nu lam = 0.664 Re 1/2 Pr 1/3, with Prandtl number Pr = 0.72 (approximate value for air S4 ), Nu turb = 0.037 Re 0.8 Pr 1 + 2.443 Re 0.1 (Pr 2/3 1), Nu sphere = 2 + (Nu 2 lam + Nu 2 turb) 1/2, Nu = (1 + 1.5 (1 ɛ)) Nu sphere. Particle drying Particle drying by evaporation of water is modelled to occur only at boiling temperature T P = T vap = 100 C. As for particle heating, a control volume V is considered. Equations (1) and (3) remain valid, but (2) is now replaced by dm water Q GP = h vap, dt where h vap = 2.257 MJ/kg is the specific vapourisation enthalpy of water at boiling point, and m water is the mass of water in the particles of the control volume. A similar calculation S4
as for particle heating leads to the evaporation time t evap = w water,fuel ρ fuel(dry) d 2 P 1 w water,fuel 6 k G Nu (T FB T vap ), where w water,fuel is the initial mass fraction of water in the fuel and ρ fuel(dry) is the particle density of dry fuel. Fuel particles are inserted into the gasifier with a given mass flow ṁ fuel,in and temperature T fuel,in. They remain in the bed until they are decomposed by pyrolysis at temperature T pyr = 450 C, S5 which is modelled as an instantanous process. Inside the bed we distinguish between wet fuel at temperature less than T vap, boiling fuel at temperature T vap, and dry fuel at temperature greater than T vap. In the bed, ˆ the mass of wet fuel is m fuel(wet),bed = t heat (T fuel,in, T vap ) ṁ fuel,in, ˆ the mass of boiling fuel is m fuel(boiling),bed = (1 w water,fuel /2) t evap ṁ fuel,in, ˆ and the mass of dry fuel is m fuel(dry),bed = (1 w water,fuel ) t heat (T vap, T pyr ) ṁ fuel,in. Entrainment of char A certain fraction of the char particles in the fluidised bed is entrained into the freeboard by bubbles that burst on top of the bed. The diameter of the bubbles is modelled according to Darton et al., S6 d bubble = min ( 0.54 ( ) 0.4 ( ) 0.8 ( ) 0.2 vsup,g v sup,g,mf hbed g m/s m m/s 2 m, d bed), S5
with h bed being the height, and d bed being the cross-sectional diameter of the bed. According to Wen & Chen, S7 char entrainment is esimated by ( ) 2 ṁ char,entr = 3.07 10 9 Abed d bubble w char,bed m 2 m ( νg ) ( ) 2.5 2.5 vsup,g v sup,g,mf kg m 2 s m/s s, ρ G kg/m 3 ( g ) 1/2 m/s 2 where A bed is the cross sectional area of the bed. Motion of char particles in the freeboard For the entrainment of char particles into the freeboard, a simplified dilute stream model is used. This means that any interaction of char particles in the freeboard is neglected. The motion of char particles is only given by their terminal velocity and the velocity of the gas stream. Both the gas and char particles are assumed to move in vertical direction. The one-dimensional drag equation reads F d = 1 2 ρ G (v G v P ) v G v P C d A ref (4) where F d is the drag force onto the particle, ρ G is the gas density, v G is the gas velocity, v P is the velocity of the char particle, C d is the drag coefficient, and A ref is a reference area of the particle. In the case of spherical particles, as are considered here for the sake of simplicity, A ref = πd 2 P /4 is the cross-sectional area of the sphere. The drag coefficient C d for a sphere is calculated according to Schuh et al., S8 24 (1 + 0.15 Re 0.687 )/Re, if Re < 200, C d = 24 (0.914 Re 0.282 + 0.0135 Re)/Re, if 200 Re < 2500, 0.4008, if 2500 Re S6
with Reynolds number Re = d P v G v P /ν G, where d P is the particle diameter and ν G is the kinematic viscousity of the gas. According to Newton s law of motion, dv P dt = F d/m P g + ρ G ρ P g (5) holds, where m P = ρ P πd 3 P /6 is the mass of the spherical particle, and g = 9.81 m/s2 is gravitational acceleration. On the right hand side of equation (5), the first term is due to drag, the second term is gravity, and the third term represents buoyancy. Using (4), equation (5) can be written in the form dv P dt = 3 C ( ) d ρ G v G v P (v G v P ) ρg + 1 g. (6) 4 ρ P d P ρ P Char particals can, in general, move in both upward and downward direction, since dv P /dt can become negative. However, in all simulations carried out in the paper, the case dv P /dt 0 has never occurred. If dv P /dt is always positive, the char load in the freeboard can be calculated in the following way: Let z be the coordinate in vertical direction, C j be the cell in the freeboard with z-values between z j 1 and z j, and v P,j 1 be the particle velocity at z = z j 1, i.e. at the bottom plane of cell C j. Then, equation (6) and equation dz P /dt = v P form a system of ordinary differential equations (ODEs) that can be solved with the initial values v P (0) = v P,j 1 and z P (0) = z j 1. With the solution z P (t) of this ODE system, we can determine the residence time t P,j of the particle in cell C j, which is given by z P (t P,j ) = z j. The particle velocity at z = z j is then v P,j = v P (t P,j ). If ṅ char,j 1 is the molar flow of char into cell C j, and ṅ char,j is the molar flow of char leaving the cell C j, then the molar amount of char in cell C j can be estimated according to n char,j = ṅchar,j 1 + ṅ char,j v P,j 1 + v P,j (z j z j 1 ). S7
Perturbed mass fractions of the pyrolysis products used in the uncertainty analysis As stated in the section Uncertainty analysis of the article, there has been designed an algorithm for the perturbation of the mass fractions of pyrolysis products. The resulting mass fractions are presented in the following table. CO CO 2 CH 4 C 6 H 6 O C 7 H 8 H 2 H 2 O C (char) reference case 18.57 11.62 4.62 9.93 9.88 0.50 24.85 20.04 w CO,pyr min. 8.57 17.64 3.71 15.83 8.57 0.42 25.22 20.04 w CO,pyr max. 28.56 5.60 5.53 4.03 11.19 0.57 24.48 20.04 w CO2,pyr min. 23.23 2.74 3.76 19.93 2.66 0.44 27.21 20.04 w CO2,pyr max. 13.94 20.45 5.47 0.00 17.05 0.55 22.50 20.04 w CH4,pyr min. 16.64 9.27 0.01 9.71 15.46 0.82 28.05 20.04 w CH4,pyr max. 21.48 15.17 11.60 10.26 1.44 0.00 20.00 20.04 w C6 H 6 O,pyr min. 19.33 13.29 4.61 0.01 17.36 0.48 24.89 20.04 w C6 H 6 O,pyr max. 17.79 9.93 4.63 19.93 2.35 0.51 24.81 20.04 w C7 H 8,pyr min. 18.34 10.01 5.07 19.89 1.74 0.50 24.41 20.04 w C7 H 8,pyr max. 18.79 13.22 4.17 0.03 17.98 0.49 25.29 20.04 w H2,pyr min. 17.80 10.85 6.16 8.58 10.34 0.00 26.23 20.04 w H2,pyr max. 20.87 13.92 0.00 13.98 8.50 1.98 20.71 20.04 w H2 O,pyr min. 19.77 21.62 9.57 10.86 1.49 0.95 15.72 20.04 w H2 O,pyr max. 17.45 2.29 0.00 9.06 17.71 0.07 33.37 20.04 w char,pyr min. 18.78 11.70 4.19 11.30 11.15 0.46 24.39 18.04 w char,pyr max. 18.35 11.54 5.04 8.56 8.61 0.54 25.31 22.04 Table S1: Mass percentage of pyrolysis products used in the uncertainty analysis S8
Graphical representation of the uncertainty analysis The realtive uncertainties defined in section Uncertainty analysis are shown graphically in the following figures. Whenever the relative uncertainty is larger than 0.1, the corresponding input parameter is called critical and used in the evaluation of the error bars shown in Figures 6 to 14 of the original article. ṁ fuel T fuel w water,fuel w C,ult w H,ult w O,ult H i,fuel(dry) d fuel ρ fuel(dry) T 1 T 2 T 3 T 4 T 5 T 6 x CO x CH4 x H2 C tar C soot H i,pg V prim T prim V sec 10 3 10 2 10 1 10 0 relative uncertainty u Figure S1: Uncertainty analysis, input parameters 1 to 12 S9
T sec all less than 10 3 w CO,pyr w CO2,pyr w CH4,pyr w C6 H 6 O,pyr w C7 H 8,pyr w H2,pyr w H2 O,pyr w char,pyr T 1 T 2 T 3 T 4 T 5 T 6 x CO x CH4 x H2 C tar C soot H i,pg m sand d sand ρ sand 10 3 10 2 10 1 10 0 relative uncertainty u Figure S2: Uncertainty analysis, input parameters 13 to 24 S10
c bed c frb c pc a 1 a 2 a 3, ins. bed a 3, outs. bed a 4 a 5 all less than 10 3 T 1 T 2 T 3 T 4 T 5 T 6 x CO x CH4 x H2 C tar C soot H i,pg a 6 a 7 a 8 10 3 10 2 10 1 10 0 relative uncertainty u Figure S3: Uncertainty analysis, input parameters 25 to 36 S11
a 9 a 10 a 11 a 12 a 13 a 14 a 15 a 16 T 1 T 2 T 3 T 4 T 5 T 6 x CO x CH4 x H2 C tar C soot H i,pg a 17 a 18 a 19 10 3 10 2 10 1 10 0 relative uncertainty u Figure S4: Uncertainty analysis, input parameters 37 to 47 Unlimited tar accumulation In the section The effects of tar recirculation: simulation results of the article, we had detected conditions that lead to an unlimited tar accumulation if tar is continuously recirculated. Some additional illustration to this behaviour will be presented here. Sufficient air supply always led to a steady state if continuous tar recirculation was applied. However, if 100 % of tar and soot were recirculated and the air supply was low, the recirculation resulted in an unlimited tar and soot accumulation. The minimum air supply required to reach a steady state actually coincided with the optimal operation air supply. S12
This means that, if 100 % of tar and soot could be recirculated, one would operate the gasifier very close to the critical unsteady state. For the case with 10 wt% fuel water content and 100 % recirculation efficiency, the change from non-steady to steady state is illustrated in Figures S5 to S7. While = 0.39 results in a temperature drop below 500 C and unlimited toluene accumulation, = 0.40 and = 0.41 approach a steady state during continuous recirculation. = 0.39 = 0.40 = 0.41 fluidised bed temperature [ C] 1000 900 800 700 600 500 0 20 40 60 80 100 recirculation iteration Figure S5: Bed temperature development during continuous recirculation, case with 10 wt% fuel water content and 100 % recirculation efficiency = 0.39 = 0.40 = 0.41 toluene concentration at P6 [g/m³ STP] 10 3 10 2 10 1 10 0 10 1 0 20 40 60 80 100 recirculation iteration Figure S6: Toluene flow at P6 during continuous recirculation, case with 10 wt% fuel water content and 100 % recirculation efficiency S13
naphthalene concentration at P6 [g/m³ STP] 80 60 40 20 = 0.39 = 0.40 = 0.41 0 0 20 40 60 80 100 recirculation iteration Figure S7: Naphthalene flow at P6 during continuous recirculation, case with 10 wt% fuel water content and 100 % recirculation efficiency References (S1) Kunii, D.; Levenspiel, O. Fluidization engineering, 2nd ed.; Butterworth-Heinemann: Boston, 1991. (S2) Oka, S. N. Fluidized bed combustion; Marcel Dekker: New York, Basel, 2004. (S3) Aerov, M. E.; Todes, O. M. Hydraulic and Thermal Principles of the Operation of Apparatus with Stationary and Fluidised Granular Beds (in Russian); Khimiya: Saint Petersburg, 1968. (S4) VDI heat atlas, 2nd ed.; Springer: Berlin, Heidelberg, 2010. (S5) Tepper, H. Zur Vergasung von Rest- und Abfallholz in Wirbelschichtreaktoren für dezentrale Energieversorgungsanlagen. Ph.D. thesis, Otto von Guericke University Magdeburg (Germany), 2005. S14
(S6) Darton, R. C.; LaNauze, R. D.; Davidson, J. F.; Harrison, D. Bubble growth due to coalescence in fluidised beds. Transactions of the Institution of Chemical Engineers 1977, 55, 274 280. (S7) Wen, C. Y.; Chen, L. H. Fluidized bed freeboard phenomena: entrainment and elutriation. AIChE Journal 1982, 28, 117 128. (S8) Schuh, M.; Schuler, C.; Humphrey, J. Numerical Calculation of Particle-Laden Flows Past Tubes. AIChE Journal 1989, 35, 466 480. S15