Fuel 107 (2013) 419–431 Contents lists available at SciVerse ScienceDirect Fuel journal homepage: www.elsevier.com/locate/fuel Estimation of gas composition and char conversion in a fluidized bed biomass gasifier A Gómez-Barea a,⇑, B Leckner b a b Bioenergy Group, Chemical and Environmental Engineering Department, Escuela Superior de Ingenieros, University of Seville, Camino de los Descubrimientos s/n, 41092 Seville, Spain Department of Energy and Environment, Chalmers University of Technology, S-412 96 Göteborg, Sweden h i g h l i g h t s " The model predicts gas composition and carbon conversion in biomass FB gasifiers " Correction of equilibrium is applied to improve the estimation of the gas composition " Kinetics models are applied to predict char, tar and methane conversion " Fluid-dynamics, entrainment and attrition are accounted for the calculation of char conversion " The model has predictive capability in contrast to available pseudo-equilibrium models a r t i c l e i n f o Article history: Received 14 August 2012 Received in revised form 17 September 2012 Accepted 27 September 2012 Available online 22 October 2012 Keywords: Gasification Fluidized-bed Biomass Model Char a b s t r a c t A method is presented to predict the conversion of biomass in a fluidized bed gasifier The model calculates the yields of CO, H2, CO2, N2, H2O, CH4, tar (represented by one single lump), and char, from fuel properties, reactor geometry and some kinetic data The equilibrium approach is taken as a frame for the gas-phase calculation, corrected by kinetic models to estimate the deviation of the conversion processes from equilibrium The yields of char, methane, and other gas species are estimated using devolatilization data from literature The secondary conversion of methane and tar, as well as the approach to equilibrium of the water–gas-shift reaction, are taken into account by simple kinetic models Char conversion is calculated accounting for chemical reaction, attrition and elutriation The model is compared with measurements from a 100 kWth bubbling fluidized bed gasifier, operating with different gasification agents A sensitivity analysis is conducted to establish the applicability of the model and to underline its advantages compared to existing quasi-equilibrium models Ó 2012 Elsevier Ltd All rights reserved Introduction Modeling and simulation of fluidized bed biomass gasifier (FBG) is a complex task Advanced models have been developed for bubbling [1–8] and circulating [9–11] FBG These models usually require physical and kinetic input, which is difficult to estimate and it is sometimes not available to industrial practitioners Simple and reliable tools to predict reactor performance with reasonable input are needed to support design and optimization Besides purely empirical models only valid for specific units, more universal approaches presented up to date have been based on gas phase equilibrium [12] Equilibrium models (EM) have been widely used because they are simple to apply and independent of gasifier design [13–15] However, under practical operating conditions in biomass gasifica⇑ Corresponding author Tel.: +34 95 4487223; fax: +34 95 4461775 E-mail address: agomezbarea@esi.us.es (A Gómez-Barea) 0016-2361/$ - see front matter Ó 2012 Elsevier Ltd All rights reserved http://dx.doi.org/10.1016/j.fuel.2012.09.084 tion, they overestimate the yields of H2 and CO, underestimate the yield of CO2, and predict a gas nearly free from CH4, tar, and char Despite these limitations, EM are widely used for preliminary estimation of gas composition in a process flowsheet However, EM are not accurate enough as tools for design, optimization, and scale-up of FBG units Quasi-equilibrium models (QEM) [16–22] improve the accuracy of the prediction of the gas composition The foundation of the QE approach was given by Gumz [16], who introduced the ‘‘quasiequilibrium temperature’’, an approach where the equilibrium of the reactions is evaluated at a lower temperature than that of the actual process The concept was applied for the simulation of a circulating FBG unit in the range of 740–910 °C [17] and for various pilot and commercial coal gasifiers [18] The approach is still applied, although the method is far from predictive Another type of QEM has been developed [14,20–22] for the simulation of biomass and coal gasifiers The essential idea of this approach was to reduce the input amounts of carbon and 420 A Gómez-Barea, B Leckner / Fuel 107 (2013) 419–431 Nomenclature A a cp c CkHlOm dch fWGSR E Fgp Ff,daf h, hf k K Katt Lb, Lfb m madd,b mc,p mc,b mch,b mch,b,crit mT,b M k, l, m n1, n2,m p Ql R Rg rc,ch rCỵH2 O rCỵCO2 T Th t u0 xi,j Xtar X CH4 Xch xadd xash,da xch,d xch,2 xch,3 xc,da xtar,d xCH4 ;d xH2 O;f xi,ga wi,f wc,b pre-exponential factor, 1/s decay coefficient, – specific heat, J KÀ1 kgÀ1 gas concentration, mol mÀ3 tar component average char particle diameter in the reactor, m coefficient of approach to WSGR equilibrium, – activation energy, kJ/mol gas yield, molgp/kgfuel(daf) flowrate of fuel, dry and ash-free (daf), kg/s specific enthalpy and enthalpy of formation, J/kg, kinetic coefficient, various units equilibrium constant, – attrition constant, – bed and freeboard heights, m mass, kg mass of additive/inert in the reactor, kg mass of carbon in a char particle, kg mass of carbon in the reactor, kg mass of char (carbon and fuel ash) in the reactor, kg critical value of mass of char in the reactor, kg mass of total inventory (additive and char) in the reactor, kg molecular mass, kg kmolÀ1 atoms in equivalent tar, C, H and O, – fragmentation coefficients in Eq (29) pressure, Pa specific rate of heat loss, W/kgfuel(daf) reaction rate, kmol mÀ3 sÀ1 universal constant of gases, J K molÀ1 overall reactivity of the char, sÀ1 intrinsic reactivity of carbon in char with H2O, sÀ1 intrinsic reactivity of carbon in char with CO2, sÀ1 temperature, K Throughput, kg/(m2 h) time, s superficial gas velocity, m sÀ1 mass of compound i in stream j per kgfuel(daf), kg/kg conversion of tar conversion of methane conversion of carbon in the char through the reactor mass of additive fed to the reactor per kgfuel(daf), kg/kg ash (non-carbon) in discharged ash (fly + bottom) per kgfuel(daf), kg/kg mass of char per kgfuel(daf) produced during fuel devolatilization, kg/kg mass of char in the bottom ash discharge (stream 2) per kgfuel(daf), kg/kg mass of char in the bottom fly ash (stream 3) per kgfuel(daf), kg/kg mass of carbon in discharged ash (fly + bottom) per kgfuel(daf), kg/kg mass tar per kgfuel(daf) produced during fuel devolatilization, kg/kg mass of methane per kgfuel(daf) produced during fuel devolatilization, kg/kg moisture (in fuel) per kgfuel(daf), kg/kg mass of i (i=O2, H2O, N2) in the gasification agent per kgfuel(daf), kg/kg mass fraction of the i-component (i = C, H, O, N, ash, m(iosture)) in the fuel, kg/kg mass fraction of carbon in the reactor, kg/kg hydrogen, fed to the control volume where the equilibrium is calculated The underlying reason for the reduction of the C–H–O in- wc,ch,b wc,ch,d wc,ch,2 wc,ch,3 wch,b,crit yi mass fraction of carbon in the char of the reactor, kg/kg mass fraction of carbon in the char after devolatilization, kg/kg mass fraction of carbon in the char of bottom ash discharge (stream 2), kg/kg mass fraction of carbon in the char of fly ash (stream 3), kg/kg critical value of the char mass fraction in the reactor, kg/ kg molar fractions of i in the produced gas, kmol/kmolgp Greek symbols r coefficient in Eq (29), – s residence time, s s2 rate constant of bottom ash discharged, s s3 rate constant of fly ash, s sR time constant of reaction (the inverse of reactivity of char sR = 1/rc,char), s u coefficient in Eq (29), – Subscripts standard conditions superficial (velocity) 2, bottom discharge, fly ash ash ash att attrition b bed, reactor C, H, O, N carbon, hydrogen, oxygen, nitrogen c carbon daf dry and ash-free ch char coar coarse particle fraction crit critical value d devolatilization da discharged ash df dry fuel f fuel, fin fine particle fraction ga gasification agent gp gas produced i, j indices mf minimum fluidization k, l, m atoms in equivalent (heavy) lumped tar p particle R reaction T total tar tar Abbreviations av average daf based on dry and ash-free substance CSTR continuous stirred tank reactor EM equilibrium model ER fuel equivalence ratio, – FBG fluidized biomass gasification (gasifier) LHV lower heating value (lower), J kgÀ1 na not available QEM quasi equilibrium model RZ reduction zone SBR steam to biomass ratio SRMR steam reforming of methane reaction WGSR water–gas-shift reaction put is that, under practical operation conditions in a gasifier, the conversion of tar, light hydrocarbons, especially methane, and char 421 A Gómez-Barea, B Leckner / Fuel 107 (2013) 419–431 are kinetically limited, and so they are controlled by non-equilibrium factors The interaction between the main four species in the bulk gas is determined by the rate of the water–gas-shift reaction (WGSR) This reaction can also be far from equilibrium, although the existing QEM have assumed it to be in equilibrium In the following, the main aspects of these conversion processes are discussed for biomass FBG:  The methane generated during devolatilization and primary conversion of gas and tar is very stable, and it is hardly affected by secondary conversion without Ni-based (or similar) catalysts at sufficiently high temperatures [22,23] Then, in intermediatetemperature gasification systems, i.e the typical situation in FBG of biomass, the amount of methane in the exit stream of the gasifier is roughly that formed by devolatilization of the fuel [22,24]  The attainment of equilibrium of WGSR has been analyzed in various gasification systems [15,22,23,25–29] The use of a synthetic catalyst allows the attainment of equilibrium above 750 °C [30] However, such catalysts are rarely used as bed material Mineral catalysts (dolomite, calcite, magnetite, olivine, etc.) are conventional bed materials, but their catalytic activity on WGSR (and also on tar reforming) is lower, and equilibrium is not generally attained at the usual temperature in biomass FBG, i.e below 900 °C, with sand or similar (bauxite, alumina, ofite) The residence time of the gas also plays a substantial role, and this can differ between the units Moreover, the real contact time with a catalyst in a FBG is usually lower than the residence time calculated using the superficial velocity of the gas The reason is that fluid-dynamic factors affect the performance of FBG, such as poor contact of gas and solid caused by the bypass of gas through the bubbles or the plumes generated during devolatilization These factors also affect other reactions in the bed, for instance, hydrocarbon reforming  The conversion of char is the most decisive factor in FBG, because the main loss of efficiency is due to unconverted carbon in the ashes The time for char conversion in an FBG is limited by entrainment and extraction of solids (if applied) Then the rate of char gasification has to be fast enough for the char to be converted during practical operation, mainly by reactions with H2O and CO2 The small amount of O2 added to the gasifier combines more rapidly with volatiles than with char It is concluded that to determine the extent of char conversion in an FBG, all these processes have to be taken into account Due to the complications discussed, the QEM are usually applied together with experimental correlations obtained for the specific system under analysis [14,20,21] Applied in this way, QEM refine the estimation of the gas phase composition compared to pure EM, but the prediction capability is limited It was attempted to overcome this inconvenience by developing a general method for the estimation of the gas composition, based on three parameters: carbon conversion, methane yield during devolatilization, and conversion of methane by steam reforming [22] Gross recommendations were given [22] for the values of the three parameters based on practical considerations: temperature, type of catalyst, and gasification agent The recommendations are useful for the evaluation, for a given fuel, of the gas composition resulting from various gasification methods (air vs steam-oxygen, catalyzed vs non-catalyzed) However, the method is not generally useful to analyze the performance of a given FBG under different operating conditions, like the change of flowrates of biomass and gasification agent, topology of the gasifier, etc The reason is that the three parameters are sensitive to the reactivity of fuel, gas velocity, and temperature in the gasifier Moreover, the distribution of the main species in the gas, CO, H2, CO2, and H2O, is governed by the rate of WGSR, a reaction which rarely attains equilibrium in biomass FBG The objective of the present work is to develop a model, taking advantage of the simple framework of QEM, but expanding their predictive capability There are three requisites: (i) to allow estimation of gas composition and solid fuel (char) conversion; (ii) to capture the effect of changes in operating conditions on the FBG performance, including velocity of the gas and the main geometry of the reactor, and therefore, to be useful for design, optimization and scale-up; and (iii) to be simple enough for implementation in flowsheet simulations, needing limited input, obtained by reasonable effort Below, the validity of such a model compared to existing QEM is discussed, underlining the advantages of the present development Model development 2.1 Model approach The process is simplified by decoupling primary (devolatilization) and secondary conversion, considering the different rates of these processes [31] Volatiles and char are assumed to be well mixed in the isothermal reactor Although sharp gradients in species concentration are observed in most FBGs [3], this occurs locally where the oxygen and fuel are injected (feed ports and gas distributor) As a result, most of the reactor remains with quasi-constant concentration, making the simplification of constant temperature and concentration reasonable The residence time of volatiles depends on the flows of the biomass and gasification agent and the geometry of the reactor, whereas the residence time of char particles also depends on the rate of removal by entrainment (mainly governed by gas velocity) and bed extraction applied to maintain smooth operation Fig presents the model concept The gas species and char are released where the fuel is devolatilized The yield of species from devolatilization depends on fuel, temperature, and heating rate and can be estimated empirically [28,32] The main yields concerned in the present model are methane, tar and char, xCH4 ;d , xtar,d and xch,d, (see Fig 1) Other species (CO, H2O, H2 and CO2) are also considered for the estimation of WGSR conversion, but only a Discharged ashes Produced gas OVERALL MASS AND HEAT BALANCE, PSEUDO-EQUILIBRIUM IN THE GAS PHASE xCH ,gp WGSR FACTOR ( f WGSR ) xchar ,gp xtar ,gp METHANE CONVERSION CHAR GASIFICATION TAR CONVERSION ( X CH ) ( X char ) ( X tar ) xCH ,d xchar ,d DEVOLATILIZATION GASIFICATION AGENT FUEL Fig Scheme of the model xtar ,d 422 A Gómez-Barea, B Leckner / Fuel 107 (2013) 419–431 rough estimate is sufficient for the present development, as explained below The devolatilization yield is the source for the subsequent conversion in the reduction zone (RZ), represented by the dashed line in Fig 1, where there is no oxygen left In fact, the devolatilization box in Fig.1 also includes the reactions of volatiles (mainly H2 and CO) with oxygen Therefore this zone is sometimes called flaming pyrolysis zone [31] In the RZ H2O and CO2 react with the char, the methane is converted by steam reforming, and the tar by reforming/cracking The main compounds in the gas phase react through the WGSR The conversions of the tar, methane, and char in RZ are Xtar, X CH4 , and Xch The factor fWGSR is the ratio of the actual coefficient K exp ¼ yCO2 yH2 =ðyCO yH2 O ) and that of equilibrium KWGSR, y being molar fraction in the gas The kinetics of WGSR are taken into account to calculate Kexp Once the four parameters Xtar, X CH4 , Xch, and fWGSR are estimated, the gas composition is evaluated by a pseudo-equilibrium model (thick solid line in Fig 1) The composition of the final (outlet) gas is obtained by the overall atomic mass and heat balance over the entire gasier 2.2 Model formulation wN2 ;f ỵ xN2 ;ga ẳ yN2 M N2 F gp wC;f ỵ wH;f ỵ wO;f ỵ wN;f ỵ wash;f ỵ wH2 O;f ỵ xO2 ;ga ỵ xH2 O;ga ỵ xN2 ;ga ỵ xadd |{z} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Gasification agentðO2 ;H2 O and N2 Þ Additive   ! MCO yCO ỵ MH2 yH2 ỵ MH2 O yH2 O ỵ MCO2 yCO2 ỵ M CH4 yCH4 þ MN2 yN2 þ MCk Hl Om yCk Hl Om F gp ỵxash;da ỵ xc;da |{z} |{z} Gas produced discharged ash All quantities in Eq (1) are in kg/kgfuel(daf) wi,f represents the mass fraction of the ith component in the dry ash-free fuel (daf), whereas xi,j is the mass of i flowing in or out in stream j of the system per kg fuel (daf) The gasification agent (‘ga’) is in general composed of oxygen, xO2 ;ga , steam, xH2 O;ga , and nitrogen, xN2 ;ga yi and Mi are the molar fraction of the species i in the produced gas (molei/molegp) and its molecular mass The gas yield (molegp/kgfuel(daf)) is Fgp The additive, xadd, can be a catalyst, sand or any material fed to the system for the improvement of the gasification performance The char is assumed to comprise the inorganic material from the fuel and unconverted carbon; small contents of hydrogen and oxygen in the char are neglected Then, discharged ash (‘da’) contains unconverted carbon in the char xc,da and ash xash,da, this latter consists of the ash from the fuel and bed material removed from the bed The discharged ash in Eq (1) includes both fly and bottom ash The tar component is given by the species CkHlOm, which can be estimated [33,34] The entire quantity of the nitrogen supplied (from the fluidisation agent and the biomass) is assumed to be released as N2 The oxygen demand will be characterized by the oxygen equivalence ratio, ER, defined as the amount of oxygen supplied to the gasifier over the oxygen required for stoichiometric combustion xO2 ;ga À 32 ỵ wH;f =4wC;f ị wO;f =32wC;f Þ ð2Þ The atomic CHON balances applied to Eq (1) are: wC;f ẳ yCO ỵ yCO2 ỵ yCH4 ỵ kytar ịM C F gp ỵ xc;da wH2 ;f ỵ 6ị whereas the ash balance is: wash;f ỵ xadd ẳ xash;da ð7Þ 2.2.2 Equilibrium of the modified gas-phase (QEM) The composition of a gas in pseudo-equilibrium is calculated according to Jand et al [22] Three quantities (Fig 1) are subtracted from the product gas to attain the equilibrium: methane, tar, and carbon (xCH4 ;gp , xtar,gp, and xc,da) calculated as Methane removed ¼ unconverted methane ¼ xCH4 ;gp ¼ xCH4 ;d X CH4 ị ẳ xtar;d X tar Þ ð8Þ ð3Þ   Á M H2 À wH2 O;f ỵ xH2 O;ga ẳ yH2 O ỵ yH2 ỵ 2yCH4 ỵ ytar M H2 F gp M H2 O 4ị 9ị Carbon in char removed ẳ unconverted carbon in char ¼ xc;da ¼ xc;ch;d ð1 À X ch Þ ð10Þ where X CH4 , Xtar, and Xch are the methane, tar, and char conversions in the RZ and xCH4 ;d , xtar,d, and xc,ch,d the corresponding yields of these compounds after devolatilization of the fuel Then, the CHON balances for the pseudo-equilibrium calculation of the gas phase, corresponding to Eqs (3)–(6), are: wC;f À xc;da À xtar;gp k 1ị ER ẳ 5ị Tar removed ẳ unconverted carbon in tar ¼ xtar;gp 2.2.1 Overall atomic balances The models for the estimation of the parameters (Xtar, X CH4 , Xch and fWGSR), as well as the yields xCH4 ;d xch,d, and xtar,d and other species from fuel devolatilization are presented in the following The fuel conversion in the gasifier related to kg of dry, ash-free fuel (daf) (1 kgdaf = wC,f + wH,f + wO,f + wN,f) can be written as (fuel + gasification agent + additive = gas produced + discharged ash): kg fuel daf M O2 wH2 O;f ỵ xH2 O;ga þ xO2 ;ga M H2 O   1 k yCO ỵ yCO2 ỵ yH2 O ỵ ytar M O2 F gp ¼ 2 wO2 ;f þ MC MC À xCH4 ;gp M tar MCH4 ¼ yCO ỵ yCO2 ỵ yCH4 ịM C F gp 11ị Á M H2 À ‘ M H2 M H2 wH2 O;f ỵ xH2 O;ga xtar;gp xCH4 ;gp 2 M tar M H2 O M CH4   ẳ yH2 O ỵ yH2 ỵ 2yCH4 M H2 F gp 12ị wH2 ;f ỵ M O2 m M O2 wH2 O;f ỵ xH2 O;ga ỵ xO2 ;ga À xtar;gp M H2 O M tar   1 ẳ y ỵ yCO2 ỵ yH2 O MO2 F gp CO wO2 ;f ỵ wN2 ;f ỵ xN2 ;ga ẳ yN2 MN2 F gp ð13Þ ð14Þ The equilibrium equations for the WGSR and SRMR (steam reforming of methane) are:    yH2 yCO2 4094 ¼ fWGSR Á 0:029 exp T yH2 O yCO y3H2 yCO yCH4 yH2 O    28116 ¼ 6:14  1013 exp À T ð15Þ ð16Þ where the terms within brackets on the right-hand side of Eqs (15) and (16) are the equilibrium constants of WGSR and SRMR [31] fWGSR is the factor that measures the approach to equilibrium of the WGSR, obtained by taking into account the kinetics as explained below To replace the contribution of methane and tar removed from the gas (Eqs (8) and (9)) in the pseudo-equilibrium calculations, a fictitious inert gaseous compound is considered [22], given by xCH4 ;d ð1 À X CH4 ị=M CH4 ỵ xtar;d X tar ị=Mtar (kmol inert/kgfuel(daf)) 423 A Gómez-Barea, B Leckner / Fuel 107 (2013) 419–431 Eqs (11)–(16) are solved for a given temperature and parameters (Xtar, X CH4 , Xch, xCH4 ;d , xtar,d, and xc,ch,d and fWGSR) yielding the composition of the pseudo-gas (yi): yCO, yH2 ; yCO2 ; yN2 ; yH2 O and yCH4 Then, the composition of the final outlet gas is obtained by restoring the amount of methane (xCH4 ;gp calculated from Eq (8)), and tar (xtar,gp calculated from Eq (9)) previously subtracted 2.2.3 Overall heat balance Once the gas composition of the outlet gas and the amount of unconverted fuel (xc,da and xash,da) have been calculated by the kinetic model described below, an energy balance over the gasifier yields for kg fuel: hf ;df ỵ Z T f ;in T0 cp;df dT ỵ wH2 O;f hf ;H2 Olị ỵ xH2 O;ga hf ;H2 Ogị ỵ xN2 ;ga hf ;N2 ỵ xO2 ;ga hf ;O2 ẳ F gp Z X yi hf ;gp;i ỵ xc;da hf ;c þ xash;da Tb cp;ash;da dT þ Q l ð17Þ T0 i¼1 The enthalpy of formation of the dry fuel hf,df, char hf,c, and tar hf,gp,tar, are calculated from their heating values The heating value of the fuel is the input from an analysis, while the heating value of char and tar are estimated from Ref [34] 2.2.4 Kinetic models for secondary conversion of gas Methane and tar conversions are calculated assuming perfect mixing of the gas in the bed and freeboard (CSTR) and first order kinetics Xi ¼ ki si i ẳ CH4 ; tar ỵ ki si 18ị The kinetics of the methane and tar reactions have been discussed in [31] The selected kinetic parameters for the two reactions are presented in Table The kinetics for the methane is that for homogeneous conversion and it has been considered pseudo-first order reaction by lumping a typical steam concentration into the kinetics coefficient The methane conversion below 1000 °C is very low so this simplification is quite insignificant If a catalyst is added to the bed, the rate should be modified to account for its influence The conversion of tar compounds is a complex process, still to be addressed in its details The objective of modeling tar decomposition in the present work is to give rough estimates of tar concentration in the gas, with the purpose of capturing the effects in the change of operation conditions of FBG The tar concentration in the outlet gas of an FBG is small compared to other components CO, and CH4, etc Although tar in the gas is a decisive issue for the utilization of the gas, its effect on the mass balance is not significant The effect of tar concentration on the heat balance could have some significance due to its high energy density Here the kinetics of Baumlin et al [35] are taken to represent the overall tar decomposition of an lumped tar in a CSTR If an active catalyst is present this kinetics should be changed to account for the impact of the bed material on tar decomposition The kinetics of WGSR have been measured [36] both for the homogeneous case and for various bed materials used in FBG The kinetics obtained were similar to those usually applied in modeling gasifiers [37], but they differ from others [38] The kinetic expressions and related parameters are presented in Table Note that for the estimation of methane and tar conversion (Eq (18)), the initial yields of methane and tar from devolatilization not need to be known as a consequence of the 1st order reactions For WGSR, however, the amounts of CO, H2O, H2 and CO2 entering RZ are needed, since the kinetics correspond to a reversible reaction (Table 1) The gas residence time is that of the total flow of gas in the bed and freeboard of the specific geometry considered (diameter and height) 2.2.5 Char conversion model Fig outlines the main input and output streams in the reactor (using quantities x, which are mass flowrate per kilogram of daf) The control volume is represented by the dashed line The fuel decomposes into char and volatiles during devolatilization, and these are the inputs to the control volume together with added material xadd The volatiles, fluidization agent, and produced gas interact with the solids, resulting in a temperature, a gas composition, and a gas velocity in the reactor The normalized flowrates of solids x are those of the additives (add) and char (ch) The solids enter the control volume (d) and leave as bottom ash (2) and fly ash (3) wc,ch,d and wc,ch,b are the carbon (c) contents in the entering char (ch) stream and in the char found in the bed (b) The solids are assumed to be perfectly mixed in the reactor so wc,ch,2 = wc,ch,3 = wc,ch,b as indicated in Fig The normalized mass flowrate of char leaving the reactor is then xch,2 + xch,3 = xch,da = xc,da + xash,da, and the corresponding normalized flowrate of carbon is xc,da=(xch,2 + xch,3)wc,ch,b (carbon is exiting the system in the solids of streams and 3, where the char particles have the same composition as the bed, wc,ch,b) Similarly, the ash balance is xash,da=(xch,2 + xch,3)(1 À wc,ch,b) + xadd Under steady state conditions a constant mass of char inventory mch,b (fuel ash and carbon) and carbon mc,b = mch,bwc,ch,b remain in the bed, constituting the char and carbon load Note the difference Table Kinetics of gas (methane reforming, tar thermal decomposition and WGSR) and char reactions (with H2O and CO2) Reaction Stoichiometry Kinetic expression Methane reforming CH4 ỵ H2 O ! CO ỵ 3H2 RCH4 ¼ kcCH4 cH2 O (kmol mÀ3 sÀ1) ÀE=Rg T k ¼ Ae A = 3.00  108 m3 kmolÀ1 sÀ1 E = 125 kJ molÀ1 [39] Thermal decomposition Tar ? lighter gas Rtar ¼ k ctar (kmol mÀ3 sÀ1) k ¼ AeÀE=RT A = 1.93  103 sÀ1 E = 59 kJ molÀ1 [35] RCO ¼ ki ðcCO2 cH2 À K e cCO cH2 O Þ (kmol mÀ3 sÀ1) ki ẳ AeE=Rg T [36] WGSR kd CO ỵ H2 O ¢ CO2 H2 Kinetics parameters Ref ki A = 1.41  105 m3 kmolÀ1 sÀ1 E = 54.2 kJ molÀ1 K e ẳ 0:029 exp4094=Tị Gasication C ỵ CO2 ! 2CO À1 r C—CO2 ¼ k p0:38 CO2 (s ) k ¼ AeÀE=Rg T A = 3.1  106 sÀ1 bar0.38 E = 215 kJ mol1 [40] Gasication C ỵ H2 O ! CO ỵ H2 r CH2 O ¼ k p0:57 H2 O (s ) k ¼ AeÀE=Rg T A = 2.6  108 sÀ1 barÀ0.57 E = 237 kJ molÀ1 [41] 424 A Gómez-Barea, B Leckner / Fuel 107 (2013) 419–431 reactor dch, is estimated from the fuel size, taking into account shrinkage, fragmentation and reaction as detailed below Eqs (21) and (22) allow the determination of s and wc,ch,b for given s2, s3 and sR The overall carbon (char) conversion in the reactor is obtained by applying a balance of carbon, i.e (carbon in – carbon out)/carbon in) to give: X ch ¼ À (a) (b) Fig (a) Control volume for the char conversion model with the main gas and solids streams (b) Solids balance in the control volume: Inlet solids stream (index d) comprises char generated after devolatilization and additive; Outlet solids streams are: extraction or bottom ash (index 2) and elutriation or fly ash (index 3) between the mass fraction of carbon in the char remaining in the bed, wc,ch,b, and that in the whole bed, which includes also the inert additives, wc,b = mc,b/mT,b = wch,bwc,ch,b The total mass of bed material (inert/additive and char) in the reactor is mT,b = mch,b + madd,b The char load at steady state depends on the char reactivity and the residence time of the char particles in the bed The main operation variables in the reactor are indicated in the figure: temperature T, superficial velocity u0, and the partial pressures pCO2 and pH2 O of CO2 and H2O A balance of char and carbon in the control volume of Fig 2b gives (in = out + reacted): xch;d ẳ xch;2 ỵ xch;3 ỵ xR 19ị xch;d wc;ch;d ẳ xch;2 ỵ xch;3 ịwc;ch;b ỵ xR ð20Þ where xR=(rc,chmc,b)/Ff,daf is the normalized rate of reaction of the carbon in the char (kg carbon reacted in the char/kgfuel,daf) By defining the residence time of char in the reactor as s = mch,b/(xch,dFf,daf) and s2 and s3 as the time constants of removal of solids material from the reactor by extraction s2 = mT,b/(x2Ff,daf) and elutriation, s3 = mT,b/(x3Ff,daf) (1/s2 and 1/s3 are the constant rates of solids removal), Eqs (19) and (20) can be solved for the two unknowns s and wc,ch,b: s¼   wc;ch;d =sR 1=s2 ỵ 1=s3 ị 1=s2 ỵ 1=s3 ỵ 1=sR ị wc;ch;b ẳ 1=s2 ỵ 1=s3 ịwc;ch;d 1=s2 ỵ 1=s3 ỵ wc;ch;d ị=sR ị 21ị 22ị where the char conversion time sR is the inverse of the reactivity of the char sR = 1/rc,ch, the latter defined as rc,ch=(1/mc,p)dmc,p/dt where mc,p is the mass of carbon in a char particle in the bed The intrinsic reactivities of biomass char with CO2 and H2O, used for the simulation presented in Section 3, are given in Table For other chars (from other fuels) the intrinsic reactivity has to be changed consistently The reactivity of a single particle, taking into account diffusion, is obtained by a simple model [31] where two effectiveness factors are calculated for a char particle of size dch in a gas at a temperature T and pressures pCO2 and pH2 O (with two coupled equations) The effective diffusivity and mass transfer coefficient, necessary for the char-particle model, are estimated by a correlation sensitive to the operating conditions (velocity, temperature, size of char, etc.) [31] The size of the average char particle in the wc;ch;b wc;ch;d  s s ỵ s2 s3  23ị wc,ch,d is given as input (or estimated as explained below), and the reactivity of the char (and so sR) is calculated as a function of the conditions in the reactor (T, pCO2 and pH2 O ) with the expressions given in Table s3 is calculated by the elutriation model presented below Various operation modes can be applied to remove bed material by bed extraction: (i) the extraction of material is adjusted to a given rate (an overflow or bottom pipe continuously removes material from the bed, or it is adjusted by a given sequence) Then s2 is known, and Eqs (21)–(23) can be directly applied to obtain the solution (ii) the char content in the bed mch,b is maintained to some prescribed value mch,b,crit in relation to the total inventory of the bed, mT,b, for instance to avoid accumulation of ash in the bed; Then s2 has to be calculated to control the bed at wch,b,crit = mch,b,crit/mT,b In such a case s is known (s = scrit = mch,b,crit/(xch,dFf,daf)) and Eqs (21)–(23) can be solved for wc,ch,b and s2 to give: wc;ch;b ẳ ỵ sR =scrit ị=2 ỵ 1=41 þ sR =scrit Þ2 À wc;ch;d s3 =scrit Þ1=2 s2 ¼ ð24Þ ð1=scrit À 1=s3 À wc;ch;b =sR Þ ð25Þ In some cases the system can operate safely at s < scrit because s3 is high enough to entrain the ash at sufficient rate to maintain the required condition In such a case 1/s2 = 0, and Eqs (24) and (25) are used Alternatively, Eqs (21)–(23) can be used directly with 1/s2 = Finally, the flowrate of the inert solids, necessary to maintain the inventory during operation, can be calculated by an overall mass balance, Eq (7): xadd ¼ mT;b F f ;daf     wc;b 1 ỵ ỵ wc;ch;b sR s s2 s3 ð26Þ In operation with low-ash fuel, such as wood, there is no bed extraction (1/s2 = 0) during a long time, so the material in the reactor is not strictly maintained steady (there is only a single value of s3 that makes xadd in Eq (26) zero for given input), but the accumulation (or loss) is slow and the system is operated in a quasi-steady manner To calculate s3 (i.e., x3) an elutriation model is applied [42] Two types of char particle are elutriated: coarse particles (xch,coar,3) generated after devolatilization and fragmentation, and fines (xch,fin,3) produced by abrasion of char in the bed Particles are carried away in the fly-ash stream x3 = xch,3 + xadd,3 with xch,3 = xch,coar,3 + xch,fin,3 xadd,3 is calculated similar to char but applying the density, size and attrition constant of the additive In the following, the case of char is explained, since the impact of inert material in x3 is negligible in steady state operation of bubbling FBG provided that the size of additive particles are large enough, i.e xadd,3 ( xch,3 Fines are assumed to be produced by attrition at a rate [43,44], xch;fin;3 ¼ K att mch;b ðu0 À umf Þ F f ;daf dch ð27Þ Katt is the dimensionless attrition constant, determined experimentally for a variety of chars and solids, ranging from  10À7 and  10À8 for various biomasses [43] dch is the average particle size of the coarse char in the reactor, calculated below, and umf is the A Gómez-Barea, B Leckner / Fuel 107 (2013) 419–431 minimum fluidization velocity corresponding to that average size The fines are assumed to be elutriated immediately as they are produced, and their conversion along the reactor is small; it takes just a few seconds for the gas to carry them away The coarse particles can be converted or elutriated depending on their size, dch, and operating conditions (mainly velocity) To calculate Fch,coar,3 a fluid-dynamic model of the FBG is solved to give xch;coar;3 ẳ xch;1 ỵ xch;b xch;1 Þ expðÀaðLfb À Lb ÞÞ ð28Þ Lb and Lfb are the height of the dense bed and the freeboard, xch,b is the entrainment flux of coarse char particles at the surface of the dense bed [45], xch,1 is the particle flux of coarse char in an imaginary long column, whose height is higher than the transport disengaging height, calculated by applying the correlation in [46] and a is the decay coefficient [47] In general, population balances on the particle sizes in the bed are necessary for precise evaluation of the processes In this work, however, an approximate method estimates dch as a function of fuel particle size df [42,48], dch % df rðu=ðn1 n2;m ÞÞ1=3 ð29Þ n1, n2m, u being parameters related with shrinkage and fragmentation of the fuel in a fluidized bed [48] In summary, x3 in s3 is calculated by x3 = xch,3 + xadd,3 where xch,3 = xch,coar,3 + xch,fin,3 xch,coar,3 is calculated by Eq (28) and xch,fin,3 by Eq (27) Similar equations are used for the additive Most of the fluid-dynamics correlations used for the solution of Eqs (27) and (28) are valid for both bubbling and circulating FB and the two types only need to be distinguished in some details [31] 425 empirical models [32,34], or by rough estimation like the one given in the following Here we have demonstrated that the exact evaluation of these yields does not significantly improve the estimation of the gas phase composition, so the following typical values can be assigned for the yields (kg/kgdaf): 0.15 for CO, 0.20 for CO2, 0.02 for H2 and 0.10 for H2O 2.3 Solution procedure The main steps to solve the model are summarized in the following: Introduction of inputs: – Geometry: internal diameter and height of bed and freeboard Total bed inventory in the reactor, or pressure drop – Fuel: Composition (elemental and ultimate analyses) and calorific value – Flow rates of biomass and gasification agent Alternatively, the model can be specified with gas velocity and temperature, from which the flowrate of the gasification agent is obtained once the iteration is finished – In Step (see below) some dedicated inputs are required The reactor temperature, flowrate and gas composition of the produced gas, gas velocity in the bed and freeboard, are assumed as guess for the first iteration (Steps 3–7, below) The conversions of methane, tar, and char are calculated, as well as the factor of approaching the equilibrium of WGSR by applying the kinetic models indicated in Sections 2.2.4 (tar, methane, and WGSR) and Section 2.2.5 (char) For the kinetic models various additional inputs are required: 2.2.6 Estimation of devolatilization yields The yield of devolatilization (xch,d, xCH4 ;d , xtar,d, xCO,d, xCO2 ;d ; xH2 ;d ; xH2 O;d ) is ideally estimated for fluidized bed conditions (fuel and temperature) similar to that to be modeled Such data have been obtained for different fuels, providing correlations as a function of temperature [28] When the yield cannot be determined experimentally, data from compilations can be taken, searching for similar fuel and operating conditions [32] The following can be generally applied: The char yield xch,d can be taken from the proximate analysis of the fuel with reasonable accuracy, since its variation with temperature and heating rate is small [28] The yield of methane xCH4 ;d depends on fuel but is in the range of 50–80 g/kgdaf for most biomass species devolatilized in FB even under quite different conditions [22] The yield of tar xtar,d can be assumed to be between 0.15 and 0.20 kgtar/kgdaf a range which is consistent with the model of tar conversion presented above This treatment is enough for the present model because the solution is not much sensitive to the actual tar concentration in the gas due to its low concentration in the produced gas of FBG, but the value chosen may be sensitive to different operating conditions For the calculation of WGSR, the yields of CO, CO2, H2 and H2O (xCO,d, xCO2 ;d ; xH2 ;d ; xH2 O;d ) have to be estimated (see the kinetic expression in Table 1) The yield of devolatilization, followed by partial combustion of the fuel gas with the O2 fed to the gasifier, is considered, following the treatment of Wang [49] This is made, knowing that O2 will be consumed rapidly, mainly by H2 and CO yielding CO2 and H2O [49] and very little char and methane are burned owing to the low combustion rates in the gasifier Instead of calculating the competition between H2 and CO for the O2, it is assumed that H2 is consumed first, because of its higher combustion rate compared to CO [31], yielding H2O, and the remaining O2 combines with CO to give CO2 The yields of CO, CO2, O2 and H2O from devolatilization of a given fuel can be estimated from correlations as a function of temperature [28], by simple pseudo- – The devolatilization yields (xch,d, xCH4 ;d , xtar,d, xCO,d, xCO2 ;d ; xH2 ;d ; xH2O;d ): these are taken as input in the form of correlations (for instance as a function of temperature) or by estimations from literature for the same fuel and operating conditions, or by the gross recommendation made in Section 2.2.6 – Size and density of fuel and additive – The kinetics of steam reforming, tar conversion, WGSR, and reactivity of char (Table 1) The former may depend on the additive used in the bed and the reactivity has to be selected for the fuel/char to be modeled – Input to the char conversion model (attrition constant, Katt, fragmentation parameters, n1 and n2m) Other parameters for the fluid-dynamic model, such as decay factor in the freeboard a, umf, are taken from the specified correlations for the properties of bed material and calculated char diameter in the bed, dch Calculation of CHO to be subtracted from QEM (Eqs (8)– (10)) Solution of QEM (Eqs (11)–(16)) for the calculation of the pseudo-gas phase (yi) Calculation of char xch,d(1 À Xch) and the bed material removed from the bed (entrainment or extraction) Then xc,da and xash,da are calculated Determination of the amount of methane (xCH4 ;gp in Eq (8)) and tar (xtar,gp in Eq (9)) to be restored to the gas phase With the gas and solids compositions in the outlet streams, the atomic balances (Eqs (3)–(6)) and the energy balance over the gasifier (Eq (17)) are solved to yield the actual gas phase composition (yi) and its temperature (the thermal losses are given as input, although this value can be determined easily) From this, the flowrate of gas produced and gas velocities in the bed and 426 A Gómez-Barea, B Leckner / Fuel 107 (2013) 419–431 freeboard are calculated The assumed values in Step are corrected, and the iterative process is repeated until convergence Results and discussion 3.1 Comparison of model with measurements The model developed has been compared with experiments conducted in a bubbling FBG with different gasification agents: air, air–steam, and oxygen-enriched air–steam The gasification agent was preheated to enter the reactor at 400 °C The fuel was wood pellets with the empirical formula CH1.4O0.64, (dry and free of ash) The moisture and ash contents were 6.3% and 0.5% (mass basis), and the lower heating value of the fuel (as received) was 17.1 MJ/kg The pellets were cylindrical with a mean diameter of mm and a height between and 10 mm The apparent density of a pellet was 1300 kg/m3, whereas the bulk density was 600 kg/m3 The bed material used in the FBG was ofite with density of 2650 kg/m3 and an average size of 290 lm Ultimate and elemental analyses as well as particle size distribution of the ofite are reported in [50] The main geometrical parameters of the FBG unit are: bed and freeboard diameters 150 and 250 mm; bed and freeboard heights 1500 and 3500 m The initial bed inventory in all tests was 12 kg, which was kept roughly constant by controlling the pressure drop across the bed The rig, test procedure, and analysis of results have been reported in detail in Refs [29,51] Other inputs needed for the simulations are the following: attrition and fragmentation parameters obtained from measurements in a lab-scale FB with wood pellets [28] and literature data for various biomasses [43] The inputs chosen for the simulations are: Katt =  10À7, n1 = 2, n2m = 3, and r = 0.8 The calculated shrinkage factor is u = 1.22, and the resulting average char particle size in the bed is dch = mm The tar component is given by the species CkHlOm with k = 6; l = 6.2; m = 0.2, estimated from [33,34] The estimated heating values of char and tar are 33 and 37 MJ/kg The char reactivity and other kinetics are given in Table Table presents the gas composition and other measured parameters together with those calculated by the model The model was run at the same temperatures as those measured in the experiments by adjusting the heat loss, which varied between 2% and 14% of the heating value of the fuel In all the tests, except in the first one, there was no mechanical extraction of material from the bed The factor fWGSR was evaluated by setting the temperature in the freeboard about 100 °C lower than that of the bed to represent the temperature drop measured in the experiments The gas composition was generally well predicted Especially, the model confirmed that the methane in the outlet gas is nearly that produced during devolatilization and calculated methane conversion was below 0.01% in all the tests This fact underlines the importance for the model of a good estimation of the methane yield from devolatilization The carbon in the gas phase is reasonably well predicted, although the distribution between CO and CO2 calculated by the model varies to some extent More importantly, the main changes during variations in the operating conditions were captured by the model The char conversion does not seem to agree too well with the two tests where it was measured Nevertheless, the measured values of char conversion reported in [29] have to be taken as rough estimates, since they were the average values calculated from the material collected in the cyclones after two or three tests conducted under different operating conditions The simulations show that the WGSR is far from equilibrium, with fWGSR ranging from 0.40 to 0.65 In all simulations, the rate of entrainment of coarse char was much smaller than that of attrition, i.e xch,coar,3 ( xch,fin,3 and x3 % xch,fin,3 The model was capable of predicting the distribution of the four main species (CO, CO2, and H2 and H2O) reasonably well, as assessed by inspection of CO, CO2, and H2 in the table (H2O was Table Comparison of model results with FB gasification tests from [29,51] Test Exp Mod Exp Mod Exp Mod Exp Mod Exp Mod Exp Flowrates Biomass (kg/h) Air (Nm3/h) Steam (kg/h) Pure oxygen (Nm3/h) 20.5 17.0 0 15.0 17.0 0 15.0 17.0 3.2 12.4 11.9 3.7 1.5 11.8 8.3 6.2 1.8 12 6.8 6.4 2.1 Representative parameters ER (kg O2fed/kg O2stoichiometric) SBR (kg steam/kg biomass) Throughput ðkg biomass=m2bed =hÞ 0.19 1160 0.27 848 0.27 0.23 850 0.36 0.32 701 0.34 0.56 667 0.33 0.57 679 Temperature and wall-heat loss Bed temperature (average) (°C) Freeboard temperature (average) (°C) Wall-heat loss (%LHVfuel) 780 687 na 2.5 805 718 na na 6.0 0.60 Gas phase outputs CO (%v/v, dry gas) H2 (%v/v, dry gas) CO2 (%v/v, dry gas) CH4 (%v/v, dry gas) N2 (%v/v, dry gas) H2O (%v/v, wet gas) Tar (g/Nm3, dry gas) LHV (MJ/Nm3, dry gas, no tar) 18.2 13.2 14.2 6.0 na na 25.8 5.9 Solid conversion outputs Carbon conversion (kg/kg) Char conversion (kg/kg) 0.87 0.65 Rate of ash removal Bottom discharged (kg/h) Fly ash elutriated (kg/h)) à 779 807 4.7 786 708 na na na 0.43 20.1 13.2 12.6 6.4 47.0 12.4 26.1 6.2 17.6 12.6 14.9 5.2 na na 23.8 5.4 0.81 0.52 0.88 0.65 787 5.2 808 715 na na 0.58 21.6 12.2 10.8 5.0 50.0 8.8 16.0 5.8 15.0 14.0 16.2 4.7 na na na 5.1 0.95 0.87 0.90 na 809 14 795 725 na na na 0.20 16.6 14.0 14.1 4.9 49.7 16.8 18.8 5.3 18.9 16.4 17.6 5.5 na na na 6.1 0.93 0.82 0.94 na 794 Mod 11 806 727 na 805 10 na na 0.22 na na 0.18 15.2 14.7 20.1 5.2 44.3 21.2 15.0 5.4 17.5 21.8 18.0 6.1 na na na 6.7 15.1 19.7 23.2 5.9 35.6 29.3 16.3 6.1 19.3 25.7 17.0 6.7 na na na 7.6 16.4 22.2 24.6 6.1 30.4 30.0 11.0 6.7 0.98 0.94 0.95 na 0.97 0.93 0.96 na 0.98 0.95 427 A Gómez-Barea, B Leckner / Fuel 107 (2013) 419–431 not measured in the experiments) Test was simulated with a bed discharge of kg/h Although the reported test is said to be without significant bed removal, the authors detected an accumulation of material in the bed during the tests, noted by the increase of pressure in the bed, so steady state conditions were not reached This is reasonable, since the throughput of Test was higher than in the rest of tests and higher than that usually attained in bubbling FBG (between 300 and 800 kg/(m2 h) The comparison is a positive proof of the prediction ability of the model However, detailed conclusions should be taken with caution because some key information from the measurements is not clearly reported, such as: char accumulation during the startup period, the run time of each test after steady state (in fact, steady state of the char load has to be reached, and in some test this is doubtful, as discussed above in relation to Test 1), the sequence of opening the bottom ash pipe for ash removal sometimes applied, the amount of fly ash collected, and its composition An attempt was made in [29,51] to minimize the heat loss during the tests in order to simulate industrial autothermal units, where the heat loss is small However, the simulation showed that the heat loss was significant and varied between the tests The most likely explanation is that steady-state operation was not completely achieved in some tests In such a case, the additional heat requirement is not a heat loss through external surfaces but additional heat required for heating up the material Due to the large size of the pilot gasifier and the limited gasification runtime, this amount of heat could be significant This aspect is common to most pilot and laboratory units As we demonstrate below by means of a sensitivity analysis of the model, this information is of concern for the simulation of the real experimental operation point 3.2 Sensitivity analysis and comparison with other QEM The model is used to analyze the performance of an FBG under different conditions Simulations are made for the same fuel as in the previous section The flowrate of biomass per unit of cross section of bed, the throughput Th kg/(m2 h) characterizes the operation of the unit, allowing scale-up of results to geometrically similar FBGs (freeboard height to bed diameter ratio and mass inventory/bed diameter) The pilot FBG analyzed in the previous X ch calculated with complete model Temperature (T), ºC 1000 Xch=0.25 0.50 900 850 0.75 800 1.00 750 700 650 600 0.2 ooo X ch 0.22 0.24 0.26 0.28 0.3 Gas lower heating value (LHV), MJ/Nm 1050 950 3.2.1 Effect of oxygen equivalence ratio (ER) and comparison with existing QEM The main reason for the development of the present model was the uncertainty caused by the assignment of an arbitrary value of char conversion Xch in the existing QEM [22] To study this aspect, Fig presents the temperature and heating value of the product gas as a function of equivalence ratio (ER) calculated with a QEM at various pre-assigned (not calculated) values of Xch Actually, the model developed here becomes a QEM by setting char, methane and tar conversion, as well as the convergence factor fWGSR, to prefixed values (not calculated as a function of process conditions) Under such conditions the model was used with X CH4 ¼ 0, Xtar = 1, and fWGSR = for various Xch, as shown in Fig The results reveal that the value assigned for Xch has a major effect on the temperature and the gas heating value, and therefore on other parameters like gas composition and cold gas efficiency The higher the char conversion, the lower the temperature of the reactor and the higher the heating value of the gas produced, because at higher conversion more heat is consumed due to the endothermicity of the char gasification reactions In other words, sensible energy from the gas is transformed into chemical energy in the gas (mainly into H2 and CO) The circle line in Fig shows the result from the present model without pre-assignment of char conversion, but keeping the other parameters at the same fixed values as used in the QEM: X CH4 ¼ 0, Xtar = 1, and fWGSR = 1) It is demonstrated that the char conversion varies significantly with the operating conditions (from about 0.5 at ER = 0.2 with a temperature around 730 °C, up to nearly at ER = 0.3, where the temperature is roughly 905 °C) The dashed–dotted line in Fig shows the result of the complete model, i.e with the calculation of all parameters Xch, X CH4 , Xtar and fWGSR as a function of operating conditions X CH4 , Xtar and fWGSR calculated with the model for ER varying from 0.2 to 0.3, range from 0.001 to 0.03, from 0.89 to 0.97, and from 0.7 to 0.8, respectively By comparison of dashed-dotted and circle lines in Fig it is 1100 section is taken as reference geometry The same fuel (wood pellets) and char reactivity and fragmentation parameters are chosen The gasification agent enters the reactor at 400 °C and the wall heat loss is 3% of LHV of the input fuel in all simulations below calculated with simplified model 7.5 6.5 5.5 0.2 1.00 0.75 0.50 X ch=0.25 0.22 0.24 0.26 0.28 Equivalence ratio (ER) Equivalence ratio (ER) (a) (b) 0.3 Fig Temperature and lower heating value of the gas produced as a function of equivalence ratio Solid lines were calculated with a QEM with X CH4 ¼ 0; Xtar = and fWGSR = 1, for various values of Xch, 0.25, 0.5, 0.75 and (each of the solid curves) The circle line curve was made with the present model calculating Xch as a function of process conditions, but with pre-assigned values of X CH4 , Xtar, and fWGSR, equal to those used in the QEM to calculate the solid lines (X CH4 ¼ 0; Xtar = and fWGSR = 1); the dashed–dotted curve is calculated by the complete model, i.e calculating all parameters Xch, X CH4 , Xtar and fWGSR as a function of process conditions 428 A Gómez-Barea, B Leckner / Fuel 107 (2013) 419–431 concluded that the influence of X CH4 and Xtar is not so significant, whereas the calculated fWGSR leads to visible differences in temperature (comparison between dashed line and circle line in Fig 3a), and, especially, in the heating value of the gas (Fig 3b) In Fig the corresponding char conversion and gas composition are shown, using the complete model The char conversion rises from 0.6 at ER = 0.2 (730 °C) to nearly at ER = 0.3 (905 °C) The molar fraction of CO in the gas presents a maximum at ER = 0.28 where the char is almost converted (carbon boundary point), whereas hydrogen decreases monotonically with ER While the available char decreases, the additional oxygen tends to burn the fuel gas, increasing the temperature and diminishing the heating value of the gas, as seen in the circle and dashed–dotted lines in Fig It is concluded that the most important parameter to be estimated is the char conversion Tar concentration in the gas is small and methane is not converted, so very little influence on the composition and thermal efficiency of the process is expected from the variation of these parameters around the pre-assigned values, and 0, respectively The approach to WGSR equilibrium changes the gas composition significantly, but its impact is less significant than that of char conversion Therefore QEM having a given char conversion has no prediction ability A char predictor inside the QEM is needed to capture the change of performance with operating conditions 3.2.2 Effect of throughput (Th) For the calculation of Fig (and the dashed–dotted lines in Fig 3), the present model was run with a throughput of 500 kg/ m2 h (in QEM the throughput does not influence the results, since QEM is not sensitive to the gas flow and other fluid-dynamic processes that affect the performance of the gasifier) The effect of the throughput is studied with the present model in Figs 5–7 The rise in Th (a higher fuel flowrate in the given gasifier) increases the gas velocity and so the rate of entrainment; the temperature and the reactivity increase, resulting in lower char load in the bed The gas velocity (in fact, u0 À umf) is roughly proportional to Th, so xch,3,fin increases through the term (u0 À umf) but decreases because mch,b is lower (see Eq (27)) Therefore, there are two competing effects The char conversion as a function of Th is plotted in Fig 5, where a weak minimum is observed in Xch at around 900 kg/m2 h at ER = 0.25 In contrast, the conversion decreases continuously with Th for ER = 0.30, but in both cases the change in Xch with Th 0.25 Molar fraction in wet gas (%v/v) Char conversion (Xch), kg/kg 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.2 0.22 0.24 0.26 0.28 CO 0.2 0.15 H2 CO2 0.1 H2O 0.05 CH 0.2 0.3 0.22 0.24 0.26 0.28 Equivalence ratio, ER Equivalence ratio (ER) (a) (b) 0.3 Fig Char conversion (a) and gas composition (b) calculated with the complete model as a function of ER for Th = 500 kg/m2 h (the corresponding temperature and LHV as a function of ER are those drawn as dashed-dotted lines of Fig 3) 0.906 Char conversion (Xchar), kg/kg Char conversion (X ch ), kg/kg ER=0.30 0.98 0.96 0.94 0.92 ER=0.25 0.9 0.88 300 400 500 600 700 800 Throughput (Th), kg/(m h) (a) 900 1000 0.904 0.902 0.9 0.898 0.896 0.894 0.892 ER=0.25 0.89 0.888 0.886 400 600 800 1000 1200 1400 Throughput (Th), kg/(m h) (b) Fig (a) Char conversion as a function of throughput for ER = 0.25 (—) and 0.30 (Á Á Á); (b) Detail of the case ER = 0.25 to visualize the minimum 429 960 ER=0.30 Temperature (T), ºC 940 920 900 880 860 840 820 ER=0.25 800 780 760 300 400 500 600 700 800 900 1000 0.25 2.5 wch,b 0.2 ER=0.25 wc,b 0.15 wch,b 0.1 0.05 ER=0.30 wc,b 300 400 500 600 700 800 900 1000 Throughput (kg/(m2h)) Throughput (Th), kg/(m2 h)) (a) (b) Char residence time (τ), h Mass fraction of char (wch,b ) and carbon (wc,b ) in the reactor, kg/kg A Gómez-Barea, B Leckner / Fuel 107 (2013) 419–431 ER=0.25 1.5 ER=0.30 0.5 300 400 500 600 700 800 900 1000 Throughput (Th), kg/(m h) (c) Fig Temperature (a), mass fraction of char and carbon in the bed (b), and residence time (c) as a function of throughput for ER = 0.25 (—) and 0.30 (Á Á Á) 0.25 Molar fraction in wet gas (%v/v) ER=0.25 0.2 ER=0.30 CO 0.15 0.1 H2 CO2 H 2O 0.05 CH 300 400 500 600 700 800 900 1000 Throughput (Th), kg/(m 2h) Fig Gas composition as a function of throughput for ER = 0.25 (—) and 0.30 (Á Á Á) Critical char mass fraction in the reactor (w ch,b,crit ), kg/kg 0.4 ER=0.2 0.3 0.2 0.25 0.1 0.30 0.05 0 0.5 1.5 -1 1/τ , h Fig Critical mass fraction of char in the bed, wch,b,crit , as a function of the constant rate of bottom ash discharge (1/s2) for various ER(0.20 (—), 0.25 (—) and 0.30 (Á Á Á)) For each ER two throughputs are displayed (Th = 500 (black) and 1000 (red) The horizontal dot–dashed line is wch,b,crit = 0.05 (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) is small The analysis is better understood by inspecting Fig 6, where the temperature (Fig 6a), mass fraction of char and carbon in the bed, wch,b and wc,b (Fig 6b), and residence time of the char, s (Fig 6c), are plotted as a function of throughput for the same conditions as in Fig Fig gives the corresponding main species in the gas during variation of Th, showing that CO and H2 decrease, whereas H2O and CO2 increase, leading to reduction of the efficiency of the processes at higher Th The small variation of char conversion with Th indicates that, for a given ER, a QEM could have been used to predict the gas composition with a constant value of char conversion for the whole range of Th However, the actual value of Xch to be used has to be calculated for each ER at least once with a model such as the one developed here The actual value depends much on the reactivity and physical characteristics of the char, such as attrition, and average size of char particle in the bed Therefore it is difficult to determine Xch without a char predictor, which is sensitive to operating conditions In addition, these conclusions are valid when 1/s2 is zero (no mechanical removal is applied) and where the bed is operated with large enough char particles to make the entrainment small compared to attrition In other cases the results may change drastically, as we will demonstrate below by allowing for variation of the rate of bottom ash discharge Once again, this conclusion supports the opinion that a char predictor inside a QEM tool is needed 3.2.3 Effect of rate of bottom ash discharge The above discussion was restricted to an FBG operating without extraction of bed material (1/s2 = 0) In this mode of operation only the elutriation of char (carbon loss in fly ash) limits the char conversion in the reactor This is the usual case during operation with low-ash fuel, such as wood However, when processing fuel with high ash content or when the ash contains impurities that can lead to sintering, control of bed inventory affects the char content in the gasifier by the removal of bottom ash at a constant rate given by 1/s2 This situation is analyzed in Figs 8–10 Fig shows the rate of solids removal 1/s2, which maintains the mass fraction of char in the bed at a value of wch,b,crit at different ER and Th The analysis in the figure is made for wch,b,crit > 0.05, a reasonable lower limit in practise 1/s2 = are the cases without bed removal, which were analyzed in previous figures It is observed that the mass fraction of char in the bed is higher at lower ER (lower temperature) and that the influence of ash extraction is higher for lower ER At a given ER, the rate of ash removal to maintain the bed below a limit wch,b,crit, is higher as the throughput increases, except for very low rates of removal (1/s2 ? 0) where this behavior is the opposite The corresponding char conversion, temperature and residence time of the char, as a function of the bottom-ash removal constant 430 A Gómez-Barea, B Leckner / Fuel 107 (2013) 419–431 1000 Char residence time (τ), h ER=0.30 950 0.8 Temperature (T), ºC Char conversion (Xch), kg/kg 0.25 0.6 0.4 0.2 0.2 900 ER=0.30 850 0.25 800 0.2 750 700 0.5 1/ τ2, h 1.5 0.5 -1 1/ τ2, h (a) 1.5 2.5 ER=0.20 1.5 0.25 0.5 0.30 -1 (b) 0.5 1/ τ2, h 1.5 -1 (c) Fig Char conversion (a), temperature (b) and char residence time (c) as a function of the constant rate of bottom ash discharge (1/s2) for various ER (0.20 (—), 0.25 (—) and 0.30 (Á Á Á)) For each ER, two throughputs are displayed: Th = 500 (black) and 1000 (red) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) conversion is not critical for the estimation of the main compounds in the produced gas in conventional FBG Though, a good estimate of the yield of methane during devolatilization is a key factor for the prediction of the methane in the produced gas The yield of methane varies with fuel type but not much with the operation conditions The conditions in the reactor, and thus the composition of the gas and the efficiency of the process, are greatly influenced when bottom ash is removed from the bed by bed extraction to maintain the ash proportion in the reactor below some specified limit As demonstrated, the model developed here is able to predict the changes in reactor performance with operating conditions Simple QEM with a given char conversion cannot be used for simulating FBG because they not have the prediction ability to capture these effects Molar fraction in wet gas (%v/v) 0.25 0.2 CO 0.15 H2 CO2 0.1 H 2O 0.05 CH4 0 0.5 1.5 Summary and conclusions -1 1/τ2, h Fig 10 Gas composition of main species in the gas as a function of the time constant of bottom ash removal, s2 for various Th = 500 kg/m2 h and ER = 0.25 rate 1/s2, are presented in Fig It is shown that the char conversion (Fig 9a) decreases with 1/s2 (more carbon is lost by removing more bed material) The temperature is seen to rise with 1/s2 up to a certain value of 1/s2, and then it falls (Fig 9b) The residence time of the char decreases significantly as the rate of bottom-ash removal is increased (Fig 9c), yielding lower char conversion, consistent with the conversion trend presented in Fig 9a The composition of the gas as a function of 1/s2 for given ER and Th is presented in Fig 10, revealing the great influence of the rate of bed extraction on the composition of the gas produced The amount of combustible gas is reduced a great deal with decrease of 1/s2, lowering the heating value of the gas and the gasification efficiency 3.2.4 Concluding remarks Overall, it is concluded that the most important parameter to estimate in an FBG is the char conversion, because it determines the temperature in the gasifier and the amount of carbon in the gas-phase The approach to WGSR equilibrium affects the gas composition markedly, but its impact is less significant than char conversion Tar concentration in the gas is small and methane is insignificantly converted, so precise prediction of tar and methane A model has been developed to predict the performance of biomass fluidized bed gasifiers (FBG) The model uses an equilibrium submodel to calculate the gas-phase composition, corrected with kinetics sub-models to predict conversion processes that deviate from equilibrium A carbon predictor is implemented as a submodel, accounting for chemical conversion, attrition, elutriation and mechanical removal of ash, allowing estimation of char conversion in the gasifier under different operating conditions The model improves the existing quasi-equilibrium models (QEM) in the sense that essential information, such as the conversions of char and water–gas-shift reaction are estimated as a part of the model in contrast to other models, where these variables are input or are based on correlations, useful only for specific systems This aspect makes the model developed here predictive, in contrast to existing QEM The model results were compared with measurements from tests conducted in a pilot plant with various gasification agents Furthermore, a sensitivity analysis was made by simulating an FBG under various operation modes (with and without removal of bottom ash), revealing their great effect on gas composition and char conversion in the gasifier The great improvement with respect to quasi-equilibrium models together with its simplicity compared to more detailed models (the number of input data is greatly reduced), makes the present model a compromise between prediction and complexity, and therefore, an ideal tool for optimization and scale up free of complex codes The model can be applied to any stand-alone bubbling FB and with minor modifications for circulating units Besides the opera- A Gómez-Barea, B Leckner / Fuel 107 (2013) 419–431 tional form (flowrate of biomass and gasification agent), the model needs the following inputs: fuel properties, kinetics (the most relevant are those for the char and WGSR reactions), reactor geometry (bed and freeboard diameter and length) and mass inventory in the bed The model can be 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