Fluid dynamic analysis of dual fluidized bed gasifier for solar applications

Fluid dynamic analysis of dual fluidized bed gasifier for solar applications M. Suárez-Almeida a,b , A. Gómez-Barea a,c, ⁎,C.Pfeifer b ,B.Leckner d a Chemical and Environmental Engineering Department, Escuela Técnica Superior de Ingeniería, University of Seville, Camino de los Descubrimientos s/n, 41092 Seville, Spain b Department of Material Sciences and Process Engineering, University of Natural Resources and Life Sciences, 1190 Vienna, Austria c Laboratory of Engineering for Energy and Environmental Sustainability, Universidad de Sevilla, Camino de los Descubrimientos, s/n, 41092 Seville,Spain d Division of Energy Technology, Chalmers University of Technology, Göteborg S412 96, Sweden abstractarticle info Article history: Received 21 October 2020 Received in revised form 12 March 2021 Accepted 8 May 2021 Available online xxxx Keywords: Dual-fluidized-bed Hydrodynamics Gasification Biomass Solar energy Model A hydrodynamic model of a dual fluidized bed gasifier (DFBG) is developed and its predictions are compared with measurements of solids flux and pressure profiles from a cold flow model (CFM). Then, the performance of a DFBG gasifier is theoretically analyzed in terms of solids circulation and solids distribution under changes in riser and loop seal aeration, solids inventory and particle size, and a sensitivity analysis is made to delimit the model prediction capability. Furthermore, the model is applied to analyze the effects of key design aspects of DFBG, such as the relative size of riser and gasifier, the connection between both units, the circulation rate of solids and their distribution around the system. The model is further used to extend the DFBG operation with external solar energy carried by heated solid particles, i.e. to design solar DFBG (SDFBG). The analysis is focused on the performance with high solids inventory in the gasifier to increase the char conversion (operation with a large solar share) and the control of solids circulation to meet the heat demand of the gasifier with the availability of solar energy. The operation with large solids inventory in the gasifier requires the size of the gasifier to increase considerably compared to that of the conventional DFBG. The substitution of the connection pipe between the riser and the bubbling bed (current design in commercial DFBG) by a lower loop seal enables better control of the solids circulation, thus, benefiting the solar design. © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction The dual fluidized bed (DFB) system is well known after a major breakthrough in the refining industry during the 1940s with its implementation in the fluid-catalytic cracking process [1]. Nowadays this system is emerging as a potential option in technologies dealing with: reduction of emissions, such as chemical-looping combustion and reforming [2], thermochemical energy storage based on gas-solids reversible reactions (e.g. hydration/dehydration of CaO/Ca(OH) 2 )[3]or production of renewable energy in processes like steam gasification of biomass [4,5]. Steam gasification in DFB gasifiers (DFBG) is a promising technology for the production of syngas with high hydrogen content from renewable solid fuels, such as biomass and wastes. The main advantage of DFBG systems is the separation of syngas and flue gas and the heat integration between the combustor and gasifier by solids circulation. This concept enables indirect gasification without dilution of the produced syngas by the nitrogen introduced with the combustion air. The highquality syngas obtained makes the technology particularly interesting for the conversion of biomass into hydrogen as well as other secondgeneration fuels, such as Fischer-Tropsch diesel, methanol, dimethyl ether, or substitute natural gas [6]. The use of solar energy as external heat source for steam reforming of fuels has been recognized as a highly attractive option [7], generating solar biofuels with maximum share of renewable energy in storable form. Given that the biomass availability and relatively high cost entails limitations in the scale and location of the plants [8], solar-biomass hybridization appears as an attractive technology for improving operational flexibility. The use of a solar DFBG (SDFBG) has been proposed recently and analyzed by the authors as a promising option for the integration of concentrated thermal solar energy within the thermochemical process [9,10]. The solid particles act as a thermal energy carrier, circulating between the solar receiver and the gasifier. Two tanks are used to store the particles heated by the receiver and the particles cooled in the gasifier allowing for temporary thermal storage of solar energy. The SDFBG will operate with high share of external heat when solar energy is available, while it will send more char to the combustor when the fraction of solar external heat decreases. The flexible control of solids circulation is a key factor in an SDFBG to adapt the heat demand of the gasifier to the availability of solar energy [9,10]. In addition, the use of solar energy enables the increase in char Powder Technology 390 (2021) 482–495 ⁎Corresponding author at: Laboratory of Engineering for Energy and Environmental Sustainability, Universidad de Sevilla, Camino de los Descubrimientos, s/n, 41092 Seville, Spain. E-mail address: [email protected] (A. Gómez-Barea). https://doi.org/10.1016/j.powtec.2021.05.032 0032-5910/© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec conversion to syngas from 20% (typical in conventional DFBG, where the rest of the char must be burned in the combustor to maintain the system thermally) up to 80%, a reasonable limit calculated in [9,10]for high-shared SDFBG. As a result, more char must be converted in the gasifier and the inventory of inert material and carbon in the gasifier needs to be increased up to ten times with respect to conventional designs of DFBG. Furthermore, it has been proved [9] that when the system is operated under high share of external heat, the solids circulation is in the order, or even lower, than those of the conventional DFBG, which is another aspect to consider when designing the solar DFBG. The new operating conditions in SDFBGs require a careful understanding of the hydrodynamics of the system, and for that purpose a hydrodynamic model of a DFBG with the potential to extend it to solar conditions has to be developed. Most of the hydrodynamics models presented in literature are based on laboratory-scale DFB cold flow models (CFM) [11–14], scaled down from conventional DFBG (in autothermal conditions). The reference model of DFBG hydrodynamics was developed and experimentally validated with the CFM at the Vienna University of Technology (TU-Wien), which was downscaled applying Glisckman's criteria from the Güssing DFBG [15,16], the most successful indirect gasification system using biomass at commercial scale [6,17]. This model was shown to be useful for analyzing the fluid-dynamic performance of the CFM and re-scaling the results to the commercial plant. However, the effort in [15,16] was focused on the model formulation itself, and the analysis of the performance of the DFBG under different operating conditions was not made in a systematic way. The present paper is focused on analyzing special features in the operation of SDFBGs, such as the large solids inventory required in the gasifier and the required control of solids circulation. A model is developed and its predictions are compared against experimental measurements from a CFM. Then themodel is used to systematically analyze the hydrodynamic performance of a DFBG (solids circulation and distribution along the loop) under different operating conditions (total solids inventory, aeration flowrates in the riser and return system) as well as design variation (key geometrical aspects and theuse of an inclined pipe versus a loop-seal as solids return system between the gasifier and combustor). Moreover, a DFBG operated under the conditions required by the solar hybridization is analyzed. 2. Model description The model of a DFBG consists of the fuel-conversion units (riser and gasifier), a cyclone for separating the particles, a loop seal, and lower pipe connecting the riser and the gasifier for the solids circulation. Fig. 1a shows the CFM at TU-Wien, one of the pioneering CFM developed to study the behavior of DFBG [15,18], which is taken as reference in this work. The model calculates the pressure and solids distribution along the system, as well as the solids flux for a given geometry, fluidization gas flowrates, total solids inventory and physical properties of the bed material. The reference model is subsequently applied to a simpler geometry (Fig. 1b) for a more general analysis of the DFBG, including the comparison of performance when using a lower loop seal (LLS) instead of a pipe connection (Fig. 1c). The model is built on two conditions that are approximately fulfilled in any circulating fluidized bed: (i) the efficiency of the cyclone at the riser outlet is assumed to be unity, and the mass inventory is constant within the system (Eq. (1)) and (ii) the difference of pressure between two points is equal to the pressure drops throughout the way between them (Eq. (2), where numbers are referred to Fig. 1a). Moreover, the pressure drops from point 7 to 8 and from point 9 to 1 are neglected. WT¼Wgasifier þWpipe þWriser þWcyclone þWloop seal ð1Þ P1−P6¼ΔPgasifier 2−1ðÞ þΔPpipe 3−2ðÞ −ΔPriser 3−5ðÞ −ΔPcyclone 5−6ðÞ ð2Þ The solution of these equations requires sub-models from the different parts of the system. Bubbling FBG Q bb Q gas Q 1 Q ULS Q bb Q 1 Q ULS Q LLS Q bb Q ULS Q gas Riser Combustor Loop seal 2 3 5 7 8 9 4 1 6 Q 1 Q 2 Pipe connection (a) (b) (c) Q gas α αα σ Fig. 1. Scheme of the DFBs modelled (the actual dimensions are listed in Table 3): (a) reference case from the CFM at TU-Wien (numbers represent the locations to which the pressures in Eq. (2) are referred); (b) simplified geometry based on (a); (c) simplified geometry replacing the connection pipe with a loop seal. M. Suárez-Almeida, A. Gómez-Barea, C. Pfeifer et al. Powder Technology 390 (2021) 482–495 483 2.1. Gasifier The inventory and pressure drop across the gasifier are given by Eq. (3) and (4) where the only unknowns are the height (h bb,gasifier ) and the voidage of the bubbling bed (ε gasifier ). Wgasifier ¼ρp1−εgasifier  hbb,gasifier Agasifier ð3Þ ΔPgasifier ¼ρp1−εgasifier  hbb,gasifier gð4Þ ε gasifier is calculated considering the bubble fraction (δ)andtheporosity of the emulsion at minimum fluidization (ε mf ): εgasifier ¼δþ1−δðÞεmf ð5Þ The bubble fraction is estimated according to a model based on the modified two-phase theory considering the throughflow, after applying the correlation of Darton [19] and using experimental data of a stationary bubbling fluidized bed [20], δ¼1 1þ1:30:15þu0,gasifier −umf ðÞ 1=3 0:26þ0:7e−3:3dpu0,gasifier−umf  −0:8ð6Þ This model accounts for thevariation of the bubble fraction alongthe bed only if the gas velocities change according to the geometry of the unit. The superficial velocity in the gasifier, u 0, gasifier , includes not only the air fed to the gasifier, Q gas , but also the gas flowing through the lower pipe connection. 2.2. Connection pipe The operation regimeof the connection pipe between thecombustor and the gasifier is controversial: the model in [15] assumes that it is fluidized (even if no aeration along the pipe is applied) while in [13]fora similar unit, the authors maintain that the connection operates as a moving bed (although they modelled it as fluidized bed). Both regimes are considered in this study, and a comparison between the two modes of operation is analyzed in Appendix A. Modelling the pipe under the moving bed regime requires solving two unknowns: the pressure drop and the gas velocity through the pipe, u g,pipe (the solids velocity, u s,pipe , is related to the net solids circulating flow throughout the system, which is constant at steady state). It is calculated according to the definition in Table 1 for the conditions of the pipe. The two required equations are given by the momentum balance of the system (gas and solid) assuming a two-fluid formulation at steady state. The momentum equation of the solid phase after neglecting the acceleration term and the spatial integration alongthelength of the pipe is 1−εpipe  ΔPpipe Lpipe ¼ρp1−εpipe  gsin αðÞ−βus,pipe þug,pipe  −λu2 s,pipe 2ρp1−εpipe  Apipe,wall Apipe ð7Þ where ΔP pipe is the integral value as defined in Eq. (2),andthetermson the right refer to the weight of solids, the gas-solid drag force, and the solids-wall friction force. The latter is assumed, following the approach presented in [15], where λis the solids-wall friction coefficient as defined in Table 2. The momentum equation of the gas phase is given by Eq. (8) when neglecting the contribution of the gas acceleration, the weight and the wall-friction force, rearranging and substituting the differential term. εpipe ΔPpipe Lpipe ¼βus,pipe þug,pipe  ð8Þ In the equations above the parameter βaccounts for the gas-particle interaction, which can be estimated with the Ergun equation (Eq. (9)) when the porosity in the system is below 0.8 [21]. β¼150 1−ε ðÞ 2 ε μg ϕdp2þ1:75 1−εðÞ ρg ϕdp usþug ð9Þ When modelling the pipe as fluidized (at incipient fluidization as considered in [15]) the gas velocity in the pipe (u g,pipe )isgiven (Eq. (10)), and just an equation is needed to calculate the pressure drop (Eq.(11), obtained after combining Eqs. (7) and (8)). ug,pipe þus,pipe ¼umf εmf ð10Þ ΔPpipe Lpipe ¼ρp1−εpipe  gsin αðÞ−λu2 s,pipe 2ρp1−εpipe  Apipe,wall Apipe ð11Þ Summing up, the pressure drop across the pipe connection, if modelled as a moving bed, is solved with Eqs. (7) and (8), while if modelled as fluidized bed at minimum fluidization it is estimated with Eqs. (10) and (11). Note that if the system is fluidized beyond the minimum fluidization velocity, the porosity of the bed should be estimated, considering the bubble fraction (with Eqs. (5) and (6) applied to the pipe conditions) and then using Eqs. (7) and (8) to estimate the gas and solids velocities through the pipe. The mass of solids in the pipe is calculated in a similar way to Eq. (3) accounting for the geometry of the pipe and the porosity. Table 1 Summary of gas and solids velocities in the loop seal (i refers to the different sections in the loop seal, LP and P). Recycle chamber, RC Supply chamber, SC/DC a Solids velocity (m s −1 )us,RC,i¼Fp 1−εRC,i ðÞ ARC,i ρp us,SC,i¼Fp 1−εSC,i ðÞ ASC,i ρp Actual gas velocity (m s −1 )ug,RC,i¼u0,RC,i εRC,iug,SC,i¼u0,SC,i εSC,i Superficial gas velocity (m s −1 )u0,RC,i¼QRC ARC,iu0,SC,i¼QSC ASC,i Relative gas velocity (m s −1 )V RC,i =u g,RC,i −u s,RC,i V SC,i =u g,SC,i +u s,SC,i a For simplicity all the variables related to the left chamber are labeled only with SC. Table 2 Summary of the model parameters. Parameter Value/Correlation [Ref] λsolids-wall friction coefficient 3.5/u s,pipe [15] E ∞ elutriation constant Colakyan & Levenpiel [36] k cyclone cyclone geometry factor 30 [15] u mf minimum fluidization velocity Grace [37] ε mf minimum fluidization porosity u t terminal velocity Haider & Levenspiel [38] C decay constant splash zone: 10 [16] transport zone: 4.2 a R RC gas fraction through the RC 0.5 (see Appendix A) a Obtained after minimizing the error of the measurements from the CFM at TU-Wien presented in Fig. 3, and used in Section 4.1; a rounded value of 4 was used when studying the performance of the system. M. Suárez-Almeida, A. Gómez-Barea, C. Pfeifer et al. Powder Technology 390 (2021) 482–495 484 2.3. Riser The riser is modelled with a dense bottom bed, a transition or splash zone, and a transport zone. Part of the air is introduced through the bottom and the rest is added along the column (primary and secondary air) [16], as depicted in Fig. 1. The dense bottom bed is modelled like the bubbling fluidized bed in the gasifier, i.e. using Eqs. (5) and (6) to estimate the porosity of the bed, and to calculate the pressure drop and mass of solids in the dense zone, such as in Eqs. (3) and (4), where the height of the dense zone is not an input, but calculated by the model. Above the dense bed there is a transition region (splash zone) with a high down-flow of solids falling back to the bed. The region downstream of the splash zone (transport zone) is characterized by solids concentrations much lower than in the splash zone and with a less pronounced decrease with height. Along the transport zone there is an upflow of solids in the core with a net lateral flow to the solids film downflowing through the walls [22]. These observations have motivated application of core-annulus models. However, there is no clear agreement on how to estimate the solids profile along these two zones, so semiempirical models valid for specific operating conditions have been used [23–26]. In 1D models, the mean solids concentration along the freeboard (splash and transport zone) decays exponentially with height as described by the simplified model [27,28]: ρhð Þ¼ρTDH þρh¼0−ρTDH ðÞexp −ahðÞ ð12Þ where ρ h=0 is the solids concentration at the top of the dense zone, ais the decay coefficient, and ρ TDH is the solids concentration at a height above the dense bed (h) which is higher than that at the total disengagement height (TDH) calculated according to Eq. (13). ρTDH ¼1−εTDH ðÞρp¼E∞ u0−ut ðÞ ð13Þ The decay coefficient, a, is the most uncertain parameter when modelling the solids distribution along the riser. A great deal of observations suggests that the decay constant increases with increasing particle size (particles are more likely to change direction and return to the dense bed), and decreases with the gas velocity (particularly for fine particle systems). These aspects have been interpreted in terms of a deposition coefficient giving the rate of particle transfer from the gas core to the falling particle film [29]. Recommendations for the value of the decay factor based on measurements are reported [30,31]. Kunni and Levenspiel [28]gathered data from literature to come up with Eq. (14), while Johnsson and Leckner [24] proposed Eq. (15) to fit the decay factor in the splash zone of a large CFB au0¼Cð14Þ au0 ut ¼Cð15Þ Although Eq. (15) is an empirical way to fit measurements, it is merely an extension of Eq. (14) taking into account the effects of particle diameter (and using the ratio u 0 /u t reported by [30] when studying the decay factor). Eq. (15) must be applied with caution when scaling up, since the vessel width is not accounted for, although it has been observed to influence the decay constant (rising agglomerates are more likely to hit the wall surface and be removed from the rising gas stream in narrower columns). A reasonable practice is to adjust the constant C with measurements for a given set of operating conditions (mainly gas velocity, particle size and column width). In this work we have modelled the decay factor using Eq. (15) but taking different values of the constant Cfor the splash zone and the transport zone (see Table 2). The value of Calong the transport zone resulted from fitting to minimize the error of all the measurements shown in Fig. 3, while that of the splash zone was taken from [15] (where the splash zone is modelled using the same approach). In the model, the splash zone is defined as the region where the gas velocity is lower than the terminal velocity of a particle. The transport zone is assumed to extend itself from this point forward. The solids density profile is estimated with Eq. (12) by integrating each of the different regions of the riser i.e., those in which the gas velocity changes dueto air injection, and different cross sections (bottom, diffuser and top), leading to different decay coefficients (a) [22]andρ TDH . In those regions where the gas velocity is below the terminal velocity, ρ TDH is assumed to be zero. The superficial velocity in the riser considers both the air fed to the riser and the gas flow through the lower pipe connection. The solids profile is discretized along the riser, in such a way that the boundary conditions at initial point of a region are the output of the previous region. If the momentum losses due to wall friction and solids acceleration can be neglected as compared with the static head of solids,the pressure drop is estimated according to Eq. (16) in each of the isections (those with different gas velocities) along the riser. ΔPriser;fb;i¼gZ Hi h¼0i ρhðÞ idh ð16Þ The effect of the solids acceleration within the momentum losses along the riser has been assessed (see Appendix A). The approach presented in [32], which results in Eq. (17) after combining the momentum equations for the gas and solids phases (neglecting the wall friction and the gas acceleration) and making some rearrangements (substituting the differentiated continuity equation for the solid phase and the definition of solids flux as in Eq. (21)) is applied. Eq. (17) (after substituted by Eqs. (18) and (19)) is solved for each of the isections along the riser (from the primary air injection forward, to avoid the bottom acceleration zone where the flow is clearly not one-dimensional) giving the pressure profile as an alternative to Eq. (16). d1−εriser,fb  dh ¼ρp2g Gs21−εriser,fb  3þρp Gs2 dP dh 1−εriser,fb  2ð17Þ where the solids fraction and its variation along the riser is calculated from Eq. (12) leading to, 1−εriser,fb  ¼ρTDH þρh¼0−ρTDH ðÞexp −ahðÞ ρp ð18Þ d1−εriser,fb  dh ¼−ρh¼0−ρTDH ðÞaexp −ahðÞ ρp ð19Þ The total pressure drop along the splash zone and the transport zone is given by summing the pressure drop of each section, while the mass ofsolidsisobtainedfromEq.(20). Wriser,fb ¼∑ i ΔPriser,fb,iAriser,i gð20Þ The total pressure drop and solids mass inventory in the riser result from adding the pressure drop and solids inventory of the dense zone to those of the splash and transport zones. The solids flux circulating within the DFB, G s (kg m −2 s −1 ), is Gs¼ρp1−εriser,fb  us,riser,fb ð21Þ The porosity and solids velocity at the top of the riser are used in Eq. (21) for the estimation of G s ; in this highly diluted region the slip M. Suárez-Almeida, A. Gómez-Barea, C. Pfeifer et al. Powder Technology 390 (2021) 482–495 485 velocity can be assumed equal to the particle terminal velocity [28]and therefore, the solids velocity can be directly estimated as us,riser,top ¼u0,riser,top εriser,top −utð22Þ ε riser,top is the porosity at the outlet point of the riser (estimated from Eq. (12)). 2.4. Cyclone The mass of solids in the cyclone (W cyclone ) is neglected. The pressure drop across the cyclone is estimated using an empirical correlation [33], where the parameter k cyclone is mainly dependent on the cyclone geometry [15], ΔPcyclone ¼kcyclone ρgu2 0;riser;top ð23Þ 2.5. Upper loop seal The model fictionally divides the loop seal in two regions, the supply chamber/downcomer (SC/DC) and the recycle chamber (RC), separated in Fig. 2 by the dashed line. The total flowrate of steam introduced (Q ULS ) is divided into that going through the RC (Q RC ) and that going through the SC/DC (Q SC ). Both, the solids and gases in the RC flow upward. In the SC and DC the solids flow downward while the gas can flow upward or downward depending on the operating conditions (in Fig. 2 it is defined positive upward). Table 1 defines the gas velocities (superficial and actual), the actual velocity of solids and the gas-solids relative velocity on both sides of the loop seal. The subscript idenotes that velocities take different values along the RC and SC/DC due to the changes in the geometry shown in Fig. 2. The estimation of the mass of solids in the loop seal requires a pressure balance since the height of solids in the downcomer (h SC/DC )isunknown. The pressure balance (considering both units opened to the same environment through the gas exit of the cyclone and the exit of the produced gas from the gasifier,i.e.P 6 =P 9 )isgivenby, ΔPDC=SC ¼ΔPRC ð24Þ Since the geometry of the loop seal has different cross sections (A LP and A P according to Fig. 2), the pressure drop of each chamber is calculated by summing the pressure drop of each section. The RC always should be fluidized to circulate the solids to the gasifier. Therefore, the pressure drop is given by the hydrostatic pressure: ΔPRC ¼∑ i¼LP,P i ρp1−εRC,i  ghRC,ið25Þ The total height (h RC ) is that of the weir, which is assumed constant during stable operation and given by the geometry (the height of the crest of solids is small compared to the weir height and therefore it is neglected). The porosity in each section of the RC is calculated with the equations for a bubbling bed (Eqs. (5) and (6)) but considering the relative superficial gas velocity (V RC,i Ɛ RC,i ), since there is a net flow of solids (in a stationary bubbling fluidized bed, the amount of solids going upward equals that going downward, so the superficial velocity of the gas is used). According to the definitions in Table 1 the only unknown for calculating the pressure drop in the RC is the actual gas velocity, u g,RC,i (since the solids velocity, u s,RC,i , is function of the solids flowrate, F p in kg s −1 , which is constant all over the system). A force balance in the loop seal stablishing the gas-solids interaction would allow calculating the gas distribution between the RC and SC [34]. However this momentum balance leads to many uncertainties. Since the loop seal in the cold model in TU-Wien is just operated for sealing the system and circulating the solids (not for controlling the solids flux) as reported in [15], a rigorous prediction of the behavior of the loop seal is not required and it can be directly assumed that a fraction of the total gas, fed to the loop seal, flows through the RC while the rest goes through the SC/DC. The fraction of gas flowing through the RC (R RC ) is analyzed in Appendix A to assess the magnitude of the incurred error under this simplification. RRC ¼QRC =QULS ð26Þ The SC/DC can operate under fluidized or moving bed regime depending on the operating conditions. There is a critical velocity defined in Eq. (27), comparing the relative superficial velocity with the minimum fluidization velocity: a positive critical velocity means that the SC/DC is fluidized, while a negative means it is in moving bed regime. According to this premise, if the bed is fluidized the pressure drop is estimated from Eq. (28), while if it is under moving bed conditions it is estimated from Eq. (29) [35]. ucritic,SC,i¼VSC,iεSC,i−umf ð27Þ ΔPSC,i ¼ρp1−εSC,i  ghSC,ið28Þ ΔPSC;i¼β εSC;i ug;SC;iþus;SC;i  hSC;ið29Þ ΔPSC ¼∑ i¼LP,P i ΔPSC,ið30Þ Note that once again the pressure drop (and the critical velocity) is estimated separately for each of the isections of the SC, and that, in the notation, SC refers in a general way to the entire left chamber of the loop seal. When the SC/DC is fluidized, the porosity of the bed (ε SC,i ) is calculated with the equations for a bubbling bed (Eqs. (5) and (6)) but considering the relative superficial gas velocity (V SC,i Ɛ SC,i ), while when operating as moving bed, it is assumed that the porosity is ε mf . Solving this set of equations together with those of the RC gives the height of the SC/DC, allowing the estimation of the solids inventory in the loop seal in a similar way as in Eq. (3), considering the geometry Fig. 2. Diagram of the loop seal (RC: recycle chamber, SC: supply chamber, ULS: upper loop seal, Q: steam flowrate, A: cross sectional area, LP: lower part, P: pipe, h: height, u g : interstitial gas velocity, u s : solids velocity). M. Suárez-Almeida, A. Gómez-Barea, C. Pfeifer et al. Powder Technology 390 (2021) 482–495 486 (and height of solids) in each chamber of the loop seal together with the porosity of each section. 3. Experimental The model predictions are compared with measurements taken from the CFM at TU-Wien (Fig. 1a). The experiments were conducted in a perspex CFM of the 8 MW th biomass gasifier demonstration plant in Güssing, Austria. The dimensions of the CFM [18](Table 3) and the properties of the inert bed material were calculated by applying the scaling criteria of Glicksman [39] to obtain a similar hydrodynamic performance of the CFM as in the demonstration plant. Bronze particles are employed as bed material (Table 4) and air under ambient conditions as fluidizing agent [15]. Experiments from [16] were carried out by varying the total solids inventory, total air flowrate fed to the riser, as well as the air staging along the riser within the ranges presented in Table 4 (it was shown that the influence of the fluidization of the gasification unit on solids circulation around the system is negligible, therefore it was held constant). Tests were conducted by measuring the pressure in each section of the CFM as well as the solids circulation rate by stopping the aeration of the loop seal and measuring the increase in the level of solids over the time. The experiments from [40] were conducted varying the bed pressure in the gasifier from 6 to 13 kPa by adding bed material (bronze-sand) into the system for three total air flowrates fed to the riser (325, 357, 390 Nm 3 /h), while keeping constant the air staging (Q 2 /Q t =0.23, Q 1 /Q 2 =3). 4. Results and discussion 4.1. Comparison of model results with measurements Fig. 3 compares the results of solids flux given by the model with the measurements from the CFM at TU-Wien presented in [15]. The total relative error (comparing the results from the model with the measurements) of the data points presented in Fig. 3 is about 11.6%. The results from the model developed here compare better with measurements than those from the model in [15]. A significant improvement is seen in the lowest range of solids flux (corresponding to the lowest air flowrate fed to the riser). It can be seen that most of the data points are scattered over a deviation of ±20% using a simpler and more general model of the transport zone compared to that presented in [15](which uses the core annulus model for the dilute transport zone). Fig. 4 characterizes the capability of the model to predict the change in solids flux with the riser aeration (total air flow rate in the riser and secondary to total air ratio). Fig. 4a shows that, as expected, the predictions are less accurate at low gas velocity in the riser while the Table 3 Geometry of the TU-Wien DFBG CFM and the simplified DFBGs in Fig. 1bandFig. 1c. TU-Wien DFGB CFM Simplified DFBG Riser Fig. 1aFig. 1b and c Total height (m) 2.093 a 2 Height primary injection (m) 0.175 0.2 Height secondary injection (m) 0.425 – Height diffuser (m) 0.567 – Length diffuser (m) 0.125 – Diameter (m) 0.150 (below diffuser) 0.165 0.175 (above diffuser) – Gasifier Fig. 1aFig. 1b and c Length lower section (m) 0.125 – Length transition section (m) 0.538 – Transition zone angle, σ(°) 60 – Diameter (m) 0.250 b (lower) 0.275 0.550 (upper) – Connection pipe Fig. 1aFig. 1b Cross sectional area, A pipe,CS (m 2 ) 0.075 × 0.150 0.075 × 0.150 Length, L pipe (m) 0.323 0.323 Inclination, α(°) 30 30 Upper loop seal Fig. 1aFig. 1b and c Cross sectional area SC, (m 2 ) 0.011 (lower part, A SC,LP ) 0.0125 0.008 (pipe, A SC,P )– Cross sectional area RC (m 2 ) 0.011 (lower part, A RC,LP ) 0.0125 0.008 (pipe, A RC,P )– Height RC (m) 0.1 (lower part, h RC,LP ) 0.1 0.1 (pipe, h RC,P )– Lower loop seal –Fig. 1c Cross sectional area SC (m 2 )–0.0125 Cross sectional area RC (m 2 )–0.0125 Height RC (m) –0.1 Height SC (m) –0.2 Diameter pipe gasifier-SC (m) –0.1 Length pipe gasifier-SC (m) –0.04 c Inclination, α(°) –30 a Taken as the intersection between the center of the riser and that of the outlet pipe according to the construction drawing of the plant [18]. b The diameter of the lower part of the gasification unit reported in [15](differentfrom that presented in [18]) was selected. c Selected to obtain a mass of solids in the LLS + pipe close to that of the pipe in the conventional configuration. Table 4 Bed material, fluidizing agent and operating conditions of the tests and the reference case used for the analysis. Tests Reference case Bed material Bronze spheres Bronze spheres Size (μm) 119 119 Sphericity 1 1 Density (kg m −3 ) 8750 8750 Fluidizing agent Air Air Temperature (°C) 20 20 Operating conditions Total inventory (kg) 105–130 105 Total gas flowrate fed to the riser, Q t (Nm 3 /h) 250–400 300 Air supply to bottom bed, Q bb (Nm 3 /h) 20–60 60 Secondary to total air ratio, Q 2 /Q t ≈0.15–0.5 0.2 Gas flowrate fed to the gasifier, Q gas (Nm 3 /h) 47 47 Gas flowrate fed to the ULS, Q ULS (Nm 3 /h) 4.5–6 a According to a a The gas flowrate fed to the ULS is not clearly reported for each of the measurements (values of 4.5 and 6 Nm 3 /h are presented in [18,41], respectively). According to [15] the loop seal is always operated in a fluidized mode. In the model, the gas flowrate to the loop seal was set with a ratio of superficial velocity in the RC to minimum fluidization velocity (V RC Ɛ mf /u mf ) of 1.15 for guaranteeing the fluidization. 0 50 100 150 200 250 0 50 100 150 200 250 G,ledomxulfsdiloS smgk( -2 s-1) Solids flux experimental, Gs(kg m-2 s-1) 130 kg 105 kg 20% Deviation Fig. 3. Comparison of the solids fluxes given by the model with measurements from the CFM at TU-Wien with two different solids inventories and riser air flowrates ranging from 250 to 400 Nm 3 /h (tests made under different distributions of the air through the bottom, primary and secondary injections). M. Suárez-Almeida, A. Gómez-Barea, C. Pfeifer et al. Powder Technology 390 (2021) 482–495 487 prediction ability significantly increases at higher gas velocities. The reason is that the decay constant in the transport zone was selected to minimize the error of the entire set of measurement, and the three points at the lower left corner of Fig. 3 represent an operation quite far from the rest. Nevertheless, it can be observed that the predictions still follow the general performance quite well. Moreover, it is seen that the model gives reasonable prediction of the air staging, keeping most of the deviations below 20% when changing the aeration through the bottom bed and the secondary-staging ratio (Fig. 4b). The pressure profiles predicted by the model are compared with measurements in Fig. 5 for two different operational points. It can be seen that the model captures well enough the general trends of the measured profiles, giving a coherent behavior when increasing the solids inventory (i.e. higher maximum pressure is reached in Fig. 5b compared to Fig. 5a). Fig. 6a presents the predicted total inventory of solids in the system when fixing the pressure drop in the gasifier for various riser gas velocities, showing good agreement with the measurements obtained from [40]. As expected, the increase in the gasifier pressure drop (i.e. solids inventory in the gasifier) leads to higher total solids inventory. Furthermore, if the pressure drop in the gasifier is kept constant as the gas velocity in the riser is increased, the solid flux is also increased and some solids need to be removed from the system (i.e. the total solids inventory is reduced). This is because the increase in the solids circulation results in higher wall friction in the connection pipe (i.e. a reduction of the pressure drop in the connection pipe) [15]. This way of operation contrasts with that keeping constantthe total solids inventory, where an increase in riser gas velocity provokes a displacement of material from the risertothegasifier, increasing the mass inventory in the latter as well as the solids circulation. This way of operation is presented in Fig. 6b 0 10 20 30 40 50 60 200 250 300 350 400 450 %,rorrE Total air flowrate, Qt(Nm3/h) 20Nm3/h 40Nm3/h 60 Nm3/h (a) 0 10 20 30 40 50 60 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Secondary air/total air, Q 2 /Q t 20 Nm3/h 40 Nm3/h 60 Nm3/h (b) Fig. 4. Relative deviation in the solids flux between the model predictions and measurements from the CFM at TU-Wien against (a) the total air flowrate fed to the riser (secondary to total aeration between 0.3 and 0.5; total solids inventory: 130 kg) and (b) the ratio of secondary to total aeration (total aeration between 327 and 346 Nm 3 /h; total solids inventory: 105 kg) for the three bottom-air flowrates shown (20, 40 and 60 Nm 3 /h). 0 0.5 1 1.5 2 2.5 100 102 104 106 108 110 112 114 116 118 )m(h,thgieH Pressure, P (kPa) Model 0 0.5 1 1.5 2 2.5 100 102 104 106 108 110 112 114 116 118 Pressure, P (kPa) Model (a) (b) 5 2 6 7-8 3 4 1 9 Fig. 5. Pressure loops obtained by the model compared with measurements from the CFM at TU-Wien: (a) W t =105kg,Q t = 353.5 Nm 3 /h, Q 2 /Q t = 0.18, Q bb /Q t =0.06;(b)W t = 130 kg, Q t = 396.8 Nm 3 /h, Q 2 /Q t =0.5,Q bb /Q t = 0.15 (solid circles represent measurements from the riser, while open circles those from the rest of the system; the point at height 0 m was not measured but estimated with the porosity given by the model for the dense zone of each test; in (a), numbers represent the pressures given by the model forpointsshowninFig. 1a). M. Suárez-Almeida, A. Gómez-Barea, C. Pfeifer et al. Powder Technology 390 (2021) 482–495 488 where the pressure drop in the gasifier is seen to increase with the riser velocity for constant total mass inventory. Fig. 7 compares the experimental and predicted fluxes of solids for the operational points included in Fig. 1, showing the effect of the riser gas velocity and the total solids inventory over the solids flux. It is clearly observed that the aeration has a huge impact over the solids flux while the solids inventory has almost not influence. Furthermore, the figure displays the good capability of the model to predict the measurements for the whole range of operating conditions. 4.2. Analysis of the hydrodynamic performance of the DFBG The hydrodynamic performance of the DFBG has been analyzed with the simplified system shown in Fig. 1b according to the geometry presented in Table 3. The performance of the simplified system in Fig. 1b is analyzed in Fig. 8.Fig. 8a shows that the solids flux is more sensitive to changes in the riser aeration than in the solids inventory, 60% increase in the solids flux can be reached increasing the air velocity by 15% (over the reference case, u 0,riser ), while an increase in the solids inventory of 60% only produces an increase in the solids flux of 17%. This behavior (experimentally verified in Fig. 7) is explained in Fig. 8b where it can be seen that an increase of 15% over the total solids inventory (of the reference case, i.e. from 105 kg to 120 kg) leads to an increase in the gasifier solids inventory of 11.4 kg but only an increase of 3.6 kg in the riser. The reason of this distribution is the difference in the cross sectional areas of the gasifier and riser, requiring a higher amount of solids in the gasifier (larger diameter) to balance the increase in pressure drop in the riser. On the other hand, as justified in the previous section, Fig. 8b shows that the higher the gas velocity in the riser, the higher the solids displacement from the riser to the gasifier. Fig. 8c shows the influence of the geometry on the solids circulations and solids residence times in the system. It is shown that for keeping constant the solids flux at 100 and 130 kg m −2 s −1 while increasing the total solids inventory of the system from 100 to 160 kg, the diameter of the gasifier needs to be increased by 60 and 68%, respectively. On the other hand, the increase in the total inventory, keeping constant the solids circulation, leads to a higher accumulation of solids in the gasifier resulting in longer space time of the reactive particles (fuel and char) in the gasifier of a real unit. It is observed that the space time (ratio of the mass inventory of the gasification unit to mass flowrate of reactive particles fed to the gasifier), is increased 2.5 and 2.8 times for the solids fluxes considered. Note that for a given total solids inventory, an increase in the solids flux requires a larger amount of solids in the riser, leading to a reduction of the amount of solids in the gasifier and, consequently, to balance the pressure loop, a reduction of the diameters ratio (i.e. a smaller diameter of the gasifier is required for compensating the higher pressure drop along the riser). Fig. 8d demonstrates that the particle size has a huge impact on the solids circulation, being the effect more significant as the gas velocity in the riser is increased. Therefore, the selection of the particle size of the bed material is extremely important for the control of the solids circulation in a DFBG. Fig. 9 shows the effect of the total riser aeration (a) and the total solids inventory (b) over the pressure loop of the system. Fig. 9a shows that the increase in the aeration increases the pressure drop across the cyclone and the pressure along the transport zone due to the higher gas velocity. On the other hand, the pressure at the bottom of the riser decreases as the gas velocity is increased due to the displacement of solids to the gasifier. Increasing the solids inventory (Fig. 9b) leads to higher pressures at the bottom of the riser and higher height of the bed in the gasifier due to thelarger amountof solids in the system. The pressure drop along the loop seal is not affected while the fluidization number in the recycle chamber (V RC ε mf /u mf ) is kept constant, and therefore, according to the assumption of the simulations no changes are observed in any scenario. 4.3. Analysis of the solids inventory in the gasification unit of a solar DFBG and the effect on the solids flux The solids inventory in the gasification unit of an SDFBG is typically 10 times higher than in a conventional DFBG since, as discussed in the Fig. 6. (a) Total solids inventory predicted by the model against pressure drop in the gasifier for three total-air flowrates fed to the riser (Q 2 /Q t = 0.23, Q 1 /Q 2 = 3) compared to measurements from [40] (it is not possible to distinguish the small difference within the total inventory for the measurements under different aerations into the riser); (b) pressure drop predicted by the model for total solids inventories of 105 and 130 kg for three total-air flowrates fed to the riser (Q 2 /Q t =0.23,Q 1 /Q 2 =3). 0 50 100 150 200 250 200 250 300 350 400 450 G,ledomxulfsdiloS smgk( -2 s-1) Total air flowrate, Qt(Nm3/h) Wt=130 kg Wt=105 kg Wt=130 kg, model Wt=105 kg, model Fig. 7. Experimental and theoretically-predicted solids fluxes as a function of the total air flowrate to the riser for two different solids inventories (tests made under different distributions of the air through the bottom, primary and secondary injections). M. Suárez-Almeida, A. Gómez-Barea, C. Pfeifer et al. Powder Technology 390 (2021) 482–495 489 Introduction, longer residence time of the char is required in the gasifier for reaching higher conversion [9,10]. The effect of increasing the solids inventory in the gasifier on the solids flux is shown in Fig. 10,usingas a reference for the solids inventory in the gasifier of a conventional DFBG that given by the model under the operating conditions of the reference case for the system in Fig. 1b(Table 4). As expected, the increase (a) 100 110 120 130 140 150 160 1 1.5 2 2.5 3 30 40 50 60 70 80 90 100 retemaidresir/retemaidreifisaG Total solids inventory, W t (kg) G s =100kgm -2 s -1 Solidsinventory in the gasifier, W g asifier (kg) G s =130kgm -2 s -1 100 110 120 130 14 0 0 50 100 150 200 250 300 Particle size, d p (m) Solids flux,G s (kg m -2 s -1 ) u 0,riser u 0,riser 0.85 u 0,riser 0.85 u 0,riser 1.15 u 0,riser 1.15 u 0,riser 100 110 120 130 140 150 16 0 0 50 100 150 200 250 300 Total solids inventory, W t (kg) Solids flux,G s (kg m -2 s -1 ) u 0,riser u 0,riser 0.85 u 0,riser 0.85 u 0,riser 1.15 u 0,riser 1.15 u 0,riser 100 110 120 130 140 150 160 0 25 50 75 100 0 25 50 75 100 Solids inventory in the gasifier, W gasifier (kg) Solids inventory in the riser, W riser (kg) 0.85 u0,riser 0.85 u0,riser Total solids inventory, W t (kg) 1.15 u 0,riser 1.15 u0,riser u0,riser u0,riser (b) (c) (d) Fig. 8. Analysis of the performance of a DFBG (Fig. 1b): (a) effect of the total solids inventory and total aeration in the riser over the solids flux; b) distribution of solids between the gasifier and riser for the operation under different solids inventories and riser gas velocities; (c) relation of diameters gasifier/riser (the diameter of the riser is kept constant) and solids inventory in the gasifier for keeping constant the solids flux at 100 and 130 kg m −2 s −1 while varying the total solids inventory; (d) effect of the particle size over the solids flux. The operating conditions not specified in the figures are those of the reference case (Table 4). 0 0.5 1 1.5 2 2.5 100 102 104 106 108 110 112 114 116 118 Pressure, P (kPa) 105 kg 90 kg 120 kg (b) 0 0.5 1 1.5 2 2.5 100 102 104 106 108 110 112 114 116 118 )m(h,thgieH Pressure, P (kPa) Qt 1.15 Qt 0.85 Qt (a) u 0, riser 1.15 u 0, riser 0.85 u 0, riser Fig. 9. Pressure profiles of the system under changes of the total aeration in the riser (a) and the total solids inventory (b). M. Suárez-Almeida, A. Gómez-Barea, C. Pfeifer et al. Powder Technology 390 (2021) 482–495 490