Pressure drop prediction of a gasifier bed with cylindrical biomass pellets

Applied Energy 113 (2014) 258–266 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy Pressure drop prediction of a gasifier bed with cylindrical biomass pellets Duleeka Sandamali Gunarathne ⇑, Jan Karol Chmielewski, Weihong Yang Royal Institute of Technology, Department of Material Science and Engineering, Division of Energy and Furnace Technology, Brinellvägen 23, 100-44 Stockholm, Sweden h i g h l i g h t s  An equation was developed for pressure drop prediction with shrinking effect  Graphical representations of correlation constants were introduced  This would provide a guide to select pellet size and designing a grate a r t i c l e i n f o Article history: Received March 2013 Received in revised form 26 June 2013 Accepted 13 July 2013 Available online August 2013 Keywords: Biomass Gasification Fixed bed Pressure drop a b s t r a c t Bed pressure drop is an import parameter related to operation and performance of fixed bed gasifiers Up to date, limited literature is found on pressure drop prediction of beds with cylindrical pellets and none was found for gasifying beds with cylindrical pellets In this paper, an available pressure drop prediction correlation for turbulent flows in a bed with cylindrical pellets which has used equivalent tortuous passage method was extended for a gasifier bed with shrinking cylindrical pellets and for any flow condition Further, simplified graphical representations introduced based on the developed correlation can be effectively used as a guide for selecting a suitable pellet size and designing a grate so that it can be met the system requirements Results show that the method formulated in the present study gives pressure drop approximation within 7% deviation compared to measured values with respect to performed runs Available empirical correlation with modified Ergun constants for cylindrical pellets gave pressure drop within 20% deviation after the effect of shrinkage was taken into account Ó 2013 Elsevier Ltd All rights reserved Introduction Biomass gasification is a promising renewable energy technology for supplying thermal energy and generating electric power Nowadays, pelletized biomass is widely used in order to overcome some problems when using conventional biomass in thermal applications like gasification including logistic problems due to low bulk density, non-uniformity of fuel, low energy density, etc Pressure drop is an important factor in fixed bed gasification of Biomass Most common and widely used method for predicting pressure drop in a packed bed is using Ergun equation which has viscous and inertial terms corresponding to laminar and turbulent flow conditions One limitation of this model when applying for a gasifier bed with biomass pellets is due to the particle shape which is essentially cylindrical shape when considering pellets Limited literature is available in pressure drop prediction for a bed with cylindrical pellets ⇑ Corresponding author Tel.: +46 790 8402; fax: +46 207 681 E-mail address: rmdsgu@kth.se (D.S Gunarathne) 0306-2619/$ - see front matter Ó 2013 Elsevier Ltd All rights reserved http://dx.doi.org/10.1016/j.apenergy.2013.07.032 One research group [1] has considered this effect and has developed an equation for pressure drop in packed bed with cylindrical shaped particles by using equivalent tortuous passage method But, the equation is limited to turbulent flow conditions and not valid for a bed with laminar or transition flow conditions Some investigators [2] have developed an empirical correlation for Ergun constants for a bed of cylindrical particles by referring the sphericity of particles But, this correlation does not show strong validity due to scatter of data and suitable only for a rough approximation of the pressure drop Lack of theoretical background is another limitation for applying this correlation Further considering these models, none of the above models for cylindrical particles are developed for active beds of particles In a gasifier, particles participate in the reaction and therefore particle size and the porosity of bed varies with time and along the height of the bed Even if steady state condition is considered, the spacial variation of porosity has to be taken into account Some researchers [3] have addressed this issue on a downdraft gasifier but with particles in spherical shape and hence Ergun equation and its’ another variation called Macdonald correlation have 259 D.S Gunarathne et al / Applied Energy 113 (2014) 258–266 Nomenclature A a B c c0 D De d d0 dp ER K1 K2 K3 Kt L LHV l mbiomass modified Ergun constant for viscous term (–) wetted perimeter (m) modified Ergun constant for inertial term (–) length of cylindrical particle at any time (m) initial length of cylindrical particle (m) diameter of gasifier (m) equivalent diameter of tortuous passage (m) diameter of cylindrical particle at any time (m) initial diameter of cylindrical particle (m) equivalent particle diameter (m) equivalence ratio (–) constant depend on c0, d0 and x (for inertial term) (–) constant depend on c0, d0 and x (for viscous term) (–) constant depend on c0, d0 and x (for Rep) (–) constant depend on roughness of particle and packing tortuosity (–) length (height) of the bed (m) lower heating value of biomass (MJ/kg) equivalent length of tortuous passage (m) mass of single biomass particle (kg) been used along with considering the wall effects Another group [4] has focused on cylindrical wood particle in a fluidized bed considering shrinking effect but only pyrolysis conditions An interesting literature [5] was found for a coal gasifier and they have found pressure drop variations within different zones in the gasifier by using Ergun equation for each zone separately This method has incorporated lots of experimental data and may be successfully used for that specific commercial gasifier model but not for any type of gasifier Therefore, none of the above cases can be used for predicting pressure drop in any fixed bed gasifiers of cylindrical pellets One of our previous works [6] concentrated on developing a model for prediction of pressure drop due to grate-bed resistance of a gasifier As the second step of that, with the objective of filling the gap on pressure drop prediction of gasifier beds with cylindrical pellets, here we focus on the bed resistance Considering limitations of previous models, an equation is developed based on the model predicted in the literature [1] including the effect of laminar and transition flow conditions and also the effect of shrinkage of particles during gasification and will be verified based on experimental data Further, it will also compare with the empirical correlation available for cylindrical pellets [2] which will also be upgraded by taking shrinking effect into account mchar DP Rep rH Sp T u Vp v x mass of single char particle (kg) pressure drop (Pa) particle Reynolds number (–) hydraulic radius (m) particle surface area (m2) temperature (°C) superficial velocity (m/s) particle volume (m3) velocity of flow through tortuous passage (m/s) mass conversion (–) Greek letters e porosity (–) U sphericity (–) k angle of inclination of tortuous passage to the mean flow (°) l viscosity (Ns/m2) q density (kg/m3) This unit is incorporated with feed gas preheater, updraft gasifier, fuel feeding system and producer gas post combustion unit Detailed description of this experimental facility is available elsewhere [7] Biomass pellets stored in the feed tank is transported to the gasifier via screw conveyor The frequency of feeder is correlated with the feeding rate Required frequency set point is predetermined in order to achieve specific biomass feed rate Preheated air from the preheater is introduced to the gasifier at the side of bottom section below the grate The system has the facility to add steam to the feed stream if required The flow of hot gases and biomass is countercurrent The grate facilitates to build up a fixed bed of biomass and small particles left after considerable reaction can pass through the grate and collected below The producer gas which is flown upwards, leave the gasifier at the side of the top section and is burned out at the combustion chamber 2.3 Experimental procedure and data reduction The feeder was pre-calibrated with biomass pellets used in the experiment Once the air temperature was reached around 1000 °C Materials and methods 2.1 Materials The biomass pellets used in the experiment (Fig 1) were supplied by Boson Energy S.A The length distribution of pellets considering 50 numbers of pellets is given in Fig It can be seen that the majority of pellets are in the range of 11– 15 mm in length Physical properties of pellets (before the experiment) can be summarized as in Table Pellet proximate and ultimate analysis along with the heating value is given in Table 2.2 Gasification system Gasification experiments were carried out in updraft High Temperature Agent Gasifier (HTAG) unit with 0.4 m diameter (Fig 3) Fig Biomass pellets 260 D.S Gunarathne et al / Applied Energy 113 (2014) 258–266 Fig Length distribution of pellets Table Physical properties of pellets Parameter Value Diameter (mm) Mean length (mm) Moisture content (%) Bulk density (kg/m3) Particle density (g/cm3) Porosity – e Sphericity – U Diameter of equivalent spherical particle (mm) – dp 14 9.8 603 1.09 0.44 0.85 11 Table Composition of pellets Parameter Value Moisture content at 105 °C Ash cont at 550 °C LHV Volatile matter Bulk density 9.8% 1.9% (dry) 16.6 MJ/kg (as received) 81.2% (dry) 603 kg/m3 Ultimate analysis Carbon C Hydrogen H Nitrogen N Oxygen O 49.4% (dry) 5.9% (dry) 0.17% (dry) 42.6% (dry) by using preheater, desired feed rate was achieved by adjusting frequency of feeder Temperatures inside the gasifier were measured with type S thermocouples located along the reactor height and recorded by data acquisition system connected to a PC Pressure inside the gasifier below the grate and three more points above the grate were measured with digital manometers so that bed pressure drop can be calculated It was assumed that the horizontal gradient of temperature and pressure is not significant Syngas composition was measured with Gas chromatography (GC) Tar samples were collected from the gas outlet pipe and analyzed later for quantity and composition For each run, 20 time interval was selected for analysis This time interval was selected based on stable temperatures and gas compositions Average values of gas compositions and temperatures within this time interval were taken for analysis From ultimate analysis of fuel, the average chemical formula of pellets was obtained as CH1.43O0.65 and it was used to calculate the stoichiometric air to fuel ratio for calculating Equivalence Ratio (ER) Gas flow rate was calculated by applying Nitrogen balance over the gasifier The average gas properties such as density and viscosity within the gasifier bed were calculated by taking volume average with gas composition data at average bed temperature Results and discussion 3.1 Process performance Table gives experimental data and Figs 4–6 show variation of temperature along the gasifier height, gas compositions and characteristic ratios respectively Table gives the tar composition and tar characteristic ratios of each run From temperature data, we see different bed temperature behaviours with two cases Run with low ER shows gradual temperature drop throughout the bed height and run with high ER shows high temperature adjacent to the grate with sudden drop after that Then it can be expected with run 2, CO2 and H2O generated by exothermic combustion reactions at high temperature zone near the grate has reduced to CO and H2 by endothermic boudouard and water gas reactions at the subsequent low temperature region As a result, high CO and H2 content can be seen with run They were respectively 4% and 5% increment compared to run In overall, low temperature was seen throughout the gasifier with low ER in run and comparatively high hydrocarbon and also tar content was observed compared to run due to cracking reactions Even with low CO and H2 contents, as a result of high CH4 and CxHy contents which were around 11% and 140% higher than run 2, LHV is slightly higher with run However, high CO and H2 content with run resulted in high gas yield and hence considerably higher efficiency Fig HTAG system 261 D.S Gunarathne et al / Applied Energy 113 (2014) 258–266 Table Experimental data Run a Table Tar composition data Dry biomass (kg/h) Feed gasa (N m3/h) ER 54.12 45.1 69 69 0.22 0.27 Quantity lg/100 ml Run (ER = 0.22) Run (ER = 0.27) Benzene Toluene m/p-Xylene o-Xylene Indan Indene Naphthalene 2-Methylnaphthalene 1-Methylnaphthalene Biphenyl Acenaphthylene Acenaphthene Fluorene Phenanthrene Anthracene Fluorantene Pyrene Phenol o-Cresol m-Cresol p-Cresol Unknown Total (g/N m3) 269.7 112.7 11.5 7.4 4.1 118.8 219.6 22.8 31.5 8.8 97 21.5 25.8 7.6 10.3 45.6 1.9 7.1 1.4 223 12.5 186.5 43 3.1 9.8 4.7 22.4 55.7 16.1 19.4 0.6 2.8 2.2 0 4.1 0 69.1 4.4 Characteristic ratios C2H6/(C2H4 + C2H2) Phenols/aromatics Indene/naphthalene 0.29 0.1 0.54 0.1 0.03 0.4 LHV (MJ/ N m3) Gas yield (N m3/kg dry biomass) Efficiency (%) Component 5.59 5.55 2.18 2.63 66.42 79.4 Feed gas contains 17% O2, 81% N2 and 2% CO2 Fig Temperature profile along the gasifier height Fig Gas compositions high temperature and longer bed There was no significant difference seen with H2/CO ratio of two cases Significant reduction of almost all the tar components was seen with run Tar characteristic ratios were also reduced and it represents that high temperature and longer bed has a positive impact on tar decomposition reactions Referring to Table 5, it was observed a considerable bed height achieved with each run When bed height is higher, residence time for both solid and gas phase reactions are larger and it is reflected by high CO and H2 content, gas yield and gasification efficiency obtained with run Specially, significant reduction of tar content is also positive However, the drawback of such large bed is large pressure drop of the system which ultimately affects the system performance Therefore, prediction of pressure drop of a gasifier bed is a quite interesting topic for anyone concerning the system performance 3.2 Prediction of pressure drop 3.2.1 Developing the correlation Total pressure drop through a gasifier bed is mainly a sum of pressure drop through the particle bed and pressure drop through the grate However, in this study, grate resistance can be considered as negligible since grate opening area is high as much as 40% and the grate thickness is low which is mm Literature [1] has derived Eq (1) based on equivalent tortuous passage method for pressure drop DP over a bed height of L in a turbulent flow using Blasius smooth pipe equation for a packed bed with cylindrical particles of diameter d and length c, Fig Gas characteristic ratios When characteristic ratios are considered, CO/CO2 ratio was higher with run CH4/H2 and CxHy/CH4 ratios were higher with run CH4/H2 and CxHy/CH4 ratios show the effectiveness of hydrocarbon cracking and cracking shows more effective in run due to Table Bed heights and pressure drop Run Bed height (m) Pressure drop across the bed (Pa) 0.55 0.6 1000 1190 262 D.S Gunarathne et al / Applied Energy 113 (2014) 258–266  ð1 À eÞ5=4 DP ¼ LK t qu2 1 þ 2c d e 5=4  1=4 l qu Kt is a constant combining roughness of the particles and packing tortuosity all together and has determined experimentally and related to porosity e as follows K t ¼ 112e3:2 Since they have considered only the inertial term of pressure drop, it can be modified to fit to laminar or transitional flows also by adding a viscous term Hagen–Poiseuille equation for pressure drop in laminar flow is, DP ¼ 32lv l D2e Fixing to the definitions in [1] which are tabulated in Table assuming equivalent inclined passage with an angle k to the direction of mean flow, Hagen–Poiseuille equation can be re-arranged as, DP ¼ 32luL ð1 À eÞ2  2 1 þ 2c d e3 ð2Þ Then, by combining Eqs (1) and (2) and rearranging, Rangel equation can be modified for any flow condition as,    DP K1 K2 ¼ 1=4 þ L qu2 Rep Rep ð3Þ qu where Rep ¼ ðlÞ K3 K ¼ 112e0:2 ð1 À eÞ K ¼ 32 ð1 À eÞ  1 þ 2c d  e 1 þ 2c d     1 K ¼ ð1 À eÞ þ 2c d U¼ " #1=3 2:25 à ðdc Þ2 À Á3 0:5 þ dc ð5Þ Then, porosity e of a bed with cylindrical particles is obtained as a function of particle size c and d 3.2.1.2 Shrinking effect of particles Due to the reaction happening in the gasifier bed, the particle size is changing along the bed This results in change of sphericity and consequently the porosity of the bed Wall effect and thickness effects on porosity variation can be neglected for the cases with tube to particle diameter ratio D/dp and bed height to particle diameter ratio L/dp are high According to [9] the values should be D/dp P 10 and L/dp > in order to neglect those effects This assumption was applied here assuming the gasification is done in a pilot scale unit with considerable diameter compared to particle size and achieving considerable height of bed which only necessitates pressure drop prediction Particle size of a reacting bed can be calculated by applying mass balance for one particle and mass of char particle mchar and mass of initial biomass particle mbiomass can be related as, mchar ¼ ð1 À xÞmbiomass Practically two types of size reductions can be expected in a gasifier; fragmentation and conversion Fragmentation can be taken as less important when it comes to wood pellets compared to wood chips gasification due to high density of pellets [10] Therefore, surface conversion was assumed to dominate in this case With surface conversion, density of biomass particle can be taken as constant throughout the conversion period Then, volume of char particle and volume of initial biomass particle can be related same as above If initial length and diameter was considered as c0 and d0 it becomes, 2 cd ¼ ð1 À xÞc0 d0 Graphical representations of above correlation constants for typical biomass pellet sizes available in the market are annexed 3.2.1.1 Relation of porosity and sphericity in a bed of cylindrical particles Some researchers [8] have formulated a relationship between porosity and sphericity U for loose random packing of cylindrical particles as given in Eq (4) This correlation shows very good agreement with their experimental data ln e ¼ U5:58 exp½5:89ð1 À Uފ ln 0:4 ð4Þ The sphericity of a cylindrical particle depends on its length Very long or very short particles give low sphericity The sphericity of cylindrical particle is given by, 1=3 ð36pV 2p Þ U¼ Sp where Vp and Sp are cylinder volume and area respectively Table Defining parameters in tortuous passage Parameter related to tortuous passage Definition fixing to [1] Velocity of flow Equivalent length u v ¼ e cos k Equivalent diameter Hydraulic radius Wetted perimeter Substituting for volume and area, ð1Þ l ¼ cosL k De = 4rH e r H ¼ a cos k S a ¼ Vpp ð1 À eÞ ð6Þ For a cylindrical wood pellet, assuming uniform thickness h is reduced for a certain time period from all its dimensions [11], after a certain time new length c and diameter d of particle is given by, c = c0 À 2h and d = d0 À 2h Avoiding unknown h, c À d ¼ c À d0 ð7Þ c d Knowing c0, d0 and x, can be obtained from Eqs (6) and (7) and used in Eq (5), in order to calculate sphericity And then, sphericity can be used in Eq (4) for calculating porosity These values along with flow properties such as velocity, density and viscosity can be used in Eq (3) in order to calculate pressure drop along the gasifier bed for a known conversion and bed height 3.2.2 Calculation of pressure drop Conversion x at the top of the bed is and at the bottom x is assumed to be The average mass conversion within the bed can be calculated based on the C, H and O molar balance Table summarizes the molar inputs, outputs and also accumulated in char From molar rates of each species accumulated in char which is equal to difference in input and output, hourly char generation can be calculated and it is 12.78 kg/h and 12.68 kg/h respectively in two cases Then, average mass conversion x in the bed is 0.79 and 0.75 respectively With conversion values calculated, referring to Section 3.2.1, c, d, U and e can be calculated and given in Table The particle diameter and average length has reduced respectively from mm and 14 mm initial values to around 4.5 mm and 10 mm at the average conversion With reduced particle sizes 263 D.S Gunarathne et al / Applied Energy 113 (2014) 258–266 Table C, H, O molar balance Run Description C (kmol/h) H (kmol/h) O (kmol/h) Input (biomass & feed gas) Output in syngas Char 2.29 1.94 0.35 3.85 2.47 1.38 2.93 2.48 0.45 Input (biomass & feed gas) Output in syngas Char 1.92 1.19 0.73 3.21 2.49 0.72 2.64 2.44 0.20 gas compositions Then, these values along with c, d and e can be used as inputs to the Eq (3) Table represents all the parameters and calculated bed pressure drop for both runs 3.2.3 Incorporating shrinking effect into available empirical correlation for comparison For cylindrical particles some researchers [2] have obtained a relationship with the sphericity and Ergun constants A and B as given in the following equation: " DP ¼ L A Table Pellet properties after conversion Initial length range (mm) Run c d U e Run c d U e 1–5 6–10 11–15 16–20 21–25 26–30 Weighted average 1.09 4.76 9.33 14.14 19.03 23.96 9.7 6.09 4.76 4.33 4.14 4.03 3.96 4.4 0.613 0.874 0.823 0.759 0.706 0.664 0.817 0.558 0.404 0.416 0.443 0.476 0.509 0.421 1.23 5.04 9.65 14.46 19.36 24.29 10 6.23 5.04 4.65 4.46 4.36 4.29 4.7 0.637 0.874 0.828 0.767 0.717 0.676 0.822 0.534 0.404 0.415 0.439 0.469 0.499 0.419 ð1 À eÞ2 l e3 U2 d2p uþB ð1 À eÞq u e3 Udp # ð8Þ 1:75 where A ¼ U150 3=2 and B ¼ U4=3 By incorporating shrinking effect this equation can be improved for a reacting bed To this, sphericity and modified Ergun constants were calculated for each initial length interval and their average values are given in Table 10 The modified constants calculated for two cases are as follows For Run 1, " DP ¼ L 204 ð1 À eÞ2 l e3 U2 d2p u þ 2:3 ð1 À eÞq u e3 Udp # For Run 2, " DP ¼ L 202 Table Summary of parameters for bed pressure drop calculation Parameter Run Run T u 887 1.11 0.2692 4⁄10À5 9.7 4.4 0.421 7.03 56.77 0.55 1005 907 1.13 0.2662 4.02⁄10À5 10 4.7 0.419 6.92 60.53 0.6 1274 q l c d e Kt Rep L DP Table 10 Summary of calculating modified Ergun constants A and B Initial length range (mm) Run Average sphericity A B Run Average sphericity A B 1–5 6–10 11–15 16–20 21–25 26–30 Weighted average 0.613 0.874 0.823 0.759 0.706 0.664 0.817 313 184 201 227 253 277 204 3.36 2.09 2.27 2.53 2.78 3.02 2.30 0.637 0.874 0.828 0.767 0.717 0.676 0.822 295 184 199 223 247 270 202 3.19 2.09 2.25 2.49 2.73 2.95 2.28 it can be expect that low porosity since small sized particles pack more tightly than large size ones Proving this, the initial porosity 0.445 has reduced up to 0.42 at achieved conversion With conversion, pellets get small and porosity is reduced Therefore, porosity at the top of the reacting bed is highest and it is lowest at the bottom Density, viscosity and superficial velocity of gas flow inside the bed can be approximated by bed temperature, gas flow rate and ð1 À eÞ2 l e3 U2 d2p ð1 À eÞq u þ 2:28 u e Udp # Ergun indices obtained are 35% and 31% increased respectively compared to original Ergun constants which are 150 and 1.75 for viscous and inertial terms respectively When bed is composed of cylindrical particles, the pressure drop is higher compared to packing spherical particles The orientation of particles, tortuosity and wetted surface are blamed regarding this increase [2] 3.2.4 Validation with experimental data Pressure drop results calculated with developed correlation and empirical correlation can be compared with experimental data as given in Fig The method formulated in the present study gives better approximation with only 7% maximum error with respect to performed two runs The available empirical equation was able to predict the pressure drop within 20% interval after shrinking effect was taken into account Fig Comparison of pressure drop results 264 D.S Gunarathne et al / Applied Energy 113 (2014) 258–266 Fig A1 Variation of K1 with conversion for pellets of mm diameter Fig A2 Variation of K2 with conversion for pellets of mm diameter Fig A3 Variation of K3 with conversion for pellets of mm diameter D.S Gunarathne et al / Applied Energy 113 (2014) 258–266 Fig A4 Variation of K1 with conversion for pellets of mm diameter Fig A5 Variation of K2 with conversion for pellets of mm diameter Fig A6 Variation of K3 with conversion for pellets of mm diameter 265 266 D.S Gunarathne et al / Applied Energy 113 (2014) 258–266 Conclusions A correlation for pressure drop prediction in a gasifier bed with cylindrical particles was proposed, compared with available empirical correlation for cylindrical pellets and verified with experimental data Based on the developed correlation, simplified graphical representations were introduced for commonly available pellet sizes in order to reduce the calculation effort The plots developed can be effectively used as a guide for selecting suitable pellet size and designing a grate so that it can be met the system requirements Acknowledgements Authors like to acknowledge KIC-innoenergy project which provided the financial support and Boson Energy S.A which provided the biomass samples for experimental work One of authors, Duleeka Sandamali Gunarathne would like to acknowledge the financial supporting from the European Commission This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein Appendix A Graphical representation of correlation constants It was reported that pellet size has the more impact on the shrinking behavior, not the composition of pellet [12,13] Commercially available pellets are commonly found with mm and mm in diameter with maximum length to diameter ratio being [14] Then, for those pellets, following figures can be used to find the K values to be used in the Eq (3) at any conversion if the initial particle size distribution is known According to Figs A1–A6, very rapid increase of K values and hence the pressure drop can be seen at the end of the conversion period which is happening in the bottom of the bed By having a grate opening area large enough to maintain conversion below 0.9 may be beneficial in this case depending on the ability of the system to overcome the pressure drop Therefore, someone can use these figures as a guide for designing a suitable grate for the system On the other hand, smaller the pellet size, larger the pressure drop in the system and it is also clearly seen in these figures With lower length to diameter ratio and small diameter, all the K values and hence the pressure drop will be high Therefore, this can be another guide for selecting a suitable pellet size for the system requirements References [1] Rangel N, Santos A, Pinho C Pressure drop in packed shallow beds of cylindrical coke stoppers Trans IChemE 2001;79(Part A) [2] Nemec D, Levec J Flow through packed bed reactors: Single-phase flow Chem Eng Sci 2005;60:6947–57 [3] Sharma AK Modeling fluid and heat transport in the reactive, porous bed of downdraft (biomass) gasifier Int J Heat Fluid Flow 2007;28:1518–30 [4] Sreekanth M, Kolar AK Progress of conversion in a shrinking wet cylindrical wood particle pyrolysing in a hot fluidized bed J Anal Appl Pyrolysis 2009;84:53–67 [5] Luckos A, Bunt JR Pressure-drop predictions in a fixed-bed coal gasifier Fuel 2011;90:917–21 [6] Donaj P, Izadpanah MR, Yang W, Blasiak W Effect of pressure drop due to grate and bed resistance on the performance of a downdraft gasifier Energy Fuels 2011;25(11):5366–77 [7] Lucas C High temperature gasification of biomass in an updraft fixed bed batch type gasifier PhD thesis, ISBN 91-7178-067-X [8] Zou RP, Yu AB Evaluation of the packing characteristics of mono-sized nonspherical particles Powder Technol 1996;88:71–9 [9] Foumeny EA, Roshani S Mean voidage of packed beds of cylindrical particles Chem Eng Sci 1991;46(9):2363–4 [10] Teixeira G, Van de Steene L, Martin E, Gelix F, Salvador S Gasification of char from wood pellets and from wood chips: textural properties and thermochemical conversion along a continuous fixed bed Fuel 2012;102:514–24 [11] Nffiez C, Cruells M, Garcia-Soto L A general shrinkage particle model for the chemical dissolution of all types of cylinders and discs Hydrometallurgy 1994;36:285–94 [12] Erlich C, Björnbom E, Bolado D, Giner M, Fransson TH Pyrolysis and gasification of pellets from sugar cane bagasse and wood Fuel 2006;85:1535–40 [13] Erlich C, Fransson TH Downdraft gasification of pellets made of wood, palmoil residues respective bagasse: experimental study Appl Energy 2011;88:899–908 [14] Cocchi M, Nikolaisen L, Junginger M, Goh CS, Heinimö J, Bradley D, et al Global wood pellet industry market and trade study, IEA Bioenergy Task 40: Sustainable international bioenergy trade; 2011