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ash deposition and near-wall segregation in slagging entrained-flow gasification of solid fuels: from experiments to closure equations
Fuel 264 (2020) 116864
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Full Length Article
Char/ash deposition and near-wall segregation in slagging entrained-flow gasification of solid fuels: from experiments to closure equations
T
⁎
Maurizio Troianoa, , Roberto Solimeneb, Fabio Montagnaroc, Piero Salatinoa a
Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università degli Studi di Napoli Federico II, P.le V. Tecchio, 80, 80125 Napoli, Italy Istituto di Ricerche sulla Combustione, Consiglio Nazionale delle Ricerche, P.le V. Tecchio, 80, 80125 Napoli, Italy c Dipartimento di Scienze Chimiche, Università degli Studi di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo, 80126 Napoli, Italy b
A R T I C LE I N FO
A B S T R A C T
Keywords: Gasification Ash Deposition Segregation Slag Entrained-flow
The performance of entrained-flow gasifiers of solid fuels is critically affected by the complex gas-solid multiphase flow patterns and near-wall segregation of char/ash particles. The impact-deposition-rebound dynamical patterns of particles, as they approach and collide onto the walls, control the establishment of near-wall segregated phases. A detailed micromechanical analysis of char/ash particles interaction with a surface is considered to characterize ash deposition onto the walls and adhesion and inelastic rebound of char particles. The effect of the residual carbon content within the particles, from char after devolatilization to ash particles, as well as the influence of the impact velocity, have been investigated for different fuels. The experimental outcomes have been used to derive closure equations describing the behaviour of char/ash particles after the collision with the wall, in terms of deposition and inelastic rebound. It has been highlighted that impact velocity and carbon conversion do affect the deposition tendency of char and ash particles, while the inelastic rebound is mainly influenced by the mechanical properties of the bulk of the particles, which are closely dependent on the particle structure developed during the gasification process.
1. Introduction Gasification is steadily keeping a pivotal role in the exploitation of solid fuels for energy conversion and production of chemicals [1]. Entrained-flow gasification is currently the prevailing technology for commercial applications thanks to the favourable range of operating conditions in relation to the quality of the syngas produced. Among the strengths of entrained-flow slagging gasifiers, there are very high carbon conversion, promoted by severe operating conditions (pressure around 4–10 MPa and temperature in the range 1300–1800 °C), good adaptability to the fuel quality (from bituminous to low-grade coals, waste and biomass), production of high-purity syngas with very small amount of tars. Furthermore, entrained-flow gasifiers (EFG) are characterized by high specific capacity and relatively small dimensions. Recently, EF gasification has also been tested for solar fuel production, as it can overcome some drawbacks typically observed in packed bed reactors [2–4]. Most industrial EFG operate in the slagging mode: char/ ash particles are heated above the ash melting point, hence they deposit on the wall, forming a slag layer which acts as a protective coating for the prevention of heat loss at the gasifier wall and for the protection of the wall materials, whose durability results improved [5,6]. In such
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multiphase reactors, particle–wall interactions play a crucial role. Fuel particles migrate toward the reactor walls, mainly due to swirled/tangential flow and “turbophoresis” promoted in the reaction chamber. Uncontrolled formation and build-up of the slag layer can cause refractory corrosion and plugging. Moreover, excessive slag deposition reduces the overall heat transfer coefficient in EFG equipped with membrane wall, whereas slag layer composition, temperature and velocity deeply influence the corrosion rate of the refractory bricks and their overall lifetime in EFG equipped with refractory lining [7]. The performance of slagging EFG may be critically affected by the behaviour of char/ash particles as they interact with the slag-covered wall [8–10]. Different micromechanical patterns can establish, depending on parameters such as particle and wall temperatures, unfused vs. molten status of the particles and of the wall layer, degree of char conversion, particle kinetic energy, surface tension of the slag layer, particle effective stiffness and char/slag interfacial tension [5,11–13]. The establishment of a particle segregated phase in the near-wall region of the gasifier was considered in the phenomenological model proposed by Montagnaro and Salatino [14]. The annular particle segregated phase is characterized by longer residence times in the gasifier when compared with the lean particle-laden gas phase, a feature beneficial to
Corresponding author. E-mail address: [email protected] (M. Troiano).
https://doi.org/10.1016/j.fuel.2019.116864 Received 30 September 2019; Received in revised form 4 December 2019; Accepted 12 December 2019 Available online 24 December 2019 0016-2361/ © 2019 Elsevier Ltd. All rights reserved.
Fuel 264 (2020) 116864
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Nomenclature
ε
A B C D k R2 vi X w α
Subscripts
parameter in Eq. (3) (–) parameter in Eq. (3) (–) parameter in Eq. (4) (–) parameter in Eq. (4) (–) constant in Eqs. (2) and (5) (–) coefficient of determination (–) impact velocity (m/s) conversion degree (–) residual content (–) mass fraction (–)
50 ad C inel
coefficient of restitution (–)
relative to 50% of cumulative distribution relative to adhesion carbon relative to inelastic rebound
Superscripts *
critical value
describing the behaviour of char/ash particles in the near-wall region of EFG, in terms of ash deposition onto the walls and char particles adhesion and inelastic rebound, on the basis of experimental results. In particular, the micromechanics of char/ash particles interaction with a surface is analysed for different fuels, considering the effect of impact velocity and of the residual carbon content in the particles from char to ash state. Closure equations are then proposed, which describe the partitioning of char/ash particles among the different segregated phases in EFG, in particular during the “dry wall” and “wet wall post-coverage” stages.
enhanced carbon conversion. In such a phenomenological framework, Troiano et al. [15] examined particle segregation considering particle migration toward the wall, interaction upon impact with the wall ash layer, coverage of the slag layer by refractory carbon particles, accumulation of char particles in the near-wall region of the gasifier and heterogeneous gasification of char. Four different stages establish along the reactor, corresponding to different modes according to which char segregation from the particle-laden lean dispersed phase to the wall takes place, as reported in Fig. 1 (see [15] for a more comprehensive analysis). The first stage, “dry wall”, occurs close to the feeding point. Char and molten ash particles are radially transferred toward the dry (i.e., not yet fully covered by the slag layer) wall. As particles impact the dry wall, they may either adhere or rebound. Deposition of molten ash on the reactor walls results in the formation of a “slag phase”, possibly associated with embedded char particles. Instead, ash and char particles rebounding with small values of the restitution coefficient give rise to a “dense-dispersed phase”, which progressively builds up as a “curtain” of particles in the near-wall region of the gasifier. When the thickness of the slag layer reaches a critical value, the fully developed slag layer incorporates all impinging ash particles (stage “wet wall precoverage”). Char particles impinging the slag layer are trapped but not fully incorporated in the slag (due to interfacial forces [14]), gradually forming a carbon-rich refractory coverage of the slag layer. During this stage particle rebound is prevented, allowing no particle flux from the walls to the dense-dispersed phase. This interaction mode is active until a uniform monolayer coverage of particles on the slag surface is established. When the slag layer is fully covered by “refractory” char particles, further impacting particles coming from the lean phase will either rebound or adhere (stage “wet wall post-coverage”). During this stage the dense-dispersed phase grows again, mainly due to the contribution of low-kinetic energy rebounds of char particles. When the thickness of the dense-dispersed phase exceeds a critical value, all particles moving to the wall lose their momentum in the dense-dispersed phase and are trapped therein (stage “fully developed densedispersed phase”). Particle input to the slag phase is likely to be very limited at this stage as a consequence of the screening effect of the dense-dispersed phase. In spite of several numerical studies on the behaviour of particles and slag in EFG [5,16–20], the fate of char/ash particles in the nearwall region of EFG still lacks accurate predictive tools based on mathematical and physical modelling of particle–wall interaction [21,22]. Experiments are essential to build closure equations describing the near-wall flow and micromechanical patterns in such reactors and which can be embedded in mathematical models or in CFD codes. Recently, this research group has carried out impact experiments under cold and hot operating conditions in order to characterize the behaviour of particles with different residual carbon content upon the collision onto a planar surface. Experiments have been performed under a variety of operating conditions and with fuel particles of different nature (coal and biomasses) [23,24]. This study aims at providing a method to develop closure equations
2. Methodology An accurate analysis of the mechanisms and behaviour of char and ash particles in confined multi-phase flows, such as EF slagging gasifiers, requires the characterization of the rebound/deposition behaviour
Fig. 1. Outline of the near-wall region of the entrained-flow gasifier, with indication of the four particle–wall interaction stages. 2
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of particles as they impact to the walls. Collisions of non-spherical particles occur onto the refractory material, the slag layer and onto other particles adhered on the slag layer. Furthermore, the interactive patterns are deeply affected by particle stickiness as a consequence of the variation of the particle mechanical properties with temperature and residual carbon content [11,19,21,25–29]. Particle–wall collisions are generally characterized in terms of a restitution coefficient ε, defined as the ratio between the rebound and the impact velocity. The coefficient takes the value ε = 1 for a perfectly elastic impact, whereas ε → 0 when the particles dissipate all their kinetic energy at the impact and adhere on the surface. The restitution coefficient embodies different phenomena like elasto–plastic deformation and viscoelastic behaviour (energy loss due to wave propagation) of solid materials, surface contact forces and particle–wall friction. Furthermore, the propensity to adhesion can be experimentally measured by means of a deposition efficiency, defined as the number of particles with ε = 0 over the total number of particles impacting the wall. In the present study, previous experimental results [23,24] are critically analyzed in order to derive closure equations that embody the detailed mechanistic description of the interaction between the particle-laden mainstream flow and the wall. Experiments were carried out in an apparatus consisting of a high-temperature furnace and a hot impact chamber. Batches of micron-sized particles (150–180 μm) were fed at the top of the furnace by means of two on/off valves and entrained towards the impact zone by a nitrogen stream. The impact chamber was purposely designed to be optically accessible and to guarantee the desired temperature. A target of refractory material was placed in the impact chamber. Particle impact velocity was controlled by regulating the nitrogen volume flow rate, and it was calculated as the sum of the gas velocity and the particle terminal velocity. Particle impact and rebound velocities were experimentally measured by particle tracking using a fast camera. The coefficient of restitution upon impacts was determined by comparing particle velocities before and after the collision. Details about the experimental tests are reported elsewhere [23,24]. Impact tests on a planar surface were performed at temperatures typical of EFG operation (1400 °C), and the effect of both carbon conversion XC and impact velocity vi was investigated. A subbituminous coal (Illinois #6) and two types of biomass were considered, namely wood chips and corn stover. As a function of the fuel nature, samples with XC in the range from 0 (char) to 1 (ash), and vi in the range from 0.5 to 2 m s−1, were considered. The degree of carbon conversion was also expressed in terms of wC (the fractional concentration of residual carbon in the particle). Pre-conversion of particles was carried out in a tubular furnace (nitrogen flux, 900 °C for coal, 750 °C for the two biomasses) to obtain fuel samples characterized by different degrees of carbon conversion. After pyrolysis, char particles underwent CO2 gasification (900 °C) for different reaction times (so as to obtain samples with different values of XC ). Details on the procedure are reported in [23,24]. Altogether, experimental results were analyzed in order to obtain two key parameters: αad , the fractional mass of particles that adhere to the wall upon impact, and αinel , the fractional mass of particles that undergo inelastic rebound upon impact on the wall and reports to the dense-dispersed phase. αad represents the tendency (in terms of mass fraction) of ash particles to deposit onto the walls to form the slag layer and the tendency of char particles to adhere onto the walls, the slag layer and other particles covering the slag layer. Thus, αad is a crucial parameter for the formation of the slag layer and for the establishment of the dense-dispersed phase. It can be expressed as a function of the particle velocity approaching the wall, vi , and of the relative amount of fusible ash and “refractory” unfused carbon in the char particles, expressed by wC , while αinel is proportional to the product between (1 – ε) and (1 – αad ) through a constant k [15]:
αad = αad (vi, wC )
Fig. 2. Cumulative distribution of the global coefficient of restitution obtained from experiments with Illinois #6 coal particles at 1400 °C and vi = 1.15 ± 0.09 m s−1. Data for samples with different values of residual carbon content (wC ) or, equivalently, carbon conversion degree ( XC ).
αinel = k (1 − ε )(1 − αad )
(2)
In order to characterize the impact-deposition-rebound behaviour of particles colliding with a planar surface, it can be useful to assess the distribution of the coefficient of restitution rather than the mean coefficient of restitution. The cumulative distributions of the global coefficient of restitution ε are reported in Fig. 2 for experiments carried out at 1400 °C with Illinois #6 char particles having different residual carbon content, at fixed impact velocity vi = 1.15 ± 0.09 m s−1. The cumulative distributions show the mean values of the coefficient of restitution with the standard deviation obtained considering a variation of ± 10% in the number of tracked particles. The distributions clearly highlight the stochastic nature of the restitution coefficient, with ε distributed in the range between 0 and 0.7. All the distributions, and in particular those with high carbon conversion (e.g. low residual carbon content), display a peculiar two-fold character, reflecting the two basic mechanisms underlying the restitution coefficient [30]: a) adhesion (when ε = 0); b) non-elastic particle interaction with the wall. The first process is ruled by interfacial forces establishing between the particle and the wall, and depends on surface properties of both. The second process is essentially dictated by plastic behaviour of the bulk of the particle. The fraction of particles with ε = 0 pertains to particles permanently deposited on the surface due to adhesion, and ranges between 0 and 30% for char particles, raising to approximately 65% for the carbon-free ash (wC = 0 and XC = 1). The fraction of particles αad that are permanently deposited is reported in Fig. 3 for char particles with different carbon conversion, as well as for ash particles ( XC = 1), for a fixed impact velocity, vi = 1.15 ± 0.09 m s−1. It is noteworthy that the deposition probability, hence αad , is larger than zero, as a consequence of the large energy losses related to the bulk properties of the impacting particles and to the surface properties of both the particles and the target. A pronounced discontinuity in both the coefficient of restitution and the deposition efficiency is displayed when char-slag transition occurs, i.e. at XC around 90% for Illinois #6 char particles [31]. In fact, the presence of the char-slag transition does affect the stickiness and thus the mechanical properties of the impinging particles. Particles not adhered upon collision, rebound. A fraction of these particles rebound close to the wall (in the dense-dispersed phase), the rest being transferred back to the lean phase, depending on the particle kinetic energy after collision. The fraction of particles which is transferred to the dense-dispersed phase, αinel , is (cf. Eq. (2)) proportional to (1 – ε), where ε can be assumed as ε50 (the value of ε corresponding to a cumulative distribution value of 50%) from the cumulative distribution
(1) 3
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stover particles were fitted to obtain closure equations for (i) the fractional mass of particles adhering onto the wall after the impact, αad , as a function of the impact velocity, vi , and the residual carbon content, wC , see Eq. (3) and [15]; (ii) ε50 (the value of the coefficient of restitution corresponding to a cumulative distribution value of 50%), as a function of wC , see Eq. (4):
A
αad (vi, wC ) =
(vi − vi∗ ) ⎡1 + exp ⎣ ε50 (wC ) = CwC + D
(
wC − wC∗ B
) ⎤⎦
(3) (4)
A, B, C and D are constant parameters, vi∗ and wC∗ represent critical values for the impact velocity and residual carbon concentration, respectively. In particular, wC∗ represents the residual carbon concentration in the particles for which the char-slag transition occurs. Eq. (3) expresses that αad decreases with increasing impact velocity and with increasing residual carbon content, while Eq. (4) expresses that ε50 increases with increasing residual carbon content. Parameters found for Eqs. (3) and (4) are listed in Table 1 for the three fuels, together with the coefficient of determination R2 when comparing experimental data and results from Eq. (3). The coefficient of determination R2 between experimental data and values obtained by applying Eq. (3) is in the range 0.71–0.94 for the different fuels, demonstrating a good fitting of the experimental results in terms of αad . Furthermore, for both the biomass types, the constant C in Table 1 is zero, confirming that for both wood chips and corn stover particles there is a negligible effect of the carbon conversion on the rebound characteristics (no clear char-slag transition). The expression obtained in Eq. (3) for αad has been used to compare the proposed closure equation with experimental data available in the literature. Li et al. [31] reported the capture efficiency of char particles of Illinois #6 coal during gasification in a laminar entrained-flow reactor. Experiments were carried out at 1400–1500 °C by using a deposition probe inserted in the laminar flow reactor. The capture efficiency was defined as the mass ratio of particles captured by the target to the particles that impacted the target, which corresponds to αad in this work. Comparison of the experimental data reported by Li et al. [31] with the proposed Eq. (3), applied to the same fuel, is reported in Fig. 10. The agreement between experimental data and the proposed model is good, confirming the reliability of the proposed closure equation in the description of the deposition efficiency of char, partially converted char and ash particles.
Fig. 3. Deposition efficiency as a function of carbon conversion for experiments with Illinois #6 coal particles at 1400 °C and vi = 1.15 ± 0.09 m s−1.
normalized with respect to the adhered particles fraction αad , as reported in Fig. 4. It is noteworthy that ε50 depends on the residual content of carbon within the particles. In particular, ε50 decreases with decreasing residual carbon concentration wC , as a consequence of the different mechanical properties of the particles with increasing carbon conversion XC . Thus, the fraction of particles transferred to the densedispersed phase, αinel , can be expressed as a function of ε50 and αad as in Eq. (2). Altogether, a schematic representation of bulk-to-wall solid transfer is reported in Fig. 5 with indication of the partitioning of particles in the different segregated phases in the near-wall region of the gasifier. 3. Development of closure equations The experimental data have been used to develop closure equations to quantitatively express the fate of char/ash particles after the collision with a surface in terms of partitioning among the different phases, i.e. slag, dense-dispersed and lean-dispersed phase. The fraction of particles αad adhering onto the wall as a function of the impact velocity is reported in Fig. 6 for coal particles with different carbon conversion values. αad decreases with increasing impact velocities, as a result of the increasingly ineffective adhesion as the kinetic energy of the impinging particle increases. In particular, αad approaches 0 for char particles ( XC = 0, 16%, 50%), around 0.2 for char particles at char-slag transition ( XC = 90%) and around 0.45 for ash particles ( XC = 100%). The values of the restitution coefficient ε50 are reported in Figs. 7–9 for Illinois coal, corn stover and wood chips particles, respectively, while varying the impact velocity and the residual carbon content. For coal particles, ε50 in Fig. 7 is roughly constant with the impact velocity, while it is affected by the residual carbon concentration. In particular, a pronounced decrease in ε50 is displayed when char-slag transition occurs ( XC = 90%). This outcome confirms that increasing the particle stickiness, larger plastic deformations occur upon the impact and thus ε50 decreases. Values of ε50 for both corn stover and wood chip particles are reported in Figs. 8 and 9, respectively. ε50 is roughly constant with the impact velocity, as reported for coal particles, while, differently from coal particles, it is not affected by the residual carbon content. This result can be explained taking into account that, for these biomass types, there is no evidence of the char-slag transition [24]. As a consequence, there is not an appreciable change in the stickiness and thus in the mechanical properties of the char particles until complete conversion is reached. All the experimental data for Illinois #6 coal, wood chips and corn
Fig. 4. Normalized (with respect to the adhered particles fraction) cumulative distribution of the global coefficient of restitution obtained from experiments with Illinois #6 coal particles at 1400 °C and vi = 1.15 ± 0.09 m s−1. Data for samples with different values of residual carbon content (wC ) or, equivalently, carbon conversion degree ( XC ). 4
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Fig. 5. Schematic representation of solid transfer towards the wall with indication of the segregated phases.
Fig. 6. Fraction of adhered particles as a function of the impact velocity for Illinois #6 coal particles (experiments at 1400 °C). Data for samples with different values of residual carbon content (wC ) or, equivalently, carbon conversion degree ( XC ).
Fig. 8. ε50 as a function of the impact velocity for corn stover particles (experiments at 1400 °C). Data for samples with different values of residual carbon content (wC ) or, equivalently, carbon conversion degree ( XC ).
Fig. 9. ε50 as a function of the impact velocity for wood chips particles (experiments at 1400 °C). Data for samples with different values of residual carbon content (wC ) or, equivalently, carbon conversion degree ( XC ).
Fig. 7. ε50 as a function of the impact velocity for Illinois #6 coal particles (experiments at 1400 °C). Data for samples with different values of residual carbon content (wC ) or, equivalently, carbon conversion degree ( XC ).
5
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have been characterized in terms of fractional mass of particles adhering onto the surface and rebounding upon the collision. The effect of the residual carbon content within the particles from char to ash particles, as well as the influence of impact velocity, have been investigated for different fuels, i.e. Illinois #6 coal, wood chips and corn stover. Closure equations were derived, which enable quantitative assessment of the fate of char/ash particles after collision with the wall, in terms of fractional mass of particles adhering and rebounding upon the collision. Impact velocity and residual carbon content in the char affect the deposition tendency of char and ash particles for all the tested fuels. Inelastic rebound is mainly influenced by the mechanical properties of the bulk of the particles, which are closely dependent on the structure and stickiness of particles during gasification.
Table 1 Parameters for the closure Eqs. (3) and (4) for the different fuels, and coefficient of determination for Eq. (3). All parameters are non-dimensional, except A and vi∗ expressed in m s−1. Fuel
A
B
C
D
vi∗
wC∗
R2
Illinois #6 coal Wood chips Corn stover
0.61 0.61 6.34
0.06 0.47 0.35
0.18 0 0
0.34 0.32 0.33
0.27 0.16 2.74
0.26 0 0
0.94 0.71 0.89
CRediT authorship contribution statement Maurizio Troiano: Conceptualization, Methodology, Formal analysis, Writing - review & editing. Roberto Solimene: Conceptualization, Methodology, Formal analysis, Writing - review & editing. Fabio Montagnaro: Conceptualization, Methodology, Formal analysis, Writing - review & editing. Piero Salatino: Conceptualization, Methodology, Formal analysis, Writing - review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Fig. 10. Comparison of deposition efficiency results obtained in this study and by Li et al. [31]. Reference fuel: Illinois #6 coal.
References
The developed closure Eqs. (3) and (4) have been derived on the basis of impact experiments, as reported in Section 2. The experiments were carried out at high temperature with a planar dry wall. For this reason, referring to Fig. 1, they apply to stage 1 “dry wall”. During this stage, Eq. (3) expresses the mass fraction of adhered particles αad while varying the impact velocity of particles and the residual carbon content. The mass fraction of particles which rebounded upon impact accumulating into the dense-dispersed phase, αinel , is described by:
αinel = k (1 − ε50 )(1 − αad )
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(5)
During stage 2, “wet wall pre-coverage”, it is assumed that αad is equal to 1, which means that mass transfer toward the dense-dispersed phase is prevented by particle deposition onto the slag layer (αinel = 0). During stage 3, “wet wall post-coverage”, particles impact a layer of char particles covering the slag layer. It is likely that, during this stage, the impact behavior resembles the one of stage 1, as the layer of char particles acts as a “wall”. Thus, it can be assumed that Eq. (3) applies also to stage 3. During stage 4, “fully developed dense-dispersed phase”, all the particles moving toward the wall lose their momentum in the dense-dispersed phase and are trapped therein, thus neither Eq. (3) nor (5) applies. It is noteworthy that, in EFG, the fractional mass of particles pertaining to the dense-dispersed phase depends also on the hydrodynamic conditions establishing in the near-wall region of the gasifier. For this reason, a constant k is present in Eq. (5). Further studies are needed for the evaluation of this parameter, in order to express the fractional mass of particles rebounding and reporting to the densedispersed phase by means of a predictive closure equation. 4. Conclusions A critical analysis of impact experiments relevant to entrained-flow slagging gasifiers of solid fuels has been performed in order to develop closure equations describing deposition and inelastic rebound of char/ ash particles after collision with the wall. The impact-deposition-rebound dynamical patterns of particles colliding with a planar surface 6
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around burner plane in an impinging entrained-flow coal gasifier. Chem Eng Sci 2019;198:85–97. https://doi.org/10.1016/j.ces.2019.01.016. Montagnaro F, Salatino P. Analysis of char-slag interaction and near-wall particle segregation in entrained-flow gasification of coal. Combust Flame 2010;157:874–83. https://doi.org/10.1016/j.combustflame.2009.12.006. Troiano M, Montagnaro F, Solimene R, Salatino P. Modelling entrained-flow slagging gasification of solid fuels with near-wall particle segregation. Chem Eng J 2018;119962. https://doi.org/10.1016/J.CEJ.2018.09.123. Weber R, Mancini M, Schaffel-Mancini N, Kupka T. On predicting the ash behaviour using Computational Fluid Dynamics. Fuel Process Technol 2013;105:113–28. https://doi.org/10.1016/J.FUPROC.2011.09.008. Xu J, Liang Q, Dai Z, Liu H. Comprehensive model with time limited wall reaction for entrained flow gasifier. Fuel 2016;184:118–27. https://doi.org/10.1016/J. FUEL.2016.06.122. Hansen SB, Jensen PA, Frandsen FJ, Sander B, Glarborg P. Mechanistic Model for Ash Deposit Formation in Biomass Suspension Firing. Part 2: Model Verification by Use of Full-Scale Tests. Energy Fuels 2017;31:2790–802. https://doi.org/10.1021/ acs.energyfuels.6b01660. Wang J, Kong L, Bai J, Zhao H, Guhl S, Li H, et al. The role of residual char on ash flow behavior, Part 2: Effect of SiO2/Al2O3 on ash fusibility and carbothermal reaction. Fuel 2019;255:115846https://doi.org/10.1016/j.fuel.2019.115846. Ramos A, Monteiro E, Rouboa A. Numerical approaches and comprehensive models for gasification process: A review. Renew Sustain Energy Rev 2019;110:188–206. https://doi.org/10.1016/j.rser.2019.04.048. Kleinhans U, Wieland C, Frandsen FJ, Spliethoff H. Ash formation and deposition in coal and biomass fired combustion systems: Progress and challenges in the field of ash particle sticking and rebound behavior. Prog Energy Combust Sci 2018;68:65–168. https://doi.org/10.1016/j.pecs.2018.02.001. Cai Y, Tay K, Zheng Z, Yang W, Wang H, Zeng G, et al. Modeling of ash formation and deposition processes in coal and biomass fired boilers: A comprehensive review. Appl Energy 2018;230:1447–544. https://doi.org/10.1016/j.apenergy.2018.08.
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Full Length Article
Char/ash deposition and near-wall segregation in slagging entrained-flow gasification of solid fuels: from experiments to closure equations
T
⁎
Maurizio Troianoa, , Roberto Solimeneb, Fabio Montagnaroc, Piero Salatinoa a
Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università degli Studi di Napoli Federico II, P.le V. Tecchio, 80, 80125 Napoli, Italy Istituto di Ricerche sulla Combustione, Consiglio Nazionale delle Ricerche, P.le V. Tecchio, 80, 80125 Napoli, Italy c Dipartimento di Scienze Chimiche, Università degli Studi di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo, 80126 Napoli, Italy b
A R T I C LE I N FO
A B S T R A C T
Keywords: Gasification Ash Deposition Segregation Slag Entrained-flow
The performance of entrained-flow gasifiers of solid fuels is critically affected by the complex gas-solid multiphase flow patterns and near-wall segregation of char/ash particles. The impact-deposition-rebound dynamical patterns of particles, as they approach and collide onto the walls, control the establishment of near-wall segregated phases. A detailed micromechanical analysis of char/ash particles interaction with a surface is considered to characterize ash deposition onto the walls and adhesion and inelastic rebound of char particles. The effect of the residual carbon content within the particles, from char after devolatilization to ash particles, as well as the influence of the impact velocity, have been investigated for different fuels. The experimental outcomes have been used to derive closure equations describing the behaviour of char/ash particles after the collision with the wall, in terms of deposition and inelastic rebound. It has been highlighted that impact velocity and carbon conversion do affect the deposition tendency of char and ash particles, while the inelastic rebound is mainly influenced by the mechanical properties of the bulk of the particles, which are closely dependent on the particle structure developed during the gasification process.
1. Introduction Gasification is steadily keeping a pivotal role in the exploitation of solid fuels for energy conversion and production of chemicals [1]. Entrained-flow gasification is currently the prevailing technology for commercial applications thanks to the favourable range of operating conditions in relation to the quality of the syngas produced. Among the strengths of entrained-flow slagging gasifiers, there are very high carbon conversion, promoted by severe operating conditions (pressure around 4–10 MPa and temperature in the range 1300–1800 °C), good adaptability to the fuel quality (from bituminous to low-grade coals, waste and biomass), production of high-purity syngas with very small amount of tars. Furthermore, entrained-flow gasifiers (EFG) are characterized by high specific capacity and relatively small dimensions. Recently, EF gasification has also been tested for solar fuel production, as it can overcome some drawbacks typically observed in packed bed reactors [2–4]. Most industrial EFG operate in the slagging mode: char/ ash particles are heated above the ash melting point, hence they deposit on the wall, forming a slag layer which acts as a protective coating for the prevention of heat loss at the gasifier wall and for the protection of the wall materials, whose durability results improved [5,6]. In such
⁎
multiphase reactors, particle–wall interactions play a crucial role. Fuel particles migrate toward the reactor walls, mainly due to swirled/tangential flow and “turbophoresis” promoted in the reaction chamber. Uncontrolled formation and build-up of the slag layer can cause refractory corrosion and plugging. Moreover, excessive slag deposition reduces the overall heat transfer coefficient in EFG equipped with membrane wall, whereas slag layer composition, temperature and velocity deeply influence the corrosion rate of the refractory bricks and their overall lifetime in EFG equipped with refractory lining [7]. The performance of slagging EFG may be critically affected by the behaviour of char/ash particles as they interact with the slag-covered wall [8–10]. Different micromechanical patterns can establish, depending on parameters such as particle and wall temperatures, unfused vs. molten status of the particles and of the wall layer, degree of char conversion, particle kinetic energy, surface tension of the slag layer, particle effective stiffness and char/slag interfacial tension [5,11–13]. The establishment of a particle segregated phase in the near-wall region of the gasifier was considered in the phenomenological model proposed by Montagnaro and Salatino [14]. The annular particle segregated phase is characterized by longer residence times in the gasifier when compared with the lean particle-laden gas phase, a feature beneficial to
Corresponding author. E-mail address: [email protected] (M. Troiano).
https://doi.org/10.1016/j.fuel.2019.116864 Received 30 September 2019; Received in revised form 4 December 2019; Accepted 12 December 2019 Available online 24 December 2019 0016-2361/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature
ε
A B C D k R2 vi X w α
Subscripts
parameter in Eq. (3) (–) parameter in Eq. (3) (–) parameter in Eq. (4) (–) parameter in Eq. (4) (–) constant in Eqs. (2) and (5) (–) coefficient of determination (–) impact velocity (m/s) conversion degree (–) residual content (–) mass fraction (–)
50 ad C inel
coefficient of restitution (–)
relative to 50% of cumulative distribution relative to adhesion carbon relative to inelastic rebound
Superscripts *
critical value
describing the behaviour of char/ash particles in the near-wall region of EFG, in terms of ash deposition onto the walls and char particles adhesion and inelastic rebound, on the basis of experimental results. In particular, the micromechanics of char/ash particles interaction with a surface is analysed for different fuels, considering the effect of impact velocity and of the residual carbon content in the particles from char to ash state. Closure equations are then proposed, which describe the partitioning of char/ash particles among the different segregated phases in EFG, in particular during the “dry wall” and “wet wall post-coverage” stages.
enhanced carbon conversion. In such a phenomenological framework, Troiano et al. [15] examined particle segregation considering particle migration toward the wall, interaction upon impact with the wall ash layer, coverage of the slag layer by refractory carbon particles, accumulation of char particles in the near-wall region of the gasifier and heterogeneous gasification of char. Four different stages establish along the reactor, corresponding to different modes according to which char segregation from the particle-laden lean dispersed phase to the wall takes place, as reported in Fig. 1 (see [15] for a more comprehensive analysis). The first stage, “dry wall”, occurs close to the feeding point. Char and molten ash particles are radially transferred toward the dry (i.e., not yet fully covered by the slag layer) wall. As particles impact the dry wall, they may either adhere or rebound. Deposition of molten ash on the reactor walls results in the formation of a “slag phase”, possibly associated with embedded char particles. Instead, ash and char particles rebounding with small values of the restitution coefficient give rise to a “dense-dispersed phase”, which progressively builds up as a “curtain” of particles in the near-wall region of the gasifier. When the thickness of the slag layer reaches a critical value, the fully developed slag layer incorporates all impinging ash particles (stage “wet wall precoverage”). Char particles impinging the slag layer are trapped but not fully incorporated in the slag (due to interfacial forces [14]), gradually forming a carbon-rich refractory coverage of the slag layer. During this stage particle rebound is prevented, allowing no particle flux from the walls to the dense-dispersed phase. This interaction mode is active until a uniform monolayer coverage of particles on the slag surface is established. When the slag layer is fully covered by “refractory” char particles, further impacting particles coming from the lean phase will either rebound or adhere (stage “wet wall post-coverage”). During this stage the dense-dispersed phase grows again, mainly due to the contribution of low-kinetic energy rebounds of char particles. When the thickness of the dense-dispersed phase exceeds a critical value, all particles moving to the wall lose their momentum in the dense-dispersed phase and are trapped therein (stage “fully developed densedispersed phase”). Particle input to the slag phase is likely to be very limited at this stage as a consequence of the screening effect of the dense-dispersed phase. In spite of several numerical studies on the behaviour of particles and slag in EFG [5,16–20], the fate of char/ash particles in the nearwall region of EFG still lacks accurate predictive tools based on mathematical and physical modelling of particle–wall interaction [21,22]. Experiments are essential to build closure equations describing the near-wall flow and micromechanical patterns in such reactors and which can be embedded in mathematical models or in CFD codes. Recently, this research group has carried out impact experiments under cold and hot operating conditions in order to characterize the behaviour of particles with different residual carbon content upon the collision onto a planar surface. Experiments have been performed under a variety of operating conditions and with fuel particles of different nature (coal and biomasses) [23,24]. This study aims at providing a method to develop closure equations
2. Methodology An accurate analysis of the mechanisms and behaviour of char and ash particles in confined multi-phase flows, such as EF slagging gasifiers, requires the characterization of the rebound/deposition behaviour
Fig. 1. Outline of the near-wall region of the entrained-flow gasifier, with indication of the four particle–wall interaction stages. 2
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of particles as they impact to the walls. Collisions of non-spherical particles occur onto the refractory material, the slag layer and onto other particles adhered on the slag layer. Furthermore, the interactive patterns are deeply affected by particle stickiness as a consequence of the variation of the particle mechanical properties with temperature and residual carbon content [11,19,21,25–29]. Particle–wall collisions are generally characterized in terms of a restitution coefficient ε, defined as the ratio between the rebound and the impact velocity. The coefficient takes the value ε = 1 for a perfectly elastic impact, whereas ε → 0 when the particles dissipate all their kinetic energy at the impact and adhere on the surface. The restitution coefficient embodies different phenomena like elasto–plastic deformation and viscoelastic behaviour (energy loss due to wave propagation) of solid materials, surface contact forces and particle–wall friction. Furthermore, the propensity to adhesion can be experimentally measured by means of a deposition efficiency, defined as the number of particles with ε = 0 over the total number of particles impacting the wall. In the present study, previous experimental results [23,24] are critically analyzed in order to derive closure equations that embody the detailed mechanistic description of the interaction between the particle-laden mainstream flow and the wall. Experiments were carried out in an apparatus consisting of a high-temperature furnace and a hot impact chamber. Batches of micron-sized particles (150–180 μm) were fed at the top of the furnace by means of two on/off valves and entrained towards the impact zone by a nitrogen stream. The impact chamber was purposely designed to be optically accessible and to guarantee the desired temperature. A target of refractory material was placed in the impact chamber. Particle impact velocity was controlled by regulating the nitrogen volume flow rate, and it was calculated as the sum of the gas velocity and the particle terminal velocity. Particle impact and rebound velocities were experimentally measured by particle tracking using a fast camera. The coefficient of restitution upon impacts was determined by comparing particle velocities before and after the collision. Details about the experimental tests are reported elsewhere [23,24]. Impact tests on a planar surface were performed at temperatures typical of EFG operation (1400 °C), and the effect of both carbon conversion XC and impact velocity vi was investigated. A subbituminous coal (Illinois #6) and two types of biomass were considered, namely wood chips and corn stover. As a function of the fuel nature, samples with XC in the range from 0 (char) to 1 (ash), and vi in the range from 0.5 to 2 m s−1, were considered. The degree of carbon conversion was also expressed in terms of wC (the fractional concentration of residual carbon in the particle). Pre-conversion of particles was carried out in a tubular furnace (nitrogen flux, 900 °C for coal, 750 °C for the two biomasses) to obtain fuel samples characterized by different degrees of carbon conversion. After pyrolysis, char particles underwent CO2 gasification (900 °C) for different reaction times (so as to obtain samples with different values of XC ). Details on the procedure are reported in [23,24]. Altogether, experimental results were analyzed in order to obtain two key parameters: αad , the fractional mass of particles that adhere to the wall upon impact, and αinel , the fractional mass of particles that undergo inelastic rebound upon impact on the wall and reports to the dense-dispersed phase. αad represents the tendency (in terms of mass fraction) of ash particles to deposit onto the walls to form the slag layer and the tendency of char particles to adhere onto the walls, the slag layer and other particles covering the slag layer. Thus, αad is a crucial parameter for the formation of the slag layer and for the establishment of the dense-dispersed phase. It can be expressed as a function of the particle velocity approaching the wall, vi , and of the relative amount of fusible ash and “refractory” unfused carbon in the char particles, expressed by wC , while αinel is proportional to the product between (1 – ε) and (1 – αad ) through a constant k [15]:
αad = αad (vi, wC )
Fig. 2. Cumulative distribution of the global coefficient of restitution obtained from experiments with Illinois #6 coal particles at 1400 °C and vi = 1.15 ± 0.09 m s−1. Data for samples with different values of residual carbon content (wC ) or, equivalently, carbon conversion degree ( XC ).
αinel = k (1 − ε )(1 − αad )
(2)
In order to characterize the impact-deposition-rebound behaviour of particles colliding with a planar surface, it can be useful to assess the distribution of the coefficient of restitution rather than the mean coefficient of restitution. The cumulative distributions of the global coefficient of restitution ε are reported in Fig. 2 for experiments carried out at 1400 °C with Illinois #6 char particles having different residual carbon content, at fixed impact velocity vi = 1.15 ± 0.09 m s−1. The cumulative distributions show the mean values of the coefficient of restitution with the standard deviation obtained considering a variation of ± 10% in the number of tracked particles. The distributions clearly highlight the stochastic nature of the restitution coefficient, with ε distributed in the range between 0 and 0.7. All the distributions, and in particular those with high carbon conversion (e.g. low residual carbon content), display a peculiar two-fold character, reflecting the two basic mechanisms underlying the restitution coefficient [30]: a) adhesion (when ε = 0); b) non-elastic particle interaction with the wall. The first process is ruled by interfacial forces establishing between the particle and the wall, and depends on surface properties of both. The second process is essentially dictated by plastic behaviour of the bulk of the particle. The fraction of particles with ε = 0 pertains to particles permanently deposited on the surface due to adhesion, and ranges between 0 and 30% for char particles, raising to approximately 65% for the carbon-free ash (wC = 0 and XC = 1). The fraction of particles αad that are permanently deposited is reported in Fig. 3 for char particles with different carbon conversion, as well as for ash particles ( XC = 1), for a fixed impact velocity, vi = 1.15 ± 0.09 m s−1. It is noteworthy that the deposition probability, hence αad , is larger than zero, as a consequence of the large energy losses related to the bulk properties of the impacting particles and to the surface properties of both the particles and the target. A pronounced discontinuity in both the coefficient of restitution and the deposition efficiency is displayed when char-slag transition occurs, i.e. at XC around 90% for Illinois #6 char particles [31]. In fact, the presence of the char-slag transition does affect the stickiness and thus the mechanical properties of the impinging particles. Particles not adhered upon collision, rebound. A fraction of these particles rebound close to the wall (in the dense-dispersed phase), the rest being transferred back to the lean phase, depending on the particle kinetic energy after collision. The fraction of particles which is transferred to the dense-dispersed phase, αinel , is (cf. Eq. (2)) proportional to (1 – ε), where ε can be assumed as ε50 (the value of ε corresponding to a cumulative distribution value of 50%) from the cumulative distribution
(1) 3
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stover particles were fitted to obtain closure equations for (i) the fractional mass of particles adhering onto the wall after the impact, αad , as a function of the impact velocity, vi , and the residual carbon content, wC , see Eq. (3) and [15]; (ii) ε50 (the value of the coefficient of restitution corresponding to a cumulative distribution value of 50%), as a function of wC , see Eq. (4):
A
αad (vi, wC ) =
(vi − vi∗ ) ⎡1 + exp ⎣ ε50 (wC ) = CwC + D
(
wC − wC∗ B
) ⎤⎦
(3) (4)
A, B, C and D are constant parameters, vi∗ and wC∗ represent critical values for the impact velocity and residual carbon concentration, respectively. In particular, wC∗ represents the residual carbon concentration in the particles for which the char-slag transition occurs. Eq. (3) expresses that αad decreases with increasing impact velocity and with increasing residual carbon content, while Eq. (4) expresses that ε50 increases with increasing residual carbon content. Parameters found for Eqs. (3) and (4) are listed in Table 1 for the three fuels, together with the coefficient of determination R2 when comparing experimental data and results from Eq. (3). The coefficient of determination R2 between experimental data and values obtained by applying Eq. (3) is in the range 0.71–0.94 for the different fuels, demonstrating a good fitting of the experimental results in terms of αad . Furthermore, for both the biomass types, the constant C in Table 1 is zero, confirming that for both wood chips and corn stover particles there is a negligible effect of the carbon conversion on the rebound characteristics (no clear char-slag transition). The expression obtained in Eq. (3) for αad has been used to compare the proposed closure equation with experimental data available in the literature. Li et al. [31] reported the capture efficiency of char particles of Illinois #6 coal during gasification in a laminar entrained-flow reactor. Experiments were carried out at 1400–1500 °C by using a deposition probe inserted in the laminar flow reactor. The capture efficiency was defined as the mass ratio of particles captured by the target to the particles that impacted the target, which corresponds to αad in this work. Comparison of the experimental data reported by Li et al. [31] with the proposed Eq. (3), applied to the same fuel, is reported in Fig. 10. The agreement between experimental data and the proposed model is good, confirming the reliability of the proposed closure equation in the description of the deposition efficiency of char, partially converted char and ash particles.
Fig. 3. Deposition efficiency as a function of carbon conversion for experiments with Illinois #6 coal particles at 1400 °C and vi = 1.15 ± 0.09 m s−1.
normalized with respect to the adhered particles fraction αad , as reported in Fig. 4. It is noteworthy that ε50 depends on the residual content of carbon within the particles. In particular, ε50 decreases with decreasing residual carbon concentration wC , as a consequence of the different mechanical properties of the particles with increasing carbon conversion XC . Thus, the fraction of particles transferred to the densedispersed phase, αinel , can be expressed as a function of ε50 and αad as in Eq. (2). Altogether, a schematic representation of bulk-to-wall solid transfer is reported in Fig. 5 with indication of the partitioning of particles in the different segregated phases in the near-wall region of the gasifier. 3. Development of closure equations The experimental data have been used to develop closure equations to quantitatively express the fate of char/ash particles after the collision with a surface in terms of partitioning among the different phases, i.e. slag, dense-dispersed and lean-dispersed phase. The fraction of particles αad adhering onto the wall as a function of the impact velocity is reported in Fig. 6 for coal particles with different carbon conversion values. αad decreases with increasing impact velocities, as a result of the increasingly ineffective adhesion as the kinetic energy of the impinging particle increases. In particular, αad approaches 0 for char particles ( XC = 0, 16%, 50%), around 0.2 for char particles at char-slag transition ( XC = 90%) and around 0.45 for ash particles ( XC = 100%). The values of the restitution coefficient ε50 are reported in Figs. 7–9 for Illinois coal, corn stover and wood chips particles, respectively, while varying the impact velocity and the residual carbon content. For coal particles, ε50 in Fig. 7 is roughly constant with the impact velocity, while it is affected by the residual carbon concentration. In particular, a pronounced decrease in ε50 is displayed when char-slag transition occurs ( XC = 90%). This outcome confirms that increasing the particle stickiness, larger plastic deformations occur upon the impact and thus ε50 decreases. Values of ε50 for both corn stover and wood chip particles are reported in Figs. 8 and 9, respectively. ε50 is roughly constant with the impact velocity, as reported for coal particles, while, differently from coal particles, it is not affected by the residual carbon content. This result can be explained taking into account that, for these biomass types, there is no evidence of the char-slag transition [24]. As a consequence, there is not an appreciable change in the stickiness and thus in the mechanical properties of the char particles until complete conversion is reached. All the experimental data for Illinois #6 coal, wood chips and corn
Fig. 4. Normalized (with respect to the adhered particles fraction) cumulative distribution of the global coefficient of restitution obtained from experiments with Illinois #6 coal particles at 1400 °C and vi = 1.15 ± 0.09 m s−1. Data for samples with different values of residual carbon content (wC ) or, equivalently, carbon conversion degree ( XC ). 4
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Fig. 5. Schematic representation of solid transfer towards the wall with indication of the segregated phases.
Fig. 6. Fraction of adhered particles as a function of the impact velocity for Illinois #6 coal particles (experiments at 1400 °C). Data for samples with different values of residual carbon content (wC ) or, equivalently, carbon conversion degree ( XC ).
Fig. 8. ε50 as a function of the impact velocity for corn stover particles (experiments at 1400 °C). Data for samples with different values of residual carbon content (wC ) or, equivalently, carbon conversion degree ( XC ).
Fig. 9. ε50 as a function of the impact velocity for wood chips particles (experiments at 1400 °C). Data for samples with different values of residual carbon content (wC ) or, equivalently, carbon conversion degree ( XC ).
Fig. 7. ε50 as a function of the impact velocity for Illinois #6 coal particles (experiments at 1400 °C). Data for samples with different values of residual carbon content (wC ) or, equivalently, carbon conversion degree ( XC ).
5
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have been characterized in terms of fractional mass of particles adhering onto the surface and rebounding upon the collision. The effect of the residual carbon content within the particles from char to ash particles, as well as the influence of impact velocity, have been investigated for different fuels, i.e. Illinois #6 coal, wood chips and corn stover. Closure equations were derived, which enable quantitative assessment of the fate of char/ash particles after collision with the wall, in terms of fractional mass of particles adhering and rebounding upon the collision. Impact velocity and residual carbon content in the char affect the deposition tendency of char and ash particles for all the tested fuels. Inelastic rebound is mainly influenced by the mechanical properties of the bulk of the particles, which are closely dependent on the structure and stickiness of particles during gasification.
Table 1 Parameters for the closure Eqs. (3) and (4) for the different fuels, and coefficient of determination for Eq. (3). All parameters are non-dimensional, except A and vi∗ expressed in m s−1. Fuel
A
B
C
D
vi∗
wC∗
R2
Illinois #6 coal Wood chips Corn stover
0.61 0.61 6.34
0.06 0.47 0.35
0.18 0 0
0.34 0.32 0.33
0.27 0.16 2.74
0.26 0 0
0.94 0.71 0.89
CRediT authorship contribution statement Maurizio Troiano: Conceptualization, Methodology, Formal analysis, Writing - review & editing. Roberto Solimene: Conceptualization, Methodology, Formal analysis, Writing - review & editing. Fabio Montagnaro: Conceptualization, Methodology, Formal analysis, Writing - review & editing. Piero Salatino: Conceptualization, Methodology, Formal analysis, Writing - review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Fig. 10. Comparison of deposition efficiency results obtained in this study and by Li et al. [31]. Reference fuel: Illinois #6 coal.
References
The developed closure Eqs. (3) and (4) have been derived on the basis of impact experiments, as reported in Section 2. The experiments were carried out at high temperature with a planar dry wall. For this reason, referring to Fig. 1, they apply to stage 1 “dry wall”. During this stage, Eq. (3) expresses the mass fraction of adhered particles αad while varying the impact velocity of particles and the residual carbon content. The mass fraction of particles which rebounded upon impact accumulating into the dense-dispersed phase, αinel , is described by:
αinel = k (1 − ε50 )(1 − αad )
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(5)
During stage 2, “wet wall pre-coverage”, it is assumed that αad is equal to 1, which means that mass transfer toward the dense-dispersed phase is prevented by particle deposition onto the slag layer (αinel = 0). During stage 3, “wet wall post-coverage”, particles impact a layer of char particles covering the slag layer. It is likely that, during this stage, the impact behavior resembles the one of stage 1, as the layer of char particles acts as a “wall”. Thus, it can be assumed that Eq. (3) applies also to stage 3. During stage 4, “fully developed dense-dispersed phase”, all the particles moving toward the wall lose their momentum in the dense-dispersed phase and are trapped therein, thus neither Eq. (3) nor (5) applies. It is noteworthy that, in EFG, the fractional mass of particles pertaining to the dense-dispersed phase depends also on the hydrodynamic conditions establishing in the near-wall region of the gasifier. For this reason, a constant k is present in Eq. (5). Further studies are needed for the evaluation of this parameter, in order to express the fractional mass of particles rebounding and reporting to the densedispersed phase by means of a predictive closure equation. 4. Conclusions A critical analysis of impact experiments relevant to entrained-flow slagging gasifiers of solid fuels has been performed in order to develop closure equations describing deposition and inelastic rebound of char/ ash particles after collision with the wall. The impact-deposition-rebound dynamical patterns of particles colliding with a planar surface 6
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