Estimation of Heat Transfer Coefficients for Biomass Particles by Direct

Research Article pubs.acs.org/journal/ascecg

Estimation of Heat Transfer Coefficients for Biomass Particles by Direct Numerical Simulation Using Microstructured Particle Models in the Laminar Regime M. Brennan Pecha,†,‡ Manuel Garcia-Perez,‡ Thomas D. Foust,† and Peter N. Ciesielski*,† †

Biosciences Center, National Renewable Energy Laboratory, 1503 Denver W. Parkway, Golden, Colorado 80401, United States Department of Biological Systems Engineering, Washington State University, L.J. Smith Hall, 1935 E. Grimes Way, Pullman, Washington 99164-6120, United States

‡

S Supporting Information *

ABSTRACT: Direct numerical simulation of convective heat transfer from hot gas to isolated biomass particle models with realistic morphology and explicit microstructure was performed over a range of conditions in the laminar regime. Steady-state results demonstrated that convective interfacial heat transfer is dependent on the wood species. The computed heat transfer coefficients were shown to vary between the pine and aspen models by nearly 20%. These differences are attributed to the species-specific variations in the exterior surface morphology of the biomass particles. We also quantify variations in heat transfer experienced by the particle when positioned in different orientations with respect to the direction of fluid flow. These results are compared to previously reported heat transfer coefficient correlations in the range of 0.1 < Pr < 1.5 and 10 < Re < 500. Comparison of these simulation results to correlations commonly used in the literature (Gunn, Ranz− Marshall, and Bird−Stewart−Lightfoot) shows that the Ranz−Marshall (sphere) correlation gave the closest h values to our steady-state simulations for both wood species, though no existing correlation was within 20% of both species at all conditions studied. In general, this work exemplifies the fact that all biomass feedstocks are not created equal, and that their species-specific characteristics must be appreciated in order to facilitate accurate simulations of conversion processes. KEYWORDS: Biomass, Pyrolysis, Heat transfer coefficient, Particle modeling, Direct numerical simulation

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INTRODUCTION In processes that involve heat transfer between solid and fluid phases, the rate at which heat can move across the solid/fluid interface is of critical importance. Such processes often couple heat conduction through the fluid and convective heat transfer, (i.e., heat that is carried throughout the system by fluid flow) to conductive heat transfer within the solid. This process is often termed “conjugate heat transfer”.1 The flux of heat across this boundary at a given time is affected by many system parameters including the bulk velocity of the fluid, the temperatures of the fluid and the solid, and geometry of the interface. Accurately representing interfacial heat transfer is paramount when modeling processes such as fast pyrolysis of biomass wherein heat is typically transferred from a hot, inert gas to biomass particles. In such processes, heating rates have a large impact on the product yields, and rapid efficient heat transfer between gas and solid particles is essential to optimize the yield of bio-oil. For example, rapid heating rates combined with reactor residence times on the order of a few seconds will shift the yields of pyrolysis products toward condensable gases (also called bio-oil) while minimizing char formation and cracking to light gases.2 One of the most critical parameters in models of conjugate heat transfer is the interfacial heat transfer coefficient © 2016 American Chemical Society

(typically denoted as h) which specifies the rate at which heat is exchanged at the gas/particle interface. The difficulties related to the experimental determination of the actual biomass particle temperature and heat transfer rates are summarized by Jacque Lede3 in his recent critical review on the research challenges regarding biomass fast pyrolysis reactors. He points out that measuring the temperatures of very fine biomass particles rapidly moving through the reactor in the presence of fast conversion reactions with a thermocouple is nearly impossible. For this reason the heating rates and temperatures are evaluated by solving mathematical models, which are built on simplifying assumptions regarding biomass particle geometry, intraparticle heat and mass transfer, and physical constants. Ledé and Authier4 have recently expanded on the topic of reaction temperature and heating rates in their newest study. By solving a simple particle model under different operating conditions, they show that pyrolysis reactions typically occur at temperatures between 620 and 780 K regardless of the heat source, temperature, or heating rates. Received: September 27, 2016 Revised: November 2, 2016 Published: November 8, 2016 1046

DOI: 10.1021/acssuschemeng.6b02341 ACS Sustainable Chem. Eng. 2017, 5, 1046−1053

Research Article

ACS Sustainable Chemistry & Engineering

Figure 1. (A) Species specific, 3D biomass particle models with explicit microstructure investigated in this study. (B) Example of a “side flow” conjugate heat transfer simulation wherein the biomass particle is oriented with its major axis perpendicular to the direction of fluid flow. One symmetry plane was used at the longitudinal midpoint of the particle for both pine and aspen models. (C) Example of a “top flow” simulation configuration wherein the particle is oriented with its minor axis perpendicular to the direction of fluid flow. In the case of the pine particle simulations, two symmetry planes were used along the longitudinal axis because of its nearly cylindrical external geometry; however, no symmetry planes could be used for the aspen particle top flow simulations because of the anisotropic external geometry.

particles are spheres20 and more recent CFD calculations have been made for packed beds with different geometries.21−23 Most single particle and reactor-level pyrolysis models simulations use one of the older correlations because the level of expected error has been tested. Newer correlations have not shown much improvement over the Gunn correlation.24−27 To model more accurately heat transfer in anisotropic irregularly shaped solids, the velocity and temperature profiles must be determined explicitly throughout the boundary layer. This approach of fully resolving these interfacial boundary layers is termed direct numerical simulation (DNS) and can be very computationally demanding.17 To approximate conjugate heat transfer to facilitate larger simulations (e.g., reactor scale), assumptions are used to approximate the effect of the thermal and velocity boundary layers. The most common of these employ the interfacial heat transfer coefficient, which approximates the interfacial heat flux as

They conclude that the biomass temperature during reactions is often significantly lower than the heat source temperature or measured reactor temperature, which might lead to significant errors in determined kinetic parameters. Thus, it is critical to develop more accurate strategies for modeling heat transfer in biomass. In another recent work, Westerhof et al.5 analyzed the impact of heat transfer on cellulose pyrolysis and found that high heat transfer leads to high yields of sugars, arriving at the same conclusions than Ledé and Authier.4 Accurately describing heat transfer in simulation work is critical to predicting product distributions. There are numerous empirical correlations for evaluating the heat transfer coefficients between the solid−gas phases which are typically functions of the Reynolds and Prandtl dimensionless numbers in order to generalize their applicability to a range of fluid conditions and system parameters. The vast majority of existing correlations are determined based on experiments performed with regular geometries (e.g., spheres, cylinders). In some cases, using the heat transfer coefficient for a single spherical particle is a reasonable approximation.6 To determine the heat transfer coefficient in coal or woody biomass, correlations such as Ranz−Marshall (1952),7 Gunn (1974),8 and Agarwal (1991)9 are typically used. The Gunn correlation8 was developed using experiments for glass and metallic particles with narrow particle size distributions (PSDs) and a mathematical analysis for small Re numbers.8 Agarwal developed a correlation for coal in a fluidized bed.10 Bird, Stewart, and Lightfoot have published general correlations for heat transfer coefficients for spheres, cylinders, and slabs.11,12 Furthermore, reviews have been published regarding experimental and numerical simulation to develop heat transfer coefficients in packed beds and fluidized beds,13−16 but these simulations do not take into account pore-level morphology of low conductivity solids with varied size and shape distributions.17 The surface morphology of biomass is substantially different from that of glass or metal spheres; for low particle sizes, the pores can create ridges with diameters on the same order of magnitude as the particle’s diameter.18 Such correlations are able to practically predict the heat transfer coefficient within ±25%.19 Papadakis et al. have calculated the heat transfer coefficients for wood in a fluidized bed by assuming the

qinterface = h(Ts − T∞) [W/m 2]

(1)

where h is the heat transfer coefficient, Ts is the surface temperature of the solid, and T∞ is the bulk temperature of the fluid. As mentioned previously, this interfacial heat flux, and therefore the heat transfer coefficient, are strong functions of the system parameters. The heat transfer coefficient is typically determined experimentally as the ratio between the heat transferred, the heat transfer area and the difference of temperature. The values obtained are highly specific to the geometry of the system used to obtain the measurements. Correlations with dimensionless numbers are typically used to account for the effect of geometrical and operational parameters. The heat transfer coefficient may also be estimated by DNS of conjugate heat transfer, because the temperature and velocity profiles within the boundary layer are fully resolved. Assuming a no-slip velocity boundary condition (i.e., u = 0 at the interface), the heat transfer across the interface can be written as qinterface = −k fluid

∂T ∂y

y=0

(2)

where T is the temperature, kfluid is the thermal conductivity of the fluid, and y is a spatial variable that is equal to zero at the 1047


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reorientation relative to the local fluid velocity field is beyond the scope of the present study; however, we performed simulations that considered several different configurations for each particle model. The “side-flow” scenario, visualized in Figure 1B, orients the particle such that its major axis is perpendicular to the directions of fluid flow. This scenario orients a relatively large amount of particle surface area normal to the direction of fluid flow. In the case of the aspen particle, 2 different side-flow orientations were considered because of the anisotropic external geometry of the particle. These configurations are denoted as “side 1”, where the narrow edge of the particle was oriented normal to the direction of fluid flow, and “side 2” where the broad edge of the particle was oriented normal to the direction of fluid flow. In the “top-flow” scenario (visualized for the pine particle in Figure 1C), the particle model is positioned such that its minor axis is perpendicular to the direction of fluid flow, which orients a smaller fraction of surface area normal to the direction of fluid flow relative to the side-flow scenarios. Coupled conservation statements for equations for mass, momentum, and heat for a fully compressible fluid were solved within the fluid domain for each simulation configuration. These equations are given respectively by

interface and increases as you move away from the solid into the fluid. This heat flux is then related to the heat transfer coefficient by the following equation: ∂T

−k fluid ∂y h=

y=0

(Ts − T∞)

(3)

Biomass particle geometry is known to be irregular and challenging to describe. Therefore, there is some uncertainty about the correlations for the external heat transfer coefficient. We recently investigated means to accurately represent the complex geometry of biomass particles and developed sophisticated methods to construct 3-D microstructured particle models based on multimodal microscopy and quantitative image analysis.28 The study further demonstrated that these structurally complex models could be used in simulations of heat and mass transfer. In the present work, we estimate the heat transfer coefficient in the laminar regime for pine and aspen particle models using CFD modeling of the heat transfer between a hot gas and a single particle with realistic geometry. Simulation results are compared to popular correlations reported in the literature. These results provide insights into variations in heat transfer that arise from differing particle geometries and orientations with respect the directionality of fluid flow.

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∂ρ + ∇·(ρ u) = 0 ∂t

ρ

SIMULATION DETAILS AND COMPUTATIONAL METHODS

(4)

⎡ ⎤ ∂u 2 + ρ u ·∇u = −∇p + ∇· ⎢μ(∇u + (∇u)T ) − μ(∇· u)I⎥ ⎣ ⎦ 3 ∂t (5)

⎛ ∂T ⎞ ρC p ⎜ + (u ·∇)T ⎟ = ∇·(k∇T ) + (τ ·∇)u ⎝ ∂t ⎠

3D Particle Models with Realistic Morphology and Explicit Microstructure. The particle models used in this study are shown in Figure 1A. These models were constructed with a longitudinal dimension of 0.5 mm to represent a particle size typical of that used in fast pyrolysis processes. These models exhibit morphological parameters that are representative of real biomass particles using geometric features extracted directly by quantitative image analysis of microscopy data as described previously. 28 These geometric parameters, including cell wall thickness, cell lumen diameter, and external shape, can vary substantially between feedstock species of origin and particle comminution methods.13 For example, the microstructure of softwoods, such as the pine species modeled in this work, lack the vessel elements present in hardwoods. Cavities resulting from cleavage along the vessel elements can be seen on the surface of the aspen particle model shown in Figure 1A. Differences in microstructure can affect the fragmentation behavior of feedstocks and result in variations in the size and shape distribution of particles generated from comminution.28 In the case of the feedstocks modeled here, the pine particles in this size range tended to exhibit a more cylindrical exterior geometry, whereas the aspen particles tended to have one axial dimension significantly smaller than the other which gives rise to a “flaky” shape. These variations in the fragmentation patterns of these feedstocks likely arise from differences in the distribution of ray cells and vessel elements (in the case of the aspen feedstock) that impart localized seams within in the material at the microstructural level where fragmentation is more favorable. Simulation Details and Mathematical Formulation. The particle models described above were used in simulations of conjugate heat transfer in order to evaluate interfacial the heat flux experienced by biomass particles in laminar flow of a hot gas. We used a conventional approach to this problem, similar to that recently published Tavasolli and collegues,21,23 wherein a constant temperature boundary condition is applied to the surface of the particle while gas with a constant inlet temperature flows around the particle and the interfacial heat flux is evaluated at steady state. In real pyrolysis scenarios, anisotropic biomass particles within a reactor will be continually reoriented as a result of local hydrodynamics. Modeling explicitly the particle dynamics that result from particle rotation and

(6)

where ρ is the density, u is the velocity vector, p is the pressure, μ is the viscosity, I is the identity matrix, τ is the viscous stress tensor, and T is the temperature (superscript T denotes the transpose operator in eq 5). The surface of the solid (particle) domain was held constant at 25 °C. The inlet gas temperature was set to 500 °C. A no-slip boundary condition was applied to the walls of the particle and the boundary layer was resolved explicitly. The flow inlet and flow outlet were set on opposite boundaries; the inlet had a fixed velocity and the outlet had a pressure boundary condition of 1 atm. Symmetry planes were utilized where possible; their locations are visualized in Figure 1B,C and described in the figure caption. Constant-pressure boundary conditions were applied to the remaining exterior simulation boundaries and held at a value of 1 atm. The particle surface was meshed initially with a maximum element size of 2 μm, and the mesh was propagated throughout the fluid domain with a growth factor of 1.1. The simulation fluid was considered to have properties of N2 gas. The fluid density (ρ) calculated in units of kg/m3 as 0.0017·T + 2.3158, where T is the temperature in Kelvin. The thermal conductivity (k) of the gas was calculated in units W/m2 as 8e-5·T + 0.0055. The viscosity (μ) of the gas was calculated in units of Pa·s/K by the expression 3e-8·T + 8e-6. The heat capacity of the gas was determined in units of J/(kg·K) from the Prandlt number (Cp = Pr· k500 °C/μ500 °C). Pr number took values of 0.1, 0.5, 1, and 1.5. The initial pressure was set to 1 atm. The inlet velocity into the larger volume was determined in units of m/s by varying the Reynolds number such that uinlet = Re·μ500 °C/L/ρ500 °C. Two-dimensional parametric sweeps were performed for each simulation geometry at Re values of 10, 100, 300, 500. All our simulations were conducted in laminar regime. Simulations were performed in COMSOL Multiphysics 5.2 and solutions were obtained using a fully coupled, direct solver with an absolute error tolerance of 10−3. Simulations were performed on a single compute node equipped with two, 8-core Intel Xeon E5-2670 SandyBridge processors and 512 GB of RAM. The stationary solutions were used to calculate the average heat transfer coefficient (h) by integrating the interfacial heat flux over the external surface of the particle and dividing by the temperature difference and the nominal surface area, as shown in eq 7. 1048


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Figure 2. Visualization of solutions for each particle and simulation configuration at Pr = 0.5 and Re = 100. (A) Aspen particle in top-flow configuration. (B) Aspen particle in side-flow 1 configuration. (C) Aspen particle in side-flow 2 configuration. (D) Pine particle in top-flow configuration. (F) Pine particle in side-flow configuration. In all cases, the narrow regions of the leading edge of the particle achieve highest interfacial heat transfer. Depressed regions of the particle surfaces such as area within partial lumen on the particle exterior display relatively lower localized interfacial heat transfer due to the low local fluid velocities within the boundary layer.

⟨h⟩ =

1 AN(Ts − T∞)

these results highlight the significant heterogeneity displayed by the local interfacial heat transfer magnitude which results from a combination of particle morphology and orientation relative to the direction of the velocity field. To compare the interfacial heat transfer experienced by these particle models over a range of flow regimes and fluid properties, Nusselt numbers were calculated for each simulation performed in the 2D parametric sweep across Reynolds and Prandtl numbers. These results are summarized in Figure 3. For both species, Nu numbers were higher for the side-flow (Figure 3A,C,D) compared with top-flow (Figure 3B,E). This expected observation implies that convective heat transfer is more effective for these orientations because a larger fraction of the exterior surface area of the particle is oriented normal to the direction of the fluid flow. The aspen particle experienced larger heat transfer than the pine particle. This result was attributed to shape and magnitude of the velocity boundary that exhibits local variations resulting from several geometric differences in the exterior geometries of the particles. First, the partially open cell lumen on both particle models create “ridges” on the particle exterior which increase convective heat transfer (analogous to fins on the exterior of a motorcycle engine). The aspen particle model has significantly smaller (and thus a higher packing density of) fibers cells which impart more ridges and higher surface to the particle exterior. Second, the relatively large cavities imparted by partial vessel elements on the surface of the aspen models result in broader, less sheltered depressions than those imparted by the axial tracheids on the surface of the pine model which facilitates higher fluid velocities, and thus higher convective heat transfer, in close proximity to these surfaces. Comparing these results to the classical Gunn correlation (Figure 3F) reveals that this correlation overestimates the Nusselt numbers at all conditions considered in the present work by up to 50% at the lowest Re and Pr (10, 0.1) and greater than 10% at the highest Re and Pr (500, 1.5). To investigate differences further in the heat transfer coefficients computed here and those previously reported in the literature, h values obtained for both particle models were

∮ −k∇T dAE AE

(7)

The nominal surface area (AN) was considered to be the external bulk surface area of the particle excluding surface roughness and the external surface area (AE) was considered to be all of the external surface area of the microstructured particle (i.e., the internal area of the cell lumen were excluded since these surfaces are not available for heat transfer). The nominal surface area (AN) of the particles was calculated using the assumptions that the top and bottom are each represented as 1/2 of an ellipsoid and the main body of the particle is an elliptical cylinder. Equations and dimensions used for this calculation can be seen in the Appendix. AN and AE are 2.58 × 10−7 m2 and 3.5236 × 10−7 m2 for pine and are 1.99 × 10−7 m2 and 2.44 × 10−7 m2 for Aspen, respectively. We chose to divide the heat flux by the nominal surface area as opposed to the external surface area in order to make the results presented here more easily extended to typical highthroughput particle size/shape characterization techniques which do not provide measurements of surface area contributed by microscale roughness and microstructure.29 The Nusselt numbers (Nu) were then computed from the average heat transfer coefficient as Nu = h·L/k using a characteristic length (L) of the longitudinal particle dimension (500 μm).

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RESULTS AND DISCUSSION Visualization of the simulation solutions for each particle and geometric configuration at Pr = 0.5 and Re = 100 are presented in Figure 2. In all cases, a boundary layer is evident in the velocities within depressed regions of the particle exterior, such as cavities introduced by partial cell lumen, which in turn causes these regions to experience relatively low interfacial heat transfer compared to the raised regions. This phenomenon extends even to the cavities on the leading edge of the particle which illustrates the significant insulating effect of the boundary layer. Regions that experience the highest interfacial heat transfer are those narrow, raised regions near the leading edge of the particle. Fluid velocities within the cell lumen in the particle interior are virtually zero; therefore interfacial heat transfer occurring in these regions is essentially negligible relative to that contributed by the particle exterior. In general, 1049


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Figure 3. Nusselt numbers calculated for pine with (A) side (radial) flow and (B) top (axial) flow of gas as well as for aspen with both side flow orientations (C and D) and top flow (E). Nusselt numbers calculated from the Gunn correlation (F) are also shown for comparison.

plotted versus Re at a fixed Pr (0.5) in Figure 4. Figure 4A compares the h values computed for each particle model at each orientation. These results further highlight the species-specific differences in the computed h values, with the aspen particle experiencing higher rates of convective heat transfer the pine particle due to differences in the external morphology. These results illustrate the importance of considering species-specific effects when developing models for thermochemical conversion processes of biomass, which will become increasingly important as many processes design cases incorporate blended feedstocks that consist of several species of biomass.30 A comparison of the orientation-averaged h values to those predicted by previously developed correlations reported by Gunn,8 Ranz−Marshall,7 and Bird, Stewart, and Lightfoot (BSL)11 is presented in Figure 4B. Averaged h values were

calculated as the arithmetic mean of the top and side orientations for pine and aspen; for aspen, each side contributes 25% and the top contributes 50%. The orientation-averaged h values for pine and aspen were 389 and 370 W/(m2·K) at Re = 10, respectively, and rose asymptotically to 1290 and 1500 W/ (m2·K) at Re = 500, respectively. A substantial variance is present between predictions from the literature correlations compared here. Foremost, the BSL slab underestimates the simulated heat transfer coefficients at all Re values by an average of 55% for pine and 59% for Aspen. The BSL cylinder correlation underestimated h by 39.4% for pine and 48.1% for aspen at Re = 500; it was within 6% for pine at Re = 100. It underestimated poplar by 20.3% at this condition. At Re = 10, the cylinder correlation overestimated h for pine by 48.4% and poplar by 66.5%. Note that this result 1050


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Figure 4. Heat transfer coefficients plotted versus Re number for (A) all simulations and (B) average orientations with other correlations from the literature.

surface-averaged interfacial heat transfer coefficients estimated by the methods employed here are not directly dependent on particle aspect ratio or surface area to volume ratio since they are normalized to the nominal surface area, the aspect ratio may indirectly affect the interfacial heat transfer of particle in a real reactor system by altering its propensity for dynamic reorientation in response to velocity fields. On the basis of the results of this work, we propose that future work should aim to develop correlations for Nu that can account for the variable geometry of biomass feedstock particle such as pore structure and particle geometry as well as the Re and Pr numbers. This generalized correlation could thus be applicable to nearly all types of biomass and improve the accuracy of heat transfer models in simulations of thermochemical conversion.

was obtained if the largest particle dimension was used, rather than the smallest dimension as is typical for this correlation; we found in results not shown here that using the BSL cylinder correlation with the smallest particle dimension because using the diameter overestimated h by a factor of 3 for both particles. The Gunn correlation overestimates h by only 13.4% at Re = 100 but 54.9% at Re = 10 and 23.5% at Re = 500; it overestimates pine by more than 34% at all Re values studied. This is likely because the Gunn correlation was developed experimentally using a packed bed of spheres and not specifically for a single particle, though it can be applied to single particles in entrained flow scenarios by setting the voidspace parameter to 1. The Ranz−Marshall (sphere) correlation provides h within 1% at Re = 300 for pine and within 4% Re = 100 for aspen, and is within 25% for both species at Re = 100 and Re = 500 (underestimating aspen by 20.9% at Re = 500). However, at Re = 10 the Ranz−Marshall correlation overestimates pine by 64.9% and aspen by 73.3%. Discrepancies between the previously published correlations and those developed in this work are generally attributed to the unique, species-specific geometries of biomass particles that depart significantly from the simplified geometries such as spheres, slabs, and cylinders upon which the previous correlations are based. This assertion is consistent with previous results that show that biomass particles are often inadequately represented by simplified shapes in conventional models of heat transfer. Wiggins et al.31 recently used CFD modeling and reduced-order approximations to simulate the effect of wood particle size and shape (without explicit porosity) on transient heat transfer in the particle. The authors determined that the surface area to volume ratio is the most significant morphological parameter to determine the rate of heat transfer into a particle. However, results were only validated for data from a large wood particle (height 100 mm, diameter 20 mm), where the pore diameter to particle diameter ratio is on the order of 0.005. In that work, the authors used a heat transfer coefficient of 350 W/(m·K) for all particle sizes for the main section of the work. The study also demonstrated the importance of particle aspect ratio, which contributes to the surface area to volume ratio, which generally decreases with particle size. Similarly, Lu et al.32 coupled experimental and modeling techniques to learn that using spheres or isothermal techniques to simulate biomass pyrolysis are not effective representatives for particles larger than 200 μm. Although the

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CONCLUSIONS Convective heat transfer for realistic particle models (500 μm) with explicit porosity and realistic morphology was simulated in order to extract heat transfer coefficients with fluid flow conditions of Re = 10−500 and Pr = 0.1−1.5. Results showed that interfacial heat transfer varies between different biomass species due to differences in the microstructure and overall morphology of the particles. Specifically, the aspen particle model exhibited a heat transfer coefficient ∼20% higher than pine under most conditions. Our results also demonstrate the convective heat transfer magnitude is largely impacted by the orientation of the particle with respect to the direction of fluid flow as expected. The Ranz−Marshal (sphere) correlation gave the closest h values to our simulations for both wood species. Much work remains in the area of transport phenomena that govern behavior of biomass particles in order to facilitate accurate, predictive simulations of thermochemical conversion process. Future work should investigate transient heat transfer conditions in the context of conversion simulations to account for changes in the particle thermal properties and morphology as it evolves over the course of the conversion process. Because the heat transfer coefficients obtained here are a function geometry only, our findings obtained using species-specific particle models may be extended to biomass species with similar microstructural features (such as cell wall thickness and lumen diameter) and external morphologies; however, additional biomass feedstock species should also be investigated in tandem with materials science studies with the goal of 1051


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Interplay between Chemistry and Heat/Mass Transfer During the Fast Pyrolysis of Cellulose. Reaction Chem. Eng. 2016, 1, 555−556. (6) Daizo, K.; Levenspiel, O. Fluidization Engineering; Butterworth Publishers: Stoneham, MA, 1991; pp 257−276. (7) Ranz, W. E.; Marshall, W. R. Evaporation from Drops, Parts I and II. Chem. Eng. Prog. 1952, 48 (3), 141−146. (8) Gunn, D. J.; De Souza, J. F. C. Heat Transfer and Axial Dispersion in Packed Beds. Chem. Eng. Sci. 1974, 29, 1363−1371. (9) Agarwal, P. K. Transport Phenomena in Multi-Particle Systems IV. Heat Transfer to a Large Freely Moving Particle in Gas Fluidized Bed of Smaller Particles. Chem. Eng. Sci. 1991, 46, 1115−1127. (10) Agarwal, P. K.; Genetti, W. E.; Lee, Y. Y. Model for Devolatilization of Coal Particles in Fluidized Beds. Fuel 1984, 63 (8), 1157−1165. (11) Bird, R.; Stewart, W.; Lightfoot, E. Transport Phenomena, Rev. 2nd ed.; Wiley: New York, 2007. (12) Sharma, A.; Pareek, V.; Wang, S.; Zhang, Z.; Yang, H.; Zhang, D. A Phenomenological Model of the Mechanisms of Lignocellulosic Biomass Pyrolysis Processes. Comput. Chem. Eng. 2014, 60, 231−241. (13) Deen, N. G.; Peters, E. A. J. F.; Padding, J. T.; Kuipers, J. A. M. Review of Direct Numerical Simulation of Fluid−Particle Mass, Momentum and Heat Transfer in Dense Gas−Solid Flows. Chem. Eng. Sci. 2014, 116, 710−724. (14) Pfeffer, R.; Rosetti, S.; Licklein, S. Analysis and Correlation of Heat Transfer Coefficient and Heat Transfer Data for Dilute Gas-Solid Suspensions. NASA TN-D 1966, 3603. (15) Breault, R. W. A Review of Gas−Solid Dispersion and Mass Transfer Coefficient Correlations in Circulating Fluidized Beds. Powder Technol. 2006, 163 (1−2), 9−17. (16) Kobro, H.; Brereton, C. Control and Fuel Flexibility of Circulating Fluidised Bed A2. In Circulating Fluidized Bed Technology; Basu, P., Ed.; Pergamon: Oxford, 1986; pp 263−272. (17) Brown, R. C.; Otten, L. A Method to Determine Thermal Properties of Grain from System Respone Analysis of a Packed Bed. Int. J. Thermophys. 1988, 9 (6), 1131−1139. (18) Wood Handbook, Wood as an Engineering Material; Forest Products Laboratory: Madison, WI, 2010. (19) Yang, W.-C. Handbook of Fluidization and Fluid-Particle Systems; CRC Press: Boca Raton, FL, 2003. (20) Papadikis, K.; Gu, S.; Bridgewater, A. V. Computational Modelling of the Impact of Particle Size to the Heat Transfer Coefficient between Biomass Particles and a Fluidised Bed. Fuel Process. Technol. 2010, 91, 68−79. (21) Tavassoli, H.; Kriebitzsch, S. H. L.; van der Hoef, M. A.; Peters, E. A. J. F.; Kuipers, J. A. M. Direct Numerical Simulation of Particulate Flow with Heat Transfer. Int. J. Multiphase Flow 2013, 57, 29−37. (22) Tavassoli, H. Direct Numerical Simulation of Dense Gas−Solids Non-Isothermal Flows. Ph.D. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2014. (23) Tavassoli, H.; Peters, E. A. J. F.; Kuipers, J. A. M. Direct Numerical Simulation of Fluid−Particle Heat Transfer in Fixed Random Arrays of Non-Spherical Particles. Chem. Eng. Sci. 2015, 129, 42−48. (24) Luo, Z.; Wang, S.; Cen, K. A Model of Wood Flash Pyrolysis in Fluidized Bed Reactor. Renewable Energy 2005, 30 (3), 377−392. (25) Trendewicz, A.; Braun, R.; Dutta, A.; Ziegler, J. One Dimensional Steady-State Circulating Fluidized-Bed Reactor Model for Biomass Fast Pyrolysis. Fuel 2014, 133, 253−262. (26) Xiong, Q.; Kong, S.-C.; Passalacqua, A. Development of a Generalized Numerical Framework for Simulating Biomass Fast Pyrolysis in Fluidized-Bed Reactors. Chem. Eng. Sci. 2013, 99, 305− 313. (27) Xiong, Q.; Kong, S.-C. Modeling Effects of Interphase Transport Coefficients on Biomass Pyrolysis in Fluidized Beds. Powder Technol. 2014, 262, 96−105. (28) Ciesielski, P. N.; Crowley, M. F.; Nimlos, M. R.; Sanders, A. W.; Wiggins, G. M.; Robichaud, D.; Donohoe, B. S.; Foust, T. D. Biomass Particle Models with Realistic Morphology and Resolved Micro-

developing more general correlations that adequately account for species specific morphological parameters. Nevertheless, the work presented here provides significant insight into the origins of interspecies differences in heat transfer in the context of thermochemical conversion processes.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acssuschemeng.6b02341. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Peter Ciesielski. Email: [email protected]. Phone: 303384-7691. ORCID

Peter N. Ciesielski: 0000-0003-3360-9210 Author Contributions

Microstructured particle models were constructed by P.N.C. Simulations were designed and performed by M.B.P. and P.N.C. All authors contributed to hypotheses, writing, and revising the paper. All authors have given approval to the final version of the paper. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support for this work was provided by the Computational Pyrolysis Consortium (CPC) funded by the Bioenergy Technologies Office (BETO) of the U.S. Department of Energy. M.B.P. and M.G.-P. also acknowledge funding from the National Science Foundation (CBET-1434073, CAREER CBET-1150430).

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ABBREVIATIONS BSL, Bird, Stewart, and Lightfoot cp, heat capacity of gas CFD, computational fluid dynamics h, External heat transfer coefficient k, thermal conductivity of the gas L, characteristic length of particle used for nondimensional analysis Nu, Nusselt number Pr, Prandtl number (cpμ/k) Re, Reynolds number (ρvL/μ) μ, dynamic viscosity

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REFERENCES

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Estimation of Heat Transfer Coefficients for Biomass Particles by Direct

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