Article pubs.acs.org/EF
Biomass Particle Models with Realistic Morphology and Resolved Microstructure for Simulations of Intraparticle Transport Phenomena Peter N. Ciesielski,*,†,‡ Michael F. Crowley,† Mark R. Nimlos,‡ Aric W. Sanders,§ Gavin M. Wiggins,∥ Dave Robichaud,‡ Bryon S. Donohoe,† and Thomas D. Foust‡ †
Biosciences Center and ‡National Bioenergy Center, National Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, Colorado 80401-3393, United States § Quantum Electronics and Photonics Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, United States ∥ Oak Ridge National Laboratory, 2360 Cherahala Boulevard, Knoxville, Tennessee 37932, United States S Supporting Information *
ABSTRACT: Biomass exhibits a complex microstructure of directional pores that impact how heat and mass are transferred within biomass particles during conversion processes. However, models of biomass particles used in simulations of conversion processes typically employ oversimplified geometries such as spheres and cylinders and neglect intraparticle microstructure. Here we develop 3D models of biomass particles with size, morphology, and microstructure based on parameters obtained from quantitative image analysis. We obtain measurements of particle size and morphology by analyzing large ensembles of particles that result from typical size reduction methods, and we delineate several representative size classes. Microstructural parameters, including cell wall thickness and cell lumen dimensions, are measured directly from micrographs of sectioned biomass. A general constructive solid geometry algorithm is presented that produces models of biomass particles based on these measurements. Next, we employ the parameters obtained from image analysis to construct models of three different particle size classes from two different feedstocks representing a hardwood poplar species (Populus tremuloides, quaking aspen) and a softwood pine (Pinus taeda, loblolly pine). Finally, we demonstrate the utility of the models and the effects explicit microstructure by performing finiteelement simulations of intraparticle heat and mass transfer, and the results are compared to similar simulations using traditional simplified geometries. We show how the behavior of particle models with more realistic morphology and explicit microstructure departs from that of spherical models in simulations of transport phenomena and that species-dependent differences in microstructure impact simulation results in some cases.
1. INTRODUCTION The potential of lignocellulosic biomass as an abundant source of renewable hydrocarbon fuels and chemical precursors is now widely recognized. However, further improvements to processes that convert biomass to liquid fuels and chemicals are required for biomass-derived products to become economically competitive with petroleum fuels and products. Strategies for biomass conversion include thermochemical routes, such as fast pyrolysis and gasification, and biochemical routes such as enzymatic and microbial digestion. The performance of each of these processes is highly dependent on transport phenomena, i.e., the mechanisms by which heat, mass, and momentum are transferred throughout a system. In the case of thermochemical biomass conversion, fast, effective heat transfer combined with rapid escape of volatile products is essential to reduce char formation and optimize the yield of desirable products. Liquid phase conversion routes including enzymatic hydrolysis and other direct catalytic conversion processes rely heavily on diffusive transport of enzymes and homogeneous catalysts to cell wall surfaces within biomass particles, and conversion products must diffuse away from the reaction zone to minimize product inhibition. Improving our understanding of these transport phenomena in the context of real biomass feedstocks will facilitate their optimization and © 2014 American Chemical Society
provide more accurate process models that will reduce economic uncertainty for commercialization. The importance of developing more rigorous models for the complex morphology and microstructure of biomass, as well as the challenges associated with this task, has been recognized previously.1 The overall size of biomass particles has been demonstrated to impact both thermochemical2 and biochemical3 conversion processes. Furthermore, the highly porous, directional network of cells within biomass complicates intraparticle models of transport phenomena by introducing spatial heterogeneity to the materials properties and directional anisotropy to conductive and diffusive fluxes. This microstructural geometry, which can vary significantly among tissue types and species of origin, functioned as structural support and as water and nutrient transport conduits throughout plants during their lifetime. Plant microstructure is retained in biomass feedstock particles after mechanical particle size reduction such as milling and grinding, unless the particles are intentionally milled to subcellulular dimensions; however, the energy required for such extreme particle size reduction is cost Received: September 30, 2014 Revised: December 2, 2014 Published: December 9, 2014 242
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finite-element-based computational environment, such “process agnostic” structural models will find future application in specific process simulation efforts. We intend to incorporate biomass transformation reaction kinetics into finite-element simulations of transport phenomena using the structural models presented here to evaluate how the particle size, morphology and microstructure from different feedstocks and milling methods impacts yields and efficiencies of various biomass conversion processes.
prohibitive for industrial processes.4 Therefore, the outcome of any conversion process that employs biomass particles as a feedstock is affected by the morphology and the microstructure of the particles. While kinetic models of biomass conversion processes have been the topic of many studies, nearly all use oversimplified biomass particle geometries. For example, the majority of thermal conversion models for wood particles approximate intraparticle heat and mass transport using one-dimensional (1D), transient differential energy and mass balances.5−12 Some investigations have incorporated the effects of size and shrinking particles treated as spheres,13−15 and others have gone so far as to include correlations to attempt to account for directional granularity of wood microstructure.16 Recently, Lu and colleagues demonstrated that modeling biomass particles as spheres can lead to significant errors in simulations of thermochemical conversion, and the authors used image data to construct particle models with more realistic shapes that facilitated more accurate simulations.17 While the aforementioned study took important strides toward improved biomass particle models, the internal microstructure still was neglected. Computational fluid dynamics (CFD) simulations of biomass pyrolysis have also attracted considerable recent interest;18−22 however, these reactor-scale models focus mainly on bulk fluid mechanics and chemical reaction kinetics and neglect entirely any effects of biomass particle microstructure. Perhaps the most thorough attempts to account for the effects of biomass microstructure on transport phenomena have been contributed by Eiteiberger and Hofstetter, wherein correlations for thermal conductivity23 and moisture diffusion24 were developed based on multiscale structural parameters. While those studies clearly demonstrated the importance of microstructure on transport phenomena, models of biomass particles with explicit, realistic microscale geometry have remained absent from the literature apart from this present work. Here we present a new platform for finite-element simulations of microscale, intraparticle transport phenomena based on biomass particle models with structural parameters measured from microscopy data. We describe general methodology for the construction of models that capture the dominant morphological parameters at the scale of typical milled biomass particles, i.e., overall size and shape of the particle, and the directional porosity contributed to by the lumen of fiber and vessel cells. While real biomass contains additional microstructural complexity, such as cell wall pits and ray cells running perpendicular to the dominant longitudinal directional porosity, these features are not included in the present models in order to focus on parameters that have the largest impact on the spatial distribution of mass at the length scales investigated here. The construction algorithms accept variable input for the parameters that define these geometric features to facilitate direct investigations of the effects of their variability on the behavior of transport phenomena. We demonstrate the versatility of this model construction method by constructing models of three different size classes of biomass particles from two different feedstock species (quaking aspen and loblolly pine), and we present comparative finite-element simulations of heat and mass transfer based on the various particle geometries. Focusing modeling efforts on biomass itself, as opposed to specific conversion processes or reactors, is generally relevant to any process that takes biomass as a feedstock. While the simulations presented in this work are largely intended to showcase the functionality of these new particle models in a
2. EXPERIMENTAL SECTION 2.1. Biomass Particle Preparation. Populus tremuloides (Po. tremuloides, quaking aspen) and Pinus taeda (Pi. taeda, loblolly pine) dry wood samples were obtained from the trunks of mature (∼15 years old) trees milled using in a Wiley mill (Thomas Scientific, Swedesboro, NJ, USA) using a 1 mm mesh screen. No additional sieving was done to the resultant particles prior to analysis. 2.2. Flatbed Scanning. Approximately 10 mg of milled biomass sample was spread to minimize particle overlap or contact. The particles were imaged using an Epson Stylus Photo (Seiko Epson Inc.) flatbed scanner scanning at 2400 dpi, and the images were captured as TIFF files with a pixel size of 10.6 μm. 2.3. Optical Profilometry. Optical profilometry was performed using a Zeta-300 optical profilometer (Zeta Instruments, San Jose, CA, USA). Samples were dispersed on an unpolished silicon surface, and the full height of the particles was measured in 200 steps. Threedimensional representations are real color, reflection mode at the measured in-focus height. 2.4. Scanning Electron Microscopy. Imaging by scanning electron microscopy (SEM) was performed using a FEI Quanta 400 FEG instrument (FEI, Hillsboro, OR, USA). Samples were freezedried prior to imaging and mounted on aluminum stubs using conductive carbon tape and sputter-coated with 6 nm of gold. Imaging was performed at beam accelerating voltages from 15 to 30 keV. 2.5. Confocal Scanning Laser Microscopy. Biomass samples were processed using microwave EM processing. The samples were dehydrated by treating with increasing concentrations of ethanol in a laboratory microwave oven (Ted Pella, Redding, CA, USA) for 1 min for each dilution. Samples were then infiltrated with LR White (London Resin Co.) by incubating at room temperature for several hours to overnight in increasing concentrations of resin. The samples were transferred to capsules, and the resin was polymerized in an oven at 60 °C overnight. Semithin (300 nm) sectioned samples were positioned on glass microscope slides and stained with 0.1 wt % acriflavine for confocal scanning laser microscopy of cell walls. Images were captured using a Nikon C1 Plus microscope (Nikon, Tokyo, Japan) using an excitation wavelength of 488 nm. 2.6. Model Construction and Visualization. CSG models were constructed by the algorithm described herein using a custom Matlab function invoking the COMSOL Matlab API (COMSOL Live Link, version 4.3b). For visualization, the models were written as POV-Ray objects using the FreeCAD Raytracing module (FreeCAD, version 0.13). The objects were then visualized using POV-Ray version 3.7 using a custom scene description script. 2.7. Finite-Element Simulations. Finite-element simulations were performed using COMSOL Multiphysics 4.3b with the CFD and CAD Import modules. COMSOL was chosen as the platform for these simulations because of the ability of this package to integrate a variety of physical phenomena into simulations with complex geometries with relative ease. Models were meshed with combination of swept and tetrahedral meshes. The tetrahedral meshes were constructed with minimum and maximum element sizes of 2 and 30 μm, respectively, using a maximum element growth rate of 1.5. Swept meshes were used to take advantage of the uniform cross-section of the particles that resulted from the extrusion operation employed during model construction. Symmetry was employed where applicable to reduce computational workload. An example of a meshed particle model is included in Supporting Information Figure S1. Solutions of 243
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Energy & Fuels the transient simulations were obtained using a fully coupled, multifrontal massively parallel sparse (MUMPS) direct solver with a relative error tolerance of 0.01. Simulations were performed in interactive mode on a high-performance computing cluster using one or two compute nodes, each of which consisted of 24 Intel Xeon E52695v2 “IvyBridge” processors with 64 GB of RAM.
3. RESULTS AND DISCUSSION 3.1. Measurement of Particle Morphology Descriptors and Microstructural Dimensions by Quantitative Image Analysis. We used multimodal microscopy with semiautomated image analyses to directly measure structural parameters and geometric descriptors from process-relevant biomass particles. These data were used to inform our model construction algorithm in order to produce models with physically accurate dimensions. We chose to analyze quaking aspen, a poplar subspecies, as a model hardwood and loblolly pine as a model softwood. The biomass material was milled with a Wiley knife mill using a 1 mm screen, which is a typical size reduction for feedstocks presently used in experimental fast pyrolysis reactors at National Renewable Energy Laboratory (NREL). First, statistical analysis of the overall size and shape of the biomass particles was performed by methods similar to those described by Igathinathane and colleagues.25 A large ensemble of particles from each biomass sample was imaged using a highresolution flatbed scanner. With proper sample preparation (i.e., dispersion of particles to minimize overlap and contact), images produced by this method were readily analyzed by semiautomated particle analysis routines. This method also allows for a large number of biomass particles to be imaged and subsequently analyzed simultaneously. In this study, a total of 26,463 poplar particles and 35,977 pine particles were analyzed. Subregions of the scanned particle images from each feedstock are shown in Figure 1. Visual inspection of these images reveals that the milling process imposes a maximum size on the ensemble of particles but still produces considerable heterogeneity in terms of size and morphology. The particles are also noticeably nonspherical in shape, which suggests that a single measure (e.g., diameter) would be insufficient to describe their geometry. We measured several parameters to quantify the size and shape of the particles, including Feret diameter (denoted DF), aspect ratio, and projected area. The Feret diameter is defined as the longest distance between two points on the particle perimeter and provides a good descriptor of the overall size. The aspect ratio is obtained by fitting an ellipse to the particle and taking the ratio of the major axis to the minor axis. The projected area measurement is the area within the perimeter of a 2D projection of the particle. An estimate of the volume of a given particle may be obtained by multiplying its projected area by the minor axis of the fitted ellipse. This quantity is roughly proportional to the particle mass as M ≈ ρbulk Ad
Figure 1. High-resolution scanner images of milled poplar (a) and pine (b) particles. Particles were classified into three size regimes based on their Feret diameters measured by image analysis. Blue arrows indicate examples of particles in the largest size class (DF > 1500 μm), green arrows indicate examples of the intermediate size regime (200 μm ≤ DF < 1500 μm), and red arrows indicate particles classified as fines (DF < 200 μm). Examples of optical profilometry data obtained from poplar (c) and pine (d) used to measure particle depth.
Histograms of Feret diameter, aspect ratio, and projected area for each biomass feedstock are presented in Figure 2. For both biomass types, the distributions of Feret diameters and projected areas clearly show that the particle populations are dominated by relatively small particles that are often referred to as “fines” (note the log scale on the histograms in Figure 2). The vast number of fines present in the data set greatly skews the global ensemble statistics toward the size and shape of these small particles. In order to calculate more informative statistics, particles were separated into one of three classes based on their Feret diameter. We delineated these classes as follows: fines, DF < 200 μm; intermediate particles, 200 μm ≤ DF < 1500 μm; and large particles, DF > 1500 μm. Several examples of each particle class are indicated in Figure 1 by colored arrows. Statistics were calculated for each particle class within each biomass species. These results, as well as global statistics for each biomass species, are reported in Table 1. We found that particles in the fines class accounted for ∼80% of the total number of particles. However, this class of particles only contributed ∼2.6% of the total mass of the poplar feedstock and ∼0.7% of the total mass of the pine feedstock as estimated
(1)
where ρbulk is the bulk density, A is the area measured by particle analysis, and d is the particle depth dimension which was obtained by optical profilometry. We note that the preceding expression may underestimate the mass of very small particles with Feret diameters less than the diameter of the cell lumen. Such particles are cell wall fragments generated during size reduction and are often denser than the bulk wood density because their dimensions can be too small to encapsulate an entire cell lumen. 244
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between the hardwood and softwood. Specifically, the packing density of axial tracheids appears higher in the poplar sample, and the cell wall thickness and lumen diameter appear larger in the pine sample. These microstructural features were measured directly from the micrographs by image analysis in order to quantify the apparent differences. The results are summarized in Table 2. The cell wall thickness was quantified using a distance map in conjunction with a medial axis transform as described previusly.26 Representative distance maps for poplar and pine are shown in Figure 4a,b, respectively. The distance maps in Figure 4 show the entire image; however, for the purposes of measuring cell wall thickness, subregions of interest were selected to avoid contributions of tangential sections of ray cells that would otherwise inflate the thickness measurement. The cell lumen areas were quantified by particle analysis of the image binary, treating the lumen interior as the particles. The circular diameter was calculated from the area as DC = 2(AL /π )1/2
(2)
where DC is the circular diameter and AL is the lumen area. In analysis of the pine images, a minimum area filter of 80 μm2 was imposed to eliminate contributions of pit cavities within the cell wall to the lumen area statistics. Histograms of the cell lumen areas from the poplar and pine samples are presented in Figure 4c,d, respectively. While the pine lumen area values display a unimodal distribution about the global mean, the lumen areas of the poplar sample form a bimodal distribution. This result is expected because of the much larger vessel elements in the hardwood. Therefore, hardwood lumen were classified into different size regimes based on their area in order to calculate statistics that reflect dimensions of axial tracheids and vessel cells separately. The distribution of vessel cells is substantially broadened with respect to that of the axial tracheids, since the vessel cells are nonuniformly subdivided. An area threshold of 200 μm2 was selected to delineate axial tracheids from vessel cells. The spatial frequency of each cell type was calculated directly as
Figure 2. Particle size and shape descriptors obtained by analyzing images of milled biomass.
by eq 1. Conversely, particles in the largest size class account for less than 1% of the total number of particles for each feedstock; however, they contribute ∼68% and ∼11% of the total mass for the poplar and pine feedstocks, respectively. Parameters describing the microstructural geometry of each feedstock were obtained by confocal scanning laser microscopy (CSLM) of sample cross sections. These images are presented in Figure 3. Visual inspection of these images reveals obvious differences in the microstructure of the two samples. The most immediately observable difference is the presence of large diameter vessel cells in the hardwood and their absence in the softwood. The axial tracheids also display noticeable differences
fC =
NC AROI
(3)
where f C is the spatial frequency, AROI is the area of the region of interest analyzed, and NC is the number of cells of a particular class found within the region of interest. These results are summarized in Table 2. 3.2. Assembly of Biomass Particle Models by Constructive Solid Geometry. A constructive solid geometry (CSG) algorithm was developed to produce three-
Table 1. Particle Analysis Resultsa sample classification poplar total pine total poplar fines (DF < 200 μm) pine fines (DF < 200 μm) poplar intermediate (200 μm ≤ DF < 1500 μm) pine intermediate (200 μm ≤ DF < 1500 μm) poplar large (DF > 1500 μm) pine large (DF > 1500 μm) a
Feret diam (μm) 159 171 75 72 448
± ± ± ± ±
257 257 43 41 275
527 ± 309 1980 ± 455 1789 ± 296
area (μm2 × 104) 2.0 2.3 0.3 0.2 6.7
± ± ± ± ±
8.5 7.4 0.3 0.3 9.5
9.3 ± 11.8 71 ± 31 53 ± 19
length-to-width ratio 2.1 2.3 1.9 2.0 3.0
± ± ± ± ±
1.1 1.3 0.8 0.9 1.5
3.4 ± 1.9 4.0 ± 1.8 4.0 ± 1.5
width-to-depth ratio
% of total particles
% of total mass
± ± ± ± ±
0.9 1.3 0.5 1.2 1.2
80.9 79.4 18.3
2.6 0.7 29.3
0.9 ± 0.4 2.4 ± 0.6 2.7 ± 1.0
20.1 0.8 0.5
87.5 68.0 11.8
2.1 2.3 1.6 3.2 2.2
Reported values respectively represent the mean and standard deviation of the measurements. 245
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Figure 3. Representative confocal scanning laser micrographs at various magnifications of thin sections from poplar (a−c) and pine (d−f) showing differences in cell wall microstructure. Direct measurements of cell wall thickness, lumen diameter, and spatial frequency of vessel cells were obtained by analysis of these image data.
Table 2. Microstructure Dimensionsa pine (loblolly pine, earlywood)
parameter b
cell wall thickness (μm) axial tracheid lumen area (μm2) axial tracheid circular diam (μm) axial tracheid spatial freq (mm‑2) axial tracheid length (mm)c vessel lumen area (μm2) vessel circular diam (μm) vessel spatial freq (mm−2)
poplar (quaking aspen)
A graphical representation of the CSG algorithm is presented in Figure 5. First, an ellipsoid is defined based on the Feret diameter, length-to-width ratio, and depth-to-width ratio to approximate the cross-sectional morphology of the particle (Figure 5a). The particle length is calculated from the Feret diameter and dimensional ratio as
symbol
3.1 ± 0.7
2.1 ± 0.6
TCW
310 ± 133
48.5 ± 36.9
ATL
19 ± 4
7.3 ± 2.9
DTL
1331 ± 140
4879 ± 976
f CT
4.0
1.2
LAT
904 ± 397 33.0 ± 7.9
AVL DVL
334 ± 100
f CV
L=
DF (1 + RLW −2)1/2
(4)
where L is the particle length, DF is the Feret diameter, and RLW is the length-to-width ratio. The particle width was calculated from the length-to-width ratio and the depth was calculated from the width-to-depth ratio as measured by profilometry. Next, circles are subtracted from the ellipsoid to approximate the lumen of axial tracheids. These circles are placed within the particle bounding cylinder using hexagonal close packing (HCP). A schematic showing the lumen HCP unit cell is presented in Figure 5b. The thickness of real cell walls varies, and is thickest at the cell corners and thinnest midway between cell corners. Similarly, the thickness of cell walls modeled using HCP placement of cell lumen varies with angular direction from the center of the lumen. The full angular period of the cell wall thickness variation is π/3 radians. We determined the HCP lattice constant for hexagonal packing of the lumen to ensure that the average cell wall thickness displayed by the model was equivalent to the average cell wall thickness obtained from the microscopy data. As shown in Figure 5c, the cell wall thickness as a function of angular direction from the center of the lumen (denoted θ) is given by
a
Reported values respectively represent the mean and standard deviation of the measurements. bValues reflect the thickness of the individual cell wall; thus the total thickness of the shared wall is twice the reported value. cValues obtained from ref 27; standard deviations were not provided.
dimensional models of biomass particles based on the geometric parameters obtained from the imaging and analysis described previously. The eventual objective for these models is to serve as simulation geometry in finite-element (FEM)-based computational environments. To that end, the model assembly algorithm was implemented in Comsol using the Matlab API to facilitate output of the models into standard CAD formats that may be imported into FEM modeling software. The function was written to accept arbitrary inputs for the parameters that define particle morphology and microstructure. Specifically, these parameters consist of the Feret diameter, length-to-width ratio, width-to-depth ratio, cell wall thickness, and axial tracheid lumen diameter and, for the case of hardwood models, the vessel cell lumen diameter and vessel cell spatial frequency. The model construction algorithm was developed with mathematical rigor to ensure that these parameters were accurately portrayed in the resultant models. For clarity, a table of symbols used and their descriptions is included in the Supporting Information.
TCW(θ ) = dMA(θ ) − RFL
(5)
where dMA is the distance from the center of the cell lumen to the medial axis of the cell wall and RFL is the average lumen radius. Employing the dodecyl symmetry of the thickness variation (i.e., half the full period), the average cell wall thickness (measured from the microscopy data) is calculated as ⟨TCW(θ)⟩ = ⟨dMA(θ) − RFL⟩ =
∫0
π /6
⎛ dMA(θ) − RFL ⎞ ⎜ ⎟ dθ ⎝ ⎠ π /6 (6)
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Figure 4. (a, b) Distance maps computed from CSLM images of poplar and pine, respectively. (c, d) Histograms of cell lumen area measured from CSLM images of poplar and pine, respectively. The cell lumen of the poplar sample display a bimodal distribution due to the presence of vessel cells, while the lumen of the pine sample display a largely unimodal distribution about the global mean.
particle height, no transverse wall will appear within the lumen. For the case of the softwood models, the algorithm is terminated after the transverse cell wall placement operations because softwoods typically do not have vessel cells. For hardwood models, additional CSG operations are performed to approximate the presence of vessel cells within the particle model. These operations consist of fusing circles back into the particle cross-section (Figure 5e) and subsequently subtracting out their interiors (Figure 5f). The outer diameter of the cylinder is given by
By the cosine identity for the right triangle formed between the cell lumen center, the center of the medial axis of the adjoining cell, and the corner of the medial axis of the two adjoining cells (shown in Figure 6b), dMA may be expressed as a function of the HCP lattice constant (a) and angular direction from the lumen center (θ) as dMA(θ ) =
a /2 a = sec θ cos θ 2
(7)
This expression is inserted into the average value integral to obtain 6 ⟨TCW(θ )⟩ = π
∫0
π /6
⎛a ⎞ ⎜ sec θ − RFL⎟ dθ ⎝2 ⎠
DO = D VL + 2TCW
(11)
where DO is the diameter of the outer cylinder and DVL is the vessel lumen diameter. The diameter of the interior (subtracted) cylinder is simply DVL. Placement of the vessel elements is sequential and determined by a random number generator. This causes some vessel lumen to overlap, similar to compound lumen structures observed in Figure 3a. Transverse walls in vessel elements are neglected in the present model, since these features typically occur with a spatial period that is typically 1−2 orders of magnitude longer than the largest particles considered in this study.28 Next, the particle models are trimmed to remove vessel cell walls that are outside of the original particle cross-section and to produce rounded edges typical of actual milled particles. 3.3. Model Visualization and Comparison to Scanning Electron Micrographs. Scanning electron microscopy was used to obtain images of actual particles from each class for comparison. These images are presented in Figure 6a−f. The morphological descriptors and geometric parameters reported in Tables 1 and 2 were used to construct biomass particle models representing each size class for both species, and the resultant particle models are visualized orthographically with scale bars in Figure 6g,h. A lineup of particle models for the three classes, shown to scale in the main panels of Figure 6g,h, effectively highlights the disparity in particle sizes present in the feedstocks. The inset panels of Figure 6g,h present zoom views
(8)
Integration and evaluation yield 3a [ln|sec θ + tan θ| − RFLθ ]0π /6 π ⎤ π 3a ⎡ ⎛ 2 1 ⎞ = + ⎟ − ln(1 − 0) − RFL ⎥ ⎢ln⎜ π⎣ ⎝ 3 3⎠ 6 ⎦
⟨TCW(θ )⟩ =
(9)
Finally simplifying and solving for a provides an expression for the lattice constant as a function of the measured parameters ⟨TCW⟩ and RFL: π a= (⟨TCW ⟩ + RFL) (10) 3 ln 3 Functionality to place transverse walls within the particle models was also added to the algorithm although this operation is not visualized in Figure 5. The vertical placement of transverse walls is determined by a random number generator and the average length of the axial tracheids (obtained from ref 27 ) as z = RzLF where z is the displacement in the long dimension of the particle, LF is average axial tracheid length, and Rz is a random number in the interval [0,1]. In the locations where the calculated vertical shift is greater than the 247
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Figure 5. Constructive solid geometry algorithm for biomass particle models. (a) An ellipsoid defined by the Feret diameter, length-to-width ratio, and width-to-depth ratio serves as the cross-section of the desired particle. (b) Lumen are placed within the model using an HCP arrangement with a lattice constant that ensures that the average cell wall thickness and lumen radius displayed by the model are equivalent to those parameters measured from the image data. The HCP unit cell is shown in blue, and the medial axes of the cell walls are shown as gray dashed lines. (c) The right triangle from which trigonometric relationships were obtained to calculate the proper lattice constant is shown. (d) Circles are subtracted from the ellipsoid to approximate the lumen of axial tracheids. For hardwood models, vessel cells are approximated by fusing new circles within the model (e) and subtracting out their interior (f). The circles are sized such that their inner diameter is equal to the average diameter of vessel cells of the biomass species. (g) The particle model cross-section is extruded through the length of the particle. (h) The particle exterior is trimmed to round the top and bottom surfaces and to remove vessel cell walls located outside of the particle cross-section. Finally, texture and color may be applied to the model for visualization purposes only (i).
of the intermediate and fine size class of particle models. The models of the fine size class demonstrate that the construction algorithm produces models that encapsulate only a single cell lumen, and models that appear as cell wall fragments result from additional reduction of the ferret diameter. Visual comparison of these models to the SEM images shows that these structures indeed bear closer structural resemblance to real biomass particles than the still commonly employed spherical and cylindrical geometric models. The nonunity dimensional aspect ratios measured by particle analysis cause the construction algorithm to produce models whose geometries that depart significantly from simple geometries and the models appear fibrous and flaky as observed in the image data. We acknowledge considerable room for improvement to increase the realism of the model construction algorithms described here, such as the inclusion of ray cells, cell wall pits, and intraparticle variation of geometric parameters. Still, the structural models presented in this work are the first to include
explicit, species-dependent microstructure and thus constitute significant progress from the oversimplified geometric models commonly employed in present simulations of biomass conversion processes. These improved particle models will facilitate feedstock-specific simulations that will elucidate relationships between the effects of particle size, shape, and species of origin on conversion efficiency and product yields. 3.4. Finite-Element Simulations of Intraparticle Transport Phenomena: Conjugate Heat Transfer. Simulations of conjugate heat transfer were performed in the temperature regime relevant to fast pyrolysis. Real physical processes that occur during fast pyrolysis are far more complex than those simulated here, and involve rapid phase transitions29 coupled to a multitude of chemical reactions with accompanying heats of reaction.30 Incorporating these additional complexities into multiphysics simulations and experimental validation thereof is indeed an eventual target of this research and will provide useful insight into these processes in the context of biomass 248
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Figure 6. Scanning electron micrographs and microstructured particle models of hardwood and softwood for each size class. Top row: SEM images showing representative particles from each size class from poplar and pine. Bottom row: orthographic visualization of particle models constructed by the CSG algorithm using the dimensions and morphological parameters measured from image analysis. Inset panels show a zoom view of the intermediate and fine size classes of each feedstock.
microstructure; however, the simulations presented at this stage are intended to exhibit the functionality of the complex geometric models developed here within a computational environment and to compare models with explicit microstructure to particle models with traditional geometries. Several scenarios were investigated to probe the effect of particle model geometry: a detailed particle model of DF = 2 mm with explicit microstructure constructed by methods described earlier (Figure 7a); a model with the same size and morphological profile of the detailed model but omitting microstructural geometry (this model will hereafter be referred to as the “solid model”, Figure 7b), and a spherical model (Figure 7c) with the same volume as the solid model. Each particle model was placed in a bounding vessel to create two separate volumetric domains (i.e., the particle model and surrounding media). A schematic of the simulation geometry consisting of these two domains is shown in Figure 7b. For the heat transfer simulations, the surrounding medium was assumed to be nitrogen gas and assigned corresponding thermophysical properties from the MatWeb material database.31 The thermophysical properties assigned to the biomass particle models were obtained from the Wood Handbook.32 The thermal conductivity was taken as k = 0.12 W/(m·K), and the heat capacity at constant pressure for dry wood was taken as Cp/[kJ/(kg·K)] = 0.1031 + 0.003867T, where T is the temperature in kelvin. In reality, the thermal conductivity of the cell wall material is likely higher than the thermal conductivity of bulk wood used in these simulations; however, for these comparative simulations each model was assigned identical thermophysical properties in order to isolate the effects of the various geometries. Each model was assigned an identical mass given by M = ρB VB = ρS VS
Figure 7. Particle model geometries used in simulations of heat and mass transfer. Three models with different spatial distributions of mass but identical thermal capacities are shown in a−c. The microstructure model (a) has the same 3D profile as the solid model (b), and the sphere model (c) has the same volume as the solid model. The solid and sphere models were assigned the bulk density of loblolly pine, and the density of the microstructure model was normalized to its void volume such that all three models contained identical mass. (d) Particle models were placed in a simulation vessel that was assumed to be filled with nitrogen in the case of the heat transfer simulations and water in the case of the mass transfer simulations. Constant temperature and concentration boundary conditions were applied to the exterior of the simulation vessel for the heat transfer and mass transfer simulations, respectively.
where M is the particle mass, ρB is the bulk density of loblolly pine (540 kg/m3),32 VB is the bulk volume (i.e., the volume of both sphere and solid models), VS is the volume of the microstructural model (or the “skeletal volume” or the particle), and ρS is the density assigned to the solid portion of the microstructural model to give it mass identical to the other two models. Since VS can be computed directly from the CAD software used to construct the models, ρS is easily determined from eq 12. By this approach, each particle model
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Figure 8. Comparative simulations of heat transfer for three model geometries with identical thermal capacity. Snapshots from the simulations at t = 0.5 s shown for the microstructure model (a), the solid model (b), and the spherical model (c) display variations in thermal gradients present throughout the model geometries. Plots of the time evolution of the volume-averaged temperature (d), surface temperature (e), and center temperature (f) show that the sphere model heats significantly slower than the other two models. The microstructure model generally behaves similarly to the solid model; however the interior of the microstructure model heats slower than the solid model due to the presence of nitrogen gas within the pores.
°C, p = 1 atm, and u = 0 were applied throughout the system. Boundary conditions of p = 1 atm and T = 500 °C were applied to the exterior of boundaries of the simulation vessel. No-slip boundary conditions (u = 0) were applied at all solid/fluid interfaces. Since these simulations provide explicit solutions for the temperature profile of the fluid, a heat transfer boundary condition at the solid/fluid interface may be applied to equate the heat carried to the solid by the fluid, the heat conducted into the solid at the interface, or
has identical thermal capacity and any disparities observed in the heating profiles may be attributed to differences in the spatial distribution of mass contributed by the various model geometries. In the fluid domain of the simulation geometry, coupled continuity, momentum, and energy equations were solved assuming a fully compressible Newtonian fluid. The fluid was considered compressible to account for variations in density that arise within the fluid domain due to the rapidly changing temperature. These equations are given respectively by
qcond = ρCp ,solid
∂ρ + ∇·(ρ u) = 0 ∂t
(13)
∂u ρ + ρ(u ·∇)u = −∇p + ∇·τij ∂t
(14)
⎛ ∂T ⎞ + (u ·∇)T ⎟ = ∇·(k∇T ) ρCp⎜ ⎝ ∂t ⎠
(15)
(17)
Note that the convective heat transfer term is neglected from the boundary condition given by eq 17 because the no-slip boundary condition implemented for the momentum equation at the solid/fluid interface implies that heat transfer across the interface is by conduction only.33 The results of these simulations for the microstructure model, solid model, and spherical model are presented in Figure 8. Simulation snapshots taken at t = 0.5 s are shown in the top row and visualize thermal gradients present throughout the models, and plots of the time evolution of the volumeaveraged, surface, and center temperatures are shown in the bottom row. In general, these results show similar behavior between the microstructure and solid models; however the spherical model heats significantly slower than the others due to its much smaller surface-area-to-volume ratio. Subtle disparities are present between the heating profiles of the microstructure and solid model. These temperature differences are most evident at the center of the models, which heats slower in the case of the microstructure model due to the presence of nitrogen gas within the pores which acts to insulate the particle interior. In general, these findings also suggest that
where ρ is the density, T is the temperature, u is the threecomponent velocity vector for a Cartesian coordinate system, p is the pressure, and τij is the viscous stress tensor given by ⎛ ⎞ 2 τij = μ⎜∇u + (∇u)T − (∇·u)I⎟ ⎝ ⎠ 3
∂T = −k fluid∇T ∂t
(16)
where μ is the viscosity, I is the identity matrix, and superscript T denotes the transpose operator. Gravity force acting on the fluid was neglected. In the solid domain, the heat conduction equation was solved which is obtained from eq 15 by omitting the convective heat transfer term (u·∇)T. A heat generation term (typically denoted as Q) was not included in eq 15 since chemical transformations and their associated heats of reaction were neglected from the simulation. Initial conditions of T = 25 250
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Figure 9. Comparative simulations of diffusive mass transfer for three model geometries. Snapshots from the simulations at t = 50 s shown for the microstructure model (a), the solid model (b), and spherical model (c) show variations in concentration gradients present throughout the model geometries. Plots of the time evolution of the volume-averaged concentration, surface concentration, and center concentration are shown in panels d, e, and f, respectively. The surface concentration of all three models is largely similar, but diffusive penetration into the solid and sphere models is substantially slower than that of the microstructure model due to the explicit cell lumen which serve as conduits that facilitate faster access to the particle interior.
10−10 for sulfuric acid in yellow poplar particles measured by Kim and Lee38 was assigned to the particle domain. Values of true intracell wall diffusion coefficients, as opposed to effective bulk diffusion coefficients, are absent from the literature for the majority of the compounds (including sulfuric acid) because of the difficulty associated with decoupling diffusive transport within the cell wall from that through the cell lumen. However, it is generally accepted that the intracell wall diffusion coefficient of a compound may be estimated from its diffusion coefficient in water as DCW = DH2O/10.39 Therefore, the intracell wall diffusion coefficient was taken as 1.06 × 10−10 m2/ s in the particle domain of the microstructure model. The initial concentration was assumed to be zero throughout the simulation geometry, and a boundary condition of C = 1 mM was applied to all exterior boundaries. The results of these diffusion simulations are presented in Figure 9. These results display trends similar to the heat transfer simulations in that diffusive penetration into the spherical model is significantly slower than the other two geometries. In contrast to the heat transfer simulations that predicted a slower temperature increase in the center of the microstructure model relative to that of the solid model, the interior concentration of the microstructure model increases faster than that of the solid model due to the presence of defined porosity. While these results are not an entirely unexpected effect of including explicit microstructure, these comparative simulations demonstrate that intraparticle transport phenomena may not be adequately represented by traditional geometric models using effective bulk transport parameters. 3.6. Simulations Comparing Particle Size and Feedstock Species. Finally, simulations of heat transfer and
accurately representing the overall shape of the particle has a larger impact on the simulation results than incorporating explicit microstructure, provided that appropriate bulk thermophysical properties are available. Thus, in cases of very large particles where including explicit microstructure is not feasible, solid models with accurate morphologies and bulk properties likely provide reasonable approximations. 3.5. Finite-Element Simulations of Intraparticle Transport Phenomena: Diffusive Mass Transport. Many biomass conversion processes involve liquid phase processing steps that rely on the infiltration of biomass particles with small molecules used in direct catalytic conversion systems34 as well as pretreatment steps prior to enzymatic hydrolysis.35 In addition, the diffusive transport of signaling molecules like Auxin throughout plant tissue plays an important role in plant developmental biology, and the simulation of this process has been the topic of numerous computational investigations.36 Here we develop a simulation for the liquid phase diffusional transport of sulfuric acid, a common pretreatment agent, into biomass particles. The simulation geometries used were identical to those shown in Figure 7, and the fluid domain was assumed to be filled with water. Neglecting convective mass transfer, the mass continuity equation for a chemical species i obtained from Fick’s second law can be written as ∂C = ∇·(D∇C) ∂t
(18)
where C is the concentration and D is the diffusion coefficient. For all models, the diffusion coefficient of sulfuric acid was taken to be isotropic with a value of 1.06 × 10−9 m2/s in the aqueous domain.37 For the case of the solid and spherical models, the effective isotropic diffusion coefficient of 1.6 × 251
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Figure 10. Heat and mass transfer simulations comparing particle sizes and feedstock species. (a) Heat transfer simulations for three particle size classes from each feedstock show that 50 and 500 μm particles reach 500 °C in ≤0.5 s. The two smaller models display little differences between feedstock species; however, the 2 mm poplar particle model heats significantly slower than the 2 mm pine model. (b) The surface and center temperatures of the 2 mm models are plotted. (c) Volume-averaged concentrations from simulations of liquid-phase diffusion for particle models of each size class from both feedstocks are shown, and (d) the surface and center concentrations of the 2 mm particles are shown. In contrast to the heat transfer simulations, particle models of both feedstock species display largely similar behavior in the diffusion simulations.
2b which shows that surface and center temperatures of the poplar model both increase slower than those of the pine model. Interestingly, the thermal conductivity of quaking aspen (the poplar species modeled in this work) is listed in the Wood Handbook32 as 0.1 W/(m·K) compared to 0.12 W/(m·K) for loblolly pine, which is in qualitative agreement with the slower heating behavior displayed by the poplar model relative to that of the pine model. This observation implies the future utility of this modeling approach to decouple observed bulk properties from microscale transport phenomena to isolate true thermophysical properties of plant cell walls. However, we remind the reader that the pine particle models investigated in this work reflect the cell wall thickness of earlywood (which is 2−3 times thinner than the cell wall thickness of latewood), which thus likely heats significantly faster than particles consisting of predominantly latewood cell walls. Furthermore, neglecting microstructural features such as pits and ray cells, which also vary between species, could affect simulation results as well. Therefore, we do not intend the simulations presented in this work to provide definitive conclusions as to the heating behavior of the two species; rather we intend these results to demonstrate that biomass microstructure may impact heat transfer in the time and temperature regimes relevant to fast pyrolysis.
diffusion were performed using microstructure particle models for both feedstock species from each delineated size class to investigate the effects of variations in particle size and internal microstructure. In order to facilitate more direct comparison of the effects of the different microstructure of the pine and poplar models, particle models were constructed using the same Feret diameter for each size class (i.e., 50 μm, 500 μm, and 2 mm for the fine, intermediate, and large size classes, respectively). Furthermore, the thermal conductivity of bulk loblolly pine was assumed in the heat transfer simulations for both species such that any differences in the heating profiles could be attributed to geometry rather than differences in thermal properties. All other simulation parameters were identical to those used in the simulations of heat and mass transfer described earlier. The results of the heat transfer simulations for each particle are presented in Figure 10a. As expected, these simulations predict rapid heating for the 50 and 500 μm particles, both of which reach an average temperature of 500 °C in ≤0.5 s, and both species display nearly identical heating profiles. In contrast, significant differences in the heating profile are observed between species for the 2 mm particles; specifically the 2 mm poplar model heats significantly slower than the pine model, even though both models were assumed to have identical thermal conductivity and heat capacity. These differences in the behavior of the 2 mm particles are further highlighted in Figure 252
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these characteristics with accurate spatial dimensions constitutes significant progress in biomass particle modeling.
Results of liquid phase diffusion simulations performed for particle models of each size class from both feedstocks are presented in Figure 10c,d. These results show that diffusive infiltration times strongly depend upon the size of the particle as expected. Unlike the heat transfer simulations that displayed dissimilar heating profiles for the 2 mm particles, the diffusion simulations do not display appreciable differences between the two different feedstocks at any particle size investigated here. This observation suggests that both variations of microstructure modeled in these simulations provide similar diffusive transport rates into the particle. This prediction is in contradiction to the findings of Jacobson and Banerjee who modeled diffusion in pine and aspen particles by fitting experimental data to particle models treated as infinite cylinders with effective radii.40 The aforementioned study determined smaller effective diffusion coefficients for aspen particles compared to pine particles with similar effective radii; however, the authors modeled pine particles with actual length, width, and height dimensions of 3.8, 1.3, and 4.8 mm, respectively, as a cylinder with an effective radius of 0.305 mm, while an aspen particle with actual dimensions of 8.9, 1.3, and 0.42 mm was modeled with an effective cylindrical radius of 0.277. Thus, aspen particles which were longer and more massive in reality were modeled with a smaller effective radius, and the infinite cylinder model from which the diffusion constants were calculated had no means of representing this disparity in particle length. This issue may account for the lower effective diffusion coefficients determined for the aspen particles reported by Jacobson and Banerjee, though additional experiments with corresponding simulations will be required to further investigate this topic. Nevertheless, these issues highlight the importance of employing realistic geometry when modeling biomass particles in order to decouple particle size, shape, and microstructure from other materials properties that may impact intraparticle transport phenomena.
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ASSOCIATED CONTENT
* Supporting Information S
Figure showing example of meshed simulation geometry used for finite-element simulations and a table listing the symbols used. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Tel.: 1-303-381-7691. E-mail:
[email protected]. Notes
Disclosure: Certain commercial equipment, instruments, or materials are identified in this document. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the products identified are necessarily the best available for the purpose. The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The constructive solid geometry algorithm, model visualization methods, and finite-element simulation portions of this work were supported by the Computational Pyrolysis Consortium funded by the U.S. Department of Energy, BioEnergy Technologies Office (BETO). Computational resources were provided by the National Renewable Energy Sciences Center supported by the DOE Office of Energy Efficiency and Renewable Energy under Contract DE-AC36-08G028308. The imaging and image analysis part of this work was supported by the Center for Direct Catalytic Conversion of Biomass to Biofuels (C3Bio), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DESC0000997.
4. CONCLUSION In summary, we have presented a new platform for the simulation of microscale transport phenomena using 3D models of biomass particles with resolved microstructure. We have shown how quantitative analysis of image data may be used to obtain morphological descriptors that describe the shape and size of biomass particles as well as dimensions that describe their internal microstructure and porosity. A general CSG algorithm was developed to construct representative particle models in a CAD environment based on these structural measurements, and this algorithm was used to construct particle models of three different size classes from two different feedstocks. Simulations of heat and mass transport were performed to demonstrate the functionality of these models in a computational environment. Compared to models with comparable size and shape with effective bulk transport parameters, simulations of particle models that included explicit microstructure exhibited a slower increase in internal temperature and faster infiltration of solute by liquid phase diffusion. Much work remains, both experimental and computational, for the development of reliable models that capture the complex physical and chemical transformations that occur during conversion processes in the context of realistic biomass particle models. However, the microstructure and morphology of biomass particles that varies among species and size reduction methods play an important role differentiating biomass feedstocks, and the capability of this approach to represent
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