Population balance model for biomass milling

Powder Technology 276 (2015) 34–44

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Population balance model for biomass milling Miguel Gil a,⁎, Ennio Luciano b, Inmaculada Arauzo a a b

Research Centre for Energy Resources and Consumption (CIRCE), Universidad de Zaragoza, CIRCE Building, Campus Río Ebro, Mariano Esquillor Gómez, 15, 50018 Zaragoza, Spain Department of Mechanical Engineering, University of Zaragoza, Mara de Luna, E-50018 Zaragoza, Spain

a r t i c l e

i n f o

Article history: Received 26 August 2014 Received in revised form 23 December 2014 Accepted 24 January 2015 Available online 7 February 2015 Keywords: Biomass Model Population balance Milling Classification

a b s t r a c t The aim of this work is to develop a model of the milling process of biomass. For this purpose, a classic approach is selected. The breakage probability, characterized by a material mastercurve, and breakage function are used to determine the breakage matrix. A classification function is also proposed, based on physics of the process itself and the calculation of the impact number for a particle. Knowing all these, the milling product characteristic in the steady state can be reproduced. The model has been tested for the milling of two biomasses: an herbaceous one (corn stalk/leaves) and a woody biomass (poplar) in a commercial laboratory mill. The model will reproduce quite reasonably to both cumulative and discrete particle size distributions for the two biomasses tested and for several operating conditions of the mill (rotor speed, sieve openings and feed rate), as shown validating the model results with experimental work. Other parameters as input size of the material show to be less important for the sizes essayed. The main novelty of this work is to present this milling model for biomass material, introducing also the classification system modeling and the calculation of the number of impact. © 2015 Elsevier B.V. All rights reserved.

1. Introduction The use of biofuel has been increasing in the last years as alternative to fossil fuels in order to decrease the greenhouse gas emissions, mainly carbon dioxide. The rationale is that the photosynthesis of growing plants removes CO2 from the atmosphere and subsequently eliminates its net contribution to the atmospheric build-up after combustion. Biomass utilization for bio-energy, bio-fuels or bio-based products requires the reduction of its size in order to make its energy conversion feasible and efficient. Intermediate size reduction i.e. chunking, chipping or shredding is widely required, nevertheless some wellknown technologies like pulverized burners, co-firing with coal in power station, pellet or briquette production for domestic or industrial boilers or some ethanol production technologies require an extra intensive size reduction by means of the milling processes. The overall goal of a grinding process is the production of a well-defined product with a reasonable cost. For biomass resources, the high cost of this process is one of the main drawbacks for the development of renewable energy technologies based on pulverized biomass. Industrial milling process involves multi-physics underlying mechanisms related to mechanics of contact and fracture, surface physics, fluidodynamics and, even possible thermal effects on materials. All of them are mixed in an intricate manner, still nowadays, incomplete and lack of physical understanding. Comminution process is related to

⁎ Corresponding author. Tel.: +34 976 762954; fax: +34 976 732278. E-mail addresses: [email protected] (M. Gil), [email protected] (E. Luciano), [email protected] (I. Arauzo).

http://dx.doi.org/10.1016/j.powtec.2015.01.060 0032-5910/© 2015 Elsevier B.V. All rights reserved.

material properties and to the design and operation variables of the mill, as well as all interactions between them. In all cases, material behavior must be known to understand the particle response under high velocity impacts (hammer mills). Other mechanisms, still uncharacterized, play relevant roles on milling process: the fluidodynamics of airparticle inside the mill chamber, the random particle-to-particle collisions and, above all, the size classification mechanism of the particle. This process has been studied at several scales from the molecular level (e.g. crack growing) to industrial field [1] (e.g. grinding circuit including feeder, mills and classifiers). The last one has been focused on developing semi-empirical theories based on energy-size relationships and on experimental test campaign to determine the effects and influences of material conditions and operational variables on specific energy consumption and on the quality of the milled product. Semi-empirical milling theories such as Rittinger [2], Kick [3], Walker [4], Bond [5], Hukki [6], or Morrell [7] developed several mathematical relationships taking into account the energy consumption involved in the particle size reduction between known input and output particle sizes. These theories have been a widespread use for brittle materials, such as glass and minerals. However, little work has been done with biomass resources. To our knowledge, only Temmerman et al. [8] adapted the Von Rittinger theory for biomass materials, specifically for wood chips and pellets. Other authors focused their experimental campaign in obtaining the milling energy consumption and product quality for different herbaceous [9–13] and forest biomasses [11,13–15], testing several mill designs [10,14,16–18] or combinations between mills and different classifiers [15,19].

M. Gil et al. / Powder Technology 276 (2015) 34–44

No relationships have been found between general laws for particle properties relevant to grinding and first principles up to the present. Conceptually, mean particle properties or methods of probabilistic breakage mechanics have to be employed [1]. Population balance models (PBM) and discrete element models (DEM) are based on this theoretical concept. Material breakage behavior is characterized by its statistical probability of particle fracture (breakage probability, S) and the size description of the new progeny of particles generated after fracture (breakage function, B). A wide experience on the characterization of breakage behavior, mainly in mineral materials, can be reviewed in scientific literature [20–31]. However, under our knowledge, only one publication reported data with biomass resources [32]. Population balance models for milling processes have been widely developed, mainly, for mineral applications from 1970s. Austin [33] performed a PBM of high speed hammer mill for limestone, incorporating also particle damage accumulation after multi-impact. Nikolov [34,35] predicted the size distribution of the product from impact crushers through a PBM, analyzing the influence of rotor velocity and feed rate, and finally, Toneva, P. and Peukert, W. [36] reported a complete review of experiences and models. Further developments on PBM are heading to the integration of this kind of particle balances into computer simulations. The advances on computational power and techniques allow one to include in these models the multi-physics events (fracture, fluidodynamics, particle fatigue, random collisions …) that can mean a great step in comminution modeling and can be the most useful and promising tool for milling models [37]. In this sense, Djordjevic et al. [38] simulated both vertical and horizontal shaft impact crushers by DEM in order to determine the effects of design and operational conditions on energy collisions and on the particle breakage behavior. Gommeren et al. [39] developed a simulation of a dynamic model of the closed loop grinding to predict particle size distribution of the product. It was validated with PSD experimental data in order to be implemented in the control system as the next step. However, traditional materials like minerals and ores have been under study, and no experiences with biomass materials have been reported. Biomass presents two important drawbacks in comparison to mineral materials that increase the complexity of the process: non-brittle fibrous behavior [40, 41] and non-spherical particle shape [14,42,43]. In this work, a population balance model of a lab-scale impact mill is carried out with two biomass resources: poplar and corn stalk/leaves. Breakage probability (S) and breakage function (B) of the material have been incorporated as well as a novel formulation of the particle classification related to the metal screen surrounding the mill chamber

35

has been developed. Section 2 reports the model details, Section 3 describes the biomass and the experimental procedure and Section 4 shows the model validation with the experimental data. Nomenclature B breakage function C classification matrix dp particle size (mm) DEM Discrete Element Model f feed material vector fMat resistance against the external load (kgJ−1 m−1) x input particle size (mm) k number of impacts h mixture of particle inside mill chamber previous to impact m impacted material vector p final product vector PBM population balance model PSD particle size distribution r recirculated material vector rev angular speed of the mill rotor (rpm) S breakage probability Wm,kin impact energy (Jkg−1) Wm,min energy threshold for particle fracture (Jkg−1) X breakage matrix

2. Population balance model Population balance model (PBM) predicts the particle size distribution of the milled product as a function of the material properties, the design and operational variables of the mill and the interactions between material and mill. It will contribute to understand the underlying mechanism that governs the milling in order to obtain a high quality product with the lowest feasible energy cost. PBM is conceptually understood as a discrete mathematical method of particle flow balance of new daughter particles generated from the fracture of the mother ones. Fig. 1 shows a scheme of the flows involved in an impact mill with size classification. Particle flows are represented by vectors whose components show their particle size distribution divided into eight discrete size ranges: 0, 0.045, 0.1, 0.15, 0.25, 0.355, 0.5, 0.8 and 1 mm. Each vector component is the mass percentage of the particles within this size range in relation to the total mass of particles. According to this scheme (Fig. 1), f is the feed material size

Fig. 1. Scheme of a mill combined with a classifier.

36

M. Gil et al. / Powder Technology 276 (2015) 34–44

distribution and m is the particle size distribution after impact. From the classifier, p is the final product and r is the recirculated particles that have been rejected in the classification step. 2.1. Breakage Particle breakage is understood as the fracture response under single impact and depends on the material properties, the impact energy and the number of impacts. It is defined by the breakage probability of the particle (S, Section 2.1.1) and by the new particle population generated upon its fracture (breakage function, B, Section 2.1.2). 2.1.1. Breakage probability Breakage probability is characterized under Vogel and Peukert's mastercurve [24,25,44]. The expression of this curve is shown in Eq. (1), where x is the initial particle size, k is the number of impacts and Wm,kin is the specific kinetic energy of the impact. Material properties are incorporated by the resistance of the material against fracture (fmat) and by the minimum specific energy required to cause breakage (Wm,min). These material parameters for poplar and corn stalk/leaves can be consulted in Gil et al. [32] and are summarized in Table 1 (Section 3.1). n
o S ¼ 1−exp − f mat xk W m;kin −W m;min

ð1Þ

2.1.2. Breakage function The breakage function (B) describes the new particle population generated from the fracture of the mother particle. The power law of Eq. (2) was applied by Vogel and Peukert [25] to describe B, in which y is the considered size, y′ is the minimum size obtained during the milling (in this case 20 μm [25,32]), x is the initial particle size and q (Eq. (3)) is an exponent that depends linearly on the impact velocity [25].  0  q 1 y−y x BðyÞ ¼ 1 þ tanh 0 2 y y

ð2Þ

q ¼ cv þ d

ð3Þ

2.1.3. Breakage matrix From Fig. 1, the vector m is calculated as a result of the Eq. (5), where X is called breakage matrix. The breakage matrix summarizes the fundamental mechanisms that rule the particle breakage after a collision against the hammer. Particle-to-particle and particle-to-screen collisions are considered negligible [45].
 m ¼X  f þr

ð5Þ

X governs the particle transition before–after impact and redistribute the broken and unbroken particles from the whole mother particle to the fragments of the daughter particles. In this context, X is obviously a lower triangular matrix because it is not possible to generate larger particles than the mother ones. Diagonal elements (Xi,i) represent the particles whose size is kept after impact, hence, the unbroken particles. Taking into account that S is the breakage probability, the unbroken particle in the diagonal are defined as:

X i;i ¼ ð1−Si Þ:

ð6Þ

The matrix elements under the diagonal represent the fraction of particles generated by the fracture of the coarser ones. It depends on the amount of broken particles after the collision (Sj) and how these particles are fragmented in each size interval i. Incorporating the breakage density function to the model, bi,j represents the percentage of daughter particles in the i size range generated from a mother particle of j size range. Taking into account that this model considers finite size intervals, the numerical value is obtained integrating the breakage density function bj between the sizes i and i + 1. Due to strong analogy with the breakage density function, this value will be called bi,j: Z bi; j ¼

iþ1 i

b j  dx ¼ B j ði þ 1Þ−B j ðiÞ:

ð7Þ

As a consequence, the breakage matrix X is obtained from breakage probability (S) and breakage function (B), in which Xi,j is defined in Eq. (9): 0

1 … 0 … 0 C C … 0 C C ⋱ ⋮ A … 1−Sn

Gil et al. [32] found that the ratio between c and d is constant for each rotor speed, at least for the size reduction ratio studied. Values obtained in their experiments where −0.013 and −0.02 for 20,000 and 13,000 rpm, respectively. Moreover, it was found out that the parameter c depends on the number of impacts (k), on the initial particle size (x), on the specific impact energy (Wm,kin) and on the two new material parameters (γ and α) that incorporate the material properties itself (Eq. (4)). For the studied materials and tested velocities, γ and α are shown in Table 1.

1−S1 B b2;1 S1 B X ¼B B b3;1 S1 @ ⋮ bn;1 S1

γ α c ¼ −
kxW m;kin

Breakage matrix X can be presented in a reduced form shown in Eq. (10), where b is a matrix, in which only the elements bi,j for i b j are not zero, S is a diagonal matrix with Si as diagonal elements and I is the identity matrix.

ð4Þ

Table 1 Material parameters descriptors of the breakage behavior for poplar and corn stalk/leaves. Breakage probability (S)

Breakage function (B)

xWm,min (m J kg–1)

fmat (kg J–1 m–1)

Revolutions (rpm)

γ

α

Poplar

0.13

0.0992

Corn stalk/leaves

0.41

0.126

13.000 20.000 13,000 20,000

0.397 0.264 0.278 0.183

0.257 0.331 0.199 0.327

0 1−S2 b3;2 S2 ⋮ bn;2 S2

0 0 1−S3 ⋮ bn;3 S3

ð8Þ

where X i; j ¼ bi; j  S j

X ¼ b  S þ I −S

ð9Þ

ð10Þ

2.2. Classification Another key factor to determine the particle size distribution of
 milled product is the particle classification. Classification matrix C is a diagonal matrix whose elements represent the classification efficiency for each size interval. In other words, it is the probability of a particle to

M. Gil et al. / Powder Technology 276 (2015) 34–44

pass through the openings of the metal screen. It was assumed that classification efficiency is kept constant and, hence, no obstruction of openings was considered. In addition, 10% of particle leaks were considered.
 The final product p is calculated in Eq. (11) and the recirculated material ðr Þ to impact zone again is obtained in Eq. (12). p ¼C m

ð11Þ


 r ¼ I −C  m

ð12Þ

Note that the time intervals prior to k's first impacts are the starting transitory period, where the mass flow leaving the mill is smaller than the mass flow of feed particles. On the same way, when the feeding flow stops, it would take a time of k ⋅ Δt for the milling chamber to be emptied.
 The dimension of the vectors h; f ; r is determined by the number of size intervals in which the whole PSD is discretized (ten size intervals for this work). The subscript of each vector component describes the lower size boundary of each interval. 0

0 ðk−1Þ 1 1 0 1 0 1 ð0Þ ð1Þ ð2Þ r r2 r2 f2 B B B B 2ðk−1Þ C C C C h2 B f ð0Þ C B r ð1Þ C B r ð2Þ C B r1 C 1 B C B 1 C B 1 C C B h1 C B ð0Þ C B ð1Þ C B ð2Þ C B r ðk−1Þ C B C B f 0:8 C B r0:8 C B r 0:8 C B 0:8 C B h0:8 C B B B B B C C C C ð0Þ B C B ð1Þ C B ð2Þ C B r ðk−1Þ C f 0:5 C B h0:5 C B B 0:5 C C B r0:5 C B r 0:5 C B C B ð0Þ B ðk−1Þ C C B ð1Þ C B ð2Þ C B h0:355 C B f 0:355 C B r 0:355 C B r 0:355 C Br C B C¼B þ B ð1Þ C þ B ð2Þ C þ ⋯ þ B 0:355 C ð13Þ ð0Þ C Bh C B B B B B r ðk−1Þ C C C C B 0:25 C B f 0:25 C B r 0:25 C B r0:25 C 0:25 B C Bh C B ð0Þ C B ð1Þ C B ð2Þ C B ðk−1Þ C B 0:15 C B f B r 0:15 C B r0:15 C B r 0:15 C B h C B 0:15 C B ð1Þ C B ð2Þ C B ðk−1Þ C B 0:1 C B ð0Þ C B Br C B C C @h A B f 0:1 C B 0:1 C C B r0:1 C B r 0:1 C 0:045 B f ð0Þ C B r ð1Þ C B r ð2Þ C B ðk−1Þ C @ 0:045 A @ 0:045 A @ 0:045 A @ r 0:045 A h0 ð0Þ ð1Þ ð2Þ ðk−1Þ f0 r0 r0 r0 0

2.3. Model fundamentals The model is assumed under steady state conditions. After a short transient period, the mass rate of milled product is the same with the mass rate of feeding material. In the model, the steady state is discretized in infinitesimal instants of time that involve several steps: one impact and the classification process, i. e. particle rejection by the screen to the mill chamber. In every discrete time Δt during steady state conditions (Fig. 2), the particle compendium inside the milling chamber is the same, as a result of a set heterogeneous blend of particles ðh Þ in which each particle has its own past (different number of impacts and rejections) that determine their size (according to its mother particle fracture sequence). This heterogeneous particle mixture inside the mill chamber ðh Þ can be expressed as a sum of vectors which represent the feeding particles
 f that have not suffered any impact and the rejected particles ðr Þ that have suffered a number of impacts inside the milling chamber because they have been rejected in the classification process (see Eq. (13)). Every rejection vector ðr Þ has to be understood as a compendium of the rejected particles by the screen from the first to the k-th impact, being k as the maximum number of impacts. The number of impacts that a progeny has suffered is represented by a superscript of each rejection vector. In addition, each vector h n represents the particle size distribution (PSD) of each set of feeding particles after n impacts.

37

1

Consequently, the final product has the same particle composition at any time, such as in the mass product rate as in particle size distribution because it is the result of the same events (impact and classification) above the same particle mixture inside the chamber mill ðh Þ. The final
 product in steady state p can be understood as a single stage of impact + classification of this heterogeneous mixture of particles: 



p ¼C X h

ð14Þ

where breakage matrix X  depends on the number of impacts suffered by the particle. It was previously reported and incorporated in its formulation (Section 2.1). In the same way as the particle mixture inside

Fig. 2. Illustration of the steady state assumption.

38

M. Gil et al. / Powder Technology 276 (2015) 34–44


 the mill chamber, the product p can be also decomposed as a result of the impact + classification events above each h vector: 0 1 1 0 ð0Þ 1 0 ð1Þ 1 ðkÞ p2 p2 p2 p2 B ð1Þ C B ðkÞ C ð0Þ C B p1 C B B C B C p1 C B C¼B C þ B p1 C þ ⋯B p1 C @ ⋮ A B @ ⋮ A @ ⋮ A @ ⋮ A ð0Þ ð1Þ ðkÞ p0 p p p 0

0

0

ð15Þ

0

k

where p represents the well-classified particle to product flow. Considering Eq. (11): p¼C

X

ð1Þ

f

ð0Þ

þ

k X

! X

ðkÞ

r

ðk−1Þ

ð16Þ

2 ðkÞ

ðkÞ

where X is the breakage matrix associated to the kth impact and r are the rejected particles again to the mill chamber after kth−1 impact. 3. Materials and methods 3.1. Biomass Two biomasses, SRF poplar and corn stalk/leaves, classified like woody and herbaceous biomass, respectively (EN 14961-1:2010), have been tested in order to analyze the differences on breakage behavior between both groups of biomass resources. SCF Poplar (Populus spp.) is a woody biomass, cultivated in Fuente Vaqueros (UTM coordinates: 30N 431306 4118679), province of Granada, south of Spain. Corn stover (Zea Mays L.) is an herbaceous residue of corn grain, a traditionally agricultural crop with one of the highest yields in human consumption. Corn stover is mainly composed of cob, stalk and leaves. Corn stalk/leaves are two of the main fractions of corn stover. For this work, only the stalk and leaves fractions were considered. It was cultivated in Sariñena (UTM coordinates: 30 N, 738030 4629314), province of Zaragoza, northeast of Spain. After harvesting, both biomasses were chipped and subsequently hammer-milled in an experimental pilot plant (facility details in [12, 13]), obtaining a product with particle sizes under 5 mm and a geometric mean diameter around 0.7 mm [13] and a moisture content of wH20 ≈ 9 %. 3.2. Test procedure The material from milling process were collected and prepared under CEN/TS 14778-1:2005 EX [46] and EN 14780:2011 [47] standard specifications, respectively. Subsequently, the samples were analyzed to

obtain the moisture content (standard EN 14774-1:2009 [48]) and they were classified as a function of their size by mechanical screening (standard sieves ISO 3310-1:2000 [49]). A part of this material was used as a feeding material for single impact test in order to obtain their particle breakage behavior in which material parameters of the breakage probability (S) and the breakage function (B), were obtained [32] (Table 1). Another part of the milled biomass was also screened to obtain particles into two different size ranges: 0.5 to 1 mm and 1 to 2 mm. Each one of these two ranges was collected to be used as the feeding material in the lab-scale milling tests (Fritsch Pulverissette 14, Fig. 3). The labscale mill presents an internal disk rotor of 87 cm diameter features 12 hammers in triangular shape. Around 30 g of material per tests were fed with a screw conveyor. Mill was operated with the metal screen surrounding the mill chamber so the particle cannot evacuate the chamber mill until its size is smaller than the openings. Two metal screens with an opening size of 0.5 and 1 mm, respectively were used. According to technical specifications, they present a specific free surface (open area) of 12.5% and 13.8%, respectively. Subsequent to milling tests, the material was collected and the particle size distribution was obtained by mechanical sieving for twenty minutes under standard specifications (standard EN 15149-2:2010 [50]). Sieving time was established in the pre-test to guarantee that any mass changes of the size fractions were below 0.3% min− 1 with respect to the total sample mass. 3.3. Design of experiments Experimental test campaign should involve all variables with a relevant influence in the process. Population balance model should describe the real conditions under different operational conditions and materials. Differences on material properties between poplar and corn stalk/ leaves have been described in Section 3.1 and in [32]. Regarding the feeding material conditions, the input particle size was also varied. In fact, the formulation of breakage probability (S) of Vogel and Peukert as well as the formulation of the breakage function (B) obtained in [32] incorporate the size effect. Regarding operational parameters, three variables were considered: 1) the opening size of the metal screen surrounding the mill chamber, 2) the revolutions of rotor and 3) the feed rate. The first one affects the particle classification, the second one affects the impact energy (basically kinetic energy of the hammers) and the third one affects the particle-to-particle interactions due to the fact that the higher the particle concentrations inside the mill chamber the higher the probability of collisions.

Fig. 3. Lab-scale mill (Fritsch GmbH, Pulverissette 14) with metal screen surrounding the mill chamber.

M. Gil et al. / Powder Technology 276 (2015) 34–44

In brief, the variables and their value ranges considered in this study are: • Type of input material: SRF poplar and corn stalk/leaves • Input particle size of feed material (x): from 0.5 to 1 mm and from 1 to 2 mm • Opening sizes of the metal screen (dtarget): 0.5 and 1 mm • Angular speed of mill rotor (rev): 13,000 rpm and 20,000 rpm • Feed rate: depending on the angular speed of the feeding screw conveyor at 104.72 and 188.5 rad/s. All combinations between these variables were performed. A total of 12 tests were carried out for each biomass (Tables 1 and 2). Only the tests in which the input particle size (0.5 mm) were lower than the opening size (1 mm) was not performed because it is not usual that the input material is finer than the imposed size restriction in the process. As it can be seen in Table 2, two tests could not be carried out due to mill clogging because of the hard operational conditions: high feed rate, low angular speed and low opening size of the screen. The code of each test identifies, firstly, the tested biomass (P: poplar and CSL: corn stalk/leaves). The next number corresponds to the input particle size (1: 1 mm, 05: 0.5 mm) as well as the next two describe the size openings of the screen. After that, 20 or 13 indicates the angular speed of rotor (20,000 and 13,000 rpm, respectively) and, finally, the last capital letter (H or L) is related to the high or low feed rate, respectively. 4. Results Final formulation of the PBM model (Eq. (16)) presents two variables that are linked in an intricate manner and both are associated with mill flow dynamics, complex to model: the classifier efficiency
 C and the number of impacts that a particle suffers (k). On one hand, the number of impacts could be calculated from the residence time of material inside the mill chamber. However it is difficult to calculate empirically this time and no research was found to characterize it. On the other hand, literature lacks general characterization laws of the classification efficiency in mills with metal screen. As a matter of fact, some authors considered that if a particle reaches the classifier size, it automatically passes through [25]. However this assumption seems to be too simplistic considering that the classification is determined by many factors like incidence angle, particle size and concentration, screen thickness, screen open area and air-solid fluidodynamics inside the mill chamber [45]. Other researchers led to formulations of classifier efficiency based on empirical parameters and proper use of equipment [34,36,51]. Only one work reported a general characterization of mill screen [45] in a graphical form. Following this starting point, a goal of this work is to find out a proper formulation to

39

describe the classification efficiency and a further goal is to obtain the number of impacts and the particle size distribution of the milled biomass according to the operational variables and material properties. 4.1. Classification function Classification function means the probability that a particle goes through the metal screen by one of its openings. This probability, basically, depends on the probability that the particle trajectory ends on one of the openings (Ctrajectory) and, finally, if the particle is able to go through the opening (Cdp). C ¼ C trayectory  C dp ¼ C fluid  C area  C dp

ð17Þ

The former (Ctrajectory) depends on the specific free surface of the screen (Carea = open area/total screen area) and on the fluidodynamics inside the mill chamber (Cfluid). According to technical specifications, Carea = 12.5% and 13.8% for the screens of 0.5 and 1 mm opening sizes, respectively. Regarding fluidodynamics, hammers rotating at high revolutions (13,000–20,000 rpm) produce a turbulent flow in which the initial trajectory of the particle may be modified by dragging. Two opposed fluidodynamic effects work in a hermetic mill chamber. The first one consists of the input air that enters together with the feeding material at the center and the air-particles are accelerated by centrifugal forces to go through the screen openings, generating preferential air flows in which particles are dragged. It increases the probability that the particle found the openings at the end. The opposed effect consists of higher revolution of hammers that also generates a higher parallel flow to the screen, making the openings only partially efficient due to the oblique trajectory of particles against the normal direction of the screen. This angle is also one of the factors that affect the particle classification once the particle reaches the screen openings. Higher angle of incidence causes lower probability of classification and increases the bounce-back to the impact zone. The particle classification depends also on other factors of difficult quantification as the particle morphology (size and shape). Particle size plays a key role because the coarser particles, of which the size is close to the opening size, have less probability of classification than the fine ones [51]. Particle shape affects the particle classification because pulverized biomass presents non-spherical shapes [14,42,43] and, hence, its classification depends on which particle dimension (length or width) goes through the screen openings. For biomass under study, Gil et al. [43] found aspect ratios from 2.13 to 3.26 and from 1.9 to 2.4 for these size intervals, respectively. After this theoretical analysis of the factor involved in the particle classification, it is concluded that is not possible to measure and quantify the effect of each factor. Therefore, a semi-empirical assessment of the probability of particle classification was developed and incorporated

Table 2 Lab-scale milling test for poplar. x (mm)

dtarget (mm)

rev (rpm)

Feed rate (kg/h)

Test code

1 1 1 1 1 1 1 1 0.5 0.5 0.5 0.5

1 1 1 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

20,000 20,000 13,000 13,000 20,000 20,000 13,000 13,000 20,000 20,000 13,000 13,000

High rate Low rate High rate Low rate High rate Low rate High rate Low rate High rate Low rate High rate Low rate

P-1-1-20H P-1-1-20 L P-1-1-13H P-1-1-13 L P-1-05-20H P-1-05-20 L P-1-05-13H P-1-05-13 L P-05-05-20H P-05-05-20 L P-05-05-13H P-05-05-13 L

Cumulative PSD (mm) of the new particle population 0

0.045

0.1

0.15

0.25

0.355

0.5

0.8

1

0% 0% 0% 0% 0% 0% – 0% 0% 0% – 0%

3.13% 4.37% 3.54% 1.46% 5.56% 3.63% – 4.35% 0.54% 2.68% – 4.36%

12.42% 14.73% 10.91% 7.90% 24.85% 23.74% – 20.52% 16.43% 19.13% – 21.66%

21.76% 24.83% 18.71% 14.79% 38.18% 37.17% – 34.47% 31.12% 32.34% – 33.61%

49.39% 52.65% 39.71% 36.97% 72.09% 67.43% – 64.44% 59.59% 60.38% – 58.20%

68.80% 69.87% 55.96% 56.21% 86.58% 82.67% – 83.09% 77.49% 72.97% – 78.68%

86.99% 86.51% 77.83% 80.72% 91.56% 86.64% – 90.26% 87.00% 76.95% – 90.64%

95.54% 94.88% 95.66% 94.58% 100% 100% – 100% 100% 100% – 100%

100% 100% 100% 100% 100% 100% – 100% 100% 100% – 100%

40

M. Gil et al. / Powder Technology 276 (2015) 34–44

Fig. 4. Semi-empirical fitting of the classification efficiency based on a dimensionless ratio between the size of the particle and the size of the screen openings.

to the model (Eq. (16)). Once the particle achieves the opening, the probability of classification basically depends on the ratio between the size of the particle and the size of the screen opening (dp/dtarget). In order to achieve a proper formulation for the classification efficiency, at first the probability that a particle passes through the classifier was adjusted in the model with a process of trial and error. The correction was applied so that the model results were as close as possible to the experimental ones, but with the constraint that a smaller particle has more probabilities to be classified than a bigger one. Plotting the results (Fig. 4), it was noted that all the points could be fitted with a single curve with an acceptable error (R2 = 0.955) and that they followed a similar path of that initially considered as a reference. The classification equation was formulated considering that C evolves in the opposite way to breakage function: has high values for smaller particles and low for bigger particles. Often, and in this case too, the cumulative classified product presents a S shape, which means a low mass percentage in the coarsest and finest fraction sizes, and a mass accumulation in the central sizes. Being B as an always increasing function with the size, C will have to take the shape of its complement to 1 (Eq. (18)). In this way, smaller and coarser sizes are controlled by the breakage and by the classifier, respectively, while in the central sizes there is the

maximum of production due to the fact that both curves have nonnegligible values. Eq. (18) has been finally implemented in the model as a unique function which describes the parameter Cdp for each experimental case: 0

C dp

1 dp !−2 −0:02C Bd B target C dtarget ¼ 1−tanhB C @ A dp 0:02

ð18Þ

where 0.02 is the minimum ratio between dp and dtarget considered achievable by a particle. Furthermore it was found out, comparing experimental and model results using Eqs. (17) and (18), that imposing a factor of 2 to the fluidodynamic coefficient (Cfluid) according to the discrepancies between theoretical and experimental data further reduced. Once the three C parameters are set, the model allows one to calculate the k number of impacts suffered by a particle, taking into account that k is the number of impact required for the last daughter particle (from successive fractures of the mother ones) that leaves the mill chamber (Fig. 2). As every particle flow vector (e.g. m, r and p) is a result of the product of probability vectors, it is required to impose a

Table 3 Lab-scale milling test for corn stalk/leaves. x (mm)

dtarget (mm)

rev (rpm)

Feed rate (kg/h)

Test code

1 1 1 1 1 1 1 1 0.5 0.5 0.5 0.5

1 1 1 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

20,000 20,000 13,000 13,000 20,000 20,000 13,000 13,000 20,000 20,000 13,000 13,000

High rate Low rate High rate Low rate High rate Low rate High rate Low rate High rate Low rate High rate Low rate

CSL-1-1-20H CSL-1-1-20 L CSL-1-1-13H CSL-1-1-13 L CSL-1-05-20H CSL-1-05-20 L CSL-1-05-13H CSL-1-05-13 L CSL-05-05-20H CSL-05-05-20 L CSL-05-05-13H CSL-05-05-13 L

Cumulative PSD (mnb of the new particle population) 0

0.045

0.1

0.15

0.25

0.355

0.5

0.8

1

0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0%

8.31% 7.60% 4.28% 2.96% 10.69% 12.36% 7.46% 5.32% 12.13% 13.95% 5.96% 6.03%

20.49% 21.69% 13.20% 11.07% 31.32% 34.67% 23.98% 24.33% 30.62% 35.56% 18.93% 20.31%

32.36% 34.80% 20.80% 19.00% 49.14% 54.60% 37.52% 38.83% 47.41% 54.70% 35.10% 32.89%

57.61% 61.41% 39.13% 39.92% 79.21% 83.12% 66.27% 68.32% 79.09% 83.94% 58.38% 63.13%

76.33% 80.63% 58.26% 57.98% 93.71% 95.18% 86.72% 88.10% 93.66% 95.59% 78.58% 83.38%

92.09% 92.84% 79.55% 78.69% 99.38% 99.12% 96.54% 98.34% 99.37% 99.59% 96.48% 96.83%

99.49% 99.41% 97.79% 97.59% 100% 100% 100% 100% 100% 100% 100% 100%

100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100%

M. Gil et al. / Powder Technology 276 (2015) 34–44

41

restriction about the residual probability that any rejected particle keeps inside the mill chamber. It was considered that the maximum number of impact is determined when the residual daughter particles are less than 5% in relation with 100% of the mother particles (feed material).

4.2. Model validation The model output shows the particle size distribution (PSD) of the new particle population generated in the milling process. The model must be sensitive to the influences and effects of the variables under study: the input particle size, the type of biomass, the angular speed of hammers, the opening size of the screen and the feed rate. Feed rate affects the particle-to-particle interactions (impacts, deviations of trajectories, changes on particle velocity). These effects were not considered in the model because they are unfeasible to measure and quantify and, moreover, are considered negligible in comparison with other effects. However, an experimental test under two different feed rates were performed in order to check if this assumption could be attainable. Negligible differences were found on the experimental PSD when the feed rate was varied (Tables 2 and 3). Analyzing the experimental particle size distributions of the milled biomass, the influences of the variables in the real process can be determined. Model fundamentals should be sensitive to the effects of the material properties and to the operational parameters. In Fig. 5, the cumulative PSDs from the tests are shown for poplar and corn stalk/leaves. For both resources, the coarsest PSDs (red line) correspond to dtarget = 1 mm and rev = 13,000 rpm. It implies low requirement of size classification (highest opening size of the screen) and the lowest impact energy due to the lowest angular speed of hammers. The second coarser PSD is again for dtarget = 1 mm but rev = 20,000 rpm due to the higher impact energy to generate higher fracture in each impact. Further, the finest PSD is determined by the lowest opening size of (dtarget = 0.5 mm) and highest revolutions (rev = 20,000 rpm). The input particle

Fig. 5. Cumulative particle size distribution from experimental tests for poplar (top) and corn stalk/leaves (bottom).

Fig. 6. Validation of the cumulative PSD between the model results and the experimental data for poplar.

size of the material does not have much relevance on the particle size distribution. Model simulations allow one to obtain a prediction of the number of impacts (k) required to mill the biomass and a prediction of the PSD of the milled product for any combination of input variables. The effects of the rotor revolutions and the opening size are incorporated in the model. The former is taken into account on the breakage matrix by means of the impact energy (Wm,kin). Impact energy is incorporated in the formulation of the breakage probability (S, Section 2.1.1) and in the breakage function (B, Section 2.1.2), increasing the probability of a particle breakage and generates new finer particle population. The restriction of the metal screen is incorporated in the matrix classification (C ) related to the ratio dp/dtarget (Eq. (17)) and to the open area of the screen (Carea). Experimental effects observed as a function of the openings size of the screen and the angular speed are in accordance with the PBM results. Regarding the prediction of the PSD of the final milled product, Fig. 6 for poplar and Fig. 7 for corn stalk/leaves show the model validation by means of the comparison between the cumulative particle size distribution obtained from the model and from the experimental data. A high agreement (R2 ≥ 0.97) was obtained for the validation of any combination of input variables. The model is sensitive to the variations generated for the variables under study. However, the model is more accurate for some conditions as a function of the material. For poplar, a huge accuracy of the PSD prediction for poplar at 13,000 rpm (Fig. 6) and for corn stalk/leaves at 20,000 rpm (Fig. 7) can be observed. However, an over-prediction of fine particles for poplar at 20,000 rpm can be checked and the opposite trend (over-prediction of coarse particles) is reported for corn stalk/leaves at 13,000 rpm. Model results also can be represented for each size interval of PSD, showing the quantity of particles within a specific interval range in a direct form. Frequently, the representation of discrete PSD presents multiple lines overlapping between the results from different tests. Therefore in Fig. 8, an individual particle size distribution is shown in each graph for a better understanding of the reader. For editing

42

M. Gil et al. / Powder Technology 276 (2015) 34–44

Fig. 7. Validation of the cumulative PSD between the model results and the experimental data for corn stalk/leaves.

constraints, only the experimental and model results of the corn stalk/ leaves at 13,000 rpm are shown. In addition, the model also calculates the number of impact required to mill completely a biomass particle (Table 4). These effects of the analyzed variables over the number of impacts are in accordance with the trends reported for the PSD results. The lower the angular speed of the hammers and the opening size of the screen, the higher the number of impacts. It means that lower energy of impact generates lower particle fracture and coarser daughter particles as well as the higher constraints on size classification means a higher rejection rate. Materials and operational conditions that require more impacts, are also identified with final coarser PSD. A less breakage particle produces coarser new daughter particles and, thus, more impacts are required. These coarser particles (after each impact) have higher times to go through the screen openings. As a result, the final PSD of the milled product has a higher percentage of coarser particles than in other operational conditions in which finer particles are generated by a higher particle fracture and, thus, these fines particles are well-classified to final product. Other relevance results to highlight is the almost negligible influence of the input particle size (within the considered particle size). Input particle size has no effect on the final PSD but also in the number of impacts. Only one more impact was obtained for some tests when the input particle size was 0.5 mm instead of 1 mm. As a result of this work, a population balance model that allows predicting the particle size distribution of the hammer-milling product was developed. The model was found reliable under different operational parameters and with different types of biomass. 5. Conclusions A population balance model (PBM) of hammer milling was performed for two biomass resources: poplar and corn stalk/leaves, classified like woody and herbaceous resources. The theoretical model incorporated the effects of material properties and of the operational

Fig. 8. Examples of PSD validation between the model result and the experimental data for corn stalk/leaves.

mill variables. The former involves the type of biomass, its input particle size and its breakage behavior. The latter comprises the angular speed of rotor and the opening size of the screen. A set of experimental tests with a lab-scale mill were carried out also taking into account these variables in order to validate experimentally the theoretical model. The population balance model incorporates the breakage behavior of these biomasses, characterized in Gil et al. [32]. It is based on the breakage probability, that was described under Vogel and Peukert's mastercurve [24,25,44], and on a new formulation of the breakage function developed in Gil et al. [32]. In addition, the model incorporates the event of particle classification by a metal screen surrounding the mill chamber. It was found out that the probability of the particle classification, once the particle reaches the screen opening, is a function of a dimensionless ratio between the particle size and the opening size of the screen. A hyperbolic formulation was developed and incorporated to the PBM. Cumulative particle size distribution of the milled particle obtained by the theoretical population balance model and by the experimental tests agrees with a R2 ≥ 0.97 for whatever combination between the mentioned variables. The feed rate did not show any effect on the final PSD. Model and experimental tests are in accordance with the effects

M. Gil et al. / Powder Technology 276 (2015) 34–44

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Table 4 Lab-scale milling test for poplar and corn stalk/leaves. x (mm)

dtarget (mm)

rev (rpm)

Feed rate (kg/h)

Test code

Impacts (k)

Test code

Impacts (k)

1 1 1 1 1 1 1 1 0.5 0.5 0.5 0.5

1 1 1 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

20,000 20,000 13,000 13,000 20,000 20,000 13,000 13,000 20,000 20,000 13,000 13,000

High rate Low rate High rate Low rate High rate Low rate High rate Low rate High rate Low rate High rate Low rate

P-1-1-20H P-1-1-20 L P-1-1-13H P-1-1-13 L P-1-05-20H P-1-05-20 L P-1-05-13 L P-1-05-13 L P-05-05-20H P-05-05-20 L P-05-05-13H P-05-05-13 L

16 16 18 18 19 19 – 23 18 18 – 22

CSL-1-1-20H CSL-1-1-20 L CSL-1-1-13H CSL-1-1-13 L CSL-1-05-20H CSL-1-05-20 L CSL-1-05-13 L CSL-1-05-13 L CSL-05-05-20H CSL-05-05-20 L CSL-05-05-13 L CSL-05-05-13 L

15 15 18 18 18 18 24 24 18 18 23 23

of the rest of variables: the higher the impact energy (higher angular speed of the rotor) and the lower the opening size, the higher the particle fracture and therefore higher concentration of fine particles. These operational conditions also require less number of impacts to mill completely the particle. Consequently finer PSD are linked to lower number of impacts. In brief, a population balance model was performed for impact mills with screen classification that is able to predict the particle size distribution at steady-state operating conditions for biomass resources and it is sensible to follow the effects and variations generated by the material properties and operational parameters. Acknowledgments This work was partially supported by the Spanish Ministry of Education, Culture and Sports (project ENE2008-03358/ALT). The authors are grateful to the agricultural cooperative of Sariñena for the corn stover supply. References [1] W. Peukert, Material properties in fine grinding, Int. J. Miner. Process. 74S (2004) S3–S17. [2] R. Rittinger, Lehrbuch der Aufbereitungskunde, Ernst and Korn, Berlin, 1867. [3] F. Kick, Das Gesetz der proportionalen Widerstande und seine anwendung felix, 1885. (Leipzig). [4] W. Walker, Principles of chemical engineering, Trans. AIME 193 (1952) 484–494. [5] F. Bond, The third theory of comminution, Trans. AIME 193 (1952) 484–494. [6] R. Hukki, Proposal for a Solomonic settlement between the theories of von Rittinge, Kick and Bond, Trans. AIME 223 (1962) 403–408. [7] S. Morrell, An alternative energy–size relationship to that proposed by Bond for the design and optimisation of grinding circuits, Int. J. Miner. Process. 74 (2004) 133–141. [8] M. Temmerman, P.D. Jensen, J. Hébert, Von Rittinger theory adapted to wood chip and pellet milling, in a laboratory scale hammermill, Biomass Bioenergy 56 (2013) 70–81. [9] S. Mani, L.G. Tabil, S. Sokhansanj, Grinding performance and physical properties of wheat and barley straws, corn stover and switchgrass, Biomass Bioenergy 27 (2004) 339–352. [10] V.S.P. Bitra, A.R. Womac, N. Chevanan, P.I. Miu, C. Igathinathane, S. Sokhansanj, D.R. Smith, Direct mechanical energy measures of hammer mill comminution of switchgrass, wheat straw, and corn stover and analysis of their particle size distributions, Powder Technol. 193 (2009) 32–45. [11] P. Adapa, L. Tabil, G. Schoenau, Grinding performance and physical properties of non-treated and steam exploded barley, canola, oat and wheat straw, Biomass Bioenergy 35 (2011) 549–561. [12] M. Gil, I. Arauzo, E. Teruel, C. Bartolome, Milling and handling Cynara cardunculus L. for use as solid biofuel: Experimental tests, Biomass Bioenergy 41 (2012) 145–156. [13] M. Gil, I. Arauzo, E. Teruel, Influence of input biomass conditions and operational parameters on comminution of short-rotation forestry poplar and corn stover using neural networks, Energy Fuel 27 (2013) 2649–2659. [14] S. Paulrud, J.E. Mattsson, C. Nilsson, Particle and handling characteristics of wood fuel powder: effects of different mills, Fuel Process. Technol. 76 (2002) 23–39. [15] L.S. Esteban, J.E. Carrasco, Evaluation of different strategies for pulverization of forest biomasses, Powder Technol. 166 (2006) 139–151. [16] C. Vigneault, T.M. Rothwell, G. Bourgeois, Hammer-mill grinding rate and energy requirements for thin and conventional hammers, Can. Agric. Eng. 34 (1992) 203–207.

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