Indirect evaluation of the porosity of waste wood briquettes by measuring the surface roughness

31 The briquette porosity is a quality characteristic known to be important for combustion analysis, heat 32 and mass transfer processes during combustion stages, determination of effective thermal 33 conductivity or other related properties. This paper describes a method to quantify the briquette 34 porosity by some surface roughness parameters that can be useful for alternative, inexpensive and at 35 hand evaluations. Porosity of briquettes manufactured with a hydraulic press from waste wood from 36 secondary processing was calculated with three methods suggested in the literature for wood; of 37 these, one was adapted here for a wet porosity model (called “general relation”) proposed for wood 38 briquettes. Briquettes density was obtained by using two stereometric methods and a liquid 39 displacement method. Correlations were examined between porosity, surface roughness parameters 40 and density of briquettes. Very strong correlations with surface roughness were identified for 41 porosity calculated with all three methods, when density was measured by one of the stereometric 42 methods. These correlations can serve as a method to indirect evaluation of the briquettes porosity 43 by measuring the surface roughness.

see if this property can be indirectly evaluated by another method, such as by measuring some 48 roughness parameters of the briquette surface in connection with briquette density. Based on 49 previous studies carried out on wood, it can be assumed that both porosity and roughness 50 parameters are properties depending on density. Porosity and density were determined in the 51 present study by using three different methods. The experimental data contribute to the existing 52 literature on briquettes properties by adding the surface roughness. The novelty of the present paper 53 consists in extending the applicability of the porosity models originally developed for wood, to the 54 wood briquettes. To the best knowledge of the present authors, the wet porosity model applied to 55 briquettes has not been reported before. 56 5 Usta [9] defined wood as a cellular/porous material composed of cell wall substance and cavities 109 containing air and extractives. Without cavities and intercellular spaces the density of the cell wall 110 substance is constant for all timbers (1530 kg/m 3 on an oven-dry mass and volume basis). However, 111 wood does not entirely consist of cell wall substance because it contains air pockets in the cell 112 lumens. Therefore, the amount of cell wall substance (K) is a function of wood density, d (K = 113 d/1530). The void volume (porosity, P) is defined in relation to the cell wall substance (P = 1-K). 114 Siau [10] regarded wood cells as a rectangular model of square cross section with unit overall 115 dimensions (Fig.1a). All cells are equally sized and the ends of the cells are neglected. The cell lumen 116 also has a square cross section. The model refers to cells at oven-dry conditions, where the lumen 117 has only dead air. A more general model of wood cells that considers the wood moisture content was 118 described by Siau [10], as well as by Hunt et al. [11], where the bound water is added as a 119 surrounding area to the outside of the squared cell cross section having the side equal to unity 120 ( Fig.1b). Porosity is one of the physical properties of wood and wood briquettes, which is important for 125 combustion analysis and modeling, heat and mass transfer processes during combustion stages, 126 determination of effective thermal conductivity and effective heat capacity or other related 127 properties, such as density or durability, transportation and storage of briquettes, and wood 128 impregnation with preservatives [1,11,12,13,14]. 129 7 immersion, as well as regarding the risk of swelling occurrence. The bulk porosity or macro-porosity 156 is specific to cylindrical wood pellets and it is determined, for example, by using the method of 157 stereometric measurements [20,21]. 158 A correlation between surface and volume (bulk) characteristics was reported by Suliman et al. [22]. 159 They described the relationships existing between porosity and surface functionality of different 160 wood biochars and soil water retention characteristics. One of their conclusions was that the 161 capability of biochar to retain soil water is a function of the combination of its porosity and surface 162 functionality, i.e. generation of oxygenated functional groups on the surface. 163 Since porosity is important for the analysis of briquettes combustion, it would be interesting to see if 164 this property can be indirectly evaluated by another method, such as by measuring some roughness 165 parameters of the briquette surface in connection with briquette density. Based on previous studies, 166 it can be assumed that both porosity [9] and roughness parameters [23] are properties depending on 167 wood density. 168 Therefore, this paper examines correlations between the following properties: porosity and density 169 of briquettes, surface roughness parameters and density of briquettes, as well as surface roughness 170 and porosity of briquettes. Porosity and density were determined by using three different methods. 171 172

Material, methods and equipment 173
The briquettes used for this research work were obtained from beech and spruce chips, in 174 uncontrolled proportions, originating as waste material from secondary wood processing in the 175 faculty workshop. The wood chips were compressed using a MB4 GOLDMARK type hydraulic 176 briquetting press with the main characteristics indicated in Table 1

Roughness parameters of briquettes 184
Ten briquettes were randomly taken from the press container and stored in a controlled 185 environment (221 o C temperature and 402 % RH). Firstly, they were subjected to roughness 186 measurements. The measurements were performed by using a MarSurf XT20 instrument 187 manufactured by MAHR Gottingen GMBH, equipped with a scanning head MFW 250 with tracing arm 188 in the range of 500 m and a stylus with 2 m tip radius and 90 tip angle, which measured the 189 briquettes lengthwise at a speed of 0.5 mm/s and at a low scanning force of 0.7 mN. The instrument 190 had MARWIN XR20 software installed for processing the measured data. 191 The briquettes were scanned on tracing lengths of 15 mm. Four profiles were scanned for each 192 specimen, at every 90 o angle of the briquette cross-section, so that a total of 40 profiles were 193 available for further evaluation of parameters. The lateral measuring resolution was 5 m and the 194 instrument provided a vertical resolution of 50 nm. 195 First, the software removed the form error and after that, the waviness. The roughness profiles were 196 obtained by filtering each profile by using a robust filter RGRF (Robust Gaussian Regression Filter) 197 specified in ISO 16610-31 [24]. The cut-off used was 2.5 mm, as recommended in previous research 198 by Gurau [23]. This filter was tested and found useful for wood surfaces. 199 After generating the roughness profiles, Ra, representing the arithmetic mean deviation of the 200 assessed profile irregularities, was calculated on sampling lengths according to ISO 4287 [25]. Other 201 calculated parameters were the material ratio curve (Abbot curve) parameters Rpk, Rk and Rvk from 202 ISO 13565-2 [26]. Rk is the depth of the roughness core profile, Rpk is the average height of the 203 protruding peaks above the roughness core profile and Rvk represents the average depth of the 204 profile valleys projecting through the roughness core profile. Rvk may be especially sensitive to the 205 species' anatomical valleys or to various gaps caused during the briquettes pressing process. Rpk is a 206 measure of fuzziness protruding above the core roughness. The sum Rk+Rpk+Rvk was also 207 determined for comparisons, because of the cumulative effect on surface roughness and together 208 with Rvk should be sensitive to variations in briquette density (and porosity). 209 For each briquette and roughness parameter, a mean value and the standard deviation were 210 calculated. 211 212

Briquettes density 213
In order to evaluate the briquettes density, two stereometric methods and a liquid displacement 214 method were applied. The reason for applying different methods was to evaluate the best 215 correlation of density with both porosity and roughness parameters. The first stereometric method 216 (St1) was based on the measurement of the length and diameter of each briquette and on calculating 217 the volume of a cylinder as regular geometrical shape. Two lengths (at right angle of each other) and 218 three diameters (at each end and in the middle) of each briquette were measured using a digital 219 pocket caliper (ULTRA, 0.01 mm accuracy). The average values and the volume were then calculated. 220 The briquettes were weighed by using a KERN-EW 3000 g technical balance (0.01 g accuracy). The 221 density was calculated as the ratio of mass to briquette volume. 222 The second stereometric method (St2) consisted in estimating the cross-section area of each 223 briquette by means of a paper sheet of known area density (80 g/m 2 ), as described in [27]. The 224 briquette was placed on the paper, its contour was drawn on the paper and the cross-section surface 225 was accurately cut. The piece of paper was then weighed and its surface was calculated from the 226 mass and the area density of the paper. The paper surface approximating the cross-section of the 227 briquette was multiplied by the average length of the briquette and the volume of the briquette was 228 thus obtained. Again, the density was calculated as the ratio of mass to briquette volume. 229 After that, the briquettes were oven dried at 103±2 o C to constant mass in order to determine the 230 moisture content (dry basis). The moisture content was calculated based on wet and oven-dry 231 briquette masses (SR EN 13183-1-2003/AC-2004 [28]). Finally, the oven-dry briquettes' dimensions 232 were measured again by using the two stereometric methods described before. Oven-dry and wet 233 briquettes densities were calculated based on relations (1) and (2) The volume of oven-dry and wet briquettes by the liquid displacement method was estimated by 242 immersing (Im) each briquette in toluene (C 6 H 5 CH 3 ) with a density equal to 865.5 kg/m 3 at 20 o C. The 243 change of the toluene density with slight environmental temperature changes was neglected. The 244 volume of the briquette was obtained from the mass of the volume of toluene displaced while 245 immersing the briquette in the liquid. Firstly, a Berzelius glass beaker was filled with toluene to a 246 fixed volume (Fig. 2a). The beaker containing toluene was weighed. Then, the briquette was placed in 247 a metallic (copper) cage that was submerged in the Berzelius glass beaker with toluene. The part of 248 the liquid that exceeded the fixed initial volume was removed. The mass was determined again by 249 weighing. The cage was fixed by means of a wire on a glass rod placed on the glass top (Fig. 2b). The 250 volume of the briquette was calculated from the density of toluene and the difference in the masses 251 of toluene before and after briquette immersion. The density of the briquettes was evaluated by 252 using this method, following Fig. 2b and the equations indicated below: 253 Eq. (4) can also be written in terms of masses and liquid density (

(6) 265
The terms m l (kg) and m l1 (kg) refer to the masses of liquid corresponding to the volumes V l and V l1 . 266 The mass of the glass rod was every time subtracted from the performed mass measurements. 267 Briquettes are porous materials. During immersion, a part of the pores (voids developed during chips 268 compression) was filled with liquid. In order to identify possible errors, the mass of the liquid, 269 briquette and cage was measured first, as indicated in Fig The volume of the cage was also determined by using the liquid displacement method and it was 286 calculated from the following relations: 287 where: V l2 (m 3 ) is the volume of the liquid existing in the glass beaker when the cage was immersed 291 and m l2 (kg) is the corresponding mass (Fig.3). 292 293 Fig. 3. Determination of the cage volume by using the liquid displacement method 294

Briquettes porosity 295
Further on, the briquettes' porosity was calculated by using three methods. One method is very 296 often mentioned in literature, for example in [16,11,18], and the other two are recommended in 297 two publications, Siau [10] and Hunt et al. [11], as presented below. 298 The first method applied in the research reported in this paper is based on relations indicated by 299 different authors. Plötze and Niemz [16] calculated the oven-dry porosity (n) of different wood types 300 from the oven-dry density () and the solid cell wall density ( s ), as: 301 They assumed that with the increase of the moisture content, the wood cell lumen size remains the 308 same, because the moisture content (bound water) is added as an outside layer to the cell wall (Fig.  309 1b). Even so, they calculated a wet porosity (see third method described below), since the cross-310 section side of the cell wall increases with an increase in moisture content (the dimensional change 311 due to the increase in moisture content is added to the outside of the cell wall dimension). 312 Similarly to Hunt et al.
[11], Huang et al. [18] calculated the porosity of oven-dried bamboo wood (ɸ) 313 from the bulk density (ρ bulk ) (including wood substance and cavities) and skeletal density (ρ s ) 314 (excluding wood cavities), as: 315 Despite the different notations used, the oven-dry porosity has, according to the afore-mentioned 317 authors, a similar expression that takes or does not take into account the density of the air. Since the 318 density of air is around 1 kg/m 3 , it can be neglected.  14)) is based on its determination by water displacement, as described by Siau in [10].
where: bw V % is the bound water volume fraction.

339
The bound water volume fraction is calculated with respect to the wood moisture content, according 340 to Eqs. (19) and (20)

16
The first method of porosity calculation, mentioned above, referred only to the calculation of 351 porosity characteristic to the dry conditions. However, in order to be able to compare it to the 352 second and third methods (for wet conditions), it was considered appropriate to develop a modified 353 equation valid for the calculation of porosity in wet conditions. As such, considering Eqs. (13) and 354 (14), similar equations can be written for the density and wet porosity of wood cells. The density can 355 be expressed as: 356 With the porosity and the briquettes' density determined by means of the three methods described 366 above, correlations were further examined between: porosity and briquette density, surface 367 roughness data and briquette density, as well as surface roughness and porosity of briquettes. 368 369

Results and discussion 370
The results obtained from the density determination of the ten briquettes at equilibrium moisture 371 content (EMC) are shown in Table 2. The equilibrium moisture content (dry basis) of the briquettes 372 ranged from 8.13% to 8.74%, with an average at 8.41%. 373 The highest density results were obtained by using the first stereometric method (St1) and lowest 374 density results were obtained by using the second stereometric method (St2) ( Table 2). 375  Table 2 indicates a high variability of the density (at EMC), which is influenced by the measurement 379 method and the briquette. The largest mean density difference was encountered between the first 380 and the second stereometric method, while the second stereometric method and the liquid 381 displacement method (Im) showed statistically similar values, as tested by ANOVA single factor, for a 382 confidence level p<0.05. However, regression analysis of density data has shown a weak correlation 383 between individual density values calculated with St2 and liquid displacement method (R 2 =0.469) 384 and a better correlation with St1 method (R 2 =0.7). Rabier et al. [27] have also obtained a high 385 variability of the density of different types of briquettes, especially for the stereometric methods. 386 They explained this variability through the intrinsic physical properties of the briquettes, such as the 387 surface roughness. They noticed that stereometric methods led to more variable results, compared 388 to immersion methods. Also, from the statistical results they concluded that the two stereometric 389 methods cannot be regarded as equivalent, which is in agreement with our findings. 390 Slight differences in briquettes moisture content can also have an influence on density variability. 391 The relationship between individual porosity and density of briquettes at EMC is shown in Figs. 4, 5 392 and 6 and the calculated values, mean values and standard deviations are included in Table 2. As 393 expected, all figures indicate the decrease of the porosity with an increase in density. This is in 394 agreement with the results obtained for wood, as indicated by [9] and [16]. There was a strong 395 correlation between the porosity determined according to Siau's and the general relation methods 396 and density, regardless the measurement method. According to the method described by Hunt et al. 397 for the determination of the porosity, the density measurement method has an influence on the 398 porosity results. While the porosity determined by Hunt et al.'s method showed high correlation with 399 density for St1 and St2 methods (0.976 and 0.939, respectively), it decreased to 0.5016 for the liquid 400 displacement method (Fig. 6). This result shows that determination of porosity with Hunt   inverse correlation with density. This may be a result of variable local density of the briquettes on 417 their circumference. The measured profiles were taken so that two profiles corresponded to the 418 generatrix with high briquette density and the other two on the generatrix with low briquette 419 density, after a visual assessment. Given the high density variation, it was considered that the 420 selection of measuring lines for each briquette can have an influence on the assessment of its overall 421 roughness. Previous studies on sanded solid wood found an inverse relationship between density 422 and surface roughness [23]. It was reasonable to expect that density of briquettes might have a 423 similar relation with their surface roughness. In order to check this assumption, a mathematical 424 procedure was applied that selects means of roughness parameters from combinations of three 425 profiles from the measured data. As such, although 4 profiles were measured, resulting in one mean 426 value of the four profiles (1,2,3,4), the calculations took into consideration more means taken from 427 groups/combinations of 3 profiles, which were further checked for their best correlation with density 428 and indirectly with porosity, respectively. For example, the combinations were means of profiles: 429 1+2+3; 1+2+4; 2+3+4 and 1+3+4. The more measurements are performed, the more are the means 430 available and the better the chance of a more reliable approximation of the surface quality. 431

21
The mathematical procedure is looking to find the linear regression roughness parameters -density, 432 with negative slope and maximum coefficient of determination. For the ten briquettes there were 433 ten densities and four different average roughness parameters (the four means mentioned above) 434 per briquette, that is, a matrix with ten rows and four columns. For the matrix, the following function 435 is considered      Table 3 shows the correlations between the average roughness parameters and the density of 446 briquettes at EMC, as well as with the briquettes porosity. 447 448 In order to analyze the correlations of density with roughness, as well as of porosity with roughness, 452 the Regression analysis tool was used. This involved performing a linear regression analysis by using 453 the "least squares" method to fit a line through a set of observations. This function analyzes how, for 454 example, briquette surface roughness is affected by the values of briquette density or porosity. High 455 correlations indicate a strong dependence of the two properties. 456 The roughness parameters values decreased with an increase in density. Fig. 7 shows an example of 457 correlation of roughness parameters and density of briquettes obtained by using the St2 method. 458 From Table 3 and from the regression analysis it can be concluded that the correlations were 459 reasonable in the case of the first stereometric density measurement method; however, significantly 460 stronger correlations were obtained for the second stereometric density measurement method. This 461 was observed especially in the correlation of the parameter Rk+Rpk+Rvk and density, where the 462 coefficient of determination was 0.911. The correlations were statistically not significant when the 463 liquid displacement method was applied. This shows that the selection of the density measurement 464 method has an important influence on the roughness parameters. 465 Table 3, too, indicates the correlations between the surface roughness and porosity obtained from 466 the three methods of calculation and for each density measuring method. From Table 3  However, when the density was calculated with the St2 method, the porosity determined with all 477 three methods showed strong positive correlations with briquettes roughness ( Table 3). The 478 correlations were almost similar between the three methods and were statistically significant for a 479 confidence level p<0.05. Very good correlations were met by all three roughness parameters 480 measured, but were best for Rk+Rpk+Rvk. The coefficient of determination R 2 was greater than 0.9 481 for porosity determined by Siau and general relation methods and the roughness composed 482 parameter Rk+Rpk+Rvk (see Fig.8 (Table  493 3). 494 If the porosity of briquettes is to be estimated by measurements of surface roughness, the best 495 correlation can be obtained when measuring the roughness parameters Rk+Rpk+Rvk, followed 496 closely by Ra. Very strong correlations with roughness were obtained for porosity calculated with all 497 three relations, but when density was determined by St2 method. The findings are encouraging as 498 they provide an alternative method to estimate the briquette porosity based on measured surface 499 roughness. 500 501

Conclusions 502
Correlations were analyzed between porosity and density, three roughness parameters and density, 503 and porosity and roughness parameters of briquettes. Porosity had a strong negative correlation 504 with density when it was calculated from Siau's equation or by using the general equation, regardless 505 the method of density determination. The correlation was weaker if the method proposed by Hunt 506 et al. was used and when the density was determined by the liquid displacement method. Strong 507 negative correlations were obtained for the roughness parameters and density, if the density was 508 determined according to the second stereometric method, while no correlation was found when the 509 liquid displacement method was used. Very strong positive correlations porosity-surface roughness, 510 were obtained for porosity calculated with all three relations, when density was determined by the 511 second stereometric method. If the porosity of briquettes is to be estimated by measurements of 512 surface roughness, the recommended parameter is Rk+Rpk+Rvk. 513 Although the number of the samples tested was rather low, the experimental data contribute to the 514 existing literature on briquettes properties by adding the surface roughness, assisting in the selection 515 of the most appropriate method for the study of porosity. 516 Further work is required to verify if those initial results remain consistent and repeatable for other 517 briquettes from different batches and for other combination of wood species. 518 The novelty of the present paper consists in extending the applicability of the porosity models 519 originally developed for wood, to the wood briquettes. To the best knowledge of the present 520 authors, the wet porosity model applied to briquettes has not been reported before; it shows 521 promising results in terms of its application to combustion analysis and heat and mass transfer 522 processes. 523 524 APPENDIX 525 The mass of a wood cell that consists of the cell wall, bound water and air in the lumen is: