Indirect Evaluation of the Porosity of Waste Wood Briquettes by Assessing Their Surface Quality

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


Introduction
Biomass is an attractive feedstock because of its renewability, abundance and positive environmental impact. It is difficult to handle, transport, store and utilize in its original form due to the high moisture content, irregular shape and sizes and low bulk density. Densification can generate products with uniform shape and sizes that can be more easily handled and thereby reduce cost associated with transportation, handling and storage [1][2][3][4]. Pelletizing and briquetting are the most common processes used for biomass densification for solid fuel applications. The five basic categories of biomass materials include: virgin wood, energy crops, agricultural residues, food wastes, industrial wastes and co-products [5]. Biomass from wood originating from forest residues or as waste resulting from wood industries is one of the most universal renewable sources of energy [6,7]. During briquetting the biomass particles self-bond to form a briquette, due to the thermoplastic flow. The briquettes' densities generally range from 900 to 1300 kg/ m 3 [8]. The lignin constituent (a major component of most plants) acts as a binder under suitable compression conditions. An adequate pressure is required to break cell walls, which is greater than around 5.0 MPa, and depends on the specific properties of the material [2]. According to Đerčan et al. [9], the technological process of briquetting crushed ligno-cellulose material without binder requires high pressures, [15][16][17][18][19][20] MPa, enabling the biomass to turn into compact briquettes. Li and Liu [10] reported that the moisture content required for good-quality compaction of wood processing residues ranges from 5 to 12%, with an optimum of about 8%. Briquettes typically have a length ranging between 50 and 400 mm [2].
The particle density of briquettes is a quality indicator of densified fuels. It has an influence on combustion properties (thermal conductivity, burning time and rate of degasification) [11]. There are several methods for the determination of particle density of briquettes, which is defined as ratio of the mass and the volume of a sample including pore volume (voids that are specific to the wood structure and that are resulting from wood particles compaction), as indicated by Rabier et al. [12]. The particle density measurements of five briquette types included stereometric methods and methods based on liquid displacement (hydrostatic and buoyancy).
Porosity is one of the physical properties of wood and wood briquettes, as well. It is important for combustion analysis and modeling, heat and mass transfer processes during combustion stages or determination of effective thermal conductivity and effective heat capacity [13][14][15]. It is also related to density or durability of briquettes [1]. Furthermore, porosity is essential in wood impregnation with preservatives [16].
Usta [17] defined wood as a cellular/porous material composed of cell wall substance and cavities containing air and extractives. Without cavities and intercellular spaces the density of the cell wall substance is constant (1530 kg/m 3 on an oven-dry mass and volume basis). Therefore, the amount of cell wall substance (K) is a function of wood density, d (K = d/1530). The void volume (porosity, P) is defined in relation to the cell wall substance (P = 1 − K).
Siau [18] regarded wood cells as a rectangular model of square cross section with unit overall dimensions (Fig. 1a). All cells are equally sized and the ends of the cells are neglected. The cell lumen also has a square cross section. The model refers to cells at oven-dry conditions, where the lumen has only dead air. A more general model of wood cells that considers the wood moisture content was described by Siau [18], as well as by Hunt et al. [13], where the bound water is added as a surrounding area to the outside of the squared cell cross section having the side equal to unity (Fig. 1b).
Wood porosity can be determined by application of pycnometric methods, displacement of various liquids and mercury intrusion porosimetry [16,19,20]. However, wood has a different configuration than wood briquettes and can be submitted to different methods of porosity measurement. Mercury porosimetry and gas pycnometry are usually used to estimate the pore size distribution and porosity of wood. According to Moura et al. [19], the 1 3 mercury porosimetry is suitable to evaluate the porosity of wood, pulp and paper, being a valuable tool to anticipate properties like surface roughness, air permeance or coating distribution. A limitation of the porosimeter that the authors have used is that voids with diameters below about 0.007 μm are not detected.
Brewer et al. [21] calculated the porosity of biochar by means of skeletal density, determined by helium pycnometry and envelope density, by using an envelope density analyzer. Additional methods were required since some macro-voids were inaccessible to helium gas.
More recently, research work [22] applied computed tomography (CT) and backscattered electron (BSE) imaging methods to investigate and quantify the porosity of wood (bamboo cross section). The authors of the research compared different methods of porosity measurement, such as mercury intrusion porosimetry, gas pycnometry, microscopy image processing and computed tomography. Considering the strengths and limitations of the existing porosity measurement techniques, they decided to simultaneously use two methods, SEM and CT scanning methods, in order to investigate the porosity distribution as function of orientation within bamboo wood.
In contrast, fewer methods have been reported for the measurement of briquettes or pellets porosity (bulk and individual porosity). The individual porosity (also called porosity index) of briquettes made of coal and corncob in different ratios, with binder, was determined by Ikelle and Ivoms [23] based on the amount of water each sample is able to absorb. The porosity index was calculated as the ratio of the mass of water absorbed to the mass of the sample immersed in water. The authors did not describe very accurately the measurements they performed and question marks can arise regarding briquettes water absorption, whether all voids were filled or not with water after immersion, as well as regarding the risk of swelling occurrence. The bulk porosity or macro-porosity is specific to cylindrical wood pellets and it is determined, for example, by using the method of stereometric measurements [24,25].
A correlation between surface and volume (bulk) characteristics was reported by Suliman et al. [26]. They described the relationships existing between porosity and surface functionality of different wood biochars and soil water retention characteristics. One of their conclusions was that the capability of biochar to retain soil water is a function of the combination of its porosity and surface functionality, i.e. generation of oxygenated functional groups on the surface.
Since porosity is important for the analysis of briquettes combustion, it would be interesting to see if this property can be indirectly evaluated by another method, such as by measuring some roughness parameters of the briquette surface in connection with briquette density. Starting from previous studies performed on wood, it can be assumed that both porosity [17] and roughness parameters [27] are properties depending on density.
To the best knowledge of the present authors, the literature does not indicate information about experimental determination of wood briquettes porosity, which is a difficult task considering the structure of wood briquettes compressed without binders. Therefore, the authors considered it useful to determine, on one hand, the extent to which the relations for the calculation of the wood porosity can be applied to briquettes and, on the other, the correlations existing between a measurable quantity, i.e. surface roughness and a calculated quantity, that is, porosity.
Therefore, this paper examines correlations between the following properties: porosity and density of briquettes, surface roughness parameters and density of briquettes, as well as surface roughness and porosity of briquettes. Porosity and density were determined by using three different methods.

Material, Methods and Equipment
The briquettes used for this research were obtained from beech and spruce chips, originating as waste material from secondary wood processing in the faculty workshop, i.e. planing and sanding. Monthly, 4 m 3 of wood are processed, from which around 1.2 m 3 is refuse due to wood defects and around 1 m 3 is waste resulting from processing. The wood processed in the workshop was beech and spruce from local sources, in a proportion 20%:80%. Its moisture content ranged from 8.1 to 11.4%, and was measured by using a capacitance moisture meter (PM1-E, Merlin). The important amount of processing waste was valorized by further compacting in briquettes. Briquettes contained mainly chips and in a very low proportion wood dust. The particle size influences the stability of the final briquettes [2]. The dimensions of the chips ranged from 2 to 40 mm in length, 2 mm to 15 mm in width and 1 mm to 1.5 mm in thickness.
The wood chips were compressed using a MB4 GOLD-MARK type hydraulic briquetting press with the main characteristics indicated in Table 1.
The mixture of chips was compressed without binders. Cylindrical briquettes with uniform circular cross section and different lengths were obtained. The size and geometry of briquettes influence the combustion behavior, as stated in [2].

Roughness Parameters of Briquettes
Ten briquettes were randomly taken from the press container and stored in a controlled environment (22 ± 1 °C temperature and 40 ± 2% RH). Firstly, they were subjected to roughness measurements. The measurements were performed by using a MarSurf XT20 instrument manufactured by MAHR Gottingen GMBH, equipped with a scanning head MFW 250 with tracing arm in the range of ± 500 μm and a stylus with 2 μm tip radius and 90° tip angle, which measured the briquettes lengthwise at a speed of 0.5 mm/s and at a low scanning force of 0.7 mN (Fig. 2). The instrument had MARWIN XR20 software installed for processing the measured data.
The briquettes were scanned on tracing lengths of 15 mm. Four profiles were scanned for each specimen, at every 90° angle of the briquette cross-section, so that a total of 40 profiles were available for further evaluation of parameters. The lateral measuring resolution was 5 μm and the instrument provided a vertical resolution of 50 nm.
First, the software removed the form error and after that, the waviness. The roughness profiles were obtained by filtering each profile by using a robust filter RGRF (Robust Gaussian Regression Filter) specified in ISO 16610-31 [28]. The cut-off used was 2.5 mm, as recommended in previous research by Gurau [27]. This filter was tested and found useful for wood surfaces. The rationale behind opting for roughness profiles was that roughness characterizes the highest frequency irregularities on the surface, which  authors considered to have a higher likelihood to be associated with briquette porosity as compared with other types of irregularities of lower frequency. After generating the roughness profiles, Ra, representing the arithmetic mean deviation of the assessed profile irregularities, was calculated on sampling lengths according to ISO 4287 [29]. Other calculated parameters were the material ratio curve (Abbot curve) parameters Rpk, Rk and Rvk from ISO 13565-2 [30]. Rk is the depth of the roughness core profile, Rpk is the average height of the protruding peaks above the roughness core profile and Rvk represents the average depth of the profile valleys projecting through the roughness core profile. Rvk may be especially sensitive to the species' anatomical valleys or to various gaps caused during the briquetting process. Rpk is a measure of fuzziness protruding above the core roughness. The sum Rk + Rpk + Rvk was also determined for comparisons, because of the cumulative effect on surface roughness and together with Rvk should be sensitive to variations in briquette density (and porosity).
For each briquette and roughness parameter, a mean value and the standard deviation were calculated.

Briquettes Density
In order to evaluate the briquettes density, two stereometric methods and a liquid displacement method were applied. The reason for applying different methods was to evaluate the best correlation of density with both porosity and roughness parameters. The first stereometric method (St1) was based on the measurement of the length and diameter of each briquette and on calculating the volume of a cylinder as regular geometrical shape. Two lengths (at right angle of each other) and three diameters (at each end and in the middle) of each briquette were measured using a digital pocket caliper (ULTRA, 0.01 mm accuracy). The average values and the volume were then calculated. The briquettes were weighed by using a KERN-EW 3000 g technical balance (0.01 g accuracy). The density was calculated as the ratio of mass to briquette volume.
The second stereometric method (St2) consisted in estimating the cross-section area of each briquette by means of a paper sheet of known area density (80 g/m 2 ), as described in [12]. The briquette was placed on the paper, its contour was drawn on the paper and the cross-section surface was accurately cut. The piece of paper was then weighed and its surface was calculated from the mass and the area density of the paper. The paper surface approximating the cross-section of the briquette was multiplied by the average length of the briquette and the volume of the briquette was thus obtained. Again, the density was calculated as the ratio of mass to briquette volume.
After that, the briquettes were oven dried at 103 ± 2 °C to constant mass in order to determine the moisture content (dry basis). The moisture content was calculated based on wet and oven-dry briquette masses (SR EN 13183-1-2003/ AC-2004 [31]). Finally, the oven-dry briquettes' dimensions were measured again by using the two stereometric methods described before. Oven-dry and wet 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 immersing (Im) each briquette in toluene (C 6 H 5 CH 3 ) with a density equal to 865.5 kg/m 3 at 20 °C. The change of the toluene density with slight environmental temperature changes was neglected. The volume of the briquette was obtained from the mass of the volume of toluene displaced while immersing the briquette in the liquid. Firstly, a Berzelius glass beaker was filled with toluene to a fixed volume (Fig. 3a). The beaker containing toluene was weighed. Then, the briquette was placed in a metallic (copper) cage that was submerged in the Berzelius glass beaker with toluene. The part of the liquid that exceeded the fixed initial volume was removed. The mass was determined again by weighing. The cage was fixed by means of a wire on a glass rod placed on the glass top (Fig. 3b). The volume of the briquette was calculated from the density of toluene and the difference in the masses of toluene before and after briquette immersion. The density of the briquettes was evaluated by using this method, following If rearranging the terms of Eq. (3), the volume of the briquette becomes:

3
Equation (4) can also be written in terms of masses and liquid density ( l ), as: and the expression of the briquette's density is therefore: The terms m l (kg) and m l1 (kg) refer to the masses of liquid corresponding to the volumes V l and V l1 . The mass of the glass rod was every time subtracted from the performed mass measurements.
Briquettes are porous materials. During immersion, a part of the pores (voids developed during chips compression) was filled with liquid. In order to identify possible errors, the mass of the liquid, briquette and cage was measured first, as indicated in Fig. 3b; then, separate measurements were made of the masses of the liquid (M l1 ), the briquette filled with liquid (m w.br. ) and, respectively, of the cage (m cage ).
The total mass is: and the sum of the individual masses is: During the successive measurements of masses, some toluene may evaporate and thus, m l1 may be different from M l1 . The difference represents the error that occurs during mass measurements. The errors that were calculated for all briquettes are very small, below 1 g. The ratio Δ M l 1 was also evaluated and it is  The volume of the cage was also determined by using the liquid displacement method and it was calculated from the following relations: or where: V l2 (m 3 ) is the volume of the liquid existing in the glass beaker when the cage was immersed and m l2 (kg) is the corresponding mass (Fig. 4).

Briquettes Porosity
Further on, the briquettes' porosity was calculated by using three methods. One method is very often mentioned in literature, for example in [13,20,22], and the other two are recommended in two publications, Siau [18] and Hunt et al. [13], as presented below.
The first method applied in the research reported in this paper is based on relations indicated by different authors. Plötze and Niemz [20] calculated the oven-dry porosity (P d ) of different wood types from the oven-dry density (ρ OD ) and the solid cell wall density (ρ cw ), as: Hunt et al. [13] determined the oven-dry wood cell porosity (P d ) from the oven-dry density (ρ OD ), the density of the cell wall (ρ cw ) and the density of air (ρ air ) using the following equations: Fig. 3 Briquette volume determination by using the liquid displacement method, a before briquette immersion, b after briquette immersion and They assumed that with the increase of the moisture content, the wood cell lumen size remains the same, because the moisture content (bound water) is added as an outside layer to the cell wall (Fig. 1b). Even so, they calculated a wet porosity (see third method described below), since the cross-section side of the cell wall increases with an increase in moisture content (the dimensional change due to the increase in moisture content is added to the outside of the cell wall dimension).
Similarly to Hunt et al. [13], Huang et al. [22] calculated the porosity of oven-dried bamboo wood (P d ) from the bulk density (ρ OD ) (including wood substance and cavities) and skeletal density (ρ cw ) (excluding wood cavities), by using a similar equation as Eq. (13).
The oven-dry porosity has, according to the afore-mentioned authors, a similar expression that takes or does not take into account the density of the air. Since the density of air is around 1 kg/m 3 , it can be neglected.
A second method, calculating the wood porosity in wet conditions, is based on Siau's equation, as indicated in Ref. [18]: where: P is the porosity or the fractional void volume of wood, 0.653 × 10 -3 (m 3 /kg) is the specific volume of the wood substance, MC (%) is wood moisture content, m 0 (kg) is the oven-dry mass of wood and V (m 3 ) is the volume of wet wood. Equation (15) was obtained by subtracting the cell wall (wood substance) volume fraction V% ws and moisture volume fraction V% M from unity: As with wood composition consisting of dry cellular walls, bound water and lumens filled with air, one can consider a similar situation in the case of briquettes, and Eq. (16) becomes valid for wood briquettes as well. The voids created during wood particles compression can be added to the wood lumens and considered as total void space.
The third method used for wood porosity calculation, proposed by Hunt et al. [13], is based on dry cell porosity and moisture content. The oven-dry density of the cell was expressed in Eq. (13) in terms of cell wall density, density of air and oven-dry porosity, and the dry porosity was defined in Eq. (14). The oven-dry cell wall density cw = 1530 kg/m 3 used in the calculation of the dry porosity (Eq. (14)) is based on its determination by water displacement, as described by Siau in [18]. The density of dry air at 20 °C is air = 1.18 kg/m 3 [32].
Wet porosity is obtained by the same authors from: where: V% bw is the bound water volume fraction. The bound water volume fraction is calculated with respect to the wood moisture content, according to Eqs. (18) and (19) [13]: or where: bw is the bound water density; for bound water volume fraction calculation, the authors [13,18] considered that bw = 1115 kg/m 3 . The equations above, developed by Hunt et al. [13] for wood, were used to calculate the effective thermal conductivity of wood briquettes with the moisture content ranging from 0% to 22.7%, dry basis [33]. Again, the wood cell is the structural component of both wood and wood briquettes, showing the validity of the method in the case of briquettes. The wood cell model applied to briquettes assumes a larger lumen that includes also the chips interspaces [33]. Fig. 4 Determination of the cage volume by using the liquid displacement method The first method of porosity calculation, mentioned above, referred only to the calculation of porosity characteristic to the dry conditions. However, in order to be able to compare it to the second and third methods (for wet conditions), it was considered appropriate to develop a modified equation valid for the calculation of porosity in wet conditions. As such, considering Eqs. (13) and (14), similar equations can be written for the density and wet porosity of wood cells. The density can be expressed as: where: cw M is the density of the cell wall with bound water.
The density of the cell wall with bound water can be obtained from the rule of mixtures: The wet porosity is obtained from Eq. (20), as follows: The new developed equation (Eq. (22)), based on the first method, was applied in this research, in order to calculate the wet porosity of briquettes. It was named in the porosity analysis as "general relation". Equation (22) is explained in detail in the "Appendix" to this paper.
With the porosity and the briquettes' density determined by means of the three methods described above, correlations were further examined between: porosity and briquette density, surface roughness data and briquette density, as well as surface roughness and porosity of briquettes.

Results and Discussion
The results obtained from the density determination of the ten briquettes at equilibrium moisture content (EMC) are shown in Table 2. The equilibrium moisture content (dry basis) of the briquettes ranged from 8.13 to 8.74%, with an average at 8.41%.
The highest density results were obtained by using the first stereometric method (St1) and lowest density results were obtained by using the second stereometric method (St2) ( Table 2). Table 2 indicates a high variability of the density (at EMC), which is influenced by the measurement method and the briquette (initial moisture content, compression pressure, particle size). The largest mean density difference was encountered between the first and the second stereometric method, while the second stereometric method and the liquid displacement method (Im) showed statistically similar values, as tested by ANOVA single factor, for a (20) confidence level p < 0.05. However, regression analysis of density data has shown a weak correlation between individual density values calculated with St2 and liquid displacement method (R 2 = 0.469) and a better correlation with St1 method (R 2 = 0.7). Rabier et al. [12] have also obtained a high variability of the density of different types of briquettes, especially for the stereometric methods. They explained this variability through the intrinsic physical properties of the briquettes, such as the surface roughness. They noticed that stereometric methods led to more variable results, compared to immersion methods. Also, from the statistical results they concluded that the two stereometric methods cannot be regarded as equivalent, which is in agreement with our findings. Slight differences in briquettes moisture content can also have an influence on density variability. The relationship between individual porosity and density of briquettes at EMC is shown in Figs. 5, 6 and 7 and the calculated values, mean values and standard deviations are included in Table 2. As expected, all figures indicate the decrease of the porosity with an increase in density. This is in agreement with the results obtained for wood, as indicated by Refs. [17,20]. There was a strong correlation between the porosity determined according to Siau's and the general relation methods and density, regardless the measurement method. According to the method described by Hunt et al. for the determination of the porosity, the density measurement method has an influence on the porosity results. While the porosity determined by Hunt et al.'s method showed high correlation with density for St1 and St2 methods (0.976 and 0.939, respectively), it decreased to 0.5016 for the liquid displacement method (Fig. 7). This result shows that determination of porosity with Hunt et al.'s method is less reliable when measuring density via the liquid displacement method. The regression analysis has revealed a weaker correlation of porosity data from Hunt et al.'s equation with porosity calculated with the other two relations, when density was determined by immersion.
A preliminary analysis of the roughness parameters results showed a high variability and a weak inverse correlation with density. This may be a result of variable local density of the briquettes on their circumference. The measured profiles were taken so that two profiles corresponded to the generatrix with high briquette density and the other two on the generatrix with low briquette density, after a visual assessment. Given the high density variation, it was considered that the selection of measuring lines for each briquette can have an influence on the assessment of its overall roughness. Previous studies on sanded solid wood found an inverse relationship between density and surface roughness [27]. It was reasonable to expect that density of briquettes might have a similar relation with their surface roughness. In order to check this assumption, a mathematical procedure was applied that selects means of roughness parameters from combinations of three profiles from the measured data. As such, although 4 profiles were measured, resulting in one mean value of the four profiles (1, 2, 3, 4), the calculations took into consideration more means taken from groups/combinations of 3 profiles, which were further checked for their best correlation with density and indirectly with porosity, respectively. For example, the combinations were means of profiles: 1 + 2 + 3; 1 + 2 + 4; 2 + 3 + 4 and 1 + 3 + 4. The more measurements are performed, the more are the means available and the better the chance of a more reliable approximation of the surface quality.
The mathematical procedure is looking to find the linear regression roughness parameters-density, with negative slope and maximum coefficient of determination. For the ten briquettes there were ten densities and four different average roughness parameters (the four means mentioned above) per briquette, that is, a matrix with ten rows and four columns. For the matrix, the following function is considered f ∶ l 1 , l 2 , … , l 10 → c 1 , c 2 , c 3 , c 4 , where l i , i = 1 … 10 represent the matrix rows and c j , j = 1 … 4 are the matrix columns. The total number of possible combinations is 4 10 = 1048576, as stated in the following theorem: the total number of functions f ∶ D → E is can be read in order to calculate the sum. The padding procedure sets zeroes in front of the values until the array reaches a certain given dimension. Table 3 shows the correlations between the average roughness parameters and the density of briquettes at EMC, as well as with the briquettes porosity.
In order to analyze the correlations of density with roughness, as well as of porosity with roughness, the Regression analysis tool was used. This involved performing a linear regression analysis by using the "least squares" method to fit a line through a set of observations. This function analyzes how, for example, briquette surface roughness is affected by the values of briquette density or porosity. High correlations indicate a strong dependence of the two properties.
The roughness parameters values decreased with an increase in density. Figure 8 shows an example of correlation of roughness parameters and density of briquettes obtained by using the St2 method. From Table 3 and from the regression analysis it can be concluded that the correlations were reasonable in the case of the first stereometric density measurement method; however, significantly stronger correlations were obtained for the second stereometric density measurement method. This was observed especially in the correlation of the parameter Rk + Rpk + Rvk and density, where the coefficient of determination was 0.911. The correlations were statistically not significant when the liquid displacement method was applied. This shows that the selection of the density Fig. 7 Porosity of briquettes as a function of the density obtained from the liquid displacement method (Im)   Table 3, too, indicates the correlations between the surface roughness and porosity obtained from the three methods of calculation and for each density measuring method. From Table 3 and the regression analysis it was observed that the surface roughness increases with briquette porosity increase.
In case of density measured by the St1 method, the porosity determined with all three relations, has shown a similar moderate positive correlation with briquettes roughness, (R 2 > 0.5), statistically significant for a confidence level p < 0.05.
However, when the density was calculated with the St2 method, the porosity determined with all three methods showed strong positive correlations with briquettes roughness ( Table 3). The correlations were almost similar between the three methods and were statistically significant for a confidence level p < 0.05. Very good correlations were met by all three roughness parameters measured, but were best for Rk + Rpk + Rvk. The coefficient of determination R 2 was greater than 0.9 for porosity determined by Siau and general relation methods and the roughness composed parameter Rk + Rpk + Rvk (see Fig. 9). The correlation of the porosity with Ra did not differ considerably with respect to the method of porosity calculation. The correlation of the porosity with Rvk was weaker in comparison with the other two parameters, but was better when Hunt et al.'s method of porosity calculation was applied.
Among the three porosity relations, only relation of Hunt et al. determined a weak positive correlation with surface roughness, for a confidence level p < 0.05, when density was obtained by immersion, while the other porosity relations produced no correlation with surface roughness (Table 3).
If the porosity of briquettes is to be estimated by assessing the surface quality, the best correlation can be obtained when measuring the roughness parameters Rk + Rpk + Rvk, followed closely by Ra. Very strong correlations with roughness were obtained for porosity calculated with all three relations, but when density was determined by St2 method. The findings are encouraging as they provide an alternative method to estimate the briquette porosity based on measured surface roughness parameters. However, for a higher reliability, the number of roughness measurements should be increased, since the briquettes are compressed wood particles, with non-uniform structure and surface, the local density on the briquettes circumference may be variable and the briquettes surface is erodible, which may change, locally, the surface topography. These limitations have to be considered; for this reason, the higher the number of roughness measurements, the more accurate the correlation roughness-porosity is expected to be. An advantage of the new proposed method is the fact it is both inexpensive and easily accessible. Further work could be to test the method for its applicability to different porous materials.

Conclusions
Correlations were analyzed between porosity and density, three roughness parameters and density, and porosity and roughness parameters of briquettes. Porosity had a strong negative correlation with density when it was calculated Fig. 8 The roughness parameters of briquettes as a function of the density obtained from the second stereometric method (St2) from Siau's equation or by using the general equation, regardless the method of density determination. The correlation was weaker if the method proposed by Hunt et al. was used and when the density was determined by the liquid displacement method. Strong negative correlations were obtained for the roughness parameters and density, if the density was determined according to the second stereometric method, while no correlation was found when the liquid displacement method was used. Very strong positive correlations porosity-surface roughness, were obtained for porosity calculated with all three relations, when density was determined by the second stereometric method. If the porosity of briquettes is to be estimated by assessing the surface quality, the recommended parameter is Rk + Rpk + Rvk.
Although the number of the samples tested was rather low, the experimental data contribute to the existing literature on briquettes properties by adding the surface roughness, assisting in the selection of the most appropriate method for the study of porosity.
Further work is required to verify if those initial results remain consistent and repeatable for other briquettes from different batches and for other combination of wood species.
The novelty of the present paper consists in extending the applicability of the porosity models originally developed for wood, to the wood briquettes. To the best knowledge of the present authors, the wet porosity model applied to briquettes has not been reported before; it shows promising results in terms of its application to combustion analysis and heat and mass transfer processes.

Appendix
The mass of a wood cell that consists of the cell wall, bound water and air in the lumen is: where m cw is the mass of the cell wall, m bw is the mass of the bound water, m air is the mass of the air in the lumen of the wood cell. By replacing the masses by corresponding volumes and densities, the following equation can be written: If dividing each term of Eq. (24) by V, Eq. (25) becomes: By definition, the porosity is: Also, the following relations can be written: and (23) m = m cw + m bw + m air , (24) ⋅ V = cw V cw + bw V bw + air V air .