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This paper investigates a method for the determination of the maximum sampling error and confidence intervals of thermal properties obtained from thermogravimetric analysis (TG analysis) for several lignocellulosic materials (ground olive stone, almond shell, pine pellets and oak pellets), completing previous work of the same authors. A comparison has been made between results of TG analysis and prompt analysis. Levels of uncertainty and errors were obtained, demonstrating that properties evaluated by TG analysis were representative of the overall fuel composition, and no correlation between prompt and TG analysis exists. Additionally, a study of trends and time correlations is indicated. These results are particularly interesting for biomass energy applications.
After the Kyoto protocol  and the 2009 Copenhagen United Nations Climate Change Conference, environmental policies have focused on climate protection. A way to advance and accelerate the progress in this area, is to reduce the use of fossil fuels for energy production by increasing production of renewable and CO2-neutral energy sources such as biomass .
Pazó et al.  considered the study of sampling maps generation and the uncertainty determination methodology for four materials: hazelnut shell, brassica pellets, poplar pellets and pine nut shell.
In this paper, the work initiated by Pazó et al.  is extended with the study of four other types of biomass: almond shell, ground olive stone, pine pellets and oak pellets. In addition to applying the same procedure to a new set of materials, a numerical study of linear trends and time correlations is presented for all eight types of biomass.
As in the previous article, TG analyses were used to provide information concerning the chemical composition, thermal behavior and reactivity of biomass in a straightforward manner [4,5]. Many studies on the accuracy of TG experiments have been published [6–10], and various sampling methods have been proposed. Currently, TG methodologies are often based on small samples obtained from large batches. Thus, careful reduction is necessary to prevent segregation and stratification problems . A good sampling method should be able to achieve a representative sample without being affected by the aforementioned problems.
By using this sample method, this paper first presents the materials used in the study and the statistical method used to choose the samples. In a following section, the thermogravimetric method used and the statistical treatment of data are explained in detail. Next, the results of TG analysis for the four types of biomass are described, revealing the moisture, volatile, ash and fixed carbon content of each. Moisture content affects the heating value of biomass, and ash determines the level of fouling and corrosion [13,14]. Moreover, volatile compounds influence the behavior of the flame. These aspects reveal the intrinsic heterogeneity values, giving us the minimum sizes of the samples to a preset error or the errors made for a default sample size. Additionally, the confidence intervals and the correlations between the moisture, volatile matter and ash content of the materials are presented. The data suggest that there is no correlation between the results of different analyses.
Finally, a study of the linear trend and the random variation components for the properties of eight materials is presented. The Pearson correlation was utilized to check the presence of linear trends, and the Ljung-Box test employed to verify the correlation in time of the random variation.
This method may contribute to a wider and more correct application of biomass for energetic purposes.
All materials were handled in the same laboratory by the same analyst. Because the materials were exposed to environmental conditions for less than half an hour, the effects of environmental variations in the properties of the materials were ignored (variations in temperature and relative humidity were considered insignificant over such a short period of time). Laboratory instruments were verified and calibrated to assure that the experimental methodology was accurate. Errors registered during the experiments were considered to be non-systematic errors and were related to the precision of the experiment. Thus, these errors were quantified in the total sampling error.
Several lignocellulosic materials derived from agricultural waste and forestry materials were investigated. Thus, the broad spectrum of solid biomass that can be used as fuel in combustion processes was evaluated. Agricultural materials, almond shell (As) and ground olive stone (Gos) were stored in large bags, while forestry oak pellets (Op) and pine pellets (Pin) were stored in sacks.
Depending on the material, sampled masses varied from 320 × 10−3 kg to 730 × 10−3 kg. Fuel samples were obtained from a tube sampler, which was designed according to the requirements specified in CEN/TS  and the work of Pierre Gy . The sampling methodology used to obtain the fuel samples is described in the literature [11,12], along with the method used to reduce the samples. Fuel samples were obtained through a tube sampler, which was designed to work with all kinds of solid biomass. The nominal maximum size “d” of the material sampled is taken as 20 mm , so the tube sampler should be able to collect at least Vmin = 0.05 · d = 0.05 · 20 = 1 dm3 = 10−3 m3 . Table 1 shows the average weight of samples selected for TG analysis. Tweezers were used to place the samples into the crucibles.
All experiments were performed on a TG-DTA/DSC SETARAM Labsys electronic thermobalance, which can achieve a maximum temperature of 1600 °C and heating rates from 0.001 to 50 °C·min−1. To avoid heat and mass transfer limitations, approximately 20 × 10−6 kg of sample were used, and platinum crucibles without lids were employed. All experiments were initially conducted under an inert flow of nitrogen at a rate of 45 mL·min−1, to prevent the samples from oxidizing and to determine the concentration of moisture and volatile material. Subsequently, dry air (45 mL·min−1) was used to determine the ash content. The parameters of the thermal analysis are shown in Table 2.
Steps 1 through 4 were conducted to determine the moisture content, while steps 5 through 10 were performed to determine the concentration of volatile material. Lastly, steps 11 through 13 were conducted to determine the ash content of the biomaterials. Most of the steps were not directly related to the determination of moisture, volatile matter or ash content. Rather, many steps were conducted to determine other thermal properties of the materials not discussed in the present paper.
The tested samples were weighed inside the crucible and uniformly distributed to avoid internal gradients of heat and gas concentration . However, a temperature gradient inside the particles was not considered due to the small size and quantity of the samples [2,17]. Because the volatile content is strongly affected by the heating rate, the results were not compared to those from previous studies [11,12].
Moisture content was determined by heating the sample to 378 K in an N2 atmosphere until a constant weight was achieved. The moisture content (M) was obtained from the following equation: M = 100· (m1 – m2)/m1, where m1 (10−6 kg) is the initial mass of the sample and m2 the constant mass at 378 K. The volatile matter was determined as the weight loss due to heating from 378 (step 5) to 873 K (step 10) in an N2 atmosphere. The volatile content (V) was calculated according to the following equation: V = 100· (m2 – m3)/m1, where m3 (10−6 kg) is the mass of the sample at 873 K. Ash is the residual inorganic matter remaining after combustion, and the ash content was obtained from the equation A = 100·m4/m1, where m4 (10−6 kg) is the mass remaining after step 13. Subsequently, the amount of fixed carbon (FC) was determined from the formula FC = 100 – M – V – A, where A, V and FC were calculated on a dry weight basis (db) and M was calculated on a wet basis (wb).
For the determination of the maximum error, the statistical treatment used in this study has been fully described in [11,12,16]. Assuming that the sampling error follows a normal distribution (SE~N(0,σ(SE)), as Central Limit Theorem states, we can ensure with a confidence level of 95% that
Because moisture, volatile matter and ash content are measured variables, SEmax represents the maximum sampling error. The amount of fixed carbon (FC) was obtained directly from the properties of the materials: . Also, the maximum error was calculated by the method of error propagation, which is fully described in the literature :
, , Ā and are the average moisture, volatile matter, ash and fixed carbon content, respectively.
Another objective of this study was the determination of confidence intervals which has been fully described in .
Moisture (wb), volatile matter (db), fixed carbon (db) and ash content (db) of the samples are presented in Table 3, including the mean and variance of each variable.
HIL, the heterogeneity invariant, was calculated according to the method described and is summarized in Table 4. The maximum sampling error of a sample with a fixed mass was obtained from the HIL, and the minimum sample size corresponded to a fixed sampling error. The minimum sample size and maximum sampling error associated with the determination of moisture, volatile matter, fixed carbon and ash content are provided in Tables 5 and and6,6, ,77 and and8,8, ,99 and and10,10, and and1111 and and12,12, respectively.
To show the utility of the minimum sample mass required to achieve an accurate representation of M, V, A and FC (Tables 5, ,7,7, ,99 and and11)11) and an inverse calculation of the previous one (Tables 6, ,8,8, ,1010 and and12),12), examples were performed in .
According to the methodology described, confidence intervals of 95% for the properties of each material were generated. Examples for the determination of the confidence intervals were performed in . To compare the results of the present paper to those of previous studies, confidence intervals for the prompt analysis presented in the literature  were calculated. The mean weights of the samples in TG analysis were approximately 1000 times less than those of the prompt analysis . Thus, the confidence intervals of TG should be significantly wider ( times). However, the accuracy of TG equipment compensates for a smaller sample weight, leading to confidence intervals that are approximately five-times greater than those of the prompt analysis. A similar conclusion was achieved in .
Volatile matter and fixed carbon contents obtained from the TG and prompt analysis are not comparable because the results are dependent on the thermal history of the particles, which are completely different in the prompt and TG analysis. However, the moisture content of the materials should be comparable. As shown in Table 13, the mean moisture content obtained in the TG analysis was lower (except Op) than the mean moisture content of the prompt analysis (same conclusion in ). Moreover, the mean ash content obtained from TG analysis was lower than the mean ash content of the prompt analysis (same conclusion in ). A box-plot of ash content illustrating the median, outliers, smallest and largest observation, and lower and upper quartiles are shown in Figure 1. The results indicated that the ash content obtained from the TG and prompt analyses were not comparable due to the methodology of the TG analysis. The ash content obtained from TG analysis was uniformly lower than that of the prompt analysis. Therefore, biomass heterogeneity was a likely cause for the discrepancy in the results. Due to the low sample weight (20 × 10−6 kg), TG crucibles were loaded with tweezers. These favor large particles against small particles and dust that have higher content in ash, as was demonstrated in . It is not possible to assure that the particle size distribution of the materials in the TG analysis is identical to that of the prompt analysis. As such, the mean ash content of these methods is not comparable. A similar explanation is proposed for the determination of moisture content. In general, these results indicate that the mean ash and moisture content obtained from the TG and prompt analysis are not comparable when the proposed methodology is applied. Thus far, all conclusions presented herein are in agreement with those obtained in paper .
To study the correlation between properties for the same material, Pearson correlation coefficients were calculated. Moisture, volatile matter and ash content of the materials were considered. Fixed carbon was excluded from this study since it was calculated from the former properties. For a significance level of α = 0.05, only ash and moisture content of oak pellets (Op) showed a non-negligible Pearson correlation coefficient of −0.68. Thus, for all other properties and materials, the value of one property cannot be explained from the others because properties are not linearly related. All three variables must be studied separately, and the analysis of one property cannot be used to infer the value of others. Similar conclusions were previously made for prompt analysis  and TG .
Even though the properties of TG and prompt analysis are not related, the maximum sampling error can be extrapolated from one analysis to the other using equation (1). The maximum sampling error of the materials from the prompt analysis  was extrapolated to the TG analysis; the extrapolated error was greater than the maximum sampling error obtained from TG analysis. To illustrate this result, the maximum sampling error of the moisture content of almond shell (As) was extrapolated as an example. According to the literature results , HIL· = 1.55 × 10−5 and the maximum sampling error for a sample with an average weight of 23.9 × 10−3 kg is 1.09 × 10−2. By taking into account the relationship between the average weights of both analyses, the maximum sampling error of TG analysis can be estimated as:
This result does not agree with those shown in Table 6, where SEmax(TG) = 1.23 × 10−1. The analysis was repeated for all materials and properties. Values of SEmax (TG) /SEmax (prompt) varied from 1 to 19 while values of varied from 18 to 33. The cumulative distribution and density functions of both quotients are shown in Figure 2. The results suggested that SEmax(TG) cannot be estimated from SEmax(prompt). SEmax(TG)/SEmax(prompt) reached a maximum value of 19 because atypical values were present in the density distribution function (Figure 2 (a)). However, when atypical values were removed, the maximum quotient was equal to 11. The HIL of the TG and prompt analyses are very different, which explains the lack of relationship between the maximum sampling errors of the methods. As shown previously, the maximum sampling error of the TG analysis should be significantly greater (18–33 times) than that of the prompt analysis. However, the accuracy of TG equipment compensates for the small sample weight, leading to maximum sampling errors that are approximately 1–11 times greater than SEmax(prompt).
Similar results were previously obtained for the same authors and other materials. Figure 3 shows the distribution of the two quotients of maximum sampling errors for eight materials — those studied in paper  and those considered in the present work. After consideration of Figures 2 and and3,3, the conclusion is that independent of the material or the property considered, the maximum sampling error cannot be extrapolated from one analysis to the other.
To observe other relationships between SEmax(TG) and SEmax(prompt), a classical correlation study was conducted on the sampling error SEmax(TG) associated with the volatile matter, fixed carbon and ash content, and the corresponding SEmax(prompt) . A significant correlation coefficient of 0.69 was obtained with p-value of 0.012. Although the correlation is significant, the low value of the correlation coefficient suggests that high levels of error would be encountered if SEmax(TG) was estimated from SEmax(prompt).
Since measurements of the properties have a natural temporal ordering, some additional analyses were made to check if there was an underlying time series structure. The traditional approach of time analysis is that series consists of three components whose joint action results in the measured values. These components are trend, seasonal variation and random variation. Trend is usually estimated by polynomial regression techniques. Seasonal variation is the periodic oscillations of a short period and is a causal component due to the influence of certain phenomena that occurs periodically. As the sequence of observations is not sufficiently long in time, the seasonal component has not been considered in the present paper. Once this trend has been removed, the residue of the fitted model shows the random variation pattern which, in time series, is correlated in time.
The linear trend and correlation in time of the random variation component were studied for the properties measured in the TG analysis. In total, eight materials were considered — four from paper  (hazelnut shell (Hs), pine nut shell (Pns), poplar pellets (Pp) and brassica pellets (Bp)) and four studied in the present work (almond shell (As), ground olive stone (Gos), oak pellets (Op) and pine pellets (Pin)). Table 14 summarizes the results of the statistical analysis applied to the sample data. The first two columns are used to verify the existence of linear trend by means of the Pearson correlation coefficient and the corresponding p-value, respectively. The third and fourth columns show the p-values of the Ljung–Box test, a statistical hypothesis test used to check the null hypothesis that the residues of a time series are not correlated.
For a significance level of α = 0.05, only pellets poplar (Pp) has a significant trend for three of its properties: moisture, volatile matter and fixed carbon. Once the trend has been removed, the Ljung-Box test detects correlation in time for several of the properties studied. In the particular cases of moisture of Hs, fixed carbon of Bp and fixed carbon of pine pellets Pin, this correlation remains through two lags in time.
In this article, statistical analyses of the sampling error and level of uncertainty associated with the properties measured in a TG analysis, as well as the corresponding confidence intervals, were conducted for four types of biomass. Results demonstrated that the sampling procedure and statistical techniques used in this study can be extrapolated to any other solid material in granular form that possesses a homogeneous particle size distribution. Additionally, a study of trends and time correlations was presented for eight types of biomass.
This method is useful for energetic biomass applications where precision has significant importance. Despite the heterogeneity of biofuels, a well planned selection of samples can lead to an extrapolation of sample properties from a large batch. Additionally, the high accuracy of TG equipment compensates for the low sample weight, producing confidence intervals that are smaller than expected.
A comparison between the results obtained with TG and prompt analyses was made. The mean values and maximum sampling errors were not correlated. Additionally, the mean and error of one analysis cannot be used to estimate the mean and error of the other method.
Significant linear trends and correlations in time of the random variation component were detected; however, no satisfactory explanation was found. This must be taken into account in future research.
The work of the first and second author was funded in part by project 08DPI003303PR. The work of the third author was funded in part by project MTM2008-03129 of the Ministry of Science and Innovation and PGIDIT07PXIB300191PR of the Xunta de Galicia.