Modeling the Calorific Value of Biomass from Fruit Trees Using Elemental Analysis Data Modeling the Calorific Value of Biomass from Fruit Trees Using Elemental Analysis Data

Pruning of fruit trees produces a great quantity of biomass each year that can be used for energy production. For this purpose, it is necessary to carry out an energy characterization of these pruned wastes, where the determination of heating value is significant. This value is usually measured by an adiabatic or isoperibolic calorimeter, which causes high economic costs and wastes time. The present study is focused on the development of indirect models for heating value prediction of biomass from orange trees Citrus × sinensis Osbeck, almond trees Prunus dulcis (Mill) D.A. Webb, and olive trees Olea europaea L. from an elemental analysis in order to reduce the time of determination as well as the economic costs. Residual biomass was classified and characterized according to CEN regulations such as received, without drying. Also, moisture content wet basis, bark ratio, density, heating value, and elemental composi‐ tion (carbon, hydrogen, nitrogen, and sulfur) were measured. The influence of these variables on the heating value was analyzed. Finally, mathematical models were developed to predict this value for this studied species. These models showed coefficients of determination between 0.83 and 0.97, being suitable for industrial use.


Introduction
A number of researchers have published mathematical models to predict the higher heating value of different biomass materials from the concentration of the main elements present, such as percentage of carbon, percentage of hydrogen, and percentage of nitrogen together with others [1][2][3][4][5][6]. On the other hand, other models have used proximate analysis [7][8][9][10] or structural analysis [9][10][11]. Indirect calculation of the higher heating value by means of these types of models is justified by the expensive cost of the use of calorimeters [3,12]. The aim of this chapter is to compare the resources used in direct heat value determination with that used in indirect calculation from elemental analysis by means of prediction models in three common lignocellulosic materials coming from pruning Mediterranean fruit trees. In this work, predictive models of the heating value of biomass from pruning of Citrus × sinensis Osbeck (orange tree), P. dulcis (Mill.) D.A. Webb (almond tree) and O. europaea L. (olive tree) have been developed; the calorific value determined directly using the isoperibolic calorimeter was compared with that determined from the elemental composition of materials. The influence of the percentage of leaves, wood moisture content, bark percentage, and percentage content of C, H, N, and S was analyzed.
The heat value is an invariable parameter for a material with constant composition, defined by the empirical form CH w O x N y S z , where w is the number of moles of hydrogen per mole of carbon, x is the number of moles of oxygen per mole of carbon, y is the number of moles of nitrogen per mole of carbon, and z is the number of moles of sulfur per mole of carbon. The moles of each element are obtained by multiplication of the sample mass with its ratio and dividing by the atomic weight of each element. The values w, x, y, and z are obtained from the division of the moles of each element in the sample by the moles of carbon.
The capacity of retaining water in the biomass, caused by its porosity, must be considered in the measurement of the calorific value. The moisture content in the material changes its molecular formula, and therefore the gravimetric percentages of C, H, O, and N. For this reason, standards to determine the calorific value for a particular material, such as UNE 164001:2005 EX [13], require the material to be obtained in the anhydrous state, or with a known moisture content.
The problem in industrial applications is that the biomass materials received for the combustion in boilers show variation in their moisture content, they are sometimes mixed with leaves and even with other materials. Under these conditions, the heat properties are not constant. In order to measure the calorific value instantly, regression models are analyzed in this paper from the percentage contents of C, H, and N of the materials as received. Currently, there are devices capable of measuring these elements in 5 min [5,6].
When there is variability in the composition, and uncertainty of the type of materials or proportion of the mixture thereof, the mathematical models for the indirect determination of the calorific value are only applicable in the scope where they were developed. This uncertainty is quite common in industry. Thus researchers, such as Francis and Lloyd [14], Ebeling and Jenkins [15], and Kathiravale et al. [16], have provided models for different types of mixtures. However, none of them showed an economical study to justify the use of the model. In this chapter, the development of models specific for the studied material is shown; in addition, an analysis was carried out to compare the cost of direct determination with an indirect mathematical model from elemental analysis.
In industrial facilities, it is very difficult to find biomass received for combustion without some moisture. Because of processes increase production costs, they are rarely used in the production of energy wood. On the other hand, open air drying rarely decreases the moisture content below 20% [17,18]. Moreover, it is normal that industrial boilers do not work with a well-defined type of material but with mixtures of different types of biomass. These reasons make the composition of the biomass used in industry variable that directly affects the expected calorific value. So, calorific determination before the introduction of the materials in the boiler is useful to understand the energy performance of the combustion. If this direct determination by the bomb calorimeter is more expensive than the indirect determination from their composition, developing predictive models is fully justified. This is studied in this work.

Vegetal material
The species studied in this work were Citrus × sinensis Osbeck (orange tree), P. dulcis (Mill) D.A. Webb (almond tree), and O. europaea L. (olive tree). These three species are widely grown in the Mediterranean region; they represent 10% of the total cultivated area in Spain [19].
The studied orange variety was "Valencia Late". This is one of the latest varieties most cultivated in Spain. The harvesting begins from March, and it is usually pruned in summer after harvesting. Its main use is fresh consumption due to its high juice content. It also has high chances of industrialization [20].
The almond variety studied was "Blaquerna". It is a self-fertile cultivar that is currently replacing other varieties of lower production. Almond pruning can be annual or biennial according to the development of the tree [21]. During the first 4 years, winter pruning is carried out focused on defining the architecture of the vegetation. From the fourth production year, pruning is performed to remove unproductive branches and to improve the fruit quality [22].
The studied olive tree variety was "Villalonga", which is the variety most widely used in Valencia, with a total cultivation area of 23,550 ha. Its main use is in the manufacture of oil and it is also used for fresh consumption [23].
To define these raw materials as biomass for biofuel, the standard UNE EN 14961-1:2011 [24] was used. According to this standard, the analyzed samples in this work were classified by their origin and sources of solid biofuels: 1.

Sample preparation
The branches of each species, obtained from pruning, were divided into six size classes (0-1, 1-2, 2-3, 3-4, 4-5, and >5 cm). Five samples of each class were taken for analysis; therefore, it resulted in 30 samples per species. For sample preparation, the methods defined by the UNE-EN 14780:2012 [25] were followed. The main purpose of sample preparation was to reduce the size of the branches in test portions with the same initial composition, being representative of the original sample. Initial wet basis moisture content average in wood was about 42.24%. In Figure 1, the process of the preparation of the sample is shown. First step was to separate the leaves and wood of the 30 branches of each species arrived at the laboratory (Figure 2a-c).
These leaves were crushed with hammer mill and stored in airtight jars with identification labels. On the other hand, the wood was milled until their sizes were lower than 3 mm. Special care was taken to avoid loss of fine particles and moisture during milling and other operations. Average wet basis moisture content in tested particles was 29.85%. The devices used for the sample preparation were as follows: -Manual saw. In order to prevent the moisture loss at the border, cuttings of the central part was used for the analytical determinations. The pieces obtained using this device are shown in Figure 2(d).
-Hammer mill crusher of stainless steel, equipped with a 3 mm screen.   Once the samples were crushed, leaves and wood were mixed in defined proportions in each group of size class. The different proportions analyzed were from 10% weight leaves/weight wood in the first sample, 20% weight leaves/weight wood in the first sample in the second, etc. up to 50% of mixture leaves/wood to the fifth sample. So, the effect of leaves on the calorific value was measured. This is very important in this study because pruned material used in boilers has always got a high percentage of leaves, and this influences the moisture content and composition. In many publications, the calorific value calculated referred to that of completely dry and bare material, but this condition is far from the actual applications. In this work, the analysis was focused on samples with variable elemental composition which is usually obtained due to variation in the percentage of leaf and bark content (caused by different size class) and the moisture content (obtained after outdoor drying). For this reason, neither the wood nor the leaf fractions were dried rigorously, but they only experience the natural loss of moisture content during the transport and storage prior to analysis.

Measurement process
Higher heating value, wet basis moisture content, and elemental composition (C, H, and N) of each sample were measured. For this, standards shown in Table 2 were used. The calorific value was measured by means of a LECO AC-500 isoperibolic calorimeter. Before analyzing the samples, the calorimeter was calibrated by the combustion of a reactive standard of a known calorific power (benzoic acid, 1 g). Subsequently, each sample was prepared with a mass between 0.1 and 1 g. This was introduced into a combustion vessel where a fuse wire caused ignition. Note that 10 ml of distilled water was added. Then, combustion vessel was sealed, and oxygen with a pressure of 3000 kPa was introduced inside the calorimeter . This container was placed in a bucket of water which was surrounded by an insulating layer to maintain a constant temperature. During analysis, the water temperature was measured by an electronic thermometer with an accuracy of 1/10,000 degree. In order to control energy exchange, the temperatures of the cuvette and the insulating layer were continuously monitored. With this, the device applies a correction to the result.The water temperature was monitored by a microprocessor in every 6 seconds. The difference between the water temper-ature before ignition and after ignition was processed through the calorimeter software, for obtaining the calorific value.

Reference of standard Standard
The weight percentage of carbon, hydrogen, and nitrogen was measured by means of a LECO TruSpec CHN analyzer. According to EN 14918, samples between 0.1 and 1 g were weighed.
Then, they were wrapped in titanium sheets that is completely inorganic. These were placed in a feeding carrousel. The analysis cycle consists of three phases: purging, combustion, and analysis. In the purge phase, the sample is casted into the load compartment, which is sealed and atmospheric gases are removed. In the second phase, the sample is casted into a compartment at 950°C, and oxygen is injected for rapid and complete combustion. The gases pass through an afterburner at 850°C to oxidize and remove particles. The combustion gases are collected in the ballast (gas collection vessel). During the analysis phase, combustion gases are homogenized in the ballast. Subsequently, an aliquot of 3 cm 3 is purged with helium through infrared detectors of CO 2 and H 2 O. Another gas loop aliquot is transported through hot copper to remove O 2 and transform the NO X to N 2 . Then, in order to remove CO 2 and H 2 O, they are allowed to flow through the tubes containing Anhydrone Lecosorb. The N content is determined on a thermal conductivity cell. The results are shown as percent or kg/mg.
In order to calculate the cost of analysis all inputs were counted. Market prices of nine enterprises were checked. Consumables, labor maintenance, and amortization were considered. Cost of technical labor was estimated in 20 €/h. Residual value of the device was considered to be 10% of investment. Time of analysis was measured.

Percentage of bark
The percentage of bark in the branches was calculated after their classification according to six diameter classes: 0-1, 1-2, 2-3, 3-4, 5-6, and >6 cm:. The diameter influences the bark ratio [26]. For each diameter, class five samples were taken, so 30 samples in total were analyzed in each species. In each branch, diameter with bark and diameter without bark were measured using of a digital caliper with 0.01 mm accuracy, as shown in Figure 3. From these diameters, the percentage of bark was calculated by Eq. (1) [26], where Bark (%) is the percentage of bark; φ cc is the diameter over bark; φ sc is the diameter without bark:

Determination of wood density
Wood density is expressed as the mass of dry wood per unit volume. To calculate the density, first the samples were immersed in a beaker with water, calibrated to 250 mL. The volume was measured by the difference between the water level before and after immersing. Then the dry weight of the samples was determined; for this purpose, samples were placed in a drying oven at a constant temperature of 105 ± 2°C for 24 h. Mean and standard deviation for the densities are obtained by Eq. (2) [26]: where ρ m is the wood density (g·cm −3 ), P s is the dry weight of the sample (g), and V v is the volume of the sample (cm 3 ).

Prediction model of heat value
To obtain predictive models by regression up to three variables (C, H, and N) have been used. For evaluating the models, the coefficient of determination (R 2 ), root mean square of the errors (RMS), and mean absolute error (MAE) were obtained. The coefficient of determination, denoted by R 2 , is a number that indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. RMS represents the sample standard deviation of the differences between predicted values and observed values. The mean absolute error is an average of the absolute errors |e i |=|f i -y i |, where f i is the prediction and y i is the true value. The model with the best fit had highest R 2 , minimum MAE, and RMS.
For all equations, 30 data were used to develop the models, and another 15 independent data were used for validation. The statistical program used was Statgraphics Centurion XV©14, even for the calculation of the significance of the variables of the mathematical prediction models by the beta coefficients and Student's t-test. The data observed in the new experiments and predicted by the model were compared with paired-sample test based on the t-Distribution.

Results and discussion
Several tests were initially applied to check the normal distribution of the data, such as Shapiro-Wilk test [27,28], Anderson-Darling test, and the Lilliefors test [29,30]. In Table 3, statistical description of the studied variables is shown for each species. It is observed that the coefficient of skewness and kurtosis are between −2 and +2. This indicates that the observed samples are normally distributed.  The calorific values are clearly influenced by the moisture content and the leaf content in the sample. The obtained calorific value for the three species was between 12 and 16 MJ/kg, which were relatively lower than values cited in the literature. This is because, in this work, we have studied samples of diverse diameters with different percentage of bark, without any drying process, and mixtures of wood and leaves in different proportions, so smaller high heat values (HHVs) were obtained. For example, González et al. [31] gave values of HHV for biomass from orange tree pruning as 16-18 MJ/kg. Yin [32] also analyzed mixtures of biomass and got HHV values 18 MJ/kg, but all these were measured on a dry condition basis.
To compare the calorific value of the three species studied, analysis of variance was performed. In Figure 4, LSD intervals are shown at 95% confidence level. It can be seen that the HHV of almond and olive trees were similar, but that of orange was significantly lower, which may be due to the characteristics of wood, leaves, and bark with moisture.     Calorific models from elemental analyses are proposed in Table 5. All models show a high R 2 and relatively low standard error (RMS) and mean absolute error (MAE). All models are considered valid for calculating the calorific value, as an alternative to the calorimeter, reducing the time and cost of analysis. The p-values for all explanatory variables were less than 0.05. It is observed that the difference between the simplest models, whose explanatory variable is only carbon, and the more complicated is very small. Therefore, we recommend using the simplest, common to all species Eq. (3). In the variance analysis of the regression models, the p-value was less than 0.01 for all variables. This means that there is a significant relationship between variables and the volume for a confidence level of 99%: Vargas-Moreno et al. [4] conducted a review of models to predict the calorific value for different biomass materials based on elemental analyses. Most of these models reviewed gave determination coefficients between 0.8 and 0.99. For this reason, the correlation coefficients obtained in this work, higher than 0.8, were considered very acceptable (Table 4). However, on the other hand, Acda [33] proposed models with higher R 2 for different materials, but their models were obtained for dry materials and without leaves, whereas the models obtained in this study were obtained from mixtures of wood and leaves, and different moisture content, as received. Therefore, they are more applicable in actual situations in industries, where the material cannot be usually dried completely and they have different leaf percentage.
Velázquez-Martí et al. [5] already applied this method to obtain prediction models to predict a high heat value on lignocellulosic waste materials from urban tree pruning. In these works, the determination coefficients obtained are similar to those of the present work, between 0.7 and 0.9. This means that the presence of moisture causes decrease in accuracy of the calorific value calculated by prediction models.
It is observed that a higher carbon content (C) provides bigger calorific values. This coincides with many other studies [2,34]. It is also shown in Table 4 with a Pearson correlation coefficient of 0.97 between HHV and C. Because of this, all proposed equations for predicting the gross calorific value (Table 5), whether univariate or multivariate, present the variable C.
The sulfur (S) is not high in all species studied ( Table 3), so it would not be a problem in biomass combustion boilers caused by this element. As it can be seen, in olive and citrus wood the S and N contents are lower than the limits established by the standard EN 14691-part 4 [35], which fix the conditions for chips used as biofuels in %N < 1% and %S < 0.1%. Almond has not got values excessive high. This allows preparing mixtures with materials with low N and S contents.
This discrepancy may be due to the extractive substances of plant biomass (sugars, tannins, sterols, fatty acids, resin acids, oligomeric terpenics, hydrocarbons, etc.) that influence the gross calorific value. Their contents depend on the species, the part of the plant, season, and the growing stage, among other factors [36]. Another explanation could be the botanical family of the studied species [37].
Once calculated using the prediction models, we proceeded to the validation of these data by applying them to new samples, whose observations were compared with the predicted values.

Comparison cost between direct and indirect measurement of HHV
Measurements with the isoperibolic LECO AC-500 calorimeter showed that the time per analyzed sample was 15 min, which includes sample preparation. As consumables, 6 L of pure oxygen measured at standard conditions (25°C and 1 atm of pressure) and a fuse for ignition of the sample are used. Table 6 shows the cost of reagents. Device depreciation and calibration cost are respectively shown in Tables 7 and 8. The total costs for different number of analyzed samples are shown in Table 9.

Price per consumable pack Consumption per sample Analysis cost (€/analysis)
Standard for calibration ref.    In Table 13, the total costs of the elemental analysis with the analyzer LECO CHNS TruSpec are shown. When Tables 9 and 13 are compared, it can be seen that the cost for determining the calorific value indirectly from elemental analysis is 23% cheaper than the direct measurement with AC500 LECO isoperibolic calorimeter for 25 samples. Moreover, time of determination is lower. The possibility to calculate the calorific value of a substance from its elemental composition reduces investment to a single computer, instead of two. This is very important in laboratories with limited resources of small and medium enterprises.

Conclusions
The advantage of using indirect methods for determining the heat value based on regression models from the analysis of C, H, and N elements has been proven this paper. Time to determine the high heat value indirectly is 40% lower than the time taken using the calorimeter directly. The cost of indirect method is 23% cheaper. Along with the cost savings, reduced analysis time is associated with a lower environmental impact linked to the reagents used.
It is proved that a higher carbon content (C) provides bigger calorific values. However, hydrogen (H) has a negative influence, with a negative Pearson's coefficient. This is due to the fact that hydrogen is associated with the water content. As it is known, the moisture content decreases the high heat value of the biomass, therefore, hydrogen presents inverse proportionality with the heat obtained from combustion. The colinearity between the moisture content and the hydrogen ratio justifies that both were rarely considered in the same model to predict the heat value.
In this paper, models for determining the calorific value in samples of Citrus × sinensis Osbeck (orange tree), P. dulcis (Mill) D.A. Webb (almond tree), and O. europaea L. (olive tree) are proposed using an elemental analysis. The accuracy is high, obtaining coefficients of determination higher than 0.95, an average error of 223.64 kJ/kg, and a RMS of 309.62 kJ/kg.
According to the thermochemical characterization of plum wood, the residual biomass from pruning can be used as chips for bioenergy. These species did not have significant differences in C and H composition, between 30 and 40% C, between 5 and 7% H. However, small differences exist with respect to N and S. Olive and citrus wood have S and N contents lower than the limits established by the standard EN 14691-part 4 [32], which fix the conditions for chips used as biofuels in %N < 1% and %S < 0.1%. Almond has not got values excessive high but still it exceeds. This leads to the preparation of mixtures with materials with low N and S contents to decrease their content.