Sustainable biomass pellets using trunk wood from olive groves at the end of their life cycle

Energy Reports 6 (2020) 2627–2640 Contents lists available at ScienceDirect Energy Reports journal homepage: www.elsevier.com/locate/egyr Sustainable biomass pellets using trunk wood from olive groves at the end of their life cycle Víctor M. Soltero a,∗, Lidia Román a, M. Estela Peralta a, Ricardo Chacartegui b aDepartment of Design Engineering, University of Seville, 41011 Seville, Spain bDepartment of Energy Engineering, University of Seville, 41092 Seville, Spain article info Article history: Received 19 September 2019 Received in revised form 4 September 2020 Accepted 19 September 2020 Available online 1 October 2020 Keywords: Sustainability Biomass Biofuel Pellets Olive tree management abstract Forest biomass is the raw material most commonly used to produce quality pellets for domestic households. However, sustainable forest biomass is not available in all regions, but there are other potential raw material sources for biomass heating systems, based on pellets. There are a large number of olive trees in the Mediterranean area, but these are not used as renewable pellet fuel because the bark cannot be used as raw material to produce quality pellets. The aim of this study is to carry out a methodology to estimate the optimal sustainable bioenergy life cycle, and the amount of sustainable residue available (trunk wood) at the end of the life of the olive grove, by optimizing the benefits, through an analysis of costs and income of the whole life process. The methodology determines the potential value of the trunks of olive trees to be used as biomass, in the form of pellets in domestic contexts and in a specific geographical area. In a case study applied to Andalusia, it has been shown that the optimal renewable life-cycle is 97 years. If policies for agricultural and energy sustainability favouring this model were adopted, this region would produce 160,000 tonnes of pellets per year, and 266,500 tonnes per year, if extended to the whole of Spain. This has a potential for providing 70.17% of the current total pellet consumption. The extension of the model to other Mediterranean countries, such as Greece and Italy, would result in an additional 124,000 and 144,000 tonnes of pellets per year, respectively. ©2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). 1. Introduction Energy, as a resource, is one of the main indicators of the human development index level (Gouveia et al.,2019;Insah and Bhattacharyya,2015;Neumayer,2001). Currently, 77.6% of the European energy supply comes from fossil fuels, whereas 11.7% is supplied by nuclear plants, and 11.1% comes from renewable energy sources. This high dependence on fossil resources produces significant environmental impacts and affects the economy. It motivates policies for promoting the development and use of renewable alternative sources. In the case of the EU-28, the use of renewable energies in 2015 accounted for 16.66% of gross final consumption, compared to 16.13% in 2014. Within these data, regarding the production of heat with biomass, in 2015, bioenergy represented 10% of total energy consumed and 61.34% of the renewable energy used (AEBIOM,2017), making biofuels currently one of the main renewable energy alternatives. ∗Corresponding author. E-mail addresses: [email protected],[email protected] (V.M. Soltero), [email protected] (L. Román), [email protected] (M.E. Peralta), [email protected] (R. Chacartegui). In this context, the use of agricultural, forestry or food residues, for their use in heating systems in buildings and individual dwellings, is a waste management strategy that offers advantages for the circular economy (Valentín et al.,2016) and reduces the dependence on fossil fuels (Agar,2017;Cheng,2017). Although it involves combustion and CO2emissions, the whole chain will be CO2neutral, being compensated throughout the useful life of the agricultural resource by the process of photosynthesis (Anon; Working Group III IPCC,2007). The development of sustainable strategies and policies based on these raw materials, assuring the economic and technical viability of systems based on their use and exploitation, requires the guarantee of medium and long-term supply, as well as a minimum low heat value (Hoogwijk et al.,2003;Werther et al., 2000). Currently, wood chips, agro-industrial residues, firewood and pellets are the main solid biofuels used for this purpose (Karkania et al.,2012;Waheed et al.,2019). Fig. 1 shows the distribution of pellet production and global trade flows (Calderón et al.,2018). As Fig. 1 shows, Europe is the world’s largest consumer of pellets with 20.3 million tonnes in 2015 (European Biomass Association (AEBIOM),2016), of which, 6.2 million tonnes were https://doi.org/10.1016/j.egyr.2020.09.017 2352-4847/©2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). V.M. Soltero, L. Román, M.E. Peralta et al. Energy Reports 6 (2020) 2627–2640 Fig. 1. World pellet map and trade flows in 2017 (Calderón et al.,2018). imported from America, Russia and Eastern Europe. Optimal energy efficiency depends on the quality of the pellet, defined from the properties of the feedstock and the pelleting process. The ISO 17225-2 (ISO,2014a) defines different parameters for the classification, according to the quality of the pellet and its use at an industrial or domestic level. At present, only forest residues have feasible technologies and associated markets for exploitation in Europe (García-Maraver et al.,2015). In the case of the Mediterranean area, those residues coming from the activities of the olive-growing sector are an important source for the manufacture of pellets, the main byproducts for energy recovery being pomace ‘‘orujillo’’ (olive cake or post oil-extraction waste) (Valenti et al.,2017), ‘‘hojín’’ (dry leaves that fall from the olive trees and that are buried as a natural fertilizer), pruned remains and olive pits (Agencia Andaluza de la Energía,2011;Consejería de Agricucltura Pesca y Desarrollo Rural,2015;Hansen,2019;Niaounakis and Halvadakis, 2006;Schipfer and Kranzl,2019). In Andalusia, in particular, the total energy potential of the by-products of the olive agroindustry amount to 567,702 toe/year, in terms of primary energy, data that make the development of forms of energy use from this resource a priority (Ekman et al.,2013;García-Maraver et al., 2012). Even with these benefits and framework, their use as a biofuel is quite reduced (García-Maraver et al.,2015), although different studies analyse the economic feasibility, mechanical behaviour and physical–chemical properties of pellets extracted from different varieties of waste (Carone et al.,2011;GarciaMaraver et al.,2014;Miranda et al.,2010;Mani et al.,2006). There are different reasons for their low use as a biofuel. Wastes are produced locally and their use involves high costs, either because of the logistical processes required for their transfer to processing or central combustion plants (high storage volume of the feedstock), or the investment required on a small scale in local installations (Barreca and Fichera,2013,2014;Caputo et al.,2003;Kinab and Khoury,2015). Main limitations for its use are associated with high moisture content, low bulk density, low ash melting point and high volatile matter content (Werther et al.,2000). It should be noted that, if the pruning feedstock (leaves and branches) of almond, black poplar, holm oak and olive species are compared, the pellets from olive residues have optimum lower heating value (LHV) and its production offers greater density and greater resistance to traction than other feedstock. However, they have a high ash content, and even though it is lower than that of separate olive leaves, it reaches a value above the threshold of domestic boiler regulation (1.5%). In terms of the different forms of residues [olive wood (bark and trunk) and olive pruning (leaves and branches)], the leaves are responsible for producing the greatest amount of ash, followed by bark and branches (Garcia-Maraver et al.,2014;Velázquez-Martí et al., 2011). On the other hand, the trunk wood offers optimal results that meet the quality required in commercial and residential applications and is therefore the most suitable part for generating pellets for domestic use. Table 1 summarizes the characteristics of the pellets by taking into account the origin of the residue and the quality (A1, A2 or B). In order to estimate the availability of residue and the potential for pellet generation, it is necessary to evaluate the whole lifecycle of the olive grove, differentiating between biological, productive and energy cycles (Fig. 2). The biological cycle is estimated to be over 2000 years, although the contrasted value in scientific studies is 700 years [27]. This cycle is divided into three stages: (i) youth (0–20 years); (ii) adult period (20–100 years) composed of the production phase (20–50 years) and the decreasing phase (50–100 years); and (iii) senescence (>100 years). Nonetheless, the optimal production cycle is reduced to a range of 40–50 years depending on the variety (Gucci and Cantini,2000). Old trees can be very productive as long as they are subjected to a rejuvenation process, although as old age is reached, i.e., after 70 years, pruning and harvesting costs increase and annual production decreases (Gucci and Cantini,2000;Pastor Muñoz Cobo and Guillén,2015). Lastly, the energy life cycle of an olive grove is calculated as the optimum cost-benefit value of the exploitation, including the income from the sale of wood for its energy recovery. At present, the biological life cycle is generally given priority over the productive life cycle on olive farms and, in the Mediterranean area in particular, the productive cycle can be longer than 200 years (Bormann,1985;Bytnerowicz and Omasa,2007; Paoletti et al.,2010). In most cases, the renewal of plantations is not carried out, due to a lack of knowledge of the optimum cost-benefit value, there are also no economic incentives. Under this framework, it is of interest to identify the optimum productive and energy cycles of the olive grove, maximizing resource productivity and, subsequently, to identify the capacity for exploitation of available wood residues at the end of life stage as an energy source and economic opportunity for this agri-food sector. 2628 V.M. Soltero, L. Román, M.E. Peralta et al. Energy Reports 6 (2020) 2627–2640 Table 1 Characteristics of the pellet studies and ISO 17225-2:2014 (Garcia-Maraver et al.,2014;ISO,2014a). Parameter Pine spain Olive wood Olive pruning Pellet A1 Pellet A2 Pellet B Proximate analysis (% wt, as received) Moisture 10.1 7.6 8.0 ≤10 ≤10 ≤10 Ash 1.0 1.4 5.5 ≤0.7 ≤1.5 ≤3.0 Ultimate analysis (% wt, dry ash free) Nitrogen 0.3 0.3 1.1 ≤0.3 ≤0.5 ≤1.0 Sulphur 0.02 <0.01 0.05 ≤0.03 ≤0.03 ≤0.04 Lower heating value (MJ/kg) 16.9 16.0 16.5 16.5–19 16.3–19 16.0–19 Durability 91.88 98.09 98.92 ≥97.5 ≥97.5 ≥96.5 Bulk Density (kg/ m3) 544 638 610 ≥600 ≥600 ≥600 Ratio L/D 1.52 3.64 3.86 0.52–40 0.52–40 0.52-40 Fig. 2. Biological and bioenergy life cycle of the olive grove. With this aim, this article develops a methodology to estimate the optimal bioenergy life cycle and the amount of residue available (trunk wood), at the end of life of the olive grove, by optimizing the sustainable exploitation of resources through an analysis of costs and income. With the results, it is possible to evaluate the potential value of the olive tree trunks that could be used as biomass for domestic use in a geographical area. In addition, it is considered that the market value of the pelleted trunk wood will contribute to the required investment for olive tree replacement, replanting for the next productive cycle. The article is organized as follows: Section 2describes the proposed methodology; Section 3develops a case study for the area of Andalusia; and finally, Sections 4and 5present the results, discussion and main conclusions of the research. 2. Materials and methods This Section develops the methodology to estimate the optimal sustainable bioenergy life cycle and the amount of sustainable residue available (trunk wood) at the end of life of the olive grove, by optimizing the benefit, through an analysis of costs and income of the whole life process. The methodology determines the potential value of the trunks of olive trees to be used as biomass, in the form of pellets in domestic contexts in a specific geographical area. In this way, the feasibility analysis sets the renewal and replanting of the olive grove at the end of its optimum productive cycle. This involves an analysis of the costs and income involved in the cultivation of the olive tree for the grower, by taking into account the energy value of the pelleted trunk wood at the end of the life cycle of the olive grove. Fig. 3 illustrates the proposed methodology. 2.1. Step 1: Delimitation and characterization of the study area The study area is selected by calculating the optimum value of the life cycle of the trees for an energy use as pellets, there are no limits of surface area, and it can be applied to different levels: country, region, locality or crop. Once selected, the type of olive grove will be characterized. If there is more than one olive variety in the area under study, it will be necessary to determine their percentage and distribution, because production data will vary according to type of olive. After that, a descending order of surface area occupied by variety is established. For an adequate level of accuracy a definition of occupation above 90% of the total is considered. For the characterization of the area it will be necessary to collect data on: total area occupied [m2]; olive tree varieties and their area occupied [type, m2]; production by variety [kg/tree]; cultivation regime (irrigated or dry); density of plantation [olive trees/ha]; age at the start of the production cycle [year]; selling price of the olive [e/kg]; selling price of the tree [e/t]; frequency of production pruning [years]; beginning of production pruning [year]; trunk perimeter growth [cm/year]; and trunk height [m]. These data can be obtained from statistical data publications such as Navero et al. (2017), Fabbri (2004), Gucci and Cantini (2000), Pastor Muñoz Cobo and Guillén (2015). 2.2. Step 2: Calculation of economic variables and estimation of individual functions The optimal productive cycle of the olive grove depends on four economic variables: production, trunk wood mass, pruning and harvesting of olives. As the objective is to determine the 2629 V.M. Soltero, L. Román, M.E. Peralta et al. Energy Reports 6 (2020) 2627–2640 Fig. 3. Proposed methodology for the evaluation of biomass optimized potential for pellet production. optimum bioenergy cycle of the olive grove, all of these variables depend on the age of the olive tree, which implies a direct relationship with the income and costs of managing the plantation. All those economic variables independent of the age of the olive tree are discarded, as they remain constant on any farm. Income comes from: (i) annual income, due to the production and sale of olives which are present throughout the productive life cycle of the olive grove; and, (ii) specific income, defined as that obtained from the sale of the tree at the end of the life cycle of the olive tree. On the other hand, the costs of an olive farm are quite diverse: pruning, harvesting, soil maintenance, foliar treatments, prevention of pests and diseases, fertilization, etc. However, only those that depend on the age of the olive tree are relevant at this step: (i) cost of annual harvesting; and, (ii) cost of variable pruning, depending on the stage of the biological cycle of the tree. In the following sections, each economic variable is defined and modelled through a time-dependent function. This study is based on statistical data related to the different parameters and factors which affect the generation and use of olive residues. These data come from studies of species and the exploitation of plantations in the Mediterranean area (Navero et al.,2017; Conserjería de Agricultura y pesca,2002a;Fabbri,2004;Gucci and Cantini,2000;Instituto de Investigación y Formación Agraria y Pesquera (IFAPA),2010;Pastor Muñoz Cobo and Guillén,2015; Tous et al.,2014). The functions are approximations to the behaviour of these data, and are chosen as the most optimal to represent each factor. 2.2.1. Olive grove production Olive grove production is defined as the kilogrammes of olives produced per hectare, the variables that most significantly affect it are: the variety of olive tree, the cultivation regime and the age of the tree (Conserjería de Agricultura y pesca,2002a). It should be noted that production decreases with ageing once the maximum productive age has been reached. The production of new plantation specimens is estimated at 1956 kg/ha; while that of adult trees is estimated at 2736 kg/ha (Conserjería de Agricultura y pesca,2002a). The use of irrigated crops increases production with respect to non-irrigated crops, for example, in the Picudo variety, irrigation produces 48 kg/tree compared to 27.50 kg/tree without irrigation (Navero et al.,2017;Fabbri,2004). For the latter case, two alternatives may be considered in the methodology: to select the majority regime in the study area (dry or irrigated), or, to take into account the productive variability by dividing into sub-areas and assigning them the occupied surface with irrigated and dry regimes. Income from production therefore depends on the previous variables (variety of olive tree, cultivation regime and age of the olive tree) and on the production level, considering: the density of the plantation, the beginning of the production cycle (age at which the specimen begins to produce), and the selling price of the olives. The price of olives varies from season to season, and their yield is taken into account in order for income to be estimated. The methodology provides two alternatives: to use an average estimation of the selling price for the olive grove, or to use a different selling price for each variety of olive tree. FIP [e/ha] will be the time evolution of income for each variety of olive tree. 2.2.2. Income linked to trunk wood mass In this energy application the optimal productive cycle of the olive tree ends with the use of the trunk wood for the generation of pellets for residential use. The wood that can be harvested is the trunk without bark. This variable allows us to determine the availability of resources for obtaining biomass in the life cycle of the olive grove or, in other words, the potential for generating pellets from a farm. Volume and mass are estimated from the diameter and height of the olive tree trunk, which depend on the variety and age of the olive tree (except cutting process, disease or accident). It 2630 V.M. Soltero, L. Román, M.E. Peralta et al. Energy Reports 6 (2020) 2627–2640 Table 2 Variation of trunk diameter according to the variety of olive tree (Instituto de Investigación y Formación Agraria y Pesquera (IFAPA),2010). Olive variety Trunk diameter [cm] Hojiblanca 10.5 Arbequina 8.5 Picual 12 Picudo 12.5 Arroniz 14 Negral 18 is considered that the perimeter of the olive tree grows by approximately 2.5 cm/year (Arnan et al.,2012), reaching maximum productivity with the diameters shown in Table 2, depending on the variety, whereas the maximum trunk height can vary between 0.8 and 1 m (Gucci and Cantini,2000;Instituto de Investigación y Formación Agraria y Pesquera (IFAPA),2010). In order to calculate the trunk wood mass, the quantity of log without bark Mi[kg] is determined depending on the variety iof the olive tree. First of all, the diameter of the trunk Di [m] is calculated as a function of the perimeter Pi[m] with the expression (1): Di=Pi π(1) Then the volume of the trunk Vi[m3] is calculated by geometric approximation to a cylinder from the expression (2),ri[m] being the radius of the trunk and hi[m] the height of the trunk [m], considering hmax between 0.8 and 1 m: Vi=π·r2 i·hi(2) With the previous data, the quantity of wood Mi[Kg/tree] is calculated depending on the volume Vi[m3] and the density of the wood dw[kg/ m3] depending on the tree variety: Mi=dw·Vi(3) Next, the expression (4) provides information on the total amount of trunk wood MT,i[kg/ha] that a variety iwill be able to produce in the life cycle of the olive grove; and the expression (5) gives information on the total income from the sale of trunk wood Iw[e/ha]. For these, the plantation density Dha [tree/ha] and the selling price of trunk wood Pw[e/kg] must be established. MT,i=Mi·Dha (4) Iw=MT,i·Pw(5) If there are different varieties of olive tree in the same plantation, the total mass of the available trunk wood will be calculated with the sum of the quantities MT,iobtained for each variety i. Finally, the annual income and the amount of annual pellets are calculated for the life cycle of the olive grove. The annual result of incomes Iyr [e/yr] is obtained from the expression (6) that relates the total income of the olive grove Iw[e/ha] with the considered productive cycle PCop [years/ha]: Iyr =Iw PCop (6) The pellet generation potential of the farm is determined from the efficiency of the pelleting process, by taking into account the trunk wood mass WT,i[kg], the percentage of wood moisture (25%) and the percentage of wood reduction by the process (15%). The study of the evolution of this economic variable, with respect to time, will result in the trunk wood income function FI.w [e/ha], which models the income derived from the sale of the wood when the olive grove reaches the end of its optimal productive cycle. This study is carried out in Section 3.2.2. 2.2.3. Pruning process During the biological cycle of the olive tree, three different pruning operations are carried out: formation pruning, production pruning and renewal pruning. The objective, and frequency, of each pruning operation is shown in Fig. 4. Formation pruning is carried out approximately every three years with the aim of remodelling the structure of the olive tree, it is characterized by being minimal because the date of beginning of the production of the olive tree depends on the number of leaves and branches respected in this pruning. The production pruning is carried out during the adult phase of the olive tree, in order to obtain a sufficient volume of crown to assure the maximum amount of harvests, and to lengthen the productive period. After harvesting, the olive tree is pruned for renewal (maintenance), which is carried out when the specimen shows signs of ageing and hardening, with recovery being a way of resolving the problem of excess wood. At this time, a period of imbalance in the leaf/wood ratio begins, which causes a decrease in harvests, a greater alternation of production, and a deterioration in the quality of the fruits (Fabbri,2004). When the olive tree reaches the senile stage, pruning becomes more frequent and renewals are more severe. In order to calculate these variables, it is necessary to set: the beginning of pruning, the frequency of the types of pruning and the pruning mechanism. For the latter, it will be necessary to know the hours invested and the hourly cost of the task. It is considered that all varieties of olive trees use the same mechanism, type and cost of pruning. The study of the evolution of these variables over time will result in the pruning cost function FC.P[e/ha], which models the costs associated with the set of pruning operations and tasks in the study area throughout the biological cycle of the olive grove. This study is carried out in Section 3.2.3. 2.2.4. Olive harvesting process There are different methods of harvesting olives: traditional (soil harvesting, milking and olive knock down) and mechanical, the choice depends on the characteristics of the soil, the crop and the growth of the crown of the olive tree (Sola-Guirado et al., 2014). The costs associated with harvesting depend on the variety of olive tree, the productivity of the olive grove [kg olive/ha], the harvesting mechanism (which defines the hours required, as well as the hourly cost of labour) and the start of the olive grove production cycle (Tous et al.,2014). 2.3. Step 3: Definition of the benefit function for each olive variety and global benefit function Once the study area and the economic variables in relation to the farm to be evaluated have been selected, the benefit function is defined for each of the olive tree varieties FB,ito maximize from the income and costs of the olive grove: MAX [FB,i]=FB,i=FI.P+FI.W t−FC.P−FC.H(7) where: •FBis the benefit function •FI.Pis the production income function [e/ha] •FI.Wis the trunk wood income function [e/ha] •FC.Pis the pruning cost function [e/ha] •FC.His the collection cost function [e/ha] •tis time [years] It is necessary to consider the different timings of the considered processes. The production income and the cost of harvesting are annual, and occur throughout the productive cycle of the olive grove. The cost of pruning depends on the frequency of the 2631 V.M. Soltero, L. Román, M.E. Peralta et al. Energy Reports 6 (2020) 2627–2640 Fig. 4. Pruning and age of olive groves (Pastor Muñoz Cobo and Guillén,2015). process, usually every two or three years, depending on the need for maintenance, so transformation to an annual value is required. Finally, income from the sale of trees occurs at the end of the productive cycle of the olive grove, therefore, IWwill be used for the annual cost per trunk wood, as reported in Section 2.2.2. 2.4. Step 4: Maximize benefit function Calculating the maximum value for the defined function FB,i, obtains the optimal duration of the productive cycle for of each variety of olive grove, and thus, the optimal bio-energy cycle period, in years. With this data it is possible to determine the potential of biomass generation for energy [kg/ha]. Finally, the data of the selected study area can be projected to other areas, depending on the cultivated surface of the olive grove and the olive tree varieties, in order to obtain an approximation of the pellet potential of other geographical areas. 3. Results This section covers the application of the developed methodology to the region of Andalusia, in the South of Spain, in order to determine the potential for generating pellets from waste trunk wood from the olive groves in the region. 3.1. Step 1. Delimitation and characterization of the study area The Mediterranean area, and Andalusia in particular, has significant tracts of olive plantations and are one of the main sectors for the economy, contributing to the generation of employment and social, territorial and cultural cohesion, as well as producing one of the main products of the Mediterranean diet. The surface area of olive tree groves is approximately 1,500,000 ha. Fig. 5 shows the biomass potential of the territory in t/ha from the Andalusian olive groves (European Union and Junta de Andalucía, 2008). As was developed in Section 2, the definition of the benefit function, and costs and income for each variety of olive tree, as economic variables, must be defined: production, trunk wood mass, pruning and harvesting. These depend on a set of factors that characterize the area of study and are shown in Table 3: variety of olive tree, type of production, age of the olive tree, density of plantation, age at the beginning of the productive cycle and sale price of the olives. The data have a high level of reliability due to the annual data updates made by growers when they apply for cultivation aids granted by the European Union, and the public register, included in the Agricultural Plots Geographical Information System. SIGPAC (Andalucía,2018;Consejería de Agricultura Pesca y Desarrollo Rural,2019). Fig. 5. Potential production of residual biomass from olive groves in Andalusia (European Union and Junta de Andalucía,2008). 3.2. Step 2: Calculation of economic variables and estimation of individual functions The following considerations were taken into account for the calculation of economic variables. The varieties of olive tree with an occupation greater than 90% were selected which, in this case, coincides with those listed in Table 3 as the main varieties: Picual, Hojiblanca, Manzanilla de Sevilla, Lechín de Sevilla, Nevadillo Negro, Picudo and Verdial de Huévar (Conserjería de Agricultura y pesca, 2002a). These have an occupation of 90.58% of the total surface area of the olive grove, disregarding the secondary variables. In relation to the production regime, most of the Andalusian olive groves are cultivated without irrigation (1,102,485 ha, which represents 73.5% of the total area), so the irrigation regime is disregarded. It is considered that the beginning of the productive cycle, for all the varieties of olive trees, begins in the fifth year of age. In addition, an average selling price of 0.65 e/kg is estimated for olives of all varieties (Andalucía,2018). 3.2.1. Olive grove production Production depends on the type of olive grove. The data for the estimation of production throughout the life cycle of the olive grove are taken from the analysis of the Andalusian olive groves (Conserjería de Agricultura y pesca,2002b), these are included in Table 4. Although the most productive varieties are Hojiblanca and Picudo, it should be noted that the yield per olive tree depends, in addition to its variety, on other factors such as climate, soil quality, presence of pests or planting density. In 2632 V.M. Soltero, L. Román, M.E. Peralta et al. Energy Reports 6 (2020) 2627–2640 Table 3 Characterization of the study area. Geographical area Andalusia 1,500,000 ha of olive grove plantation Olive varieties Main (1,358,684 ha; 90.58%): Picual, Hojiblanca, Manzanilla de Sevilla, Lechín de Sevilla, Nevadillo Negro, Picudo and Verdial de Huévar. Secondary (141,316; 9.42%): Arbequina, Gordal Sevillana, Aloreña, Verdial de Vélez-Málaga, Lechín de Granada, Pico Limón, Manzanilla Serrana, Alameño Blanco. Cultivation regime Area: 73.5% dry land; 26.5% irrigated land Density of olive wood 960 kg/m3 Plantation Density 100 olive trees/ha Age at the start of the production cycle Age 5 Olive sale price 0.65 e/kg Trunk wood sale price 30 e/t Production pruning frequency 2 years Start of production pruning 20 year old olive grove Renewal pruning frequency 3 years Renewal pruning start 50 year old olive grove Trunk perimeter growth 2.5 cm/year Trunk height 1 m Table 4 Average production per olive variety (Conserjería de Agricultura y pesca,2002b). Olive variety Average production [kg/tree] Hojiblanca 27.00 Lechín de Sevilla 10.42 Manzanilla de Sevilla 20.30 Nevadillo Negro 14.35 Picual 29.04 Picudo 22.63 Verdial de Huévar 12.06 Table 5 Estimation of the production income function. FI.PParameter values Variety a b c Picual 0.2878 54.55 306.76 Hojiblanca 0.2727 50.03 227.5 Manzanilla de Sevilla 0.2142 39.146 154.45 Lechín de Sevilla 0.1298 23.797 39.428 Nevadillo negro 0.1644 30.084 90.9 Picudo 0.2705 51.384 160.28 Verdial de Huévar 0.1515 27.952 71.133 addition, the choice of variety is made by taking into account the fatty yield of the fruit, with Verdial de Huévar, Picual, Picudo and Nevadillo Negro being the varieties that have better fatty yield compared to Lechín de Sevilla, Manzanilla and Hojiblanca. Applying the procedure defined in Section 2.2.2, the time evolution of the olive grove is calculated for each variable, obtaining the time production income function FI.P. The results are shown in expression (8),Table 5 and Fig. 6. FI.P= −a·t2+b·t+c(8) The relationship of production income (e/ha) to the age of the olive tree (years), gives a quadratic function whose graphical representation is an inverted parabola (a<0). As Fig. 6 shows, the same trend is established for all varieties. Production increases as the olive tree grows to reach the vertex of the parabola, coinciding with the maximum yield of the olive tree, from which time, production begins to decrease. On the other hand, as Table 5 shows, the value of production differs between varieties (parameters a, b and c), with the foreseeable result as discussed in Table 4, with the highest producing olive varieties being Picual, Picudo, Hojiblanca and Manzanilla de Sevilla, followed by Nevadillo Negro, Verdial de Huévar and Lechín de Sevilla. 3.2.2. Income by quantity of trunk wood mass For the calculation of the trunk wood mass, the following factors were required: variety of olive, perimeter of the trunk, maximum height of the trunk, and, density of the wood. For the seven selected varieties, it was considered that the perimeter of the trunk grows by 2.5 cm annually, that there is a maximum height of 1 m and a wood density of 960 Kg/m3. Also, to determine the income for trunk wood, the plantation density data (100 olive trees/ha) and sale price (30 e/t) were used. Applying the procedure reported in Section 2.2.2, the evolution of the olive grove is calculated for the economic variable studied, obtaining the time functions of trunk wood mass MW, and income for trunk wood FI.W, the results are shown in expressions (9) and (10), Table 6 and Fig. 7. MW=a·t2+b·t−c(9) FI.W=a·t2+b·t−c(10) The relationship between income (e/ha) and the age of the olive tree (years) results in a similar increasing function for all varieties, which can be seen from the parameters listed in Table 6. As Fig. 7 shows, the amount of trunk is directly proportional to the age of the olive tree, with the same trend being established for all varieties. This is due to an increase in the perimeter, when the increase in height of the olive tree is limited to 1 metre. In this case, the variety is not a determining factor. In the first years of the olive tree cycle, the amount of trunk is similar for all varieties, but only in those in the range of 50–100 years can some difference be seen. It can therefore be established that the relationship between income from the sale of the tree and the variety is not significant. There is a difference of only 100e/ha between the varieties of olive trees at 100 years of age. 3.2.3. Olive grove pruning process For the pruning of the seven varieties of olive tree, the same mechanism, type and cost was used. The following data were taken to characterize the process: beginning of formation pruning at 2 years of age of the tree, carried out with a triennial frequency; beginning of production pruning at 20 years of age, with a biennial frequency; beginning of renovation pruning at 50 years, with triennial frequency. Finally, Table 7 lists the pruning activities, the hours dedicated to these activities, depending on the growth phase of the olive tree, and the cost associated with the process. As Table 7 shows, and taking into account the assumptions described, a pruning cost of 135.38 eevery three years is foreseen, 2633 V.M. Soltero, L. Román, M.E. Peralta et al. Energy Reports 6 (2020) 2627–2640 Fig. 6. Distribution of values for production income function. Table 6 Estimation of trunk wood mass and trunk wood income function. Variety Parameter values for MWParameter values for FI.W a b c a b c Picual 14.827 433.66 7130.8 0.0445 1.301 21.392 Hojiblanca 14.798 426.83 707.6 0.0444 1.2805 21.224 Manzanilla de Sevilla 13.598 358.29 6013.2 0.0408 1.1049 18.04 Lechín de Sevilla 13.598 368.29 6013.2 0.0408 1.1049 18.08 Nevadillo negro 13.598 368.29 6013.2 0.0408 1.1049 18.04 Picudo 14.829 433.91 7132.1 0.0445 1.3017 21.396 Verdial de Huévar 13.6 367.93 5998.5 0.0408 1.038 17.995 Fig. 7. Distribution of values for trunk wood income function. Table 7 Pruning mechanism, hourly cost and hours invested (Fundación CITOLIVA,2007). Activity Cost [e/h] Formation pruning [h] Production pruning [h] Renovation pruning [h] Pruning with chainsaw 12.95 6 12 18 Cleaning and collection of firewood 7.21 4 9 15 Burning of pruning waste 7.21 4 9 15 TOTAL [e/ha]135.38 285.18 449.4 2634 V.M. Soltero, L. Román, M.E. Peralta et al. Energy Reports 6 (2020) 2627–2640 Table 8 Estimation of the pruning cost function. Variety Parameter values for FC.P a b Picual, Hojiblanca, Manzanilla de Sevilla, Lechín de Sevilla, nevadillo negro, picudo, verdial de Huévar 0.5085 96.368 from year 2 to year 19 of the olive tree. In year 20, the biennial pruning cost increases to 285.18 euntil year 50, then becoming triennial and amounting to 449.40 e. Applying the procedure defined in Section 2.2.3, the evolution of the olive grove is calculated for the variable studied, obtaining the pruning cost function FC.P[e/ha]. The results are shown in expression (11),Table 8 and Fig. 8. The function is defined, at intervals, although an annual transformation is made for the different frequencies (biennial and triennial). FC.P=a·t+b(11) The relationship between pruning costs (e/ha) and the age of the olive tree (years) gives a function defined at intervals. This is due to the fact that pruning operations are biennial, or triennial, depending on the life cycle of the olive grove, thus there is a zero cost in periods without pruning. In order to define the pruning cost function, appropriate to the objective of the study, the average annual cost was considered, giving the representation shown in Fig. 8. As Table 8 shows, a linear relationship is established between the cost of pruning and the age of the olive tree, with the same trend for all varieties. As the age of the olive tree increases, more numerous and intensive pruning operations are required to compensate for the loss of the yield of the tree with age (as described in the production income function in Section 3.2.1). 3.2.4. Olive harvesting process To calculate the cost of harvesting, the following factors were taken into account: variety, production [kg/ha], harvesting mechanism, and, the beginning of the productive cycle (5 years). The harvesting mechanism varies depending on the type of olive grove. For a traditional mechanized olive grove, (i) milking, (ii) branch vibrator with complementary process (knock down), and, (iii) collection with canvases, depending on the age of the specimens, are used (AEMO (Asociación Española de Municipios de Olivo),2012;Agriculture and Rural Development,2012). Specifically, for young olive trees and up to the age of 50, traditional methods such as milking are used which, in this case, and bearing in mind that the operators collect 250 kg/day in a 7-hour day with rest, the cost amounts to 54.42 e/day. From the age of 50 until the end of the productive life, a branch vibrator is used with a complementary process (knock down) and collected with canvases, as long as the olive trees have a non-bifurcated trunk, a trunk height greater than 0.7 m, three or four main branches and an upright posture, the cost being 0.17 e/kg in non-irrigated crops (Navero et al.,2017;Fabbri,2004). Applying the procedure defined in Section 2.2.4, the evolution of the olive grove is calculated for the variables studied in order to obtain the collection cost function FC.H. The results are shown in expression (12),Table 9 and Fig. 9. FC.H=a·t3−b·t2+c·t+d(12) The relationship between the pruning cost (e/ha), and the age of the olive tree (years), provides the set of parameters listed in Table 9, which represent the harvesting cost function. As Fig. 9 shows, the harvesting cost is directly proportional to productivity (kg fruit/olive tree), growing exponentially up to the maximum point of the curve, from which point it begins to decrease. The Table 9 Estimation of the harvesting cost function. Variety Parameter values for FC.H a b c d Picual 0.0019 0.4684 31.108 175.15 Hojiblanca 0.0018 0.4544 30.677 97.981 Manzanilla de Sevilla 0.0014 0.3564 24.034 76.323 Lechín de Sevilla 0.0008 0.2052 14.352 21.705 Nevadillo negro 0.001 0.2692 18.756 24.603 Picudo 0.0016 0.0414 29.213 82.833 Verdial de Huévar 0.0009 0.2257 15.966 36.568 different yields of each variety also affect harvesting costs. Finally, the cost depends on the harvesting technique used, which is more efficient according to the level of production, and the size of the crown. Picking by hand, when the specimens are young, involves a higher cost, and a branch vibrator, optimal when the olive tree is more productive, reduces harvesting time and costs. 3.3. Step 3 and 4: Definition of the benefit function and the optimum life cycle for each olive variety With the data obtained in Step 2, and with the individual functions of the four economic variables, the benefit function FB,iis obtained for each olive variety. After that, the maximum benefit function is calculated and, thus, the optimal life cycle for each variety. The results are shown in expression (13). The results shown in Table 10 are obtained by maximizing this expression: the PCop value corresponds to the optimum cycle of an olive grove, in years, for each variety. As can be seen from the results, the differences between varieties are small, and Picudo, with 100.31 years, and Picual and Verdial, with 97.5 years, are highlighted. MAX [FB,i]=FIP,i+FIW,i t−FCP,i−FCH,i(13) = −αi·t2+βi·t−γi t−δi It is possible to calculate data on the exploitation of the olive grove, by using the PCop. This demonstrates the total tons of wood available in each region. As an example, the Picual variety would produce 155,590.21 tons of trunk wood per year, with respect to the optimal life cycle of 97.41 years, with an annual replanting need for 8652.51 ha. Considering the optimum life cycle, the area occupied and the plantation density of each variety, the trunk wood mass is estimated to be obtained at the end of the productive cycle of the olive grove, with the expression (9) developed in Section 3.2.2. The results are summarized in Table 11. The values shown in Table 11 are associated with 90% of the area occupied by the olive groves in Andalusia. Correcting this data, the Andalusian olive groves could provide a total of 266,664 tonnes/year. On the other hand, taking into account that olive wood contains 20%–25% humidity and estimating a 15% decrease, in the waste pelleting process, 159,998.50 t pellets/year would be obtained. To analyse the influence of each of the incomes and costs that appear in the expression (13), the case is made for the Picual variety. It is possible to identify which is the determinant factor among the costs or incomes to define the optimal life cycle of the olive tree. Fig. 10 shows the income, costs and benefits over the years. The profit line will reach its maximum when the optimal life cycle of the olive tree is reached. As can be seen in Fig. 10, the variable that has the most influence in determining the optimal time of exploitation of the olive tree is the income per production. Harvesting costs are the next 2635