Estimating the energy return on investment of forestry biomass: Impacts of feedstock, production techniques and post‐processing

The Energy Return On Investment (EROI) is a recognised indicator for assessing the relevance of an energy project in terms of net energy delivered to society. For woody biomass divergences remain on the right methodology to assess the EROI leading to large variations in the published estimates. This article presents an in‐depth discussion about the EROI of woody biomass in three different forms: woodchips, pellets and liquid fuels. The conceptualisation of EROI is further developed to reach a consistent definition for biomass post‐processed fuels. It considers, on top of the external energy investments, the grey energy associated with the energy used to enrich the fuel. With the proposed methodology, all woodchips have an EROI of the same order of magnitude, between 20 and 37, depending on forestry types, operations and machineries. For secondary residues, the first estimate is 170 if, as co‐products, no energy investment is allocated to the forestry operations and transport. On the basis of a mass allocation for forestry operations and transport, the EROI for secondary residues becomes of the same order of magnitude as that for wood chips. Woodchips can be further post‐processed into pellets or liquid fuels. Pellets have an EROI of 4–7 if the heat is externally supplied and 8–23 if internally supplied (self‐consumption of part of the raw material). Liquid fuels derived from primary wood and residues through gasification and Fischer‐Tropsch synthesis have an EROI between 4 and 16. Fuel enhancement with hydrogen (Power & Biomass to Liquids) impacts negatively the EROI due to the low EROI of hydrogen produced from renewable electricity. However, these fuels offer other advantages such as improved carbon efficiency. A correct estimate of EROI for forestry biomass, as proposed in this work, is a necessary dimension in assessing the suitability of a project.


| INTRODUCTION
Within the framework of the energy transition, the Energy Return On Investment (EROI) is an important and practical indicator to evaluate the relevance of a project (Colla et al., 2020).The EROI is usually defined as the ratio between the energy output from a process and the energy inputs in the process, on its whole life cycle.It is represented in Equation 1 where E out counts the final energy outputs and E in gathers the external energy invested in the different steps of the process: extraction, transport and transformation as illustrated in Figure 1.
The EROI is an appreciated indicator as it is a simple value that relates to the net energy delivered to society.Indeed, it allows to determine whether a project will supply significant amount of net energy to the system.Moreover, it allows easy comparison between projects (Colla et al., 2020).However, as any indicator, the EROI shows some limitations.It does not consider the quality of the energy (the exergy) and it aggregates, in the energy investments, energy fluxes that might have different qualities.Despite this simplification, EROI remains a very useful indicator.A consensus currently emerges in the literature regarding the usefulness and the challenges associated with EROI analysis (Delannoy et al., 2023).The results should be discussed carefully.As it aggregates data covering the entire life cycle and hides some dynamics (e.g., intermittency) and differences in the terms of the sum (e.g., quality difference: electricity vs. heat inputs).Caution is even more required when EROIs of different fuels are compared, because they might have different qualities and related final uses, and cannot be directly compared (Murphy et al., 2022).
Calculating the EROI is a complex task that requires careful consideration to ensure a fair comparison.This is due to the methodological subtleties and controversies arising from differing perimeters (Murphy et al., 2022).
For forestry products the challenges related to EROI estimates are exacerbated due to the multiple origins and final uses of the woody biomass.Indeed, the energy invested in the forest products depends on the types of forest, on the silvicultural systems, the related machineries and on the nature of the products, that is primary wood, primary residues or secondary residues.Those three products categories are the usual ones considered for forestry biomass (Titus et al., 2021).Primary wood is defined as roundwood extracted, from forest from stems and main parts of trees.Primary woody residues are defined as residues from logging operations including tops, crowns and branches.Secondary woody residues are defined as industry by-products, bark and post-consumer wood.For the EROI methodology, the residues, as by-products, imply allocation methodologies to divide the energy investment between main products (lumber) and residues, and this has a significant impact on the EROI.Additionally, the same initial feedstock can be transformed into different final products, such as woodchips, wood pellets or liquid fuels, which adds a level of complexity.Therefore, the EROI methodology presents some challenges for forestry products that complicate the estimates and the discussion.Yet, forestry biomass is a versatile resource, key for the energy transition (International Energy Agency, 2018).Therefore, it is important to correctly characterise and discuss its EROI.
In the literature, the EROI of first generation biofuels is largely developed, with numerous discussions to determine whether the EROI is higher than one and the reasons for different estimates (Hall et al., 2011).Indeed, the energy inputs can be large if inputs are used in the cultivation steps (fertiliser, pesticides, etc.) (Hammerschlag, 2006).However, for forestry products there are only few publications that estimate the EROI of wood products (Nikodinoska et al., 2017;Pandur et al., 2016;Raugei et al., 2020;Raugei & Leccisi, 2016;Wang et al., 2021).Most of the time there is no discussion around the final EROI presented as a single value in a data set.Even in meta-analysis and reviews only few papers for wood products are included.For the studies focusing specifically on woody biomass, in (Pandur et al., 2016) the authors detailed the entire chain with the machineries and the different steps considered.They estimate the EROI of wood log (ca.64) and of woodchip (ca.25).Similarly in (Nikodinoska et al., 2017), the EROI of woodchips was estimated to 22.4.Finally recently (Bilot et al., 2023) studied the EROI of wood chips from European beech depending on the silvicultural operations and related wood fuel demand scenarios.They estimated the EROI at around 20 with details on the different operations (thinning cycles and final harvesting).Yet in their studies, they mention that other tree species and silvicultural options could be investigated.In (Murphy et al., 2022) where the authors aimed to review and harmonise the EROI method of major energy carriers, they include only one article for woodchips with a EROI of 32 and for wood pellets with a EROI of 1.6-while mentioning that there is a diversity of estimates, not considered or discussed in their study.
Similarly in (Wang et al., 2021), they considered only two articles related to woody biomass in their meta-analysis.
Those two papers are about wood pellets from wood residues (only one paper includes the forestry practices) with EROIs of 9.5 and 11.1 compared with 1.6 in (Murphy et al., 2022).Hence, a large difference in terms of final estimations for wood pellet exists in the literature, yet a clear discussion on this variation is lacking.Thus, none of the mentioned studies discuss the EROI variations depending on (i) the types of forest and feedstock: wood or residues, primary or secondary, (ii) the machineries and forestry practices (iii) the methodological allocation of embodied energy for residues and (iv) the potential post-process.Therefore, this paper proposes to study the different EROI of forestry products, to discuss the main influencing parameters for the feedstock production (forest types, practices, allocation methods).Additionally, three possible post-processes of this feedstock are discussed: (i) woodchips, (ii) wood pellets and (iii) liquid fuel from gasification and Fischer-Tropsch process.
Indeed, biomass is versatile and can be transformed into different fuels for different uses thus it is relevant to compare different forms.Thus, pelletisation was selected as pellets are a convenient fuel and largely traded (Gauthier & Avagianos, 2021), and a large EROI variation was spotted in the literature.Pelletisation allows to highlight some conceptual challenges of the EROI for postprocessed fuels related to autothermal processes that will be addressed in this work.In addition, gasification and Fischer-Tropsch of woodchips for liquid fuel production is studied as it is a technical solution that is considered for replacing fossil fuel in the transportation sector (Ail & Dasappa, 2016;Leyva et al., 2021).Moreover, no study estimating and discussing the related EROI was found.
Two processes are included: Biomass to Liquid (BtL), and Power & Biomass to Liquid (PBtL).BtL refers to the gasification with Fischer-Tropsch using biomass as only feedstock.PBtL refers to similar process but, in addition to biomass gasification, electricity is used to produce hydrogen and thus enrich the syngas before recombination into liquid fuel through the Fischer-Tropsch synthesis (Figure 2).This PBtL route presents interesting features to increase the carbon efficiency of the process (Peduzzi et al., 2018).Yet, this fuel enrichment also highlights some conceptual challenges of the EROI that needs to be clearly addressed to ensure fair estimates and discussion.Therefore, this paper first undertakes an in-depth analysis on the woodchips EROI considering forestry types, operations and machinery.It then expands the discussion on the EROI methodology for post-processed biomass fuels (pellets and liquid fuels) from woodchips-a topic currently little addressed and discussed in the literature.Therefore, this paper proposes transparent and consistent estimates and discussions on the EROI of fuels derived from forestry biomass, taking into account and discussing the complexity of forest products and the EROI methodology.

| METHODOLOGY
The article studies woodchips, wood pellets and liquid fuels-the last two using woodchips as input feedstock.The woodchips can come from different types of forest and products that influences the energy investment (Section 2.1).The energy investments consider the silvicultural management, the harvesting, the skidding, the chipping and the first transportation (50 km) with diesel truck to a central point (for post-processing or storage).From this step, the woodchips can either be considered as the final energy carrier or be densified into pellet or liquid fuel (Section 2.2), which raises some EROI challenges for post-processed fuels from biomass (Section 2.3), before final transportation to point of use (Section 2.4).

| Woodchips from forestry products-Energy costs
We used in this work the data from (Ademe, Analyse du cycle de vie du bois energie collectif et industriel, 2021), where they detailed the energy invested depending on the types of product, the tree species and types of forestry: high forest of Douglas, oak or chestnut coppice.The wood products are chipped at roadside and naturally dried as in (Ademe, Analyse du cycle de vie du bois energie collectif et industriel, 2021).For the residue's categories, it raises the question of energy investment allocation as they are by-products and not the main products.For primary wood residues, there are two options: (i) either the operations (cutting and skidding) can be easily accounted explicitly (e.g., for thinning) (ii) or allocation ratios are used to divide the total energy investment between lumber and residues for energy (based on mass harvested) (Ademe, Analyse du cycle de vie du bois energie collectif et industriel, 2021).For secondary residues, the different steps are interlinked and allocation assumptions are used.Several allocation methods exist: mass or volumetric allocation (similar to volumetric allocation for this case (Jungmeier et al., 2002;Sgarbossa et al., 2020)), market value allocation or full allocation to the main final products.In general for secondary residues no allocation is considered for the forestry operations, only the last handling steps in the sawmill industry are accounted (Sgarbossa et al., 2020).In this work, we consider both the mass allocation and the full allocation for the main final products.We will discuss the impacts of the mass allocation (based on 50% of residues (Sgarbossa et al., 2020))-depending on the perimeters considered: including (i) all steps: from forestry to sawmill operations (ii) the sawmill energy only or (iii) the forestry energy only as the sawmill aims specifically at timber production.The market value allocation was not considered because the value of the different products can be biased with incentives and market evolution inducing volatility in the allocation that complicates the discussion.Yet in the study of (Ademe, Analyse du cycle de vie du bois energie collectif et industriel, 2021), the market/economic allocation was applied to illustrate the fact that if this method is used, all the residual products decreased their impacts by a factor of around 5 for the greenhouse gas emissions for forestry operations compared with mass allocation.Thus, discussing those two allocation methods, that is (i) the full allocation to main final products and (ii) mass allocation allows to discuss the ranges of values in which market allocation would navigate.
To discuss the impact of machineries and the different technical routes for wood harvesting and extraction we used data from (Kühmaier & Kral, 2022) where they highlight the impact of harvester or chainsaw, forwarder, tractor or skidder.Indeed, it has been shown that forestry practices related to logging and skidding have a significant impact on the energy investment based on the F I G U R E 2 Flowchart of the gasification and Fischer-Tropsch synthesis selected processes with the two options for increasing the H/C ratio (i) water gas shift or (ii) electrolysis.
work of (Berg & Lindholm, 2005).The data presented in (Kühmaier & Kral, 2022) are expressed in terms of GHG emissions, it was turned into energy considering diesel with 88.73 g CO 2 eq/MJ from (JRC, JRC GHG calculations for solid and gaseous biomass, Eur.Com, 2012).The obtained value for energy investment in forestry practices with data from (Kühmaier & Kral, 2022) are consistent with results presented in (Ademe, Analyse du cycle de vie du bois energie collectif et industriel, 2021).In (Pandur et al., 2016) they showed that fuel use was the vast majority of energy invested while the energy required for the production of machinery was responsible for around 9%.In first approximation, thus this embodied energy is neglected in this study.
For the silvicultural system and species impact, the data from (Cardellini et al., 2018) is used as reference.They present analysis based on three distinctions (i) the species with seven categories, for example light-demanding conifers (pine) or slow-growing light-demanding deciduous (oak), (ii) the sylvicultural system with seven groups, for example continuous cover forest management or even-aged forest management with clear-cutting and

| Post-process of woodchips
Once the woodchips are characterised in terms of energy investment depending on the forest types and silvicultural operations, we can study the two postprocessing options and the related energy investment: (i) for pelletisation (Section 2.2.1) and (ii) for liquid fuel production (Section 2.2.2).Up to the first steps, that is from forestry to woodchips, the EROI does not pose any conceptual challenge.Yet it does once woodchips are turned into other energy carriers (pellets or liquid fuel).Indeed, usually the energy invested includes only the external energy as developed in Figure 1.However, for the energy invested from internal feedstock for fuelling the process itself (e.g., for drying in the pelletisation process) (arrow 4 in Figure 1) it is unclear if it should be included or not.Both options relate to different conceptualisation of the EROI (Walmsley et al., 2018) and can explain the difference of estimates in the literature (Murphy et al., 2022;Wang et al., 2021).The biomass to liquid process poses similar challenges that pelletisation as it can be autothermal.The Power & Biomass to Liquid raises an additional challenge as it adds an external energy flow used for fuel enrichment and as an energy input, that is electricity is used to produce hydrogen that increases the ratio H/C and enrich the final fuel (arrow 5 in Figure 1).It is unclear how this should be accounted for in the energy investment as all, or part, of the energy will be embedded in the final fuel.As this flow is for fuel enrichment, it is part of the feedstock and is usually not counted as energy investment-as for electricity for hydrogen production (Palmer et al., 2021).Thus, there are two fuzzy areas related to the EROI (arrows 4 and 5 of Figure 1) for the biomass post-processed fuels, one related to internal uses of feedstock for auxiliary energy and another one related to external energy inputs for fuel enrichment.This will be further discussed in Section 2.3.

| Pelletisation energy costs
A review of different articles analysing the energy invested in pelletisation is presented in Table 1.Values vary with a factor of almost four between the two extremes.Yet they all agree that heating is the most energy intensive step (around 75-80%).The variation can be explained mainly by the different perimeters of the studies, but is also representative of the field variety (locations, feedstock moisture and other features, machineries efficiency and scale).The three smallest values are explained by the fact that only the non-renewable energy investment is considered.Thus, if the drying step is done with wood residues then it is not counted.The other values include all energy with no distinction if the heat is supplied with internal of external T A B L E 1 Energy investment for pelletisation in different studies.

References
Energy invested for pelletisation (MJ/t) (Wang et al., 2017) 1437 (Murphy et al., 2022) 1445 (Wang et al., 2021) 1725 (Giuntoli et al., 2017) 2390 (Uasuf & Becker, 2011) 2624 (Giuntoli et al., 2017) 4029 (Sgarbossa et al., 2020) energy flows.The two values from (Giuntoli et al., 2017) are in the middle of the range and are the two references value for the European Renewable Energy Directives (European Parliament, 2018).(Giuntoli et al., 2017) will be used as reference in this work, they refer to two different moisture contents of primary feedstock: (i) the lower value (2390 MJ/t) is for pellet from industrial residues with 40% of dry sawdust and the rest of wet sawdust with 50% of moisture content, (ii) the higher value (4029 MJ/t) is for fresh woodchip feedstock with 50% of moisture content.
For those two values of reference, the energy for heating is evaluated to 1887 MJ/t and 3145 MJ/t, respectively.(Uasuf & Becker, 2011) implemented similar methodologies and converged to similar results comforting the order of magnitude from 2400 to ca. 4500 MJ/t depending on the moisture content of the feedstock.Two higher values were found (ca.7000-9000 MJ/t; Furtula & Danon, 2017;Murphy et al., 2022) but discarded because irrelevant for methodology or experimental reasons when compared to the range of values from Table 1.Pelletisation illustrates the previously mentioned conceptual challenge for the EROI.Indeed, the initial EROI conception does not consider the consumption of the resources itself and thus should not count the internal energy flows.For biomass, there is a fuzzy area where woodchips once produced can be considered as external or internal consumption if used for further processing, and thus impact the EROI differently.The pelletisation can be autothermal, that is the heat is supplied with internal use of woodchips, or allothermal, that is the heat is supplied externally (e.g., by a gas boiler).This relates to two different pelletisation set-up, the estimates of EROI will be discussed in Section 4.2.In Section 2.3, the different approaches for the EROI estimates are presented and explained with different considerations for internal energy flows.
The embedded energy related to the pellet plant materials and construction is neglected as it represents a minimal share of total embedded energy on the whole life cycle, around 17 MJ/ton of pellets (Wang et al., 2016) which represents up to 1% of the energy invested presented in Table 1.The loss of biomass feedstock during pelletisation are estimated between 1 and 8% depending on the sources (Giuntoli et al., 2017;Sgarbossa et al., 2020;Sultana et al., 2010), 5% was considered in this case (Sgarbossa et al., 2020).Another relevant factor is the average capacity size as it influences the requirement in terms of the feedstock supply and thus the related transportations.For pellet plants, the average capacity size in Belgium in 2021 is 71 kt/year (Bioenergy Europe, Report Pellets, 2022).For the first estimate, we consider a radius of supply of 50 km as it is usually advised for costs reasons (Pandur et al., 2016), with a tortuosity factor of roads taken at 1.5 (Fan et al., 2011).This will allow to discuss the density of feedstock required and the related transportation.It will be briefly discussed in Section 4.

| Gasification for liquid fuel production-Energy costs
The production of liquid hydrocarbons by gasification can be achieved through a wide variety of processing routes (Peduzzi et al., 2018).Several variations are found at each step of the process: preparation, gasification, adjustment of the syngas H/C ratio, recycling after Fischer-Tropsch synthesis.Some processes simply exploit part of the biomass's intrinsic energy (Biomass to Liquid) while others require substantial external energy addition (Power and Biomass to Liquid) (Bernical et al., 2013).In this study, we chose two relevant types of processes and represented them in Figure 2.They both include a biomass preparation phase with torrefaction and a gasification step in an autothermal entrained flow reactor to produce the syngas (H2 + CO).The Fischer-Tropsch synthesis requires an optimal ratio H/C of 2. A first option is to use a Water Gas Shift reaction to increase H 2 proportion, which removes a significant part of the carbon from the process with CO 2 release.The alternative is to use an electrolysis step to make up for the lack of hydrogen, keeping a more significant part of the carbon inside the process but requiring a large amount of external energy.
A review of several articles studying this type of process was carried out to estimate the overall energy required for the transformation.The chosen cases and results are reported in Table 2.The external energy invested (Equation 2), internal efficiency (Equation 3) and overall efficiency (Equation 4) are calculated according the following equations: where E biomass is the energy content of the biomass input, E fuel is the energy content of the liquid fuel output (naphta, kerosene, diesel) based on an average LHV of 43, 07 MJ. kg −1 , e ext. is the net external energy input, V fuel is the output volume of fuel produced.In the first cases (BtL), the net external energy consumption is only constituted of auxiliary electric needs E aux. and power generation E output .In the last cases (PBtL), it also includes the energy required to hydrogen adjustment E elec_H2 .
Looking at the net external energy invested for BtL cases, results are varying on a range from −4.23 to 5.89 MJ/L.To provide pure oxygen for the entrained flow reactor, the two most energy-consuming BtL cases (Dossow et al., 2021;Hillestad et al., 2018) are using an air separation unit which is the biggest electricity consumers.For the other cases, most of the external energy consumption is coming from successive pumps and compressors throughout the different stages of the process.Negative values are explained by the energetic self-sufficiency of some processes.For these cases, power generation from turbines and biomass energy exceed the electricity needs of the process.
For the PBtL cases, the external energy invested is one or two order of magnitude higher than BtL cases: from 13.65 to 36.48 MJ/L.Correlations between the external energy input and internal or overall efficiency are represented in Figure 3. Differences among the PBtL cases are explained by the level of carbon conversion reached.A high carbon conversion requires an important hydrogen addition to avoid CO 2 losses in a water gas shift reaction.CO 2 losses from gasification can also be recycled in the process using an extra H 2 production and a reverse water gas shift reaction (rWGS; Dossow et al., 2021).Maximising the carbon conversion of the process increases both the external energy consumption and the internal efficiency.As a result, differences of external energy invested between cases do not deeply T A B L E 2 Energy invested for the gasification and Fischer-Tropsch synthesis steps depending on the reference, set-up and considerations, more details in the relevant references.
affect the overall efficiency (Figure 3).For data availability reasons and for coherency of data set, we used data from (Peduzzi et al., 2018) for our estimates in this work.
The BtL process highlights a similar challenge for EROI estimations than pelletisation as it can be autothermal.The internal energy flow can thus be counted or not counted as energy investment in the EROI.The PBtL, on its side, poses an additional challenge as there is an external energy flow used to enrich the fuel itself-it is thus not an energy investment as such as the energy will be recovered (at least partially) in the final fuel.Section 2.3 will detail and discuss how this flow should be considered in the EROI concept.
The energy embedded in the infrastructure, as for pellet plant is not considered usually in the literature (Polednik et al., 2021;Trivedi et al., 2015) while it will decrease the EROI slightly-some estimations mention 10-15% of the energy investment (Wang et al., 2021).The size of those installations is usually from 200 MW th -being the compromise of economic and feedstock supply reasons, to higher capacity with the constraints of the availability of biomass supply (Peduzzi et al., 2018).This will influence the sourcing area and thus the related transportation required.

| The different EROI approaches for biomass fuels
For the woodchips fuel, the EROI calculation is straightforward as all energy investment are clearly defined, there is no need of internal consumption or fuel enrichment.For the post-processed fuels from woodchips, there are challenges for the EROI methodology.The pelletisation and BtL poses the issues of autothermal process and how to consider the internal energy flow to produce the required heat.Usually in the literature, there is the standard EROI that considers all energy investment flows and the external EROI that considers only the energy flow from the exterior of the studied system (Walmsley et al., 2018).The PBtL process adds another challenge for the EROI as external electricity (for hydrogen through electrolysis) is used for enrichment of the fuel itself and not for auxiliary energy.Therefore, it should not directly impact the denominator of the EROI according to standard EROI definition.We have summarised the different challenges and related approaches in three different methods for EROI consideration as illustrated in Figure 4 and in Equations 5, 6 and 7.
EROI 1 is counting all energy investments used as auxiliary no matter their origins (i.e., including the internal consumption of the feedstock for the process) and considering the loss related to the fuel enrichment, if any.Those losses are considered in this conception as energy investment for the sake of the process.This grasp the efficiency of use of the internal resources.This is shown in Equation 5. With: • E fuel : energy delivered by the final fuel • E enrichment : additional energy in the final fuel due to enrichment • E ext : external energy investment • E int : internal (i.e., from the same feedstock) energy investment • ƞ electrolyser : the efficiency of the electrolyser ( 5) F I G U R E 4 Schematic view on the three different conceptualisations of the EROI for post-processed fuel from woodchips.The EROI3 (green boxes) is the reference definition in this paper.
E elec : the energy from the electricity added for fuel enrichment In the initial concept of the EROI, the possible use of the resource as energy in the process is not included as the aim is to relate energy invested in a system and energy delivered by the system.Therefore, internal use of the resource itself is not relevant for the EROI.Thus, we argue that including this in the EROI poses problem as it mixes different information and do not really refer to net energy delivered to society.Yet it is relevant to consider it more broadly through other indicators such as resource utilisation factor as suggested in (Walmsley et al., 2018).They also highlight that this conceptualisation of the EROI is less reliable because of arbitrary choices in the methodology (Walmsley et al., 2018).
In contrast with EROI 1 , the second method (EROI 2 ) counts only the external energy investment, this external EROI was discussed as a more reliable indicator in the classic EROI methods (Walmsley et al., 2018).Additionally, there is no consideration of the loss related to fuel enrichment in the energy investment in the EROI 2 .This is expressed in Equation 6.In this case, the internal feedstock consumed for heat production is not counted as such in the energy investment.Yet the internal consumption impacts the output loss (as shown in Figure 1) and thus reducing the final energy output, that is the numerator of the Equation.This conceptualisation poses problem in the case of fuel enrichment as it is not considered in the energy investment while increasing the numerator.Thus, this can artificially boost the EROI while this enrichment comes at a certain cost.We need thus to integrate the fuel enrichment steps in the denominator as well, this is done in the EROI 3 .
The last method-EROI 3 -is an adaptation of the EROI based on the limits of EROI 1 and EROI 2 discussed previously.Therefore, EROI 3 counts the external energy investment for auxiliary energy, but it also counts as energy investment the grey energy related to the fuel enrichment.To do so, as shown in Equation 7, the total quantity of energy for fuel enrichment is divided by the related EROI (considering the upstream energy investment and losses).This approach seems more correct and sticks to the initial principle of the EROI: to relate energy performance in terms of ratio between energy delivered and invested in the system (Equation 7).The results will thus only discuss the EROI 3 for the different biomass fuels.

| Transportation energy costs
The transportation energy costs depend on the types of transport but also the form of biomass transported, related to energy density and volume.The data are presented in Table 3, and are extracted from the JRC reports used for GHG calculations in the renewable energy directives (Edwards et al., 2019;Giuntoli et al., 2017).In practice, there are also logistic constraints for minimal volume transported based on the transportation types.Moreover, train and boat are usually combined with truck transportation for the first and last steps of the trades.Yet this simple data will allow to analyse easily the impacts of both parameters (types and forms of transportations).

| RESULTS
In this section, the results are presented first for woodchips from main silvicultural routes.From those reference results (presented in Table 4) alternative scenarios are investigated for silviculture system, species groups and energy allocation methods as presented in Section 2.1.Then, from the woodchips produced the impact on EROI of the pelletisation and gasification and Fischer-Tropsch (BtL & PBtL) are presented-Section 3.2.Finally, we present the impacts on the EROI of the final transportation depending on the fuel forms and transportation type-Section 3.3.different influencing parameters for those reference sults on woody products EROI: forest types (species and management) and machineries.The order of magnitude of EROI for woodchips from primary wood and residues presented in Table 4 is comparable of the estimates mentioned in the literature (Murphy et al., 2022;Nikodinoska et al., 2017;Pandur et al., 2016).Variations are observed, yet all estimates remain between 20 and 37. Deciduous trees (hardwood) present slightly higher EROI as shown in Tables 4 and 5. Table 6 illustrates the median EROI based on data for energy inputs in forestry operations per silvicultural systems (Cardellini et al., 2018), the variations are discussed in Section 4.1.In practice, the silvicultural system is in relation with the forest species and the machinery used for the different forestry operations.The variety showed in the work of (Cardellini et al., 2018) illustrated in Tables 5 and 6 is mainly due to the different machineries used in the different eco-regions.To have a clearer view on machinery energy consumption, we compared data from (Kühmaier & Kral, 2022) reported in Table 7 in energy inputs per unit of energy output in the form of wood.Considering data from Table 7, the EROI of case 1 (primary woody residues from hardwood forest) from (Ademe, Analyse du cycle de vie du bois energie collectif et industriel, 2021) could save energy inputs by using forwarder rather than skidder but here the choice of machinery implies specific scheme of exploitation and forest management discussed further in Section 4.1.Extracting wood can be more energy intensive than the felling and related operations as shown in Table 7.This emphasise the importance of forestry operation planning to optimise forest operation and extraction distances (Kühmaier & Kral, 2022).

| EROI of woodchips
For secondary residues, from Table 8, it is clear that allocation has a strong impact on the EROI, if all the steps are considered with the mass allocation (50%), the EROI drops to around 11 or 13.However, the most logical option could be to consider the forestry steps but not the sawing steps as this is fully devoted to the production of lumber.Those scenarios are represented by cases 6b and 6c in Table 8 (for soft and hardwood, respectively), and they show similar results than for woodchips from primary residues (EROIs of around 20-30).

| Impact of post-treatments
The post-treatment of biomass into densified fuel poses some conceptual issues for the EROI as introduced in the Section 2.2.A method was proposed to correctly estimates the EROI of post-processed fuels-that is EROI 3 presented in Figure 4.This section presents the results  4.

| Pelletisation
As shown in Table 9, the EROI of wood pellets decreases to approximately 3-6 when heat is supplied externally, even for secondary residues, despite their initial woodchips EROI of 170 (Table 4).If heat is provided internally with the same feedstock, that is the process is 'autothermal', then the EROIs are higher by a factor from 2 to 3 (Table 9).Yet the drop in EROI from woodchips to wood pellets is still significant; with a reduction factor between 2 and 4 for primary wood and residues and from 7 to 14 for secondary residues.The range of EROI for each case in Table 9 is representative of possible variation of moisture content of the feedstock as discussed in Section 2.2.

| Gasification
The EROI of gasification for liquid fuel is presented in Table 10.The EROIs are higher than for pellets and this is mainly due to the fact that the process is self-sufficient in energy.Thus, the EROI is only impacted at the numerator by the efficiency of fuel production.Yet if the internal flows are considered in case of allothermal process then the EROI would drop under one.The PBtL process presents lower EROI performance than BtL, this is related to the EROI considered for the hydrogen used for enrichment.For the results presented in Table 10, this hydrogen EROI is considered to be 3, from solar photovoltaics panels and with electrolyser efficiency of 73% according to data and results from (Tripathi & Subramanian, 2022).

| Point of use EROI and related final transportation
Once the final fuel is produced, it still needs to be transported to the final point of use, this final transport will increase the energy investment and therefore decrease the EROI at point of use. Figure 5 shows that woodchips start with higher EROI but if traded over long distances (>800 km) the EROI at point of use will be lower than for pellets by boat.Pellets and liquid fuel are less impacted by transportation because this energy investment represent a low share of total energy investment in the post-processing.

| DISCUSSION
This study describes the variation of EROI from woody products, the sections below discuss the results presented in Section 3 for woodchips, wood pellets, liquid fuels T A B L E 5 Energy inputs and related EROI in forestry operation depending on the species group (median value) as defined in Cardellini et al. (2018) and comparison with Ecoinvent data-all extracted from (Cardellini et al., 2018).and the final the variation of EROI of woodchips is discussed based on the different parameters studied (types of wood, of forestry operations and of machineries).Secondly, the impacts on the EROI of postprocessing the woodchips into pellets and liquid fuels is discussed.Finally, the impacts of final transportation on the EROI is analysed.In this paper, the EROIs of different biomass fuels produced from forestry products were presented.These estimates are intended to be used in further work requiring EROI of various fuels as input, for example in (Capellán-Pérez et al., 2020;Jacques et al., 2023), and for further comparison with other fuels with similar characteristics in terms of quality/final uses, for example in (Amaducci et al., 2017;Trivedi et al., 2015), as mentioned in the introduction.Yet, a direct comparison of the EROIs of the different fuels derive from forestry products discussed in this work (chips, pellets or liquid fuels) is relevant, even though they do not have the same quality or final uses, because they are produced from the same initial feedstock T A B L E 8 Secondary residues energy investments and EROI depending on allocation methods: (i) no investment allocated to residuesas they are by-products-except the last chipping step for final transformation (case 6), (ii) mass allocation (50%) for the silviculture and transportation steps but no energy from the sawing steps as it is not the main products except the energy for chipping the residues at the sawmill (cases 6b and 6c), (iii) mass allocation (50%) without distinction between main and by-products for all the steps (cases 6d and 6e).The allocation is based on mass allocation and on energy inputs data reported in (Ademe, Analyse du cycle de vie du bois energie collectif et industriel, 2021) for the forestry operations and mass allocation for the part to be attributed to the sawmill residues as in (Sgarbossa et al., 2020).

Case number
T A B L E 9 EROI of pellet for the 6 different cases with pelletisation data from (Giuntoli et al., 2017) where energy for heating is included (external supply) or excluded (internal supply with woody feedstock) in the investments.

Case number EROI of pellets with heat supplied externally EROI of pellets with heat supplied internally
1-roundwood from secondary part of the tree (hardwood) 4-5 8-13 2-residues from tops and small branches (hardwood) 4-6 9-14 3-coppice (hardwood) 3-5 8-12 4-roundwood from secondary part of the tree (softwood) 3-5 7-10 5-residues from tops and small branches (softwood) 4-6 8-14 6-secondary residues from sawmill 4-6 12-23 T A B L E 7 Energy inputs in forestry operation depending on the machinery used based on data from (Kühmaier & Kral, 2022).(i.e., Comparing their EROIs allows to discuss relevance of woodchips post-processing in terms of reduction in EROI and the resulting increase of the fuel quality.Such a comparison can help to choose the optimal final form depending on the requirements in terms of net energy and specific final service.

| EROI of woodchips
There are variations of EROI for woodchips depending on the forest types and operation systems, yet the EROI remains of the same order of magnitude.When comparing by forest type, using raw data from (Cardellini et al., 2018), it can be seen that deciduous trees present higher EROI (Tables 5 and 6).This is due to their higher energy density, but also to the forestry operations that are more efficient in deciduous forest than conifers according to the data from (Cardellini et al., 2018).Indeed, the harvester shows an average efficiency of 17-18 m 3 /h in deciduous forest, where for coniferous it is reported between 14 and 15 m 3 /h.Note that those general trends should be taken with caution as they are average value and each forest is a specific case with multifactorial influencing parameters from the production to the harvest through maintenance (geography, market, machineries etc.).The impact of forest management illustrated in Table 6 is mainly correlated to the machinery used as the main impacting steps are thinning, felling and skidding.The variety showed in the work of (Cardellini et al., 2018) is largely explained by the difference in machineries in the eco-regions.In Europe, the continuous cover forest presents the highest median EROI (Table 6) and is mainly represented by shade tolerant conifers and slow-growing light-demanding deciduous (Cardellini et al., 2018).The light-demanding conifers on their side are mainly present in even-aged forest with clear-cut system or with shelterwood cut (with the lowest median EROI as shown in Table 6).For this forest management, the operations are carried out with harvesters and forwarders mainly but also a significant share of skidders.This last presents a smaller productivity per hours for skidding operations when compared to forwarders, thus lower energy performances (Table 7).Additionally, harvesters show lower productivity in conifers forest when compared to deciduous trees (Cardellini et al., 2018), as discussed previously.These two reasons in addition to the lower energy density for coniferous wood than for deciduous can explain the lower EROI.Following the same logic, the category continuous cover forest management presents the highest EROI because the vast majority of respondents of the questionnaire for this category used forwarder for forest extraction which is the most energy effective machinery (Table 7) and is composed largely with deciduous treeshigher density and higher machinery efficiency in terms of cubic meters per hours.
The best route for machinery in terms of energy invested would be felling, delimbing and crosscutting with chainsaw and extraction with harvesters (Table 7).However, this combination is very rare in the statistics as chainsaw and forwarder have two different productivities (in m 3 /h) that would present contradictions in the operation plans.Chainsaw harvesting could be combined with horse skidding and this would present good energy performance as shown in (Magagnotti & Spinelli, 2011).But this practice induces lower productivity questioning thus the scheme of exploitation.Indeed, the choice of machineries also implies volume of production and parallel infrastructure that shapes the forest and its operation.For wood energy, there is an additional degree of complexity as, most of the time except for coppice, wood is a co-product and lumber is the main product.There is thus crossed dynamics for forestry management which however relates more volume and market dynamics rather than the EROI On the choice of the most relevant allocation methods for secondary residues, we argue that it depends on the context of wood exploitation and the main products and the real incentive to extract the stemwood from the forest.In the context of the transition to more renewable energies and materials, the need for more bio-based products is likely to rise.Thus, it seems reasonable to consider that stemwood are needed as such with the main added value.Therefore, residues can have low or no allocation (Table 8 case 6b, 6c and 6) of energy invested.In the end, it is not necessary to know the precise EROI of the residues but rather to evaluate the order of magnitude depending on the context of their exploitation.The main outputs of Table 8 is that, regardless of the allocation methods, the EROI for secondary residues is higher than 5 which is showed as the energy cliff in the literature related to the net energy delivered to society (King & Van Den Bergh, 2018).

| Impact of post-treatments
The pelletisation process smoothes the variation of the EROI, mainly when heat is provided externally (Table 9) due to its predominance in terms of energy investment in the drying step as discussed in Section 2.2.Hence the forestry practices have limited impact on the EROI for the pellet final form if the heat is supplied with external energy.The set-up for heat supply in the pelletisation has a strong impact on the EROI (Table 9).Indeed, pellets with heat supplied internally with similar feedstock show an EROI around twice higher than pellets with heat supplied externally (e.g., with gas boiler).We argue that the pelletisation set-up considered should be clearly specified to have relevant and coherent counting methodology, which is usually not the case in the literature.It explains the large differences of EROI estimates observed in the literature (Murphy et al., 2022;Wang et al., 2021).
Another important factor is the influence of the minimum capacity size of the pellet plants and the related requirement in terms of feedstock supply and transportation.In Table 9, the transportation of the feedstock is considered at 50 km if the radius of supply needs to be increased for feedstock availability then the EROI will be impacted.50 km of radius corresponds to a mean feedstock density of 140 kg/ha/year (for a capacity plant of 71 kt/year).If the radius is increased at 500 km then pellets plant can be installed in an area with a mean feedstock density of 1.4 kg/ha/year reducing the final EROI from 8 to 5.6 (case 1) depending on the pellet plant set-up for heat supply.The feedstock density relates to the potential of feedstock technically available and to the competing uses for this feedstock.However, the economic constraints related to the additional transport is not considered here.Indeed, transporting woodchips by truck on large distances is unlikely to happen due to its economic impacts.Generally in biomass supply studies, the distance is kept from 50 to 150 km for economic viability (Moskalik & Gendek, 2019), which correspond to a mean feedstock density of 140 to 15 kg/ha/year respectively.Therefore, the impact of feedstock transportation on the EROI would be limited as shown in Figure 5 for the impact of truck transportation.
The EROI of liquid fuel from woodchips trough BtL are quite high when compared to other liquid biofuels in the literature (around 1 or 2 for bioethanol from corn) (Basset et al., 2010).Yet it was already mentioned in the literature that cellulosic ethanol had the potential to present higher EROI (Basset et al., 2010).In this case as the process is autothermal and produce surplus of electricity depending on the set-up, it really allows good performances in terms of EROI.The PBtL presents lower EROI due to the hydrogen EROI considered to be 3.Thus, it is pulling down the global EROI.However, it allows to boost carbon efficiency and to store electrolytic hydrogen in the final fuel.Boosting carbon efficiency enables a better utilisation of the limited resource that is biomass.
Additionally, the BtL and PBtL plants require large installation for economic reasons and thus large supply areas.Considering 200 MW th presented in Section 2.2.2, it represents a supply of around 450,000 tonnes of woody biomass per year (around six times higher than for the average pellet plant).If this has to be supplied within a radius of 50-150 km, it represents region with a mean feedstock density of 870-100 kg/ha/year, respectively.In Belgium, only two provinces would be eligible and this is considering the full potential of woody biomass from ENSPRESO database (Ruiz et al., 2019) as being fully available for the plant.It is more likely that those BtL and PBtL plant would increase their sourcing area and thus increasing the energy invested in transportation.For primary woody residues from hardwood, the EROI of liquid fuel from BtL is 13 for a sourcing area with a 50 km radius, 11 for a 150 km radius, and 6 for a 500 km radius.If the plants import wood pellets as feedstock then the EROI drops to around 3 or even 1 in the worst case presented here, that is pelletisation with external supply of heat.Hence the location of the plants will significantly impact the relevance of the project in terms of EROI.
The losses of biomass are impacting the numerator of the EROI, but the EROI is not the right indicator to assess and discuss the loss of feedstock, that is the efficient uses of the resource (Walmsley et al., 2018).Indeed, you can have relatively high share of loss (e.g., due to internal consumption) and yet having a higher EROI than other processes with lower losses, for example as for BtL to PBtL.However, biomass is a source with limited stock and various end Thus, the efficient use of this resources and arbitration of its uses as a versatile resource emerges as an important question to handle that requires further indicator than EROI.Energy system modelling can be a good tool for helping investigating this optimal use of biomass (Colla et al., 2022).

| Final transportation and further considerations
Although from an EROI perspective, the woodchips could be traded on large distance (Figure 5), those exchanges are unlikely due to economics constraints (Moskalik & Gendek, 2019); the costs of labour are not represented in the EROI.Hence this shows that for biomass trade, economics constraints are more restrictive than EROI implications.Figure 5 clearly shows that pellet and liquid fuel transport are efficient in terms of energy investment and should be favoured for long distance transportation.Boat transportation shows best performances but it should be kept in mind that those data are for Supramax boat, that is 54,000 tonnes of payload.Therefore, it represents large quantities of biomass that relies on other supply chains before shipping, which likely includes trucking.
The choice between pellet or liquid fuel for long distance transportations depends on the final use.EROIs of fuels with distinct qualities and end uses should be discussed with caution as they are not directly comparable as pointed out in the introduction (Murphy et al., 2022).Liquid fuel will be used in mobility mainly while pellets or chips will be used for heat or electricity.The biofuels should be compared with other liquid fuels or with electricity for electric vehicle-also considering the difference in terms of conversion efficiency of thermal versus electric motors.Yet Figure 5 illustrates the EROIs of different final fuels produced from the same initial feedstock, that is woodchips.These results highlight the need for arbitration on the optimal use of biomass in the system (Colla et al., 2022), in order to discuss the possible decrease in EROI relative to the utility of the fuel in the system, as discussed in (Dumas et al., 2022).
An important advantage for the biomass fuels is that the energy investments are mainly direct, that is in the form of direct energy in the process/supply chain.This contrasts with wind and solar energy for which the energy investments are mostly indirect, that is in the infrastructure.This can have significant impacts on the dynamic of the transition.Indeed, as discussed in (Jacques et al., 2023), an energy transition solely based on wind and solar energies would prove very challenging since all the energy investments would require to be provided upfront, that is during the first years of the transition, creating a temporary 'energy crunch' where the energy system would swallow a significant fraction of total energy production.Adding biomass to the renewable energy mix should therefore smooth out the negative dynamics discussed by (Jacques et al., 2023).

| CONCLUSION
In this article, we explored the EROI of woody biomass as a resource used to produce three different energy carriers: woodchips, wood pellets and liquid fuels.First, we examined the variety of woodchips EROI as a function of product type, trees species and forest management.We showed that the EROI varies from 20 to 37 and that deciduous trees tend to show higher EROI due to higher density and higher machineries productivity.Yet all woodchips present EROI of the same order of magnitude.For secondary residues, the first estimate is of 170, if we consider that no energy investment is allocated to the upstream stages, since these are residues from the sawmill industries.If we consider a mass allocation for forestry and transport, the EROI is of the same order of magnitude as that of standard woodchips.Next, the article analysed the EROI of post-processed fuels using woodchips as raw material: wood pellets and liquid fuel through gasification and Fischer-Tropsch (Biomass to Liquid, and Power & Biomass to Liquids).The EROI conceptualisation was discussed in order to converge to the best method, that is considering only external energy investments and the grey energy associated with the energy used for fuel enrichment.With this method, the pellets have an EROI of 4 to 7 if the heat is supplied externally and 8 to 23 if it is supplied internally, that is auto-consumption of part of the feedstock.For liquid fuel, the EROI has been estimated from 4 to 16 for primary wood and residues.The Power & Biomass to Liquids processes reduce the EROI due to lower EROI of hydrogen.However, these processes present other advantages such as improving the carbon efficiency.This article therefore provides an extensive discussion on EROI of woody biomass and highlights the need for consistent approach to achieve a meaningful EROI.Woody biomass shows good performance in terms of EROI with the additional advantage to be mainly composed of direct energy investment.We also discussed the limitations of the EROI and the need for multi-criteria analyses to assess a project from a systemic point of view, that is by also including social, environmental or economic aspects.The net energy analysis grasped by the EROI is Diagram of the different steps and related investment of energy and energy output for fuels from forest biomass.
(iii) the ecoregion for Europe with five divisions, for example central-West Europe or central-East Europe.Their data are based on questionnaire largely distributed across Europe.Their discussion and open source data are very informative showing the variability in each category.They also include comparison with Ecoinvent data and their results have shown more precise data and discussion as Ecoinvent values are average of different systems with less geographical varieties.

T
A B L E 4 Energy inputs and related EROI for different feedstocks in the form of woodchips all cases are from (Ademe, Analyse du cycle de vie du bois energie collectif et industriel, 2021) except case 6 from(Sgarbossa et al., 2020).Those results are the reference cases for the post-processed fuels in Section 3.2.and liquid fuel production through gasification and Fischer-Tropsch (BtL and PBtL) for the six different reference cases presented in Table

F
Impact of transport distance on the EROI, depending on the form of biomass for truck and boat transport from primary residues of hardwood (case 1) and considering pelletisation with internal production of heat and Power & Biomass to Liquid process for the liquid fuel.T A B L E 1 0 EROI of the liquid fuels produced from Biomass to Liquid and Power & Biomass to Liquid for the 6 different cases of feedstock.

group MJ in /MJ wood EROI (with roadside chipping and 50 km transportation added) Cardellini et al. (2018) Ecoinvent (Cardellini et al. (2018) Ecoinvent
(Cardellini et al., 2018) operation depending on the forest management in place based on data and assumptions from(Cardellini et al., 2018)(median values) and related EROI with roadside chipping and 50 km transportation added.