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Life Cycle Assessment of Biogas from Separated slurry

Processes G.15 to G.18: Biogas production, co-generation of heat and power and avoided heat and electricity production

• G.15. Biogas production
  • G.15.1 Biogas principles
  • G.15.2 Biomass mixture entering the biogas plant
  • G.15.3 Energy consumption during biogas production and heat value of the biogas produced
  • G.15.4 Emissions of CH₄ and CO₂
  • G.15.5 Emissions of NH₃ and N₂O
  • G.15.6 Life cycle data and mass balances for anaerobic digestion process
  • G.15.7 Material consumption for the anaerobic digestion plant
• G.16 Co-generation of heat and power from biogas
• G.17 Avoided electricity production
• G.18 Avoided heat production

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G.15. Biogas production

G.15.1 Biogas principles

Biogas production occurs in anaerobic environments where organic matter is degraded by biological activity. The result of the anaerobic digestion is the release of gasses and nutrients. The produced gas is rich in methane (50-70 %) and carbon dioxide (50-30%) and with smaller amounts of other gasses such as hydrogen sulphide and nitrogen (N₂). The relative composition of the biogas mixture depends of the process conditions and the substrate digested (Nielsen, 2009), but is however mostly constituted of CH₄ and CO₂. Biogas is considered as a valuable energy source because of CH₄, since it is because of this gas that biogas is combustible (Nielsen, 2009).

According to Nielsen (2009), when pig manure is anaerobically digested at 50°C, there is between 50 and 70 % of CH₄ and between 30 and 50 % of CO₂ in the biogas. In this project, it is assumed that the biogas produced is constituted of 65 % CH₄ and 35% CO₂. This is in accordance with the biogas composition reported in the recent literature. In fact, Møller et al. (2007a) measured an average of 65 % CH₄ in a digester where a total of 60 % of fibre fraction was gradually incorporated to the biomass mixture (consisting of liquid manure from fattening pigs mixed with the fibre fraction). The biogas composition found in the Ecoinvent database (Jungbluth et al., 2007, p.180) consists of 67% CH₄ and 32.05% CO₂, the remaining 0.95 % being a mixture of N₂, O₂ and H₂S.

The biogas density^[8] is 1.158 kg/Nm³. Based on a heat value for methane of 9.94 kWh/Nm³ CH₄, the heat value of the biogas is 6.46 kWh/Nm³ biogas^[9]. The lower heat value of the biogas in the Ecoinvent database is 24.043 MJ/Nm³ (for the biogas used in the biogas engine, Jungbluth et al., 2007, page 180) which is in the same magnitude as the heat value in this study, namely 23.26 MJ/Nm³ (i.e. 6.46 kWh/Nm³ biogas * 3.6 MJ/kWh).

Biogas is not the only output of the process, as digested slurry is also produced. This digested slurry is recognized to have slightly different properties as compared to undigested slurry as a result of the digestion process. In fact, during the anaerobic degradation nutrients bound to the organic matter are released and thereby made more accessible for uptake by plants.

The biogas plant considered in this project consists of bioreactors for the biogas production, of receiving facilities and storage tanks for raw and degassed (digested) biomass, respectively, and of a co-generation unit allowing to produce heat and electricity from the biogas. In the current context, the biogas plant used for the calculations is based on a two-step digestion with an annual treatment capacity of 100 000 m³ of biomass. Both steps are continuously operated and fully mixed in overflow tanks with a hydraulic retention time defined by the ratio between the digester volume and the daily biomass input volume.

The first step typically yields 80-90 % of the final biogas yield and is a carefully controlled process in terms of temperature, retention time and loading. The second step is a post-digestion tank often without temperature control and with a relatively low loading. The biogas plant is an air-tight system and therefore principally without any uncontrolled gaseous emissions.

The rate of biogas production depends on the nature of the biomass input (e.g. VS-content, degradability and nitrogen content) and the process conditions applied. Process temperature is highly determining for maximum gas production rate. Industrial biogas systems are typically operated at either mesophilic temperatures (around 37 °C) or thermophilic temperatures (around 52 °C). The potentially higher gas production rate in a thermophilic process can be counteracted by a temperature dependent ammonia inhibition. As the biogas scenarios investigated in the present LCA comprises a biomass with high nitrogen loading, the biogas model system will be mesophilic thereby eliminating nitrogen loading as a limiting factor when biomass mixtures are calculated.

In order to determine the final output in terms of energy, the efficiency of the co-generation unit must be known for both heat and electricity. This is further detailed in section G.16.

Table G.20 summarizes the different parameters used in this project as regarding biogas production.

Table G.20 Summary of the main parameters characterizing the biogas process

^a See section G.16.

G.15.2 Biomass mixture entering the biogas plant

The biomass mixture input in the anaerobic digester is constituted of raw slurry (the composition of which is shown in table G.3) and fibre fraction (the composition of which is shown in table G.8). According to the composition and the degradability of both fractions, the amount of both fractions in the mixture is determined in order to obtain a biomass mixture that has a DM of approximately 10% during the digestion in the reactor, in order to obtain realistic production conditions (Jensen, 2009).

According to calculations provided by Xergi (Jensen, 2009), the 1000 kg mixture of the biomass entering the biogas plant consists of:

• 800.20 kg raw slurry (ex pre-tank)
• 199.80 kg fibre fraction

The mixture composition and mass balances is shown in table G.21 below.

Table G.21. Mass balances for the biomass entering the biogas plant, i.e. a combination of fibre fraction and raw cow slurry (slurry from dairy cows).

a) Same as in table G.3 (which is from ex-housing slurry in Annex A)

b) Same as in table G.8

c) Composition of biomass mixture of slurry and fibre fraction entering the biogas plant, i.e. the biomass input into the digester

In this project, the functional unit is “Management of 1000 kg slurry ex-animal”. The biogas production therefore has to be related to the functional unit by the use of mass balances, i.e. the values expressed per 1000 kg of biomass mixture must be converted in order to be expressed per 1000 kg of slurry ex-animal. To do this, the amount of biomass mixture (800.20 kg raw slurry plus 199.80 kg fibre fraction) used per 1000 kg of slurry ex-animal must be calculated. This calculation can be done in 6 steps:

• Step 1: Defining the total amount of “ex-animal” slurry involved – contribution from the raw slurry input
  The 800.20 kg raw slurry entering the biogas plant is “ex pre-tank” corresponds to the same amount of “ex-animal” slurry, since it is assumed that no water was added during the storage in the pre-tank. Therefore, the amount of raw slurry ex-animal from this input is 800.20 kg.
   
• Step 2: Defining the total amount of “ex-animal” slurry involved – contribution from the fibre fraction input
  The 199.80 kg of fibre fraction origins from 690.90 kg slurry ex-housing as 289.19 kg of fibre fraction is produced from 1000 kg of ex pre-tank (and hereby the same as ex-housing) cow slurry that is mechanically separated (table G.8)^[10]. The mass of slurry ex-housing is considered to be the same as the slurry ex-animal (see table A.4 and A.9, Annex A). This means that 690.90 kg of slurry ex-animal were necessary to produce the 199.80 kg of fibre fraction.
   
• Step 3: Defining the total amount of “ex-animal” slurry involved – sum of the two biomasses input
  It means that a biomass mixture of 800.20 kg raw slurry + 199.80 kg fibre fraction origins from: 800.20 kg + 690.90 kg = 1491.10 kg cow slurry ex-animal.
   
• Step 4: Relating the 800.20 kg of raw slurry input to the functional unit (1000 kg slurry ex-animal)
  As the functional unit in this study is 1000 kg slurry ex-animal, the amount of “raw slurry for biogas mixture” is: 800.20 kg *1000 kg / 1491.10 kg = 536.65 kg raw slurry (ex pre-tank) per 1000 kg slurry ex-animal (and 536.65 kg raw slurry ex pre-tank corresponds to approximately 536.65 kg slurry ex-animal, as there is no water addition during the in-house storage).
   
• Step 5: Relating the 199.80 kg of fibre fraction input to the functional unit (1000 kg slurry ex-animal)
  The amount of fibre fraction needed for the biogas mixture is: 199.80 kg *1000 kg / 1491.10 kg = 134.00 kg fibre fraction per 1000 kg slurry ex-animal (and 134.00 kg fibre fraction corresponds to approximately 463.36 kg cow slurry ex-animal^[11]).
   
• Step 6: Total biomass input needed per functional unit
  The biomass needed for the process is then 536.65 kg cow slurry (ex pre-tank) + 134.00 kg fibre fraction = 670.65 kg “biomass mixture” entering the biogas plant per 1000 kg of slurry “ex-animal”.

G.15.3 Energy consumption during biogas production and heat value of the biogas produced

The amount of biogas produced is calculated assuming that the amount of VS corresponds to 80 % of DM. The following specific methane yields in Nm³ per ton VS were assumed: cow slurry 231 Nm³ per ton (210 Nm³ per ton from primary digester + 10 % extra from secondary step); fibre fraction 231 Nm³ per ton (210 Nm³ per ton from primary digester + 10 % extra from secondary step). Slurry and fibre fraction methane yield are based on Møller (2007). The fibre fraction data used are those referred to as “solids flocculated with polymer” by Møller (2007). Also, it must be remembered that it was assumed that the biogas is constituted of 65 % CH₄ and 35 % CO₂ (table G.20).

Using these figures, it means that a total of 43.36 Nm³ biogas ^[12] per 1000 kg of “biomass mixture” is produced. The biogas density being 1.158 kg/Nm³, a mass of 50.2 kg of biogas per 1000 kg of “biomass mixture” is therefore produced. The heat value of the biogas corresponds to 1008 MJ per 1000 kg biomass mixture”^[13].

During the process, both heat and electricity are consumed. The electricity consumed for the production of biogas corresponds to the electricity used for the process plant (pumping, stirring etc.). This electricity consumption depends on the amount of biomass handled. The electricity consumed for producing the biogas is estimated as 5% of the net energy production (Jensen, 2009). This estimate is based on measurements. The electricity therefore consumed for producing the biogas corresponds to 5.60 kWh per 1000 kg “biomass mixture”^[14]. This means a consumption of 0.129 kWh per Nm³ biogas (5.60 kWh/1000 kg “biomass mixture” * 1000 kg “biomass mixture”/43.36 Nm³ biogas). The magnitude of this value is in accordance with the values found in the literature. Jungbluth et al. (2007) reports a value of 0.132 kWh per Nm³ biogas corresponding to the average electricity consumption for 14 Swiss biogas plants. Nielsen (2002) estimates that the internal electricity used corresponds to 0.09 kWh of electricity per m³ of biogas produced. The value of 0.129 kWh per Nm³ biogas used in this project therefore seems to correspond to the middle of the range of reported values. In some cases, however, the electricity consumption corresponds to 10% of the electricity produced (Jensen, 2009). Yet, this is not anticipated to be a major influence to the environmental impacts of the overall scenarios, so no sensitivity analysis was carried out for this. Instead, it is taken as a discussion point in the interpretation of the results.

The heat consumption for the process is calculated based on heating the fibre fraction and liquid from 8°C to the process temperature of 37°C (a temperature difference of 29°C), corresponding to 116.49 MJ per 1000 kg “biomass mixture” ^[15].The plant is insulated in order to reduce heat loss. Yet, some plants are equipped with heat exchangers in order to reduce the temperature difference to 15-20 °C (Rosager, 2009). The influence of this in the overall system is anticipated to be rather small and is raised as a discussion point in the interpretation of the results.

In summary, the energy consumption during the production of biogas consists of:

• 5.60 kWh of electricity per 1000 kg “biomass mixture”
• 116.49 MJ of heat per 1000 kg “biomass mixture”.

G.15.4 Emissions of CH₄ and CO₂

As the biogas plant is constructed tight in order to reduce losses of biogas, the emissions to air during the digestion are assumed to be rather small.

Jungbluth et al. (2007, page 206) made a review of several references of methane emissions from agricultural biogas plants and found a range of the methane emissions of 1-4% of the produced methane for biogas plants with covered stocks. These authors however used a methane emission of 1% of the produced methane. Similarly, Börjesson and Berglund (2007) assumed that the uncontrolled losses of methane from the production of biogas correspond to 1 % of the biogas produced when the biogas is used for heat or combined heat and power. Börjesson and Berglund (2006) mention that due to the difficulties in measuring and quantifying net losses of methane from biogas production, such data are uncertain and limited. They also reports that these losses were typically assumed to 2 to 3 % in previous life cycle assessments. Sommer et al. (2001) estimated that 3% of the produced methane is lost to the environment due to leakages and non-combusted methane in the biogas engines. In this project, the estimate used by Jungbluth et al. (2007) as well as Börjesson and Berglund (2007), i.e. 1 % of the produced methane, will be used. This gives a CH₄ emission to air of 0.2025 kg (see calculations in table G.22).

For the emissions of CO₂, Jungbluth et al. (2007) used an emission of 1 % of the produced CO₂ in the biogas. In this project, the calculated ratio between emissions of CO₂ and CH₄ in anaerobic conditions will be used, i.e. 1.67 kg CO₂ per kg CH₄ (see section G.5.5). This gives a CO₂ emission of 0.338 kg/1000 kg biomass mixture. This corresponds to 1.1 % of the CO₂ produced in the biogas^[16], which is in the same magnitude as the 1% estimate of Jungbluth et al. (2007).

G.15.5 Emissions of NH₃ and N₂O

The emissions of NH₃ and N₂O from the biogas plant are assumed to be insignificant. This is based on recent publications (e.g. Marcato et al., 2008; Massé et al., 2007) where measurements showed that there are no significant losses of N during the anaerobic digestion (of pig slurry).

G.15.6 Life cycle data and mass balances for anaerobic digestion process

In this scenario, the biogas is not upgraded (which is necessary if it is going to be used as fuel for transport). The biogas is used for co-production of electricity and heat. Table G.22 presents the life cycle data for the anaerobic digestion process.

Table G.22. Life cycle data for the anaerobic digestion process. Data per 1000 kg biomass mixture into the biogas plant.

The composition of the degassed slurry after biogas production is shown in table G.23. It is based on mass balances from data presented in table G.22 for the total mass, the DM content and the total N.

It is acknowledged that some elements may remain in the reactor (e.g. as a precipitate). With a mixture consisting of pig slurry only, Massé et al. (2007) measured statistically significant accumulation of: 25.5 ± 7.5 % of the initial P, 41.5 ± 14.8 % of the initial Cu and 67.7 ± 22.9 % of the initial S. These represent averages obtained in two cycles. For Zn, Ca and Mn, Massé et al. (2007) measured an average retention of 18.4 ± 17.7 %, 8.7 ± 9.8 % and 21.0 ± 21.9 % respectively, but this was statistically significant only for one cycle. Similarly, in an experiment where pig slurry was digested, Marcato et al. (2008) observed significant losses for P, Ca, Mg and Mn (36 %, 44 %, 32.5 % and 32 % of the respective elements were lacking in the output slurry as compared to the input slurry). Marcato et al. (2008) explained these losses by the accumulation of these elements in the form of a precipitate in the reactor, which they confirmed by scanning electron microscopy observations. As opposed to the results of Massé et al. (2007), there were no significant losses of S, Cu and Zn in the results of Marcato et al. (2008). However, both studies agree as regarding losses of P in the bioreactor, and the magnitude are comparable. Nevertheless, it was decided, based on interviews with managers and experts of Danish biogas plants (Karsten Buchhave, 2009; Jesper Andersen, 2009 and Henrik Laursen, 2009), to consider that no losses are involved through precipitation. Given the performances of the agitator systems found in the digesters nowadays in Denmark, it is reasonable to assume that no precipitates are formed in the digesters (Norddahl, 2009). Moreover, based on the interviews mentioned above, it is considered that no acid is added in the slurry in order to prevent the formation of such a precipitate. This situation is judged representative of the recently built Danish biogas plants as well as of those to be built in the future.

Table G.23. Mass balances for the biogas mixture before and after the biogas plant

a) All the data are the same as in the precedent column, but adjusted to be expressed per 1000 kg of degassed mixture, instead of per 918.8 kg of degassed mixture.

b) This loss corresponds to the biogas produced, expressed in mass terms.

c) No water loss and therefore change in dry matter is equal to change in total mass.

d) This corresponds to the losses in the biogas itself and the losses that occurred during the digestion process:

Losses in the biogas are calculated as the sum of CH₄-C and CO₂-C: (43.36 Nm³ biogas * 65 % CH₄ * 0.717 kg CH₄/Nm³) * (12.011 g/mol /16.04 g/mol) + (43.36 Nm³ biogas * 35 % CO₂ * 1.977 kg CO₂/Nm³) * (12.011 g/mol /44.01 g/mol) = 23.320 kg C
Losses from the digestion process are the aggregated losses as CO₂-C + CH₄-C: 0.338 kg CO₂ * (12.011 g/mol /44.01 g/mol) + 0.2025 kg CH₄ * (12.011 g/mol /16.04 g/mol) = 0.244 kg C
Total C loss : 23.320 kg C + 0.244 kg C = 23.56 kg C.

G.15.7 Material consumption for the anaerobic digestion plant

The materials for the anaerobic digestion plant are taken from the Ecoinvent process “Anaerobic digestion plant covered, agriculture” (Jungbluth et al., 2007, p. 197) with a capacity of 500 m³ (biomass) and a life time of 20 years (table G.24). A typically Danish biogas plant has a treatment capacity of 100 000 m³ biomass a year (Jensen, 2009). This includes the bioreactor only, i.e. the storage tanks and co-generation unit are not included. Electronics for operating the system are however included.

Table G.24. Material consumption for an anaerobic digestion plant.

a) The computer and electronics for the operating system is not included in the Ecoinvent database. It is added in this study.

G.16 Co-generation of heat and power from biogas

The biogas produced is used for the production of electricity and heat. A biogas engine is used for this purpose. In order to estimate the net heat and electricity production, the engine efficiencies (for conversion of biogas to both heat and electricity) are needed. The efficiencies of the best available technology have been applied. According to the technical description of biogas engines from GE Energy (GE Energy, 2008), the efficiency for the electricity production is in the range of 36.7%-40.8% and the efficiency for heat production is in the range of 42.9%-48.9%, with a maximum total efficiency of 82.5-86%. Accordingly, the calculations have been carried out considering an electricity efficiency of 40% and a heat efficiency of 46%.

As detailed in section G.15.3, the system produces 43.36 Nm³ biogas per 1000 kg of biomass mixture. As there are 670.65 kg biomass mixture per 1000 kg slurry ex-animal (see detailed calculation in section G.15.2), this corresponds to a production of 29.1 Nm³ biogas per 1000 kg slurry ex-animal^[17]. The net energy production after the co-generation unit is therefore 311.36 MJ heat plus 75.2 kWh electricity (270.7 MJ) per 1000 kg slurry ex-animal^[18].

As also detailed in section G.15.3, some of the produced heat is used to fulfil the heat demand of the biogas production. The amount of heat needed for this purpose is 116.49 MJ per 1000 kg mixture input, which corresponds to 78.1 MJ per 1000 kg slurry ex-animal^[19]. The heat consumption by the biogas plant thus corresponds to 78.1 MJ/ 311.36 MJ = 25 % of the heat produced. The surplus heat for the system is 311.36 MJ – 78.1 MJ = 233.26 MJ for the total system.

Yet, not all of this surplus heat can actually be used. In fact, the amount of “usable” surplus heat from the biogas plant must reflect the fact that in Denmark, according to the seasonal variations, there are periods with a surplus of heat production, which means that the heat produced at the biogas plant cannot be used during these periods, as there is no demand for it.

In the framework of the Danish LCAfood project, Nielsen (2004) assumed that only 50 % of the net heat produced by farm scale biogas plants is actually used, the remaining 50 % being simply wasted.

In the case of this project (joint scale biogas plants), it was assumed that 60 % of the surplus heat produced at the biogas plant is used, the remaining 40 % being wasted. This is a rather rough assumption based on the averaged national monthly heat demand distribution.

Therefore, out of the 233.26 MJ per 1000 kg slurry ex-animal of net surplus heat, only 139.96 MJ (i.e. 233.26 MJ * 60%) are used to fulfil the heat demand. The wasted heat thus corresponds to 93.3 MJ.

The energy produced from the biogas can be summarized as:

• 75.2 kWh electricity (270.7 MJ) per 1000 kg slurry ex-animal, all used through the national electricity grid, low voltage electricity.
• 311.36 MJ heat per 1000 kg slurry ex-animal, of which:
  • 78.1 MJ per 1000 kg slurry ex-animal is used for fulfilling the heat demand of the biogas process itself;
  • 139.96 MJ per 1000 kg slurry ex-animal is used to fulfil national heat demand;
  • 93.3 MJ per 1000 kg slurry ex-animal is wasted.

The emissions from the biogas engine were estimated from recent data from the Danish National Environmental Research Institute (DMU, 2009) (plants in agriculture, combustion of biogas from stationary engines).

Table G.25 presents the life cycle data related to the co-generation of heat and power from the biogas engine.

Table G.25. Life cycle data for the co-generation of heat and power from biogas. Data per 1 MJ energy input.

G.17 Avoided electricity production

The electricity that is replaced is the marginal electricity on the grid to which the plant is connected. As described in Annex A (section A.3.6), the modelling of marginal electricity in Denmark is based on Lund (2009), who considered detailed energy system analysis in order to determine a mix electricity marginal, considering that the marginal supplying technology differs every hour. Based on this, the Danish marginal electricity used in this project consists of 1% wind, 51% Power Plant (coal), 43% Power Plant (natural gas) and 5% electric boiler.

As 100 % coal or 100 % natural gas is generally the marginal electricity considered in life cycle assessments (Mathiesen et al., 2009), these have been used for the sensitivity analysis.

G.18 Avoided heat production

As for electricity, the heat avoided is the heat produced by the marginal heat source, i.e. the source that is actually replaced when heat is produced by the biogas engine. Yet, the marginal heat source may be variable in function of the biogas plant location. For example, if the biogas plant is connected to the district heating grid, then the heat from the biogas plant replace the marginal energy source of the combined heat and power (CHP) producing plant. This marginal energy source is then likely to be coal or natural gas. On the other hand, the biogas plant may also be connected to the natural gas grid and inject the (upgraded) biogas in the grid, as this is likely to be the case for many plants in Denmark in the future (Jensen, 2009b; Utoft, 2009), in which case the biogas would replace natural gas. Another possibility is that the biogas plant may be located in a remote location and thereby replace heat that was produced through individual boiler. There is then a range of possibilities regarding the marginal heat source for these individual boilers: wooden pellets, straw, fuel-oil. In this study, based on what is envisioned to be the future trends, it is assumed that the biogas plant is not located in a remote location, i.e. it is (or can be) connected to the district heating grid or the natural gas grid. This involves that the marginal heat source is likely to be whether coal (generating heat through CHP) or natural gas (generating heat through CHP or as used through the natural gas grid).

Coal through CHP was assumed to be the marginal heat avoided in this project (Ecoinvent process “Heat, at hard coal industrial furnace 1-10MW/RER U”, described in Dones et al. (2007 ), table 11.10,p.224), but a sensitivity analysis was carried out for:

• Natural gas (through CHP; Ecoinvent process: “Heat, natural gas, at boiler condensing modulating >100kW/RER U”, described in Faist- Emmernegger et al. (2007), table 13.10, p.161);

• Natural gas (through the natural gas grid; Ecoinvent process: “Natural gas, high pressure, at consumer/DK U”, described in Faist- Emmernegger et al. (2007), table 8.19, p.89-90). In this case, it is not heat that is avoided but the use (and production) of natural gas. This also means that no cogeneration takes place (no electricity or heat are produced, only biogas). This sensitivity analysis does not include the upgrading process (and neither the losses occurring during this process), so it should be considered that the actual environmental benefits are slightly lower than the results presented by this sensitivity analysis.

It can be noticed that the processes used for modelling CHP production are processes corresponding to production of heat only, for coal and for natural gas. This means that the co-production of electricity at the CHP plant is not accounted for. Though this is not correct, it was judged to be the option allowing to reflect the environmental consequences of this scenario the most accurately. This is because the Ecoinvent processes for co-generation of heat and electricity are allocated, which is incompatible with the methodology used throughout this study, i.e. consequential life cycle assessment, so it would be inconsistent to use allocated data at this stage. Un-allocating these data would however be well beyond the framework of this project, would be highly uncertain and would require external validation in order to meet the high quality standards of the Ecoinvent data. Therefore, the best compromise was judged to use the high quality data of the Ecoinvent database, but for generation of heat only, even though this project considers that CHP production is replaced and not heat only. This must be taken into account when interpreting the results.

As described in section F.16, not all the heat surpluses from the biogas plant can be used for fulfilling the national heat demand, but only 60 % of these surpluses, as there are periods where the heat demand is rather low as compared to the heat produced.

As a sensitivity analysis, the extreme situation where the surplus heat produced at the biogas plant is not used at all (i.e. no replacement) is investigated.

[8] 65% CH₄ with a density of 0.717 kg/Nm³ plus 35% CO₂ with a density of 1.977 kg/Nm³ gives a total density of (0.65*0.717 + 0.35*1.977) kg/Nm³ = 1.158 kg/Nm³.

[9] The heat value is calculated as: 9.94 kWh/Nm³ CH₄ x 65 % CH₄ = 6.46 kWh/Nm³ biogas.

[10] 199.8 kg fibre fraction * (1000 kg slurry ex pre-tank/289.19 kg fibre fraction) * (1000 kg slurry ex-animal/1000 kg slurry ex pre-tank) = 690.90 kg slurry ex-animal.

[11] 134.00 kg fibre fraction * (1000 kg slurry ex pre-tank/289.19 kg fibre fraction) * (1000 kg slurry ex-animal/1000 kg slurry ex pre-tank) = 463.36 kg slurry ex-animal.

[12] From cattle slurry: 800.20 kg slurry* 113.20 kg DM/ 1000 kg slurry * 0.8 kg VS per kg DM * 231 Nm³ CH₄ per ton VS / 0.65 Nm³ CH₄ per Nm³ biogas * ton/1000 kg = 25.75 Nm³ biogas.

From fibre fraction: 199.80 kg fibre fraction * 310.0 kg DM/1000 kg fibre fraction * 0.8 kg VS per kg DM * 231.00 Nm³ CH₄ per ton VS / 0.65 Nm³ CH₄ per Nm³ biogas * ton/1000 kg = 17.61 Nm³ biogas.

Total biogas produced per 1000 kg of “biomass mixture”: 43.36 Nm³ biogas (25.75 Nm³ from slurry + 17.61 Nm³ from fibre fraction).

[13] This is calculated using the heat value and the total biogas produced: 6.46 kWh/Nm³ biogas (see table G.20) * 43.36 Nm³ biogas/1000 kg “biomass mixture” * 3.6 MJ/kWh = 1008 MJ/1000 kg “biomass mixture”.

[14] Estimated internal consumption of electricity in kWh per 1000 kg biomass mixture : 43.36 Nm³ biogas/1000 kg biomass mixture x 6.46 kWh/Nm³ biogas x 40 % engine power efficiency x 5 % internal consumption = 5.60 kWh per 1000 kg biomass mixture.

[15] It is assumed that the average temperature for the biomass is 8 °C when entering the process and that it is heated to 37°C (the process temperature). Specific heat is calculated based on the content of DM and water (calculated as 1-DM), assuming that the specific heat for DM corresponds to 3.00 kJ/kg°C and to 4.20 kJ/kg°C for water. As the DM for biomass mixture is 152.52 kg/1000 kg biomass mixture (table G.21), it involves that the water content is 1000kg – 152.52 kg = 847.48 kg/1000 kg biomass mixture. The heat consumption for heating the biomass mixture from 8°C to 37°C is thus :

For DM: 152.52 kg DM/1000 kg biomass mixture * 3.00 kJ/kg DM*°C * (37-8) °C = 13 269.24 kJ/1000 kg biomass mixture;

For water : 847.48 kg water/1000 kg biomass mixture * 4.20 kJ/kg DM*°C * (37-8) °C = 103 223.06 kJ/1000 kg biomass mixture;

Total : (13 269.24 + 103 223.06) kJ/1000 kg biomass mixture * MJ/1000 kJ = 116.49 MJ/1000 kg biomass mixture.

[16] CO₂ produced in the biogas: 43.36 Nm³ biogas * 35% CO₂ * 1.977 kg CO₂/Nm³ CO₂ = 30 kg CO₂. The CO₂ emissions of 0.338 kg estimated in this project correspond to: 0.338 kg/30 kg * 100% = 1.1% of the CO₂ produced in the biogas.

[17] 670.65 kg biomass mixture (per 1000 kg slurry ex-animal) * 43.36 Nm³ / 1000 kg biomass mixture = 29.1 Nm³ biogas per 1000 kg slurry ex-animal.

[18] Heat produced: 29.1 Nm³ biogas (per 1000 kg slurry ex-animal) * 23.26 MJ/ Nm³ biogas (heat value of the biogas, see table G.20) * 0.46 (engine efficiency for heat) = 311.36 MJ heat per 1000 kg slurry ex-animal.

Electricity produced: 29.1 Nm³ biogas (per 1000 kg slurry ex-animal) * 23.26 MJ/ Nm³ biogas (heat value) * 0.40 (engine efficiency for electricity) = 270.7 MJ electricity per 1000 kg slurry ex-animal. This corresponds to 270.7 MJ * kWh/3.6 MJ = 75.2 kWh electricity per 1000 kg slurry ex-animal.

[19] There is 670.65 kg biomass mixture per 1000 kg slurry ex-animal, see section G.15.2. The heat required for the process is 116.49 MJ per 1000 kg mixture (section G.15.3). The heat needed per functional unit corresponds to: 670.65 kg biomass mixture / 1000 kg slurry ex-animal * 116.49 MJ / 1000 kg biomass mixture = 78.1 MJ per 1000 kg slurry ex-animal.

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Version 1.0 August 2010, © Danish Environmental Protection Agency