Modelling, analysis and optimization of thermal energy balance in anaerobic digestion

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Modelling, analysis and optimization

of thermal energy balance in

anaerobic digestion

Modellering, analys och optimering av

termisk energibalans i rötningsprocessen

Pierre BERNARD

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Master of Science Thesis EGI_2017-0015 MSC EKV 1179

Modelling, analysis and optimization of thermal energy balance in anaerobic

digestion

BERNARD Pierre

Approved Examiner

Andrew Martin

Supervisor

Vera Nemanova

Commissioner Contact person

Sammanfattning

För att bedöma lönsamheten hos en biogasanläggning krävs det insikt om den termiska självkonsumtionen. Detta examensarbete syftar till att ge en heltäckande modell för att beräkna den termiska självkonsumtionen för två olika typer av biogasanläggningar (våt- och torrötning). Beräkningarna omfattar energi för att värma upp råmaterialet, förlorad energi med vattenavdunstning och förluster i de olika tankarna under processer. Särskild uppmärksamhet ägnades åt en dubbelmembran tak.

Olika kontroller utfördes för att bedöma modellers giltighet, vars resultat stämde överens ganska väl.

Den termiska självkonsumtion av en biogasanläggning är i huvudsak definierad av den värme som behövs för att värma upp råmaterialet och förlusterna från dubbelmembrans tak. För att förbättra den termiska konsumtion av biogasanläggning är det viktigt att fokusera på råvaran initialtemperatur som svarar för en betydande del av värmebehovet. Dessutom uppgick upp till 80% av förlusterna i en kokare (våt biogas anläggning) och 60% av förlusterna i en torr biogas anläggning från dubbelmembrans tak. Takisolering med en 3:e membran för att bryta konvektion har därmed studerats och besparingar i uppvärmning som resultat av denna lösning är lovande.

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Abstract

Assessing the profitability of an anaerobic digestion (AD) plant requires knowing its thermal self- consumption. This Master Thesis aims at providing a comprehensive model to calculate the thermal self- consumption of two different types of AD plants: wet (Continuous Stirred Tank Reactors) and dry (Garage- type dry AD). The energy to warm up the feedstock, the energy lost with water evaporation and the losses of the different tanks of the process were considered. A particular attention was paid to the double- membrane roof.

Different reality checks were carried out in order to assess the validity of the model, whose results agree reasonably well. The thermal self-consumption of a plant is mainly defined by the heat necessary to warm up the feedstock and by the losses from the double-membrane roof. To improve the thermal performance of AD plants, it is needed to focus on the feedstock initial temperature (storage modes …) which accounts for a significant part of the heat requirements. Furthermore, losses from the double- membrane roof amounts up to 80% of the losses of a digester (wet AD plant) and 60% of the losses of a dry AD plant. Insulating the roof with a 3^rd membrane in order to break convection has thus been studied and the savings in heating due to this solution are promising.

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List of Abbreviations

AD Anaerobic Digestion

BMP Biochemical Methane Potential CFD Computational Fluid Dynamic CHP Combine Heat and Power CSTR Continuous Stirred Tank Reactor

DM Dry Matter

FM Fresh Matter

GTDAD Garage-Type Dry Anaerobic Digestion MSW Municipal Solid Wastes

ORC Organic Rankine Cycle

OM Organic Matter

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1 Introduction

The current ecological situation forces us to think more about developing massively alternative energies. Biomass and particularly agricultural wastes are one possible source of energy. It accounts for a large part of renewable supplies across the world, enables to enhance energy security of countries and to mitigate climate change. Biomass is therefore one of the main solution to change the energy systems and reduce the dependence on fossil fuels.

Though anaerobic digestion (AD) is a known and developed process in countries such as Germany (World Bioenergy Association, s.d.) where the market is already saturated, France is lagging behind and there is still a lot of potential for new AD plants.

Biogas is the product of anaerobic digestion – the biodegradation of organic matter in the absence of oxygen. It is mainly composed of methane and carbon dioxide (each of them represents roughly 50% of the composition) and some other gases in small proportions depending on the feedstock and the conditions (Moletta, 2011). Biogas can be used for different purposes: it can be used for direct combustion, electricity generation or as a fuel for transportation means.

Two types of AD plants exist: wet AD and more recently dry AD. These plants operate at mesophilic conditions (around 35-40°C) and there is consequently a need for heat.

NASKEO Environnement is a company specialized in anaerobic digestion of effluents and agricultural by-products (NASKEO Environnement, 2015). Based on the transformation of pollution into renewable energy, Naskeo technologies enable significant reductions in the discharge concentration of processed by- products and lead to the production of biogas rich in methane and directly convertible into energy at the industrial site. NASKEO Environnement has generated 10 million € in sales in 2015 with a team of 37 employees. Its mission: supporting biogas project developers in the various steps of his project: from feasibility study, laboratory analysis, technical design, business plan optimization, up to the construction, commissioning and maintenance of the plant. Naskeo has 10 years of experiments in which the company has studied nearly a hundred projects from 50 kWel to 3.2 MWel. There are more than 18 turnkey projects now under operation, 30 projects studied by Naskeo obtained their operating permit and are under construction or operation, and 50 other projects in France and others countries on any size or technology are in the process of drafts or administrative phase

The produced biogas used to be valued with Combined Heat and Power (CHP) engines: electricity can be sold to the national grid and the heat can be used to heat houses, farms or henhouses for instance. The main income is thus coming from electricity sales and the heat consumption of the biogas plant does not affect greatly the business model. Conversely, some new projects shall be started with the aim to upgrade the produced biogas and to inject it into the national grid. In this case, the French legislation decrees that the heat requirements of the plant shall be fulfilled by burning the produced biogas. The thermal self- consumption of the biogas plant would thus dramatically impact the profitability of the project.

This Master thesis aims at providing a method to estimate the thermal consumption of a plant and possible improvements to reduce it. These results would further enable to assess the profitability of future AD plants built at farms. Therefore, the two types of AD plants have been studied in this work. An analysis of the different reasons for heat consumption has been carried, the thermal consumption of the plants has been modelled, validated through reality checks and optimized.

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2 Background

Anaerobic digestion is a promising technology as it produces energy from wastes, without preventing agricultural spreading. Digestate can indeed be used as a fertilizer because the substances such as nitrogen or phosphorus remain in the outgoing digestate (Axaopoulos, et al., 2001). It addresses energetic problematics without inferring on agricultural needs.

There are two main technologies of anaerobic digestion: dry and wet digestion. The choice of the technology depends on the analysis of the forecasted feedstock which will be used in the plant. By studying the quality, the quantity and the seasonality of the feedstock supplied, one can determine the type and the size of the plant.

When the overall feedstock has a Dry Matter (DM) content of more than 25%, a garage-type dry AD shall be chosen (Angelonidi & Smith, 2015). Conversely, a wet AD process shall be chosen when the feedstock DM content is lower than 18% (M.Y. Qian, 2016). In between those values, the possibility to dilute the feedstock to use it in a wet AD process shall be studied. There is indeed a need that the DM content of the digestate inside the tanks does not exceed 10% so that stirring can be achieved and also that the DM content of the feedstock after dilution remains below 13% in order to be able to pump the mixture to the digester.

Biogas plants are usually designed to use a specific feedstock. The two main types are Municipal Solid Wastes (MSW) and agricultural rests. Using MSW requires a sorting and collecting process in order to separate organic and inorganic wastes (Deublein & Steinhauser, 2011). Agricultural feedstock can be composed of wastes from animals (e.g. manure), ensilage, cereal offal, dedicated or intermediate crops (sorghum, miscanthus). One must however ensure that the seasonality of the different wastes will enable to run the plant all year long.

Figure 1 : Wet AD plant in Nouzilly, France

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Wet AD (Figure 1) through Continuous Stirred Tank Reactors (CSTR) is the most classical and known technology when it comes to biogas production.

Figure 2 : General design of a wet AD plant (BIOS BIOENERGIESYSTEME GmbH, s.d.)

The feedstock, which in this case must be possible to pump, is processed in an enclosed and controlled reactor which is constantly stirred and heated to keep mesophilic conditions (35-40°C). Organic matter is biodegraded under the action of microorganisms during a retention time of usually around 45-50 days. Agitators are required to stabilize the digestion process (Deublein & Steinhauser, 2011) as the connection between microorganisms and the feedstock is achieved by stirring in the digester.

A wet AD plant (Figure 2) is usually composed of an incorporation tank where pre-mixing of the feedstock is achieved, a grinder, one (or several) digester and one (or several) post-digester. Post-digesters enable to increase the overall retention time by preventing from short-circuiting and thus to ensure a complete biodegradation of the feedstock. The digestate would then undergo a phase separation where the liquid phase can be reused to dilute the in-going solid substrate if necessary whereas the solid phase would be stored and used for agricultural spreading. This phase separation is usually achieved by the combined means of a screw press and a centrifuge (Figure 3).

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Figure 3 : Screw press (left) and centrifuge (right)

Conversely, dry AD consists in using solid feedstock. Both continuous and batch dry AD process exist. Only batch AD will be studied here.

Figure 4: Garage-Type Dry Anaerobic Digestion Plant in Sornay, France

A Garage-Type Dry AD (GTDAD) plant (Figure 4) such as those built by NASKEO Environnement is composed of 4 garages and 2 percolate tanks. Every garage is emptied and refilled every 40 days (which is the retention time), with new feedstock by a wheel loader. As GTDAD is a batch process, it is necessary to have 4 garages at different production stages to have an overall smoother production curve of biogas.

This is achieved by loading 1 garage every 10 days. Inside the garages, percolate is recirculated and regularly sprayed over the feedstock. The aim is to improve the biodegradation by spreading the bacteria in the whole pile and to replace what is done by stirring in CSTR. To achieve the same purpose, some digestate is always reused as an inoculum on the new feedstock.

Figure 5 shows the process for a general GTDAD plant. The garages as well as the percolate tanks are isolated and heated by the floor. As the Volatile Fatty Acids are flushed by the percolates, it is necessary to collect the biogas produced in the percolate tanks.

In order to keep an overall good quality of biogas, the biogas is collected in a garage only when its composition reaches 40% of methane (NASKEO Environnement, 2015).

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Figure 5 : General design of a GTDAD plant (M.Y. Qian, 2016)

GTDAD exhibits the advantage of allowing feedstock with a higher DM content. In addition, as little process equipment is required, this enables a low electrical consumption (M.Y. Qian, 2016) and small maintenance costs. On the other hand, the initial investment is higher and the biogas production per unit feedstock is lower than for a wet AD plant (Angelonidi & Smith, 2015).

Anaerobic digestion can either be done in mesophilic (32°C – 42°C) or thermophilic (48°C - 55°C) conditions (Deublein & Steinhauser, 2011) but in both cases large heat inputs are necessary in order to supply the plants thermal needs. Several attempts have therefore already been done in order to model the energy needs of AD plants. Wet AD is the most widespread technology for biogas production and has consequently been the subject for most of the studies. Different types of digester however exist and this design impacts the energy need of the plant. The overall energy balance for the biological reaction happening is globally neutral (Gebremedhin, et al., 2005; Deublein & Steinhauser, 2011) and consequently doesn’t need to be considered.

A lot of efforts were put to model the different heat losses from a tank. The concept of thermal resistances is widely used in the different model and a recurring pool of data exists for the values of the different parameters required to compute heat losses, from the walls (under and above ground), the roof, and the concreate apron (Merlin, et al., 2012; Rennuit & Sommer, 2013; Kishore, 1989). The main problems researchers had to face were to take into account sun irradiation and to model the losses through the ground (Georgina Terradas-Ill, 2014; Gebremedhin, et al., 2005; Kishore, 1989).

The design of the tanks studied in this Master Thesis is however different: all the walls and the concrete apron are insulated and the losses are therefore not significant when compared to the double-membrane roof: this has been the major study point related to the tank itself. On the other hand, the problem of the ground losses has been solved running a finite element simulation.

Due a lack of predominant thermal resistance, the computation of the losses through the membranes cannot be done by neglecting some phenomena like radiative heat transfer which is most often the case in the literature. The heat lost due to radiative heat transfer is however of the same order of magnitude as the convective heat transfers (Taine & Iacona, 2011; Kishore, 1989). Sun and wind, less often considered, are other important phenomena to take into account.

Due to high temperatures, feedstock heating represents by far the main thermal expense for thermophilic plants (Zupancic & Ros, 2003). This is also true to a lesser extent for mesophilic plants (Gebremedhin, et al., 2005). This value of this energy need depends however a lot on the value of the feedstock heat capacity. Most of the authors assumed it equal to the one of water (Basrawi, 2010;

Gebremedhin, et al., 2005) which is most likely an overestimate of the reality. It was indeed shown for

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instance that dairy cattle manure heat capacity ranges between 2.0 and 3.6 kJ.kg^-1.°C^-1, so far below the heat capacity of water (4.2 kJ.kg^-1.°C^-1). This reveals the complexity of handling this thermal need which depends on the feedstock used in the digestion process but also shows a lack of data on this subject.

This Master Thesis aims at building a comprehensive thermal model for digesters with a double- membrane roof, including all phenomena which are often neglected: the heat losses due to the evaporation of water in the biogas (Kishore, 1989) and the thermal input from electrical devices (Pain, et al., 1988). Little literature could moreover be found on GTDAD which is however characterized by an overall lower thermal consumption and a different type of heating system (M.Y. Qian, 2016). This Master Thesis also aims at providing a model for this technology.

3 Thermal modelling of an anaerobic digestion unit

The aim of the model is to be able to have an estimate of the thermal-self consumption of the plant, in order to:

- Size the heating system

- Forecast the available heat that can be used for other purposes (farm or domestic heating, Organic Rankine Cycle) in the case of a CHP unit.

- Calculate the profitability of a plant in the case of biogas injection into the grid.

Dry and wet AD plants have different structures, needs and inputs. Each technology should thus be studied separately to build a thermal model.

3.1 Modelling of a wet AD plant

A wet AD plant is composed of several buildings, inflows, outflows. The feedstock undergoes various steps in the process (Figure 6). It is thus necessary to identify the scope at first.

Figure 6 : The different steps of the process in a wet AD plant

One must properly define what needs to be taken into account, isolate subsystems and check that they don’t share common needs (so that all the thermal needs can be summed up in the end).

Once all the needs are identified, it is necessary to take into account the different heat inputs which were considered to be: the stirrers, the sun and the heating system that is to size.

Depending on the plants, the post-digester can be or not be heated. This depends on choices (such as the profitability of the plant) but also on the weather conditions. As heating the post-digester implies other thermal needs, two different model need to be built.

The different subsystems or needs that have been isolated are:

- The thermal losses of the digester (through the ground, the walls and the roof) (𝑄1) - The thermal losses in the incorporation tank (heat lost during pre-mixing) (𝑄2)

- The energy to warm up the feedstock from its initial temperature to the digester temperature (𝑄3)

- The energy used to evaporate all the water contained in the biogas as vapour (𝑄4) - The thermal losses of the pipes of the heating system (𝑄5)

Feedstock

Pre-

mixing Digester Post-

digester Phase

separation

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In the case of a heated post-digester, two additional needs shall be considered:

- The thermal losses in the pipes from the digester to the post-digester (𝑄6 )

- The thermal losses of the post-digester (through the ground, the walls and the roof) (𝑄7) Any other loss would not be relevant for this model. As an example, the thermal losses of the post- digester if the latter is not heated or the thermal losses during the phase separation would only lead to a decrease in the digestate temperature but there is no need to counterbalance it with a heat input as the digestate will be stored outside before agricultural spreading for instance.

One must however be careful about the fact that all the previously listed needs are not different heat inputs or necessary heating systems as the only heating systems are the heating coil in the digester and possibly in the post-digester. This is only a mean to identify the global heating requirement of the plant.

The heat to supply through the heating coils can consequently be calculated with:

∑ 𝑄_𝑖

5 (𝑜𝑟 7)

𝑖=1

= 𝑄_{𝑠𝑡𝑖𝑟𝑟𝑒𝑟𝑠}+ 𝑄ℎ𝑒𝑎𝑡𝑖𝑛𝑔 𝑐𝑜𝑖𝑙𝑠

3.2 Modelling of a dry batch AD plant

Modelling a GTDAD plant is far easier than a wet AD plant but there are loads of similarities between them.

Figure 7: Schematic of a GTDAD plant

A GTDAD plant (Figure 7) is made of only one building composed of 4 garages and 2 rectangular tanks for percolates. Heating coils enable to keep a target temperature in the percolates tanks whereas the garages are equipped with underfloor heating.

Digestate is transported with a wheel loader so there are no pipes for it. There are some pipes in order to pump percolates from the tanks to spray the garages but as the distances are quite small and the pipes are buried in the ground, the losses were assumed to be negligible. Similarly, losses through the warm water pipes were neglected as this value is far lower than the other losses.

Finally, before loading the garages, operators are asked to put the feedstock into windrows so that it can start to compost and warm up for 1 to 3 days. No specific heating is thus required to warm up the feedstock as this appears to be a natural reaction. In November, temperatures measured for these windrows were as follows: the surface temperature was around 13°C but some centimetres deeper the feedstock reached around 45°C and even up to 55-58°C at the very middle of the windrow. As a comparison, the target temperature of the garages is 45°C.

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The different subsystems or needs that have been isolated are:

- The thermal losses of the digester (through the ground, the walls and the roof) (𝑄₁) - The energy used to evaporate all the water contained in the biogas as vapour (𝑄4)

The heat to supply through the heating coils can consequently be calculated with:

𝑄₁+ 𝑄₄= 𝑄ℎ𝑒𝑎𝑡𝑖𝑛𝑔 𝑐𝑜𝑖𝑙𝑠

3.3 Thermal losses of the digester or post-digester (𝑸

_𝟏

)

For this part, let’s consider a digester for a wet AD plant. It is similar for a digester in a dry AD plant with small changes that will be explained below. The digester has been assumed as a steady-state system. In reality the feedstock inflow is not permanent, neither is the outflow. However, as the volume of the digester is much bigger than the transferred volumes, the influence on the inside temperature or the volume can be neglected.

The outdoor temperature changes continually as well as the sun irradiance. A transient model would thus be required to be able to simulate the losses across a day. The aim is however to have an estimate of the losses for each month. A steady-state model has consequently been built using average temperatures and average solar irradiance.

The different thermal interfaces that have been identified (Figure 8) are:

- The concrete apron (1) - The underground walls (2)

- The outside walls in contact with the digestate inside (3) - The outside walls in contact with the biogas inside (4) - The double-membrane roof (5)

Figure 8 : Losses from a digester or a post-digester

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The method that has been used to calculate the losses of the digester was to model it as thermal resistances. The electrical analogy is here valid under certain assumptions: thermal conductivities are assumed homogeneous, isotropic and independent of the temperature in the considered range, the model is steady-state and the radiative heat transfers can be linearized (Taine & Iacona, 2011).

The aforementioned losses were thus assumed to be in parallel and the effects that one can have on another were neglected. For instance, the vertical thermal gradient in the outside walls has been neglected:

the part of the wall in contact with the digestate is assumed to be at the same temperature everywhere and the same for the part of the wall in contact with the biogas.

The losses through the ground (1 & 2) cannot be properly modelled as series thermal resistances because of the shape of the temperature gradient through the ground. However, as a simple predictive tool to estimate the losses was required, the series thermal resistances were modelled as described on Figure 9 (at the bottom the inner thermal resistance, at the top the outer thermal resistance):

Conduction through the ground Conduction through the insulating material

Conduction through the concrete

Convection between the digestate and the concrete

Figure 9 : Model of thermal resistances for ground losses

The thermal resistances are calculated as follows:

- For conduction: 𝑅 =^𝑡_λ with 𝑅 the thermal resistance in K.m²/W, 𝑡 the thickness in m, λ the thermal conductivity W.m^-1.K^-1

- For convection: 𝑅 =¹_h with h the conductive heat transfer coefficient in W/m²/K - For radiative heat transfer of 2 face-to-face bodies: 𝑅 =_1−(1−ε^4.𝑇³^σ.ε¹^.ε²

1)(1−ε2) with σ the Stephan- Boltzmann constant, ε1 and ε2 the emissivities of body 1 and 2, and 𝑇 the average temperature of the bodies. (Enguehard, s.d.)

The equivalent resistance is the sum of all these resistances as they are in series, and the heat flux Ф in W is calculated as Ф =^∆𝑇_𝑅 . 𝑆 with 𝑆 the surface, 𝑅 the equivalent resistance and ∆𝑇 the overall temperature difference (between the inside and the outside).

To define a proper “thickness of earth”, a finite-element simulation has been run and the thickness was consequently chosen in order to match the results. The simulation was performed using free or open source software: FreeCAD to create the geometry, Gmesh for the meshing, Elmer as solver and Paraview for the visualization and exploitation of the results.

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Figure 10 : Temperature (K) distribution in the ground

Figure 11: Heat flux (W/m²) through the digester underground walls

The simulation was run for a digester with a diameter of 24m, an outside temperature of 0°C and a ground temperature at -6m of 10°C. The vertical thermal gradient through the ground was assumed to be linear. The aforementioned phenomena were simulated. The simulation gives the following results (Figure 10 & Figure 11): the losses represent 2025W through the apron (451 m², average heat flux density: 4.5 W/m²) and 2001W through the vertical walls (229m², average heat flux density: 8.74W/m²).

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For the losses through the outside walls (3 & 4), the model of thermal resistances is described on Figure 12.

Outside radiative heat transfer Outside convection Conduction through the insulating material

Conduction through the concrete Inside convection

Figure 12 : Model of thermal resistances for side walls

If the wall is in contact with the digestate inside, a forced convection due to the stirrers takes place between the digestate and the walls. If it is in contact with the biogas, the 1^st thermal resistance corresponds to natural convection of biogas.

The outside convection (𝑅1) and the radiative heat transfer (𝑅2) are two phenomena happening in parallel. The equivalent thermal resistance (𝑅𝑒𝑞) is calculated as:

1 𝑅_𝑒𝑞= 1

𝑅₁+ 1 𝑅₂

Depending on the weather, the outside convection can either be the natural convection of air on the walls of the digester or a forced convection due to wind. To simplify, an average value has been taken.

Similarly, the radiative heat transfer has been simplified. The insulating material act as a rate-limiting resistance and the other resistance which are in series consequently do not affect a lot the losses, this is why a simplification is possible. In the model, it has been assumed that the concrete walls are radiating towards only one material of emissivity equal to 1 and of temperature equal to the outside temperature. In reality, the concrete walls are radiating partly towards the ground, partly towards the atmosphere whose temperature is different from the outside temperature (Georgina Terradas-Ill, 2014).

The biggest difficulty is to model the double-membrane roof (5) and its possible insulating options in a simple 1D model. In an anaerobic digestion plant, it is necessary to have some gas storage. The technology chosen by NASKEO is the double-membrane roof. The lower membrane indeed acts as batch storage as it can go up and down whereas the upper membrane is fixed and acts as a weather protection. In order to keep a defined pressure inside the digester, air is blown in between the membranes and exhausted through a differential valve. This represents a first problem as air is blown from one side, is warmed up and exhausted at the opposite side and is consequently not at all a 1D problem.

In addition, insulation possibilities (3^rd membrane, insulation of the outer membrane) that will be described in Part 5 were considered.

Finally, the solar radiation must be included in the model as it can experimentally be noticed that temperatures increase quite a lot with the sun shining. All things considered, the different phenomena interacting on the thermal losses through the double-membrane roof – taking into account the different possible insulating options – are represented on Figure 13

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Figure 13 : Heat transfers through the double-membrane roof with insulation possibilities

Using the electrical analogy, the scheme is too complex to be able to compute an equivalent resistance using series or parallel resistances. The problem has been solved computing a linear system of 8 equations with 8 unknowns. The 8 unknowns are the intermediary temperatures (Ti) whereas the 8 equations are obtained using Millman’s theorem at the 8 nodes corresponding to these 8 temperatures. The system obtained can be written as:

{

𝑎_1,1. 𝑇₁+ ⋯ + 𝑎_1,8. 𝑇₈= 𝑏₁

⋮

𝑎_8,1. 𝑇₁+ ⋯ + 𝑎_8,8. 𝑇₈= 𝑏₈ The system is then written in a matrix format as 𝐴𝑋 = 𝐵 with

𝐴 = (

𝑎_1,1 ⋯ 𝑎_1,8

⋮ ⋱ ⋮

𝑎_8,1 ⋯ 𝑎_8,8) 𝑋 = ( 𝑇₁

⋮

𝑇₈) 𝐵 = ( 𝑏₁

⋮ 𝑏₈)

And the solution 𝑋 = 𝐴⁻¹. 𝐵 is obtained by reversing the matrix 𝐴. The thermal resistances and the temperatures are now known; it is thus possible to compute the heat flux.

The total losses for the digester (𝑄1) are consequently the sum of all the heat flux on the different surfaces.

cv: convection cd: conduction co: condensation R: radiation cv

cv+co cv cv

cv+co cv

cv cv

cv

cd

R R

Solar irradiation

Air blown

T

₁

T

₂

T

₃

T

₄

T

₅

T

₆

T

₇

T

₈

T

_inside

T

_outside

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For a dry AD plant, computing the different losses through the ground (1), the walls (3 & 4), the double-membrane roof (5) of the garages and the concrete roof (6) of the percolate tanks are calculated identically as for a wet AD plant. The model has just to be adapted to match the geometry.

Contrary to a wet AD plant, there is no convection of digestate as it is a solid pile. The inner thermal resistance corresponds to the conduction of the digestate over a thermal boundary layer which was assumed to be 20cm. The thermal resistances (3) thus become for side walls (

Figure 14):

Conduction through the concrete Conduction through the digestate

Figure 14 : Model of thermal resistances for side walls

Losses through the ground (1) were computed likewise, the only difference for the garages is that the inner temperature was set to 45°C due to underfloor heating.

For the doors which are parts of side walls but not in contact with the digestate (4), it has to be taken into account that the door is filled with an insulating material. The structure is however made of steel which creates a thermal bridge. Therefore, the doors were modelled as follows (Figure 15), with a surface of insulating material which amounts to 70% of the total surface of the door and 30% for steel:

Outside radiative heat transfer Outside convection Conduction through the insulating material Conduction through the

metal Inner convection

Figure 15 : Model of thermal resistances for the doors

3.4 Thermal losses in the incorporation tank (𝑸

_𝟐

)

The incorporation tank is a cylindrical tank as the digester and the steady-state losses are consequently modelled similarly. The difference comes from the fact that this tank can either have an isolated covering or just be open (Figure 16).

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Figure 16 : Uncovered (left) and covered (right) incorporation tanks

In the case an isolated covering the thermal resistances of the roof are (Figure 17):

Conduction through the concrete

Inside radiative heat transfer Internal convection

Figure 17 : Model of thermal resistances through an insulated roof

whereas if the tank is open, it simply becomes (Figure 18):

Radiative heat transfer Convection

Figure 18 : Model of thermal resistances for an uncovered tank

The incorporation tank is however not filled with feedstock all day long. It is used temporary to mix the feedstock and the digestate and then emptied into the digester. The thermal losses should consequently be computed as two different parts: the steady-state losses when the tank is full and the losses corresponding to the cooling of the volume remaining in the tank after emptying it.

The steady-state losses are calculated as for the digester but during a smaller time period, approximately 6 hours a day which corresponds to the average time needed by the operators for the incorporation of new feedstock. The temperature of the mixture held in the tank is a function of the feedstock temperature and the quantity of digestate pumped back to the incorporation tank in order to dilute the feedstock. Knowing the DM content of the digestate and the feedstock, it is possible to compute the volume of digestate to pump back in the incorporation tank – and consequently the temperature of the mixture – in order to reach a target DM content of 11.5% to ensure that the mixture can be pumped.

The cooling of the remaining volume which is a transient state is consequently a step-by-step calculation:

𝑚. 𝐶_𝑝. ∆𝑇 = 𝑄̇. ∆𝑡

where 𝑚 is the mass of the cooled volume, 𝐶𝑝 the feedstock heat capacity, ∆𝑇 the decrease in temperature of the volume during the time step ∆𝑡 and 𝑄̇ the thermal power lost which depends on the temperature of the cooled volume. An appropriate time step must therefore be chosen so that the decrease in temperature is not too big during a time step.

Similarly, the losses due to the pipes in between the digester and the incorporation tank are separated between the steady-state losses of the pipes during the daily time needed to pump the volume of one tank to the other and the cooling of the volume remaining in the pipes after pumping. As this volume is quite small and the pipes are not insulated, it has been assumed that the inner volume reaches the outer temperature at the end of the cooling period.

The total losses (𝑄2) are consequently the sum of these transient and steady-state losses.

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3.5 Energy needed to warm up the feedstock (𝑸

_𝟑

)

The method used to estimate this thermal need is mainly based on experience and barely has a theoretical anchor. The initial temperature of each waste is a function of the outdoor temperature to which a temperature supplement is added. This value is purely based on experience and expresses the fact that some wastes start to ferment when they are stored which leads to an increase in their temperature.

Table 1 shows an example of estimated temperatures for different wastes for a plant being built at the moment in Pays de Loire, France. Table 2 exhibits some properties of the feedstock.

Table 1 : Examples of feedstock for a project in Pays de Loire, France

Month Unit Cattle Manure Grass

clippings Outdoor

January °C 18 8 6.6

February °C 18 8 7.2

March °C 21 11 9.9

April °C 23 13 12.1

May °C 27 17 15.6

June °C 30 20 18.7

July °C 31 21 20.4

August °C 32 22 20.5 September °C 29 19 17.9 October °C 26 16 15.0 November °C 21 11 10.3 December °C 18 8 7.2 Average °C 24 14 13.4 Temperature

supplement °C 11 1

From this point, the energy required to warm up the feedstock is calculated as 𝑄₃= 𝑚 𝐶𝑝 ∆𝑇

where 𝑚 is the mass of feedstock, 𝐶𝑝 the feedstock heat capacity, ∆𝑇 the difference between the digester temperature and the feedstock initial temperature.

Table 2 : Examples of feedstock properties

Properties Unit Cattle Manure Grass clippings

Fresh matter (FM) t/year 7421 1000

Dry matter (DM) content (%) t DM / t FM

(%) 28 26

Organic matter (OM) content (%) t OM/ t DM

(%) 81 77

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Density t FM / m³ 0.6 0.6

Estimated degradation yield of Organic

matter (%) t OM/t OM (%) 60 70

Biochemical Methane Potential (BMP) in laboratory

Nm³CH4 / t

OM 250 300

Forecasted Biochemical Methane Potential Nm³CH4/ t OM 247 297

Nm³CH4 / t FM 56 59

Forecasted methane production Nm³CH4 / hour 48 7

Nitrogen content / FM kg N / t FM 4.8 5.7

Phosphorus content / FM kg P / t FM 1.1 0.8

Potassium content / FM kg K / t FM 7.0 5.2

Feeding process Liquid/Solid Solid Solid

Since the water concentration in the feedstock is high (DM content of the overall feedstock <20%) the feedstock heat capacity has been taken equal to the one of water 𝐶𝑝 = 4185 J.kg^-1.K^-1 (Basrawi, 2010).

This value is deliberately taken higher than in reality in order to be able to size the heating systems. Heating of feedstock is indeed one of the major items of the plant’s thermal self-consumption. In reality, the values are however lower: the specific heat of manure ranges for instance from 2.0 kJ.kg^-1.K^-1 to 3.6 kJ.kg^-1.K^-1 (M.A. Nayyeri, 2009).

For particular plants it has however been considered that some digestate could be recirculated in order to dilute the feedstock when the latter has a too high DM content. This digestate would most often come from the post-digester which can be unheated. In this case, a specific calculation module is required to estimate the temperature of the digestate which will need to be heated up again to the digester temperature. This module is explained in part 3.9.

3.6 Energy to evaporate water (𝑸

_𝟒

)

A first experience in the production of biogas reveals that the biogas produced is always saturated with water vapour. An important question related to this observation is to know the origin of the energy which is required to evaporate water. The lack of literature on this subject might express a poor understanding of the phenomenon. In none of the literature studied for the subject the energy to evaporate liquid water into the biogas has been considered as a thermal need. On the other hand, water vapour is barely a product of the methanation reaction, even rather a reactant (Deublein & Steinhauser, 2011).

Consequently, it can be assumed that, if the water vapour is not produced in a chemical reaction, it has been evaporated from liquid water, which requires energy.

Therefore, this has been assumed as a thermal need in the model: a thermal input is required to balance the energy lost in this way. Assuming that the biogas is a perfect gas, these losses are calculated as:

𝑄₄=𝑃_𝑠𝑎𝑡. 𝑉_{𝑏𝑖𝑜𝑔𝑎𝑠}. 𝑀_𝐻₂_𝑂 𝑅. 𝑇_{𝑏𝑖𝑜𝑔𝑎𝑠} . 𝐿_{𝑒𝑣𝑎𝑝}

where 𝑄 is the energy lost with this phenomena (or the energy input required to balance it) over one year, 𝑇_{𝑏𝑖𝑜𝑔𝑎𝑠} the temperature of the biogas produced, 𝑃_𝑠𝑎𝑡 the saturation vapor pressure at this temperature,

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𝐿_{𝑒𝑣𝑎𝑝} the latent heat of evaporation at this temperature, 𝑉_{𝑏𝑖𝑜𝑔𝑎𝑠} the volume of biogas produced over one year, 𝑀𝐻₂𝑂 the molar mass of water and 𝑅 the constant of the perfect gas.

3.7 Thermal losses of the pipes of the heating system (𝑸

_𝟓

)

Hot water is used in order to heat the plant. It is either produced by the CHP engine or by a boiler and then flows through pipes into the digester heating coils for instance. The heat transferred in the coils is actually used as a heat source however the losses in the pipes between coils and the engine is really a loss and has to be considered.

A distinction is done between the underground pipes and the outdoor pipes. The outdoor pipes have the following thermal resistance scheme (Figure 19):

Outside convection

Conduction through the insulating material Conduction through the pipe material

Inside convection

Figure 19 : Model of thermal resistances for outdoor pipes

where 𝑅 =^ln(

𝐷𝑜𝑢𝑡𝑒𝑟 𝐷𝑖𝑛𝑛𝑒𝑟)

2𝜋𝐿𝜆 is the thermal resistance (in K.W^-1) for conduction taking into account the cylindrical shape of the pipe; 𝐷_{𝑖𝑛𝑛𝑒𝑟} and 𝐷_{𝑜𝑢𝑡𝑒𝑟} the inner and outer diameters, 𝐿 the pipe length and 𝜆 the thermal conductivity of the material.

Similarly, for the underground pipes (Figure 20):

Conduction through the ground Conduction through the insulating material

Conduction through the pipe material Inside convection

Figure 20 : Model of thermal resistances for underground pipes

As for the pipes between the digester and the incorporation tank, one must distinguish two situations: a steady state and the cooling of the pipes when the warm water circulating pump is off.

3.8 Case of a heated post-digester (𝑸

_𝟔

+ 𝑸

_𝟕

)

When the post-digester is an unheated tank, all the thermal losses happening after the digester don’t need to be taken into account: it only results in a gradual decrease in temperature of the digestate.

Conversely, whenever the post-digester is heated, the heating coils should balance:

- The thermal losses in the pipes from the digester to the post-digester (𝑄₆)

- The thermal losses of the post-digester (through the ground, the walls and the roof) (𝑄₇) The thermal losses in the pipes are calculated in a similar manner as for those in between the incorporation tank and the digester whereas the losses from the post-digester are calculated as for the digester (the two tanks are similar; they might just have a different size).

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The thermal need can however be lower as the simple addition of the two aforementioned losses:

when the choice is made to heat the post-digester at a lower temperature than the digester, the energy input from the heating coils necessary to keep the post-digester at the target temperature has to been diminished by the amount of the heat regularly provided by the warmer inflow of digestate from the digester. The energy equilibrium can consequently be written as:

𝑄_{𝑐𝑜𝑖𝑙𝑠}+ 𝑚. 𝐶_𝑝. ∆𝑇 = 𝑄₆+ 𝑄₇

where 𝑄6 are the thermal losses from the pipes, 𝑄7 the thermal losses from the post-digester, ∆𝑇 the difference in target temperatures between the digester and the post-digester, 𝑚 the mass of digestate transferred from the digester to the post-digester over the period considered and 𝐶𝑝 the specific heat of digestate.

3.9 Calculating the temperature of recirculated digestate

As previously mentioned, liquid digestate that has undergone a separation phase can be reused and reincorporated in the process when the feedstock has an overall too high DM content. In that case, it is necessary to know the temperature of this liquid digestate to know the heat input necessary to bring it back to the target temperature of the digester (as mentioned in part 3.5). In addition, one would like to estimate the temperature of the post-digester if the latter is unheated to know if it would be sufficient for the biological process.

To do so, one must compute the losses in temperature of the digestate after each step, i.e.:

If the post-digester is not heated:

- In the pipes from the digester to the post-digester - In the post-digester

And then in any case:

- In the pipes from the post-digester to the phase separation process - In the storage tanks after phase separation

- In the pipes from the storage tanks to the incorporation tank For each step, the losses in temperature are calculated as

𝑚̇. 𝐶_𝑝. ∆𝑇 = 𝑄̇

where 𝑚̇ is the mass flow of digestate, 𝐶_𝑝 the digestate specific heat capacity, ∆𝑇 the decrease in temperature for this step and 𝑄̇ the thermal power lost which is a function of the temperature of the digestate under this step. This calculation is consequently an iterative process which converges after few steps as the decrease in temperature is relatively small. In reality, the decrease in temperature is small enough not to need to iterate the calculations for all the different steps except inside the digester.

Figure 21 : Digestate cooling in December for a project in Pays de Loire, France Pipes digester

 post-digester Post-digester (iteration)

Pipes post- digester 

phase separation Storage tanks

Pipes storage tanks

incorporation tank

-0.3°C -5.8°C -0.4°C -0.8°C -0.4°C

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As the losses depends on the inside temperature, they also depend on the outside temperature. The scheme here above (Figure 21) shows the decrease in temperature for each step for the project in Pays de Loire, France, in case of an unheated post-digester in December (average outside temperature: 7.2°C). As a result, the temperature of the liquid digestate to recirculate would be 29.3°C and the inner temperature of the post-digester 30.9°C.

3.10 Heat inputs

To balance all these losses, 3 main heat inputs were modelled: the sun, the stirrers and the heating coils. The power delivered by the heating coils is actually the thermal need of the plant, the thermal power that the engine is supposed to deliver to ensure the thermal equilibrium of the plant. The model is precisely built in order to compute this value.

The sun irradiance has been directly modelled within the complex modelling of the double- membrane roof. It indeed impacts the different intermediate temperatures of the membranes and consequently acts more as a lowering agent in the losses through the membranes than as a real heat input in the system. The sun irradiance has only been taken into account on the surface of the roof. Its impact on the side walls or the other tanks (incorporation tank, storage tanks…) was neglected. A homogeneous irradiance on the whole surface of the roof was additionally assumed. This thermal model indeed only takes into account 1D effect. Moreover, the ultimate goal is to have an averaged thermal self-consumption of the plant over one month: a single average value – including all possible reasons for change: day and night, sunny or cloudy days, sun elevation … – was used to model this phenomenon.

Finally, one additional heat input (𝑄𝑠𝑡𝑖𝑟𝑟𝑒𝑟𝑠) was modelled: the power delivered by the stirrers. Once the feedstock/digestate has been set in motion, no more mechanical energy is delivered to it. Consequently, it was considered that the energy from the stirrers is converted in thermal energy (the mechanical energy delivered is constantly dissipated as heat due to friction). The efficiency of the stirrers reaches on average 90% of electrical power converted into mechanical power. Consequently, for external stirrers it can be assumed that 90% of the electrical power of the stirrer is converted as heat transferred to the digestate (10%

is lost as heat from the motor located outside of the tank) whereas this value reaches 100% for submerged stirrers. One must then consider the average daily running time of the stirrers to estimate their global thermal input.

The power of the stirrers is significant and has to be considered as a “free” thermal input so far as stirring is necessary from a biological point of view and reduces the need for heating through coils. However, this subject has surprisingly never been considered in the literature studied – which only focuses on the losses. The assumptions made have a significant impact on the model as the power of the stirrers’ amounts to several kilowatts. Uncertainty is whether a part of the mechanical power from the stirrers could be used to break chemical bonds.

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4 Analysis of the results

From the model built as described in the previous part, it is possible run calculations in order to understand the distribution of the losses or energy needs. This finally aims at suggesting improvements to increase the thermal performance of the plants.

4.1 Wet AD

A simulation has been carried out for a wet digestion plant characterized by:

- 12 kT of incoming feedstock per year - 10kT of digestate recirculated per year - 1,250,000 Nm³ of biogas produced per year - The sizes of the tanks defined in Figure 22

Figure 22 : Size of the plant simulated

In the base case, with a heated digester and an unheated post-digester, the results obtained are as follows (Figure 23):

Figure 23 : Distribution of the heating requirements over a year Digester

43%

Pre-mixing tank 5%

Feedstock heating

46%

Pipes 0%

Water evaporation

6%

10,5m 5,5m

24m 6m

6m

22m

Total: 682 MWh

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All the losses amount to 682MWh over a year. The thermal input from the stirrers amounts to 226MWh (among which 178MWh represents the stirrers of the digester and 48MWh the stirrers of the incorporation tank). The heat to provide with heating coils is therefore the difference between the total losses and the stirrers input, i.e. 455MWh a year.

It can be noted that the two main energy losses are feedstock heating and the thermal losses of the digester. Acting on the initial temperature of the feedstock is rather complicated. One can either try to improve storage modes to keep the feedstock as warm as possible or use bulky and costly systems to try to preheat the ingoing feedstock with the outgoing digestate. On the other hand, acting on the digester losses can be much easier. Therefore, the different losses from the digester were isolated (Figure 24 & Figure 25):

Figure 24 : Distribution of digester losses for December (average T=7°C)

Figure 25 : Distribution of digester losses for August (average T=20.5°C) Double-membrane

roof79%

Walls, biogas-air 2%

Walls, digestate-air 5%

Underground walls 3%

Concrete apron

11%

Double-membrane roof Walls, biogas-air 70%

2%

Walls, digestate-air 5%

Underground walls 5%

Concrete apron 18%

Total: 41.7 kW

Total: 24.5 kW

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The losses from the double-membrane roof clearly represent the biggest part of the losses at any season in the year. This can easily be understood as all the other part of the digester are insulated: the roof thus represents a thermal bridge for heat losses.

Another option is to heat the post-digester as well to keep it at a temperature of 39°C. This can be done in order to improve the biological activity and to ensure the complete biodegradation of the feedstock.

In that case, feedstock heating, the losses of the digester and the losses of the post-digester are the 3 main reasons for thermal self-consumption (Figure 26).

Figure 26 : Distribution of the annual heating requirements (no additional roof insulation, heated post-digester)

It can be noticed that heating the post-digester increases dramatically the annual thermal self- consumption (+200 MWh) as compared to the first case. This solution should consequently only be considered in case of the valorisation of biogas through a CHP engine with an excess of heat available. The digester indeed represents up to 90% of the production of biogas: heating the post-digester to improve the biological activity is therefore not necessary.

4.2 Dry AD

A simulation has been carried out for a dry digestion plant characterized by:

- 4 garages of size: 22m x 5.6m x 5m - Percolate tank: 15m x 5m x 4m

- Annual biogas production: 580,000 Nm³ - Feedstock: 9kT per year

The overall annual heat consumption amounts to 322MWh for such a plant (Figure 27).

Digester 33%

Post-digester 29%

Feedstock heating 29%

Water evaporation 5%

Pre-mixing tank

4% Pipes

0%

Total: 882 MWh

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Figure 27 : Annual losses for the simulated dry AD plant

As no feedstock heating is required for a dry AD plant thanks to pre-composting in windrows, improvements can consequently only be done on the buildings insulation. The same conclusions can be drawn for a dry digestion plant as for a wet digestion plant: the double-membrane roof represents most of the losses from the buildings, but to a lower extent. The global surface of walls and apron is indeed much larger than for wet digestion and consequently stands for a higher part of the losses. In addition, the percolate tank roof which is not insulated because of equipment on its top is also responsible for a significant part of the losses (Figure 28).

Figure 28 : Distribution of the losses in December (average outside temperature: 5°C) Buildings

97%

Water evaporation 3%

Total: 322MWh

Walls biogas-air

2% Doors

2% Walls digestate-air 5%

Concrete apron 15%

Percolate tank roof 17%

Percolate tank walls biogas-

air Percolate tank 1%

walls percolate-air 1%

Double- membrane roof

57%

Total: 44.3 kW

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5 Optimization

Reduction in thermal self-consumption is above all a major target for plants designed to produce and purify biogas in order to inject it into the national grid. Heating the plant implies burning biogas which represents a loss of earnings. Therefore, improving the thermal efficiency of the plant is a way to improve the profitability of the plant. On the other hand, the business model of CHP plants relies on electricity sales:

heat is anyway produced and the thermal self-consumption of the plant is therefore usually not a problem.

This model however enables to assess the feasability of AD plants in cold climates – in order to check if the heat consumption is lower than the heat produced – or the profitability of an ORC system for instance. In both cases, knowing how to reduce the thermal self-consumption would be profitable.

In the previous part, it was identified that most of the losses from the tanks (digester, post-digester) are due to a poor insulation of the roof. Insulating the roof has thus been the main option studied. Two possibilities were considered: either putting a 3^rd membrane inside the biogas to reduce the inner convection or insulating the upper membrane. In case of a 3^rd membrane (Figure 29), the gasholder membrane should keep acting as batch storage. This implies that the 3^rd membrane should contain holes in order to let the biogas go up and down. Polyethylene Foam is additionally added on a net to reduce heat transfers between the volumes of biogas.

Figure 29: Insulation with a 3^rd membrane

To insulate the upper membrane, Polyethylene Foam could be welded to it. However, it would not be possible to cover the whole surface with the insulating material and the thermal bridge thus created should be taken into account. This solution is not the easiest one as the membrane is supple and cannot consequently be loaded with too much insulation on it.

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5.1 Wet AD

For a wet AD plant, the losses from the roof clearly represent the biggest part of the losses from the digester at any season in the year. Any improvement in the digester insulation should consequently be related to the double-membrane roof. The solutions aforementioned were simulated for the same plant as in part 4.1.

Figure 30 : Roof losses for December (average T=7°C)

Both solutions enable dramatic reduction of the losses from the digester. However, from a technic- economic point of view, the 3^rd membrane enables slightly better results while being cheaper. In particular, Figure 30 shows that this solution enables a 60% decrease in the losses from the roof. The comparison (Figure 31) has therefore been drawn between the base case with a simple double-membrane roof and in case of a 3^rd membrane on the digester and post-digester.

Figure 31 : Annual heat requirements

The digester losses are logically much lower (about half the value) with an additional thermal insulation which directly impacts the total yearly thermal self-consumption (163 MWh lower with a 3^rd

0

10

20

30

40 R oof loss es (kW)

3rd membrane insulation

Base case - Double-membrane

0 100 200 300 400 500 600 700 800

Digester Pre-mixing

tank Feedstock

heating Pipes Water

evaporation Total

Heat requirements (MWh)

Base case

3rd membrane insulation

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membrane on the digester and post-digester). Additionally, the energy needed to warm up the feedstock is lower. 10kt a year of outgoing digestate are indeed recirculated in the plant. Insulating the post-digester enables to increase its inner temperature and consequently the temperature of the outgoing digestate: the energy required to heat it up back to the digester temperature is consequently lower. However, in a case where digestate is not recirculated, insulating the post-digester would lead to no reduction in the thermal self-consumption. This would only possibly lead to a better yield of biogas production in the post-digester because of a higher temperature.

Conversely, if the post-digester is heated, feedstock heating, the losses of the digester and the losses of the post-digester are the 3 main needs for thermal self-consumption. In that case, a 3^rd membrane insulation really has an interest.

Figure 32: Annual heating requirements with a heated post-digester

By reducing of about half the losses from the 2 main tanks (Figure 32), the 3^rd membrane insulation has a strong impact on the overall thermal need (240 MWh lower per year). It can be noted however that in this case the energy required for feedstock heating is not reduced: in both case the digestate in the post- digester is at the same target temperature (39°C). Adding a 3^rd membrane only reduces the need for heating the post-digester but does not impact the temperature of the outgoing digestate that will be recirculated.

5.2 Dry AD

Similarly, simulations have been conducted for the same plant as in part 4.2 but equipped with the solutions aforementioned.

The different insulating possibilities lead to significant decreases in the losses from the buildings. Adding a 3^rd membrane on the garages enable a reduction of 20% of the heat losses in December (Figure 33). Due to a lower share of the losses from the roof, the impact of insulation is also lower than for a wet AD plant.

0 100 200 300 400 500 600 700 800 900 1000

Heating requirements (MWh)

Base case

3rd membrane insulation

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Figure 33 : Distribution of the losses in December with 3^rd membrane insulation (average outside temperature: 5°C)

The yearly thermal self-consumption for the different cases is shown in Figure 34.

Figure 34 : Annual heat consumption for GTDAD plants with different insulations

The same conclusions appear as for a wet AD plant when it comes to comparing the efficiency and the profitability of the insulation of the outer membrane with the 3rd membrane. As mentioned previously, the reduction in heat consumption is not as big as for a wet AD plant. Still with a yearly gain in thermal self- consumption of 57 MWh corresponding to a 18% decrease, adding a 3^rd membrane remains an attractive option.

Walls biogas-air

3% Doors

2% Walls digestate-air 6%

Concrete apron 18%

Percolate tank roof 22%

Percolate tank walls biogas-air

1%

Percolate tank walls percolate-air

2%

Double-membrane roof46%

0 50 100 150 200 250 300 350

Heat consumption MWh

Base case 3rd membrane

insulation outer membrane Total: 35.1 kW

Modelling, analysis and optimization of thermal energy balance in anaerobic digestion