Methodology for the design and economic assessment of anaerobic digestion plants to produce energy and biofertilizer from livestock waste

Science of the Total Environment 685 (2019) 1169–1180

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Science of the Total Environment journal homepage: www.elsevier.com/locate/scitotenv

Methodology for the design and economic assessment of anaerobic digestion plants to produce energy and biofertilizer from livestock waste Sergio Arango-Osorio, Oscar Vasco-Echeverri ⁎, Gabriel López-Jiménez, Jorge González-Sanchez, Idi Isaac-Millán Grupo de transmision y distribucion de energia (T&D), Facultad de Ingenieria Quimica and Facultad de Ingenieria Electrica, Universidad Pontificia Bolivariana, Circular 1a No. 70 – 01, Medellín, Colombia

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T

• The methodology is programmed in MS Excel. • It can be used to calculate basic engineering anaerobic digestion plants. • Technical parameters such as energy production efficiency can be obtained. • Performance of a strategy to calculate capital and operating expenses for an anaerobic digestion plant • The financial viability of the project is assessed by calculating the net present value.

a r t i c l e

i n f o

Article history: Received 10 May 2019 Received in revised form 30 May 2019 Accepted 2 June 2019 Available online 19 June 2019 Editor: Huu Hao Ngo Keywords: Anaerobic digestion Electric generation Methodology Bioreactor design Biogas Economic assessment

a b s t r a c t The generation and poor disposal of waste from livestock industries is the major cause of pollution of water sources, soil, and air. Therefore, profitable alternatives are required for their correct disposal and use. Anaerobic digestion plants are a technologically viable solution to overcome this problem. In this study, it is proposed a methodology for the design and economic assessment of projects using anaerobic digestion plants to produce electrical energy, thermal energy, and biofertilizer from livestock waste. The methodology is developed based on the assumption that the process is mainly composed of an anaerobic digester and an electric generator having a Diesel-cycle internal combustion engine. It is programmed in “MS Excel” sheet and assessed using technical and economic data from a three real anaerobic digestion plants. The methodology obtains technical parameters such as energy production efficiency with an average difference of 35% compared to the real plants data. In addition, the unit capital costs are calculated, obtaining a value of €3789/kW with a difference of 21.1%, as well as unit operating costs of €729/kW per year with a difference of 15.2%. The financial viability of the project is assessed by calculating the net present value and obtaining €577,050 with a difference of 17.8% and an internal rate of return with a percentage difference of 3%. The proposed methodology specifies the technical parameters and the basic engineering of an anaerobic digestion plant in a stationary state, where the basic streams and dimensions of primary equipment, such as anaerobic reactors and electric generators, are specified. Moreover, the methodology calculates capital and operating expenses for an anaerobic digestion plant, which may be useful to assess the technical and financial feasibility for a project of this type. © 2019 Elsevier B.V. All rights reserved.

⁎ Corresponding author. E-mail address: [email protected] (O. Vasco-Echeverri).

https://doi.org/10.1016/j.scitotenv.2019.06.015 0048-9697/© 2019 Elsevier B.V. All rights reserved.

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1. Introduction In the agricultural industry, livestock waste is traditionally discharged directly into soil, waterways, or applied to soils as a fertilizer after composting. Since this practice was found to lead to the degradation of air, soil, surfaces water represented by water bodies like lakes, oceans, seas and natural streams, new regulations for protecting the environment have been promulgated to control land application of animal manure (Kuriqi et al., 2016) (Gebrezgabher et al., 2010). For several decades, new technologies, such as anaerobic digestion, have been studied. In this process, organic matter contained in the waste is converted into biogas and biofertilizer in the absence of molecular oxygen (Vasco, 2016). In fact, implementing anaerobic digestion plants for treating livestock waste is an ideal solution that can foster the production of electricity via non-conventional renewable fuels as well as the production of a treated fertilizer for agricultural lands, thus avoiding the release of methane into the atmosphere as well as animal waste into the soil and water sources (Hidalgo and Martín-Marroquín, 2015). In the last decades, researchers around the world have a high interest to the organic matter, especially to the nutrients (phosphorus, nitrogen) concentrations because the high presences of nutrients in the water cause algae growth, oxygen depletion and other additional problems also (Kuriqi, 2014). Although this technology is extensively used for treating the waste produced in the agricultural industry, a methodology for its design and operation is yet to be established. Igoni et al. classified anaerobic reactors by their operating conditions according to the type of waste. Their study determines that “Low-Rate Anaerobic Sludge Digesters” are used for liquid manure with solid content not exceeding 2%; “Complete-Mix-Digesters” are used for animal waste with solid content between 2% and 10%; and “Plug Flow Reactors” for waste with solid content between 11% and 13% (Hilkiah Igoni et al., 2008). The sizing of these digesters primarily lies in the calculation of their reaction volume, which depends on the hydraulic retention time and the feed rate of the waste (Lemos Chernicharo, 2007). For designing these reactors, the detailed design may be determined using heuristic rules (Henao and Velásquez, 2010). Another factor to consider while designing an anaerobic digestion plant is the operating temperature and the mechanical elements (mixers and pumps) that require energy for its operation because the energy demand of the plant cannot exceed the energy produced by biogas (Gebremedhin and Inglis, 2007). Therefore, predictive models are required to calculate the production of biogas. These models are obtained from experimental studies known as biochemical methane potential (BMP) (Gebremedhin and Inglis, 2006). Based on the calculations of the quantity of biogas produced and through the simulation of thermodynamic cycles, it is possible to estimate the quantity of electrical energy produced by an internal combustion engine generator and calculate the operating conditions required to achieve a certain efficiency (Moran et al., 2014a)(Afazeli et al., 2014). BMP also determines the amount of solid eliminated in the anaerobic digestion process, which helps estimate biofertilizer production (Carhuancho et al., 2015). Once the technical parameters have been calculated, another aspect that must be considered is the economic viability. At this point, the capital (CAPEX) and operational (OPEX) expenditure, as well as financial parameters, such as the net present value (NPV) and the internal rate of return (IRR), are estimated. These values basically define the financial viability of the project and determine the economic and environmental benefit of implementing this technology (Ruiz et al., 2018). In this study, we integrate different methodologies for the energetic and economic characterization of livestock waste, reactor design, predictive models for biogas production, simulation of thermodynamic cycles for power generation, as well as CAPEX and OPEX models for the conceptual and basic engineering design of anaerobic digestion plants. The proposed methodology allows for calculating technical and financial parameters such as the volume and dimensions of the anaerobic

reactor, electric generator power, process streams, CAPEX, OPEX, NPV, and IRR. The methodology is programmed in an “MS Excel” sheet and assessed based on the environmental and economic data reported by Ruiz (Ruiz et al., 2018) for an anaerobic digestion plant located in Asturias, Spain. 2. Methods To develop a mathematical model for the basic design of an anaerobic digestion plant to treat agricultural waste, as well as to estimate the possible economic benefits that this may bring to a specific project. The following sections thoroughly describe the experimental procedures and calculation models that were used to execute this methodology. The mathematical model proposed to execute the steps is limited to the design of an anaerobic digestion plant that was composed primarily of a low-rate anaerobic sludge digester, a complete-mix-digester, or a plug flow reactor (DA-1). An electric generator with a diesel-cycle internal combustion engine is shown in the process flow diagram of Fig. 1. The methodology starts with characterizing the waste, where the feeding stream is specified. Moreover, the mass flow, the density, the temperature, the pressure, and the content of total and volatile solids are measured, production yield and the concentration of fixed gases in the biogas are determined using a biochemical methane potential (BMP) study. Table 1 lists the process streams from Fig. 1 and specifies the variables that must be fed to the mathematical model and the variables that are calculated. The hydraulic retention time and the environmental conditions of the site, where the project will be developed, must be specified. From these values, the dimensions of the main equipment, the diameter and the height of the anaerobic reactor (digester), and the electrical power required for the generator are calculated. Table 2 describes the process equipment considered in the calculation model, as well as the input and output variables of the model. HRT: hydraulic retention time (days), Pa: atmospheric pressure (bar), Ta: average of annual ambient temperature (°C), D: diameter (m), L: length (m), PW: power (kW). 2.1. Waste characterization Waste characterization provides important input parameters for designing the anaerobic reactor. First, it helps to determine the type of reactor according to the total solid concentration (Lemos Chernicharo, 2007)(Oregon Department of Energy, 2017). Second, it calculates the biogas production via kinetic models based on energy parameters, such as methane production yield calculated via BMP test, and environmental parameters, such as the concentration of volatile solids

Fig. 1. Process diagram of an anaerobic digestion plant to produce electrical energy and biofertilizer.

S. Arango-Osorio et al. / Science of the Total Environment 685 (2019) 1169–1180 Table 1 Description of process flow diagram currents for the anaerobic digestion plant for the production of electric energy and biofertilizer. Stream No.

Stream Name

1 2 3 4 5 6

Waste inflow Biogas produced B-F C.G C.G.H Exhaust gases Cold exhaust gases Air generator Energy consumption Energy injection

7 8 w1 w2

Mass Flow

Properties Composition ρ

T

P

ST SV βo CH4 CO2 O2 E. F

I C C C C C

I C – C C C

I C – C C C

– C – C C C

I – – – – –

I – – – – –

I – – – – –

– I – – – –

– I – C C C

– I – C C C

– – – – – –

C

C

C

C

–

–

–

–

C

C

–

C

C

I

I

–

–

–

–

–

C

–

–

–

–

–

–

–

–

–

–

–

C

–

–

–

–

–

–

–

–

–

–

C

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flows upward, the sludge particles and other floating materials accumulate on the surface and form a scum layer. The substrate inside the reactor is stratified into four zones: scum zone, clarified liquid zone, active digestion zone, and stabilized sludge zone (Lemos Chernicharo, 2007). To leverage the hot exhaust gases of the electrical generation system, a heating jacket is implemented in this digester, as shown in Fig. 2. This digester is sized according to the method proposed by Henao and Velásquez (2010). Eq. (2) is used to calculate its diameter, and Eq. (3) is used to determine its height. vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u   4:V 3 DR ¼ u t L π: :ð1−Vf F Þ D R

LR ¼

ð2Þ

  L :DR D R

ð3Þ

3

I: input variable, C: calculated variable, ρ: density (kg/m ), T: temperature (°C), P: pressure (bar) TS: total solids (%), VS: volatile solids (%), βo: Yield according to Biochemical Methane Potential Tests (LCH4/gsv), CH4: methane content (%), CO2: carbon dioxide content (%), O2: oxygen content (%), E.F: Energy Flow (kWh/h), B-F: Biofertilizer (t/h), C.G: combustion gases (t/h), C.G.H.: combustion gases to heat, mass flow (t/h).

(Gebremedhin and Inglis, 2006). As a first step, the methodology recommends the environmental characterization of the waste to quantify the organic content that will be fed into the plant as Kreuger recommends (Kreuger et al., 2011)(Angelidaki et al., 2009). However, energetic waste characterization is performed through a BMP test, which determines the methane production yield per amount of organic material that is fed or disposed (Fitamo et al., 2017). The methodology proposes as a second step to conduct this BMP characterization as per the experimental procedure proposed by Kafle and Chen (2016). 2.2. Anaerobic reactor design Once the data have been collected for the environmental and energetic characterization of the selected waste, the methodology proposes to continue with designing the anaerobic reactor. This design is based on three aspects, i.e. the selection of the type of digester; the calculation of the reaction volume based on Eq. (1); and the sizing of the reactor, which the diameter and height are calculated according to the reaction volume and the type of digester selected. V rxn ¼ HRT∙u

where DR is the digester diameter (m); LR is the digester height (m);  ðL D ÞR is the height–diameter ratio, in which Henao et al. recommend values between 1 and 2; and VfF is the free volume fraction, where Henao recommends values between 0.1 and 0.2 (Henao and Velásquez, 2010). 2.2.2. Continuous stirred tank reactor (CSTR) The continuous stirred digester is primarily composed of an anaerobic tank incorporated into a mechanical agitation system that promotes a homogeneous mixture in its interior, thus preventing the formation of zones, as shown in Fig. 3. This reactor is sized as described in the Section 2.2.1. The continuous stirred digester is commonly implemented for industrial wastewater treatment plants (Lansing et al., 2008) with a total solid content between 2% and 10% (Hilkiah Igoni et al., 2008). The agitation power required for this digester is calculated using Eq. (4). W R ¼ w∙V

ð4Þ

where WR is the mixer power for the digester (kW); w is the power factor, which Henao et al. recommends values between 0.01 and 0.1 kW/m3 (Henao and Velásquez, 2010).

ð1Þ Biogas Outlet

where Vrxn is the reaction volume (m3); HRT is the hydraulic retention time (days); and u is the inlet volumetric flow of the waste (m3/day). This methodology proposes three types of digesters, which are described below. 2.2.1. Low-rate anaerobic sludge digester The low-rate anaerobic sludge digester is used for waste with solid content that does not exceed 2% (Hilkiah Igoni et al., 2008) and for small treatment plants. Considered as the simplest of its kind, this digester is composed of a single tank and does not have any mixing devices. Moreover, it is fed in the active digestion zone. As the biogas

Combustion gases out

Supernatant outlets

Waste input LR Combustion gases in

Table 2 Description of process diagram equipment for the anaerobic digestion plant for the production of electric energy and biofertilizer. Equipment No.

Equipment name

Type

DA-1 GE-1

Anaerobic digester Electrical generator

C Diesel

Operation conditions

Dimensions

HRT

Pa

Ta

D

L

PW

I –

I I

I I

C –

C –

– C

Slugde Outflow DR Fig. 2. Anaerobic sludge digester with heating jacket.

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Combustion gases out

Mixing device

Biogas

Biogas Outlet

DsR Sludge out

Waste in

Waste input Combustion gases out

Combustion gases in LR

LR Waste in digestion

Combustion gases in

a ) General arrengement

Slugde Outflow

St Dt . 2 . dt

DR Fig. 3. Continuous stirred digester with heating jacket.

Pt = Dt . 2 . dt . St 2.2.3. Plug flow reactor (anaerobic digester) The Plug Flow Reactor (PFR) is a digester that is commonly used on a small scale because of its low manufacturing and installation price, which represents lower capital expenses compared to the abovementioned digesters (Lansing et al., 2008). This type of reactor is suggested for total solids content between 10% and 13% (Hilkiah Igoni et al., 2008). This methodology proposes sizing a PFR with heating tubes for leveraging the hot exhaust gases at the generator outlet. The diagram of this anaerobic reactor is shown in Fig. 4. The sizing of the reactor, as shown in Fig. 4a, consists in the calculation of the diameter and the length using Eq. (5) and Eq. (6), respectively. The number of the heating tubes is calculated using Eq. (7). 0 12 3 v ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi B4∙ðD þ 2δ þ S u V C B C t t t u DSR ¼ B ð5Þ u  C t L A @ π  Dt Ds R  LR ¼ DSR

Nt ¼

L DS

b ) Rectangular arrengement of the tubes Fig. 4. Anaerobic plug flow reactor with a bank of heating tubes.

the one initially proposed by Hashimoto, which is expressed in Eq. (8) (Chen and Hashimoto, 1978). γv ¼

ð6Þ R

4∙V π∙D2t ∙LR

ð7Þ

where DSR is the reactor diameter (m); LR is the reactor length (m); (L/DS)R is the relationship between the length and the diameter of the reactor and takes values between 2 and 10 according to Henao and Velásquez (2010); Nt is the number of the heating tubes; Dt is the internal diameter of the heating tubes (m); δt is the thickness of the internal heating tubes (m); and S t is the distance between the heating tubes (m). 2.3. Kinetic models to calculate biogas production Using environmental data and energetic characterization of the waste, the production of biogas may be predicted using kinetic models for the plant reactor. In this methodology, it is assessed two kinetic models reported by Gebremedhin and Inglis (2006). The first model is

ð8Þ

where γv is the production of methane accordance to volume reactor (m3/m3-day); Bo is the methane production yield calculated through the BMP test (LCH4/gsv); So is the concentration of volatile solids determined through an environmental characterization (gsv/L); μm is the bacterial growth rate, (day−1); and K is a dimensionless kinetic parameter. The second model is proposed by Minott et al., which is expressed as Eq. (9) (Minott and Scott, 2002). BG ¼



  Bo ∙So K ∙ 1− HRT∙μ m −1 þ K HRT

b Ta ∙½C o −C T ðx; t Þ∙V∙ HRT To

ð9Þ

where BG is the daily biogas production (m3/day); b is the methane production yield calculated through the BMP test (m3/kgSV); Co is the concentration of volatile solids defined through an environmental characterization (kgSV/m3); Ta is the average annual temperature (K); To is the operating temperature of the anaerobic reactor (K); CT(x,t) is the rate of degradation of the substrate inside the reactor calculated using Eq. (10).  3   31 1 0 2 2 HRT HRT −μ m ∙ −μ m ∙ K B 6 6 7 7C K K ∙@ðV∙μ m −2u∙K Þ∙41−e 5 þ HRT∙u∙μ m ∙41 þ e 5A

−

C T ðx; t Þ ¼ C o ∙K∙e

μ 2 ∙V∙HRT m

ð10Þ The parameters K and μm are calculated by implementing Eq. (11) and Eq. (12), respectively. K ¼ 0:6 þ 0:0206∙e0:051∙So μ m ¼ 0:013∙T o −0:129

ð11Þ ð12Þ

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2010). The simulation of stroke one consists in calculating the air flow required to burn the biogas inside the engine by implementing Eq. (15).

2.4. Calculation of the thermodynamic biogas properties Once the biogas flow and its primary compounds have been determined, a thermodynamic characterization may be performed. This characterization allows i) to conduct mass and energy balances and to determine the efficiency of the processing equipment such as compressors or generators, and ii) to obtain the flow of net energy production from the plant (Moran et al., 2014b). The thermodynamic properties required to simulate a generator of electrical energy from biogas are lower heating values, enthalpies, and entropies, calculated at the operating conditions of each stream. Next, the methods for calculating the aforementioned thermodynamic properties are proposed. 2.4.1. LHV calculation LHV is calculated for a fuel according to the ASTM E955 standard (ASTM, 2009), which comprises making a stoichiometric balance of the combustion reaction shown in Eq. (13) (Moran et al., 2014b). xCH4 CH 4 þ xCO2 CO2 þ xO2 O2 þ xN2 N2 þ xH2O H 2 O þ α ðO2 þ 3:76N 2 Þ→nCO2 CO2 þ nH2O H2 O þ nN2 N2

ð13Þ

where xCH4, xCO2, xO2, xN2, xH2O is the volumetric composition of fixed biogas gasses (%); α is the stoichiometric coefficient to determine the air moles required to burn 1 mol of biogas (mol); and nCO2, nH2O, nN2 are the moles of the byproducts from biogas combustion (mol). Finally, LHV is calculated using Eq. (14). LHV ¼

NC X

NC   X ° ° ° ° xi ∙hi þ α∙hO2 þ 3:76∙α∙hN2 − ni ∙hi

i¼1

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ð14Þ

i¼1

where LHV is in kJ/kmol; xi is the volumetric composition of substance “i” in biogas (%); h°i is the formation enthalpy of the substance “i” (kJ/ kmol); and NC is the number of compounds present in the biogas stream or in the exhaust gas stream. The formation enthalpies for the biogas compounds, air, and exhaust gases are reported in Table 3 (Velásquez et al., 2015). 2.4.2. Entropy and enthalpy calculation The thermodynamic properties may be calculated using a state equation. Because the biofuel is primarily composed of methane, the Patel–Teja state equation modified by Forero et al. for gases and hydrocarbons (Forero and Velásquez, 2013) has been implemented for this methodology.

MAF ¼

4:76α∙BG∙ρbio ∙AE MW bio ∙86; 400

where MAF is the molar air flow admitted to the engine (kmol/s); ρbio is the biogas density (kg/m3); MWbio is the molecular weight of the biogas stream (kg/kmol); and AE is the air excess ratio (dimensionless). At stroke two, the compression work is calculated using Eq. (16).   h i real W real T real com ¼ MAF∙ h2 2 ; P 2 −h1 ðT 1 ; P 1 Þ

Once the fuel flow rate (biogas) and thermodynamic properties are determined, at the operational conditions of each stream, the electric generator power can be calculated. This methodology assumes that this equipment has an internal combustion engine with a diesel cycle, which works in four strokes: at first stroke, the amount of air admitted to the engine is calculated; at stroke two, the admitted air is compressed to a volumetric ratio of 21:1; at stroke three, the biogas combustion reaction occurs; and at stroke four, the exhaust gases formed are expanded and expelled to generate a mechanical power that is ultimately converted into electrical energy (Fiveland and Assanis, Table 3 Formation enthalpy values and molecular weight of the biogas and exhaust gas compounds for LHV calculation. Compound

Molecular formula

h°(kJ/kmol)

Molecular weight (kg/kmol)

Methane Carbon Dioxide Oxygen Nitrogen Water

CH4 CO2 O2 N2 H2O

−74,520 −393,510 0 0 −241,810

16.043 44.010 31.999 28.014 18.015

ð16Þ

real real where Wreal com is the work of effective air compression (kW); h2 (T2 ,P2) is the compressed air enthalpy at the temperature and pressure conditions of the engine (kJ/kmol); and h1(T1,P1) is the enthalpy of the air entering the engine at environmental conditions. Isentropic compression efficiency is calculated using Eq. (17), which relates ideal compression work to effective compression work and considers values between 60% and 80% (Elliott and Lira, 2001).

Efscom ¼

W ise com

ð17Þ

W real com

where Efscom is the isentropic compression efficiency between 60% and 80% and Wise com is the ideal or isentropic compression work (kW), which can be calculated using Eq. (18).  h  i ise ise W ise com ¼ MAF∙ h2 T 2 ; P 2 −h1 ðT 1 ; P 1 Þ

ð18Þ

ise where hise 2 (T2 , P2) is the isentropic air enthalpy at ideal conditions and Tise 2 is an implicit variable within the isentropic enthalpy calculation. The value of this variable is found by solving Eq. (19).

  s1 ðT 1 ; P 1 Þ ¼ s2 T ise 2 ; P2

ð19Þ

where s1(T1, P1) is the entropy of inlet air to the engine at environmental conditions (kJ/kmol-K); and s2(Tise 2 ,P2) is the compressed air entropy at ideal conditions. P2 is an implicit variable calculated using the compression ratio expressed by Eq. (20). 21 v1 ðT 1 ; P 1 Þ  ¼  1 v T real ; P 2

2.5. Electrical generator sizing

ð15Þ

ð20Þ

2

2

where v1(T1, P1) is the specific inlet air volume to the engine at environmental conditions (m3/kmol); v2(Treal 2 , P2) is the specific volume of compressed air at non-ideal conditions. At stroke three, the combustion reaction occurs as shown in Eq. (13). To solve this reaction, the method proposed by Reklaitis is used, which consists in performing a mass balance per component participating in the reaction, as shown in Eq. (21) (Reklaitis, 1989). Nout ¼ Nin i i þ

R X

σ ir :r r With i ¼ 1; …; i

ð21Þ

r¼1

where Nout is the molar flow of product “i” (kmol/s); Nin i i is the molar flow of reactant “i” (kmol/s); σir is the stoichiometric coefficient of substance “i” in the “r” reaction; and rr is the kinetic coefficient of the “r” reaction (kmol/s). To close the degrees of freedom in the mass balance, the conversion of the limit reagent must be calculated using Eq. (22). x¼

out Nin i −N i

Nin i

ð22Þ

where x is the conversion of the limit reagent for a combustion reaction

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with a value near to 1, where is exothermic and increase the products temperature, which is calculated using Eq. (23). bio

real

Nbio 3 ∙h3 ðT 1 ; P 1 Þ þ MAF∙h2

  G:C G:C T real 2 ; P 2 ¼ N 4 ∙h4 ðT 4 ; P 2 Þ

ð23Þ

where Nbio 3 is the molar flow of the biogas produced in the anaerobic digester (kmol/s); hbio 3 (T1, P1) is the enthalpy of biogas at inlet conditions C to the generator (kJ/kmol); NG. is the molar flow of compressed ex4 G. C haust gases (kmol/s); and h4 (T4, P2) is the enthalpy of compressed exhaust gases (kJ/kmol). At stroke four, the mechanical work produced is given by Eq. (24). h  i G:C real G:C T real W real Exp ¼ N 4 ∙ h4 ðT 4 ; P 2 Þ−h5 5 ; P5

C M ¼ F CM :C °Eq

W real Exp

ð25Þ

W ise Exp

where EfsExp is the isentropic efficiency in the process of exhaust gases expansion and it takes values between 60% and 80% (Elliott and Lira, 2001); and Wise Exp is the ideal or isentropic expansion work (kW), where is calculated by implementing Eq. (26). W ise Exp

¼

NG:C 4 :

h

G:C ise h4 ðT 4 ; P 2 Þ−h5

 i T ise 5 ; P5

ð26Þ

ise where hise 5 (T5 , P5) is the isentropic enthalpy of the expanded exhaust gases (kJ/kmol). Temperature Tise 5 is an implicit variable within the entropy balance is presented in Eq. (27).

  s4 ðT 4 ; P 4 Þ ¼ s5 T ise 5 ; P5

ð27Þ

where s4(T4, P4) is the entropy of the compressed exhaust gases (kJ/ kmol-K); and s5(Tise 5 , P5) is the entropy of the expanded exhaust gases. Finally, the effective mechanical work performed by the generator is calculated by Eq. (28). real real W real EG−1 ¼ W Exp −W com

ð28Þ

where Wreal EG−1 is the effective mechanical work performed by the internal combustion engine of the generator (kW). However, the overall efficiency of the cycle is calculated by Eq. (29). ηGE1 ¼

W real EG−1 ðPCI∙BG∙ρbio Þ=ðMW bio ∙86; 400Þ

ð30Þ

ð24Þ

real real where Wreal Exp is the effective expansion work (kW); h5 (T5 , P5) is the enthalpy of the expanded exhaust gases (kJ/kmol). The isentropic efficiency for the expansion process is expressed in Eq. (25). This equation relates the effective expansion work to the ideal or isentropic expansion work.

Ef sExp ¼

be assessed for the treatment and application of the waste from agricultural activities for the production of electrical energy and biofertilizer. There are multiple models used for estimating expenses in chemical processes. However, according to Petley, these models may be divided into three types: exponential, factorial, and functional unit (Petley, 1999). This methodology proposes the exponential economic model reported by Shabani and Yekta (2006), which consists to determine the CAPEX of the process equipment based on sizing through experience factors. The model starts with the estimation of the unit costs of each equipment piece using Eq. (30).

ð29Þ

where ηGE1 is the overall efficiency of the Diesel-cycle internal combustion engine with values between 0 and 1.

where CM is the unit cost of a process equipment piece, $USD; FCM is the unit cost factor, calculated through Eq. (31); and C°Eq is the benchmark acquisition cost, $USD. F CM ¼ B1 þ B2 :F M :F P

where B1 and B2 are the calculation coefficients for the unit cost factor (See Table 4); FM is the material factor (See Table 4); FP is the operating pressure factor; for the operating pressures between −0.5 and 3.7 barg, FP = 1; for the operating pressures less than −0.5 barg, FP = 1.25; for the operating pressures between 3.7 and 400 bar, FP using Eq. (32). 2

F p ¼ 0:5146 þ 0:6838∙ logðP Þ þ 0:2970∙ð logðP ÞÞ 6 8 þ 0:0235∙ð logðP ÞÞ þ 0:0020∙ð logðP ÞÞ

2.6.1. Estimation of capital and operating expenses The calculation of CAPEX and OPEX contributes to developing the economic assessment and estimating the feasibility of a project (Henao and Velásquez, 2010). In this particular case, the project must

ð32Þ

where P is the operating pressure of the equipment (bar). The acquisition cost is calculated by solving Eq. (33) and depends on the equipment sizing.  log C °Eq ¼



 i IP Act h 2 ∙ K 1 þ K 2 ∙ logðAK Þ þ K 3 ∙ð logðAK ÞÞ IP Ref

ð33Þ

where K1, K2, and K3 are the coefficients to calculate the cost of an equipment piece (See Table 4); IPAct is the current price index; IPRef is the benchmark price index (382); and AK is the process equipment size. For the anaerobic digester, AK is its height or length in meters. For the electric generator, AK is its effective power in kilowatts. The fixed capital investment is calculated using Eq. (34). In this equation, the unit expenses of each equipment are added and Table 4 CAPEX parameters and calculation coefficients for an anaerobic reactor and an electric generator. Equipment

Diameter (m)

B1

Vertical Anaerobic Reactor

0.3 0.5 1 1.5 2 2.5 3 4 0.3 0.5 1 1.5 2 2.5 3 4

2.5 1.7 3.34 3.47 3.62 3.76 3.95 4.05 4.11 4.39 1.6 1.5 2.92 3.10 3.36 3.42 3.76 3.68 3.77 4.16 0 2 2.70

2.6. Economic model Once the streams and dimensions of the process equipment are specified, the economic parameters such as the CAPEX, OPEX, NPV, and IRR may be estimated. These values define the financial viability of a project and determining the economic benefits to implement the technology (Ruiz et al., 2018).

ð31Þ

Horizontal Anaerobic Reactor

Electrical Generator

B2

K1

K2

K3

Material

FM

0.55 0.59 0.53 0.64 0.46 0.46 0.61 0.29 0.51 0.58 0.59 0.81 0.37 0.71 0.72 0.22 0.81

0.29 0.21 0.21 0.17 0.16 0.17 0.05 0.18 0.13 0.06 0.11 0.00 0.20 0.04 0.05 0.25 0.00

Polyethylene

0.1

Carbon Steel

1

S·S Coating

2.5

Stainless Steel (S·S) Nickel Coating Nickel

4

Titanium Coating Titanium

4.5 9.8 4.9 10.6 1

S. Arango-Osorio et al. / Science of the Total Environment 685 (2019) 1169–1180

1175

5 w1 2a1

w2

wa1

7

7a1

4

2 5a1

2a2

wa2

GE-1

1a CSTR 1A

1 2b1 1b

6

7a2

3a1

8

5a2

wb1

CSTR 2A 3a2 7b1 5b1

2b2 CSTR 1B

wb2 7b2

3b1

5b2 3b2

CSTR 2B

DA-1 3

Fig. 5. Process diagram of the thermophilic anaerobic digestion plant for methodology validation.

multiplied by a contingency factor of 15% and an additional cost factor of 3%. FCI ¼ 1:18∙

Neq X

C MðkÞ

ð34Þ

where Cdep is the annual depreciation expenses of the plant ($USD/ year); Npv is the depreciation period of the plant (10 years); and S is the annual depreciation value with values between 10% and 50% of the fixed CAPEX.

K¼1

where FCI is the fixed capital investment ($USD); Neq is the total number of equipment pieces in the plant; and CM(k) is the unit cost of the “K” plant equipment ($USD). The operating and maintenance expenses of an anaerobic digestion plant are according to Fig. 1, preventive maintenance, corrective maintenance, laboratory tests and energy consumption. These expenses are calculated using Eq. (35) (Henao and Velásquez, 2010). OMC ¼ FCI∙ðK lab þ K mant Þ þ EC

ð35Þ

where OMC is the operation and maintenance cost of the anaerobic digestion plant (%USD/year); EC is the annual energy consumption cost ($USD/year); Klab is the constant of the laboratory test expenses with values between 0.01 and 0.1, and Kmant is the constant of the maintenance expenses with values between 0.01 and 0.1 (Henao and Velásquez, 2010). Another important aspect for the financial analysis of the plant is the depreciation expense, which is given by Eq. (36). C dep ¼

ICF−S Npv

ð36Þ

Table 5 Description of the process diagram streams of the anaerobic digestion plant for the methodology. Stream No.

Mass flow

Properties ρ

T

P

ST

1 2

2.96 2E-1 7.8E −2

1.0E3 1.22

12 0

1 1

18 16 4.1E2 – – – – 60

– 40

– 0

– –

–

–

–

–

–

–

–

–

–

–

1.4E3 1.2 –

–

–

–

13

3

–

1.4E3 1.2 –

–

–

–

13

3

–

1.4E3 1.2 –

–

–

–

13

3

–

6.0E2 1

–

–

–

–

13

3

–

12 – –

– – –

– – –

– – –

– – –

– – –

21 – – 58.22 – 308.22

3 4 5 6 7 8 w1 w2

1.65 6.5E −1 9.9E −1 6.5E −1 1.45 – –

2.9E −1 2.9E −1 2.9E −1 3.9E −1 1.23 – –

Composition

1 – –

SV βo

CH4 CO2 O2 F.E

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Table 6 Technical comparison parameters between the methodology used and data from real anaerobic digestion plants.

Biogas production yield (Nm3/t) Energy production yield (kWh/t) Biogas energy transformation yield (kWh/Nm3) Biofertilizer production yield (tB-F/ tRes)

Calculated with the Methodology

(Ruiz et al., 2018)

Calculated with the Methodology

(Lansing et al., 2008)

Calculated with the Methodology

(Ishikawa et al., 2006)

68.3 103.9 1.52 2.60E-02

50.0 76.9 1.53 –

6.82 1.19 2.09 9.92.E-04

5.04 1.88 2.27 1.44.E-03

25.68 42.95 1.67 –

30.00 30.51 1.86 –

2.6.3. Calculation of the net present value (NPV) and the internal rate of return (IRR) NPV and IRR help to determine the financial viability of a project in a rough manner. NPV is calculated by solving Eq. (40) (Ross, 1995). NPV ¼

N X

GP n :ð1 þ iÞ−n

ð40Þ

n¼0

where i is the discount rate (%); n is the project life time (years); n is the project time period (years); and GPn is the revenue after taxes ($USD/ year). IRR is calculated by solving Eq. (41).

Fig. 6. Boxplot of sensitive analysis between some variables obtained from anaerobic digestion plants and the methodology proposed.

0¼

N X

GP n :ð1 þ IRRÞ−n

ð41Þ

n¼0

3. Results and discussion 2.6.2. Economic benefit calculation The economic benefits of an anaerobic digestion plant are primarily derived from the sale of energy and biofertilizer; other economic benefits have not been considered such as subsidies or tax exemptions according to Colombian regulations. The economic benefits of the sale of these products are calculated according to Eq. (37). EAB ¼ W real EG−1 ∙t op ∙EP þ ðTS−VSÞ∙u∙BFP∙365

ð37Þ

where EAB is the annual revenue of the anaerobic digestion plant from energy and biofertilizer sales ($USD/year); top is the annual operation time of the electric generator (h/year); EP is the sale price for electrical energy ($USD/kWh); TS is the concentration of total solids in the waste stream (kg/m3); VS is the concentration of volatile solids in the waste stream (kg/m3) and BFP is the biofertilizer price ($USD/kg). Tax expenses are calculated using Eq. (38).

if PBT N0→C tx ¼ PBT∙TR if PBTb0→C tx ¼ 0

ð38Þ

where Ctx is the annual tax ($USD/year); TR is the tax rate defined by a government entity; and PBT is the profit before taxes, as calculated using Eq. (39). PBT ¼ EAB−OMC−C dep

ð39Þ

The abovementioned methodology was based on the environmental and economic data reported by a thermophilic anaerobic digestion plant located in Asturias, Spain. This plant is divided into two phases, i.e. the digestion phase (DA-1; Fig. 5) consisting of two parallel lines, which each consist in 1000 m3 thermophilic reactor (CSTR 1A and CSTR 1B; Fig. 5) operating at a temperature of 55 °C, and a 975 m3 mesophilic reactor (CSTR 2A and CSTR 2B; Fig. 5) that operates at a temperature of 39 °C, with both CSTR reactors and the plant operating at a 30-day HRT. The electric generation phase has a combined cycle generator (GE-1 Fig. 5) that produces an energy stream of 2000 MW-h/year. The plant is fed with 6500 t/year of pig slurry, 6500 t/year of cow slurry, 7200 t/year of sewage sludge, and 5800 t/year of agricultural waste (Ruiz et al., 2018). The process diagram for the plant is shown in Fig. 5. The process stream specification was made after considering the bank of anaerobic reactors from Fig. 5 as a single control volume (DA1) and specifying only the streams and energy flows shown in Table 5. The values listed in Table 5 were determined according to the provisions mentioned in Table 1 and Fig. 5. Using the values from Table 5, the following technical yield factors were estimated: biogas production in terms of the amount of waste fed (Nm3/t); energy production in terms of the waste flow fed (kWh/ t); energy production in terms of biogas flow (kWh/Nm3); and the biofertilizer production yield in terms of the waste fed (kg/kg). Subsequently, these factors were compared against the yield from other anaerobic digestion plants reported in the literature, as shown in Table 6.

Table 7 Description of the process diagram equipment of the anaerobic digestion plant for the validation of the methodology. Equipment No.

Equipment name

Type

Operation conditions

Dimensions

HRT

Pa

Ta

D

L

PW

CSTR 1A, CSTR 1B CSTR 2A, CSTR 2B DA-1 GE-1

Thermophilic anaerobic digester Anaerobic mesophilic digester Digester bank Electrical generator

Continuously stirred Continuously stirred Continuously stirred Diesel

– – 30 –

1 1 1 1

55 39 – 12

10 9.91 – –

15 14.87 – –

– – – 338

S. Arango-Osorio et al. / Science of the Total Environment 685 (2019) 1169–1180 Table 8 Characterization of the waste that is fed to the anaerobic digestion plant in Spain. Waste

Total solids (%)

Volatile solids (%)

BMP (LCH4/kgSV)

[CH4] In BMP (%)

Pig waste Cow manure WWTP sludge Agricultural

1.88 26.74 30.07 15.31

1.27 21.62 27.08 13.61

558 323 342 425

65 55 66 52

Three anaerobic digestion plants were analyzed to compare with the present methodology, the first one is the thermophilic anaerobic digestion plant located in Asturias, Spain (Ruiz et al., 2018) described above. The second anaerobic digester is a 146 m3 pilot plant of EARTH University in Costa Rica, where uses 2.18 m3/day of dairy wastewater in codigestion with 4.5 m3/day of pig manure to produce 33.5 m3/day of biogas (Lansing et al., 2008). The third is a 1500 m3 anaerobic digester that treats 50 m3/day of dairy cow to produce 62.5 m3/day of biogas (Ishikawa et al., 2006). The comparison between the pilot plants and the methodology allows a sensitive analysis, where a boxplot shown in Fig. 6 were used. The difference between the biogas yield reported by Ruiz et al. (2018), Lansing et al. (2008), Ishikawa et al. (2006) and the obtained using the present methodology, can be produced for different reasons: the operating temperature, the characteristics of the waste in the feed stream, and the HRT. All of those are independent variables in Eq. (9) and used for calculating the biogas production according to Minott and Scott (2002). A minor error is observed for this parameter at the plant compared to Ishikawa pilot plant, because this plant reports some characteristics of the waste that the model uses, and the anaerobic digester is a PFR, which are important parameters to the model. The biogas production yield is different in all cases because there is a difference between the volatile solids of all plants, and biochemically the VS changes de biogas production yield. Moreover, the energy production parameter is directly linked to the fuel flow of the generator; therefore, the analysis for this parameter is similar to the biogas production parameter. The methodology error accordance to Spain's case for the energy and biogas production yield may be linked to the fact that the model implemented to biogas flow calculation was solved for a PFR, whereas CSTR reactors are assessed in this plant (Gebremedhin and Inglis, 2007). There were some considerations that increase the error percentage, where the methane production in Costa Rica's anaerobic digestion plant was 323 LCH4/kg for dairy wastewater and 558 LCH4/kg for pig manure, both were assumed using the data reported by Hidalgo et al., and these assumptions could originate some errors in the methodology (Hidalgo and Martín-Marroquín, 2015). Regarding the yield from biofertilizer transformation, the Spain plant does not report this stream flow; therefore, it was not possible to compare this parameter against the study case. However, this yield value was compared against a plant reported by (Lansing et al., 2008). In that plant, a 31.1% error was observed, this difference could be originated because the plant do not eliminate the volatile solids from the waste, however, the results show good accuracy. The parameter with the lowest error was the yield from the transformation of biogas stream to electrical energy with 0.65% error for the Spain plant, 8.04% error for the plant in Costa Rica and a 10.22% error

1177

for the plant reported by Ishikawa et al. This error is associated to operation time of the generator, generator yield, and the concentration of methane in the biogas. However, it is evident that the thermodynamic model proposed is adequate to simulate this type of processes because there is good approximation to the actual value. In the present study more comparison was pretended, but there were no reliable data to compare to the actual methodology. The equipment from Fig. 5 was sized according to the volume data reported by Ruiz et al. (2018). Subsequently, the sizing of the generator was performed using the thermodynamic model described above. The equipment sizing values are found in Table 7. It is observed that the power of the calculated generator represents a 26% error. The difference between the calculated and the reported generator power is caused by the approximation error of the biological model for the biogas produced using Minott's model. About the size of the anaerobic digesters, no significant differences were observed between the reported and the calculated values using the abovementioned methodology. 3.1. Waste characterization To characterize the waste fed to the plant, Hidalgo methodology, who characterized a different agricultural waste from Castilla and León using BMP tests was used (Hidalgo and Martín-Marroquín, 2015). The characterization data for the waste fed into the process is listed in Table 8 (Hidalgo and Martín-Marroquín, 2015). For waste characterization, a greater yield of methane production per concentration of volatile solids is observed for pig manure. This occurs because the microbiological load contained in the waste, which allows for the accelerated degradation of the organic content in methane (Peu et al., 2006). 3.2. Anaerobic reactor design As previously mentioned, four anaerobic CSTR digesters are implemented in this plant. For its sizing, Eqs. (2)–(4) were implemented for the calculation of diameter, height, and mixing power, respectively. The dimensions calculated for each reactor and the mixing energy consumption are reported in Table 5 and Table 7. 3.3. Biogas flow calculation The Hashimoto model produced a biogas flow of 2,458,984 Nm3/year, while the Minott model produced a biogas flow of 776,896 Nm3/year. The results from this model obtained a difference of 47% against the results reported by Ruiz et al. (2018). However, the Minott model presented a difference of 26.8% against the actual value; moreover, it presents a closer approximation to reality because it implements a degradation factor that depends on the HRT, the bacterial growth factor, and the reaction kinetics (Gebremedhin and Inglis, 2007). Therefore, for calculating inflow fuel, the generator was sized using the Minott model (Chen and Hashimoto, 1978)(Minott and Scott, 2002). 3.4. Thermodynamic properties calculation Based on the data from the waste energy characterization, a methane concentration of 60% and a carbon dioxide concentration of 40%

Table 9 Sizing solution for the Diesel engine of the electric generator. Stroke

Flow (kmol/h)

T (°C)

P (bar)

V (m3/kmol)

H (kJ/kmol)

S (kJ/kmol-K)

Wreal EG−1 (kW)

ηGE1 (%)

Air admission Compressed air (actual) Compressed exhaust gases Expanded exhaust gases (actual)

50.3 50.3 57.67 57.67

12 895 2310 1148

1 89.5 89.5 1.2

23.28 1.10 2.42 98.55

−424.43 27,678 85,304 39,704

2.81 9.44 40.84 53.41

338

34.4

T: Temperature, P: Pressure, V: Specific volume, H: Enthalpy, S: Entropy.

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Table 10 Estimation of CAPEX for the anaerobic digestion plant. Equipment

FP

FCM

C°Eq (€)

CM (€)

ICF (€)

Unit capital costs methodology (€/kW)

Unit capital costs reported (€/Kw)

CSTR 1A CSTR 1B CSTR 2A CSTR 2B GE-1

1 1 1 1 1

4.2 4.2 4.2 4.2 2

87,978 87,978 87,978 87,978 51.602

369,510 369,510 367,294 367,294 103.204

1,860,641

5508.54

5905.78

were assumed in the biogas according to the BMP reported by Hidalgo and Martín-Marroquín (2015). Using Eq. (13) and Eq. (14), a LHV value of 17,584 kJ/kg and a stoichiometric air ratio of 5.69 was found for the biogas. Hosseini and Wahid (2013) reported a biogas LHV between 13,720 and 27,440 kJ/kg, thus the value calculated by the methodology was within the reported range. Moreover, Bedoya et al. (2009) reported a stoichiometric air ratio of 6.05 for biogas, which represents a difference of 0.54% with respect to the value calculated by the methodology. The value of the stoichiometric air is close to the reported value, which indicates that the model implemented in the methodology is adequate to determine the amount of air necessary to perform biogas combustion in the generator. 3.5. Electrical generator sizing As described above, the Diesel cycle electric generator was sized according to the four thermodynamic strokes. The results of the simulation are listed in Table 9. Bora assessed an internal Diesel cycle combustion engine with a biogas-diesel mixture, showing an efficiency at a maximum engine load of 29% (Bora et al., 2014) and a 15.7% error with respect to the calculated value. The efficiency error of the motor may be caused by the fuel mixture conditions and errors associated to the state equation and the energy balances. Even so, the calculated efficiency is close to the reported value; therefore, the model implemented in the methodology is adequate for making an approximation in generator sizing. 3.6. Financial model validation The values of CAPEX itemized by equipment are found in Table 10 shown in the process diagram from Fig. 5. For a financial comparison between the methodology and the actual case of the anaerobic digestion plant in Asturias, the unit capital costs were estimated for the amount

of money required to install 1 kW of electrical energy. It must be taken into account that, to compare actual unit capital costs to the values obtained with the methodology, only the plant construction item was assessed without including land or detail engineering costs. Note that, a 7.2% error was determined for this item. The model assumed an error using experience factor selection. However, the model makes a good approximation to reality, which allows the estimation of CAPEX and undertake the basic engineering of the project. For the OPEX described in Table 11, the operational costs were compared against the total energy produced by the plant in one year. The results produced a 21.7% difference between the data calculated with the methodology and the values reported for the Spain plant by Ruiz et al. (2018). This difference is because of the assumptions made by the model, where an experience factor is assumed for the operating and maintenance expenses. Moreover, operation labor expenses are not considered because an automated plant is assumed. Finally, no consumption expenses are assumed for feedstock or transportation. Finally, the NPV was estimated (Table 12) based on the CAPEX and OPEX and the annual revenue from the sales of electrical energy and biofertilizer, yielding a 6.84% error and a 3.67% IRR difference against the actual reported values. Those differences are due to the approximation and assumption of the technical and economic made. To compare the model against the Asturias plant, the values from Table 10, Table 11, and Table 12 were adjusted using an exchange rate of 0.88 €/$USD. Furthermore, the change in NPV was assessed for the discount rate, as shown in Fig. 7. A similar behavior was observed to the one reported for the Asturias plant with an affectation of NPV and variation in the discount rate (Ruiz et al., 2018). 4. Conclusions The proposed methodology allows for an initial estimation of the technical performance of an anaerobic digestion plant in steady state using the specification of process equipment and streams. The methodology presents an average percentage difference of 26% for the biological model and an average error of 6% in the thermodynamic model. The percentage difference in the biological models is primarily in the characterization of the waste feedstock and the methane concentration in the biogas stream because, when comparing the technical performance parameters to other anaerobic digestion plants, the error increases considerably. Therefore, the methodology recommends starting with an environmental characterization by determining the concentration of total and volatile solids, followed by an energy characterization using a BMP in the waste stream. For economic matters, the proposed methodology is able to estimate CAPEX related to basic engi-

Table 11 OPEX determined using the methodology for the anaerobic digestion plant. Item

Unit value €/kWh

K

OMC (€/year)

Unit operation costs - methodology (€/kW-year)

Unit operation costs - reported (€/kW-year)

Electrical Energy Thermal Energy Maintenance Laboratory Tests Depreciation Costs Taxes

0.12 0.12 – – – –

– – 0.02 0.02 – –

60.899 134.279 37,212 37.212 167,457 31,447

907

710

Table 12 Calculation of economic benefits and financial parameters for the anaerobic digestion plant. Item

Unit value (€/kWh)

Unit value (€/kg)

Annual revenue (€/year)

GPn (€/year)

NPV mod (€)

IRR mod (%)

NPV rep (€)

IRR rep (%)

Electrical Energy Thermal Energy B-F

0.12 0.12 –

– – 0.13

317.057 134.279 90,549

240,834

444,010

10.6

474.375

10.2

S. Arango-Osorio et al. / Science of the Total Environment 685 (2019) 1169–1180

0.90

1179

Declaration of Competing Interest

0.80

The authors declare that they have no competing interests.

0.70

NPV (€/KW)

0.60

Acknowledgements

0.50

The authors would like to thank to Universidad Pontificia Bolivariana to providing financial and equipment support involved in the present manuscript.

0.40 0.30 0.20

References

0.10 0.00 -0.10

0%

2%

4%

6%

8%

10%

12%

14%

Discount rate(%) Fig. 7. NPV value calculated with the methodology for the anaerobic digestion plant, assuming different discount rates.

neering, which includes acquisition and installation of primary equipment. When comparing the calculated unit capital costs against the reported unit costs, a 7.2% error is determined. In a similar manner, the methodology calculates OPEX with a 21.7% error respect to the actual value. For financial parameters, the NPV exhibits a difference of 6.84% against the actual value and the IRR reports a difference of 3.67%. The errors linked to the approximations and assumptions of the implemented economic model. Implementing the methodology proposed in this study is useful for estimating the technical and financial feasibility of a project, which is related to the production of electrical energy by implementing anaerobic digestion for the treatment of livestock waste. Ethics approval and consent to participate Not applicable. Consent for publication Not applicable. Availability of data and material Not applicable. Funding The Universidad Pontificia Bolivariana provided all financial support the present research, the translation and all the materials and equipment involved. Authors' contributions Conceptualization; Data curation; Formal analysis; Funding acquisition; Investigation; Methodology; Project administration; Resources; Software; Supervision; Validation; Visualization; Roles/Writing - original draft; Writing - review & editing. IIM, GJL and JGS analyzed the electrical generator calculations and the economic model, they also contribute in the conceptualization, project administration, methodology in energy issues and supervision. OVE analyzed the anaerobic reactor design, kinetic models, the second contributor in writing and the reviewer of the manuscript, supervision, validation and formal analysis. SAO made the methodology, thermodynamic biogas calculations, and he was the major contributor in writing the manuscript. All authors read and approved the final manuscript.

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Shabani, M.R., Yekta, R.B., 2006. Suitable method for capital cost estimation in chemical processe industries. Cost Eng. 48, 22–25. https://doi.org/10.13140/RG.2.1.1545.7762. Vasco, O., 2016. Producción de energía a partir de residuos agrícolas en biorreactor por etapas. Universidad de Antioquia. Velásquez, J.A., Forero, L.A., Rincón, E., 2015. Base de datos Termo-UPB. Sergio Arango-Osorio (SAO): Master student at the Universidad Pontificia Bolivariana (UPB). Chemical Engineer. Oscar Vasco-Echeverri (OVE): Corresponding author. Chemical Engineer, master in biotechnology and Ph.D in Biotechnology. Teacher and researcher in Chemical Engineering faculty at the Universidad Pontificia Bolivariana (UPB). Adress: Circular 1a No. 70–01. Block 11. Phone: +574 4488388. Jorge González-Sanchez (JGS): Electrical Engineering, Ph.D in Engineer. Teacher and researcher in Electrical Engineering faculty (UPB). Gabriel López-Jiménez (GLJ): Electrical Engineering, Ph.D in Engineer. Teacher and researcher in Electrical Engineering faculty (UPB). Idi Isaac-Millán (IIM): Electrical Engineering, Ph.D in Engineer. Teacher and researcher in Electrical Engineering faculty (UPB).